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of the South African Institution of Civil Engineering Volume 55 Number 1 April 2013
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CONTENTS
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013
of the South African Institution of Civil EngineeringVolume 55 No 1 April 2013 ISSN 1021-2019
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© South African Institution of Civil Engineering
2 Estimating car ownership and transport energy consumption:
a disaggregate study in Nelson Mandela Bay
C J Venter, S O Mohammed
11 Experimental and numerical investigation of the natural frequencies
of the composite profi led steel sheet dry board (PSSDB) system
F A Gandomkar, W H Wan Badaruzzaman, S A Osman, A Ismail
22 Improving water quality in stormwater & river systems:
an approach for determining resources
N Nel, A Parker, P Silbernagl
36 Design implications on capital and annual costs of smallholder irrigator projects
A F Hards, J A du Plessis
45 A model for the drying shrinkage of South African concretes
P C Gaylard, Y Ballim, L P Fatti
60 Pile design practice in southern Africa Part I: Resistance statistics
M Dithinde, J V Retief
72 Pile design practice in southern Africa Part 2: Implicit reliability of existing practice
J V Retief, M Dithinde
80 Optimising dosage of Lytag used as coarse aggregate in lightweight aggregate concretes
S Ahmad, Y S Sallam, I A R Al-Hashmi
85 Centrifuge modelling of a soil nail retaining wall
S W Jacobsz
94 2D Linear Galerkin fi nite volume analysis of thermal stresses during sequential layer settings
of mass concrete considering contact interface and variations of material properties:
Part 1: Thermal analysis
S Sabbagh-Yazdi, T Amiri-SaadatAbadi, F M Wegian
104 2D Linear Galerkin fi nite volume analysis of thermal stresses during sequential layer settings
of mass concrete considering contact interface and variations of material properties:
Part 2: Stress Analysis
S Sabbagh-Yazdi, T Amiri-SaadatAbadi, F M Wegian
114 Discussion:
Weak interlayers in fl exible and semi-fl exible road pavements: Part 1
Comment by Dr CJ Semmelink and response by Dr Frank Netterberg and Dr Morris de Beer
116 Discussion:
The eff ects of placement conditions on the quality of
concrete in large-diameter bored piles
Comment by Prof Mark G Alexander
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 20132
TECHNICAL PAPER
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 2–10, Paper 777
PROF CHRISTO VENTER is an Associate Professor
of Transportation Engineering in the
Department of Civil Engineering at the
University of Pretoria. His teaching, research and
consulting activities focus on public transport,
transport planning, travel demand modelling,
and social aspects of mobility. He is registered
as a professional civil engineer.
Contact details:
Associate Professor
Department of Civil Engineering
University of Pretoria
Pretoria
South Africa
0002
T: +27 12 420 2184
F: +27 12 362 5218
SEMIRA MOHAMMED is currently a researcher at
the CSIR Built Environment (Council for Scientifi c
and Industrial Research) where she has been
working for the last eight years. She completed
her BSc Civil Engineering degree at the
University of Asmara, Eritrea, and her MSc
Transportation Planning at the University of
Pretoria, South Africa. She has been involved in
a number of research projects ranging from traffi c management to
passenger transport, with emphasis on transport energy, the environment
and road safety.
Contact details:
Researcher
Built Environment Unit
CSIR
PO Box 12417
Hatfi eld, Pretoria
0028
South Africa
T: +27 12 841 3991
F: +27 12 841 4044
Keywords: travel behaviour, energy consumption, land use, vehicle ownership
model, travel demand management
INTRODUCTION
Transport energy consumption is emer-
ging as a major area of public and political
concern worldwide. The transport sector is
a significant consumer of energy – estimates
for Cape Town, for instance, indicate that
transport accounts for just over half of all
energy consumed in the city (SEA 2003).
Given that about 97% of transport energy
in South Africa comes from liquid fuels, of
which the lion’s share is refined imported
crude (Cooper 2007), concerns centre around
energy security, the exposure of the economy
to international oil price volatility, and the
environmental impacts of transport fuel use.
Potential strategies to reduce the trans-
port sector’s dependence on oil include
technological improvements such as increas-
ing the energy efficiency of the vehicle parc,
behaviour change, reducing the demand for
travel by individual commuters, or shifting
towards less energy-intensive modes of travel
(Vanderschuren et al 2008). Behavioural
change objectives are being pursued through
the various public transport upgrading and
travel demand management strategies being
implemented in South African cities (DOT
2007). What complicates these efforts is the
extent to which energy concerns are inter-
woven with many other social and economic
goals, from urban restructuring and poverty
relief to industrial development. There is
thus increasing interest in understanding
the drivers of energy use, and their linkages
with other urban processes. Local empirical
studies of transport energy consumption
have tended to focus at the city or provincial
level (e.g. Cooper 2007; SEA 2003; Maré
& Van Zyl 1992), typically using aggregate
fuel sales data. Goyns (2008) analysed fuel
consumption and emissions in Johannesburg
for a sample of instrumented vehicles under
various vehicle, driving and traffic condi-
tions, but could not link it to demographic
or land use variables. Goyns’s work showed
that, as travel demand and conditions vary at
a fine grain across space and time, patterns of
transport energy consumption vary consider-
ably at the intra-metropolitan level. A greater
understanding is needed of the relationships
between transport energy consumption and
the socio-economic, land use, and transport
supply characteristics in cities before the
energy and sustainability impacts of urban
management policies can be predicted; and
before effective policies and interventions can
be fashioned that are aimed specifically at
addressing energy concerns.
With that in mind, the paper aims to
answer the following questions:
■ Can detailed and disaggregate informa-
tion on transport energy use be derived
from available travel survey data?
■ Which socio-economic and land use
variables significantly influence energy
consumption in personal transport?
Estimating car ownership and transport energy consumption: a disaggregate study in Nelson Mandela Bay
C J Venter, S O Mohammed
This paper investigates energy consumption patterns by households and individuals during travel on a typical day. A methodology is developed to estimate trip-by-trip energy consumption using standard 24-hour travel survey data, and applied to the Nelson Mandela Metropolitan Area using their 2004 household travel survey. Baseline energy consumption patterns by different modes, times of day, and user groups are established. Across the population, energy use is very skewed: 20% of people consume about 80% of transport energy, mainly due to the disproportional contribution of car use to energy expenditure. We then estimate a disaggregate vehicle ownership model and link it to a model of household transport energy consumption to explore the underlying socio-economic and land use variables driving energy consumption. Land use factors (especially job accessibility) significantly affect energy use, but do so differently for low and for high-income households, suggesting that accessibility-enhancing land use and transport measures could have unintended consequences for overall energy and environmental management.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 3
■ How do these variables affect household
car ownership and transport energy use?
■ What are the implications for urban
policy and management?
The data is taken from the Nelson Mandela
Metropolitan Area Travel Survey (NMMM
2004) conducted in 2004, supplemented by
transport supply data. The study is restricted
to personal surface transport modes and
excludes freight and commercial transport.
The focus is furthermore on the end-user
consumption of energy only, in terms of the
marginal amount of fuel (in the case of road
transport) or electricity (in the case of rail)
consumed by a traveller during each trip.
Full accounting of energy use could include
the energy used in the construction of infra-
structure and the manufacture of vehicles,
but such life-cycle assessments (e.g. Chester
& Horvath 2008) fall outside the scope of
this paper.
The following section provides a brief
introduction to previous work on the rela-
tionships between transport energy, land use,
and travel behaviour, followed by a descrip-
tion of the research design and methodology
used. The final sections describe the results
of the analysis, including two disaggregate
models estimated on car ownership and
energy use. Lastly, conclusions are drawn as
to the meaning of the findings for strategies
to reduce or manage energy use in the pas-
senger transport sector.
TRANSPORT ENERGY
CONSUMPTION, LAND USE
AND TRAVEL BEHAVIOUR
The links between land use, travel
behaviour and energy consumption
Relationships between land use and energy
use have been studied widely internation-
ally. The earliest studies focused on urban
density. In perhaps the most well-known
(although not uncontested) work, Newman
and Kenworthy (1989) measured per capita
petroleum consumption and population
densities in a number of large cities around
the world, and found a clear negative
relationship between the two. Car usage
was lower and provision of public transport
higher in the cities with the highest densities.
Others have argued that the transport policy
environment accompanying higher densities
– including parking management and fuel
pricing – often contribute as much to the
achievement of high public transport shares
as density per se (e.g. Gomez-Ibanez 1991).
In recent years a significant body of
research has emerged around the links
between land use and travel behaviour. Travel
behaviour – the amounts, types, lengths and
modes of travel undertaken by trip-makers
with various characteristics – is important
as an intermediate factor determining the
amount of energy consumed during travel.
The range of land use variables examined
has also broadened from aggregate density
towards more microscopic factors reflecting
the quality of the urban environment, includ-
ing neighbourhood safety, attractiveness
for walking and bicycling, block sizes and
mixed land uses (e.g. Crane & Crepeau 1998;
Zegras 2010). The general conclusion has
been that land use variables account for some
variation in travel patterns, but that socio-
economic characteristics and preferences
are at least as important in determining the
desire and opportunity for travel (e.g. Ewing
& Cervero 2001; Banister 2005). Among the
most important socio-economic variables
identified were car ownership and employ-
ment – travel patterns and distances tend to
change significantly once a household owns a
motor vehicle.
Models of vehicle ownership
Vehicle ownership models, central to the
analysis of transport energy consumption,
have a long history. Mokonyama and Venter
(2007) provide a brief overview of modelling
approaches used in South Africa, and discuss
the limitations of conventional ownership
models using time-series or income variables
only (e.g. Sweet 1988). In short, significant
evidence exists of the benefits of using pric-
ing, land use and demographic factors to
help explain vehicle ownership. Disaggregate
choice models of the kind used in this paper
are ideally suited to this task, provided the
data is available at the household or indi-
vidual level. One local application has been
found of a logit model used to investigate
the choice between petrol and diesel vehicles
(Naude 2002), but the model did not go so
far as to examine the initial vehicle purchase
decision.
Methodologies for studying land
use / transport energy relationships
Studies of the effects of urban form on vehi-
cle usage and energy consumption can be
divided into aggregate and disaggregate stud-
ies. Aggregate studies use spatially defined
averages for all variables, with observations
usually at the city or metropolitan level.
Besides the work by Newman and Kenworthy
(1989), recent applications of this approach
include comparisons of transport energy
consumption across cities in developed and
developing countries (Daimon et al 2007).
A major problem with cross-sectional
aggregate approaches is the difficulty in
controlling for cultural, political, historical
and economic differences. Handy (1996)
reviewed many studies, and concluded that
aggregate studies are generally not capable of
uncovering true relationships between land
form measures and travel.
Disaggregate studies, on the other
hand, use household observations of
vehicle usage and city-wide, zonal or
neighbourhood averages for urban form
variables. These allow energy use for
transport to be compared to characteristics
of the household and the residential area
(e.g. Golob & Brownstone 2005; Lindsey
et al 2011). For example, Naess et al (1995)
used data collected from 321 households
in 30 residential areas in Greater Oslo to
investigate variations in travel distances,
modal splits and energy use, and found that
residents of high-density, centrally located
communities travel considerably shorter
distances and use considerably less energy
per capita than those who live in low-density,
outer areas. A similar approach is applied in
this paper to the Nelson Mandela Bay area.
RESEARCH DESIGN
Background and study area
The study area is the Nelson Mandela
Metropolitan Area located in the Eastern
Cape Province. It has a population of
approximately 1.5 million and a land area of
1 845 square kilometres (NMMM 2004). The
metropolitan boundary includes the city of
Port Elizabeth, its surrounding low-income
residential areas, and the nearby towns of
Despatch and Uitenhage. Thirty-four per
cent of households have access to one or
more cars, very similar to the average of 36%
for other metropolitan areas in South Africa
(DOT 2005). Nelson Mandela Bay is fairly
well served by public transport. Minibus
taxis transport about 20% of daily trips,
while the Algoa Bus Company, the sole bus
operator in the area, serves about 6% of all
trips on a fairly extensive bus route network
connecting outlying areas with the Port
Elizabeth (CBD) Central Business District
(NMMM 2005). A single commuter rail line
connects the CBD with Uitenhage, but trans-
ports less than 1% of trips. The overall split
between public and private modes is 40:60
(excluding walking).
Although the modal mix and mode
shares in Nelson Mandela Bay are typical of
metropolitan areas in South Africa, it has
some unique topographical features. These
include the coastline which directs growth
towards the north and north-west, and the
Swartkops River to the north of the metro,
both of which might lead to longer travel
distances than in other comparable-sized
metros.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 20134
Travel survey data
In 2004, the Nelson Mandela Metropolitan
Municipality undertook a travel survey to
determine travel demand characteristics in
the area. A total of 2 828 randomly chosen
households (10 200 individuals) were included
in the survey. The survey included a 24-hour
weekday travel diary. As one of the first travel
surveys in South Africa that extended beyond
peak periods it offered much more complete
travel data than traditional survey sources.
Data on standard vehicle ownership and
demographics was also collected.
To estimate energy consumed for trans-
port, the data on trip distances and public
transport occupancies was obtained from
secondary sources. Trip distances were
extracted from a zonal distance matrix
based on shortest route road distances
between zone centroids. Public transport
occupancy figures were obtained from the
municipality’s Current Public Transport
Record (CPTR), which recorded bus and taxi
occupancies by route and time of day.
Land use data and
accessibility measures
The land use intensity variables that we used
included population density and a job acces-
sibility index. The population density per
residence zone was derived from the 2001
national census data.
The accessibility of a household in a par-
ticular zone is generally defined as the ease
of reaching opportunities in the surrounding
area, and is affected both by the location of
the household relative to potential destina-
tions, and the quality of the transport system
available. In order to test our hypothesis that
the amount of transport energy consumed
is affected by the level of accessibility a
household enjoys, we constructed an acces-
sibility index for each home zone. A standard
gravity-based measure was used (El-Geneidy
& Levinson 2007), defined as follows:
Ai = ∑dj ∙ f(wij)
∑dj
(1)
where:
Ai = accessibility index of zone i to
opportunities;
dj = the amount of job opportunities
available at zone j;
f(wij) = an impedance function expressing
the increasing difficulty of travel-
ling between i and j as the distance
increases;
wij = the road distance between zones i
and j.
We used a locally calibrated impedance func-
tion of f(wij) = e–0.15wij obtained from the trip
distribution model of the NMMM strategic
transport model; it thus reflects the actual
sensitivity of trip makers in the area to travel
distance, averaged over trip purpose and
income levels (NMMM 2004). Two assump-
tions are that access to jobs reflects the level
of access to other opportunities (including
shopping, social, and business opportunities);
and that road distance as a proxy for travel
friction captures the main effect of interest,
even though it ignores congestion.
Estimating transport
energy consumption
The transport energy estimation process
requires determining the energy intensity
for each individual trip made. Studies have
shown that fuel consumption per vehicle-
kilometre depends on many factors, inclu ding
vehicle engine size, fuel type, traffic condi-
tions, environmental conditions and driving
style (Goyns 2008; Wong 2000). We used
average fuel consumption figures for passen-
ger vehicles and for minibuses as suggested
by Schutte and Pienaar (1997), and averaged
across petrol and diesel vehicles according
to the number of each fuel type registered in
the Nelson Mandela Metropolitan Area. The
figures for passenger vehicles accord with
fuel consumption rates measured by Wong
(2000) in coastal regions of South Africa.
Sivanandan and Rakha (2003) showed that
energy intensity estimates based on an aver-
age composite vehicle tend to produce con-
clusions that are consistent with the explicit
modelling of the various vehicle types.
The average fuel consumption estimates
for buses were obtained from the Algoa Bus
Company. A summary of the final fuel inten-
sity figures (in litres per 100 veh-km) used for
each mode in the survey is given in Table 1.
The fuel consumption for each trip made
by each individual interviewed during the
survey was calculated as:
l/person-trip = km × l/veh-km
vehicle occupancy (2)
where:
l/person-trip = fuel consumption
km = distance
l/veh-km = fuel consumption intensity
Trip distances were estimated from the
shortest-path route between the origin
and destination of each trip. Equation (2)
is applicable to all modes of travel, except
for passenger rail. Rail transport in Nelson
Mandela Metropolitan Area uses electric
power. In order to convert the electric
power consumption to the same unit as the
other modes, the energy consumption and
maximum occupancy figures (for 9 M com-
muter rail trains) suggested by Del Mistro &
Aucamp (2000) were used, namely 10.3 MJ/
coach-km and 255 passengers respectively.
The average occupancy per coach, based on
100% occupancy in peak direction and 20%
in the opposite direction, is taken as 60%.
Thus the energy consumption per rail pas-
senger trip was calculated as:
MJ/person-trip)
= km × Mj/coach-km
60% × maximum occupancy per coach (3)
where:
MJ/person-trip = energy consumption
km = distance
Mj/coach-km = energy consumption
intensity
Results from Equation (2) were converted to
Megajoules (MJ) to enable comparison across
different modes using a conversion factor of
36.7 MJ/litre of fuel. The final step was the
summation of the energy consumption by
trip according to the levels of analysis.
Modelling disaggregate energy
consumption: analytical issues
When attempting to model the relationship
between transport energy consumption and
household, individual or spatial explanatory
Table 1 Fuel consumption and energy intensity rates used to estimate energy consumption
Mode usedFuel consumption
(litres/100 veh-km)Energy intensity
(Megajoules/100veh-km)
Walk 0 0
Bicycle 0 0
Motor cycle 2.8 102.8
Bakkie taxi 12.3 451.4
Minibus taxi 14.0 513.8
Commuter rail --- 10.3 (MJ per couch-km)
Bus 47.5 1 833.5
Motor vehicle 10.8 396.4
Note: See text for data sources
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 5
variables, one is confronted with a number of
analytical problems. The first relates to the
problem of self-selection bias. This kind of
problem occurs when cross-sectional data is
used to assess how land use variables, such
as density or accessibility, influence people’s
travel behaviour (see Mokhtarian & Cao 2008)
or travel energy consumption. Self-selection
refers to the fact that households are not ran-
domly distributed across space: households
who prefer (or are unable) to own a car may
choose to locate in an area that provides
opportunities for walking and public trans-
port use. If statistical analysis then identifies a
correlation between being located in an acces-
sible neighbourhood and high use of public
transport, it is not clear that this behaviour
can be attributed to the neighbourhood
features rather than to preference variables.
In other words, causality is unclear. Methods
exist for dealing with problems of simultane-
ity (see for instance Mokhtarian & Cao 2008),
but these require more advanced research
designs involving control groups that are not
available for this study. We do not correct for
self-selection bias here. The results, therefore,
must be interpreted with caution: we can, at
best, infer association between land use and
energy consumption, rather than causality.
A second problem relates to endogene-
ity, in this case with respect to the effect of
unobserved taste variations on car ownership
and energy use. We expect (and will later
prove) that income (and the values and life-
style choices normally associated with a cer-
tain income level) strongly affects the deci-
sion to buy a motor vehicle. The same values
and preferences also affect the amount of
travel undertaken (and therefore the amount
of energy consumed). For statistical reasons
we cannot specify a single regression model
of transport energy consumption containing
the household’s number of motor vehicles as
an independent variable, as this variable may
be correlated with the unobserved values and
preferences (and thus with the regression
model’s error term). Instead we develop an
instrumental variable, the predicted number
of cars in a household, and use this predicted
value rather than the observed number of
cars owned as the explanatory variable in the
regression model (see Zegras 2010).
What the need for an instrumental
variable implies is that a separate model of
household car ownership choice must first
be estimated on the data set, before energy
consumption can be modelled. We therefore
specify a multinomial logit (MNL) model to
capture the household decision of whether
to own zero, one, or two or more vehicles, as
a function of demographic and spatial vari-
ables. Apart from its usefulness in supplying
the instrumental variable for the energy
use model, the MNL model also provides
additional insight into the factors affecting
a household’s decision of whether or not to
buy a car.
A third problem relates to the use of the
energy consumption metric as a dependent
variable, as the variable is calculated across
all persons and households in the sample,
and therefore includes many zero observa-
tions. In fact, the data shows that 34% of
individuals consumed no energy during
travel, as their trips consisted exclusively of
walking or bicycle trips on the survey day.
The data is thus left-censored, with many
observations clustered at zero, and can
not be modelled using a simple linear OLS
model for continuous dependent variables.
This would produce biased and inconsist-
ent parameter estimates (Washington et al
2003). The solution is to use a Tobit model
(a model formulation developed specifically
to deal with such cases), and estimated
Maximum Likelihood methods. The Tobit
model is encountered in the travel behaviour
literature in the analysis of travel expendi-
ture data, which is frequently left-censored
when no money is spent on transport (e.g.
Thakuriah & Liao 2005). The paper does not
elaborate on the specification or estimation
of the Tobit model; suffice to say that Tobit
model results and test statistics can be inter-
preted in the same way as those of ordinary
least squares models.
ENERGY CONSUMPTION
PATTERNS ACROSS SUB-
GROUPS OF THE POPULATION
We look firstly at patterns of daily transport
energy consumption by aggregating our
trip-level energy consumption estimates by
mode used, by time of day, and by zone. We
then aggregate across demographic charac-
teristics, such as gender and occupation, in
order to examine intergroup differences in
energy use.
Transport energy use by
mode and time of day
Figure 1 plots the distribution of daily
transport energy consumption per person.
It is clearly a very skew distribution, with
about 34% of individuals in the sample using
no fuel, and 83% consuming less than 40 MJ
per day to travel (40 MJ is approximately the
energy consumed during one 10-kilometre
long car trip made by a single occupant). The
cumulative distribution in Figure 1 shows
Figure 1 Daily and cumulative daily energy consumption by persons in the sample
(unweighted, n = 7 000 persons)
500
450
400
350
300
250
200
150
100
50
0
MJ
pe
r p
ers
on
pe
r d
ay
Cu
mu
lati
ve %
of
tota
l d
ail
y e
ne
rgy
con
sum
pti
on
100
90
80
70
60
50
40
30
20
10
0
Percentage of individuals
0 20 40 60 80 100
Daily transport energy consumption Cumulative transport energy consumption
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 20136
that 80% of residents in Nelson Mandela Bay
contribute only 22% to the overall energy bill,
with the remaining 20% of people consuming
78% of the total.
The reason for this skewness is apparent
from Table 2, which shows the distribution
of trips by mode in the sample. Almost half
of all trips are made on foot or on bicycles.
The car is used in a quarter of person-trips,
but these trips consume three to five times
the amount of energy as trips by motorcycle,
minibus taxi or bus. This is due to the car’s
low occupancy rather than to long trip
distances; mean car trip lengths are similar
to trip lengths by taxi, and less than trip
lengths by bus and train. Surprisingly, the
mean energy consumption per bus trip
is about 50% higher than that per trip in
a minibus taxi. Two reasons account for
this: buses have an energy intensity that is
more than three times higher than that of
minibuses (Table 1); and bus passengers tend
to make longer trips than taxi passengers.
When controlling for trip distance, however,
the energy consumed per bus passenger on a
per-kilometre basis is about equal to that of a
minibus taxi passenger. The higher carrying
capacity of buses offsets their higher energy
intensity, but perhaps not to the extent
expected. Trains are by far the most efficient
mode due to their high passenger capacities.
When comparing transport energy con-
sumption across different times of the day,
marked differences are observed. As shown in
Table 3, average energy use of trips made dur-
ing peak hours is 60% higher than that of trips
made during the rest of the day. Both occu-
pancies and trip distances vary depending on
the time of the day. Table 2 shows that only
buses are significantly fuller during the peaks
than during the off-peaks; minibus taxis have
about the same average occupancy through-
out the day, while private cars actually have
lower occupancy during peaks – an indication
that the car trip to work tends to be predomi-
nantly single-occupancy. Furthermore, mean
trip distances are higher during the peak than
the off-peak (Tables 2 and 3), contributing
further to peak period energy use.
Spatial patterns of
transport energy use
Figure 2 shows the zonal average household
transport energy consumption, plotted
on the transport analysis zones used by
NMMM. The figure indicates how demo-
graphic, spatial and transport supply factors
interact to determine energy consumption
patterns in the study area. High transport
energy consumption is recorded in outlying
areas towards the north (around Coega) and
south, but these are in fact sparsely popu-
lated areas of low significance. Low income
residential areas that are well-served by pub-
lic transport, such as Motherwell, iBhayi and
Kwanobuhle, have relatively low transport
energy consumption; so do the Despatch and
Uitenhage areas which are close to the rail
line and to local factory jobs. Higher-income
areas such as Bluewater Bay, Summerstrand
and the PE central suburbs are located closer
to the Port Elizabeth CBD, but have higher
energy consumption – this despite having
relatively good taxi and bus coverage. The
metro’s unique topography may also contrib-
ute to higher energy consumption across the
river to the north, from where residents have
longer travel distances to access major work
nodes to the south.
Table 2 Comparison of transport energy use by travel mode
Mode of travelNumber of
person-trips observed
Percentage of trips
Mean energy use
(MJ/person-trip)
Average occupancy(persons/vehicle)
Average trip distance (km/trip)
Time of day Time of day
Off-peak Peak Off-peak Peak
Non-motorised 9 785 46.1 0.0 1.00 1.00 1.8 1.9
Motor cycle 50 0.2 5.6 1.03 1.00 5.9 4.7
Motor vehicle 5 333 25.1 25.8 2.02 1.95 8.3 10.2
Minibus taxi 4 751 22.4 4.8 9.30 9.43 8.0 9.5
Bakkie taxi 89 0.4 11.1 4.67 4.87 12.9 10.9
Bus 1 120 5.3 7.1 32.94 44.38 12.3 14.6
Train 57 0.3 1.7 51.0a 255.0a 32.0 23.8
Other 45 0.2 8.9 2.80 2.81 5.9 7.0
Notes: Sources: Mean energy use estimated. Average occupancy of motor vehicle trips as reported in survey. Average occupancy of public transport trips obtained from Current Public Transport Record, 2004. a = Train occupancies based on national averages. Average occupancy shown per coach.
Table 3 Comparisons of transport energy use by time of day
Period Mean energy use (MJ/person-trip) Mean trip distance (km/trip)
Peak period 9.7 6.9
Off-peak period 6.0 5.2
All trips in sample 8.1 6.1
Notes: Peak period is defined as 6:00-9:00 and 15:00-18:00. Off-peak period is all the other hours of the day
Figure 2 Estimated average daily household transport energy consumed (MJ), shown per
transport analysis zone
Uitenhage
KwaNobuhle Despatch
Ibhayi
Motherwell
Coega
PE Central
Summerstrand
Bus routeRail routeTaxi route
Average Transport Energy (MJ/HH)
0–5050–100100–250>250N/A
0 3.75 7.5 15 kilometres
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 7
TRANSPORT ENERGY USE BY
GENDER AND EMPLOYMENT STATUS
To examine patterns of transport energy use
across segments of the population, trip-level
consumption figures are aggregated for
each individual and grouped by gender and
employment status (see Table 4). Gender is
considered here as it relates to the different
roles played by men and women in society,
and has frequently been found to account for
significantly different travel patterns across a
population (e.g. Turner & Fouracre 1995). In
this sample, the mean energy consumption
by male travellers is significantly higher than
that of women. Men make slightly fewer trips
per day than women, but, on average, travel
longer distances. This is consistent with
previous findings indicating that, compared
to men, women tend to make more non-work
trips, and tend to visit destinations closer to
the home (e.g. Venter et al 2007). Men also
tend to use cars more: 28% of all trips by
men are made by car, compared to 22% for
women.
A similar grouping by occupation type
shows the importance of employment status
as a predictor of transport energy consump-
tion. People who are employed and travel to
work consume 47 MJ during travel per day,
compared to 14 MJ for unemployed people
or homemakers, and 9 MJ for students and
scholars. Thus giving one unemployed
person a job would tend to increase their
transport energy use more than three-fold,
everything else being equal, as employment
is associated with both longer travel dis-
tances and more frequent use of the car. The
strength and nature of the income effect on
energy consumption is examined further in
the following section.
DISAGGREGATE RELATIONSHIPS
BETWEEN LAND USE,
DEMOGRAPHICS AND TRANSPORT
ENERGY CONSUMPTION
The objective here is to assess to what extent
energy use during travel is affected by a
household or individual’s own characteristics
(such as income and gender), by zone-level
land use characteristics (such as density), and
by zone-level accessibility to surrounding
opportunities. Some of the variables were
already examined in the previous section,
but we now include them in a multivariate
model to assess the relative strength of
each in explaining variations in energy use.
Theory suggests that higher incomes are
associated with higher energy use, as both
car ownership and travel activity tend to
increase as incomes grow. Higher densities
are associated with lower energy use, all else
being equal, because opportunities for walk-
ing and reducing trip lengths grow as more
activities are available close to home. The
influence of accessibility is unpredictable;
being located in more accessible areas close
to the city centre might lead to reduced trip
lengths and thus reduced energy require-
ments, but it might equally lead to increased
trip making as the opportunities for interac-
tion improve.
As explained earlier, we first estimate a
model of household vehicle ownership choice
to examine the factors driving the decision
to purchase a vehicle, and to supply an
instrumental variable of predicted car own-
ership that can be used in the subsequent
energy use models.
Household vehicle ownership choice
A multinomial logit (MNL) model of vehicle
ownership choice was estimated, using a
category-dependent variable with three
potential outcomes, namely zero cars (the
base case), one car, or two and more cars
in a household. Household characteristics
tested as explanatory variables included
the monthly household income reported by
respondents, the number of workers in the
household, and household size, which was
interacted with income to test the possibil-
ity that household size has a differential
effect on vehicle ownership depending on
socio-economic status. All correlations
among explanatory variables are below 0.5,
indicating sufficient independence. Zonal
population density and job accessibility
index variables were included as land use
descriptors.
Table 5 shows the parameter estimates
and the t-values for each coefficient, as well as
the goodness-of-fit statistics. Almost all coef-
ficients are significant, and the adjusted rho-
squared value of 0.31 is good for disaggregate
Table 4 Comparisons of transport energy use and travel, by gender and occupation
GroupMean energy use (MJ/person/day)
Mean number of trips (trips/person/day)
Mean daily travel distance
(km/person/day)
Gender
Female 20.8 3.1 18.0
Male 28.9 2.9 19.3
Employment status
Working outside home 46.9 3.3 27.8
Not working outside home 13.8 3.3 14.7
Scholars and students 8.8 2.7 11.8
All individuals in sample 24.7 3.0 18.6
Notes: ‘Working outside home’ includes part and full-time workers. ‘Not working outside home’ includes people working from home, home-makers, unemployed, retired.
Table 5 Estimation results: Multinomial logit model of vehicle ownership choice
Variables0 vehicles
(base)
1 vehicle 2+ vehicles
Beta T-value Beta T-value
Household characteristics
No of workers 0.353 4.69** 0.703 6.79**
HH income (R’000s) 0.149 5.67** 0.264 9.57**
HH size (low incomea) –0.138 –3.92** –0.146 –2.50**
HH size (high incomea) 0.001 0.025 –0.047 –0.86
Zone characteristics
Population densityb –0.148 –9.183** –0.366 –11.945**
Job access indexc 6.847 4.476** 6.720 3.491**
Constants –1.003 –5.87** –1.898 –7.72**
Number of observations 1 648 534 411
Likelihood ratio test (full model)Chi-squared =
1 475**
Adjusted rho-squared 0.314
** = Significant at 95%a = Low-income households are below the median income of R2 500 per month; high-income is aboveb = Population density of household zone (in 1 000 persons per square kilometre) c = Accessibility index by road to job opportunities (see text for explanation)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 20138
choice models. Household income and the
number of workers show a positive and strong
relationship to vehicle ownership – this can
be expected and agrees with evidence from
previous studies. Household size has an
interesting differential effect on the likelihood
of buying a car, depending on the income. For
low-income households, an increasing house-
hold size is associated with a lower likelihood
of buying a car, even controlling for the level
of income itself. Increasing household sizes
indicate the presence of either more children
or dependent elderly people in the family, who
represent a competing claim on household
resources, leaving less for the purchase and
maintenance of a vehicle. Amongst high-
income households, however, the number of
people in the household has no statistically
significant relationship with the number of
vehicles – evidently, once incomes are high
enough, children’s impact on household
resources is not significant enough to affect
vehicle purchase decisions.
The density of people in a household’s
neighbourhood has a negative association
with the likelihood of buying a vehicle, as
was expected. This strong relationship is,
however, not necessarily an indication that
land use by itself influences car owner-
ship – the problem of self-selection bias
described above prevents us from drawing
any conclusions regarding causality. A look
at population density figures for NMMA
confirms that the highest density zones are
found in lower income townships like Ibhayi
and Motherwell. It is likely, therefore, that
households who cannot afford to buy a vehi-
cle locate in higher density residential areas
for a host of reasons, including historical or
community ties, housing affordability, and,
perhaps, the nearby location of social and
educational opportunities.
The accessibility index, as a measure of
relative location on a metro-wide scale, is
significant and positive. The more accessible
a home is via the road network, the more
likely the household is to own one or more
vehicles. The implication is, once again, not
necessarily one of causality. The result might
as well be an outcome of historic settlement
patterns typical to the South African city:
higher income households have historically
had the opportunity to locate in more cen-
tral, more accessible places with good road
networks, and are also more likely to afford
and own more vehicles. It is important to
note that there is at this stage no evidence
that city-scale accessibility patterns influ-
ence vehicle ownership decisions – a more
detailed investigation, controlling for socio-
economic variables and preferably using
time-series data, is needed to examine such
a question.
Household transport
energy consumption
Table 6 presents the results of a Tobit model
of transport energy consumption estimated
at the household level, and using household
characteristics and spatial properties of the
household’s home zone as independent vari-
ables. Household income is omitted from the
model due to its high correlation with the
expected vehicle ownership variable.
Parameter estimates are largely signifi-
cant and of the expected sign, and the model
performs well according to the likelihood
ratio test. The positive signs of the household
variables indicate that, all else being equal,
households consume more transport energy
if they have more workers or more people
in the household overall. More workers
mean more work trips – which we already
showed tend to be energy intensive – while
bigger households make more trips overall.
Expected vehicle ownership dwarfs all
other variables in the model (looking at the
t-values), confirming that this is the single
most important driver of household trans-
port energy use (Goyns 2008).
The land use variables show interesting
results. Population density of the home zone
is insignificant: by itself it does not explain
household transport energy consumption.
Read in conjunction with the previous
model’s results, this implies that the density
effect is indirect rather than direct: lower
density is associated with higher car owner-
ship, thus indirectly affecting travel patterns
via mode use; but once the car is bought,
lower population density is not associated
with more trip-making. This is consistent
with the findings of Mirrilees (1993) that
factors such as the distribution and distances
between different land uses, the location of
services with respect to one another, and
vehicle ownership play a larger role in trans-
port energy demand than urban density.
The estimates for the job accessibility
variables show that, indeed, a household’s
location relative to job (and by implication
other opportunities in the surrounding
metro area) does affect the amount of
transport energy consumed, even after
controlling for vehicle ownership. The effect
differs, however, across households. In order
to account for a potential accessibility/
income relationship suggested by the MNL
model, the accessibility index was interacted
with a household income dummy which
categorised the household as either below
or above the median income level for the
area. The parameter estimates show that a
household’s accessibility significantly affects
Table 6 Estimation results: Tobit models of transport energy consumption
VariablesHousehold model Individual model
Beta T-value Beta T-value
Household characteristics
No of workers
HH size
Expected vehicles owneda
15.181
2.865
104.54
6.45**
3.19**
20.83** 38.32 27.7**
Individual characteristics
Gender (1 = male)
Age
Employed (1 = employed)
Studying (1 = scholar/student)
3.605
0.593
31.07
–10.48
2.67**
10.41**
16.68**
–4.17**
Zone characteristics
Population densityb 0.964 1.67 –0.066 –0.33
Job access indexc
Low-income HHd
High-income HHd
–31.304
–263.73
–0.55
–4.06**
97.68
–0.186
4.53**
–1.09
Constants –34.971 –5.92** –44.02 –12.80**
Number of observations 2 593 7 000
Number (%) of zero observations 363 (14%) 2 380 (34%)
Likelihood ratio test (full model)Chi-squared =
1 201**Chi-squared =
3 039**
** = significant at 95%Dependent variable = Megajoules of transport energy consumed per day (per individual/household)Empty cells denote variable not used in modela = Estimated as 0*P(0) + 1*P(1) + 2.3*P(2+), where the values of P(n), the probability of owning n vehicles (calculated from the MNL model estimated above), and the value 2.3 is the mean number of vehicles owned by all households in the sample who own two or more vehicles.b = Population density of household zone (in 1 000 persons per square kilometre) c = Accessibility index by road to job opportunities (see text for explanation)d = Low-income households are below the median income of R2 500 per month; high-income is above
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 9
transport energy consumption only if the
household is high-income: richer households
tend to consume less transport energy if
they live in more accessible places. This
suggests that, once a vehicle is available,
households benefit from being located in
more central, accessible places by gaining
the ability to reduce their travel distances
and, by extension, their transport energy
consumption. Low-income households do
not gain this benefit from being located in
accessible places (as indicated by the non-
significant parameter estimate). The reason
is probably that low-income households are
more likely to have low transport energy
consumption levels anyway – being more
likely to walk or use public transport – so
that any additional gains in travel distances
do not impact energy expenditures
significantly.
Individual transport energy
consumption
The results of the transport energy con-
sumption model estimated at the individual
level indicate similar findings (see Table 6).
Once again, expected household car owner-
ship is the strongest predictor of energy use.
Personal characteristics also explain energy
use: all else being equal, being male, being
older, and being employed raises a person’s
energy expenditure, while being a student or
scholar reduces energy use (relative to being
unemployed). These findings are consistent
with the results of the bivariate analyses
presented earlier.
Population density is again non-signifi-
cant. However, the interacted access index
variable reverses its significance and sign:
persons living in low-income households
are now more likely to have higher energy
expenditures, while no effect is found among
high-income persons. What this might
indicate is that accessibility is associated
with increased travel activity among lower-
income people, as one might expect if there
was significant latent or suppressed demand
for travel among low-income persons, which
is released once travel becomes easier or less
expensive due to improved accessibility. This
interpretation matches the general finding
regarding the differential benefits of acces-
sibility suggested by the previous model:
that accessibility plays a different role for
different people, depending on their socio-
economic status and the extent of mobility
they already enjoy. Among high-income (car
owning) people, higher levels of access are
associated with travel activity savings and
a reduction in energy use; among lower-
income people, higher access is associated
with increased motorised travel and higher
energy expenditures.
CONCLUSIONS: IMPLICATIONS
FOR URBAN MANAGEMENT
Methodologically the study demonstrated
the feasibility of using travel survey data to
establish disaggregate patterns of transport
energy consumption at the individual, house-
hold or neighbourhood levels. This provides
opportunities for using existing travel data
sources for establishing baseline data to moni-
tor impacts and changes over time. Marginal
methodological improvements might come
from improved data collection (especially the
inclusion of vehicle size and fuel type data in
questionnaires), and marrying travel route
information with more accurate link-level
speed information to improve the accuracy of
vehicle energy consumption estimates.
Our results clearly showed how skewed
energy expenditure is across the population.
Car users, although they make only 25% of
trips, contribute 70% of the passenger trans-
port energy consumption in metropolitan
Nelson Mandela Bay. The strong influence
of car ownership and income level on energy
consumption is a common finding globally.
From the urban policy perspective this high-
lights the challenges inherent in addressing
urban sustainability issues. If the objective
were simply to reduce transport energy use,
the largest pay-off would come from reduc-
ing private vehicle use through, for instance,
the pricing of low-occupancy car travel.
However, energy reduction goals are traded
off against other policy objectives such as job
creation. Workers spend three times more
energy travelling daily than the unemployed;
should residential and work locations remain
fixed, employment gains will result in sig-
nificant increases in South Africa’s energy
needs, unless a significant proportion of
such travel can be shifted to non-motorised
modes or to rail.
What might transport interventions do to
energy consumption? Compared to the dif-
ference between cars and non-car modes, the
difference in energy use between road-based
public transport modes is relatively small.
So is the average difference between peak
and off-peak travel (although this difference
might be larger in cities with higher conges-
tion levels than NMMM). More specifically,
on a per-passenger-kilometre basis, the
energy consumption of minibus taxi trips is
similar to that of bus trips, due to the high
energy efficiency of small vehicles and the
relatively low occupancy of metropolitan
bus services. This suggests that – in energy
terms – little can be gained from travel
demand management (TDM) strategies such
as peak spreading, or from public transport
interventions such as bus rapid transit (BRT),
unless they are coupled with appreciable
increases in bus occupancy, introduction of
more fuel efficient vehicles, significant speed
gains by avoiding congestion, and a signifi-
cant amount of switching from car (rather
than taxi) to BRT. The predominant focus of
first-generation BRT schemes on replacing
minibus-taxi services is likely to do little for
energy and environmental concerns unless
they delay the car purchase decision among
medium-income future car owners. This is a
challenging proposition given the sensitivity
of car ownership to income growth.
A significant element of the urban sustain-
ability agenda is concerned with changing
the density and form of land use in cities.
Our findings suggest that such efforts will
have a variety of impacts on travel behaviour,
energy consumption and sustainability – and
not all of it in a desirable direction. High
neighbourhood densities are correlated with
lower car ownership (and thus with reduced
transport energy use), but the data does not
allow us to establish causality – in other
words to conclude that densification strategies
would necessarily lead to better sustainability
outcomes. Further research using time-series
data (perhaps using repeated panel surveys) is
needed to allow researchers to tease out the
effects of density (and other land use factors)
from other historic and taste-based variables.
Metropolitan-wide accessibility – the
ease of reaching job (and other) opportuni-
ties within a reasonable travel time – does
seem to affect travel behaviour and transport
energy consumption. An important finding
is that this relationship appears to depend on
the socio-economic status of a household or
individual. Among high-income households,
better accessibility is associated with lower
travel. It is likely that access-enhancing strat-
egies, such as those promoting mixed-use
developments in accessible, centrally located
nodes, would reduce driving distances and
the energy and environmental costs of travel.
However, the same accessibility improve-
ments could have the opposite effect on
lower-income (non-driving) households, as
the time or cost savings brought about by
the access improvements could be converted
into increased travel, releasing some of the
pent-up demand for mobility. This is where
coordination between land use and transport
is key: attractive, upgraded public transport
should then be available to capture this
additional demand in energy-efficient ways.
Otherwise, uncoordinated land use measures
could have unintended consequences and
contribute to deteriorating sustainability
outcomes in our cities.
ACKNOWLEDGMENTS
The authors gratefully acknowledge the
help of the Nelson Mandela Metropolitan
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201310
Municipality in providing access to the data.
Findings and conclusions are not necessarily
those of the Municipality.
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Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 11
INTRODUCTION
The PSSDB system is a lightweight compos-
ite load-bearing structural system consisting
of profiled steel sheet (PSS) and dry board
(DB). They are attached by self-drilling and
self-tapping screws, as illustrated in Figure 1.
The system was developed by Wright et al
(1989) as a flooring system with many advan-
tages (Wan Badaruzzaman & Wright 1998).
It can be applied in domestic buildings, office
buildings or during renovation (Wright et al
1989) for various structural purposes such as
floors, roofs and walls (Ahmed et al 2000).
According to some researchers on the
static behaviour of the PSSDB system, the
screw spacing has a significant effect on the
stiffness of the system, as a panel with lower
screw spacing is stiffer than a panel with
higher screw spacing (Wan Badaruzzaman et
al 2003; Ahmed et al 1996; Ahmed & Wan
Badaruzzaman 2006). This stiffness has a direct
effect on the natural frequencies of the system.
Soedel (2004) stated that knowledge of
the frequency of a structure is crucial for two
reasons: firstly, from a design point of view,
for example prediction about the occurrence
of resonance conditions on the structure;
and secondly, measurement of natural fre-
quency is needed to obtain forced response
of the structure.
TECHNICAL PAPER
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 11–21, Paper 783
DR FARHAD ABBAS GANDOMKAR obtained his BEng
in Civil Engineering from Shahid Chamran University
of Ahvaz in 1996, his MSc in Structural Engineering
from Isfahan University of Technology in 1999, and his
PhD in Structural Engineering from Universiti
Kebangsaan Malaysia in 2012. He has been a full-time
lecturer at the Ahvaz branch of the Islamic Azad
University, Iran, since 1999 and is a member of the Khouzestan Construction
Engineering Disciplinary Organization. He has more than 13 years’ experience
in teaching, training, research, publication and administration.
Contact details:
Department of Civil & Structural Engineering
Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia
43600 Bangi, Selangor, Malaysia
T: 00603 8925 5760/1492, F: 00603 8925 5703,
PROF WAN HAMIDON WAN BADARUZZAMAN
obtained his PhD in Structural Engineering from the
University of Wales, Cardiff , UK, in 1994. He is Professor
of Structural Engineering at the National University of
Malaysia, where he began his career almost 30 years
ago. His research interest focuses on the profi led steel
sheeting dry board (PSSDB) system, a lightweight
composite structural system that he has developed
over the years. He has published many papers related to research fi ndings on
this patented and award-winning construction system.
Contact details:
Department of Civil & Structural Engineering
Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia
43600 Bangi, Selangor, Malaysia
T: 00603 8925 5760/1492, F: 00603 8925 5703
PROF SITI AMINAH OSMAN is Associate Professor in
Civil and Structural Engineering, and is a member of
the Board of Engineers Malaysia. She graduated
from Universiti Teknologi Malaysia in 1992 with a
BEng (Hons), MSc in Structural Engineering from the
University of Bradford, UK (1995) and a PhD in Civil
and Structural Engineering from Universiti
Kebangsaan Malaysia (2006). After her undergraduate studies, she started
lecturing at Universiti Kebagsaan Malaysia. Her interests are structural
engineering, wind engineering and industrial building system construction.
Contact details:
Department of Civil & Structural Engineering
Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia
43600 Bangi, Selangor, Malaysia
T: 00603 8921 6221, F: 00603 8921 6147
PROF AMIRUDDIN ISMAIL obtained his BEng in Civil
Engineering from the University of Pittsburgh, USA, in
1983, his MSc in Transportation and Urban Systems from
the University of Pittsburgh in 1984, and his PhD in
Transportation Engineering from Universiti Kebangsaan
Malaysia in 2002. He is currently Professor in Civil &
Structural Engineering at Universiti Kebangsaan Malaysia, and has more than
25 years’ experience in teaching, training, research, publication and
administration.
Contact details:
Department of Civil & Structural Engineering
Faculty of Engineering & Built Environment, Universiti Kebangsaan Malaysia
43600 Bangi, Selangor, Malaysia
T: 00603 8921 6203, F: 00603 8921 6147
Keywords: natural frequency, profi led steel sheet dry board, frequency response
function, low and high frequency fl oors, human comfort
Experimental and numerical investigation of the natural frequencies of the composite profi led steel sheet dry board (PSSDB) system
F A Gandomkar, W H Wan Badaruzzaman, S A Osman, A Ismail
This paper investigates the natural frequencies of the profiled steel sheet dry board (PSSDB) system. Frequency response functions (FRFs), estimated experimentally, were used to determine the natural frequencies of three different PSSDB panels with different screw spacing. Finite element models (FEMs) were developed to predict the natural frequencies of the tested panels. The FEMs were verified by comparing their results with results of the experimental test, and these confirmed the natural frequencies of the system. The effect of screw spacing on the natural frequencies of the system was studied experimentally and numerically. The numerical results uncovered the effect of various parameters, such as the PSS and DB thicknesses and boundary conditions, on the fundamental natural frequency (FNF) of the system. Fifteen finite element models were developed to determine the FNF of the PSSDB system with practical dimensions. When applied as a flooring system these panels are categorised as low-frequency floor (LFF) or high-frequency floor (HFF), to determine occurrence of resonance, design criteria, and whether or not they would be comfortable for humans.
Figure 1 Profiled steel sheet dry board system
Self-drilling and self-tapping screw
Dryboard
Profiled steel sheet
SS/2
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201312
Table 1 Characteristics of the experimental samples
Name of sampleScrew spacing
(mm)
Characteristics of samples
PSS DB Screw
PSSDB100 100
Peva45(t = 0.8 mm)
Plywood(18 mm)
DS-FH 432 self-drilling and
self-tappingPSSDB200 200
PSSDB300 300
Figure 3 Placing of selected points in plan to determine FRFs of PSSDB100, PSSDB200 systems
Point1
Point2
Point3
Point4
Point5
Point6
Point7
Point8
Point9
Point10
Point11
200 mm 200200200200200200200200200200200
Many reports and studies are available
to show that the FNF of a floor system is
the most important value to determine its
serviceability for human activities. In this
case Wiss & Parmelee (1974) presented a
response rating formula, Murray (1981)
proposed a formula for the critical damping
ratio, Ellingwood & Talin (1984) predicted
the maximum acceleration of a floor mid-
span, Ebrahimpour & Sack (2005) presented
literature on the critical FNF for wood and
lightweight construction, and Murray et al
(1997) proposed a design criteria graph with
respect to the peak acceleration and FNF of a
floor system.
Over a number of decades studies have
been performed on the dynamic character-
istics of the structural system, focusing on
natural frequencies. Hurst & Lezotte (1970)
conducted an analytical and experimental
study on the natural frequency of the
plywood-joist system, considering the effect
of joist size on the results. In their study ply-
wood was nailed to joists. In the same study,
Filiatrault et al (1990) revealed the natural
frequency and mode shapes of a plywood-
joist system for different boundary conditions
by the finite strip method, which, when
compared, agreed well with experimental
test results. They also discussed the effects of
different parameters on the natural frequency
of the system. Fukuwa et al (1996) evaluated
dynamic properties of a prefabricated steel
building by obtaining the natural frequency
and damping ratio of the system for various
construction stages. Effects of non-structural
members on the results were investigated
in their study. El-Dardiry et al (2002) deter-
mined the natural frequency of a long-span
flat concrete floor by using a suitable FEM
and an experimental heel-drop test. They
considered several FEMs and refined them
by comparing their results with experimental
test results, and then presenting the most
suitable FEM. Ferreira & Fasshauer (2007)
performed a free vibration study on a com-
posite plate by an innovative numerical meth-
od. Results of different thickness-to-length
ratios were determined and discussed in
their study. Ju et al (2008) developed a new
composite floor system, and measured the
natural frequencies and damping ratios of
the system by experimental testing for three
different construction stages: steel erection
stage, concrete casting stage, and finishing
stage. They compared the results with inter-
national codes to evaluate the serviceability
of the proposed floor system and obtained
good vibration characteristics. Xing & Liu
(2009) derived successfully the natural modes
of a rectangular orthotropic plate by exact
solution of mathematical statements for three
different boundary conditions. Two studies
were carried out on the modal analysis of an
orthotropic composite floor slab with profiled
steel deck (De A Mello et al 2008) and a pre-
and post-impacted nano-composite laminates
system (Velmurugan 2011). Both studies were
performed to find dynamic characteristics of
composite floor systems, similar to the study
by Bayat et al (2011) to determine the vibra-
tion frequencies of tapered beams. Honda &
Narita (2012) presented an analytical method
to determine the natural frequencies and
vibration modes of laminated plates having
such cantilever reinforcing fibres.
Figure 2 The PSSDB system with 200 mm
screw spacing during test
Figure 4 Placing of selected points in plan to determine FRFs of PSSDB300 system
Point1
Point2
Point3
Point4
Point5
Point6
Point7
300 mm 300300 300 300 300 300 300
Figure 5 (a) Bruel & Kjaer portable and multi-channel PULSE analyser type 3560D (b) ENDEVCO
uniaxial accelerometer type 751-100 (c) Impact hammer type 2302-10
(a) (b) (c)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 13
Study of the natural frequency of the
PSSDB system is limited to an experimental
study done by Wright et al (1989) to identify
the FNF of the system, considering PMF100
as the PSS and chipboard as the DB. It was
reported that, since the PSSDB system is
slender and flexible by nature, its FNF may
be low. Vibration of such floors during
human activities may therefore be perceiv-
able. It has also been stated that floors with
FNFs lower than approximately 7 Hz are
considered uncomfortable for users (Wright
1989). In addition, Gandomkar et al (2011)
determined the natural frequencies of the
PSSDB system experimentally and numeri-
cally with in-filled concrete in the trough
of the PSS. They also evaluated the effect of
various parameters on the FNF of the men-
tioned system.
There is little energy in high frequency
floors (of approximately 10 Hz) (Middleton
& Brownjohn 2010). A floor is an HFF if it
has an FNF above 10 Hz, but it is known
as an LFF if it is dominated by resonance
from the first four harmonics of a walking
force. Ljunggren et al (2007) stated that
some researchers suggested two different
design criteria for floors: deflection criteria
for HFF and an acceleration limit for LFF.
However, Murray et al (1997) recommended
acceleration limits for LFF and HFF, and a
minimum static stiffness of 1 kN/mm under
concentrated load as an additional check for
HFF. Therefore, knowing the FNF of a floor
system will determine the design of the floor
and whether it should be an LFF or HFF
floor, and hence its level of comfort.
Using non-structural systems, such as
partitions, on a completed floor has an effect
on the damping value of the floor system
(De Silva & Thambiratnam 2009). Knowing
the damping ratio of a bare floor system can
therefore help designers to select a realistic
damping ratio for the dynamic analysis of
the system.
This paper presents natural frequencies
of the PSSDB system, focusing on three
main goals. The first goal is to estimate the
natural frequencies and damping ratios of
the system through experimental study by
considering the effect of different screw
spacing. The natural frequencies and
damping ratios will be used to verify finite
element models (FEMs) and determine
the dynamic response of the system under
human walking load respectively. The
second goal is to develop FEMs to identify
the natural frequencies of various configu-
rations of the PSSDB systems. The third
goal is to determine the effect of various
selected parameters, such as the PSS and
DB thicknesses, and also different bound-
ary conditions, on the FNF of the system
through verified FEMs. The FNFs of panels
with practical dimensions are investigated
for different boundary conditions; then the
panels are categorised as LFF or HFF sys-
tems, which will determine how comfort-
able the panels would be for users.
EXPERIMENTAL DETAILS
In the PSSDB system, the value of partial
interaction between the PSS and DB is
influenced by the screw spacing. The study
of the effect of partial interaction between
the PSS and the DB on the FNF of the PSSDB
system is carried out by experimental tests
to meet the first goal of this paper. For
this purpose, three different samples were
prepared to measure the natural frequencies
and damping ratios of the studied systems
with 100 mm, 200 mm, and 300 mm screw
spacing. The characteristics of the samples
are presented in Table 1.
The length and width of all samples were
selected as 2 400 mm and 795 mm respec-
tively. Figure 2 shows the PSSDB system with
screw spacing of 200 mm during the test.
Natural frequencies of the samples were
measured by estimating their FRFs, as shown
in Figures 3 and 4. Eleven points were select-
ed for the determination of the FNFs of the
PSSDB100 and PSSDB200 samples (Figure
3). In these samples the accelerometer was
fixed very close to Point 10 (Figure 3). In
addition, for sample PSSDB300, seven points
were considered, as illustrated in Figure 4,
and the accelerometer was fixed near Point 6
(Figure 4).
The excitation and response signals
of the studied systems were recorded and
measured. Bruel & Kjaer portable, and
multi-channel PULSE analyser type 3560D
ENDEVCO accelerometers type 751-100,
and impact hammer type 2302-10 were used
as the measuring devices (Figure 5), as well
as the Bruel & Kjaer Pulse LabShop as mea-
surement software. Damping ratios of the
systems were also outcomes of these tests.
STRUCTURAL MODEL
The structural model of the samples is
depicted in Figure 6.
According to Murray et al (1997), the
dynamic modulus of elasticity for steel can
be chosen similar to its static value (BS
5950 Part 4:1994), i.e. 210 GPa. Stalnaker
& Harris (1999) stated that plywood is
nearly isotropic because of its manufacturing
process. Also, Ahmed (1999) declared that,
although dry boards may be found to be
isotropic or orthotropic by nature, they can
easily be modelled as isotropic plates with
very good results. Based on the study carried
out by Narayanamurti et al in Hu (2008),
Matsumoto & Tsutsumi (1968), and Bos &
Bos Casagrande (2003), the dynamic Young’s
modulus of plywood was found to be higher
than its static value. In this study, the static
modulus of elasticity of plywood, available
in the local market, is adopted as 7 164 MPa
(Yean 2006), considering an isotropic sheet-
ing, while the dynamic value is chosen 10%
greater than the static value according to Bos
& Bos Casagrande (2003).
The density of Peva45 and plywood has
been chosen as 7 850 kg/m3 and 600 kg/m3
respectively.
In the PSSDB system, the stiffness of the
screws which is obtained by experimental
push-out tests (Ahmed 1999; Akhand 2001;
Nordin et al 2009) is directly used as input
data for the FEMs (Nordin et al 2009). A
study was performed to identify the connec-
tion stiffness between Peva45-Cemboard,
Cemboard-Timber, and Peva45-Plywood by
push-out tests. Also, the shear connection
stiffness between Peva45 and plywood for
Figure 6 Structural model of the PSSDB100, PSSDB200 and PSSDB300: (a) Longitudinal section (b) Transverse section
(a) (b)
PlywoodPeva45
Screw
Pin support Roller support
Y = 0 Y = 2 400 mm
75 mm75 mm X = 0Peva45
X = 795 mm
Plywood
DS-FH432 screw
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201314
the same configuration was found to be
610 N/mm (Nordin et al 2009), which is the
same as in this paper.
COMPUTATIONAL MODEL
To cover the second goal of this paper, three
FEMs were developed to obtain natural
frequencies of the PSSDB100, PSSDB200,
and PSSDB300 systems. The FEMs are
implemented using ANSYS finite element
computer program (ANSYS 2007).
Two methods were used to evaluate the
natural frequencies of the systems. The “Block
Lanczos” and “QR damped” methods were
utilised to extract undamped and damped
natural frequencies of panels respectively.
In the FEMs, the PSS and DB were assigned
by element of SHELL281 (Figure 7) as it is
suitable for analysing thin to moderately thick
shell structures (ANSYS 2007). It comprises
an 8-noded element having six degrees of
freedom at each node: translation in and rota-
tion about the x-, y- and z-axes. In addition,
the screws were represented by an element
of COMBIN14 (Figure 8) as the connection
between Peva45 and plywood. COMBIN14
possesses longitudinal or torsional capability
in 1-D, 2-D or 3-D applications (ANSYS 2007).
The longitudinal spring-damper option is a
uniaxial tension-compression element having
up to three degrees of freedom at each node:
translation in the nodal x-, y- and z-directions.
No bending or torsion is considered. The
spring-damper element has no mass. Mass
can be added by using the appropriate mass
element. The spring or the damping capability
may be removed from the element (ANSYS
2007). In this paper, the capability of damping
was removed (Cv = 0) from the element.
Figure 9 illustrates the procedure of
modelling Peva45 and plywood in a simula-
tion for one bay of the studied system. The
connection between elements of Peva45 and
plywood in the simulation is performed by
using spring element (COMBIN14) in three
directions (X, Y, and Z). In this case, and
according to Figure 9, the nodes D2 and D10
were respectively connected to the nodes P2
and P10 in which stiffness of springs were
adopted as 610 N/mm (Nordin et al 2009) in
X and Y directions, and as 105 N/mm in Z
(vertical) direction (see Figure 9).
OBSERVATION OF RESULTS
AND COMPARISON
Results are presented in two parts – experi-
mental and finite element simulation. Then
the experimental and finite element results
are compared to present the accuracy of
the FEMs.
Experimental results
The FRFs of studied systems are shown in
Figure 10 and according to the figure the
first six natural frequencies (NFs) of the
systems are presented in Table 2. Damping
ratios (DRs) corresponding to the NFs of the
systems are also summarised in Table 2.
The status of the natural frequency in
Table 2 was missing for the mode number 5
while the natural frequency of this mode was
available in its FEM (Table 3). The reason for
this absence has been revealed by evaluation
of its mode shape. This mode was in the
transverse direction of accelerations that
were measured. Therefore, the mode did not
appear in the experiments.
According to earlier studies, the
PSSDB100 is stiffer than PSSDB200, and
Figure 7 SHELL281 (ANSYS 2008)
MN
K
OP
I
J
L
2
6
3
1
4
5
8
4
5
1
2
6
7
3
Z0
X0
Y0
Figure 8 COMBIN14 (ANSYS 2008)
J
K
I
Cv
X
Y
Z
Figure 9 (a) One bay PSSDB structural system (b) Positioning of nodes in elements of one bay PSSDB system
P1 P2 P3
P4 P5
P6
P7 P8
P9 P10 P11
D1 D2 D3 D6 D9 D10 D11
(a) (b)
Plywood
Peva45
Figure 10 Experimental estimation of FRF between excitation at point A and response at point B for (a) PSSDB100 (b) PSSDB200 (c) PSSDB300
0.8
FR
F [
(m/s
2)/
N]
0.6
0.4
0.2
0
(a) (b) (c)
1008060400 20
Frequency (Hz)
0.8
FR
F [
(m/s
2)/
N]
0.6
0.4
0.2
01008060400 20
Frequency (Hz)
0.8
FR
F [
(m/s
2)/
N]
0.6
0.4
0.2
01008060400 20
Frequency (Hz)
Note: The points A (Point 6 in Figure 3 and Point 4 in Figure 4) and B were selected in y = 1 200 and y = 2 200 mm (Figure 6(a)) respectively, along the length and middle
point of width for both points
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 15
the latter is stiffer than PSSDB300 due to
the number of screws. On the other hand,
the mass of the PSSDB100, PSSDB200 and
PSSDB300 is almost the same. As a result
it can be predicted that the FNF of the
PSSDB100 should be greater than that of
PSSDB200, and the latter greater than that of
PSSDB300. This issue was verified by results
of the experimental test. Table 2 shows that
the partial interaction between two main
elements of the PSSDB system had an effect
on the natural frequencies of the systems,
as the FNF of the system increased by 3.55%
and 11.24% respectively for changing the
screw spacing from 300 mm to 200 mm, and
300 mm to 100 mm. However, reduction
of the screw spacing decreases the damp-
ing of the system. The FNFs of the studied
panels were measured by the test well above
10 Hz. Therefore all panels fell in the HFF
category (Middleton & Brownjohn 2010) and
were also comfortable for users (Wright et
al 1989).
Finite element results
The experimentally observed FRFs of the
systems presented their damped natural
frequencies. Therefore, in the simulation,
damped natural frequencies of the systems
were determined by the QR damped method
via the ANSYS finite element package. In
the QR damped method, damping of the
system is introduced by the Rayleigh damp-
ing approach (see more detail in Clough &
Penzien 1993). According to Chowhury &
Dasgupta (2003), only the first few modes
of a structure with large degrees of freedom
(around three at minimum and about 25
at maximum) contribute to the dynamic
response of a structure. In this study, the
first six modes are assumed to be significant
in the dynamic behaviour of the system.
Then the Rayleigh damping coefficients were
determined (Chowhury & Dasgupta 2003)
and used in the simulation.
Three finite element models were devel-
oped to identify the natural frequencies of
the PSSDB100, PSSDB200 and PSSDB300
systems. The first six undamped and damped
natural frequencies of the studied systems
are summarised in Table 3.
According to simulation results, the
FNF of the PSSDB100 was greater than the
PSSDB200, and the latter was greater than
PSSDB300. This point is also confirmed by
the experimental results. Table 3 shows small
differences between undamped and damped
natural frequencies of the systems. The
results also show that the undamped natural
frequencies of all systems were greater
than their corresponding damped natural
frequencies. Caughey & O’Kelly (1961) stated
that, in a system with classical normal
modes, the damped natural frequencies
are always less than or equal to their cor-
responding undamped natural frequencies.
Piersol et al (2010) mentioned that generally
classical normal modes exist in a structure
without damping or with particular types
of damping. According to the results of this
study, the measured damping can be consid-
ered as particular damping for each system;
therefore they can be used in the dynamic
analysis of the bare PSSDB systems with dif-
ferent screw spacing.
Comparison of experimental
and finite element results
As stated, the FRFs of the systems present
their damped natural frequencies. However,
undamped and damped natural frequencies
of the studied systems were calculated very
close to one another by the numerical meth-
od. Nevertheless, damped natural frequen-
cies of the systems which were determined
by FEM are compared with their damped
natural frequencies that have been evaluated
by the tests in order to reveal more accurate
errors. The errors of numerical results are
calculated by Eq (1) and presented in Table 4.
Error (%) = T4Ci
= [test value – finite element value]
test value × 100
= [T2Ci – T3Ci]
T2Ci × 100, i = a, b, c (1)
where:
T2Ci: column i = a, b, c of Table 2
T3Ci: column i = a, b, c of Table 3
T4Ci: column i = a, b, c of Table 4
Table 2 First six experimental natural frequencies and damping ratios of studied systems
Mode No
PSSDB100 PSSDB200 PSSDB300
NF (Hz)(a) DR (%) NF (Hz)(b) DR (%) NF (Hz)(c) DR (%)
1 18.8 1.230 17.50 1.400 16.9 3.140
2 23.1 1.500 21.3 1.890 21.9 0.984
3 46.9 0.732 46.3 0.840 41.9 0.959
4 55.0 0.936 55.6 0.994 52.5 0.914
5 64.4 0.511 Missing – 62.5 0.767
6 81.3 0.43 67.5 0.884 68.8 1.06
Note: For further discussions, the labels (a), (b) & (c) have been adopted respectively as T2Ca, T2Cb & T2Cc in the following. T2Ca means Table 2 Column a.
Table 3 First six numerical undamped and damped natural frequencies of the studied systems
Mode No
PSSDB100 PSSDB200 PSSDB300
Undamped Damped(a) Undamped Damped(b) Undamped Damped(c)
1 18.072 (Hz) 18.070 (Hz) 17.563 17.561 17.410 17.402
2 23.207 23.206 22.026 22.024 22.303 22.295
3 46.790 46.788 44.851 44.848 44.481 44.465
4 60.053 60.049 57.233 57.228 57.303 57.276
5 62.887 62.882 57.278 57.273 58.639 58.611
6 76.707 76.700 69.880 69.873 74.025 73.978
Note: For further discussions, the labels (a), (b) & (c) have been adopted respectively as T3Ca, T3Cb & T3Cc in the following.
Table 4 Error of numerical method in the studied systems (%)
Mode No PSSDB100(a) PSSDB200(b) PSSDB300(c)
1 3.88 0.35 2.97
2 0.46 3.40 1.80
3 0.24 3.13 6.12
4 9.18 2.93 9.10
5 2.36 – 6.22
6 5.66 3.52 7.53
Note: For further discussions, the labels (a), (b) & (c) have been adopted respectively as T4Ca, T4Cb & T4Cc in the following.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201316
The mentioned errors show that the FEMs
can predict the natural frequencies of the
PSSDB system with accuracy. Therefore,
performed convergence studies on the finite
element models and selected elements of
the models which were combinations of the
SHELL281 and COMBIN14 elements were
suitable for the purpose of the study. The
difference between the experimental and
FEM results may be due to reasons such as:
■ Finite element method is a numerical
approximate method.
■ Imperfections of the PSS, DB and screws
in the test specimens were not captured
in the FEMs.
PARAMETRIC STUDY
A series of parametric studies based on
the FEMs for the PSSDB200 system were
performed to show the effect of different
conditions on the FNF of the system. The
PSSDB system with a length of 2 400 mm
and a width of 795 mm was chosen as the
control sample, adopting 0.8 mm thick
Peva45 as PSS, 18 mm thick plywood as DB,
DS-FH 432 self-drilling and self-tapping
screws at 200 mm screw spacing as the
connectors, and pin support at Y = 0 and
roller support at Y = 2 400 mm both at the
bottom flange of the PSS (Figure 6(a)). A
series of studies were performed to uncover
the FNF of the PSSDB panels with practical
dimensions. Their categorisation and level of
comfort were also revealed. All supports in
these studies were considered at the bottom
flange of the PSS. Only in one case supports
were assumed at the bottom, top and web of
the PSS (see Figure 12).
Effect of thicknesses of Peva45
and plywood
The thickness of the considered Peva45 is
0.8 mm and 1.0 mm, whilst the thickness
of the plywood is 9.252, 12.7, 18, 23 and
25 mm. Both products are available on the
local market. The effect of the thicknesses
of Peva45 and plywood on the FNF of the
system is presented in Table 5. The percent-
age difference between the FNF of the con-
trol sample and the FNF of the panel with
other thicknesses for Peva45 and plywood
are also presented in Table 5.
According to the results, increasing
the thicknesses of the Peva45 and the
plywood enhanced and decreased the FNF
of the system respectively. By enhancing
the thickness of the Peva45 from 0.8 mm
to 1.0 mm, and the thickness of the
plywood from 9.252 mm to 25 mm the FNF
increased and decreased by an average value
of 4.91% and 18.56% respectively. It can
therefore be seen that the obtained results
are a manifestation of the effect of the mass
and stiffness of Peva45 and plywood on the
FNF of the system. The highest value of the
FNF occurred for the maximum thickness
of Peva45 and minimum thickness of
plywood (20.677 Hz), whilst the lowest
value of the FNF occurred for the minimum
thickness of Peva45 and maximum
thickness of plywood (16.566 Hz).
Therefore, by changing the thickness of
main elements the FNF can be increased by
a maximum value of 24.82%. The minimum
value of the FNF of the studied system
showed well above 10 Hz. The studied
system was therefore in the HFF category
and also comfortable for occupants.
Effect of boundary conditions
The effect of boundary conditions on the
FNF of the system was taken into account
in three situations: effect of sliding and
rotation at the end supports perpendicular
to the strong direction of the PSS (sliding
parallel with Y direction of the plan, Figure
11); effect of locating support under the top
flange and web of the PSS at two ends of
the length (Figure 12); and effect of adding
support parallel with the strong direction of
the PSS (parallel with Y direction of the plan,
Figure 13).
Table 6 FNF of the PSSDB system under different types of end supports perpendicular to the
strong direction of the PSS
Type of support P-R P-P P-F R-F F-F
FNF (Hz) 17.569 23.126 23.214 17.802 23.304
PI (%) 0 31.63 32.13 1.33 32.64
Figure 11 Various end support conditions perpendicular to the strong direction of the PSS
YX Y = 0
R P F F F
P P P R F
Y = 2 400 mm
Table 5 Effect of thickness of Peva45 and plywood on the FNF of PSSDB system
Peva45
Plywood
t = 9.252 mm t = 12.7 mm t = 18 mm t = 23 mm t = 25 mm
FNF (Hz) PD (%) FNF PD FNF PD FNF PD FNF PD
t = 0.8 mm 19.935 13.42 18.826 7.12 17.569 0 16.787 –4.41 16.566 –5.64
t = 1.0 mm 20.677 17.62 19.665 11.88 18.480 5.16 17.710 0.82 17.486 –0.44
PD = Percentage of difference compared with control sample
Figure 12 Illustration of supports under top and bottom flanges and web of the PSS
Top flange Web Bottom flange
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 17
Effect of sliding and rotation
of supports
The effect of sliding and rotation at the
end supports perpendicular to the strong
direction of the PSS (X direction, Figure
11) on the FNF of the system is investigated
for various support conditions, as shown in
Figure 11. These involve (i) pin (P) and roller
(R) (control sample), (ii) P-P, (iii) P-F (fixed),
(iv) R-F and (v) F-F end supports.
The FNF results for these conditions are
presented in Table 6. The percentages of the
increase (PI) in the FNF of the various mod-
els over the control sample are also shown in
Table 6.
The results show that if sliding is con-
strained parallel with the strong direction
of the PSS (P-R support converted into
P-P support), then the FNF is increased
significantly. Chao & Chern (2000) and Jalali
(2012) affirmed this observation. On the
other hand, changing a pin support to a fixed
support (P-F instead of P-P, and F-F instead
of P-P) did not show a considerable effect on
the FNF value. Therefore, the control of rota-
tion at the bottom flange of the PSS at the
end support did not significantly affect the
FNF of the system.
Effect of adding support under
top flange and web of PSS
The supports for the control sample were
only considered under the bottom flange
(Case 1) of the PSS. Table 7 shows the FNF
and PI in the FNF for various models over
the control sample of the system if additional
supports are provided at both the top and
bottom flanges of the PSS (Case 2), and at
the top and bottom flanges and the web
(Figure 12) of the PSS (Case 3).
When comparing the results of Cases 1
and 2, it is clear that the FNF of the system
is enhanced significantly if supports are
added at the top and bottom flanges of the
PSS. Also, by comparing the results of Cases
2 and 3, it is demonstrated that additional
supports at the web do not have any signifi-
cant effects on the FNF of the system. This
may be because adding support on the top
flange already prevents rotation of the PSS,
so adding more support on the web does not
make a big difference. By keeping the above-
mentioned three cases in mind, designers
can decide on the shape of supports (beams)
which can be used under the PSS of the
PSSDB floor system to reduce its natural
frequencies.
Effect of adding support parallel
with longitudinal side edges
The supports of the longitudinal side edges
(support in X = 0 and 795 mm parallel with
Y direction of the plan as in Figures 6(b) and
13) for the control sample were considered
free (unconstrained). Various additional sup-
port conditions studied at the longitudinal
side edges are shown in Figure 13. Table 8
shows the FNF and PI in the FNF for various
models in the control sample.
As shown in Table 8, when only one of
the longitudinal side edges was supported
(leaving one side edge free), as in the R-Fr
and P-Fr cases, the FNF increased slightly. It
can be seen that restraining sliding perpen-
dicular to the strong direction of the PSS (X
direction of the plan) would not change the
FNF of the system much (2.8% = 10.59%–
7.79%) if only one of the longitudinal side
edges were supported. However, the increase
in FNF was much more significant, based on
restraining both longitudinal side edges as
in the R-R, P-R and P-P cases. The control of
sliding perpendicular to the strong direction
of the PSS shows a pronounced effect on
increasing the FNF of the system (20.57% =
103.87%–83.30%), where both longitudinal
side edges of the panel were supported (P-P
instead of R-R).
FNF of panels with practical
dimensions
Peva45 is available on the local market in
widths of 795 mm and maximum lengths of
15 m. Also, the maximum length and width
of plywood is 2 400 mm and 1 200 mm
respectively. Therefore, to prepare bigger
practical panels, some pieces of Peva45 and
plywood should be used together. Fifteen
panels in four different lengths of 1 200 mm,
2 400 mm, 3 600 mm and 4 800 mm involv-
ing one, two, three and four repeating sec-
tions of the system were developed, which
were combinations of elements similar to the
control sample, verified by experiments, as
shown in Figure 6(b) and Figures 14–16. In
all fifteen panels, the length and width of all
pieces of plywood were chosen as 2 400 mm
and 795 mm respectively. Also, the length of
Peva45 was used as the length of the panels.
The connection between two adjacent
side-by-side panels (detail A) was represented
Table 7 Effect of adding supports under top flange and web of the PSS on the FNF
Support condition
P-R support in bottom flange only (Case 1)
P-R support in bottom and top flanges (Case 2)
P-R support in bottom and top flanges and web of PSS (Case 3)
FNF (Hz) 17.569 (Hz) 26.256 26.332
PI (%) 0 49.44 49.88
Table 8 Effect of adding supports parallel to the strong direction of the PSS on the FNF
Support condition Fr-Fr R-Fr P-Fr R-R P-R P-P
FNF (Hz) 17.569 (Hz) 18.938 19.430 32.204 33.403 35.818
PI (%) 0 7.79 10.59 83.30 90.12 103.87
Figure 13 Different support conditions parallel to the strong direction of the PSS
Y
X Y = 0
P P
Y = 2 400 mm
P P P P
R R R R R R
Fr Fr R Fr P Fr R R P R P P
Figure 14 The PSSDB panel with two repeating sections
771.5 mm
1 545 mm
Detail A
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201318
by a typical lap joint idea as shown in Figure
17. Wright & Evans (1987) presented the
connectivity characteristics of such a joint.
As can be seen in Figure 17, nodes i(2) and
j(2) are connected to node i(3) and node j(3)
respectively, assuming complete freedom in
the longitudinal and rotational directions,
whilst assumed to have complete connection
in the vertical and lateral directions (Wright
& Evans 1987). It should be noted that con-
nections between i(1) and j(1) respectively
to i(2) and j(2) (Peva45 to plywood) are
represented by results of the study by Nordin
et al (2009).
The joint does not exist perpendicularly
to the strong direction. Figure 18 shows the
connection between plywood and Peva45
according to their dimensions.
Table 9 shows the characteristics and the
FNF of the developed panels with practi-
cal dimensions. The categorisation (LFF
or HFF) and level of comfort of the panels
are also undertaken. All panels had pin-
roller supports perpendicular to the strong
direction of the PSS and free-free supports
parallel with the strong direction of the PSS
(Model 0).
The width of the panels with only end
supports perpendicular to the strong direc-
tion of the PSS did not significantly affect
the FNF of the system, as the panels with
the same length and widths of 795 mm,
1 545 mm, 2 295 mm and 3 045 mm had
close values in terms of the FNF. The reason
for this was the enhancement of the stiffness
and mass by increasing the width. However,
Figure 18 Connection between plywood and Peva45 along the panel
Figure 15 The PSSDB panel with three repeating sections
2 295 mm
Detail A
771.5 mm 748 mm
Figure 16 The PSSDB panel with four repeating sections
771.5 mm
Detail A
748 mm
3 045 mm
Figure 17 Detail A: (a) Constructional model (b) Analytical model
(a) (b)
Plywood Plywood Plywood Plywood
Screws
Peva45 Peva45
i(1) j(1)
i(2) j(2)
i(3) j(3)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 19
Table 10 FNF and status of the LFF panels under different models of boundary conditions
Name of Model
Model I Model II Model III
FNF (Hz)Status
FNF (Hz)Status
FNF (Hz)Status
(a) (b) (a) (b) (a) (b)
1PP3LL 24.723 HFF Ok 27.876 HFF Ok 29.425 HFF Ok
1PP4LL 22.974 HFF Ok 25.763 HFF Ok 26.538 HFF Ok
2PP3LL 10.242 HFF Ok 10.634 HFF Ok 12.755 HFF Ok
2PP4LL 6.8417 LFF Failed 7.1381 LFF Ok 8.1045 LFF Ok
3PP3LL 8.9882 LFF Ok 9.1947 LFF Ok 11.584 HFF Ok
3PP4LL 5.5847 LFF Failed 5.7750 LFF Failed 6.9614 LFF Failed
4PP3LL 8.5472 LFF Ok 8.6555 LFF Ok 11.177 HFF Ok
4PP4LL 5.1182 LFF Failed 5.2264 LFF Failed 6.5480 LFF Failed
(a) Categorisation of the system as LFF or HFF (Middleton & Brownjohn 2010)(b) Level of comfort of the panels for occupants (Wright 1989)
the FNF of the 3 045 mm wide panel was
a bit greater than the FRF of the 2 295 mm
wide panel, etc. This may be due to the
increased stiffness of the panels when using
lap joints in the panels, with two pieces of
Peva45 (one-lap joint), three pieces of Peva45
(two-lap joints), and four pieces of Peva45
(three-lap joints), compared to panels with
one piece of Peva45 without a lap joint
(795 mm wide).
It is obvious that the length of the system
has a direct effect on the FNF of the system.
The results showed that the FNF of a PSSDB
system with a length of more than 3 600 mm
and widths of 795 mm, 1 545 mm, 2 295 mm
and 3 045 mm fell in the LFF category. Also,
panels that were 3 600 mm and 4 800 mm
long, with any widths, were respectively
shown to be comfortable and uncomfortable
for users.
An increase in the FNF of a floor system
(less resonance) is required for user comfort.
If panels are supported on all sides, the FNF
of the system will be higher. This can be
used to increase the FNF (stiffness) of the
panels via boundary conditions. Depending
on the control of sliding at supports, roller or
pin supports can be used on all sides. In this
case, all panels with lengths of 3 600 mm
and 4 800 mm were selected in order to
increase their FNFs through three boundary
conditions as shown in Figure 19. Table 10
summarises the increased FNFs of the panels
corresponding to these boundary conditions
(models I, II, and III). It also illustrates the
level of comfort of the studied panels.
The PI in the FNF of the selected panels
are listed in Table 11 by comparing the FNFs
of the panels under boundary conditions
of models I, II, and III with the FNFs of
the panels under boundary conditions of
model 0.
Table 11 shows that control of sliding
parallel with the strong direction of the PSS
in the multi-panel systems had a significant
Table 9 Characteristics, the FNF, and evaluation of the developed PSSDB models (Model 0)
Name of Model Length (mm) Width (mm) FNF (Hz) (b) (c)
1PP1LL 1 200 795 49.581 HFF Ok
1PP2LL(a) 2 400 795 17.569 HFF Ok
1PP3LL 3 600 795 7.8663 LFF Ok
1PP4LL 4 800 795 4.4606 LFF Failed
2PP1LL 1 200 1 545 52.678 HFF Ok
2PP2LL 2 400 1 545 17.755 HFF Ok
2PP3LL 3 600 1 545 7.9337 LFF Ok
2PP4LL 4 800 1 545 4.4958 LFF Failed
3PP1LL 1 200 2 295 52.733 HFF Ok
3PP2LL 2 400 2 295 17.824 HFF Ok
3PP3LL 3 600 2 295 7.9578 LFF Ok
3PP4LL 4 800 2 295 4.5081 LFF Failed
4PP1LL 1 200 3 045 52.753 HFF Ok
4PP2LL 2 400 3 045 17.859 HFF Ok
4PP3LL 3 600 3 045 7.9700 LFF Ok
4PP4LL 4 800 3 045 4.5143 LFF Failed
(a) Control sample(b) Categorisation of the system as LFF or HFF (Middleton &Brownjohn 2010)(c) Level of comfort of the panels for occupants (Wright 1989)
Figure 19 Model of boundary conditions for increasing the FNF of LFF panels
P
R
R R
X
Y
R
PX
Y
P P
P
P P
X
Y
Model I Model II Model III
P
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201320
effect on the FNF of the system. However,
control of sliding perpendicular to the strong
direction of the PSS considerably affected the
FNF of the 795 mm wide panel and did not
have a significant effect on the FNF of the
panels wider than 795 mm. Even by using the
model III boundary condition (pin supports
in all sides), the panels that were 4 800 mm
long, with widths of 1 545 mm, 2 295 mm
and 3 045 mm were still in the category of
LFF. Also, panels with a length of 4 800 mm
and widths of 2 295 mm and 3 045 mm were
not comfortable for users.
CONCLUSIONS
This paper reveals experimentally and numer-
ically the natural frequencies of the PSSDB
system, considering the effect of the level of
interaction between the PSS and the DB. It
is shown that the PSSDB system with lower
screw spacing has higher FNF. The damping
ratio of the PSSDB system is inversely related
to the stiffness of the system, as the damping
ratio of the PSSDB with lower screw spacing
is greater than the system with higher screw
spacing. A series of parametric studies reveal
the effects of different parameters on the FNF
of the system. It is proved that the FNF of
the PSSDB system is significantly influenced
by (i) screw spacing or level of interaction
between the PSS and DB, (ii) thicknesses of
the PSS and DB, (iii) control of sliding along
the strong direction of the PSS, (iv) using sup-
port under both the top and bottom flanges
of the PSS, and (v) the number of side edges
being supported. On the other hand, the FNFs
are not much affected by (i) control of sliding
along the weak direction of the PSS at the side
edge supports, (ii) rotations at all end and side
edge supports, and (iii) the support conditions
under the web of the PSS. Identification of the
FNF of the panels with practical dimensions
with end supports only shows that the FNF of
the panels with the same length and different
widths are very close to one another. However,
a small difference may occur by increasing the
thickness of Peva45 in the location of the lap
joint. It is proved that a significant increase
in the FNF of the PSSDB floor system with
practical dimensions is possible via boundary
conditions.
ACKNOWLEDGEMENTS
The authors would like to acknowledge
the Mechanical Engineering Department
of Universiti Kebangsaan Malaysia for
granting permission to conduct the experi-
mental tests. The authors also express their
gratitude to Mr Alireza Bahrami and Dr
Mohammad Hosseini Fouladi for their con-
tributions to some parts of this study.
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Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201322
TECHNICAL PAPER
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 22–35, Paper 797
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management and development.
Contact details:
Head of Catchment Planning
City of Cape Town: Catchment Stormwater and River Management Branch
PO Box 1694
Cape Town
8000
South Africa
T: +27 21 400 1385
F: +27 21 400 4554
PETER SILBERNAGL (Pr Eng, CEng, Pr CPM), a past
president of Consulting Engineers South Africa)
graduated from UCT with a BSc Eng, GDEng and
an MBA. His fi elds of expertise include project
management, management of multi-
disciplinary teams and subconsultants in
general project management, but particularly in
the areas of water and waste management. He
has developed expertise in human resource and organisational development.
He is currently a director at PD Naidoo & Associates Consulting Engineers.
Contact details:
Director
PD Naidoo & Associates Consulting Engineers (Pty) Ltd
PO Box 7786
Roggebaai
8012
South Africa
T: +27 21 440 5060
F: +27 21 418 6440
Keywords: City of Cape Town, stormwater, pollution, methodology, resources
In the end, all water is stormwater.
– A Parker, 2010
Whatever its origin or use, all water,
whether from roofs, roads, wastewater
treatment works, boreholes or bottles,
becomes stormwater.
INTRODUCTION
The City of Cape Town (the City) has an
extensive network of rivers and wetlands
which fulfil diverse ecological, aesthetic,
recreational and infrastructure network
functions. They form an important part of
the natural landscape, provide beauty and a
sense of place and belonging to the people,
encourage tourism, and provide recreational
opportunities, health benefits, natural hazard
regulation and other ecosystem services.
Over the past few decades, however,
many of these watercourses have been
adversely impacted by pollution. In terms
of the Department of Water Affairs (DWA)
water quality guidelines for recreation and
aquatic ecosystems, 69% of vleis and 42% of
rivers in Cape Town have poor to bad water
quality (City of Cape Town 2008). This
poses a significant risk to human health and
aquatic biodiversity.
The impacts of poor water quality may be
far-reaching, as the forgoing of recreational
opportunities, for instance, may result in
socially less desirable behaviour, negatively
affecting the wellbeing of society and placing
strain on social services in the City. Also,
poor quality water used for urban farming
activities may severely compromise food
production, which is a source of income for
many. Ultimately poor water quality poses a
significant threat to human health, aquatic
biodiversity and the added value that good
quality water brings to the economy.
The challenge, therefore, is to protect the
inland waters from the impact of pollution,
and to improve inland water quality to an
acceptable level. Current human and finan-
cial resources to manage pollution in inland
waters are inadequate.
The Catchment, Stormwater and
River Management (CSRM) Branch of the
Transport, Roads, Stormwater and Major
Projects Directorate of the City decided to
launch a project to determine the additional
resources required to manage pollution in
stormwater and river systems to improve
inland water quality compliance to an
“acceptable level”.
This paper is a showcase of the method-
ology used in this multifaceted and inter-
disciplinary project where the causes and
solutions to water pollution are extremely
complex, and large amounts of data, litera-
ture, opinions and information were at hand.
The methods used to achieve the following
project outputs are discussed:
■ Identification of criteria for “acceptable
water quality”
Improving water quality in stormwater & river systems:an approach for determining resources
N Nel, A Parker, P Silbernagl
This paper is a showcase of the approach used to determine the additional resources required to improve inland water quality in the City of Cape Town to an acceptable level. As the improvement of water quality falls in the more complex realm of modern municipal engineering – where many of the issues are so-called “soft” in nature and the problems and solutions are not straightforward – the methods discussed in this paper were instrumental in creating an holistic overview of the state of the rivers and wetlands in the City of Cape Town, highlighting the complexity of the problem and assisting to plot a way forward to provide proactive, sustainable measures for the management of water pollution. The paper discusses: the evaluation of water quality data, catchment analysis and determination of pollution sources, a risk assessment, and a prioritisation exercise, and concludes with the novel points and obstacles encountered. In all, the methods discussed provide a significant contribution towards the quest to improve water quality in the City of Cape Town.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 23
■ Identification of catchment pollution
sources
■ Risk assessment of catchments to deter-
mine their vulnerability
■ Prioritisation of catchments, rivers and
wetlands for intervention
■ Provision of prioritised cost estimates
per district/region/subcouncil for the
management of the various pollution
sources, and identification of implemen-
tation mechanisms/partnerships.
ACCEPTABLE WATER QUALITY
One of the main challenges in the project
was to determine what is meant by “accept-
able water quality” in order to verify practi-
cal and achievable objectives in terms of
water quality and to package vast amounts of
water quality data in a meaningful manner
to achieve the project objectives. Water qual-
ity standards and criteria ultimately drive
the interventions necessary to bring water
quality to a desired level.
City of Cape Town sampling,
monitoring and evaluation
of water quality
An inland surface water monitoring network
with monitoring sites within each of the
major catchment areas is maintained by the
City. There are approximately 100 active
sampling points which are located at strate-
gic locations as indicated in Figure 1. Both
rivers and wetlands are monitored and this
occurs on a monthly basis, with both histori-
cal and current data being available.
Eighteen microbiological and chemical
constituents are measured in inland water
samples. There are therefore, for a 10 year
period, 216 000 data points (18 constituents
for around 100 sampling points taken on a
monthly basis over 10 years). The key is to
present this data in a meaningful way.
Reporting on water quality
For broad reporting purposes, the City
currently assesses these monthly water
quality results for inland waters from two
perspectives: “ecosystem health” and “public
health”. The relevant Department of Water
Affairs and Forestry (DWAF)1 Water Quality
Guideline series provides the basis for this
evaluation.
Aquatic ecosystem health
For ease of reporting, total phosphorus is
used by the City as an “indicator” of general
chemical water quality in inland waters and
provides a proxy measurement of the state of
an aquatic system.
The median2 “total phosphorus” con-
centration is calculated for river and vlei
monitoring points in various systems, and
compared to concentration ranges which
indicate the trophic tendencies and condi-
tions described in Table 1:
Public Health
“Faecal coliforms” is the constituent used by
the City as an indication of the suitability
Table 1 Trophic tendencies for phosphorus concentrations in inland water
Trophic tendency
Phosphorus range (mg/l P)
“Condition”
Oligotrophic <0.005 Excellent: Low levels of nutrients and no water quality problems
Mesotrophic 0.005 – 0.025Good: Intermediate levels of nutrients with emerging water quality problems
Eutrophic
0.025 – 0.125Fair to poor: High levels of nutrients and increasing frequency of water quality problems
0.125 – 0.25
Hypertrophic >0.25Bad: Excessive nutrient levels and water quality problems are almost continuous
Figure 1: City of Cape Town: Inland monitoring network
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201324
of inland water for intermediate contact
recreational use (activities involving an inter-
mediate degree of water contact, e.g. sailing,
canoeing and fishing).
The DWAF Water Quality Guideline for
Recreation (DWAF 1996a) sets safe standards
for the limits of pollutants that may be used
for intermediate contact recreational use and
states that samples should not exceed 1 000
faecal coliform organisms per 100 ml. The
percentage of samples with ≤1 000 faecal
coliform counts for the twelve-month period
is thus used as an indication of the level of
compliance.
Table 2 SASS5 categories for the river health programme
Category Description
Natural No or negligible modification (relatively little human impact)
GoodBiodiversity and integrity largely intact (some human-related disturbance but ecosystems essentially in good state)
FairSensitive species may be lost, with tolerant or opportunistic species dominating (multiple disturbances associated with socio-economic development)
PoorMostly only tolerant species present; alien species invasion; disrupted population dynamics; species are often diseased (high human densities of extensive resource exploitation)
UnacceptableRiver has undergone critical modification; almost complete loss of natural habitat and indigenous species with severe alien invasion
Table 3 Public health criteria: ranges for full contact and intermediate contact recreation
Unit
DWAF Recreational Use Guidelines (Vol 2)
Full Intermediate
Ta
rget
Acc
epta
ble
Ris
k
Un
acce
pta
ble
Ta
rget
Acc
epta
ble
Ris
k
Un
acce
pta
ble
Faecal Coliform count / 100 ml
0–130
131–600
601–2 000
>2000
0–1 000
1 001–2 000
2 001–4 000
>4 000
Management 1
Management 2
Management 3
Management 1
Management 2
Management 3
2 001–10 000
10 001–100 000
>100 0004 000–
10 00010 001–
100 000>100 000
E.coli count / 100 ml
0–130
131–200
201–400
>400
No guideline
No guideline
No guideline
No guideline
No guideline
No guideline
Management 1
Management 2
Management 3
401–2 400 2 401–20 000 >20 000
Table 4 Ecosystem health criteria: categories
Variable Units Natural Good Fair Poor Unacceptable Comments
Temperature*# °CDepends on background (Upper boundary = 90th percentile; Lower
boundary = 10th percentile); Good ±2°C; Fair ±4°C; Poor ±>4°CNeed to determine typical background water quality – not essential for prioritisation exercise
Total suspended solids*#
mg/l Depends on background (Not more than 10% higher than background)Need to determine typical background water quality – not essential for prioritisation exercise
Conductivity (EC)*# mS/m Depends on background (not more than 15% different from normal cycles)Need to determine typical background water quality – not essential for prioritisation exercise
pH* units 8–6.59–8 or
6.5–5.7510–9 or 5.75–5
>10; <5Need to determine typical background water quality – not essential for prioritisation exercise
Dissolved oxygen* mg/l >8 8–6 6–4 4–2 <2
Also dependent on background DO levels to some extent. No unacceptable range given but if one selects equal bands then 2 mg/l is the next logical band and is applicable to assessing the actual data
Soluble reactive phorphorus*
mg/l <0.005 0.005 – 0.025 0.025 – 0.125 0.125–0.250 >0.250 Ranges as recommended in the latest water quality benchmarks for the ecological reserve (DWAF 2005)Total inorganic
nitrogen*mg/l <0.25 0.25–1 1–4 4–10 >10
Ammonia (NH3-N)* mg/l <0.015 0.015–0.058 0.058–0.1 0.1–0.2 >0.2No unacceptable range given but if one selects equal bands then 0.2 mg/l is the next logical band and is applicable to assessing the actual data
Blue-green algae toxins (microcystins)@ μg/l <10 10–50 >50
Ranges as recommended in the World Health Organisation (WHO) guidelines
Algae (Chl-a)* μg/l <10 10–20 20–30 30–40 >40No unacceptable range given but if one selects equal bands then 40 μg/l is the next logical band and is applicable to assessing the actual data
# South African Water Quality Guidelines (DWAF 1996b)
* Ecological reserve water quality benchmarks (Jooste & Rossouw 2002)
@ World Health Organisation Recreational Guidelines (2003)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 25
River health programme
The City is a participant in the River Health
Programme (RHP) which is a national bio-
monitoring programme that uses a range of
biological indices for determining the ecologi-
cal health of rivers. The SASS5 index (South
African Scoring System Version 5) is the most
widely utilised bio-monitoring index in the
RHP and consists of an assessment of aquatic
macro-invertebrate communities present to
determine ecological river health.
The local bio-monitoring programme
of the City has been undertaken annually
(where human resources allow) at approxi-
mately 40 river locations. Ideally it should be
undertaken in spring, summer and autumn,
which is now being done (Haskins, personal
communication 2010).
The RHP utilises four descriptive cate-
gories of river condition as shown in Table 2.
The fifth category (“unacceptable”) was
introduced for the purposes of this analysis,
due to the need to address the severely modi-
fied rivers within the municipal boundaries
(Belcher, personal communication 2010).
Methodological approach
for the determination of
acceptable water quality
A Water Quality Sub-Committee was
established in order to determine “accept-
able water quality” criteria and standards.
Participants included the consultant team,
water quality specialists and scientists and
other relevant parties from the City.
The section below discusses the criteria
decided upon, which were used to evalu-
ate and colour-code the water quality data
obtained from the City in order to provide a
visual depiction of the water quality status of
the rivers and wetlands of Cape Town.
Public health criteria
While it is acknowledged that public health
risks associated with recreational water may
be due to the presence and interaction of a
range of constituents, faecal coliforms and
Escherichia coli (E. coli) are considered to be
reasonable “indicator” micro-organisms to
assess health risks, as these are indicators of
probable faecal pollution.
The “target”, “acceptable”, “risk” and
“unacceptable” water quality categories for
faecal coliforms and E. coli for both full con-
tact recreation (swimming) and intermediate
contact recreation (canoeing, waterskiing,
sailing, angling, etc.)3 were based on the
South African Water Quality Guidelines
(DWAF 1996a) (see Table 3).
As many of the E. coli and faecal coliform
counts in the rivers within the municipal
boundaries were found to fall within the
“unacceptable” category (red); subdivisions
of this category named Management 1,
Management 2 and Management 3 were
created. This is intended as a management
tool to help establish the responses and actions
needed, to prioritise rivers and wetlands, and
to help determine the sources of pollution.
For instance, an E. coli count of 1 000 000
is likely to indicate a different source of
pollution (probably a sewer overflow) than
a count of 10 000, even though both are
“unacceptable”.
An analysis of all the E. coli counts for
ten years of water quality data for all of
the monitoring points in the Cape Town
municipal area was undertaken to provide
guidance on what the Management 1 to 3
sub-categories should be. It was found that a
third of the data above the unacceptable (400
E. coli organisms/100ml) limit fell between
400 and 2 400 E. coli organisms/100ml,
a third between 2 400 and 20 000 E. coli
organisms/100ml, and the last third above
Results from Bacteriological Tests (EK19)
DateFaecal Coliforms E. coli
Full Inter mediate Full
12/6/2003 1 300 1 300 700
16/10/2003 17 000 17 000 16 000
18/12/2003 5 400 5 400 3 700
15/1/2004 2 900 2 900 2 100
11/3/2004 48 000 48 000 20 000
10/6/2004 4 000 4 000 4 000
2/9/2004 2 300 2 300 1 800
9/12/2004 20 000 20 000 12 000
13/1/2005 100 000 100 000 100 000
10/3/2005 150 000 150 000 90 000
9/6/2005 15 000 15 000 18 000
8/9/2005 2 000 2 000 1 200
17/10/2005 1 600 1 600 1 700
8/12/2005 1 000 1 000 1 000
12/1/2006 900 900 400
14/3/2006 3 100 3 100 1 700
29/6/2006 15 000 15 000 15 000
21/9/2006 1 400 1 400 1 400
14/12/2006 100 100 100
18/1/2007 400 400 200
8/3/2007 380 380 280
14/6/2007 46 000 46 000 16 000
13/9/2007 330 000 330 000 90 000
6/3/2008 1 000 000 1 000 000 1 000 000
12/6/2008 5 000 5 000 5 000
4/9/2008 32 000 32 000 29 000
4/12/2008 26 000 26 000 17 000
15/1/2009 46 000 46 000 18 000
12/3/2009 1 000 000 1 000 000 1 000 000
18/6/2009 7 900 7 900 1 400
Target Unacceptable (red 1)
Acceptable Unacceptable (red 2)
Risk Unacceptable (red 3)
Table 5 Kuils River colour-coded public health and aquatic ecosystem health water quality results:
monitoring point E19 – northern reaches, upstream of the Bottelary confluence
Results from Aquatic Ecosystem Tests (EK19)
Date DO tpon nh3 srp
12/6/2003 7.1 3.426 0.081 0.125
18/12/2003 5.7 1.35 0.073 0.162
15/1/2004 7.5 0.937 0.083 0.209
11/3/2004 3.3 1.123 0.135 0.263
10/6/2004 7.4 1.229 0.075 0.107
14/10/2004 7.2 1.31 0.056 0.075
9/12/2004 8 2.268 0.107 0.076
13/1/2005 3.5 1.556 0.011 0.186
10/3/2005 5.8 2.244 0.345 0.21
9/6/2005 7.2 2.281 0.065 0.076
8/9/2005 9.7 2.746 0.186 0.105
8/12/2005 8.9 4.889 0.099 0.285
12/1/2006 7.3 1.672 0.302 0.101
14/3/2006 1.1 7.92 6.13 0.044
29/6/2006 5.7 2.79 0.289 0.01
21/9/2006 6.6 2.53 0.13 0.01
14/12/2006 3.1 1.59 0.66 0.041
18/1/2007 3.2 1.747 0.346 <0.001
8/3/2007 4.1 1.366 0.161 0.034
14/6/2007 5.9 3.56 0.761 0.025
13/9/2007 6.2 3.275 0.221 0.051
13/12/2007 1.4 2.809 0.628 0.133
6/3/2008 1.1 1.095 0.016 0.184
12/6/2008 7.7 1.745 0.157 0.066
4/9/2008 7.4 4.25 0.228 0.048
4/12/2008 7 2.805 0.424 0.01
15/1/2009 5.4 1.906 0.12 0.145
12/3/2009 4.7 0.852 0.021 0.066
18/6/2009 6.5 2.591 0.1 0.067
Natural Poor
Good Unacceptable
Fair
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201326
20 000 E. coli organisms/100ml. These divi-
sions are purely to guide management and to
assist with the allocation of resources. These
limits were then used for Management 1, 2
and 3 (i.e. the sub-categories of the “unac-
ceptable” range).
The same method was used to determine
the three sub-categories of the “unaccept-
able” range for the faecal coliform counts.
Ecosystem health criteria
The values for the various categories for
the ecosystem health criteria were derived
from both the South African Water Quality
Guidelines (DWAF 1996b) and the ecological
reserve water quality benchmarks (Jooste
& Rossouw 2002). As many of the rivers in
the Cape Town municipal area were found
to fall within the “poor” category (red), an
additional “unacceptable” category (dark red)
was created as a management tool to be able
to prioritise rivers, to establish the responses
needed and to help determine the sources of
pollution (see Table 4).
Temperature, total suspended solids (TSS),
conductivity and pH are dependent on vegeta-
tion, geology etc, and the background levels of
these would need to be determined for each
of the water systems to establish applicable
water quality ranges for each of these constit-
uents within the various categories. Therefore,
for the purposes of the project, the following
constituents (highlighted in blue in Table 4)
were decided upon under the auspices of the
Water Quality Sub-Committee:
■ Dissolved oxygen (DO)
■ Ammonia (NH3)
■ Total inorganic nitrogen (TIN)
■ Soluble reactive phosphorus (SRP)
All of these constituents relay different
information in terms of water quality, and
they would trigger different management
responses. They are, however, all linked
and a particular intervention can often
result in an improvement in all constituent
concentrations.
Algae (A), monitored in some wetlands
(“vleis”), was a further constituent used to
assess water quality specifically within the
vleis. The occurrence of blue-green algae
(Cyanophyceae) – a group known to produce
toxins under certain conditions – is particu-
larly important for assessing potential health
risk.
All the public health and ecosystem
health water quality data for all of the moni-
toring points were colour-coded according to
the categories discussed above.
By way of illustration, Tables 5 – 7 are
examples of colour-coded quarterly data
for three monitoring points along the Kuils
River (a river east of the Cape Town CBD).
The first monitoring point (EK19) is in the
Results from Aquatic Ecosystem Tests (EK09)
Date DO tpon nh3 srp
18/1/2000 6.2 2.998 1.929
23/3/2000 5.1 29.18 6.909 2.749
6/6/2000 2.9 21.36 7.846 2.436
21/9/2000 4.1 21.76 12.32 0.23
16/11/2000 9.7 20.54 19.12 2.702
18/1/2001 6.2 22.31 12.59 2.093
15/3/2001 4.5 11.64 1.018 0.348
5/7/2001 8 9.06 1.26 0.681
6/9/2001 9.3 12.29 2.019 0.329
6/12/2001 3.9 23.63 20.84 3.098
24/1/2002 11.8 12.39 9.713 0.977
14/3/2002 8.4 22.68 19.91 15.19
20/6/2002 5 10.26 1.696 1.443
19/9/2002 6.2 20.14 14.87 1.911
12/12/2002 4.6 4.3 1.347
23/1/2003 7.4 8.92 3.475
18/3/2003 5.3 6.157 1.977 1.078
12/6/2003 6.4 16.51 11.48 3.618
18/9/2003 15.8 4.296 0.01 0.192
18/12/2003 5.3 11.69 9.121 4.652
15/1/2004 6.8 11.52 9.117 0.945
11/3/2004 4.5 12.42 8.812 3.997
10/6/2004 6.6 8.598 6.734 1.23
2/9/2004 5.5 16.88 11.15 6.4
9/12/2004 12.8 7.177 2.637
13/1/2005 5.1 16.18 11.72 4.104
10/3/2005 7.3 3.239 0.32 2.272
9/6/2005 8.9 9.924 2.583 1.361
8/9/2005 7.7 18.21 10.12 4.159
8/12/2005 6.3 13 9.728 2.293
12/1/2006 3 7.004 4.977 2.277
14/3/2006 5.5 9.44 2.86 5.77
29/6/2006 6.8 8.51 0.61 2.18
21/9/2006 5.8 10.41 5.65 2.27
14/12/2006 2.4 19.9 19.49 7.63
18/1/2007 4.7 9.421 6.814 1.881
8/3/2007 4.4 11.16 8.58 2.653
14/6/2007 6.1 8.04 2.22 1.06
13/9/2007 6.1 9.519 3.962 1.711
13/12/2007 4.6 26.28 25.25 5.901
6/3/2008 7.6 10.96 7.597 2.084
12/6/2008 4.8 5.794 0.212 1.025
4/9/2008 7.5 7.481 3.537 1.779
4/12/2008 5.3 19.87 18.55 5.421
15/1/2009 2.3 20.94 19.18 3.537
12/3/2009 1.6 22.39 20.68 6.323
Natural Poor
Good Unacceptable
Fair
Table 6 Kuils River colour-coded public health and aquatic ecosystem health water quality results:
monitoring point EK09 – middle reaches at Bellville WWTW discharge at Rietvlei Road
Results from Bacteriological Tests (EK09)
DateFaecal Coliforms E. coli
Full Intermediate Full
18/1/2000 30 000 30 000 3 000
23/3/2000 4 000 000 4 000 000 3 500 000
6/6/2000 3 100 000 3 100 000 2 200 000
19/10/2000 1 100 000 1 100 000 600 000
18/1/2001 66 000 66 000 58 000
15/3/2001 4 000 4 000 3 000
7/6/2001 6 000 6 000 5 200
6/9/2001 140 000
6/12/2001 100 000 100 000 100 000
24/1/2002 100 000 100 000 100 000
14/3/2002 100 000 100 000 100 000
20/6/2002 82 000 82 000 60 000
19/9/2002 45 000 45 000 26 000
12/12/2002 41 000 41 000 21 000
23/1/2003 66 000 66 000 30 000
18/3/2003 200 000 200 000 160 000
12/6/2003 420 000 420 000 230 000
16/10/2003 34 000 34 000 27 000
18/12/2003 79 000 79 000 39 000
15/1/2004 580 000 580 000 390 000
11/3/2004 170 000 170 000 60 000
10/6/2004 430 000 430 000 190 000
2/9/2004 310 000 310 000 200 000
9/12/2004 25 000 25 000 11 000
13/1/2005 240 000 240 000 130 000
10/3/2005 150 000 150 000 30 000
9/6/2005 5 000 5 000 1 000
8/9/2005 600 000 600 000 270 000
8/12/2005 57 000 57 000 38 000
12/1/2006 150 000 150 000 60 000
14/3/2006 55 000 55 000 10 000
29/6/2006 9 000 9 000 2000
21/9/2006 46 000 46 000 39 000
14/12/2006 65 000 65 000 45 000
18/1/2007 260 000 260 000 80 000
8/3/2007 270 000 270 000 190 000
14/6/2007 13 000 13 000 9 000
13/9/2007 160 000 160 000 60 000
13/12/2007 680 000 680 000 580 000
6/3/2008 180 000 180 000 100 000
12/6/2008 29 000 29 000 11 000
4/9/2008 330 000 330 000 270 000
4/12/2008 960 000 960 000 770 000
15/1/2009 2 300 000 2 300 000 1 600 000
12/3/2009 8 300 000 8 300 000 4 600 000
18/6/2009 46 000 46 000 25 000
Target Unacceptable (red 1)
Acceptable Unacceptable (red 2)
Risk Unacceptable (red 3)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 27
northern, upper reaches of the river, upstream
of its confluence with the Bottelary River;
the second point (EK09) is in the middle
reaches at the Bellville Wastewater Treatment
Works (WWTW); and the third point (EK11)
is in the lower reaches downstream of the
Zandvliet WWTW discharge point.
The tables give a visual depiction of the
quality of the water at these particular points
over a 10-year period, thus creating insight
into possible sources of pollution. At moni-
toring point EK19, shown in Table 5, the
“unacceptable” levels of faecal coliforms and
E. coli (reds and dark reds) in recent years in
an area that is relatively affluent, and where
there is no industry and wastewater treat-
ment, is perhaps indicative of leaking sewers
and/or stormwater ingress or infiltration.
Further downstream, at monitoring point
EK09 (Table 6), the water quality worsens
(more reds and dark reds) from both a public
health and ecosystem health perspective.
This is perhaps a result of poor quality efflu-
ent from the Bellville WWTW. Even further
downstream, at monitoring point EK11
(Table 7), the water quality from a public
health perspective improves slightly (more
blues, greens and yellows). It can be conclud-
ed that, in contrast to the concrete-lined sec-
tions higher up in the Kuils River, the natural
wetlands in the vicinity of monitoring point
EK11 are able to attenuate the bacteriological
pollutants. The microbiological constituents,
however, remain “unacceptable”.
CATCHMENT ANALYSIS AND
SOURCES OF POLLUTION
An analysis of each of the catchments, rivers
(including canals) or river reaches, as the
case may be, depending on the water quality
information from the monitoring points, was
undertaken to obtain an understanding of
the situation in each of these discrete units.
A Project Steering Committee (including
any interested parties and all City officials
involved in water quality management)
was established to provide assistance in
this regard. Meetings were held every two
months, or as necessary, and involved work-
shopping of ideas, sharing of knowledge and
findings, and seeking consensus between the
various City Departments.
Field visits to various informal settle-
ments, industries, wastewater treatment
works, pump stations, rivers and wetlands
were held to gain further insight into water
quality issues around Cape Town.
A literature review of previous reports
made available by the City and the evaluation
of historic water quality data created insight
into the state of the rivers and wetlands in
the municipal area of Cape Town.
Table 7 Kuils River colour-coded public health and aquatic ecosystem health water quality results:
monitoring point EK11 – lower reaches, downstream of Zandvliet WWTW discharge
Results from Bacteriological Tests (EK11)
DateFaecal Coliforms E. coli
Full Intermediate Full
18/1/2000 1 900 1 900 1 600
23/3/2000 4 000 4 000 4 000
6/6/2000 610 610 580
19/10/2000 1 000 1 000 1 000
18/1/2001 680 680 500
15/3/2001 8 000 8 000 6 000
7/6/2001 4 100 4 100 3 600
6/9/2001 300
6/12/2001 1 200 1 200 1 000
24/1/2002 430 430 290
14/3/2002 410 410 240
20/6/2002 13 000 13 000 1 2000
19/9/2002 170 170 170
12/12/2002 850 850 790
23/1/2003 3 200 3 200 2 000
18/3/2003 1 000 1 000 600
12/6/2003 2 800 2 800 2 600
16/10/2003 2 800 2 800 2 600
18/12/2003 640 640 430
15/1/2004 3 800 3 800 3 000
11/3/2004 900 900 700
10/6/2004 350 350 270
8/7/2004 4 400 4 400 3 600
14/10/2004 13 000 13 000 12 000
9/12/2004 2 100 2 100 1 800
13/1/2005 2 100 2 100 900
10/3/2005 25 000 25 000 20 000
9/6/2005 1 500 1 500 1 400
8/9/2005 1 900 1 900 1 900
8/12/2005 520 520 450
12/1/2006 440 440 170
14/3/2006 10 10 10
29/6/2006 350 350 310
21/9/2006 620 620 590
14/12/2006 560 560 410
8/3/2007 500 500 200
12/7/2007 360 360 320
18/10/2007 220 220 160
13/12/2007 4 200 4 200 4 200
6/3/2008 7 200 7 200 1 100
12/6/2008 700 700 200
4/9/2008 80 80 70
4/12/2008 6 200 6 200 3 300
15/1/2009 2 200 2 200 1 300
12/3/2009 8 700 8 700 2 900
18/6/2009 89 000 89 000 41 000
Target Unacceptable (red 1)
Acceptable Unacceptable (red 2)
Risk Unacceptable (red 3)
Results from Aquatic Ecosystem Tests (EK11)
Date DO tpon nh3 srp
18/1/2000 2.6 3.106 0.744 1.403
23/3/2000 5.468 0.717 1.346
6/6/2000 6.5 7.061 2.924 1.589
21/9/2000 8.1 9.433 0.778 1.537
16/11/2000 4.1 4.724 1.878 1.694
18/1/2001 7.1 6.097 0.512 1.585
15/3/2001 6.4 8.016 4.021 0.037
7/6/2001 8.8 4.527 0.108 1.093
6/9/2001 7.7 3.525 0.03 0.107
6/12/2001 7.3 7.694 2.092 2.307
24/1/2002 5.2 3.868 0.158 1.5
14/3/2002 7.7 5.718 0.426 1.907
20/6/2002 5.6 4.732 0.223 1.25
19/9/2002 5.9 7.074 0.308 1.338
12/12/2002 4.3 0.6 2.17
23/1/2003 4.9 0.081 2.395
18/3/2003 5 6.584 0.072 2.224
12/6/2003 6.9 12.22 0.07 2.53
18/9/2003 5 4.72 0.143 1.629
18/12/2003 6.5 4.662 0.104 3.095
15/1/2004 8 4.964 0.31 3.256
11/3/2004 5.4 4.612 0.137 3.155
10/6/2004 6.8 3.952 0.864 1.544
2/9/2004 6.3 6.496 0.736 2.492
9/12/2004 8 5.489 0.173 1.616
13/1/2005 5.8 5.568 0.06 2.419
10/3/2005 8.8 5.109 0.2 1.944
9/6/2005 6.4 3.691 0.06 0.967
8/9/2005 7.7 4.485 0.064 1.484
8/12/2005 8.689 1.463 2.718
12/1/2006 9.2 5.496 0.778 2.586
14/3/2006 5.4 6.21 1.1 1.82
29/6/2006 5.5 4.85 0.076 1.65
21/9/2006 5.4 5.28 0.09 1.82
14/12/2006 2.6 4.74 2.76 4.66
18/1/2007 3.3 5.561 3.6 4.188
8/3/2007 3.8 6.683 5.979 2.99
14/6/2007 6.3 2.86 0.274 0.749
13/9/2007 4.4 5.106 2.234 1.342
13/12/2007 2.9 23.73 23.2 6.274
6/3/2008 1.6 14.87 12.99 3.429
12/6/2008 4.8 6.665 4.326 1.884
4/9/2008 5.1 4.048 0.601 1.31
4/12/2008 2.2 10.45 9.699 4.935
15/1/2009 2.2 15.55 14.14 4.594
12/3/2009 1.5 21.88 19.09 5.805
18/6/2009 3.5 3.422 1.888 1.028
Natural Poor
Good Unacceptable
Fair
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201328
Catchment Workshop November 2009
Name
Surname
Catchment Silvermine
River/Wetland Silvermine River
Monitoring Points sil02, sil04
Water Quality (Bacto)
Water Quality (Eco)
Water Quality over time
Land Use: SANParks, Silvermine Dam, Clovelly residential, public open space, Fishhoek township, Clovelly CC and golf course
Water Use
Possible sources of pollution
Sewer pumps
Golf course runoff
Informal areas
Urban runoff
De
pa
rtm
en
t
Ty
pe
of
Inte
rve
nti
on
Timing Budget
Importance Scale of
1 (Important) to 5 (Not important)
Comments
0–
1y
ea
r
1–
5 y
ea
rs
5–
10
ye
ars
10
–2
0 y
ea
rs
>2
0 y
ea
rs
R0
–R
10
0 0
00
R1
00
00
0–
R1
mil
l
R1
mil
l–R
10
mil
l
R1
0 m
ill–
R1
00
mil
l
>R
10
0 m
ill
Pu
bli
c H
ea
lth
En
vir
on
me
nta
l
Eco
no
mic
Gro
wth
(e
.g.
tou
rism
)
e.g Water and Sanitation
e.g. upgrade WWTW x x 5 5 1
Figure 2 Template used in water quality workshops
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 29
Consultations were also held with the
following organisations and entities in the
interest of information-sharing and future
collaboration:
■ DWA
■ South African National Parks (SANParks)
/ Table Mountain National Parks (TMNP)
■ Swartland Municipality
■ Stellenbosch Municipality and
Cape Winelands District Municipality
■ Department of Agriculture
Stakeholder engagement was sought
through a two-day workshop (16 and
17 November 2009). The workshop was held
with various area managers from the City
in order to determine pollution sources,
to suggest possible solutions and to gain
management consensus. Water quality at the
various monitoring points was discussed and
attendees filled out templates as per Figure 2.
Through the process the sources of pol-
lution with respect to water quality in river
systems and stormwater, which stand out
from the many, many types of point or dif-
fuse sources of pollution, were found to be
the following:
■ Perceived major pollutors:
■ Blockages and overflows of sewers
(whether due to extraneous waste
disposed into sewers, illegal rainwater
disposal or previous bad practice in
construction)
■ Greywater and sewage from informal
settlements
■ Sewage pump stations
■ Solid waste in water courses and such
open areas
■ Wastewater treatment works
■ Perceived minor pollutors:
■ Agriculture
■ General urban runoff
■ Golf courses
■ Industry and construction
■ Canalisation of rivers4
RISK ASSESSMENT
The purpose of the risk assessment was to
determine the vulnerability of a catchment
to human and ecological health impacts,
should there be a pollution incident or water
quality-related set of circumstances. It is
not a reflection of what is happening on
the ground, but rather an illustration of the
inherent risk (without a management system
in place) as opposed to the residual risk.
The risk assessment is one of the criteria
that was fed into the catchment prioritisation
exercise, as described later in this paper.
Risk events and their associated con-
sequences were identified by the Project
Steering Committee and Water Quality Sub-
Committee as per Table 8:
Each inland environmental monitoring
point or group of monitoring points (i.e.
river reach) was assessed against the above
risk events. The probability of the event hap-
pening and the potential impact of that risk
were determined. A resultant risk or vulner-
ability score was obtained per river reach, as
shown in Figure 3, where a high probability
and high impact equate to a high vulner-
ability (red); and a low probability and low
impact equate to a low vulnerability (blue).
Table 9 shows how the risk assessment
works, with results for the Hout Bay River,
Hout Bay catchment, as an example of what
was carried out for all of the City’s rivers and
wetlands
Overall, the risk events which resulted in
the highest vulnerability scores included:
■ Ongoing and chronic risk events:
■ Deteriorating municipal infrastructure
■ Increased informal settlement
■ Insufficient maintenance of municipal
infrastructure
■ Sporadic risk events:
■ WWTW breakdown
■ Pipe blockage or overflow
PRIORITISATION OF CATCHMENTS,
RIVERS AND WETLANDS
The catchment prioritisation exercise was
intended to assist the City’s management
structures with the allocation of resources.
The exercise provides guidance on a starting
point for the allocation of resources. Ad hoc
and emergency events that affect water qual-
ity will, however, still need to be attended to
as the need arises.
The methodology, scores, weighting and
input criteria for the prioritisation exercise
were workshopped by the Project Steering
Committee, Water Quality Sub-Committee
and the Consultant Team.
Input criteria
The following criteria were used to prioritise
catchments:
■ Water usage (WU)
■ Public health (PH)
■ Ecosystem health (EH)
■ Risk (R)
■ Downstream impact (DI)5 [rivers] or algae
(A) [wetlands]6
■ Pollution load (PL)7
Initially “cost of intervention” and “time for
implementation” were included as possible
criteria, but after intensive debate at the
various forums, these two criteria were
withdrawn. These could, however, still
be considered at a later stage to further
prioritise catchments for management
interventions.
Table 8 Risk events and risk consequences
Risk event Consequence
WWTW breakdownPartially or untreated sewage effluent (ecosystem and public health risk)
Pipe blockage or overflow Sewage spill (ecosystem and public health risk)
Pump station breakdown & overflow Sewage spill (ecosystem and public health risk)
Agricultural pollution incident Ecosystem and public health risk
Inappropriate disposal of solid waste Aesthetic, ecosystem and public health risk
Long-term degradation of land Increased runoff-flooding, contamination
Densification/hardening of surfaces Increased runoff-flooding, contamination
Increased informal settlements
Less water and sanitation capacity (ecosystem and public health risk), inappropriate greywater disposal, and less solid waste capacity and illegal dumping
Industrial pollution incident Ecosystem and public health risk
Insufficient maintenance of municipal infrastructure
Sewage/stormwater leakage/intrusion (ecosystem and public health risk)
Leaking (i.e. due to ageing) and deteriorating infrastructure (new and old)
Sewage/stormwater leakage/intrusion (ecosystem and public health risk)
Figure 3 Methodology for obtaining the
vulnerability score
Pro
ba
bil
ity
of
risk
eve
nt
100
66
33
00 33 66 100
Impact of risk event
Low
Medium
High
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201330
Table 9 Risk assessment results for Hout Bay River, Hout Bay catchment
CatchmentRivers
and Wetlands
Reach/Description
Monitoring point
Risk Event Risk Consequence ProbablityImpact(0/Low/
Med/High)
Priority/Riskiness
(0/Low/Med/High)
Hout BayHout Bay
Upper(Longkloof Rd)
dr04
WWTW breakdown Raw sewage effluent – ecosystem and public health risk
0
Pipe blockage or overflow Sewage spill – public health risk 1 411
P/S breakdown and overflow Sewage spill – public health risk 0
Agricultural pollution incident
Ecosystem health risk 850
Inappropriate disposal of solid waste
Aesthetic, public health and/or ecosystem health risk
850
Long-term degradation of the urban environment
Increased runoff-flooding, contamination
289
Increased densification/hardening of surfaces
Increased runoff-flooding, contamination
289
Increased informal settlements
Less water and sanitation capacity – public health risk
1 411
Industrial pollution incident Ecosystem and public health risk 0
Insufficient maintenance of infrastructure
Sewage/stormwater leakage –ecosystem and public health risk
1 411
Leaking deteriorating infrastructure (new and old)
Sewage/stormwater leakage –ecosystem and public health risk
1 411
MiddleVictoria Rd
dr02
WWTW breakdown Raw sewage effluent – ecosystem and public health risk
0
Pipe blockage or overflow Sewage spill – public health risk 4 150
P/S breakdown and overflow Sewage spill – public health risk 0
Agricultural pollution incident
Ecosystem and public health risk 850
Inappropriate disposal of solid waste
Aesthetic, public health and ecosystem health risk
4 150
Long-term degradation of the urban environment
Increased runoff-flooding, contamination
1 411
Increased densification/hardening of surfaces
Increased runoff-flooding, contamination
1 411
Increased informal settlements
Less water and sanitation capacity – public health risk
6 889
Industrial pollution incident Ecosystem and public health risk 0
Insufficient maintenance of infrastructure
Sewage/stormwater leakage/intrusion – ecosystem and public health risk
4 150
Leaking deteriorating infrastructure (new and old)
Sewage/stormwater leakag/intrusion – ecosystem and public health risk
4 150
Lower Princess St & estuary
dr05 (bacto)dr01
WWTW breakdown Raw sewage effluent – ecosystem and public health risk
0
Pipe blockage or overflow Sewage spill – public health risk 4 150
P/S breakdown and overflow Sewage spill – public health risk 6 889
Agricultural pollution incident
Ecosystem and public health risk 0
Inappropriate disposal of solid waste
Aesthetic, public health and ecosystem health risk
4 150
Long-term degradation of the urbam environment
Increased runoff-flooding, contamination
1 411
Increased densification/hardening of surfaces
Increased runoff-flooding, contamination
1 411
Increased informal settlements
Less water and sanitation capacity – public health risk
6 889
Industrial pollution incident Ecosystem and public health risk 0
Insufficient maintenance of infrastructure
Sewage/stormwater leakage/intrusion – ecosystem and public health risk
6 889
Leaking deteriorating infrastructure (new and old)
Sewage/stormwater leakage/intrusion – ecosystem and public health risk
6 889
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 31
Point scoring system
A point scoring system was then developed
for each of the criteria given above. The
approach for the point allocation was as
shown in Table 10.
Catchments (or river reaches) with good
water quality, low levels of use, low risk of
negative events, low pollution loads and low
downstream impacts would have a lower
priority for intervention than catchments (or
river reaches) where all these attributes would
score badly and thus achieve a higher score.
Each monitoring point or grouping of
monitoring points (i.e. river reach) was
assessed according to the above criteria
and given a score between 1 and 5 as per
Table 10.
The points allocated for Water Usage and
Downstream Impact in each of the rivers
and wetlands were derived from literature,
and in consultation with the Project Steering
Committee, Water Quality Sub-Committee
and through the Consultant Team.
The points for Ecosystem Health, Public
Health and Algae were derived from the
Water Quality Results, whereas the points
for Pollution Load were derived as follows:
■ Pollution Load = {Q (m3/s)*(Ecosystem
Health) (points allocated to the con-
centration (1–5))} + {Q (m3/s)*(Public
Health) (points allocated to the concen-
tration (1–5))} + {Q (m3/s)* (Sandiness
of the area and/or propensity for solid
waste)}
■ Q: Flows for the various rivers and
wetlands within the Cape Town
municipal area were obtained from
reports (Ninham Shand et al 1999),
through personal communication with
City officials (Wood, personal com-
munication 2010) and from low-flow
monitoring undertaken by the City in
May 2002. Outstanding flows were
further derived through inference
of the available flows, the size of the
relevant catchment and the land use
in the catchment.
■ Ecosystem Health and Public
Health: The points allocated for the
Public Health and Ecosystem Health
Water Quality concentration results
(1–5), as described earlier in this
paper, were utilised.
■ Sandiness of the area/propensity for
solid waste: An allocation of 1 to 5
was given according to an area’s sandi-
ness and propensity for litter. A sandy
area with high litter such as Guguletu
obtained a score of 5 and an urban
area with low litter such as Cape Town
CBD obtained a score of 1.8
The final values obtained for the
Pollution Load equation for each of the
Table 10 Points allocation for prioritisation exercise
Water Usage(WU)
Water usage Score
Full contact(formal and informal)
Intensive all yr 5
Intensive part of yr 4
Often used 3
Seldom used 1
Intermediate contact (formal and informal)
Intensive all yr 4
Intensive part of yr 3
Often used 2
Seldom used 1
Irrigation 3
Industry 3
Non-contact 1
Public & Ecosystem Health (PH & EH)
Category Score
Very Bad (mostly red) 5
Bad (yellow/red) 4
Intermediate (all colours) 3
Good (blue/green) 2
Very Good (mostly blue) 1
Risk (R)(Vulnerability Score)
Category Score
Very Bad (reds & oranges) 5
Bad (orange & yellow) 4
Intermediate (yellow/all colours) 3
Good (green) 2
Very Good (blue) 1
Downstream Impact (DI) (rivers only)
Category Score
Large impactLarge population, Blue Flag/intensively used beach, conservation area, tourism, recreational vlei, food source agriculture
5
Medium to large impactFairly large population, beach, sea, vlei, some agriculture
4
Medium impact Medium population size, sea 3
Low to medium impact Small population 2
Low impact No downstream impact 1
Algae (A) (Microcystin Toxins)* (wetlands only)
Category Score
High toxin levels (>50 μg/l) 5
Medium to high toxin levels (25–50 μg/l) 4
Medium toxin levels (10–25 μg/l) 3
Medium to low toxin levels (10–20 μg/l) 2
Low toxin levels (<10 μg/l) 1
Pollution Load (PL)
Category Score
High pollution load 5
Medium to high pollution load 4
Medium pollution load 3
Low to medium pollution load 2
Low pollution load 1
* Microcystin toxin levels measured as a means to monitor the propensity of a wetland to develop harmful algal blooms (HABs)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201332
river reaches and wetlands ranged from 0
to 25. Values from 0 to 5 were then given
a score of 1, values from 6 to 10 a score of
2, values from 11 to 15 a score of 3, values
from 16 to 20 a score of 4, and values
from 21 to 25 a score of 5 as the final
input in the prioritisation exercise. As an
example, Table 11 indicates the Pollution
Load results for the rivers in the Eerste/
Kuils catchment.
■ Points for risk were derived as described
earlier in this paper.
Weighting of criteria
The final scores allocated for each of the
criteria were then weighted as per Table 12
and added to obtain an overall prioritisa-
tion score for each of the river reaches and
wetlands.
The prioritisation scores for each river
reach and wetland within the various catch-
ment areas were added and averaged to
prioritise entire catchments.
Table 11 Pollution Load: Eerste/Kuils catchment
CatchmentRivers/
WetlandsReach/
DescriptionMonitoring
PtLow Flow
(Q)Concentration
PHConcentration
EHSandiness/
LitterPollution
Load
PollutionLoad(1–5)
Eerste/Kuils
Kuils
Upper u/s of Bottelary confluence
ek19 0.05 5 4 3 0.60 1
Bellville WWTW discharge
ek09
0.7 5 4 3 8.40 2(Rietvlei Rd) u/s of Stellenbosch Arterial Rd
ek05
d/s of Baden Powell Bridge
ek08
1.2 4 4 5 15.60 4d/s of Zandtvliet discharge
ek11
Eerste
At N2 freeway-u/s of Kuils confluence
ek13 0.5 3 4 4 5.50 2
Eerste River estuary
ek17 1.5 4 4 4 18.00 4
Kleinvlei Canal
ek 15 0.01 5 4 4 0.13 1
Moddergat-spruit
ek18 0.01 3 4 5 0.12 1
Bottelary At Amandel Road ek03 0.043 3 3 0.26 1
Table 12 Weighting for prioritisation criteria
Criteria Weighting
Public health (PH) 32%
Ecosystem health (EH) 32%
Water usage (WU) 8%
Downstream impact/algae (DI/A) 8%
Risk (R) 8%
Pollution load (PL) 12%
Table 13 Full results for the prioritisation exercise, Hout Bay River
CatchmentRivers/
WetlandsReach/
DescriptionMonitoring
point
Prioritisation criteria
Criteria Points Weighting Score
Hout Bay Hout Bay
Upper(Longkloof Rd)
dr04
PH 1 32.0% 3
EH 2 32.0% 6
WU 1 8.0% 1
DI 5 8.0% 4
R 1 8.0% 1
PL 1 12.0% 1
Total 16
MiddleVictoria Rd
dr02
PH 5 32.0% 16
EH 4 32.0% 13
WU 3 8.0% 2
DI 5 8.0% 4
R 4 8.0% 3
PL 1 12.0% 1
Total 40
Lower Princess St & estuary
dr05(bacto only)dr01
PH 5 32.0% 16
EH 4 32.0% 13
WU 4 8.0% 3
DI 5 8.0% 4
R 5 8.0% 4
PL 1 12.0% 1
Total 41
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 33
Table 15 Summary of general recommendations (extract)
RecommendationDuration Benefit
Budget implication (R mill)Priority:
T, H, M, LDescription Capex Opex
Approach to determining resources for stormwater and river systems
Allocate more budget to and prioritise proactive measures
PermanentMore efficient allocation of resources for sustainable water quality improvement; reduces risk in longer term
– – T
Adopt “prevention is better than cure” as guiding principle
PermanentReduction in costly, after-the-event solutions ensuring sustainable water quality improvement
– – T
Institutional issues
Establish inter-departmental water quality forum at senior level
Short-term to permanent
Consolidation of efforts, roles and responsibilities and improved knowledge sharing
– – H
Establish consolidated pollution task teamShort-term to
permanent
Optimisation of resources to address pollution and avoidance of unintended consequences
– – H
Technical issues
Use proactive asset management approach, including audits and inspections for timeous replacement and upgrading of infrastructure
Permanent Greater budget, effort and energy efficiency – – T
Establish programme for eradication of cross-connections, including documentation on GIS
Short- to medium-term
Improved knowledge and records of cross-connections, and therefore improved management response and water quality
R10.0 R5.0 H
Priority range – colour-coding
All the final prioritisation results were
colour-coded in terms of four priority ranges:
■ Red: High priority
■ Yellow: Medium to high priority
■ Green: Low to medium priority
■ Blue: Low priority
These ranges were obtained by determin-
ing the difference between the highest and
lowest priority scores in the prioritisation
exercise and then dividing the number range
into four equal ‘bands’.
Prioritisation results
Table 13 is an example of the working and
final scores for the prioritisation exercise for
the Hout Bay River.
Overall prioritisation results for rivers
were then obtained by averaging the scores
for the various river reaches where applicable.
In such cases it is important to view the river
prioritisation exercise holistically. In the
instance of the Hout Bay River, for example,
it gets a low to medium priority in the overall
river prioritisation exercise; while the middle
to lower reaches are a high priority and the
upper reaches are a very low priority.
By way of example, the prioritisation
results for the vleis/wetlands in the Cape
Town municipal area are shown in Table 14.
Prioritisation: way forward
The prioritisation results are based on a
multi-criteria model using several inputs to
determine those rivers, wetlands and catch-
ments that should receive priority attention
for the proposed interventions.
The prioritisation model, although
rigorous in its composition, can easily be
expanded to include new criteria, or should
a sensitivity analysis be required (to answer
“what if?” questions).
DETERMINATION OF ADDITIONAL
RESOURCES TO MANAGE
POLLUTION IN STORMWATER
AND RIVER SYSTEMS
The methods discussed above culminated in
the determination of interventions, imple-
mentation mechanisms, resources and costs
required by the City to reduce the burden
of pollution in the inland water systems of
the Cape Town municipal area. Proactive,
sustainable measures were recommended as
far as possible and were listed generally and
per catchment.
It was concluded that R675.3 million in
capital or once-off expenditure and R277.15
million in operational expenditure are
required as additional resources to manage
pollution in stormwater and river systems.
General resources applicable throughout
most catchments were discussed under the
following headings:
■ Institutional issues
■ Technical issues
Table 14 Prioritisation results for vleis/wetlands
Catchment Vlei/Wetland Score Priority
Zeekoe Zeekoevlei 49High
Diep Milnerton Lagoon 47
Diep Rietvlei 40
Medium to HighZeekoe Rondevlei 40
Noordhoek Wildevoëlvlei 36
Diep Zoarvlei 34
Low to MediumSand River Die Oog 31
Sand River Little Princessvlei 30
Sand River Langevlei 29
Zeekoe Princessvlei 26
LowSand River Zandvlei 25
Sand River Westlake Wetland 24
South Peninsula Glencairnvlei 19
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201334
■ Planning and policy
■ Communication and liaison
Table 15 is an extract of the summary table
used to list general recommendations,
indicating the duration, benefit and budget
implications for each recommendation (an
action and comments column have been
omitted for the sake of clarity).
In addition to the general recommenda-
tions, the resources required to manage water
pollution per catchment were discussed where
catchment-specific details were necessary.
Table 16 is an extract of the summary
table as used to list the catchment-specific
recommendations. The table is in order of
priority, as per the prioritisation exercise.
CONCLUSIONS
This paper discussed the inputs towards
determining resources to manage inland
water pollution in the City of Cape Town.
In the more complex realm of modern
municipal engineering (where many of the
issues are so-called “soft” in nature, and the
problems and solutions are not straightfor-
ward) the methods discussed were instrumen-
tal in creating a holistic overview of the state
of the rivers and wetlands in the City of Cape
Town, highlighting the complexity of the
problem and assisting to plot a way forward
to provide proactive, sustainable measures for
the management of water pollution.
The main obstacle was the time-con-
suming nature of some of the methods. The
colour-coding of data and the compilation of
inputs from the stakeholder workshops were
particularly lengthy.
Another minor obstacle was agreeing on
the points allocated for each of the prioritisa-
tion criteria. There was the later realisation,
however, that the system was fairly robust
and slight deviations in these points made
little or no difference to the ultimate level
of prioritisation of the particular river or
wetland.
Some novel points included: the colour-
coding exercise which helped to convert
vast quantities of hard, scientific data into
something meaningful and tangible to all
involved; the risk assessment and prioritisa-
tion exercise to assist with the allocation of
resources; getting inputs from a vast number
and array of stakeholders; and the ultimate
allotment of actions to City Managers for
each recommendation.
In all, the methods discussed provided a
significant contribution towards the quest
to improve water quality in the City of Cape
Town.
ACKNOWLEDGEMENTS
We wish to thank the following persons for
their valuable contributions throughout this
project:
Table 16 Summary of catchment-specific recommendations (extract)
RecommendationDuration
Budget implication (R mill)Priority
1 – 10 (H – L)Number Description Capex Opex
4.6.1 Diep River catchment: catchment priority: 1
• The recommendations for the Diep River catchment should be read in conjunction with the report for project 233C/2008/09 (Improving the quality of the stormwater discharging into the Diep River – Milnerton), being compiled by iCE Group consulting engineers.
• Appoint additional pollution control inspector for each of five high-priority river reaches where intensive intervention programmes are to be launched
Medium-term – R0.5 1A
• Appoint project manager for each of five identified priority areas to drive integrated improvement programme
Long-term (to move to next priority)
– R0.75 1A
4.6.1.1 Mosselbank River: priority level: high
• Further improvements to Kraaifontein WWTW, including sludge management, phosphate removal, duplicate disinfection unit
Permanent R15.0 R2.0 2
• Implement in Scottsville area in particular findings from a report Advice on the elimination of ingress of stormwater and infiltration of groundwater into the sewer system
Medium-term R1.0 – 3
• Active campaign to reduce agricultural pollution Medium-term – – 6
• Removal of alien vegetation (including aquatic) and restore river banks Long-term R1.0 R0.5 10
• Monitor 15 sewage pump stations for spillage and pollution Permanent – – 5
• Expand solid waste services to areas not currently serviced (e.g. water courses) and increase street sweeping
Permanent – – 4
4.6.1.2 Diep River: priority level: high
• Further upgrade to Potsdam WWTW, including duplicate disinfection unitPermanent R5.0 R1.0 2
• Collaboration with Swartland Municipality and DWA Medium-term – – –
• Provide ablution and car-washing facilities at Bayside Mall taxi rank Medium-term R1.0 R0.1 1B
• Track pollution from Montague Gardens industrial area Short-term – – 7
• Monitor and resolve water quality from Theo Marais Park Short-term R0.5 – 3
• Active campaign to reduce agricultural pollution, including runoff from Milnerton stables
Short-term – – 6
• Monitor nine sewage pump stations for spillage and pollution Permanent – – 5
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 35
■ Mr Abdulla Parker for his leadership,
patience, unwavering commitment to the
cause and passion to make a difference.
■ Mr Barry Wood for his invaluable exper-
tise, guidance and support.
■ Ms Candice Haskins for her commitment
and insights into water quality in the City
of Cape Town.
■ Ms Jeanette Kane for her unfailing will-
ingness to help with GIS expertise.
■ Mr Johan Massyn for his willingness to
share his local knowledge and unique
personal experiences.
■ Mr Richard Kotze for his reliability and
for sharing his passion and knowledge.
Many thanks to the project team for their
time, commitment to improving water quality,
enthusiasm, expertise and inspiring insights:
■ Dr Jo Barnes
■ Ms Lyn Viviers
■ Mr Simon Nicks
■ Ms Toni Belcher
Sincere thanks also go to members of the
Steering Committee and the Water Quality
Sub-Committee, and workshop participants.
NOTES
1 The Department of Water Affairs and Forestry
(DWAF) has since become known as the Department
of Water Affairs (DWA)
2 Taken over time
3 It is important to note that while some of the City’s
rivers and water bodies are utilised for formal
full and intermediate contact recreation activities
(e.g. Zandvlei, Milnerton Lagoon, Zeekoevlei and
Rietvlei), the majority of systems are used on a more
informal basis.
4 This is an indirect pollution source, as pollution is
not attenuated in canals as well as it is in natural
rivers, therefore resulting in higher pollution levels.
Furthermore, canals are not as aesthetically pleas-
ing as natural river systems, and may therefore
induce less considerate behaviour towards their
preservation.
5 E.g. Blue Flag beaches, nature reserves, human
habitation, sensitive environment, tourism hotspot
etc, downstream of the water quality monitoring
point.
6 While most wetlands do not have a downstream
impact per se, their algal content (not measured in
the rivers) had to be taken into account as it is an
indication of the propensity for a vlei/wetland to
develop harmful algal blooms (HAB) and therefore
is significant in terms of public health. A distinction
was therefore made between rivers and wetlands
with these criteria.
7 It should be noted that the determination of the pol-
lution load did not form part of the original scope
of works and was later included as an ad hoc inves-
tigation, for which provision existed in the project
budget.
8 Relevant data was obtained from Mr Barry Wood
(CSRM, City of Cape Town).
REFERENCES
Belcher, A (Aquatic water scientist) 2010. Personal
communication.
City of Cape Town (2008) City of Cape Town State of
the Environment Report 2007/8. Cape Town: City of
Cape Town, Environmental Resource Management
Department.
DWAF (Department of Water Affairs and Forestry)
(1996a). South African Water Quality Guidelines,
2nd edition. Vol. 2. Recreational uses. Pretoria: CSIR
Environmental Services.
DWAF (Department of Water Affairs and Forestry)
(1996b). South African Water Quality Guidelines,
2nd edition. Vol. 7. Aquatic ecosystems. Pretoria:
CSIR Environmental Services.
Haskins, C (City of Cape Town) 2010. Personal
communication.
Jooste, S & Rossouw, J N 2002. Hazard-based water
quality ecospecs for the ecological reserve in fresh sur-
face water resources. Report No N/0000/REQ0000,
Pretoria: Department of Water Affairs and Forestry,
Institute for Water Quality Studies.
Ninham Shand, Southern Waters, Cape Metropolitan
Council 1999. Kuils/Eerste River System evaluation
of nutrient flux downstream of Bellville Wastewater
Treatment Works. Report No 3028/8851, Cape Town.
Wood, B (City of Cape Town) 2010. Personal
communication.
World Health Organisation (WHO) 2003. Guidelines
for Safe Recreational Water Environments, Volume 1,
Coastal and Fresh Waters. Geneva.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201336
INTRODUCTION
Irrigation scheme planning and design can
be relatively complex. A scheme’s ultimate
success depends on many things – soils,
water, farmer skills, markets and financing.
By incorporating these factors at the various
design levels, each scheme can be tailored to
the user’s individual circumstances.
The irrigation sector – smallholder irriga-
tors in particular – has been the focus of
much discussion and on-going government
financial assistance. Programmes include
the Revitalisation of Smallholder Irrigation
Schemes of the Limpopo Province and other
ad hoc developments, led by general policy
during the last decade. The Department of
Water Affairs, for instance, has developed a
financial assistance policy for poor farmers
(DWAF 2004), most of whom are small-
holder irrigators.
It is often believed that irrigation is the
key to alleviating poverty, especially in rural
areas. The development of smallholder irri-
gators has a political aspect, because provid-
ing assistance to rural communities through
irrigation aligns directly with national pover-
ty alleviation goals. As a result, governments
place considerable emphasis on smallholder
irrigation, and allocate funds expressly to
develop these irrigators.
By using the correct design philosophy
and optimising the irrigation system, the
project life cycle costs can be minimised
and the best use can be made of the limited
funding.
When designing a new scheme or one
due for revitalisation, two questions arise:
what is the best design approach, and what
will influence the design and profitability?
The answers usually depend on whether
one is designing on a commercial basis, or
altering the design to cater specifically for
the operational needs of the smallholder
irrigator. This paper aims to provide guid-
ance on the expected cost ranges and the
design approach to be adopted under specific
circumstances. The primary aim of the
study is to determine whether an irrigation
scheme’s design should be tailored to the
particular irrigator or broadly structured
Design implications on capital and annual costs of smallholder irrigator projects
A F Hards, J A du Plessis
While agricultural producers on commercially operated irrigation schemes will aim to achieve the recommended high crop yields, those on a smallholder irrigation scheme usually produce moderate to low crop yields. The water demand by these two irrigator types also differs and is reflected in the variations in crop yields. Because smallholder irrigators produce lower crop yields and use less water, they should use a system suited to this lower water demand. Many irrigation schemes have the opportunity for participants to assess their farming objectives and models. The irrigators can then use the assessment results to determine their water demands, reduce their infrastructure capacity and reduce their capital, operation and maintenance costs. On many smallholder schemes, the system has been designed for commercial crop yields and water use. If smallholders never achieve commercial levels of production, they have overcapitalised and subjected themselves to additional operational strain. In this study, six irrigation schemes based in the Eastern Cape were evaluated according to three levels of irrigation supply: a commercial irrigator, a smallholder irrigator and the commercial under-utilised irrigator. The irrigation infrastructure for each of the six schemes was designed, and the associated costs determined, for each level of supply. The study investigates the impact of different designs on the amount of water and land used, and resultant costs of the infrastructure. The results show that a smallholder irrigator using a scheme sized for commercial operation can have significantly higher (between 5% and 29%) annual operation and maintenance costs. The study clearly shows that the farmer type should be considered when designing each irrigation scheme.
TECHNICAL PAPER
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 36–44, Paper 875
ADRIAN HARDS (Pr Eng, MSAICE, MSABI
Designer) has practised in the fi eld of water
engineering for 11 years, gaining most of his
experience in the Eastern Cape. He is particularly
interested in pipeline transient analysis, pump
stations, pipe structural design and irrigation
systems. In 2001 Adrian obtained his BSc in Civil
Engineering from the University of Natal, and in
2008 he obtained Approved Designer status from the South African Irrigation
Institute.
Contact details:
Department of Civil Engineering
Stellenbosch University
Private Bag X1
Matieland
7602
South Africa
T: +27 21 808 4358
F: +27 21 808 4351
DR KOBUS DU PLESSIS (Pr Eng, MSAICE, MIMESA)
has lectured in hydrology, water engineering
and environmental engineering for the past ten
years at the Stellenbosch University. During his
more than 25 years of experience in the water
sector, he has also worked for the Department
of Water Aff airs, the City of Cape Town and the
West Coast District Municipality. His special
interest is integrated management of water resources in South Africa as
applied by local authorities. He obtained his PhD (Water Governance), MSc
(Water Resource Management) and BEng (Civil) from the Stellenbosch
University.
Contact details:
Department of Civil Engineering
Stellenbosch University
P/Bag X1
Matieland
7602
T: +27 21 808 4358
F: +27 21 808 4351
Key words: appropriate irrigation design, smallholder irrigators, smallholder
water supply, smallholder production costs
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 37
for commercial water use, and whether the
latter, the traditional practice, is the reason
for the high economic risk associated with
smallholder irrigation projects.
LITERATURE REVIEW
Irrigation management
transfer and revitalisation
The most recent stage of smallholder irrigation
in South Africa can be referred to as the era of
irrigation management transfer and revitalisa-
tion (Van Averbeke & Mohamed 2007). The
strategy coincides with the political change in
the country and the ideologies that came with
that change. The planned changes were first
implemented through the Reconstruction and
Development Programme, which was then
followed by the Growth, Employment and
Redistribution Policy.
Existing schemes were targeted first.
Part of the process involved transferring the
responsibility of managing, operating and
maintaining the irrigation scheme from the
state to the farmers. The process is known as
irrigation management transfer (IMT) (Van
Averbeke & Mohamed 2007).
With the current focus on the revitalisa-
tion of irrigation schemes, many lessons can
be learned from previous development mis-
takes. Backeberg (2004) showed that returning
to the previous focus on infrastructure at the
expense of social relationships, land tenure,
water entitlements, economic location and
market access, financial capital and support
services, technical and financial viability, and
resources of households, risks repeating the
mistakes of previous generations.
One of the most comprehensive initiatives
has been the Revitalisation of Smallholder
Irrigation Schemes (RESIS) of the Limpopo
Province (Arcus Gibb 2005). It included the
WaterCare programme and involved revital-
ising the scheme’s infrastructure, leadership,
management and productivity.
The existing smallholder schemes in
South Africa and their characteristics are
summarised in Table 1.
Revitalisation differs from rehabilita-
tion: it does not concentrate solely on the
engineering aspect of the schemes. Denison
(2005) identified that revitalisation takes a
holistic approach in which human develop-
ment (individually and organisationally),
empowerment, access to information, mar-
keting and business strategy development are
given the same emphasis as the engineering
aspects.
Design aspects found in
smallholder irrigation
Each irrigation system installation should
take into account the circumstances and
needs of that scheme. The typical develop-
ment options may need to be adapted to
allow for such issues as:
■ availability of infrastructure for installa-
tion and on-going maintenance
■ availability of support services for main-
tenance of specialist equipment
■ affordability
■ soil and selection of a system that will
prevent soil water management problems
■ the appropriateness of systems such
as short-furrows and the management
requirements needed to ensure their
success.
Productivity of farmers is affected by
education and infrastructure (Fan & Zhang
2004). If inputs and markets are made more
accessible, more rural farmers will be able
to use them, which will lead to greater
productivity (Kamara 2004). However, poor
road conditions, high transport costs and
distant markets prevent good market access
for smallholder irrigators (Nieuwoudt &
Groenewald 2003).
Access to basic general services, such
as finance and communication, affects the
effectiveness of smallholder irrigators and
directly affects their ability to access inputs
and the market in general. Poor access to
services limits the ability of farmers to adopt
new or better technology (Perret & Stevens
2003). Even though they may be regarded
as simple services, they must be remem-
bered during the process of revitalisation
(Chaminuka et al 2008).
Investment costs
The International Water Management
Report (Inocencio et al 2007) investigated
314 projects in 50 countries to find the
factors influencing the cost of revitalising
smallholder irrigation projects. They are:
■ Project size (total irrigated area
benefited by a project)
This is the most important factor
influencing the project costs. The larger
the project, the lower the unit cost; this
is primarily due to the engineering
economies of scale that result from larger
projects.
■ Average area of irrigation systems
involved in a project
As with the project size, larger system
sizes will have lower unit costs than
smaller systems. It was, however, shown
that the larger the system, the lower the
economic performance of the project.
■ Degree of complexity
The degree of complexity does not affect
the development costs of a project.
Increased complexity does, however, have
a negative effect on the rate of return for
the project.
■ Government funding
It was found that the greater the portion
of government funding, the lower the unit
cost for the project.
■ ‘Soft costs’
The ‘soft costs’ include components such
as engineering management, technical
assistance, agricultural support, institu-
tional development, training of staff and
beneficiary farmers. Higher ‘soft costs’
resulted in lower unit costs.
■ Rainfall
The amount of annual rainfall was found
not to have a significant impact on the
costs of projects, but it improved the
economic returns.
■ Macro-economic factors
The greater the gross domestic product
per capita, the higher the unit cost.
■ Farmer contribution to initial costs
No impact was found on the unit cost
where farmers contributed to a project.
When farmers contributed to the initial
costs, the project performance increased.
■ Conjunctive water use
‘Conjunctive water use’ involves the use
of both surface and ground water. It
was found that this did not impact on
Table 1 Categories of existing smallholder irrigation schemes
EraNo of
schemesArea (ha)
Mean area per scheme
(ha)Main technology used
Smallholder canal scheme(1930–1969)
74 18 226 246Gravity-fed surface irrigation
Independent homeland(1970–1990)
62 12 994 210Different forms of overhead irrigation
Irrigation management transfer and revitalisation (1990–present)
64 2 383 37Pump and sprinklers or micro-irrigation
Year of establishment uncertain 117 15 897 136Mostly overhead irrigation
Total 317 49 500 156
Data supplied by Denison (2006)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201338
the unit cost, but increased conjunctive
use did significantly improve project
performance.
■ Operation and maintenance (O&M),
and farmer participation
Three approaches may be taken to
managing O&M – first, through a gov-
ernment agency alone; second, through
a joint venture between government and
farmers; and third, by farmers them-
selves. Farmer-managed systems have
lower unit costs than systems managed
by government agencies. The deeper
involvement of farmers results in tailor-
made, appropriate technology that meets
the farmer’s real needs and reduces the
project costs.
■ Type of crop irrigated
The systems for irrigating rice are sig-
nificantly more expensive than those for
any other crop type. The more valuable
the crop irrigated, the higher the project
performance and profitability. Fruits, veg-
etables and livestock products generally
result in better project performance.
The project size, rainfall and the type of crop
irrigated all affect the costing of the schemes
analysed in the research. Due to the nature
of the study and the engagement of the com-
munity, the degree of complexity, ‘soft costs’
and farmer participation should all result
in lower costs and more efficient schemes.
However, the effect of these items has not
been quantified in this study.
Smallholder production and
reduced crop water requirement
The aim of any irrigation venture is to pro-
duce the best possible crop yield permitted
by the soil, water and fertility (Doorenbos &
Pruitt 1977). Smallholder irrigators tend to
apply significantly less water than commer-
cial irrigators, largely because of their lower
plant densities and low-input cultivation.
Smallholder irrigators farm in a manner
aimed at reducing risk (Perret & Stevens
2003). By reducing risk they lower input
costs. The direct result is reduced crop water
requirements and reduced system capacity.
The reduced system capacity reduces initial
costs and on-going operational costs. If the
system requires less water than its design
requires, its full capability might be underu-
tilised (Crosby et al 2000).
When the system is being designed, the
future needs of the farmer must be deter-
mined. The system can then be designed to
allow flexible operation, and expansion if
required.
Conventional design norms for cal-
culating crop water requirements gener-
ally suit intensive farming practices, and
infrastructure is designed to the peak water
requirement. However, a smallholder irriga-
tor scheme generally has lower yields than an
intensive scheme. When this fact is ignored
and the intensive system is proposed for
the smallholder irrigator, the oversizing can
negatively affect the financial evaluation
of the project; the project might then be
rejected based on sustainability or initial
capital costs. If, when calculating crop water
requirements, crop coefficients were adapted
to reflect the conditions on smallholder
schemes, the proposed infrastructure is
likely to be smaller in capacity and lower in
cost (Crosby et al 2000).
Farmer types and risks
Denison & Manona (2006) and Van Averbeke
& Mohamed (2005) developed farmer
typologies for irrigation schemes. These
typologies are very useful for suiting the
system design to the application. The farmer
types are closely linked to the level of risk
the farmer is willing to accept (i.e. how will-
ing the farmer is to risk losing money). This
willingness to accept risk determines how
farmers operate, another factor in determin-
ing the farmer type. The farmer types also
measure success according to their own
criteria, which might not include financial
aspects. Four farmer types were identified:
■ Business farmer
Business farmers are commercially
oriented producers aiming to produce
an income from their farming activities.
They usually have high skill levels, an
understanding of markets and greater
financial resources. These farmers are
likely to accept higher risks and aim for
higher crop yields.
■ Smallholder farmer
Smallholder farmers are traditionally
plot holders. They do not rely on farm-
ing alone, but generate income from a
variety of livelihoods. As a result, they
rely less on outside markets for their cash
income. They are more risk-averse than
the business farmer and use lower-risk
farming styles. They may struggle to be
financially sustainable on larger schemes
and pump systems with high O&M costs.
Their operations are more suited to
gravity schemes with lower annual costs.
They will generally reduce their inputs
to reduce risk, and consequently achieve
lower yields.
■ Equity labourer
Some large, expensive irrigation schemes
are open to partnerships. They consist of
a number of plot holders who are unable
to farm in a business farmer model.
Instead, an outside commercial partner
operates the scheme and farming enter-
prise, and the plot holders become equity
labourers who make their resources
– soils, water and infrastructure – avail-
able. As equity labourers, the plot holders
enjoy the benefits of employment and
receive dividends from the enterprise
profits.
■ Food producer
Food producers may be plot holders on
a scheme. They have limited access to
resources such as labour and finance.
Generally, food producers are on the pov-
erty line and their objective is simply to
supply their households with food. They
want to avoid risk completely and may
not use irrigation, due to the initial costs,
risks and their low skill level.
One of the most important findings of the
Van Averbeke & Mohamed (2005) study was
the attitude of the farmers. There was no
evidence that farmers of one type aspired
to achieve the higher level of production of
another type. This finding is of particular
importance as it shows that a scheme for
smallholder irrigators should not be designed
on the assumption that they will, over time,
become business farmers. The objectives of
the farmers determine their type. Only when
the objectives of the farmer alter would they
move into a different type.
The scheme design must therefore be
based on direct interaction with the farm-
ers so that the design matches the farmers’
objectives.
METHODOLOGY
The research presented in this paper is based
on the input data from a project undertaken
by ARCUS GIBB for the Department of
Table 2 Pre-feasibility scheme identification
Scheme name Location Size (ha) Water source Existing or proposed
Kama Furrow Zanyokwe 50.90 Keiskamma River Existing bulk
Wolf River Keiskammahoek 25.00 Sandile Dam Proposed
Philane/Ncambedlana Mthatha 85.00 Mtata Dam Existing
Tamboekiesvlei Kat River 33.84 Kat River Dam Proposed
Mantusini Port St Johns 30.00 Mngazi River Proposed
Kruisfontein Ext Humansdorp 19.21 Seekoei River Existing
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 39
Water Affairs (Arcus Gibb 2004a–f) in 2003
and 2004 – the Eastern Cape Resource Poor
Farmers Irrigation Pre-Feasibility Study.
However, all cost calculations were based on
2007 values.
The schemes selected to form the basis of
the research are shown in Table 2. Figure 1
shows each scheme schematically.
Design development
The proposed system for each scheme
was developed in consultation with the
beneficiaries and the characteristics of
each scheme. During the study, multiple
development options were evaluated for each
scheme. The economics of these different
options were then evaluated. Only the eco-
nomically most favourable option for each
scheme was used in the analysis presented in
this paper.
The most favourable economic option
was developed for the commercial farmer
and the smallholder irrigator. For each farm-
er type, the water demands were calculated
and the favourable option designed to cater
for the required flow capacity of the system
to meet the irrigation demand. The water
demands were calculated using the SAPWAT
(Crosby & Crosby 1999) software. BEWAB
(Bennie 1993) software was used to estimate
the reduction due to the lower yields and
crop density of smallholder irrigators. For
the purpose of the study, the term ‘level of
supply’ (LOS) has been used to identify the
farmer type and the resulting system capa-
city design.
The calculation of the costs of the
schemes and evaluation does not take into
account everything that affects irrigators.
The initial capital investment in the selected
schemes covers only the construction cost
and related engineering fees. The financial
impacts of training and organisational and
institutional development were excluded.
The training requirements are not always
directly linked to the scheme type and
size, but are more likely to be linked to the
number of beneficiaries and existing skill
levels.
The scheme types are also limited in the
variety of infrastructure options. These were
limited to:
■ pump-based schemes with only sprinklers
and draglines, and
■ gravity schemes that include sprinklers
and draglines, drip irrigation and short
furrow flood irrigation options.
The impact of these limited selections for
this study on the design, costs and results are
as follows:
■ The analysis is biased towards draglines
and sprinklers.
■ Results are limited to the cost associated
with these pre-selected options.
■ Annual O&M costs are calculated only
on the actual infrastructure.
■ A large portion of the O&M costs are
attributed to the electrical costs of the
pumping equipment.
■ O&M costs allow for water charges of
67 cents per cubic metre of water.
■ Kama Furrow, Wolf River and
Ncambedlana have formalised their
union as the Water Users Association,
with an associated management cost of
R250 per hectare per annum.
Financial evaluation
The gross margin analysis was based on
one hectare under irrigation, planted with a
mixture of field crops and vegetables. The crop
types were green mealies, potatoes, tomatoes,
carrots, maize and dry beans (summer crops)
and cabbage (winter crop). The costs for each
crop type excluded management, but included
indicative market selling prices and transport
to markets. The crop types were chosen to
provide a fair representation of crops and a
profitability that could realistically be achieved.
The hectare would be fully planted with the
six summer crops, but only 30% of the area
would be used for cabbages in winter. The
gross margin was calculated for each LOS con-
sidering the overall yield difference between a
commercial and smallholder irrigator. In terms
of efficiency of production, the evaluation
is based on smallholder irrigators achieving
production levels of 60% of the commercial
yields, as would be expected from the regional
Figure 1 Scheme schematics
Existing bulk gravity main
New bulk gravity main
Existing main
Existing Sandile Dam
Schematic for Kama Furrow
51 ha(Refurbishment of existing sprinkler
infrastructure)
Existing reservoir
End of existing pipeline
Schematic for Tamboekiesvlei
New drip infield infrastructure
33.89 ha
New distribution main
New dam
Existing Sandile Dam Existing Mthatha Dam
12 ha
Existing reservoir
Existing booster pump station (to be rehabilitated)
Rehabilitated sprinkler system
New sprinkler system
Existing bulk gravity main
New pump station
Schematic for Wolf River
Schematic for Mantusini
Mngazi River
New rising mains
New sprinkler infrastructure
New pump stations 3
0 h
a
Schematic for Ncambedlana
12 ha
Mthatha River
Existing Mthatha dam
New elevated tank
No infield infrasructure
85 ha
New rising main
Rehabilitated sprinkler system
7.41 ha11.8 ha
Schematic for Kruisfontein
Existing Klaas se Dam
Existing Dan se Dam
Existing Frank se Dam
New canal
New distribution
main
New infield infrastructure
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201340
Computerised Enterprise Budgets (COMBUD)
published by the Department of Agriculture.
Additional key elements of the evaluation were:
■ The financial analysis includes the DWA
Bulk Water subsidy of R 10 000 per
hectare with a maximum of R 50 000 per
eligible farmer.
■ The analysis does not make provision for
the replacement of infrastructure.
■ The tax rate used for the financial evalu-
ation is 15%.
■ Infrastructure loans will be at an interest
rate of 8%.
■ It is assumed that farmers will require loans
for 100% of their operational costs during
the first two years and that thereafter they
will reduce their requirements to 50%.
SUMMARY OF FINDINGS
Summarising the costs of the interventions
of each of the schemes allows us to evaluate
the type of system applied and whether there
are similarities between the schemes. Table 3
shows the characteristics of the different
types of schemes evaluated in this study.
Capital costs
For each scheme, a design was created for the
commercial and smallholder levels. A sum-
mary of the associated development capital
costs are presented in Table 4. Table 4 shows
that the initial capital costs are likely to be
linked to the type of scheme. A ‘rehabilitated’
scheme is likely to cost less than any other
type of scheme; a new ‘pumped’ scheme
costs more than a rehabilitated scheme; and
a new ‘gravity’ scheme is the most expensive.
Operation and maintenance costs
From the capital costs developed for each
scheme, the associated O&M costs have
been calculated and presented in Table 5.
The actual cost per hectare of the schemes,
based on the annual O&M costs, reveals
four distinct groups. These are: Wolf River
and Kruisfontein, Mantusini, Wolf River and
Kamma Furrow, and Ncambedlana. Table 5
shows that gravity schemes are likely to have
lower O&M costs than pumped schemes.
However, a gravity scheme with significant
infrastructure would have higher O&M
costs, making it similar to a smaller pumped
scheme. A pumped-to-storage scheme has
higher O&M costs than any other scheme.
The costs given in Table 5 include:
■ O&M: These include the annual mainte-
nance costs of the proposed infrastruc-
ture; and operational costs, including
water charges, water user association
charges and electrical operational costs.
No additional allowances have been made
for increases in electricity costs.
Table 3 Scheme characteristics
Scheme Area (ha) Type Source
Kamma Furrow, extension of pipeline 50.9 Gravity with bulk supply Bulk pipeline
Wolf River, section in Zanyokwe 25 Rehabilitation pumped Bulk pipeline
Ncambedlana 85 Pumped to storage Run of river
Tamboekiesvlei 33.84 Gravity with bulk supply Dam
Mantusini 30 Pumped to infield Run of river
Kruisfontein 19.21 Rehabilitation gravity Dam
Table 4 Summary of capital costs
SchemeArea(ha)
Commercial LOS Smallholder LOS
Variation in cost
Capital cost Capital cost
R x 106 R/ha R x 106 R/ha
Kamma Furrow, extension of pipeline 50.90 8.34 163 874 6.97 136 886 16%
Wolf River, section in Zanyokwe 25.00 1.08 44 027 1.06 42 433 4%
Ncambedlana 85.00 10.78 126 877 9.24 108 704 14%
Tamboekiesvlei 33.84 5.28 155 888 3.50 103 488 34%
Mantusini 30.00 2.40 80 089 2.17 72 352 10%
Kruisfontein 19.21 0.64 33 397 0.45 23 485 30%
Table 5 Summary of O&M costs
SchemeArea(ha)
Commercial LOS Smallholder LOS
Variation of O&M
costs
Variation of annual
cost of water
O&M (R/ha)
Annual cost of water
(R/m3)
O&M (R/ha)
Annual cost of water
(R/m3)
Kamma Furrow, extension of pipeline
50.90 2 503 0.29 2 344 0.38 6% –34%
Wolf River, section in Zanyokwe
25.00 2 527 0.30 2 156 0.36 15% –22%
Ncambedlana 85.00 11 734 1.60 7 553 1.47 36% 8%
Tamboekiesvlei 33.84 635 0.08 442 0.08 30% 1%
Mantusini 30.00 2 811 0.64 2 209 0.72 21% –12%
Kruisfontein 19.21 213 0.03 150 0.03 30% 0%
Table 6 Summary of costs for commercial under-utilised LOS
SchemeArea (ha)
Capital costO&M (R/ha)
Annual cost of water (R/m3)R x 106 R/ha
Kamma Furrow, extension of pipeline 50.90 8.34 163 874 2 479 0.41
Wolf River, section in Zanyokwe 25.00 1.08 43 303 2 425 0.41
Ncambedlana 85.00 10.78 217 855 10 409 2.03
Tamboekiesvlei 33.84 5.28 155 888 618 0.11
Mantusini 30.00 2.40 80 088 2 418 0.79
Kruisfontein 19.21 0.64 33 396 199 0.04
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 41
■ Annual cost of water: The value shows
the annual O&M cost of water used on
the scheme. The cost does not allow for
capital repayment. The cost of operating
the scheme in R/m3 was based on level
of consumption. The lower the cost per
cubic metre, the greater the value to the
user, because it will cost less to use the
same amount of water.
Variation of costs
It is important to determine the impact of the
variation between the two LOS designs on
capital, O&M and water costs. To illustrate this
variation between the costs, the percentage
variation of the commercial LOS to the small-
holder irrigator LOS is shown in Tables 4 and 5.
Zero percent indicates that there is no
variation; a positive percentage that the
commercial LOS has a higher value than the
smallholder irrigator LOS; and a negative per-
centage that the commercial LOS has a lower
value than the smallholder irrigator LOS.
The capital cost has a variation range
of costs between 4% and 34%, with the
average about 18%. The increased costs are
not proportional to the increased volume
of water used, which was expected due to
economies of scale. For example, the infra-
structure required to deliver 30% more water
would not need to cost 30% more.
Commercial under-utilised
level of supply
Tables 4 and 5 compare the commercial and
smallholder LOSs, and show how they affect
the initial capital and on-going operational
costs. The impacts on the smallholder irriga-
tor caused by over-designing the scheme are
revealed, not by simply comparing the com-
mercial and smallholder irrigator costs, but by
considering the full scenario of the commercial
under-utilised LOS. Commercial under-use
occurs when a smallholder irrigator is placed on
a commercially designed scheme, but still oper-
ates like a smallholder. To evaluate the impacts
of this, the costs for the commercial designed
scheme and the water use of the smallholder
LOS need to be compared. Table 6 summarises
the costs associated with this option.
The costs in Table 6 for the commercial
under-utilised LOS projects provide the
best information for comparison with the
smallholder irrigator’s costs. The commercial
under-utilised LOS and the commercial LOS
have been compared to the smallholder LOS
in Figure 2.
Figure 2 shows that the capital and O&M
costs of the commercial under-utilised LOS is
on average 18% more expensive than a correctly
sized scheme. If the capital costs do not need
Figure 2: Percentage comparison of commercial, commercial under-utilised against smallholder irrigators
Va
ria
tio
n b
etw
ee
n c
om
me
rcia
l u
nd
er-
uti
lise
d L
OS
a
nd
co
mm
erc
ial
LO
S f
or
sma
llh
old
er
LO
S (
%)
40
35
30
20
25
15
10
0
5
–5
–10
–15
–20
–25
–30
–35
–40
Scheme
Kamma Furrow Wolf River Ncambedlana Tamboekiesvlei Mantusini Kruisfontein
Captital cost O&M – Commercial O&M – Commercial under-utilised
Annual cost of water – Commercial Annual cost of water – Commercial under-utilised
16%
6% 5% 5%
–34%
–22%
2%
15%
11% 11%
14%
36%
27% 27%
8%
34%
30% 29% 29%
1%
10%
21%
9%9%
–12%
30% 30%
25% 25%
0%
Figure 3 O&M cost of scheme vs scheme area for all three LOSs
O&
M c
ost
(R
1 0
00
/ha)
14
0 2010 30 40 6050 70 80 90
Area (ha)
Commercial LOS – pumped
Smallholder LOS – gravity
Small holder LOS – pumped
Commercial under-utilised LOS – pumped
Commercial LOS – gravity
Commercial under-utilised LOS – gravity
12
10
4
6
8
0
2
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201342
to be repaid, it may not have the initial negative
impact that it would have if the farmers needed
to fund the construction themselves. However,
the O&M costs of the larger capacity system
affect the farmers on an on-going basis. They
are between 5% and 29% higher than if the
system were designed for the smallholder LOS
only, and farmers must pay these higher costs
each year, which affects their financial viability.
A commercial farmer would be produc-
ing a higher yield crop than a smallholder
irrigator on the same system, and unlike the
smallholder, would recoup the additional costs.
The variation in O&M costs for the three LOSs
is depicted in Figure 3. It would be expected
that the larger schemes would benefit from
economies of scale and that the annual O&M
cost per hectare would decrease as the scheme
size increased. Figure 3 indicates that the char-
acteristics of the selected schemes for the study
outweigh the economies of scale and have a
greater effect on the annual O&M.
The O&M costs for the commercial LOS
are higher and generally vary from 5% to
34% compared to the other LOSs. A further,
distinct variation occurs between the gravity
and pumped schemes: the pumped system
has higher O&M costs, which are largely
attributable to electricity charges.
The higher annual O&M cost per cubic
metre for the commercial under-utilised LOS
is shown in Figure 4. While the O&M cost
per cubic metre for the commercial LOS and
smallholder LOS are roughly the same, the
commercial under-utilised LOS has signifi-
cantly higher annual O&M cost per cubic
metre – between 5% and 29% – than the
commercial and smallholder LOSs.
Financial evaluation
Table 7 presents the results of a financial
evaluation for each scheme and LOS. The
return on investment presented in Table 7
has been calculated at year 5 when the initial
infrastructure capital debt repayments have
reduced and normal working capital require-
ments account for the lending needs of the
farmers. The full calculations show the same
return on investment from year 5 until year 19
(not presented here). The return on invest-
ment was calculated using the net benefit
after financing divided by the initial capital
outlay. The cash surplus is the net benefit after
financing divided by the irrigable area.
The results of the financial evaluation
show that a commercially operated farm pro-
vides the best net present value (NPV) and
cash surplus. The higher NPV is expected,
since commercial farmers will have higher
returns from their crops. The smallholder
irrigator has the second best NPV for each of
the schemes, except for Ncambedlana, which
provided the best NPV. ‘Commercial under-
utilised’ ranks third in each category.
For normal investment purposes, a nega-
tive NPV would indicate that a project is not
viable in its current form and should be either
abandoned or revised to determine a suitable
strategy for achieving a positive return.
CONCLUSIONS
The higher water use associated with the
commercial LOS results in infrastructure
with greater capacity, but with higher
construction costs and higher annual O&M
costs. The infrastructure for the smallholder
LOS has been reduced to suit its lower needs,
reducing its capital and O&M costs.
The evaluation of the two LOSs has
shown that the capital cost for the com-
mercial LOS is approximately 18% higher
than for the smallholder LOS, and the O&M
costs are 6% to 36% higher. The initial capital
cost may, in some cases, be grant-funded
Table 7 Financial evaluation of each scheme and LOS
Scheme LOSNPV (R)
Net return on investment in year five
Annual cash surplus (R/ha)
Kama Furrow
Commercial –4 391 249 4.06% 17 762
Smallholder –4 794 580 2.41% 8 823
Commercial under-utilised –6 306 129 1.94% 8 98
Wolf River
Commercial 3 265 699 35.34% 20 422
Smallholder 1 685 013 21.69% 12 078
Commercial under-utilised 1 615 857 20.61% 11 909
Ncambedlana
Commercial –8 316 079 1.28% 7 260
Smallholder –1 125 785 2.72% 4 999
Commercial under-utilised –9 340 435 0.39% 2 223
Tamboekiesvlei
Commercial –243 546 8.03% 22 251
Smallholder –250 038 7.21% 13 258
Commercial under-utilised –2 169 384 4.69% 12 988
Mantusini
Commercial 2 244 703 16.13% 20 352
Smallholder 820 951 10.73% 12 224
Commercial under-utilised 555 314 9.58% 12 079
Kruisfontein
Commercial 4 227 572 68.39% 23 034
Smallholder 2 604 644 58.27% 13 801
Commercial under-utilised 2 426 184 40.85% 13 759
Figure 4 Annual O&M cost of water vs scheme area
Co
st o
f w
ate
r (R
/m3)
2.5
0 2010 30 40 6050 70 80 90
Area (ha)
Commercial LOS – pumped
Smallholder LOS – gravity
Small holder LOS – pumped
Commercial under-utilised LOS – pumped
Commercial LOS – gravity
Commercial under-utilised LOS – gravity
2.0
1.5
0.5
1.0
0
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 43
by the government, but the on-going O&M
costs will be funded by the farmer. If farmers
are producing the yields associated with the
different LOSs, they will have no additional
financial burden, as the infrastructure has
been sized to suit that LOS.
The evaluation, even though based on
limited specific projects, provides a general
estimate of possible costs associated with
each scheme type and LOS. As the calcu-
lated costs depend on each scheme’s indi-
vidual requirements and location, they will
not be applicable to every similar scheme.
The schemes that were investigated can be
grouped into five general scheme types:
■ Gravity schemes that need rehabilitation,
where the bulk supply is in place and no
augmentation or rehabilitation is required
(e.g. Kruisfontein)
■ Rehabilitated schemes where water is
supplied from a nearby bulk pipeline and
pumped directly to the lands (e.g. Wolf
River)
■ Run-of-river schemes where water is
abstracted and pumped directly to the
lands (e.g. Mantusini)
■ Run-of-river schemes where water is
abstracted and pumped to storage (e.g.
Ncambedlana)
■ Gravity schemes where bulk supplies
need to be installed (e.g. Tamboekiesvlei
and Kama Furrow)
A summary of the indicative costs of the
different scheme categories is provided in
Table 8.
A a new irrigation system may have been
designed for a commercial LOS because the
designer either had not taken into account
the irrigator type or had expected that the
smallholder irrigator would attain a commer-
cial LOS. If the smallholder irrigator attains
a commercial LOS, they would receive a ben-
efit because the system would cater for the
higher LOS they require. If the irrigator has
neither the desire, necessary skills, mainte-
nance support, sufficient training, access to
credit, nor links to markets needed to attain
a commercial LOS, they would continue to
operate at a smallholder LOS, but with the
additional challenges associated with the
cost of water, due to the over-designed sys-
tem. Where the smallholder irrigator is never
going to achieve a commercial LOS, they will
find they must use a system that is optimised
to neither their skills nor their water needs.
A comparison between the commercial
under-utilised LOS and the smallholder LOS
has shown that the capital cost for commer-
cial under-utilised LOS is 2% to 34% higher,
and the O&M costs 5% to 29% higher, than
for the smallholder LOS. The O&M variation
is higher with the same water use, indicating
that the costs of maintaining the higher cost
infrastructure and of operating higher capa-
city pumps have a significant impact on the
smallholder irrigator.
The smallholder irrigator on a com-
mercial LOS scheme is therefore at a definite
disadvantage to a smallholder irrigator on a
smallholder LOS scheme. Even if the initial
capital costs are grant-funded by govern-
ment, the irrigator must pay higher annual
O&M costs. The higher O&M costs will
directly affect the farmers’ margins and how
much they will profit from the venture. It
could also affect the farmers’ sustainability;
they would need to consolidate land and
manage larger areas to generate greater
profits to overcome their higher O&M costs.
Failure rates of these farmers would also
probably be higher.
A further indication of the cost effective-
ness of the smallholder LOS is illustrated in
the annual O&M costs per cubic metre of
water used. This figure is significant – the
commercial LOS and smallholder LOS have
similar values, showing that their design and
water use are being optimised. The O&M
costs of the commercial under-utilised LOS
are significantly higher, ranging between
5% and 29%. The higher values indicate that
smallholder irrigators using less water on a
commercial LOS are not operating optimally
and their water use is not as cost-effective as
that on the correctly designed schemes.
The financial evaluation provides further
evidence that a commercial scheme offers
little benefit for a smallholder irrigator. The
smallholder irrigator will achieve lower
returns and faces additional risk due to high
debt. Table 8 shows that the commercial
under-utilised LOS provides the lowest NPV,
net return on investment and annual cash
surplus. A summary of the indicative finan-
cial return of the different scheme categories
is provided in Table 9.
RECOMMENDATIONS
To appropriately apply the information
provided by the study, the individual
Table 8 Indicative cost on irrigation schemes
Scheme type
Commercial LOS Smallholder LOS
Capital cost(R/ha)
O&M(R/ha)
Annual cost of water (R/m3)
Capital cost(R/ha)
O&M(R/ha)
Annual cost of water (R/m3)
Pumped – rehabilitation 44 027 2 527 0.30 42 433 2 156 0.36
Run of river – pumped to field 80 089 2 811 0.64 72 352 2 209 0.72
Run of river – pumped to storage 126 877 11 734 1.60 108 704 7 553 1.47
Gravity with bulk supply 163 874 to 155 888 2 503 to 635 0.29 to 0.08 136 886 to 103 488 2 344 to 442 0.38 to 0.08
Gravity – rehabilitation 33 397 213 0.03 23 485 150 0.03
Table 9 Financial evaluation of each scheme type
Scheme type
Commercial LOS Smallholder LOS
NPV (R)
Net return on investment (%)
Annual cash surplus (R/ha)
NPV (R)
Net return on investment (%)
Annual cash surplus (R/ha)
Gravity – rehabilitation 4 227 572 68.39% 23 034 2 604 644 58.27% 13 801
Pumped – rehabilitation 3 265 699 35.34% 20 422 1 685 013 21.69% 12 078
Run of river – pumped to field 2 244 703 16.13% 20 352 820 951 10.73% 12 224
Run of river – pumped to storage –8 316 079 1.28% 7 260 –1 125 785 2.72% 4 999
Gravity with bulk supply –243 546 to –4 391 249 8.03% to 4.06% 22 251 to 17 762 –250 038 to – 4 794 580 7.21% to 2.41% 13 258 to 8 823
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201344
circumstances of each scheme and the farm-
ers involved in it must be understood.
Business farmers are likely to require the
commercial LOS. They are willing to accept
higher risk, have financing to cover the
higher inputs and have market access to sell
their larger amount of produce.
Smallholder farmers will require a design
based on the smallholder LOS, as this is most
suited to a more risk-averse farming style
where inputs are reduced and reliance on out-
side assistance is not an important component.
Understanding the farmer types and the
appropriate LOS allows the results from the
evaluated schemes to be correctly correlated.
The farmer types, anticipated LOS and associ-
ated costs have been incorporated in Table 10.
The design of any scheme must involve
consultation with the end users to determine
their main objectives and ability to manage
risk. Once these have been determined, the
scheme can be designed for an appropriate
LOS and the associated costs can be evalu-
ated. When approaching a new project for
which the farmer type and scheme type have
been determined, Table 10 can be used to
provide a starting point for the anticipated
LOS and associated costs. Site-specific
design and economic calculations will then
need to be completed for the proposed
scheme to determine its capital costs and
financial viability.
REFERENCES
Arcus Gibb 2004a. Eastern Cape Resource-poor Farmers
Irrigation Scheme Feasibility Study: Kama Furrow
final report. Report No PWMA12/000/00/1807,
Pretoria: Department of Water Affairs and Forestry.
Arcus Gibb 2004b. Eastern Cape Resource-poor Farmers
Irrigation Scheme Feasibility Study: Kruisfontein final
report. Report No PWMA12/000/00/1107, Pretoria:
Department of Water Affairs and Forestry.
Arcus Gibb 2004c. Eastern Cape Resource-poor Farmers
Irrigation Scheme Feasibility Study: Mantusini final
report. Report No PWMA12/000/00/1707, Pretoria:
Department of Water Affairs and Forestry.
Arcus Gibb 2004d. Eastern Cape Resource-
poor Farmers Irrigation Scheme Feasibility
Study: Ncambedlana final report. Report No
PWMA12/000/00/2007, Pretoria: Department of
Water Affairs and Forestry.
Arcus Gibb 2004e. Eastern Cape Resource-poor Farmers
Irrigation Scheme Feasibility Study: Tamboekiesvlei
final report. Report No PWMA12/000/00/1007,
Pretoria: Department of Water Affairs and Forestry.
Arcus Gibb 2004f. Eastern Cape Resource-poor Farmers
Irrigation Scheme Feasibility Study: Wolf River final
report. Report No PWMA12/000/00/1907, Pretoria:
Department of Water Affairs and Forestry.
Arcus Gibb 2005. RESIS – The Limpopo programme for
the revitalisation of smallholder irrigation schemes:
A description and critique. Report No 5 of WRC
Project K5/1464/4, East London: Arcus Gibb.
Backeberg, G R 2004. Research management of water
economics in agriculture – An open agenda.
Agrekon, 43(3): 357–374.
Bennie, A T P 1993. Besproeiingswater
Bestuursprogram (BEWAB): Hersiene weergawe.
[Irrigation Water Management Programme, revised
version]. Bloemfontein: University of the Orange
Free State, Department of Soil Science.
Chaminuka, P, Senyolo, G M, Makhura M N & Belete,
A 2008. A factor analysis of access to and use of
service infrastructure amongst emerging farmers in
South Africa. Agrekon, 47(3): 365–378.
Crosby, C T & Crosby, C P 1999. SAPWAT – A comput-
er program for establishing irrigation requirements
and scheduling strategies in South Africa. WRC
Report No. 624/1199, Report to the Water Research
Commission, Pretoria: MSS Consulting Engineers.
Crosby, C T, De Lange, M, Stimie, C M & Van der
Stoep, I 2000. A review of planning and design
procedures applicable to small-scale farmer irriga-
tion projects. WRC Report No 578/2/00, Report to
the Water Research Commission, Pretoria: MSS
Consulting Engineers.
Denison, J D 2005. A comparative analysis of South
African and international irrigation revitalisa-
tion approaches. Report No 10, WRC Project No
K5/1463/4, Pretoria: Water Research Commission.
Denison, J D 2006. Data base on smallholder irrigation
schemes in South Africa. WRC Project No K5/1463/4,
Pretoria: Water Research Commission.
Denison, J D & Manona, S 2006. Principles, approaches
and guidelines for the participatory revitalisation
of smallholder irrigation schemes. Vol 1: A rough
guide for irrigation development practitioners. WRC
Report No TT 308/07, Pretoria: Water Research
Commission.
Doorenbos, J & Pruitt, W O 1977. Guidelines for
Predicting Crop Water Requirements. FAO Irrigation
and Drainage Paper No 24, Rome: Food and
Agriculture Organization of the United Nations.
DWAF (Department of Water Affairs and Forestry)
2004. Policy on the Financial Assistance to Resource-
poor Irrigation Farmers. Pretoria: DWAF.
Fan, S & Zhang, X 2004. Infrastructure and regional
economic development in China. China Economic
Review, 15: 203–214.
Inocencio, A, Kikuchi, M, Tonosaki, M, Maruyama,
A, Merrey, D, Sally, H & De Jong, I 2007. Costs and
performance of irrigation projects: A comparison of
sub-Saharan Africa and other developing regions.
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International Water Management Institute.
Kamara, A B 2004. The impact of market access on
input use and agricultural productivity: Evidence
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202–216.
Nieuwoudt, L & Groenewald, J 2003. The Challenge of
Change: Agriculture, Land and the South African
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265–282.
Perret, S R & Stevens, J B 2003. Analysing the low
adoption of water conservation technologies by
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Van Averbeke, W & Mohamed, S S 2005. Smallholder
farming styles and development policy in South
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Smallholder Agriculture.
Van Averbeke, W & Mohamed, S S 2007. Smallholder
irrigation schemes in South Africa: Past, present and
future. Pretoria: Tshwane University of Technology,
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Smallholder Agriculture.
Table 10 Anticipated cost of irrigation schemes according to farmer type
Farmer type LOS Cost
Scheme type
Gravity – in-field
rehabilitation
Pumped – rehabilitation
Run of river – pumped
to field
Run of river – pumped to storage
Gravity with bulk supply
Commercial (business) farmer
Commercial
Capital cost (R/ha) 33 397 44 027 80 089 126 877 163 874–155 888
O&M (R/ha) 213 2 527 2 811 11 734 2 503–634
Annual cost of water (R/m3) 0.03 0.30 0.64 1.60 0.29–0.08
Smallholder farmer
Smallholder
Capital cost (R x 103/ha) 23 485 42 433 72 352 108 704 136 86–103 488
O&M (R/ha) 150 2 156 2 209 7 553 2 344–441
Annual cost of water (R/m3) 0.03 0.36 0.72 1.47 0.38–0.08
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 45
TECHNICAL PAPER
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 45–59, Paper 792
DR PETRA GAYLARD holds a PhD in Chemistry
and an MSc in Statistics from the University of
the Witwatersrand. This publication arises from
the research report for her MSc in Statistics.
Contact details:
School of Statistics and Actuarial Science
University of the Witwatersrand
Private Bag 3, Wits, 2052
South Africa
T: +27 11 486 4836
F: +27 86 671 9895
PROF YUNUS BALLIM holds BSc (Civil Eng), MSc
and PhD degrees from the University of the
Witwatersrand (Wits). Between 1983 and 1989 he
worked in the construction and precast concrete
industries. He has been at Wits since 1989,
starting as a Research Fellow in the Department
of Civil Engineering and currently holds a
personal professorship. He was the head of the
School of Civil and Environmental Engineering from 2001 to 2005. In 2006 he
was appointed as the DVC for academic aff airs at Wits. He is a Fellow of SAICE.
Contact details:
School of Civil & Environmental Engineering
University of the Witwatersrand
Private Bag 3, Wits, 2052
South Africa
T: +27 11 717 1121
F: +27 11 717 1129
PROF PAUL FATTI is Emeritus Professor of
Statistics at the University of the Witwatersrand
and acts as consultant in Statistics and
Operations Research to a broad range of
industries. He holds a PhD in Mathematical
Statistics from the University of the
Witwatersrand and an MSc in Statistics and
Operational Research from Imperial College,
London. He spent most of his professional career at the University of the
Witwatersrand, including 18 years as Professor of Statistics. His other
employment includes the Chamber of Mines Research Laboratories, the
Institute of Operational Research in London and the CSIR.
Contact details:
School of Statistics and Actuarial Science
University of the Witwatersrand
Private Bag 3, Wits, 2052
South Africa
T: +27 11 880 6957
F: +27 11 788 9943
Keywords: concrete; shrinkage, model prediction, dataset
INTRODUCTION
Shrinkage is an important property of
concrete as it influences the durability,
aesthetics and long-term serviceability of the
concrete, as well as its load-bearing capacity
(Addis & Owens 2005). Thus, the accurate
prediction of shrinkage is important in
the design stage of any concrete structure
(American Concrete Institute 2008). Most
existing shrinkage prediction models do not
take into account the effect of concrete raw
materials, such as different supplementary
cementitious materials and aggregate types.
Furthermore, these models were generally
developed using data derived from non-
South African concretes and thus do not take
into account the effects of local materials,
which may differ substantially from those
used elsewhere.
This paper presents a hierarchical,
non-linear model for predicting the drying
shrinkage of concrete intended for structural
use. Using historical data for shrinkage of
South African concretes, the model was
developed by firstly identifying the most
appropriate nonlinear shrinkage-time growth
curve for individual shrinkage profiles.
Secondly, the parameters of this growth
curve model were fitted to each measured
shrinkage profile individually, in terms of
suitable known covariates (independent
variables), namely, the composition of the
concrete, its other engineering properties, as
well as shrinkage test conditions. The model,
referred to as the WITS model, is therefore
intended to account for the raw materials
used to make the concrete, the composition
of the concrete (expressed through both
the mixture design and the measured
engineering properties of the hardened
concrete), and lastly, the environmental
conditions of exposure when shrinkage
occurred. With reference to the database
of measured shrinkage on South African
concretes that was gathered for this project,
the WITS model was compared to several
shrinkage models that are already in use in
the concrete industry.
The importance of the study is two-fold:
This is the first comprehensive model to
bring together laboratory data on the shrink-
age of concrete generated in South Africa
over a span of around 30 years, identifying
the covariates which are the most important
contributors to both the magnitude and
rate of concrete shrinkage. Secondly, the
concept of hierarchical nonlinear model-
ling (Davidian & Giltinan 1995), as briefly
outlined above, has been applied for the first
time to the modelling of concrete shrink-
age. This approach could prove useful to
other researchers seeking to model concrete
shrinkage and related time-dependent prop-
erties such as creep. Within the limitations
of the study, particularly the use of historical
data, the model provides a starting point
for further, statistically designed, tests and
assessments to more fully explore the effects
of the key variables.
DESCRIPTION OF THE MODEL
A detailed description of the data used in the
study, its limitations and the mathematical
A model for the drying shrinkage of South African concretes
P C Gaylard, Y Ballim, L P Fatti
This paper presents a model for the drying shrinkage of South African concretes, developed from laboratory data generated over the last 30 years. The model, referred to as the WITS model, is aimed at identifying the material variables that are the most important predictors of both the magnitude and rate of concrete shrinkage. In comparison with several shrinkage models already in use in the South African concrete industry, namely the SANS 10100-1, ACI 209R-92, RILEM B3, CEB MC90-99 and GL2000 models, the WITS model exhibited the best performance across a range of goodness-of-fit criteria. The ACI 209R-92 model and the RILEM B3 model showed reasonably good prediction. However, since the B3 model could be used to predict just over two-thirds of the data set, it was thus arguably the best alternative to the WITS model for the South African data set. The SANS 10100-1 model performed poorly in its predictive ability at early drying times. This may indicate that its 30-year predictions are more suited to the South African data set than its six-month predictions.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201346
Figure 1 Summary of the WITS model for concrete shrinkage
ln(γ) = 3.04
+ Cement type factor (choose one cement type):
–0.01 CEM III A GGBS
0 CEM I, CEM II A-D, CEM II A-L, CEM II A-M(L), CEM II A-S, CEM II A-V, CEM II B-M(V/L), CEM II B-S, CEM II B-V, CEM III A GGCS and CEM III A GGFS
0.19 CEM V A
+ Stone type factor (choose one stone type):
0 Andesite, Dolerite, Dolomite, Greywacke, Pretoria Quartzite, Shale, Wits Quartzite
0.01 Quartzite
0.05 Tillite
0.34 Granite
+ Sand type factor ( choose one sand type unless given proportions indicate otherwise):
–2.58 River Vaal (0 to 20%)
–0.44 Wits Quartzite
–0.40 Shale
–0.36 Granite
–0.12 Natural
–0.03 Andesite
0 Cape Flats, Dolomite, Ecca Grit, Pretoria Quartzite, Quartzite (0 to 80%), River (0 to 25%), Tillite (0 to 80%)
0.02 Klipheuwel Pit
0.50 Dolerite
+ 0.16 * ln(cement content in kg/m3)
+ 0.08 * Aggregate/Binder mass ratio
– 0.62 * ln(2*Volume to surface area ratio in mm)
– 0.08 * Temperature
ln(β) = 9.76
+ Cement type factor (choose one cement type):
–0.29 CEM III A GGBS
0 CEM I, CEM II A-D, CEM II A-L, CEM II A-M(L), CEM II A-S, CEM II A-V, CEM II B-M(V/L), CEM II B-S, CEM II B-V, CEM III A GGCS and CEM III A GGFS
0.79 CEM V A
+ Stone type factor (choose one stone type):
–0.32 Tillite
0 Andesite, Dolerite, Dolomite, Greywacke, Pretoria Quartzite, Shale, Wits Quartzite, Quartzite
0.33 Granite
+ Sand type factor ( choose one sand type unless given proportions indicate otherwise):
–0.64 Wits Quartzite
–0.49 Shale
–0.42 Natural
–0.36 Granite
–0.35 River Vaal (0 to 20%)
0 Cape Flats, Dolomite, Ecca Grit, Pretoria Quartzite, Quartzite (0 to 80%), River (0 to 25%), Tillite (0 to 80%)
0.04 Andesite
0.43 Klipheuwel Pit
1.22 Dolerite
+ 0.01 * ln (cement content in kg/m3)
– 0.05 * Aggregate / Binder mass ratio
– 1.76 * ln(2*Volume to surface area ratio in mm)
– 0.26 * Temperature in ºC
α = –2245.19
+ Cement type factor (choose one cement type):
–3.85 CEM V A
0 CEM I, CEM II A-D, CEM II A-L, CEM II A-M(L), CEM II A-S, CEM II A-V, CEM II B-M(V/L), CEM II B-S, CEM II B-V, CEM III A GGCS and CEM III A GGFS
8.63 CEM III A GGBS
+ Stone type factor (choose one stone type):
–43.02 Granite
0 Andesite, Dolerite, Dolomite, Greywacke, Pretoria Quartzite, Shale, Wits Quartzite
211.75 Tillite
302.21 Quartzite
+ Sand type factor ( choose one sand type unless given proportions indicate otherwise):
0 Cape Flats, Dolomite, Ecca Grit, Pretoria Quartzite, Quartzite (0 to 80%), River (0 to 25%), Tillite (0 to 80%)
99.54 Andesite
134.27 Dolerite
139.92 Klipheuwel Pit
170.57 Natural
201.75 Granite
260.15 Wits Quartzite
321.77 Shale
43.08 River Vaal (0 to 20%)
+ 55.71 * ln (cement content in kg/m3)
+ 2.54 * Water content in kg/m3
– 0.05 * Stone content in kg/m3
+ 25.35 * Aggregate/Binder mass ratio
+ 173.17 * ln(2*Volume to surface area ratio in mm)
+ 44.34 * Temperature in ºC
Mean shrinkage strain in the cross-section: εsh(t – t0) = α(1 – e–β(t–t0))γ
Ranges covered by the model:
Cement content: 112–536 kg/m3
Water content: 160–225 kg/m3
Aggregate/Binder ratio: 3.18–8.74
Stone content: 900–1400 kg/m3
2*Volume to surface area ratio: 16.5–75.0
Temperature: 21–25ºC
Humidity: 43–72%
For combinations of cement, stone and sand covered by the model, see Table 1.
Abbreviations:
GGBS Ground Granulated Blast-furnace Slag
GGCS Ground Granulated Corex Slag
GGFS Ground Granulated Ferro-manganese Slag
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 47
development of the model is given in an
associated publication (Gaylard et al 2012). A
key limitation of the data set must be noted
here, which is that the individual studies
making up the data set were not necessarily
carried out with the development of a model
for shrinkage as the main aim. This has
two consequences. Firstly, not all important
factors affecting shrinkage were varied over
sufficiently wide ranges. In fact, some factors
were kept constant because they were known
to have a significant effect on shrinkage,
most notably the levels of environmental
temperature and humidity maintained
during the shrinkage tests. Secondly, not all
data required for this study was recorded in
some of the studies making up the data set.
High levels of missing data led to certain
potentially useful covariates (for example
the 28-day compressive strength and elastic
modulus of the concrete) being excluded
for consideration as part of the model.
However, a model can still be developed with
these limitations in mind, and can then be
enhanced by further, designed, experiments
to include such factors.
The form of the growth curve model
selected is given by
εsh(t – t0) = α(1 – e–β(t–t0))γ (1)
where εsh(t – t0) is the mean shrinkage strain
in the cross-section (in microstrain) at dry-
ing time t – t0 (in days) (where t is the age
of the concrete and is the age at first drying
in days), α represents the ultimate shrinkage
(when (t – t0) is very large), β represents the
rate of shrinkage development with time and
γ is a growth curve shape parameter which
does not have a direct physical interpreta-
tion. The parameters α, β and γ in turn
depend on known properties of the concrete,
namely its composition, its other engineering
properties and the shrinkage test conditions.
The types and combinations of cement,
stone and sand covered by the WITS model
are given in Table 1. These are limited to the
data which was available for the derivation of
the model. The model parameters are given
in Figure 1.
The operation of the model therefore
requires that the user has to calculate
the appropriate values of α, β and γ from
Figure 1. These values are then substituted
into Equation 1 to produce a shrinkage-time
relationship for the particular concrete under
consideration.
To give an indication of the fit of the
model to the raw data, the two shrinkage
profiles with predicted values of α closest to
the observed asymptote (long-term shrink-
age), as well as the two shrinkage profiles
with predicted values of α furthest from the
Table 1 Types, levels and combinations of cement, stone and sand covered by the WITS model
Stone type
Cement type
CE
M I
CE
M I
I A
-D
CE
M I
I A
-L
CE
M I
I A
-M(L
)
CE
M I
I A
-S
CE
M I
I A
-V
CE
M I
I B
-M (
V/L
)
CE
M I
I B
-S
CE
M I
I B
-V
CE
M I
II
A CE
M V
A
Andesite √ √ √ √ √ √ √ √ √
Dolerite √ √ √ √ √ √ √ √
Dolomite √ √ √
Granite √ √ √ √
Greywacke √ √ √ √
Pretoria Quartzite √
Quartzite √
Shale √
Tillite √ √ √ √
Wits Quartzite √ √
Sand type
Cement type
CE
M I
CE
M I
I A
-D
CE
M I
I A
-L
CE
M I
I A
-M(L
)
CE
M I
I A
-S
CE
M I
I A
-V
CE
M I
I B
-M (
V/L
)
CE
M I
I B
-S
CE
M I
I B
-V
CE
M I
II
A CE
M V
A
Andesite √
Cape Flats √ √ √
Dolerite √ √ √ √
Dolomite √ √ √ √ √ √ √
Ecca grit √
Granite √ √ √ √ √ √ √ √
Klipheuwel pit √ √
Natural √ √ √ √
Pretoria Quartzite √
Quartzite (up to 80%*) √
River (up to 25%*) √ √
River Vaal (up to 20%*) √ √ √ √
Shale √
Tillite (up to 80%*) √ √ √ √
Wits Quartzite √ √
* indicates maximum proportion of sand type in total sand content
Sand Type
Stone Type
An
de
site
Do
leri
te
Do
lom
ite
Gra
nit
e
Gre
y-w
ack
e
Pre
tori
a
Qu
art
zit
e
Qu
art
zit
e
Sh
ale
Til
lite
Wit
s Q
ua
rtz
ite
Andesite √
Cape Flats √
Dolerite √
Dolomite √ √
Ecca grit √
Granite √ √
Klipheuwel pit √
Natural √ √
Pretoria Quartzite √
Quartzite √
River √
River Vaal √ √ √ √ √ √ √ √
Shale √
Tillite √
Wits Quartzite √ √
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201348
observed asymptote, from the experiments
in the data set, are shown in Figure 2. The
American Concrete Institute (2008) notes
that the variability of shrinkage test mea-
surements prevents models from matching
measured data closely, and it is thus unreal-
istic to expect results from shrinkage predic-
tion models to be within less than 20% of the
test data. In this case, the two predicted pro-
files exhibiting the largest deviations from
the raw data (Figure 2 (c) and (d)) show the
last data points having deviations of 16.2%
and 22.9%, respectively, which indicates that
the model lies in the range of acceptable
prediction.
The covariates (independent variables)
which have the most significant effect on the
parameters α, β and γ are listed in descend-
ing order in Table 2.
With reference to Table 2, we first con-
sider the material parameters that influence
the dependent variable α, which represents
the ultimate shrinkage. The different sand
types feature very strongly in the model,
with three sand types (granite, natural and
Wits Quartzite) making the largest contri-
bution to high values of α. All seven sand
types which were found to be significant had
positive coefficients relative to the reference
sand type, dolomite, which is considered to
be the sand type showing the lowest shrink-
age of the aggregates covered by this study
(Alexander 1998). This is not an unexpected
result, since a number of researchers have
shown the strong influence of aggregate
type on concrete shrinkage (Roper 1959;
Alexander 1998; Ballim 2000). Such research
indicates that this effect is due to the shrink-
age of the aggregate itself, the stiffness of the
aggregate and the surface characteristics of
the aggregate in modifying the aggregate-
cement paste interface in concrete.
The next most important parameter
influencing the variable α was the environ-
mental temperature. As expected, a higher
temperature leads to a higher ultimate
Table 2 The ranking of the significant terms for each of the three parameters α, β and γ for the
WITS model
α ln(β) ln(γ)
Sand Granite (+)*
Sand Natural (+)
Sand Wits Quartzite) (+)
Temperature (+)
Sand Klipheuwel Pit (+)
Aggregate/Binder Ratio (+)
ln(2*Volume to Surface Area)(+)
Sand Shale (+)
Stone Tillite (+)
Stone Quartzite (+)
Water Content (+)
Sand River Vaal (+)
Sand Andesite (+)
ln(2*Volume to Surface Area) (–)
Temperature (–)
Sand Dolerite (+)
Sand Natural (–)
Sand Klipheuwel pit (+)
Sand Wits Quartzite (–)
Sand Granite (–)
Cement CEM III A GGBS (–)
Cement CEM V A (+)
Stone Content (–)
Stone Granite (+)
Sand Shale (–)
Sand River Vaal (–)
ln(2*Volume to Surface Area) (–)
Aggregate/Binder Ratio (+)
Sand Granite (–)
Sand Wits Quartzite (–)
Temperature (–)
Stone Granite (+)
Sand Dolerite (+)
Stone Content (–)
Sand Shale (–)
* The sign of the coefficient is indicated.
Figure 2 Mean (solid line) and 95% confidence interval (dashed line) predictions for the two shrinkage profiles with predicted values of α ((a) and (b))
closest to the observed asymptote and ((c) and (d)) furthest from the observed asymptote
Sh
rin
ka
ge
(mic
rost
rain
)700
600
500
400
300
200
100
01 000100101
Time (days
WITS#0225(a)
Sh
rin
ka
ge
(mic
rost
rain
)
700
600
500
400
300
200
100
01 000100101
Time (days
WITS#0228(b)
Sh
rin
ka
ge
(mic
rost
rain
)
700
600
500
400
300
200
100
01 000100101
Time (days
WITS#0214(c)
Sh
rin
ka
ge
(mic
rost
rain
)
700
600
500
400
300
200
100
01 000100101
Time (days
WITS#0032(d)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 49
shrinkage. The effect of the aggregate-binder
ratio may be understood in terms of the
restraining effect of the aggregate volume
(Alexander & Mindess 2005). The specimen
size effect (as represented by the ratio of
the volume to the surface area of the speci-
men) is unexpected: the positive sign of the
coefficient suggests that specimens with a
lower surface area available for moisture
loss, relative to their volume, are expected to
reach higher levels of ultimate shrinkage. It
must be noted that this variable was subject
to some multi-collinearity (mostly with sand
type dolerite and temperature) and thus the
meaning of the magnitude and sign of the
coefficient should not be over-interpreted
(Gaylard et al 2012). This is certainly an
aspect requiring further investigation.
The two stone types which were found
to have a significant effect on α had positive
coefficients relative to the reference stone
type, andesite. Given the range of stone
types for which sufficient data was available,
andesite stone concretes showed the lowest
shrinkage, and andesite was therefore used
as the reference stone. Finally, the water
content of the concrete also plays a role in
influencing ultimate shrinkage. As expected,
increasing the water content of the concrete
mix increases the ultimate shrinkage.
Much less is known about the factors
which influence the rate of shrinkage.
However, the significant terms in the regres-
sion equation for ln(β), which represents the
rate of shrinkage development with time,
may be interpreted as follows: As expected,
the specimen size effect is the strongest con-
tributor to the rate of shrinkage development
with time – specimens with a higher surface
area available for moisture loss, relative to
their volume, lose moisture more rapidly.
The rate of shrinkage decreases with increas-
ing temperature. This is unexpected, but is
likely to be linked to the very narrow range
of temperatures covered by this study (21–
25ºC) as a result of the near-constant labora-
tory conditions under which the shrinkage
experiments were carried out. Sand type
plays an important role in determining the
rate of shrinkage. In contrast to the findings
for the ultimate shrinkage, here the signs of
coefficients for the different sand types are
both positive and negative. A few cement
types have an effect on the rate of shrinkage.
Cements with high levels (36–65%) of GGBS
(i.e. CEM III A) appeared to slow the rate of
shrinkage. The effect was not statistically
significant for comparable concretes contain-
ing Corex or Ferro-manganese slag. Cements
containing both GGBS (18-30%) and fly
ash (18–30%) (i.e. CEM V A) appeared to
increase the rate of shrinkage. Increasing
stone content decreases the rate of shrinkage,
Figure 3 An illustration of the effects of the different model parameters, α, β and γ, in modifying
the rate and magnitude of predicted concrete shrinkage development by the WITS model
Sh
rin
ka
ge
(mic
rost
rain
)
700
600
500
400
300
200
100
01 000100101
Drying time (days)
α = 450, β = 0.02, γ = 0.40 α = 450, β = 0.02, γ = 0.90
α = 450, β = 0.02, γ = 0.65
α = 650, β = 0.02, γ = 0.65
α = 650, β = 0.03, γ = 0.65
α = 650, β = 0.01, γ = 0.65
α = 250, β = 0.02, γ = 0.65
Table 3 Covariates included in the published models as well as the WITS model
Covariates
Model
AC
I 2
09
R-9
2
RIL
EM
B
3
CE
BM
C9
0-9
9
GL
20
00
SA
NS
1
01
00
-1
Eu
ro-
cod
e 2
WIT
S
Concrete raw materials and composition:
Cement type * √ √ √ √ √
Cement content √ * √
Water content √ √ √
Water / cement mass ratio *
Air content √
Sand type √
Stone type √
Stone content √
Sand / total aggregate mass ratio √
Aggregate / cement mass ratio *
Aggregate / binder mass ratio √
Testing conditions:
Curing method * √ *
Age at first drying √ √ *
Specimen shape √
Specimen volume to surface area ratio √ √ √ √ √
Specimen ratio of cross-sectional area to exposed perimeter √ √
Temperature * * √
Humidity √ √ √ √ √ √
Concrete properties:
28-day compressive strength √ √ √ √
28-day elastic modulus √
Slump √
The symbol √ denotes that the covariate is required for model prediction calculations, while the symbol * denotes that the covariate is only required to assess the applicability of the model
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201350
presumably due to the restraining effect of
the aggregate. One stone type, granite, was
found to increase the rate of shrinkage rela-
tive to the reference stone type, andesite.
The growth curve shape parameter ln(γ)
itself is difficult to interpret in the context
of the growth curve equation, and thus its
interpretation in terms of the significant
covariates is even more difficult and was not
attempted.
By way of illustration, Figure 3 shows a
range of shrinkage profiles that are obtained
with the model proposed here, using values
of α, β and γ that lie within the range of
values for the data set used in developing
the model. Figure 3 shows the effects of
the different model parameters in varying
both the rate and magnitude of shrinkage
development.
COMPARISON OF THE WITS MODEL
TO OTHER PUBLISHED MODELS
FOR CONCRETE SHRINKAGE
In the published literature, the most thorough
model comparisons have been based on the
RILEM data bank, a collection of 490 con-
crete shrinkage profiles mainly from North
American and European research groups
(Bažant & Li 2008). The RILEM B3 model
was developed on an older version of the
current RILEM data bank (Bažant & Baweja
1996; Bažant 2000). In this study, model
comparisons were based on the local data set,
which may be considered as a smaller, South
African, version of the RILEM data bank.
Five published models were used as
comparisons to the WITS model developed
in this study:
■ The ACI 209R-92 model developed by the
American Concrete Institute (1982)
■ The RILEM B3 model developed by
Bažant and co-workers (Bažant & Baweja
1996; Bažant 2000)
Table 4 Ranges of applicability for the published models as well as the WITS model
Constraints
Model
ACI209R-92
RILEMB3
CEBMC90-99
GL2000 SANS 10100-1 Eurocode 2 WITS
Concrete raw materials and composition:
Cement type Type I and III Type I, II and III see Table 1
Cement content 279–446 kg/m3 160–720 kg/m3 112–536 kg/m3
Water content 150–230 kg/m3 160–225 kg/m3
Water / cement mass ratio 0.35–0.85
Aggregate / cement mass ratio 2.5–13.5
Aggregate / binder mass ratio 3.18–8.74
Sand type see Table 1
Stone type see Table 1
Stone content 900–1400 kg/m3
Testing conditions:
Curing method and timemoist: ≥ 1 day
or steam: 1–3 days
moist: ≥ 1 day or steam
moist ≤ 14 daysmoist: ≥ 1 day
or steam
Specimen volume to surface area ratio1.2*exp
(–0.00472*V/S) ≥ 0.2
16.5–75.0
Specimen ratio of cross-sectional area to exposed perimeter
Temperature 21.2–25.2ºC 10–30ºC 21–25ºC
Humidity 40–100% 40–100% 40–100% 20–100% 20–100% 20–100% 43–72%
Concrete properties:
28-day (cylinder) compressive strength 17–70 MPa 15–120 MPa 16–82 MPa 20–90 MPa
Figure 4 The percentage of the data set which could be predicted by each of the models
Pre
dic
tio
n m
od
el
WITS (data used for model)
WITS (data not used for model)
WITS (all data)
ACI 209
RILEM B3
CEB MC90-99
GL2000
Eurocode 2
SANS 10100-1
Percentage of data set predicted by model
100806040200
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 51
■ The CEB MC90-99 model developed by
the Comité European du Beton (1999)
■ The GL2000 model developed by Gardner
and Lockman (2001)
■ The SANS 10100-1 model adopted by the
South African Bureau of Standards (2000)
■ The Eurocode 2 (EN 1992-1-1) model
adopted by the European Committe for
Standardization (2003).
The covariates (other than drying time) used
in each of these models are given in Table 3
and the ranges of applicability of each model
are summarised in Table 4. The ranges of
applicability of the WITS model given in
Table 4 are equivalent to the ranges of the
data used in fitting the model. However, the
actual ranges of applicability could well be
wider.
A predicted shrinkage profile was cal-
culated for each model, including the WITS
model, for each qualifying experiment in the
data set (in terms of the range of applicabil-
ity of each model – see Table 4), and the
goodness-of-fit of these predictions to the
actual data was assessed. Since the WITS
model was also derived from this data set, its
assessments were divided into two groups,
namely the experiments used to derive the
model, and the experiments which qualified
to be predicted by the model but which were
not used to derive the model as a result of
poor quality data, for example shrinkage
profiles which had not reached any indication
of their long-term shrinkage value by the time
measurements ceased. Combined goodness-
of-fit statistics for the two groups are also
Figure 5 Illustration of the fit of the models to six experiments in the data set. The experiments illustrated in (a) to (d) were part of the data set used
to derive the WITS model, while the experiments illustrated in (e) and (f) were not
700
600
500
400
300
200
100
01 000100101
WITS
#0115
(a)
Sh
rin
ka
ge
(mic
rost
rain
)
Time (days)
ACI 209 RILEM B3 CEB MC90-99
GL2000 SANS 10100-1Eurocode 2
700
600
500
400
300
200
100
01 000100101
WITS
#0117
(b)
Sh
rin
ka
ge
(mic
rost
rain
)
Time (days)
ACI 209 RILEM B3 CEB MC90-99
GL2000 SANS 10100-1Eurocode 2
700
600
500
400
300
200
100
01 000100101
WITS
#0181
(c)
Sh
rin
ka
ge
(mic
rost
rain
)
Time (days)
RILEM B3 CEB MC90-99
GL2000 SANS 10100-1
Eurocode 2
700
600
500
400
300
200
100
01 000100101
WITS
#0082
(d)
Sh
rin
ka
ge
(mic
rost
rain
)
Time (days)
ACI 209 RILEM B3
GL2000 SANS 10100-1
Eurocode 2
700
600
500
400
300
200
100
01 000100101
WITS
#0007
(e)
Sh
rin
ka
ge
(mic
rost
rain
)
Time (days)
ACI 209 RILEM B3
GL2000 SANS 10100-1
Eurocode 2
700
600
500
400
300
200
100
01 000100101
WITS
#0024
(f)
Sh
rin
ka
ge
(mic
rost
rain
)
Time (days)
ACI 209 RILEM B3
GL2000 SANS 10100-1
Eurocode 2
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201352
presented. The ACI 209R-92, RILEM B3, CEB
MC90-99 and GL2000 models were imple-
mented according to the model specifications
given in the American Concrete Institute
Committee 209’s guide for modelling and
calculating shrinkage and creep in hardened
concrete (American Concrete Institute 2008).
In the ACI 209R-92 model, the air content was
set at the standard value of 6%, making the air
content factor equal to one, since data on this
variable was not available. For the RILEM B3,
CEB MC90-99, GL2000 models, 28-day cube
compressive strengths were converted to the
corresponding cylinder strengths using the
conversion table given in the British Standard
Common Rules for Buildings and Civil
Engineering Structures (British Standards
Institution 2004). The effective section thick-
nesses of most of the specimens used in the
study were smaller than the minimum value
of 100 mm presented in the Eurocode 2 model
(European Committee for Standardization
2003). The values given in the standard were
thus extrapolated to the required effective
section thickness to determine the required
value of the coefficient kh:
kh = 1.2 – 0.00225h0 + 0.0000025h20
(R2 = 0.999)
where h0 is the effective section thickness.
The SANS 10100-1 model was implemented
according to the South African Bureau of
Standards SANS 10100-1 standard (2000) for
the prediction of shrinkage in concrete. The
effective section thicknesses of the speci-
mens used in this study were smaller than
the minimum value of 150 mm presented in
the SANS 10100-1 model. The values given
in the standard were thus extrapolated to
the required effective section thickness (and
interpolated to the required relative humid-
ity) by applying separate quadratic models
(for the six-month and 30-year shrinkage)
fitted to the shrinkage data read from the
nomograph at relative humidities of 40, 50,
60, 70 and 80% and effective section thick-
nesses of 150, 300 and 600 mm:
6-month shrinkage (microstrain)
= 314.0 + 1.035H – 1.025u + 0.003494Hu
– 0.02962H2 + 0.0007302u2 (R2 = 0.994) (2)
30-year shrinkage (microstrain)
= 395.6 + 6.231H – 0.6173u + 0.003239Hu
– 0.09595H2 + 0.0002922u2 (R2 = 0.994) (3)
where H is the humidity in % and u is the
effective section thickness in mm.
After correction for the water content of
the concrete, the predicted six-month and
30-year shrinkage values were used to deter-
mine the time-shift factor, α, in the hyper-
bolic growth curve (Gilbert 1988; Ballim
1999) used to determine the shrinkage at
other drying times:
εsh(t – t0) = t
α + t ∙ εsh(30 years) (4)
where
α = 183 days ∙ εsh(30 years) – εsh(6 months)
εsh(6 months) (5)
Firstly the proportion of the data set which
could be predicted by a particular model
was determined. This analysis is presented
in Figure 4. As a result of its minimalist
input requirements, the SANS 10100-1
model could be used to predict all the
experiments in the data set. The WITS
model had the next highest proportion of
experiments which could be predicted (87%).
Those experiments which did not qualify,
failed to do so mostly because they used
aggregate types which were not included in
the derivation of the model or because of the
poor quality of the shrinkage data, some-
times showing significant but unexplained
deviations from the characteristic shrinkage
development curve. Of this 87%, just over
three-quarters of the data had been used
in the development of the model, while the
rest (47 experiments) had been excluded
from model development because the data
was insufficient to allow a realistic predic-
tion of the ultimate shrinkage, but these
experiments still qualified for prediction by
the model. This latter set can thus not be
regarded as a true validation data set since
it comprises poor quality data compared to
the overall data set. In the discussions which
follow, reference to the WITS model includes
consideration of all three subsets of data
unless specifically indicated otherwise. The
other models were able to predict lower pro-
portions of the data set due to a combination
of missing data and experiments not meeting
the qualifying criteria.
The fit of the various models to six
shrinkage profiles is illustrated in Figure 5.
The illustrated profiles were randomly
selected from the 57 experiments to which
five or all six of the models could be fit-
ted. While the selection of the experiments
was random, some effort was made to
select experiments which spanned the range
of shrinkage profiles in both magnitude
and rate of shrinkage development. The
full database containing the concrete
details and shrinkage results for the 290
experiments used in this study is available at
www.cnci.org.za for download at no cost.
It is clear from Figure 5 that the WITS
model performed well, which was to be
expected since the model was derived from
the data. The SANS 10100-1 and GL2000
models tended to under- and over-predict,
respectively. No particular trend regarding
the performance of the other models is
immediately obvious from an inspection of
the results in Figure 5.
Many goodness-of-fit measures have been
used by different researchers in the develop-
ment of models for concrete shrinkage. The
American Concrete Institute (2008) is of the
opinion that “the statistical indicators avail-
able are not adequate to uniquely distinguish
Table 5 Parameters of the linear relationship between the actual and predicted shrinkage values
for the models
Model nAdjusted
R2
Slope(95% confidence
interval)
Intercept(95% confidence
interval)
WITS (data used for model development)
2 603 0.920.97
(0.96–0.99)18
(15–21)
WITS (data NOT used for model development)
483 0.870.89
(0.86–0.92)19
(11–27)
WITS (all data) 3 086 0.910.96
(0.95–0.97)18
(15–21)
ACI 209R-92 850 0.710.96
(0.92–1.0)53
(42–64)
RILEM B3 2 581 0.670.73
(0.71–0.75)17
(10–23)
CEB MC90-99 868 0.760.62
(0.59–0.64)–6
(–16–4)
GL2000 3 005 0.530.52
(0.50–0.54)39
(31–46)
SANS 10100-1 3 376 0.591.08
(1.05–1.11)118
(113–123)
Eurocode 2 2 903 0.540.69
(0.66–0.71)34
(27–42)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 53
Figure 6 Plots of the actual vs predicted shrinkage values for the models
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
800
800
800
800
800
800
800
800
800
600
600
600
600
600
600
600
600
600
400
400
400
400
400
400
400
400
400
200
200
200
200
200
200
200
200
200
0
0
0
0
0
0
0
0
0
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
800
800
800
800
800
800
800
800
800
200
200
200
200
200
200
200
200
200
0
0
0
0
0
0
0
0
0
Ac
tua
l sh
rin
ka
ge
(mic
rost
rain
)A
ctu
al
shri
nk
ag
e (m
icro
stra
in)
Ac
tua
l sh
rin
ka
ge
(mic
rost
rain
)A
ctu
al
shri
nk
ag
e (m
icro
stra
in)
Ac
tua
l sh
rin
ka
ge
(mic
rost
rain
)
Ac
tua
l sh
rin
ka
ge
(mic
rost
rain
)A
ctu
al
shri
nk
ag
e (m
icro
stra
in)
Ac
tua
l sh
rin
ka
ge
(mic
rost
rain
)A
ctu
al
shri
nk
ag
e (m
icro
stra
in)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
600
600
600
600
600
600
600
600
600
400
400
400
400
400
400
400
400
400
WITS (data used for model)
WITS (all data)
CEB MC90-99
GL2000
Eurocode 2
WITS (data not used for model)
ACI 209R-92
RILEM B3
SANS 10100-1
The line of equality is shown in red
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201354
Figure 7 Plots of the actual vs predicted shrinkage values, on a log scale, for the models
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
100
100
100
100
100
100
100
100
100
10
10
10
10
10
10
10
10
10
0
0
0
0
0
0
0
0
0
1 000
1 000
1 000
1 000
1 000
1 00010
10
10
10
10
10
10
10
10
1
1
1
1
1
1
1
1
1
Ac
tua
l sh
rin
ka
ge
(mic
rost
rain
)
Ac
tua
l sh
rin
ka
ge
(mic
rost
rain
)A
ctu
al
shri
nk
ag
e (m
icro
stra
in)
Ac
tua
l sh
rin
ka
ge
(mic
rost
rain
)A
ctu
al
shri
nk
ag
e (m
icro
stra
in)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
Predicted shrinkage (microstrain)
100
100
100
100
100
100
100
100
100
WITS (data used for model)
WITS (all data)
CEB MC90-99
GL2000
Eurocode 2
WITS (data not used for model)
ACI 209R-92
RILEM B3
Ac
tua
l sh
rin
ka
ge
(mic
rost
rain
)A
ctu
al
shri
nk
ag
e (m
icro
stra
in)
Ac
tua
l sh
rin
ka
ge
(mic
rost
rain
)A
ctu
al
shri
nk
ag
e (m
icro
stra
in)
SANS 10100-1
The line of equality is shown in red
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 55
between models”. Given this concern, it was
thought best to use a broad range of these
measures, both graphical and numerical,
to assess the relative performance of the
different models. Where possible, a critical
assessment of these measures from a statisti-
cal point of view is also given.
Plots of the actual versus predicted
shrinkage values are shown in Figure 6.
The points from an ideal model would lie
entirely on the line of equality. Bažant et al
(Bažant & Baweja 1995; Bažant 2000) recom-
mend focusing on the longer drying times,
where predictions are most important, since
such plots are typically dominated by data
gathered at short drying times. For most
concrete engineering projects, designers are
more concerned with long-term shrinkage.
However, this is not to say that early-age
shrinkage is unimportant. For example,
prediction of early-age shrinkage would be
very important in post-tensioned, prestressed
concrete structures. The results in Figure 6
show that the WITS model, particularly at
longer drying times, remained closest to the
line of equality, thus indicating the best fit to
the data. The adjusted R2, as well as the slope
and intercept, of the fitted lines to the plots
are given in Table 5. A good model would
have a slope close to 1 and an intercept close
to 0, as well as a high adjusted R2 value.
The WITS model exhibited the least scatter
(highest R2) and the slope closest to 1, while
its intercept was the third closest to zero of
all the models. This is to be expected, since
a large proportion of the data was used to
develop the WITS model.
Nevertheless, it is interesting to note
that the international models generally
over-predict the shrinkage of South African
concretes. This may be related to the fact
that South African concretes are generally
made with crushed aggregates, resulting in
a higher water demand than many northern
hemisphere concretes where natural gravels
are more commonly used as aggregates. On
balance of the three regression criteria, the
CEB MC90-99 and ACI 209R-92 models
performed the next best. The over-prediction
by the RILEM B3, ACI 209R-92, CEB MC90-
99, Eurocode 2 and GL2000 models, as well
as the under-prediction by the SANS 10100-1
model, was evident from both the plots and
the regression statistics.
Plots of the actual versus predicted
shrinkage values on a log scale are also
useful since they illustrate the relative
errors, which should decrease as shrinkage
strain increases as a consequence of the
homoscedasticity of errors (Bažant & Baweja
1995; Bažant 2000). These plots, and the
parameters of their fitted lines, are shown in
Figure 7 and Table 6 respectively. The WITS
model was again closest to the unity line and
exhibited the least scatter, indicating it to
be the best model when viewed according to
these criteria. The RILEM B3 model exhib-
ited more scatter of the data around the line
of equality (i.e. greater positive and negative
residuals) at longer drying times than the
WITS model, while the performance of the
other models was worse.
In the above analysis of the results, all the
concretes were allocated the same weight-
ing. Of course, this unreasonably weights
the older, lower-strength concretes, which
exhibit higher levels of shrinkage strain at a
given drying time. To correct for this, plots
of actual versus predicted shrinkage values
were both multiplied by:
fc28,i
fc28,av
where fc28,i is the 28-day compressive
strength for the experiment and fc28,av is
the average 28-day compressive strength for
the data set (Bažant & Baweja 1995; Bažant
2000). This effectively normalised shrinkage
according to compressive strength. However,
this analysis did not change the conclusion
that the WITS model performed the best,
while the RILEM B3 and ACI 209R-92 mod-
els exhibited the next best performance.
Plots of the differences between mea-
sured and predicted shrinkage (residuals)
against Log10(time) are shown in Figure 8.
These residuals should not fan out (indicat-
ing increased deviation of a model from the
raw data at longer drying times – where
prediction is more important) or show any
other obvious pattern or trend (McDonald &
Roper 1993, Al-Manaseer & Lam 2005). The
over- and under-prediction of the different
models, as discussed previously, can clearly
be seen in these plots. The mean residuals
for the WITS model were the closest to zero
and the most consistent across the different
intervals of drying time, whereas the abso-
lute values of the mean residuals of the other
models tended to increase with drying time.
The ACI 209R-92 and RILEM B3 models
exhibited the next best performance on this
criterion.
A MORE DETAILED ANALYSIS
OF VARIATION
In order to further assess the suitability
of the proposed WITS model, a range of
numerical goodness-of-fit summary statistics
were determined. Bažant’s coefficient of
variation, ωBP (Bažant & Baweja 1995; Bažant
2000, Al-Manaseer & Lam 2005) for all the
data, as well as that calculated separately
for three time intervals (on a log10 scale)
spanned by the shrinkage profiles, for the
different models is shown in Table 7. The
WITS model exhibited the lowest coefficient
of variation overall, as well as across all three
intervals of drying time, followed by the ACI
209R-92 model. The coefficient of variation
of the WITS model, calculated on the South
African data set from which the model was
derived, was found to be 27%. This compares
favourably to the 34% coefficient of variation
for the RILEM B3 model calculated on the
RILEM database, from which it was derived
(Bažant 2000). This said, it should be noted
that the RILEM model was developed on a
Table 6 Parameters of the linear relationship between the actual and predicted shrinkage values,
on a log scale, for the models
Model nAdjusted
R2
Slope(95% confidence
interval)
Intercept(95% confidence
interval)
WITS (data used for model development)
2 603 0.860.96
(0.94–0.97)0.11
(0.08–0.14)
WITS (data NOT used for model development)
483 0.840.76
(0.73–0.79)0.55
(0.48–0.62)
WITS (all data) 3 086 0.850.93
(0.91–0.94)0.18
(0.15–0.22)
ACI 209R-92 850 0.670.70
(0.67–0.74)0.76
(0.67–0.84)
RILEM B3 2 579 0.681.06
(1.03–1.09)–0.29
(–0.36––0.22)
CEB MC90-99 868 0.671.33
(1.27–1.39)–1.1
(–1.3––0.96)
GL2000 3 005 0.591.04
(1.01–1.07)–0.35
(–0.43––0.28)
SANS 10100-1 3 374 0.710.54
(0.53–0.55)1.31
(1.28–1.33)
Eurocode 2 2 906 0.620.85
(0.82–0.87)0.24
(0.18–0.30)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201356
Figure 8 Plots of the residuals vs log10 (time) for the models
700
700
700
700
700
700
700
700
700
100
100
100
100
100
100
100
100
100
–300
–300
–300
–300
–300
–300
–300
–300
–300
–700
–700
–700
–700
–700
–700
–700
–700
–700
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
1 000
10
10
10
10
10
10
10
10
10
1
1
1
1
1
1
1
1
1
Re
sid
ua
lsR
esi
du
als
Re
sid
ua
lsR
esi
du
als
Re
sid
ua
ls
Re
sid
ua
lsR
esi
du
als
Re
sid
ua
lsR
esi
du
als
Drying time (days)
Drying time (days)
Drying time (days)
Drying time (days)
Drying time (days)
Drying time (days)
Drying time (days)
Drying time (days)
Drying time (days)
100
100
100
100
100
100
100
100
100
WITS (data used for model)
WITS (all data)
CEB MC90-99
GL2000
Eurocode 2
WITS (data not used for model)
ACI 209R-92
RILEM B3
SANS10100-1
–100
–100
–100
–100
–100
–100
–100
–100
–100
–500
–500
–500
–500
–500
–500
–500
–500
–500
500
500
500
500
500
500
500
500
500
300
300
300
300
300
300
300
300
300
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 57
Table 7 Summary of the numerical goodness-of-fit statistics calculated for the models
Model
WITS(data used for model
development)
WITS(data NOT
used for model development)
WITS(all data)
ACI209R-92
RILEMB3
CEBMC90-99
GL2000SANS
10100-1Eurocode
2
Bažant’s coefficient of variation
ωBP (overall) (%) 25 35 27 49 84 84 130 76 73
ωBP (1-9 days) (%) 37 45 39 70 76 133 136 105 100
ωBP (10-99 days) (%) 21 25 22 36 49 59 87 75 57
ωBP (100-999 days) (%) 13 20 13 33 40 71 67 48 40
CEB coefficient of variation
VCEB (overall) (%) 22 32 23 43 54 83 95 63 62
VCEB (0-10 days) (%) 37 45 39 68 75 126 135 104 98
VCEB (11-100 days) (%) 21 25 21 36 49 58 86 74 57
VCEB (101-365 days) (%) 13 20 14 33 36 57 58 53 36
VCEB (366-730 days) (%) 13 13 18 50 79 87 22 49
VCEB (731-1095 days) (%) 15 15 54 77 93 5 52
CEB mean square error
FCEB (overall) (%) 35 34 34 38 141 174 212 53 126
FCEB (0-10 days) (%) 70 45 66 55 293 356 426 84 247
FCEB (11-100 days) (%) 24 30 25 38 76 89 135 66 99
FCEB (101-365 days) (%) 15 24 17 33 45 65 85 45 48
FCEB (366-730 days) (%) 13 13 16 55 83 91 17 54
FCEB (731-1095 days) (%) 14 14 55 80 94 10 55
CEB mean relative deviation
MCEB (overall) 0.99 1.01 0.99 0.96 1.25 1.40 1.41 0.76 1.23
MCEB (0-10 days) 1.04 0.91 1.02 0.89 1.47 1.76 1.75 0.42 1.28
MCEB (11-100 days) 0.98 1.05 0.99 0.98 1.20 1.30 1.37 0.60 1.25
MCEB (101-365 days) 1.01 1.05 1.02 0.97 1.14 1.25 1.22 0.77 1.07
MCEB (366-730 days) 0.97 0.97 1.01 1.23 1.34 1.35 0.97 1.21
MCEB (731-1095 days) 0.94 0.94 1.23 1.33 1.37 1.02 1.23
Gardner mean residuals
3-9.9 days 10 16 11 49 -36 -94 -89 84 -37
10-31.5 days 16 -3 12 35 -56 -120 -137 140 -82
31.6-99 days 18 -33 10 38 -79 -107 -163 181 -78
100-315 days -3 -23 -6 72 -60 -196 -144 188 -18
316-999 days 26 53 27 7 -159 -263 -282 50 -130
Gardner root mean square of residuals
3-9.9 days 32 39 33 70 64 108 116 97 90
10-31.5 days 48 44 47 81 97 137 180 156 127
31.6-99 days 54 61 55 114 127 140 222 202 137
100-315 days 54 79 59 149 145 219 236 222 144
316-999 days 50 144 54 143 184 272 317 116 180
Gardner coefficient of variation
ωG (overall) (%) 17 27 18 36 49 71 83 60 51
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201358
larger database with a possibly greater varia-
tion in concrete types.
In the calculation of the CEB-FIP coef-
ficient of variation, mean square error and
mean relative deviation (Al-Manaseer &
Lam 2005), all the data is pooled and then
grouped into six intervals of drying time:
0-10 days, 11-100 days, 101-365 days, 366-730
days, 731-1095 days and above 1 095 days.
The disadvantage of these three measures
is that the data is immediately grouped into
drying time intervals, which means that,
although time intervals are weighted equally,
different experiments are not weighted
equally in the calculation of the overall
mean statistics. Bažant’s approach, described
above, does not suffer this weakness and
satisfies both these objectives. The use of the
mean of the shrinkage values for a given time
period rather than the grand mean of all the
shrinkage values in the calculation of the
CEB coefficient of variation results in large
values of the coefficient of variation for short
drying time intervals and vice versa. This
in turn means that the calculated value of
the overall coefficient of variation is unduly
influenced by the short drying time data.
With respect to both the Bažant and CEB
coefficients of variation, it should also be
noted that, for the WITS model at least, the
model fit was obtained by minimising the
variance, not by minimising the coefficient
of variance. The use of the relative errors
in the calculation of the CEB mean square
error is prone to over-emphasise the errors
in low shrinkage values, which are relatively
less important, and vice versa. The CEB
mean relative deviation is a useful statistic
as it identifies the magnitude and direction
of bias in the predicted values. The results
from all the above calculations are given in
Table 7. Results for only five time intervals
are shown, since there was no data at drying
times longer than 1 095 days in the data set
used in this study. The WITS model exhib-
ited the lowest overall CEB coefficient of
variation, followed by the ACI 209R-92 and
RILEM B3 models. Over the different time
intervals, the WITS model had the lowest
coefficient of variation, except for the longest
drying time interval (731-1 095 days) where it
was superseded by the SANS 10100-1model.
It appeared that the SANS 10100-1model
is a good predictor of shrinkage at longer
drying times, but under-predicts at shorter
drying times, perhaps due to poor prediction
of the six-month shrinkage, as illustrated in
Figure 5, and also in Figure 9 for an experi-
ment which includes data at very long drying
times. The over-emphasis of the CEB mean
square error statistics for low shrinkage
values (and vice versa), as discussed above,
can clearly be seen (Table 7). The WITS
model, closely followed by the ACI 209R-92
and SANS 10100-1 models, performed better
than the other models on this measure. The
CEB mean relative deviation statistics are
shown in Table 7, which illustrate the magni-
tude and direction of the bias in the different
models (discussed previously), as a function
of drying time. The WITS model showed the
least bias across all time intervals, closely
followed by the ACI 209R-92 model. The
narrowing difference between the actual and
predicted values of the SANS 10100-1 model
with increasing drying time is shown clearly
here, again indicating that the longer-term
(30-year) predictions of this model are more
in line with the measured data than the
shorter-term (six-month) predictions.
In the method used by Gardner (2004),
the observations are grouped into half-log
decades (starting at a drying time of three
days). Within each time interval, the average
and the root mean square (RMS) values of the
differences between the actual and predicted
values (residuals) are calculated. The trend of
the average residual with time shows whether
there is over- or under-estimation (bias) with
time by the model, while the trend of the
RMS values with time shows if the deviation
of the model increases with time. Next, the
RMS values are simply averaged. The average
RMS values are then normalised by dividing
by the average of the average shrinkage values
(for the different time intervals) to produce
a measure analogous to a coefficient of
variation. This formula given by Gardner is,
however, incorrect, since the mean squares,
not RMS values, should be averaged. In this
study, the corrected formula for the Gardner
coefficient of variation, ωG, was applied. As in
the case for the overall CEB statistical indica-
tor, ωG also suffers from the disadvantage
that the data is immediately grouped into
drying time intervals, which means that,
although time intervals are weighted equally,
experiments are not weighted equally in the
calculation of this overall mean statistic.
Figure 9 Illustration of the fit of the models to an experiment with data at long drying times
700
Sh
rin
ka
ge
(mic
rost
rain
)
600
500
400
300
200
100
01 000100101
Drying time (days)
WITS
#0177 RILEM B3 CEB MC90-99GL2000
SANS 10100-1Eurocode 2
Figure 10 Comparison of the goodness-of-fit measures for the different concrete shrinkage models
WITS (all data)
WITS (data used for model)
WITS (data not used for model)
ACI 209
RILEM B3
SANS 10100-1
Eurocode 2
CEB MC90-99
GL2000
ωBP (%)
V(CEB) (%)
F(CEB)M(CEB)
1.00
0.80
0.60
0.40
0.20
0
ωG (%)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 59
The Gardner average residuals and the root
mean squares of the residuals for the dif-
ferent time periods for all the models are
given in Table 7. The WITS model had the
lowest mean residuals, followed by the ACI
209R-92 model. The bias towards over- or
under-prediction by the other models can
clearly be seen. The Gardner coefficient of
variation also identified the WITS model as
the best model according to this criterion,
as did the root mean squares of the residuals
for the different drying time intervals. The
latter statistic showed that the deviations of
all the models increased with time, with the
exception of the WITS model (over all drying
times) and the SANS 10100-1 model (at long
drying times).
The discussion above has shown that
there is no single goodness-of-fit statistic
which can adequately capture all aspects of
the performance of a model for the shrink-
age of concrete. In order to summarise the
information contained in the different overall
numerical goodness-of-fit measures discussed
above, their calculated values for the different
models are represented in Figure 10 by means
of a radar chart. This plot showed that,
across all the goodness-of-fit measures, the
WITS model performed the best. This was
perhaps to be expected, since the model was
derived largely from this data. However, even
the performance of the model on the data
which was not used in the development of the
model was excellent, although, as was men-
tioned earlier, this small data set should not
be regarded as a true validation data set. The
ACI 209R-92 model exhibited the second-best
performance, but here it must be noted that
this model could be used to predict only 36%
of the data set. The third best performance
across the goodness-of-fit indicators was
shown by the RILEM B3, SANS 10100-1 and
Eurocode 2 models indicating that these are
arguably the best alternative models to the
WITS model for the South African data set.
The SANS 10100-1 model performed poorly
relative to the other models, but as discussed
above, its predictive ability at longer drying
times was better than that at shorter drying
times. This may indicate that its 30-year pre-
dictions are more suited to the South African
data set than its six-month predictions, i.e.
that the time development of shrinkage of the
model may need to be adjusted relative to the
British Standard from which the model was
directly taken.
CONCLUSIONS
The WITS model presented in this paper
represents a first attempt at applying the
concept of hierarchical nonlinear modelling
to the prediction of shrinkage for South
African concretes. Furthermore, this is
the first time that a shrinkage model has
been derived from a gathering of test data
on the shrinkage of concretes which had
been generated by a range of South African
laboratories over a span of 30 years. The
proposed model identifies the material and
environmental covariates that are the most
important contributors to both the magni-
tude and rate of concrete shrinkage. Based
on a range of reliability and goodness-of-fit
measures, the WITS model was found to
perform better than a number of local and
international models on the basis of the mag-
nitude and rate of prediction at both early
and late drying times. The coefficients pro-
posed for the model have yet to be confirmed
through further testing with a wider range of
material and environmental variables. This
will require further, statistically designed,
shrinkage tests that are aimed at exploring
the effect of key variables more fully. This
approach could also prove useful to future
research seeking to model concrete shrink-
age and related time-dependent properties
such as creep.
ACKNOWLEDGEMENTS
The provision of data and helpful com-
ments by Prof Mark Alexander and Dr
Hans Beushausen (Department of Civil
Engineering, University of Cape Town, Cape
Town, South Africa) are gratefully acknowl-
edged. The authors are also grateful to the
Cement and Concrete Institute for their data
and logistical support and, together with
Eskom, for their financial support to our
research programme.
REFERENCES
Addis, B J & Owens, G (Eds) 2005. Fundamentals
of Concrete. South Africa: Cement and Concrete
Institute, 35–49.
Al-Manaseer, A & Lam, J-P 2005. Statistical evalua-
tion of shrinkage and creep models. ACI Materials
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Alexander, M G 1998. Role of aggregates in hard-
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Alexander, M G & Mindess, S 2005. Aggregates in
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American Concrete Institute (ACI) 1982. Prediction of
creep, shrinkage and temperature effects in concrete
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concrete structures, ACI 209R-82, Detroit: American
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Ballim, Y 1999. Localising international concrete
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Bažant, Z P & Baweja, S 1996. Creep and shrinkage
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– Model B3. Materials and Structures, 28: 357–365
(with errata in 29: 126).
Bažant, Z P & Li, G-H 2008. Comprehensive database
on concrete creep and shrinkage. ACI Materials
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1:2004I: Common Rules for Buildings and Civil
Engineering Structures. London: British Standards
Institution.
Davidian, M & Giltinan, D M 1995. Nonlinear Models
for Repeated Measurement Data, 1st ed. London:
Chapman & Hall.
European Committee for Standardization 2003. EN
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– Part 1: General Rules and Rules for Buildings.
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Performance. Updated Knowledge of the CEB/FIP
Model Code 1990. FIB Bulletin, Vol. 2, Lausanne,
Switzerland: Federation Internationale du Beton,
37–52.
Gardner, N J & Lockman, M J 2001. Design provisions
for drying shrinkage and creep of normal strength
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Gardner, N J 2004. Comparison of prediction provi-
sions for drying shrinkage and creep of normal-
strength concretes. Canadian Journal of Civil
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Gaylard, P, Fatti, L P & Ballim Y 2012. Statistical mod-
elling of the shrinkage behaviour of South African
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South African Statistical Journal.
Gilbert, R I 1988. Time Effects in Concrete Structures.
Amsterdam: Elsevier.
McDonald, D B & Roper, H 1993. Accuracy of predic-
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Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201360
TECHNICAL PAPER
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 60–71, Paper 813 Part 1
DR MAHONGO DITHINDE (Visitor) holds a PhD in
Civil Engineering from the Stellenbosch
University, an MSc in Foundation Engineering
from the University of Birmingham (UK), and
BEng in Civil Engineering from the University of
Botswana. He works as a Senior Lecturer at the
University of Botswana. His specialisation and
research interests are in the broad area of
geotechnical reliability-based design. In addition to academic work, he is also
a geotechnical partner for Mattra International where he is active in
consultancy work in the fi eld of geotechnical engineering.
Contact details:
Department of Civil Engineering
Stellenbosch University
Private Bag X1
Matieland
7602
South Africa
Department of Civil Engineering
University of Botswana
Private Bag UB 0061
Gaberone
Botswana
T: +267 355 4297
F: +267 395 2309
PROF JOHAN RETIEF (Fellow of SAICE) has, since
his retirement as Professor in Structural
Engineering, maintained involvement at the
Stellenbosch University, supervising graduate
students in the fi eld of risk and reliability in civil
engineering. He is involved in various standards
committees, serving as the South African
representative to ISO TC98 (basis of structural
design and actions on structures). He holds a BSc (cum laude) and a DSc from
the University of Pretoria, a DIC from Imperial College London, and an MPhil
from London University. Following a career at the Atomic Energy
Corporation, he joined Stellenbosch University in 1990.
Contact details:
Department of Civil Engineering
Stellenbosch University
Private Bag X1
Matieland
Stellenbosch
7602
T: +27 21 808 4442
F: +27 21 808 4947
Key words: pile foundation design, southern African practice, pile load tests,
model factor, statistical characterisation
INTRODUCTION
Geotechnical design is performed under a
considerable degree of uncertainty. The two
main sources of this uncertainty include:
(i) Soil parameter uncertainty and (ii) cal-
culation model uncertainty. Soil parameter
uncertainty arises from the variability
exhibited by properties of geotechnical mate-
rials from one location to the other, even
within seemingly homogeneous profiles.
Geotechnical parameter prediction uncer-
tainties are attributed to inherent spatial
variability, measurement noise/random
errors, systematic measurements errors, and
statistical uncertainties. Conversely, model
uncertainty emanates from imperfections of
analytical models for predicting engineer-
ing behaviour. Mathematical modelling
of any physical process generally requires
simplifications to create a useable model.
Inevitably, the resulting models are simpli-
fications of complex real-world phenomena.
Consequently there is uncertainty in the
model prediction even if the model inputs
are known with certainty.
For pile foundations, previous studies (e.g.
Ronold & Bjerager1992; Phoon & Kulhawy
2005) have demonstrated that calculation
model uncertainty is the predominant com-
ponent. One of the fundamental objectives
of reliability-based design is to quantify and
systematically incorporate the uncertainties
in the design process. The current state of
the art in the quantification of model uncer-
tainty associated with a given pile design
model entails determining the ratio of the
measured capacity to theoretical capacity.
Accordingly, in this paper a series of pile per-
formance predictions by the static formula
are compared with measured performances.
To capture the distinct soil types for the
geologic region of southern Africa, as well as
the local pile design and construction experi-
ence base, pile load tests and associated
geotechnical data from the southern African
geologic environment are used.
In reliability analysis and modelling, both
materials properties and calculation model
uncertainties are incorporated into a perfor-
mance function representing the limit state
design function in terms of basic variables
which express design variables (loads, mate-
rial properties, geometry) as probabilistic
variables. The objective of this paper is to
present detailed statistical characterisation
of model uncertainty for pile foundations.
The analysis is an extension of the model
uncertainty characterisation reported by
Dithinde et al (2011). The purpose of the
characterisation is to relate southern African
pile foundation design practice to reliability-
based design as it has been developed and
Pile design practice in southern Africa Part I: Resistance statistics
M Dithinde, J V Retief
The paper presents resistance statistics required for reliability assessment and calibration of limit state design procedures for pile design reflecting southern African practice. The first step of such a development is to determine the levels of reliability implicitly provided for in present design procedures based on working stress design. Such an assessment is presented in an accompanying paper (please turn to page 72). The statistics are presented in terms of a model factor M representing the ratio of pile resistance interpreted from pile load tests to its prediction based on the static pile formula. A dataset of 174 cases serves as sample set for the statistical analysis. The statistical characterisation comprises outliers detection and correction of erroneous values, using the corrected data to compute the sample moments (mean, standard deviation, skewness and kurtosis) needed in reliability analysis. The analyses demonstrate that driven piles depict higher variability compared to bored piles, irrespective of materials type. In addition to the above statistics, reliability analysis requires the theoretical probability distribution for the random variable under consideration. Accordingly it is demonstrated that the lognormal distribution is a valid theoretical model for the model factor. Another key basis for reliability theory is the notion of randomness of the basic variables. To verify that the variation in the model factor is not explainable by deterministic variations in the database, an investigation of correlation of the model factor with underlying pile design parameters is carried out. It is shown that such correlation is generally weak.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 61
standardised for geotechnical and structural
design. The derived statistics constitute the
backbone of all subsequent pile foundations
limit state design initiatives in southern
Africa. Specific usage of the derived statistics
include: assessment of reliability indices
embodied in the current southern African
pile design practice, as presented in the
accompanying paper (Retief & Dithinde
2013 – please turn to page 72); derivation of
the characteristic model factor for pile foun-
dations design in conjunction with SANS
10160-5 (2011); and reliability calibration of
resistance factors. The following topics are
presented subsequently:
■ The geotechnical background to the
dataset is briefly reviewed, including the
basis and application for classification
into homogeneous datasets and the for-
mal definition of the model factor M to
represent model uncertainty.
■ An assessment and detection of outliers
and correction of erroneous samples,
considering the sensitivity of reliability
analysis to even a limited number of such
values in a dataset.
■ Using the corrected data and conven-
tional statistical methods to compute
the sample moments: mean, standard
deviation, skewness and kurtosis for the
respective datasets.
■ Verification of randomness of the dataset
through investigation of any system-
atic dependence on the relevant design
variables.
■ Determination of the appropriate prob-
ability distribution to represent model
uncertainty provides the final step in
characterising model factor statistics.
PILE LOAD TEST DATABASE
Although this paper primarily considers the
statistical characteristics of southern African
pile model uncertainty, as based on the data-
base of model factors reported by Dithinde
et al (2011), with additional background
provided by Dithinde (2007), it is also neces-
sary to appreciate the geotechnical basis and
integrity of the dataset. This section presents
an extract of the way in which the dataset
has been compiled and a formal definition of
a model factor (M).
The database of static pile load tests
reported by Dithinde et al (2011) include
information on the associated geotechnical
data, such as soil profiles, field and labora-
tory test results. A comprehensive range of
soil conditions, pile geometry and resistance
is incorporated in the dataset, to provide
extensive representation of southern African
pile construction practice. Although the pile
load test reports were collected from various
piling companies in South Africa, a signifi-
cant number of pile tests were performed
in countries such as Botswana, Lesotho,
Mozambique, Zambia, Swaziland and
Tanzania. The main pile types in the data-
base include Franki (expanded base) piles,
Auger piles, and Continuous Flight Auger
(CFA) piles. In addition, there are a few cases
of steel piles and slump cast piles. The steel
piles are mainly H-piles, with one case where
a steel tubular pile was used.
The collected pile load test data was
carefully studied in order to evaluate its
suitability for inclusion in the current
study. For each load test, emphasis was
placed on the completeness of the required
information, including test pile size (length
and diameter), proper record of the load-
deflection data, and availability of subsur-
face exploration data for the site. Only cases
where sufficient soil data was available
for the prediction of pile resistance were
included in the database.
The pile load tests were used to deter-
mine the measured pile resistance, while the
geotechnical data was used to compute the
predicted resistance. The measured resis-
tances from the respective load-settlement
curves were interpreted on the basis of
Davisson’s offset criterion (Davison 1972).
However, for working piles, Chin’s extrapola-
tion (Chin 1970) was carried out prior to the
application of the Davisson’s offset criterion.
The predicted resistance was based on the
classic static formula which is essentially the
generic theoretical pile design model based
on the principles of soil mechanics. The
soil data that was obtained from the survey,
and used for the predicted resistance, was
mainly in the form of borehole log descrip-
tions and standard penetration (SPT) results.
Soil design parameters were selected on the
basis of common southern African practice
(Dithinde 2007).
Model factor statistics
The primary output of the database of pile
load tests reported by Dithinde et al (2011)
consists of the interpreted pile resistance (Qi)
and the predicted pile resistance (Qp) from
which a set of observations of the Model
Factor (M) as given by Equation [1] can be
obtained:
M = Qi
Qp
(1)
where:
Qi = pile capacity interpreted from a
load test, to represent the measured
capacity;
Qp = pile capacity generally predicted using
limit equilibrium models, and
M = model factor.
Each case of pile test included in the dataset
is consequently treated as a sample of the set
of n cases under consideration. In Dithinde
et al (2011) the complete set of 174 cases was
further classified in terms of four theoretical
principal pile design classes based on both
soil type and installation method. These
fundamental sets of classes include:
(i) driven piles in non-cohesive soil (D-NC)
with 29 cases, (ii) bored piles in non-cohesive
soil (B-NC) with 33 cases, (iii) driven piles
in cohesive soils (D-C) with 59 cases, and
(iv) bored piles in cohesive soils (B-C) with
53 cases. In this paper, the principle four data
sets are now combined into various practical
pile design classes considered in design codes
such as SANS 10169-5 (2011) and EN 1997-1
(2004). The additional classification schemes
include:
■ Classification based on pile installation
method irrespective of soil type. This is
the classification adopted in EN 1997-1
(2004) and it yields: 87 cases of driven
piles (D) and 83 cases of bored piles (B).
■ Classification based on soil type. This
classification system is supported by the
general practice where a higher factor of
safety is applied to pile capacity in clay
as compared to sand. This combination
results in 58 cases in non-cohesive soil
(NC) and 112 cases in cohesive soil (C).
■ All pile cases as a single data set irrespec-
tive of pile installation method and soil
type. This is the practical consideration
presented in SANS 10160-5 (2011) where
a single partial factor is given for all com-
pressive piles. The scheme yields 174 pile
cases (ALL).
DETECTION OF DATA OUTLIERS
The presence of outliers may greatly
influence any calculated statistics, lead-
ing to biased results. For instance, they
may increase the variability of a sample
and decrease the sensitivity of subsequent
statistical tests (McBean & Rovers 1998).
Therefore prior to further numerical treat-
ment of samples and application of statistical
techniques for assessing the parameters of
the population, it is absolutely imperative to
identify extreme values and correct errone-
ous ones.
The statistical detection and treatment
of outliers in the principal four sets were
reported by Dithinde et al (2011). The meth-
ods used include (i) load-settlement curves,
(ii) sample z-scores, (iii) box plots, and (iv)
scatter plots. The results for cases with outli-
ers are reproduced in Figure 1. Inspection
of Figure 1(a) reveals two potential outliers
(i.e. cases 27 and 54). The curves for these
two cases depict different behaviour from
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201362
Figure 1(a) Load-settlement curves method
1.6
1.6
1.6
1.6
Q /
Qi
Q /
Qi
Q /
Qi
Q /
Qi
1.2
1.2
1.2
1.2
0.8
0.8
0.8
0.8
0.4
0.4
0.4
0.4
0
0
0
0
30
30
30
30
25
25
25
25
20
20
20
20
15
15
15
15
10
10
10
10
5
5
5
5
0
0
0
0
Settlement, s (mm)
Settlement, s (mm)
Settlement, s (mm)
Settlement, s (mm)
Case 27
Driven piles in non-cohesive soilsN = 29
Case 54
Driven piles in cohesive soilsN = 59
Bored piles in non-cohesive soilsN = 33
Bored piles in cohesive soilsN = 53
Figure 1(b) Box plot methods
Box Plot of B-CSpreadsheet1 10v*174c
Box Plot of B-NCSpreadsheet1 10v*174c
M
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
Median = 1.1154
25%–75% = (0.9615, 1.3202)
Non-Outlier range = (0.5436, 1.7478)
Extremes
Outliers
M
2.2
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
Median = 1.9911
25%–75% = (0.7953, 1.1481)
Non-Outlier range = (0.4894, 1.5241)
Extremes
Outliers
#53#156
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 63
the rest of the curves (case 27 with a soft
initial response and case 54 with a large
normalised capacity). Visual inspection of
Figure 1(b) for outliers shows one data point
marked as outlier for B-NC and B-C data
sets. The tagged data points correspond to
pile cases number 53 and 156. However, it
should be noted that the box plot method for
identifying outliers has shortcomings, par-
ticularly for small sample sizes as is the case
here. Accordingly the identified cases will
have to be corroborated by other methods.
Examination of Figure 1(c) shows two data
points with z-score values at a considerable
distance from the rest of the data points.
These data points belong to B-NC (case 53)
and B-C (case 156) with z-scores of 3.13
and 2.95 respectively. Although the z-score
for case 156 is less than the criterion limit
value of 3, and therefore technically is not an
outlier, it is sufficiently close to the limit to
require further scrutiny. The results of the
scatter plots of pile capacity (Qi) versus the
predicted capacity (Qp) revealed the same
outliers detected by the other methods.
Aggregate of outliers
A total of five observations were detected
as potential outliers, namely cases 27, 53,
54, 55 and 156. However, it is not proper to
automatically delete a data point once it has
been identified as an outlier through statisti-
cal methods (Robinson et al 2005). Since an
outlier may still represent a true observation,
it should only be rejected on the basis of
evidence of improper sampling or error.
Accordingly the five data points identified as
outliers were carefully examined by double-
checking the processes of determination
of interpreted capacities and computation
of predicted capacities. This entailed going
back to the original data (pile testing records
and derivation of soil design parameters) and
checking for recording and computational
errors. Following this procedure the correc-
tions were as follows:
■ Cases 53, 54 and 55: Examination of
records for these cases showed that an
uncommon pile installation practice was
employed. The steel piles were installed
in predrilled holes and then grouted. The
strength of the grout surrounding the
piles contributed to the high resistance
and hence the higher interpreted capaci-
ties. Since the installation procedure
for these piles deviates from the normal
practice, they represent a different
population. These were the only piles in
the database constructed in this rather
unusual method. These data points were
therefore regarded as genuine outliers and
were deleted from the data set.
■ Case 27: There was no obvious physical
explanation for the behaviour of pile case
27. The depicted behaviour is attributed
to extreme values of the hyperbolic
parameters representing the non-linear
behaviour of the test results. Since piles
in terms of pile type, size and soils condi-
tions (i.e. cases 28 and 29) did not show
similar characteristics, it was concluded
that an error was made during the execu-
tion of the pile test. Accordingly this pile
case was regarded as having incomplete
information, and was therefore deleted.
■ Case 156: Again there was no obvious
physical explanation for the behaviour of
this pile case. Furthermore, the location
of this data point on the scatter plot of
Qi versus Qp fits the general trend for
the dataset. Therefore no correction was
justified for this pile case.
In summary, four outliers were removed and
one retained, bringing the dataset to n = 170
cases in total and for the respective subsets
nD-NC = 28; nB-NC = 30; nD-C = 59; nB-C = 53.
SCATTER PLOTS OF QI VS QP
Scatter plots of Qi versus Qp can serve as a
multivariate approach to outlier detection.
However they are presented here to provide
an indication of whether the variance of
the data set is constant or varies with the
dependent variable (i.e. homoscedasticity).
The ensuing scatter plots are presented in
Figure 2. Visual inspection of the scatter
plots seems to suggest variation in the degree
of scatter increases with values of Qp. In this
regard, it is evident that there is reduced
scatter at smaller values of Qp. However, due
to the small sample size, the case for large
values of Qp is not sufficiently clear to make
any firm conclusion. Furthermore, Figure 2
gives the impression that the variance of
the points around the fitted line increases
linearly, thereby suggesting that the standard
deviation increases with the square root
of the values of Qp. This explains why the
scatter tends to flatten off for large values of
Qp. The foregoing assumption implies that
weighted regression analysis must be used
to establish the relationship between Qi and
Qp. Such regression analysis was applied in
this study (Figure 2) with the regression line
forced to pass through the origin. In this
case, the slope of the regression line is an
estimate of the model factor M.
SUMMARY STATISTICS
Following the outlier detection and removal
process, the descriptive statistics for M
consisting of mean (mM), standard deviation
(sM), skewness and kurtosis are presented
in Table 1. The sample descriptive statistics
were computed using conventional statistical
analysis approach. These are quantities used
to describe the salient features of the sample
and are required for calculations, statisti-
cal testing, and inferring the population
parameters.
The sample mean mM indicates the aver-
age ratio of Qi to Qp, with mM > 1 indicating
a conservative bias of Qi exceeding Qp. This
is generally the case, with a positive bias
of between 1.04 and 1.17 shown in Table 1,
except for the B-NC case where Qi is on
average slightly less than Qp with mM = 0.98,
which is slightly un-conservative. The
general conservative bias reflected by mM is,
however, small in comparison to the disper-
sion of M as reflected by the sample standard
deviation sM for which values range from
0.23 to 0.36; the dispersion is also presented
Figure 1(c) Z-score method
Figures 1(a)–(c) Outlier detection results (after Dithinde et al 2011)
Z-s
core
3
4
1
2
0
–1
–3
–2
M
0 1 2 3
D-NC B-NC D-C B-C
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201364
in normalised form as the coefficient of
variation VM = sM/mM.
The combined effect of values of mM
close to 1 and the relatively large values
of sM or VM indicate large probabilities of
realisations of M in the un-conservative
range M < 1. The lower tail of the distribu-
tion of M derived from the dataset and M
statistics is therefore of specific interest
for application of the results in reliability
assessment.
A comparison of the standard deviations
or coefficient of variations for the respective
cases indicates small differences. However,
there seems to be a distinct trend that is
influenced by the pile installation method
(i.e. driven or bored). In this regard, driven
piles depict higher variability compared to
bored piles, irrespective of soil type. This
Table 1 Summary of statistics for M
M nMean
mM
Confidence -75%
mM; -0.75
Std. Dev.sM
Upper CI SD 75%sM; +0.75
COV Skewness Kurtosis
D-NC 28 1.11 1.03 0.36 0.40 0.33 0.35 –1.15
B-NC 30 0.98 0.93 0.23 0.26 0.24 0.14 –0.19
D-C 59 1.17 1.12 0.3 0.32 0.26 –0.01 –0.74
B-C 53 1.15 1.10 0.28 0.30 0.25 0.36 0.49
D 87 1.15 1.11 0.32 0.34 0.28 0.1 –0.95
B 83 1.09 1.05 0.28 0.30 0.25 0.41 0.47
NC 58 1.04 1.00 0.30 0.32 0.29 0.55 –0.37
C 112 1.16 1.13 0.29 0.30 0.25 0.15 –0.29
ALL 170 1.1 1.07 0.31 0.32 0.28 0.24 –0.75
Figure 2 Scatter plots of Qi versus Qp
Qi
(kN
)Q
i (k
N)
Qi
(kN
)
Qi
(kN
)Q
i (k
N)
8 000
8 000
15 000
14 000
6 000
6 000
10 000
10 000
4 000
4 000
5 000
6 000
2 000
2 000
2 000
0
0
0
0
(a) All driven piles
(c) All piles in non-cohesive soil
(e) All piles
(b) All bored piles
(d) All piles in cohesive soil
0
0
0
0
2 000
2 000
5 000
2 000
4 000
4 000
10 000
4 000
6 000
6 000 6 000
8 000
8 000
15 000
14 000
Qp (kN)
Qp (kN)
Qp (kN)
Qp (kN)
Qp (kN)
12 000
8 000
4 000
14 000
10 000
6 000
2 000
0
12 000
8 000
4 000
8 000 10 000 12 000
0 2 000 4 000 6 000 14 0008 000 10 000 12 000
Qi = 1.0685Qp Qi = 1.1018Qp
Qi = 1.1189QpQi = 0.9901Qp
Qi = 1.0886Qp
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 65
implies that the densification of the soil sur-
rounding the pile emanating from the pile
driving process is not well captured in the
selection of the soil design parameters. Even
the bias for the driven piles dataset is rela-
tively higher, thereby reiterating the notion
that current practice is conservative in
selecting design parameters for driven piles.
Furthermore, the variability in non-cohesive
materials is higher than that in cohesive
materials. This is attributed to the fact that
in cohesive materials the un-drained shear
strength derived from the SPT measurement
is directly used in the computation of pile
capacity, while in non-cohesive materials,
the angle of friction obtained from the SPT
measurement is not directly used. Instead,
the key pile design parameters in the form
of bearing capacity factor (Nq), earth pres-
sure coefficient (ks) and pile-soil interface
friction (δ) are obtained from the derived
angle of friction on the basis of empirical
correlation, thus introducing some additional
uncertainties.
Skewness provides an indication of the
symmetry of the dataset. The skewness
represented in Table 1 is generally positive,
indicating a shift towards the upper tail
(conservative) of the values for M. There is,
however, no consistent trend amongst the
values for the respective datasets. The value
of 0.24 for the combined dataset (ALL)
could therefore be taken as indicative of the
general trend. As a guideline it should be
noted that the skewness of the symmetrical
normal distribution is 0; for a lognormal
distribution it is dependent on the distribu-
tion parameters, with a value of 0.83 based
on the parameter values for the combined
dataset.
Values of kurtosis indicate the peakedness
of the data, with a positive value indicating a
high peak, and a negative value indicating a
flat distribution of the data. Negative values
generally listed in Table 1 indicate flat dis-
tribution of the data, particularly for driven
piles. Since these characteristics can only be
captured by advanced probability distribu-
tions not generally considered in reliability
modelling, kurtosis is not further considered.
In order to provide for uncertainties in
parameter estimation, Table 1 also presents
the confidence limits of the mean and stan-
dard deviation at a confidence level of 0.75;
this is the confidence level recommended by
EN1990:2002 for parameter estimation for
reliability models with vague information
on prior distributions. The lower confidence
limit of the mean (mM; -0.75) and the upper
confidence limit of the standard deviation
(sM; +0.75) is used to present conserva-
tive estimates of the range of parameter
estimates.
CORRELATION WITH PILE
DESIGN PARAMETERS
Although the mean and standard deviation
values presented in Table 1 provide a useful
data summary, they combine data in ways
that mask information on trends in the data.
If there is a strong correlation between M
and some pile design parameters (pile length,
pile diameter and soil properties), then part
of its total variability presented in Table 1
is explained by these design parameters.
The presence of correlation between M and
deterministic variations in the database
would indicate that:
■ The classical static formula method does
not fully take the effects of the parameter
into account.
■ The assumption that M is a random vari-
able is not valid.
Reliability-based design is based on the
assumption of randomness of the basic
variables. Since the model factor is among the
variables that serve as input into reliability
analysis of pile foundations, it is critical to
verify that it is indeed a random variable.
This was partially verified by investigating
the presence or absence of correlation with
various pile design parameters. The measure
of the degree of association between variables
is the correlation coefficient. The basic
and most widely used type of correlation
coefficient is Pearson r, also known as
linear or product-moment correlations.
The correlation can be negative or positive.
When it is positive, the dependent variable
tends to increase as the independent variable
increases; when it is negative, the dependent
variable tends to decrease as the independent
variable increases. The numerical value of
r lies between the limits -1 and +1. A high
absolute value of r indicates a high degree
of association, whereas a small absolute
value indicates a small degree of association.
When the absolute value is 1, the relationship
is said to be perfect and when it is zero,
the variables are independent. For the
numerical correlation values in-between the
limits a critical question is, “When is the
numerical value of the correlation coefficient
considered significant?” Several authors
in various fields have suggested guidelines
for the interpretation of the correlation
coefficient. For the purposes of this study an
interpretation by Franzblau (1958) is adopted
as follows:
■ Range of r: 0 to ±0.2 – indicates no or
negligible correlation
■ Range r: ±0.2 to ±0.4 – indicates a low
degree of correlation
■ Range r: ±0.4 to ±0.6 – indicates a moder-
ate degree of correlation
■ Range r: ±0.6 to ±0.8 – indicates a
marked degree of correlation
■ Range r: ±0.8 to ±1 – indicates a high
correlation
The statistical significance of the correlation
is determined through hypothesis testing
and presented in terms of a p-value. In this
regard, the null hypothesis is that there is no
correlation between M and the given design
parameter (indicative of statistical independ-
ence). A small p-value (p < 0.05) indicates
that the null hypothesis is not valid and
should be rejected. Values for the correlation
between M and the respective pile design
parameters with the associated p-values are
listed in Table 2. The results indicate that
R < 0.4 for all the pile design parameters and
therefore the degree of correlation is low.
The associated p-values are generally much
greater than 0.05, confirming that the cor-
relation between the model factor and the
various pile design parameters is statistically
insignificant. Therefore, variations in the
model factor are at least not explainable by
systematic variations in the key pile design
parameters, and a random variable model
appears reasonable.
For visual appreciation of the correlation
results in Table 2, some of scatter plots of M
versus pile design parameters are shown in
Figure 3.
Table 2 Correlation with pile design parameters
Design parameter
Case
Spearman rank correlation
R p-value
Pile length
D 0.11 0.29
B 0.11 0.31
NC –0.25 0.05
C 0.17 0.07
ALL 0.02 0.75
Shaft diameter
D 0.01 0.92
B 0.12 0.26
NC 0.13 0.34
C –0.02 0.82
ALL 0.05 0.53
Base diameter
D –0.16 0.15
B 0.05 0.63
NC 0.00 1.00
C –0.06 0.51
ALL –0.03 0.67
φ-base NC 0.19 0.16
φ-shaft NC 0.19 0.16
Cu-base C –0.002 0.98
Cu-shaft C –0.21 0.02
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201366
PROBABILISTIC MODEL FOR
THE MODEL FACTOR
The theory of reliability is based on the
general principle that the basic variables
(actions, material properties and geometric
data) are considered as random variables
having appropriate types of distribution. One
of the key objectives of the statistical data
analysis is to determine the most appropriate
theoretical distribution function for the basic
variable. This is the governing probability
distribution for the random process under
consideration and therefore extends beyond
the available sample (i.e. the distribution of
the entire population). Once the probability
distribution function is known, inferences
based on the known statistical properties of
the distribution can be made.
For reliability calibration and associated
studies, the most commonly applied distribu-
tions to describe actions, materials properties
and geometric data are the normal and log-
normal distributions (Holický 2009; Allen et
al 2005). Accordingly, for the current analysis
only the normal and lognormal distribution
fit to the data are considered. The fit is inves-
tigated through (i) a cumulative distribution
function (CDF) plotted using a standard
normal variate with z as the vertical axis, and
(ii) direct distribution fitting to the data.
The cumulative distribution function
is the most common tool for statistical
characterisation of random variables used in
reliability calibration (e.g. Allen et al 2005).
In the context of the current analysis, the
CDF is a function that represents the prob-
ability that a value of M less than or equal to
a specified value will occur. This probability
can be transformed to the standard normal
variable (or variate), z, and plotted against
M values (on x-axis) for each data point.
This plotting approach is essentially the
equivalent of plotting the bias values and
their associated probability values on normal
probability paper. An important property
of a CDF plotted in this manner is that
normally distributed data plot as a straight
line, while lognormally distributed data on
the other hand will plot as a curve. The fol-
lowing steps were used to create the standard
normal variate plot of the CDF:
■ The capacity model factor values in a
given data set were sorted in a descending
order, then the probability associated
with each value in the cumulative distri-
bution was calculated as i/(n +1).
■ For the probability value calculated in
Step 1 associated with each ranked capac-
ity model factor value, z was computed in
Excel as: z = NORMSINV(i/(n +1)) where
i is the rank of each data point as sorted,
and n is the total number of points in the
data set.
■ Once the values of z have been calculated,
z versus model factor (X) was plotted for
each data set.
The ensuing plots are presented in Figure 4(a)
from which it can be seen that the CDF for
the five data sets plot more as curves than
straight lines, thereby implying that the data
follow a lognormal distribution. A further
characterisation entailing fitting predicted
normal and lognormal distributions to the
CDF of the data sets is carried out. These
theoretical distributions are also shown in
Figure 4(a). Both distributions seem to fit
the data reasonably well. However, with the
exception of the bored piles data set, the
lognormal distribution has a better fit to the
lower tail of the data, which is important for
reliability analysis and design.
Figure 3 Correlation with some of the pile design parameters
MM
MM
2.2
2.0
2.2
2.2
0
24
200
0
5
28
300
400
10
32
400
800
15
34
500
1200
35
42
900
L
Phi shaft
Shaft diameter (mm)
Cu-base
2.0 2.0
2.0
1.8
1.8
1.8
1.8
1.6
1.6
1.6
1.6
1.4
1.4
1.4
1.4
1.2
1.2
1.2
1.2
1.0
1.0
1.0
1.0
0.8
0.8
0.8
0.8
0.6
0.6
0.6
0.6
0.4
0.4
0.4
0.4
All piles cases
Phi shaft
All piles cases
Cu-base
20
36
600
1600
25
38
700
2000
30
40
800 1 000
26 30
L:M: r = 0.0245, p = 0.7512 Shaft diameter:M: r = 0.0486, p = 0.5288
Phi shaft:N-C: r = 0.01868, p = 0.1604 Cu-base:C: r = –0.0021, p = 0.9822
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 67
To further confirm that the data best
fits a lognormal distribution, z-scores are
plotted as a function of Ln (M). The plots
would follow a straight line if the data in
fact follows the lognormal distribution. The
results are presented in Figure 4(b) from
which it is apparent that all the data sets plot
as a straight line. This therefore confirms
the strong case for a lognormal distribution
assumption for the data.
In Figure 5 the histogram of M for the
respective datasets are compared to normal,
lognormal and general lognormal (also three-
parameter 3P) probability density function
distributions based on the sample moments
listed in Table 1 as distribution parameters.
The graphic comparison indicates the degree
to which the alternative distributions provide
a reasonably smoothed representation of the
M data. At the same time the approximate
nature of the M data is indicated by the
Figure 4(a) CDF plots with normal and lognormal fit
No
rma
l st
an
da
rd v
ari
ab
le,
zN
orm
al
sta
nd
ard
va
ria
ble
, z
No
rma
l st
an
da
rd v
ari
ab
le,
zN
orm
al
sta
nd
ard
va
ria
ble
, z
3
3
2.5
3
0.4
0.4
0.4
0.4
0.4
0.9
0.9
0.9
0.9
0.9
1.4
1.4
1.4
1.4
1.4
1.9
1.9
1.9
1.9
1.9
2.4
2.4
2.4
2.4
2.4
M
M
M
M
M
2
2
2.0
2
1
1
1.0
1
0
0
0
0
–1
–1
–1.0
–1
–2
–2
–2.0
–2
–3
–3
–2.5
–3
(a) Driven piles
(c) Piles in non-cohesive soil
(e) All
(a) Bored piles
(d) Piles in cohesive soil
–1.5
–0.5
1.5
0.5
No
rma
l st
an
da
rd v
ari
ab
le,
z
2.5
2.0
1.0
0
–1.0
–2.0
–2.5
–1.5
–0.5
1.5
0.5
Normal dist fit
Lognormal dist fit
CDF of data
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201368
uneven nature of the histogram. The quan-
titative assessment of the difference between
the empirical data frequencies and the
assumed distributions is provided by the chi-
square goodness-of-fit test. In this regard, the
p-value is a measure of the goodness-of-fit,
with larger values indicating a better fit.
In testing the hypothesis that the
distribution of the data is similar to the
selected probability distribution (normal
or lognormal), the hypothesis is rejected if
p < 0.05. The p-values for chi-square testing
are presented in Table 3 from which it is
apparent that such values for all the data sets
are greater than 0.05 and therefore there is
no evidence to reject the null hypothesis of
either normal or lognormal distributions.
However, on the basis of the magnitude of
the p-values, the lognormal distribution
seems to show a better fit compared to
the other two distributions. The general
Figure 4(b) Z-score vs LN(M)
2.0
3 3
3
10
(a) Driven piles
(c) Piles in non-cohesive soil
(e) All
(b) Bored piles
(d) Piles in cohesive soil
Z-s
core
Z-s
core
Z-s
core
Z-s
core
Z-s
core
LN(M)
LN(M) LN(M)
LN(M)
LN(M)
1.5
2 2
2
5
1.0
1 1
1
00.5
0
0 0
0
–0.5
–5
–1.0
–1
–10
–1.5
–1 –1
–2
–15
–2.0
–2 –2
–3
–20
–2.5
–3 –3
–4
–25
–1.0
–1.0 –1.0
–1.0
–1.0
–0.5
–0.5 –0.5
–0.5
–0.5
1.0
1.0 1.0
1.0
1.0
0.5
0.5 0.5
0.5
0.5
0
0 0
0
0
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 69
Figure 5 Normal and lognormal distribution fit to the data
(a) Driven piles
(c) Piles in non-cohesive soil
(b) Bored piles
(d) Piles in cohesive soil
f(M
)0.26 0.36
M
0.240.32
0.22
0.280.20
0.24
(e) All
0.18
0.20
0.16
0.16
0.14
0.12
0.12
0.10
0.08
0.080.06
0.040.04
0.02
0 00.6 0.8 1.0 1.2 1.4 1.6 1.8 0.6 1.8 2.00.8 1.0 1.2 1.4 1.6
f(M
)
M
0.36 0.30
0.320.26
0.280.24
0.24
0.22
0.20
0.20
0.16
0.18
0.12
0.16
0.08
0.14
0.04
0.12
0 0
f(M
)
f(M
)
0.6 0.8 1.0 1.2 1.4 1.6
0.28
0.10
0.08
0.06
0.04
0.02
0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
M M
f(M
)
0.26
0.24
0.22
0.20
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
00.6 0.8 1.0 1.2 1.61.4 1.8 2.0
M
Histogram
Lognormal
Lognormal (3P)
Normal
Note: LN and LN (3) fits coincide
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201370
lognormal distribution provides distributions
which are generally intermediate between
the normal and lognormal distributions
(Figure 5), with similar results for the
p-values (Table 3).
On the basis of the results of the two
standard distribution fitting approaches
studied, it can be concluded that the
data fits both the normal and lognormal
distributions, although the ordinary
lognormal distribution has a slight
edge, particularly towards the lower tail
(Figure 5). However, theoretically M
ranges from zero to infinity, resulting in
an asymmetric distribution with a zero
lower bound and an infinite upper bound.
The lognormal probability density function
is often the most suitable theoretical
model for such data, as it is a continuous
distribution with a zero lower bound and
an infinite upper bound. On the basis of
this practical consideration, past studies
(e.g. Phoon 2005; Briaud & Tucker 1988;
Ronold & Bjerager 1992; Titi & Abu-Farsakh
1999; FHWA-H1-98-032 2001; Rahman et
al 2002) have recommended the lognormal
distribution as the most suitable theoretical
model for model uncertainty. Furthermore,
in the Probabilistic Model Code by the Joint
Committee on Structural Safety (JCSS)
(2001), model uncertainty is modelled by
the lognormal distribution. Therefore the
lognormal distribution is considered a valid
probability model for M. Nonetheless, it
should be acknowledged that there could
be some other distributions that can
provide a better fit to the tails. Generally
such advanced and complex distributions
require a large sample size. For a small
sample size, as is the case in this study, such
distributions may only lead to a refinement
of the results, but not a significant
improvement.
CONCLUSIONS
Pile foundation design uncertainties are
captured by the M statistics. The M statistics
constitute the main input into reliability
calibration and associated studies. Since
the M statistics are derived from raw data,
statistical characterisation of such data is
of paramount importance. Accordingly
characterisation of the data collected for
pile foundation reliability studies have been
presented in this paper. The key conclusions
reached are as follows:
■ Based on the mean values for M, the
static formula yields a positive bias of
between 1.04 and 1.17, except for the
B-NC data set where Qi is on average
slightly less than Qp with mM = 0.98,
which is slightly un-conservative.
■ There is a distinct trend that driven
piles depict higher variability compared
to bored piles, irrespective of materials
type. This suggests that the densification
induced by pile driving is not fully cap-
tured by existing procedures for selecting
design parameters.
■ The variability in non-cohesive materials
is higher than that in cohesive materials.
This is attributed to the high degree of
empiricism associated with the selection
of pile design parameters (Nq, ks and δ) in
non-cohesive soils.
■ The values of mM close to 1 and the
relatively large values of sM or VM
indicate large probabilities of realisa-
tions of M in the un-conservative range
M < 1. Therefore the lower tail of the
distribution of M is of specific interest
for application of the results in reliability
assessment.
■ At the customary 5% confidence level,
the chi-square goodness-of-fit test results
indicate that both the normal and log-
normal distributions are valid theoretical
distributions for M. However, when
taking into account other practical con-
siderations, the lognormal distribution
is considered to be the most appropriate
distribution for M.
■ None of the pile design parameters is
significantly correlated with the model
factor. From the probabilistic perspec-
tive, this implies that the variation in
the model factor is not caused by the
variations in the key pile design para-
meters. Therefore it is correct to model
the model factor as a random variable.
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Table 3 Chi-Square goodness-of-fit test results
Pile class
Chi-Squared test p-value
Normal LognormalGeneral Lognormal
(3P)
Driven piles 0.32 0.60 0.43
Bored piles 0.07 0.77 0.20
Piles in non-cohesive soil 0.32 0.81 0.81
Piles in cohesive soil 0.69 0.68 0.70
All piles 0.29 0.62 0.51
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 71
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SANS 2011. SANS 10160-5:2011: Basis of Structural
Design and Actions for Buildings and Industrial
Structures. Part 5: Basis for Geotechnical Design
and Actions. Pretoria: South African Bureau of
Standards.
Titi, H H & Abu-Farsakh, M Y 1999. Evaluation of
bearing capacity of piles from cone penetration test
data. Project No. 98-3GT, Baton Rouge: Louisiana
Transportation Research Centre.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201372
INTRODUCTION
The model factor statistics presented in the
accompanying paper (Dithinde & Retief 2013
– please turn to page 60) provide a clear indi-
cation of the need for a systematic treatment
of the variability and uncertainty of design
parameters and procedures in geotechnical
design practice. The principles of reliability-
based design providing the conceptual basis
for such systematic treatment are sufficiently
established to be captured in standardised
procedures such as the International
Standard ISO 2394:1998 (adopted as SANS
2394:2004) and converted into operational
basis of design procedures such as Eurocode
EN 1990:2002. The standardised procedures
are based on limit states design format with
a reliability-based framework to ensure
appropriate performance levels for the load-
bearing capacity and characteristics of the
structure or civil engineering works.
Sufficient advances in the theory of reli-
ability have been made to derive guidelines
for levels of performance as expressed in
terms of reliability representing probability
of failure (Pf) for classes of structures and
facilities. For various reasons, however,
there is insufficient information available to
develop reliability-based procedures purely
on frequentist or statistical probability
models. The most compelling argument for
taking information from existing practice
into account when reliability-based design
procedures are developed comes from the
success of present practice and codes which
primarily rely on experience-based expertise
and judgement.
Capturing the reliability performance
from existing practice which is deemed
to be acceptable, such as presented in the
accompanying paper, is an important source
of information for the development of
standardised design procedures. One of the
possible applications of the information on
existing practice is to obtain an indication of
acceptable levels of reliability, in comparison
to other ways in which target reliability
is established. This is the purpose of the
Pile design practice in southern Africa Part 2: Implicit reliability of existing practice
J V Retief, M Dithinde
Limit state design has become the basis of geotechnical design codes worldwide. With the semi-probabilistic limit state design approach, load and resistance factors of (deterministic) design functions are calibrated on the basis of reliability theory. The calibration is done to obtain procedures that will ensure that a target level of reliability is exceeded under the design conditions within the scope of the design function. This is conventionally expressed in terms of the reliability index (β), which is related to the probability of failure (Pf). Acceptable existing design practice is an important source of information on appropriate levels of reliability. This paper uses the results from a pile load test database to evaluate the reliability levels implied in the current South African pile design approach. The results of the analysis indicate that the reliability index values for ultimate limit state failure of single piles implicit to present design practice vary with the pile class. However, the influence of the probability model applied is more significant. Based on conventional and standardised procedures for reliability analysis, a representative implicit reliability index value βI,Rep 3.5 is obtained, corresponding to a probability of failure Pf = 2.10-4. The values for various sets of pile conditions range from βI = 3.1 (Pf = 1.10-3) to βI = 4.3 (Pf = 1.10-5). This compares well with target levels of reliability for structural and geotechnical performance of βT = 3.0 as set in SANS 10160-1:2011 Part 1 Basis of structural design. These indicative results provide a useful reference base to establish the reliability of existing and therefore acceptable South African pile design practice. It could also be interpreted as indicative of geotechnical design practice in general. The standard SANS 10160-5:2011 Part 5 Basis for geotechnical design and actions provides the framework for future calibration investigations.
TECHNICAL PAPER
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 72–79, Paper 813 Part 2
PROF JOHAN RETIEF (Fellow of SAICE) has, since
his retirement as Professor in Structural
Engineering, maintained involvement at the
Stellenbosch University, supervising graduate
students in the fi eld of risk and reliability in civil
engineering. He is involved in various standards
committees, serving as the South African
representative to ISO TC98 (basis of structural
design and actions on structures). He holds a BSc (cum laude) and a DSc from
the University of Pretoria, a DIC from Imperial College London, and an MPhil
from London University. Following a career at the Atomic Energy
Corporation, he joined Stellenbosch University in 1990.
Contact details:
Department of Civil Engineering
Stellenbosch University
Private Bag X1
Matieland
Stellenbosch
7602
T: +27 21 808 4442
F: +27 21 808 4947
DR MAHONGO DITHINDE (Visitor) holds a PhD in
Civil Engineering from the Stellenbosch
University, an MSc in Foundation Engineering
from the University of Birmingham (UK), and
BEng in Civil Engineering from the University of
Botswana. He works as a Senior Lecturer at the
University of Botswana. His specialisation and
research interests are in the broad area of
geotechnical reliability-based design. In addition to academic work, he is also
a geotechnical partner for Mattra International where he is active in
consultancy work in the fi eld of geotechnical engineering.
Contact details:
Department of Civil Engineering
Stellenbosch University
Private Bag X1
Matieland
7602
South Africa
Department of Civil Engineering
University of Botswana
Private Bag UB 0061
Gaberone
Botswana
T: +267 355 4297
F: +267 395 2309
Key words: pile foundations, South African practice, geotechnical design,
reliability level
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 73
present paper. In the process, representative
probability models for pile resistance are
obtained, that could subsequently be used
for reliability calibration of standard design
procedures.
A brief overview is firstly provided of the
state of limit states design in South Africa –
the standardised way in which the principles
of reliability is formulated and related to
limit states design, including a discussion of
target levels of reliability in general and as
established for South Africa, serves as basis
for comparison of implicit levels of reliability
derived for existing practice. Ultimately
such implicit levels of reliability are derived,
considering alternative probability models
from the results of the accompanying paper,
and determining representative cases and
probability models.
RELIABILITY-BASED GEOTECHNICAL
LIMIT STATES DESIGN
The need of converting the now defunct
Code of Practice for Pile Foundation Design
(SABS 088:1972) to limit states design princi-
ples was recognised by the South African pil-
ing industry as far back as 1993. A concerted
effort was also made by the Geotechnical
Division of the South African Institution
of Civil Engineering (SAICE) to adopt and
apply geotechnical limit state design in
South Africa, as summarised by Day &
Retief (2009). Recent international and local
developments have now added impetus to
the introduction of probabilistic-based limit
state geotechnical design in South Africa.
These include:
i. Increased interest in harmonisation of
technical rules for design of building and
civil engineering works internationally
as is demonstrated for instance by the
activities of the ISSMGE (Orr et al 2002)
and across disciplines, as demonstrated
by the Eurocode set of design standards
(CE 2002).
ii. The international acceptance of semi-
probabilistic limit states as the standard
basis on which the new generation of
geotechnical codes are being developed
today, such as Eurocode EN 1997:2004
Geotechnical design (EN 1997:2004)
and the FHWA Manual for Load and
Resistance Factor Design (LRFD) of
bridge substructures (FHWA 2001).
iii. The publication of the revised South
African Loading Code (SANS 10160:2011
Basis of structural design and actions
for buildings and industrial structures)
providing the reliability framework in
Part 1 Basis of structural design, with
the implication that the subsequent
materials codes will be based on the
same framework. Geotechnical design is
included in this framework with the first
step taken in Part 5 Basis of geotechnical
design and actions as related to buildings
and similar industrial structures.
The main advantage of the derivation of geo-
technical limit states design procedures from
the principles of reliability is that it provides
a rational basis for such practice. In addition
to enhancing the rationality of design for a
specific situation (limit state, failure mode,
construction type, etc) it also improves the
consistency between the various situations
within a single construction (geotechnical,
substructure, superstructure, structural
materials) or extends to the scope of applica-
tion of the design procedures.
Common principles of reliability provide
the rational basis for unification of geo-
technical and structural design. This is an
essential requirement for interrelated but
specialised design procedures, not only since
both elements are shared by individual con-
structions, but also for the purpose of tech-
nical communication between geotechnical
and structural design practitioners.
At the highest level a rational basis for
the underlying models and procedures is the
only way in which international harmonisa-
tion of design practice can be maintained.
The importance of sharing the wealth of
international experience on the basis of
harmonisation is usually appreciated, but
the ability to provide optimally for local
conditions whilst maintaining fundamental
alignment with internationally accepted
procedures is not always achieved or even
attempted.
The theory of reliability, as applied
to determine the performance of civil
engineering works, is sufficiently mature
to formulate standardised procedures
for its application in design practice:
The International Standard General
principles on reliability for structures, ISO
2394:1998, was adopted as a South African
National Standard SANS 2394:2004. The
Joint Committee on Structural Safety
Probabilistic Model Code (JCSS-PMC 2001)
provides more detailed pre-normative reli-
ability procedures and models. A notable
development is the conversion of general
reliability concepts into operational proce-
dures as captured in the Eurocode Standard
EN 1990:2002 Basis of structural design
which provides a common basis for the
set of Eurocodes. SANS 10160-1:2011 and
SANS 10160-5:2011 respectively provide
harmonisation with the Eurocode for the
basis of design and geotechnical design. EN
1990 Annex C Basis of partial factor design
and reliability analysis serves as reference
for standardised reliability practice, with
probabilistic models taken from Annex D
Design assisted by testing in this paper.
A critical element of converting reliability
analysis into design procedures is the estab-
lishment of acceptable levels of reliability.
Some guidance on appropriate levels of reli-
ability is given in SANS 2394:2004 and JCSS-
PMC:2001. Application of appropriate levels
of reliability in South African structural
design is discussed by Retief & Dunaiski
(2009). The implicit levels of reliability of
existing design practice are recognised in
standardised procedures such as SANS
2394:2004, EN 1990:2002 and FHWA HI-98-
032 (FHWA 2001) as a basis for selecting
target levels of reliability.
MOTIVATION AND PURPOSE
OF INVESTIGATION
Given the importance of the reliability
performance of existing practice serving as
starting point for the calibration of more
refined limit states design procedures, the
purpose of this paper is to provide such an
assessment of present pile construction and
design practice in southern Africa. Implicit
reliability serves as baseline for acceptable
practice. Inconsistency in reliability across
the scope of application can be identified,
considering possible remedies and adjust-
ments. Systematic calibration of the provi-
sions of SANS 10160-5:2011 is another pos-
sible application of the results reported here.
The purpose of this paper is to assess the
reliability performance of southern African
pile design practice by exploring the applica-
tion of the database of model uncertainties
of pile resistance as reported by Dithinde et
al (2011) where particulars of pile load tests
and associated geotechnical information,
design parameters and descriptive statistics
are fully reported. Information from this pile
database, together with additional statistical
treatment as reported in the accompany-
ing paper, serves as input to the reliability
assessment reported here. A comprehensive
range of soil conditions, pile geometry and
resistance is incorporated in the database, to
provide extensive representation of southern
African pile construction practice in this
assessment.
RELIABILITY CONCEPTS
The concepts of reliability, as developed
for geotechnical and structural design, are
defined in SANS 2394: 2004. The operational
basis for partial factor design and reliability
analysis as presented in EN 1990:2002 is fol-
lowed here since these guidance procedures
also apply to SANS 10160-1:2011 for the gen-
eral basis of design and SANS 10160-5:2011
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201374
specifically for the geotechnical basis of
design.
The reliability-based performance func-
tion for a structure g(X1; … Xj) as a random
function of the random variables (X1; … Xj)
is expressed as a limit state function indica-
ting the state beyond which the structure
no longer satisfies the design performance
requirements, as shown in Equation 1. The
random variables consist of a specified set
of variables representing physical quantities
which characterise actions, and material
properties (including soil properties and geo-
metrical quantities) conventionally defined
as basic variables. The probability of failure
of the structure Pf is given by Equation 2. Pf
can also conveniently be expressed in terms
of the reliability index β and the cumula-
tive normal distribution function Ф or the
inverse normal distribution function Ф-1 as
given by Equation 3.
g(X1, … Xj) = 0 [1]
Pf = P[g(X1, … Xj) < 0] [2]
Pf = Φ(–β) or β = –Φ -1(Pf) [3]
Two distinct formats of reliability-based
design applies, with Equation 1 representing
the probabilistic format. The deterministic
partial factors format for standardised limit
states design is defined in SANS 10160-
1:2011; the application of the partial factors
format to geotechnical limit states design is
defined in SANS 10160-5:2011. Reliability
calibration is the process of determining
appropriate values for the partial factors to
achieve a specified level of reliability for a
given limit state as derived from Equation 1.
Since partial factors design procedures are
expressed in deterministic format with vari-
ous partial factors calibrated on principles
or probabilistic reliability, it is classified as
a semi-probabilistic procedure or Level 1
reliability-based design (EN 1990:2002).
Although the theory of reliability is
firmly rooted in the mathematical theory of
probability and related statistics, its success
as an operational basis for geotechnical and
structural design is directly related to the
simplification and approximation applied to
the representation of the basic variables (Xi)
and solving of the performance function,
Equation 1. The ultimate approximation
comes from the conversion of Equation 1
into a deterministic design function which
employs partial factors that are based on the
theory of reliability (see for example Holický
et al 2007).
The most important level of approxi-
mation is related to the degree to which
sources of variability and uncertainty are
treated comprehensively. On the one hand
it is granted that reliability modelling does
not provide for a vital component of failure,
which derives mainly from phenomena
such as gross human error. Therefore reli-
ability levels are often referred to as notional
reliability. On the other hand reliability
modelling presents a powerful tool for iden-
tification of critical sources of uncertainty,
providing the basis for quality management
measures in defence against gross error.
The most compelling argument for reli-
ability theory to provide for variability and
uncertainty is its modelling and predictive
capability, equivalent to structural mechan-
ics modelling of load bearing behaviour for
structural and geotechnical design.
TARGET LEVEL OF RELIABILITY
Central to the reliability basis of design
procedures is the calibration of partial fac-
tors, which consists of an inverse reliability
analysis process of calculating partial factors
to exceed a given or target level of reliability
(βT) as an initial step. The establishment
of an appropriate level of reliability in
accordance with the design case under
consideration therefore plays a key role in
reliability-based limit states design, or more
specifically the calibration of standardised
design procedures.
Several approaches for setting the target
reliability index are available. A pragmatic
approach which is mostly followed is to apply
a combination of the various methods. The
methods include:
■ Risk-based cost-benefit analysis and
optimisation
■ Failure rates estimated from actual case
histories
■ Value set by regulatory authorities for a
given limit state
■ Range of beta values implied in the cur-
rent design practice.
Risk-based optimisation of reliability
The most rational approach for establish-
ing the target level of reliability is through
cost-benefit analysis and optimisation.
Cost-benefit analysis entails the study of the
variation of the initial cost, maintenance
costs, and the costs of expected failure. It
therefore represents the determination of
reliability in the context of risk optimisa-
tion. The matter of the necessary inclusion
of the loss of human life leads this process
to be highly controversial. However, the
relatively recent development of the concept
of the Life Quality Index (LQI) which relates
human life in neutral terms of marginal
changes in life expectancy and working life
(see for example Rackwitz 2008) should
resolve this controversy. Although the LQI
concept developed rapidly in recent years, no
operational guidelines are available as yet,
particularly for South African conditions.
Reliability levels for
geotechnical design
The target probability of failure for a given
structure can be established on the basis
of failure rates estimated from actual case
histories. For the case of foundations it is
estimated that probability of failure (Pf)
ranges from 0.001 to 0.01 – about one-and-
a-half orders of magnitude below a “mar-
ginally acceptable” level and half an order
of magnitude below an “acceptable” level
according to the FHWA Manual for LRFD
bridge pile design (FHWA 2001). However,
many authors (e.g. Phoon 1995; Baecher
& Christian 2003; Christian 2004) have
cautioned that the probability of failure for
constructed facilities is not solely a function
of the design process uncertainties, as is the
case for the calculated failure probabilities.
Therefore, for comparison with calculated
failure probabilities, the rate of failure from
FHWA (2001) should be adjusted by one
order of magnitude downward (Phoon 1995).
If the suggested adjustments are effected,
the probability of failure for foundations
becomes 0.001 to 0.0001 which corresponds
to target reliability index values (βT) of
between 3.1 and 3.7.
Reliability levels for South
African practice
The target levels of reliability for South
African constructions within the scope of
the revised Loading Code SANS 10160-
1:2011 are discussed by Retief & Dunaiski
(2009). Motivation is provided for maintain-
ing the reference level of βT = 3.0 to be the
same as that applied in SABS 0160:1989
(Milford 1988). The decision was based
mainly on the argument that there was no
evidence or justification for adjusting the
level of reliability for South Africa. The
reference reliability agrees with practice in
countries such as the USA and Canada. It
is consistent with guidance given in SANS
2394:2004 when South African economic
conditions are taken into account.
The most serious challenge to maintain-
ing the reference level of reliability for South
Africa came from the default value of βT =
3.8 applied in Eurocode. It should be noted,
however, that this value is not normative
in Eurocode, but since safety is treated as a
national issue βT can be selected by member
countries. The high value of reliability
applied in Eurocode was also judged to
reflect higher levels of economic develop-
ment, which implies lower relative cost of
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 75
construction (or higher affordability) and
consequent higher safety levels obtained in
risk-based optimisation.
A factor which moderates the difference
between South African target reliability and
the Eurocode default value is that in calibra-
tion the reliability is seen as a constraint,
whilst the Eurocode value is often seen as a
target to be attained on average (SAKO 1999).
The implication is that βT = 3.0 as a con-
straint differs less from βT = 3.8 as an average
target than it may appear at first glance.
Another moderating factor is that the
South African reference value applies to a
more restricted reliability class of construc-
tion (RC2, typically buildings up to four
storeys high) which corresponds to the lower
part of the corresponding Eurocode reliabil-
ity class (RC2). For the next South African
reliability class (RC3, typically buildings of
five to fifteen storeys) βT = 3.5 approaches
that of the undifferentiated Eurocode RC2.
Implicit reliability levels
of acceptable practice
Keeping the design methodology compat-
ible with the existing experience base is
consistent with the evolutionary nature of
codes and standards that require changes to
be made cautiously and deliberately (Phoon
1995). In the spirit of a Bayesian approach
towards reliability, proven experience is an
important source of information that can be
combined with other sources of data on vari-
ability and uncertainty in reliability-based
design.
Accordingly this paper investigates
the level of reliability of pile foundations
designed in accordance with the static
formula. This is done by determining the
implicit levels of reliability for the current
working stress design (WSD) methods for
piles by comparing design values to reli-
ability models for pile resistance. Reliability
modelling of pile resistance is based on the
uncertainty of pile resistance, as observed by
the comparison of the interpreted resistance
from pile tests and the predicted value for
an extensive survey of pile tests done across
southern Africa, representing a wide range of
conditions, pile construction practices and
configurations.
CONCEPTS OF RELIABILITY
ANALYSIS AND CALIBRATION
Although reliability calibration and the
analysis of existing practice form two dis-
tinct components of the application of reli-
ability theory in design, they are so closely
related that some concepts of their treatment
in practice can share a common formula-
tion. The common concepts are related to
a specific level of reliability over a defined
range of conditions. The following issues are
relevant to reliability calibration of design
procedure such as partial factor limit states
design; therefore by implication also to reli-
ability assessment of existing practice:
■ The representative level of reliability
is either the target reliability in the case
of calibration, or the implicit reliability in
the case of assessing acceptable existing
practice; conventionally expressed in
terms of a reliability index as βT and βI
respectively. The following alternative
approaches apply to the representative
reliability:
■ An average value is taken across the
range of conditions, although the
value may be significantly exceeded in
some cases – this is the view generally
taken in Eurocode, also associated
with relatively high levels of reliability
(typically βT = 3.8).
■ A lower limit value is taken as a con-
straint, generally to be exceeded – this
view is taken in South Africa, where
the representative value is also rela-
tively low (typically βT = 3.0).
■ Consistency of reliability over the range
of application is an objective to ensure
that significantly different levels do not
occur under different design conditions
or cases; in particular systematically as
a function of classes of applications (for
example construction and/or soil type in
the case of piles) or other design para-
meters. The following effects need to be
considered:
■ Conditions under which the lowest
level of reliability is achieved will
control the measures taken.
■ Systematic exceeding of the repre-
sentative reliability represents
conditions which may be unjustifiably
conservative.
■ Consistency of reliability can be
assessed in terms of the absence of
different levels and the absence of
trends, or at least smooth transi-
tions related to continuous design
parameters.
■ The level of confidence of calibration
or assessment should take into account
that it is at best an approximate process,
due to the predictive nature of design. It
is based on limited information, either for
parametric calibration or assessment of
existing practice such as presented here,
or on the actual conditions in the case of
design of a specific project. Calibration or
assessment should therefore be moder-
ated on the following basis:
■ A limited level of confidence applies
to both the required reliability levels
(target or implied) and measures to
achieve these – all based on acceptable
performance of present practice.
■ Best estimates of reliability is there-
fore generally acceptable, only revert-
ing to conservative modelling when
there is specific justification for such
measures.
It should be noted that calibration back to
existing practice does not imply maintaining
the status quo just in a more complex format!
With calibration, allowance can subsequent-
ly be made for rectifying conditions where
reliability is inconsistent with the (present)
general practice, either insufficient or unjus-
tifiably conservative. Where insufficient reli-
ability derives from uncertainty, as opposed
to variability, appropriate measures can be
considered, such as additional investigation
consisting of gathering of data and improved
modelling.
RELIABILITY MODELLING
OF PILE RESISTANCE
The two predominant classes of uncertainty
for geotechnical design can be distinguished
as (i) uncertainties associated with design
soil properties and (ii) calculation model
uncertainties. With regard to geotechnical
property uncertainties, significant research
has been done to generate statistics on
individual components of soil parameter
uncertainty. Conversely, model statistics are
relatively scarcer. In fact, the lack of model
statistics is considered to be a key impedi-
ment to the development of geotechnical
reliability-based design (Phoon 2005). This
consideration provided the motivation for
the investigation of model uncertainty of pile
resistance as reported in the accompanying
paper and by Dithinde et al (2011).
Model uncertainty, as defined for exam-
ple in ISO 2394:1998, EN 1990:2002 and
JCSS PMC (2001), reflects uncertainties of
the structural mechanics model. Variability
of variables, mainly actions, material proper-
ties and geometry is represented explicitly as
basic variables in the performance function,
as defined in Equation 1. In experimental
determination of model uncertainty, values
of basic variables are determined determin-
istically through testing. The implication is
that model uncertainty represents not only
the effect of the structural mechanics model,
but also of all the sources of uncertainty, and
even variability that is not explicitly captured
in the testing process.
The modelling uncertainty reported in
the accompanying paper not only reflects the
uncertainty of the static pile design formula,
but also the interpretation of site investiga-
tions and conversion of measurements into
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201376
material properties. Due to the uncertainty
of material properties and the absence of its
representation as basic variables, the model
factor can be considered to represent a prob-
ability model of pile resistance as predicted
by the static pile formula. The procedure for
using soil properties based on subsurface
data surveys to predict pile resistance as
described by Dithinde (2007) implies that the
uncertainties from soil properties are incor-
porated in the predicted values. The pile
resistance probability model can therefore be
taken from the distributions and summary
statistics presented in the accompanying
paper.
In applying working stress design (WSD)
procedures through the static pile design
function, the emphasis is predominantly
placed on pile resistance. Whilst loads are
treated at nominal un-factored values,
safety is treated by the application of a fac-
tor of safety to pile resistance. The initial
parametric investigation of pile design
practice is therefore based on considering
pile resistance only. The effect of consider-
ing variability of loading is then considered
subsequently.
Pile resistance only
In the definition of model uncertainty given
in the accompanying paper, given here as
Equation 4, the interpreted pile capacity (Qi)
can be taken to represent the probability rep-
resentation of the pile resistance (RRel), and
the predicted capacity (Qp) the deterministic
nominal pile resistance (Rn). RRel can there-
fore be expressed by Equation 5. The static
pile design function is given by Equation 6 in
terms of a factor of safety (FS) and nominal
dead load (Dn) and live load (Ln). From
Equations 5 and 6, the specific performance
function given by Equation 7 can be convert-
ed into a parametric limit state function as
shown in Equation 8. The implicit reliability
index value (βI) can then be obtained from
Equation 9 in terms of the probability model
for M and the factor of safety FS which has a
deterministic value.
M = Qi
Qp
[4]
RRel = M.Rn [5]
Rn
FS = Dn + Ln [6]
g = RRel – (Dn + Ln) [7]
g = M × Rn – Rn
FS = 0 = M –
1
FS [8]
βI = Φ–1[Pf(M < 1
FS)] [9]
Values for βI can be obtained in terms of the
pile classes identified in the accompanying
paper. This is done by applying the reported
statistics as parameter estimates for
probability models for M. Comparison of
βI-values for alternative pile classes provides
an indication of the representativeness and
consistency of implicit reliability across the
range of conditions represented by the M
statistics.
As a point of departure the case of a
single combined pile class (ALL) is used as
a representative case to estimate βI,Rep. This
case is then used to investigate the influence
of the probability distribution on βI-values.
The influence of pile class on βI-estimates is
considered below.
The estimate for βI,Rep is based on the
lognormal distribution as standardised prac-
tice for resistance. Generally an overall factor
of safety of 2.5 is regarded as an acceptable
value for piles and has become a norm in
southern Africa (Byrne & Berry 2008). As
indicated in the accompanying paper, the
normal distribution, which is convention-
ally used as the default first approximation
distribution in reliability analysis, could also
be considered. The mild degree of skew-
ness indicated from the sample statistics
presented in the accompanying paper can
be taken into account by considering the
general lognormal distribution. The results
are summarised in Table 1, where values for
the estimated distribution parameters are
also given.
The value for βI,Rep is clearly sensitive
to the distribution applied to represent M
and therefore needs some interpretation:
The value of βI,Rep = 3.5 as obtained from
the lognormal distribution is taken as an
estimate of acceptable practice in accordance
with standardised reliability procedures. The
value of βI,Rep = 2.3 obtained from the nor-
mal distribution is considered to be too low
to reflect acceptable practice. The low value
of skewness taken into account by the gen-
eral lognormal distribution provides a slight
improvement on this apparently low level of
reliability; this result should be considered as
a lower limit estimate of implicit reliability,
as βI,Low = 2.4.
An indication of the representativeness
of these values of βI across the range of pile
classes is presented in Table 2. The value for
βI,Rep = 3.5 listed in Table 1 for the combined
group (ALL) generally lies in the lower range
of the values obtained for the various pile
classes as listed in Table 2. The value of 3.5
is therefore taken to be in agreement with
the approach of defining target reliability at
a lower constraint value, and is thus ranked
to indicate the mid-range value of implicit
reliability.
The class of piles driven in non-cohesive
soil (D-NC) is ranked at a special-range
due to its low value in comparison to the
representative implicit reliability. The more
general pile class of non-cohesive soil (NC)
is classified to be in the low-range. For all
other pile classes, higher values for βI,Rep are
obtained (Mid+); with significantly higher
values (High) obtained for bored piles in
cohesive soils (B-C), as listed in Table 2.
It is therefore concluded that the values
for βI,Rep and βI,Low obtained from Table 1
provide a reasonable representation of the
Table 1 Representative implicit reliability βI,Rep for alternative probability distributions for
combined pile class (ALL) and FS = 2.5
Distribution parameters Distribution Indicator βI
Mean 1.10 Lognormal Representative 3.52
Standard deviation 0.31 Normal – 2.26
Skewness 0.24 General Lognormal Low 2.45
Table 2 Range of implicit reliability values βI and associated pile classes (FS = 2.5)
Range Pile class Lognormal (βI,Rep)
Special Driven piles in non-cohesive soil (D-NC) 3.1
Low Non-cohesive soil (NC) 3.2
Mid Combined group (ALL) 3.5
Mid +
Driven piles (D) 3.7
Bored piles (B) 3.8
Bored piles in non-cohesive soil (B-NC) 3.75
High
Driven piles in cohesive soil (D-C) 4.1
Cohesive soil (C) 4.2
Bored piles in cohesive soil (B-C) 4.3
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 77
implicit reliability of existing practice, but
that the special case of driven piles in non-
cohesive soils (D-NC) should be considered
separately for systematically lower levels of
reliability.
In addition to obtaining a lower limit
estimate of the implicit reliability as based
on the probability distribution, confidence
level estimates of the distribution para-
meters can be applied. For this purpose the
confidence limit estimates presented in the
summary statistics in the accompanying
paper are utilised. A single-sided 75% con-
fidence limit estimate is used, as suggested
by Eurocode EN 1990:2002 for cases where
parameter estimation is based on vague
prior distributions. The lower confidence
limit value is used for the mean and the
upper limit for the standard deviation. The
confidence limit estimates βI,Conf are listed
in Table 3 for the two cases identified above
as representative (ALL) and the special lower
pile class (D-NC). Values are based on the
confidence level distribution parameters,
also listed in Table 3, applied to the lognor-
mal distribution.
Although the confidence limit implicit
reliability listed in Table 3 is reduced for
the representative case of the combined
pile conditions listed in Table 1, the change
from 3.5 to 3.2 is not too significant. For the
special case D-NC the change from 3.3 to 2.2
is, however, indicative of not only the ten-
dency of systematic lower value of implicit
reliability, but also of the poor quality of its
prediction.
The influence of the FS-value selected
in pile design on βI-estimates is shown in
Table 4. For comparison, target levels of reli-
ability (βT) are also listed, as given by SANS
10160-1:2011 for different reliability classes
of building structures. The comparison indi-
cates reasonable agreement between βI,Low
for FS(2.0, 0.5 and 3.0) and βT for reliability
classes (RC1, RC2 and RC3}. The values
for βI,Rep generally exceed that for the cor-
responding βT showing a trend of widening
of the difference for the higher FS values and
reliability classes.
Implicit reliability based on
resistance and loads
Expression of the performance function
given by Equation 1 in terms of probabilistic
models for resistance (R), dead (D) and live
(L) is given in Equation 10.
g(R, D, L) = R – (D + L) [10]
A normalised reliability model for Equation
10 can be obtained for parametric reliability
analysis by representing each basic variable
(X) by the ratio of mean to nominal value
(μX/Xn) and the relationship between the
nominal values (Rn, Dn and Ln) given by
the static pile design function (Equation 6).
Similar to the treatment above, the resis-
tance R is represented by the probability
model for M as given by Equation 5. The
load models reported by Kemp et al (1987)
used for the conversion of structural design
in South Africa from working stress to limit
states design procedures listed in Table 5 can
be used for models of D and L.
Different loading conditions can be
treated parametrically through the ratio
Ln/Dn. A typical range of Ln/Dn ratios is 0.5–
1.5 for concrete structures and 1–2 for steel
structures (Melchers 1999). For foundations
dead load would dominate, tending towards
the lower range of load ratios. Based on this
information, a practical range of Ln/Dn ratio
of 0.5 to 2 was adopted as sufficiently repre-
sentative of structures in general. The special
cases of dead and live loads only are indica-
tive of the outer limits of load conditions. For
this reason the range of analysis was done for
Ln/Dn between 0 and 2; the case for Ln only
was also calculated. Parametric reliability
analysis of Equation 10 was done using
Second Order Reliability Method (SORM)
software provided by Holický (2009).
The results for the representative reli-
ability analysis (βI,Rep) based on the model
for the complete dataset (ALL) are shown in
Figure 1(a); the results for the special case
of driven piles in non-cohesive soil (βI,D-NC)
are shown in Figure 1(b). Separate graphs are
provided for the values of FS (2.0, 2.5 and
3.0). The results for the analysis of the com-
plete version of Equation 10 are labelled as
M,D,L(FS); the off-scale case of live load only
is indicated as an arrow () labelled M,L(FS);
the results from the previous analysis consid-
ering pile resistance only are indicated as the
horizontal line labelled M(FS).
As can be expected, the inclusion of the
effects of loading reduces the level of implicit
reliability. Furthermore, the effects are
dependent on the ratio of live to dead load
(Ln/Dn), with trends similar to that obtained
with load calibration analyses (Holický &
Retief 2005). The lower values of implicit
reliability occur for conditions dominated
by live load, which generally can only be
expected under exceptional conditions for
pile foundations. Over the operational condi-
tions of loading dominated by Dn the values
for βI,Rep compare well with the target reli-
ability index values βT listed for the various
reliability classes listed in Table 4. For the
special case of driven piles in non-cohesive
soils, the values obtained for βI,D-NC are
systematically lower than the corresponding
values for βT.
Table 3 Confidence limit (βI,Conf) values of implicit reliability as based on lognormal distribution
and listed parameters (FS = 2.5)
Combined group (ALL) Driven, non-cohesive (D-NC)
βI,Conf 3.2 2.3
Confidence level distribution parameters
Mean 1.07 1.03
Standard deviation 0.32 0.40
Table 4 Implicit reliability (βI) as function of the selected value for FS, as compared to target
reliability (βT) for reliability classes
FS = 2.0 FS = 2.5 FS = 3.0
Combined group (ALL) (βI,Rep) 2.7 3.5 4.2
Driven, non-cohesive (D-NC) (βI,Low) 2.4 3.1 3.6
SANS 10160-1 Reliability Class RC1 RC2 RC3
Target reliability (βT) 2.5 3.0 3.5
Table 5 Load models for reliability calibration (Kemp et al 1987)
Type of load CodeMean load /
Nominal loadCoefficient of variation
Type of distribution
Dead (permanent) load
ANSI A58 1.05 0.10 Normal
Australian 1.05 0.10 Lognormal
SABS 0160 1.05 0.10 Lognormal
Live (office): lifetime max
ANSI A58 1.0 0.25 Gumbel
Australian 0.7 0.26 Gumbel
SABS 0160 0.96 0.25 Gumbel
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201378
DISCUSSION AND CONCLUSIONS
The resistance statistics for pile design
practice in southern Africa, as reported
in the accompanying paper, are applied in
this paper to assess the implicit levels of
reliability of such practice. This is done by
deriving reliability models for pile resistance
by applying the model statistics as parameter
estimates to internationally standardised
probability distributions for geotechnical and
structural resistance. Values for implicit reli-
ability, as expressed by the reliability index
(βI), are determined to obtain a measure of
the representative level of performance of
pile design practice. In addition to obtaining
best estimate values for βI, conservative esti-
mates are also made in terms of more severe
interpretation of parameter estimates or
probability distributions for pile resistance.
Consistency of reliability is also investi-
gated across the range of pile construction
practice.
Implicit levels of reliability are derived for
two reliability performance models:
i. Considering pile resistance only and
neglecting loading as basic variable, in
accordance with design practice reflected
by the working stress design format for
pile design, where a single factor of safety
is applied to pile resistance.
ii. Including reliability models for dead (per-
manent) and live (variable) loads into the
performance function, using the models
on which the implementation and calibra-
tion of limit states design for South Africa
were based.
The two main issues of concern for deter-
mining model statistics and applying these
to reliability models for pile resistance
identified in the accompanying paper are
(i) the probability distribution used, and (ii)
the scope of application as based on dif-
ferentiated classes of pile conditions. It was
found that the different plausible probability
distributions have a more significant influ-
ence on the levels of implied reliability than
differentiation into classes of pile conditions.
The default distribution applied in
reliability analysis is generally the normal
distribution, to represent the basic step from
deterministic design practice to at least pro-
vide for the dispersion of basic variables. The
lognormal distribution function at the same
basic level of approximation has the added
utility of not predicting negative values. This
is particularly relevant when the lower tail
of the distribution is considered, such as for
resistance. However, values for βI vary from a
low value βI,N = 2.3 for the normal distribu-
tion to a relatively high value βI = 3.5 for the
lognormal distribution, in both cases for the
combined set of pile conditions and general
design practice based on FS = 2.5. When
skewness obtained from the model statistics
is taken into account by applying the general
lognormal distribution, βI = 2.4 is obtained.
Selecting the lognormal distribution as
basis to obtain a representative value for the
reliability index βI,Rep = 3.5 is based on con-
sideration of standardised practice for reli-
ability analysis, supported by the marginal
preference obtained from the model statistics
results presented in the accompanying paper.
In accordance with Equation 3 the reliability
index value corresponds with a probability of
failure Pf of 2.10-4.
A lower estimate βI,Low = 2.4 (Pf = 8.10-3)
is based on the general lognormal distribu-
tion. Another lower limit estimate of βI is
based on the 75% confidence limit estimates
of the distribution parameters, obtaining a
value of βI,CL = 3.2 (Pf = 7.10-4).
Comparing the values for βI for the
combined set of pile conditions to the various
pile classes, the following observations can
be made: βI,Rep = 3.5 provides a lower limit
estimate value for βI; values for other pile
classes based on construction method and/or
soil type generally provide higher values. The
exception is the case for driven piles in non-
cohesive soil, where βI,D-NC = 3.1 (Pf = 1.10-4)
is obtained; alternatively for non-cohesive soil
βI,NC = 3.2. When confidence level estimates
are made, it is shown that the confidence limit
value for driven piles in non-cohesive soil is as
low as βI,Conf = 2.2 (Pf = 1.10-2).
Figure 1 Implicit reliability of pile design including loading
Re
lia
bil
ity
ind
ex
Re
lia
bil
ity
ind
ex
4.5 4.5
4.0 4.0
3.5 3.5
3.0 3.0
2.5 2.5
2.0 2.0
1.5 1.5
1.0 1.0
(a) Representative implicit reliability (βI,Rep) (b) Implicit reliability for the special case D-NC (βI,D-NC)
0 00.5 0.51.0 1.01.5 1.52.0 2.0
Ln/Dn Ln/Dn
M,D,L(2.0)
M(2.0)
M,L(2.0)
M,D,L(2.5)
M(2.5)
M,L(2.5)
M,D,L(3.0)
M(3.5)
M,L(3.0)
M,D,L(2.0)
M(2.0)
M,L(2.0)
M,D,L(2.5)
M(2.5)
M,L(2.5)
M,D,L(3.0)
M(3.5)
M,L(3.0)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 79
When loads are also modelled as basic
variables, the values for βI,Rep is somewhat
reduced in the typical range of ratios for live
to dead load to be expected for pile founda-
tions. Values above 3.2 are obtained for live
load less than dead load. The limited reduc-
tion in βI,Rep is indicative of the fact that
reliability is dominated by the influence of
pile resistance reliability. The reduction in βI
values for situations dominated by live load
is indicative of the increasing role of the reli-
ability of live load, which should optimally be
provided for in terms of partial load factors,
rather than being of concern for pile design
reliability as such.
Comparison of values for βI,Rep cor-
responding to commonly adopted values for
factor of safety FS (i.e. 2 – 3) generally shows
good agreement with the target reliability
βT set in SANS 10160-1:2011 for different
reliability classes. The values for implicit
reliability for the three values of FS for dead
load dominating conditions βI,Rep (2.5, 3.2
and 3.7) compares well with target reliability
for the first three reliability classes βT (2.5,
3.0 and 3.5). Nonetheless, the range of βI,Rep
values obtained seem to be on the higher
side for single piles, suggesting that current
practice is conservative.
The reliability assessment of pile design
practice does not only provide insight into
the sufficiency of existing practice, but could
also form the basis for achieving appropri-
ate performance levels through reliability
calibrated procedures. The rational basis
for reliability calibration provided in SANS
10160-1:2011 can be applied in accordance
with geotechnical limit states design proce-
dures presented in SANS 10160-5:2011.
LIST OF NOTATIONS FOR
RELIABILITY INDEX (β)
β Reliability index, as related to prob-
ability of failure given by Equation 3
βT Target level of reliability obtained
through calibration of design
expression
βI Reliability level implicitly achieved
by existing practice, expressed in
terms of the reliability index β
βI,Rep Indicative level of reliability taken
to be representative of the set of
pile conditions under consideration,
usually considering pile design in
general
βI,Low Lower limit estimates of implicit
reliability based either on the selec-
tion of the probability distribution
or the pile class
βI,Conf Reliability index value based on
confidence limit estimates of distri-
bution parameters
βI,D-NC Implicit reliability index value for
the special case of driven piles in
non-cohesive soil
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Stellenbosch: SUN MeDIA Press.
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Highway Bridge Substructures. Publication No.
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Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201380
TECHNICAL PAPER
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 80–84, Paper 852
ASSOC PROF SHAMSAD AHMAD, who holds a
PhD in Civil Engineering from the Indian
Institute of Technology (IIT), Delhi, India, has
been involved in several funded research
projects. He has published over 40 research
papers in refereed journals and conference
proceedings, and has taught many graduate
and undergraduate courses mainly related to
mechanics, structural materials and durability of concrete structures.
Presently he is Associate Professor in the Civil Engineering Department at the
King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia.
Contact details:
Civil Engineering Department
King Fahd University of Petroleum & Minerals
PO Box 1403
Dhahran-31261
Saudi Arabia
T: +966 3 860 2572
F: +966 3 860 2879
PROF YASSIN SHAHER SALLAM holds a PhD
(NDT Engineering) from the Rouen University,
Haut Normandie, France. He has published
more than fi fty scientifi c articles and held many
positions, including Engineering Consultant,
Head of Civil Engineering Department,
Vice-Dean, and Dean. Presently he is Professor of
Structural Engineering in the Building Science
and Technology Department of the College of Architecture and Planning,
University of Dammam, Dammam, Saudi Arabia.
Contact details:
Department Building Science & Technology
College of Architecture and Planning
PO Box 2397
University of Dammam-31451
Saudi Arabia
T: +966 3 857 7000 x 3244
F: +966 3 857 8739
ISHAQ ABDUL RAZZAQ AL-HASHMI holds a BS in
Building Engineering from the University of
Dammam, Dammam, Saudi Arabia. Presently he
is working as Assistant Lecturer in the
Department of Building Engineering at the
College of Architecture and Planning, University
of Dammam.
Contact details:
Department of Building Engineering
College of Architecture and Planning
University of Dammam
PO Box 695
Alkhobar-31952
Saudi Arabia
Keywords: Lytag, lightweight aggregate concrete, dosage, mixtures,
optimisation
INTRODUCTION
Lytag is a product used as lightweight
coarse aggregate in producing lightweight
concretes. Fly ash, bentonite and water are
used as raw materials in manufacturing
Lytag. The production of Lytag consists of
mixing fly ash, bentonite and water together
and then pelletising the mixture into spheri-
cal balls. Finally these rounded pellets are
heated on a sinter strand to a temperature of
around 1 300°C. This aggregate, with particle
sizes typically ranging from 0.5 to 12 mm, is
called sintered fly ash lightweight aggregate,
more commonly known as Lytag lightweight
aggregate (EuroLightCon 2000). The
manufacturing of Lytag, using fly ash, has
been frequently reported in literature (Moss
1976; Anon 1978; Buttler 1987). However,
the production of other types of lightweight
aggregate similar to Lytag has also been
reported (Wainwright et al 2002; Boljanac et
al 2007). Lytag is produced on an industrial
scale by Lytag Ltd from its production units
in the United Kingdom, Holland, Poland and
China. Recently, Bulk Material International
(BMI) has signed an agreement with Lytag
Ltd for the marketing of Lytag lightweight
aggregate in the Middle East.
Swamy and Lambert (1981), in their
study on microstructure of Lytag aggregate,
reported that the overall structure of a Lytag
pellet is basically made up of unreacted
cenospheres, which are fused together
at their points of contact and/or are sur-
rounded by a solidified honeycomb type
structure, probably formed when some of
the raw materials became semi-molten and
gases escaped through them. They have
revealed through X-ray spectroscopy that
the major chemical elements from which
Lytag pellets are composed are silica and
alumina, with smaller amounts of calcium,
iron, magnesium and potassium. They found,
furthermore, that an excellent bond forms
between the Lytag pellets and a sand-cement
matrix. The microstructure, chemical
composition, and particle size distribution of
Lytag aggregate are important factors which
affect the performance of Lytag lightweight
aggregate concretes. The microstructure of
Lytag aggregate affects its strength, absorp-
tion and pozzolanic activity. These three
properties of Lytag aggregate jointly have
an influence on the strength of lightweight
concretes (Wasserman & Bentur 1997).
Some of the important physical properties
of Lytag aggregate, typically reported by
EuroLightCon (2000), are as follows: porosity
of particles (40%), particle density (1 400
kg/m3), 30-minutes water absorption (15%),
and 24-hours water absorption (18%). The
particle size distribution of Lytag aggregate is
specified in terms of percentages of different
individual fractions. An individual fraction
means a portion of aggregate belonging to
particles of a specific size range. In their
Optimising dosage of Lytag used as coarse aggregate in lightweight aggregate concretes
S Ahmad, Y S Sallam, I A R Al-Hashmi
Lytag, manufactured first by pelletisation of a mixture of fly ash, bentonite and water, and then by sintering the spherical pellets at about 1 300C, is used as coarse aggregate for producing lightweight plain and structural concrete mixtures. The weight of lightweight concretes is reduced significantly without compromising the structural integrity. The reduced dead load results in significant savings in the cost of foundations and reinforcement, as well as reduction in the sizes of columns, beams and slabs, which in turn reduce the overall volume of concrete and the costs of formwork and scaffolding. This paper reports on the results of an experimental study which consisted of designing, preparing and testing different mixtures of lightweight aggregate concrete considering four dosages of Lytag, used as coarse aggregate. It was found that the density and workability of concrete mixtures significantly decreased with increase in the dosage of Lytag. Concrete mixtures containing Lytag were found to be stronger than normal weight concrete. However, the strength of the lightweight aggregate concrete is found to be maximum at an optimum dosage of the Lytag.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 81
study on properties of Lytag-based concrete
mixtures, EuroLightCon (2000) typically
considered different particle size distribu-
tions made up of the individual fractions, as
follows: 0.5-4 mm, 0.5-6 mm, 4-8 mm, and
6-12 mm. Most of the mixtures studied by
EuroLightCon (2000) were made with 60%
of Lytag belonging to 0.5-6 mm fraction, and
40% of Lytag belonging to 6-12 mm fraction.
Swamy and Lambert (1983) carried out a
study on mix design and properties of con-
crete made from Lytag coarse aggregates and
sand. They considered several initial trial
mixtures with target strengths ranging from
20 to 60 MPa. Based on these trials they
finally recommended three mixtures with
target strengths of 30, 45 and 60 MPa with
a slump in the range of 75 to 100 mm. For
all three these mixtures, they kept effective
water content and Lytag content constant at
175 and 715 kg/m3, respectively, and varied
the cement content (250, 335 and 485 kg/m3),
sand content (715, 645 and 515 kg/m3),
and effective water/cement ratio (0.70, 0.53
and 0.36) respectively for mixtures hav-
ing target strengths of 30, 45 and 60 MPa.
Lytag Ltd (2006) has published the data on
typical mix designs for Lytag concrete. The
comprehensive data on mix designs consists
of the proportioning details of various types
of Lytag concretes, such as: skip mix (Lytag
granular / natural sand), pump mix (Lytag
granular / natural sand), skip mix (Lytag
granular / PFA / natural sand), pump mix
(Lytag granular / PFA / natural sand), skip
mix (Lytag granular / GGBS / natural sand),
pump mix (Lytag granular / GGBS / natural
sand), skip mix (Lytag granular / Lytag fines),
and pump mix (Lytag granular / Lytag fines).
Beattie (2005) reported the development
of mixtures of Lytag self-compacting and
pumpable concretes.
Several researchers have reported the
properties of Lytag concrete (Swamy &
Lambert 1983; Bamforth 1987; Wainwright
& Robery 1997; Bai et al 2004; Zhang 2011).
Lytag concrete mixtures are typically used
where low density concrete is required
with the same structural integrity as that
of normal weight concrete. Structural
lightweight concretes, produced using Lytag
as coarse aggregate and natural sand as fine
aggregate, reduce unit weight by approxi-
mately 25% (oven-dry densities in the order
of 1 750 kg/m3) over the normal weight
concrete and still offer strengths exceeding
60-70 MPa. Reduction in the unit weight
of concrete can lead to considerable cost
savings, as the size and number of concrete
sections, foundations and other structural
members can be reduced. Compared to nor-
mal weight concrete, it has been found that
Lytag concrete is easier to place, and has
better compacting and finishing properties,
enhanced durability, reduced coefficient
of thermal expansion, improved insulating
properties, and better fire resistance.
The work on which this paper is based
was conducted to obtain an optimum
mixture of structural lightweight aggregate
concrete made using Lytag as coarse aggre-
gate and natural sand as fine aggregate.
For this purpose, four mixtures of Lytag
concrete were designed, prepared and tested,
considering different percentages of Lytag
and sand, keeping cement content and water/
cement ratio constant at their typically
selected values. A mixture of normal weight
concrete was also considered in the study
to compare the properties of Lytag concrete
mixtures with the properties of normal
weight concrete.
EXPERIMENTAL PROGRAMME
Materials
Type I cement (ordinary Portland cement)
conforming to ASTM C150-07 was used
in all the mixtures. Lytag aggregate having
a maximum size of 19 mm and conform-
ing to ASTM C-33-4 was used in all four
mixtures of structural lightweight concrete.
The chemical composition and physical
properties of Lytag are presented in Table 1.
The fine aggregate used in this investigation
was dune sand. Specific gravity and water
absorption of sand were measured to be 2.66
and 0.8% respectively. The grading curves
of the Lytag and fine aggregates are shown
in Figure 1. The crushed stone particles,
Table 1 The chemical composition and physical properties of Lytag aggregate
Chemical constituent/physical property Measured value
SiO2 53%
Al2O3 25%
Fe2O3 6%
CaO 4%
MgO 2.9%
Acid soluble sulfate SO3 (≤1.0%) 0.3%
Total sulfate (≤1.0%) 0.4%
Cl– (≤0.03%) 0.01%
Loss on ignition (≤4.0%) 3.1%
Particle density (1 350 kg/m3 ± 150 kg/m3) 1 310 kg/m3
Bulk density (loose) 687 kg/m3
Bulk density (rodded) 733 kg/m3
Water absorption 15%
Specific gravity 1.8
Figure 1 Grading curves of Lytag and fine aggregates
% P
ass
ing
100
Sieve size (mm)
90
80
70
60
50
40
30
20
10
00.05 0.5 505
Lytag aggregate Fine aggregate
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201382
with a maximum size of 25 mm, were used
as coarse aggregate for preparing normal
weight concrete. The specific gravity and
water absorption of coarse aggregate were
measured to be 2.65 and 1.65%, respectively.
Potable water from the laboratory tap was
used to prepare and cure the specimens.
Superplasticiser was used in all the mixtures
for achieving adequate workability.
Design of concrete mixtures
Four mixtures of Lytag concrete were
designed, with the following percentage
combinations of Lytag and sand: (i) 45%
Lytag and 55% sand; (ii) 50% Lytag and 50%
sand; (iii) 55% Lytag and 45% sand; and (iv)
60% Lytag and 40% sand. Combined grading
of Lytag and sand was carried out for all four
combinations in accordance with ASTM
C330-4. The combined aggregate grading
curves obtained individually for all four mix-
tures of Lytag concrete are shown in Figures
2 to 5. For all four mixtures, cement content,
micro-silica content, and water/cementitious
materials ratio were kept constant at 400
kg/m3, 40 kg/m3 and 0.36 respectively. The
cement content and water/cement ratio for
the normal weight concrete mixture were
the same as for the Lytag concrete mixtures.
The coarse to fine aggregate ratio for normal
weight concrete was kept as 1.5. For all five
mixtures, the dosage of superplasticiser was
kept as 5 litre/m3.
The design of all the concrete mixtures
was carried out using the absolute volume
method, assuming entrapped air contents
of approximately 2% for Lytag concrete
mixtures and 1% for normal weight con-
crete mixtures. The proportions of all five
mixtures considered under this study are
presented in Table 2.
Specimen preparation and testing
Concrete mixtures were prepared by mixing
the ingredients in accordance with ASTM C
192. Fresh concrete mixtures were tested for
slump, air content and density in accordance
with ASTM C 143, ASTM C 173, and ASTM
C 138, respectively. After testing the fresh
concrete mixtures, casting of cylindrical
specimens was carried out for determining
compressive strengths in accordance with
ASTM C 39 after seven and 28 days of water
curing. Oven-dry and air-dry densities of
the specimens were also determined after 28
days of water curing.
RESULTS AND DISCUSSION
The results of the air content in fresh
concrete mixtures are presented in Table 3.
Normal weight concrete mixture with a
maximum aggregate size of 25 mm has 1.8%
Figure 2 Combined aggregate grading curve (45% Lytag and 55% sand)
% P
ass
ing
100
90
80
70
60
50
40
30
20
10
0
Mix curve
Maximumlimit curve
Minimumlimit curve
0.075 0.150 0.300 0.600 1.18 2.36 4.75 9.5 12.5 19 25 37.5 50 61 75
Sieve size (mm)
Fine m
ix
Coarse m
ix
Figure 3 Combined aggregate grading curve (50% Lytag and 50% sand)
% P
ass
ing
100
90
80
70
60
50
40
30
20
10
0
Mix curve
Maximumlimit curve
Minimumlimit curve
0.075 0.150 0.300 0.600 1.18 2.36 4.75 9.5 12.5 19 25 37.5 50 61 75
Sieve size (mm)
Fine m
ix
Coarse m
ix
Figure 4 Combined aggregate grading curve (55% Lytag and 45% sand)
% P
ass
ing
100
90
80
70
60
50
40
30
20
10
0
Mix curve
Maximumlimit curve
Minimumlimit curve
0.075 0.150 0.300 0.600 1.18 2.36 4.75 9.5 12.5 19 25 37.5 50 61 75
Sieve size (mm)
Fine m
ix
Coarse m
ix
Figure 5 Combined aggregate grading curve (60% Lytag and 40% sand)
% P
ass
ing
100
90
80
70
60
50
40
30
20
10
0
Mix curve
Maximumlimit curve
Minimumlimit curve
0.075 0.150 0.300 0.600 1.18 2.36 4.75 9.5 12.5 19 25 37.5 50 61 75
Sieve size (mm)
Fine m
ix
Coarse m
ix
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 83
air content against the approximately speci-
fied air content of 1.5% for 25 mm aggregate
size. Lytag concrete mixtures with 19 mm
maximum aggregate size should have air
content of approximately 2%. However, it can
be observed from Table 3 that the air content
for the Lytag mixture with 45% Lytag aggre-
gate is 2% and that air content increases with
increase in the Lytag content.
A plot of slump test results is shown
in Figure 6. It was found that the slump
decreases significantly with increase in the
Lytag content due to the high water absorp-
tion capacity and lower density of Lytag
lightweight aggregate. Compared to normal
weight concrete, the reduction in the slump
was found to be 23% with 45% Lytag, and
62% with 60% Lytag. The average decrease
in the slump is around 15% for every 5%
increase in the Lytag content.
The variation in the density of fresh con-
crete with Lytag content is shown in Figure 7.
As can be seen from Figure 7, the fresh den-
sity of Lytag concrete is reduced by around
12% at a Lytag content of 45%, and the den-
sity decreases with an increase in the Lytag
content to around 21% at a Lytag content of
60%. It can be noted that the reduction in
density is more significant when the Lytag
content was increased from 45 to 50% than
the reduction in the density when the Lytag
content was increased beyond 50%. The
variation in air-dry and oven-dry densities of
the concrete mixtures after 28 days of curing
is shown in Figure 8. As with fresh density,
the reduction in air-dry and oven-dry densi-
ties was also more significant when the Lytag
content was increased from 45 to 50%. The
reduction in air-dry and oven-dry densities is
insignificant when the the Lytag content was
increased beyond 50%. The reductions in
air-dry and oven-dry densities at 50% Lytag
content were found to be around 22% and
26%, respectively. The results of both fresh
and hardened densities indicate that the 50%
dosage of Lytag can be considered as the
optimum dosage for reducing the density of
Lytag concrete.
The variation in 7-day and 28-day
compressive strengths of concrete mixtures
with Lytag content is shown in Figure 9. It
should be noted that the difference between
7-day compressive strength in normal weight
concrete is more than that of Lytag concrete.
Furthermore, the strengths of the Lytag
concrete mixtures are more than that of
normal concrete. However, the strength of
Lytag concrete increases with an increase in
Lytag content only up to 50%, and then the
strength decreases with increase in Lytag
content. Therefore, from a strength point
of view, the optimum dosage of Lytag was
found to be 50%.
Table 2 Mixture proportions for producing 1 m3 of concrete
Ingredient
Normal weight
concrete mixture
Lytag concrete mixtures
45% Lytag55% sand
50% Lytag50% sand
55% Lytag45% sand
60% Lytag40% sand
Cement (kg) 400 400 400 400 400
Micro-silica (kg) – 40 40 40 40
Water (kg) 144 158 158 158 158
Lytag aggregate (kg) – 672 732 791 846
Fine aggregate (kg) 762 822 732 647 564
Stone aggregate (kg) 1 143 – – – --
Admixture (litre) 5 5 5 5 5
Table 3 Air content in fresh concrete mixtures
Mixture Air content (%)
Normal weight concrete 1.8
Lightweight concrete (45% Lytag and 55% sand) 2.0
Lightweight concrete (50% Lytag and 50% sand) 2.5
Lightweight concrete (55% Lytag and 45% sand) 3.0
Lightweight concrete (60% Lytag and 40% sand) 3.2
Figure 6 Slump variation with Lytag content
Slu
mp
(m
m)
140
120
100
80
60
40
20
0
Lytag aggregate (%)
0 45 50 6055
80
100
130
70
50
Figure 7 Variation of fresh density with Lytag content
De
nsi
ty (
kg
/m3)
2 700
Lytag aggregate (%)
0 45 50 60551 500
2 500
2 300
2 100
1 900
1 700
2 492
2 183
2 0481 990 1 968
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201384
CONCLUSIONS
Based on the results of the experimental
investigation presented in this paper, the fol-
lowing conclusions may be drawn:
1. All four mixtures of Lytag concrete fulfil
the requirements of lightweight concrete,
as they have dry densities of less than
1 900 kg/m3.
2. At the same water/cement ratio and
cement content, the Lytag concrete mix-
tures have better strength than normal
concrete. However, at the same superplas-
ticiser content the workability of Lytag
concrete mixtures is significantly reduced
due to higher water absorption and lower
density of Lytag aggregate.
3. At 50% Lytag content the reduction in the
dry density is around 25%. Beyond 50% of
Lytag content, the reduction in the den-
sity is insignificant. The strength of Lytag
concrete is found to be maximum at 50%
Lytag content. Therefore, the optimum
dosage of Lytag aggregate can typically be
considered as 50% (by mass).
ACKNOWLEDGEMENT
The authors gratefully acknowledge support
received from the Department of Building
Engineering and Technology, College of
Architecture and Planning, University of
Dammam, Saudi Arabia.
REFERENCES
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weight concrete. Concrete (London), 21(4): 8–9.
Beattie, A 2005. Developments in lightweight self-com-
pacting and pumpable concrete. Concrete (London),
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Boljanac, T, Vlahovic, M, Martinovic, S & Vidojkovic, V
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Wainwright, P J, Cresswell, D J F & Van der Sloot, H A
2002. The production of synthetic aggregate from a
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Figure 8 Variation of 28-day air-dry and oven-dry denisties with Lytag content
De
nsi
ty (
kg
/m3)
2 500
Lytag aggregate (%)
0 45 50 60551 500
2 300
2 100
1 900
1 700
2 447
1 953.51 900 1 893.5 1 879
1 868.51 815 1 808.5 1 794
Oven dry Air dry
Figure 9 Variation of 7-day and 28-day compressive strengths with Lytag content
Co
mp
ress
ive
stre
ng
th (
MP
a)
40
Lytag aggregate (%)
0 45 50 605522
38
36
26
24 25
28-day 7-day
34
32
30
28
31.5
37.237.7 37.5
36.6
34.1
35.3
33.6
32.1
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 85
TECHNICAL PAPER
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 85–93, Paper 907
PROF SW JACOBSZ (Pr Eng, MSAICE) graduated
with an MEng in Geotechnical Engineering from
the University of Pretoria in 1996 and worked for
Jones & Wagener before leaving for the United
Kingdom in 1999 to study towards a PhD in
Geotechnical Engineering at the University of
Cambridge. He returned to Jones & Wagener in
2004 where he worked as geotechnical
engineer before joining the University of Pretoria in 2010 as Associate
Professor in the Department of Civil Engineering. His primary interest is
physical modelling of geotechnical problems in the geotechnical centrifuge.
Contact details:
Department of Civil Engineering
University of Pretoria
Pretoria
0002
T: +27 12 420 3124
Keywords: soil nail, centrifuge model, strength mobilisation, sand,
residual andesite
INTRODUCTION
Centrifuge modelling of soil-
nailed retaining walls
Various analytical methods can be used
to assess collapse loads of geotechnical
problems, e.g. plasticity solutions like the
slip-line method or the limit equilibrium
methods which have traditionally been the
most widely used method (Shen et al 1982).
However, limit equilibrium methods require
assumptions regarding the shape of the
failure surface and the distribution of stress
along the failure surface. As these assump-
tions affect the solution of the problem, it
is important that they are realistic. Failure
mechanisms and deformation behaviour of
soil-nailed structures can be back-analysed
from full-scale case studies, which are rare
and costly, or from laboratory model studies.
The non-linear stress-strain properties of
soils require the stress levels in models to be
corrected to that of the full scale to ensure
realistic results. This necessitates the use of a
geotechnical centrifuge.
Shen et al (1982) reported on one of the
first centrifuge model studies conducted to
model a soil nail retaining wall in sand and
compared test results against the predictions
from analytical models. A comprehensive
study of soil-nailed walls in sand was also
carried out by Tei (1993). Zhang et al (2001)
carried out parametric studies of soil nail
retaining structures, experimenting with nail
lengths and spacings, and found that failure
surfaces of nailed surfaces were deeper than
without reinforcement. Shen et al (1982) and
Tei (1993) observed curved failure wedges
(logarithmic spirals, according to Tei et al
1998; see also Bolton & Pang 1982), initiat-
ing from the toe of the retained face and
reported good agreement with critical failure
wedges predicted from limit equilibrium
analysis.
Physically modelling all elements of the
process of constructing a soil nail retained
face in the centrifuge presents many dif-
ficulties. In the available case studies, the
soil nails were pre-installed during model
preparation. Modelling of the excavation
can, however, be achieved relatively easily by
draining a fluid selected to exert a horizontal
pressure approximately equal to that of the
soil once the desired acceleration had been
achieved (e.g. Tei 1993). Other researchers
did not model the excavation process and
simply accelerated the completed model to
the required acceleration (e.g. Shen et al
1982 and Zhang et al 2001). Despite some
obvious discrepancies, both reported the
performance of the model to be comparable
to that of the full-scale situation yielding
realistic results.
The geotechnical centrifuge
The Department of Civil Engineering at the
University of Pretoria, South Africa, has
recently acquired a geotechnical centrifuge
with a capacity of 150 G-ton, meaning that
the centrifuge is capable of accelerating a
payload weighing up to one ton to 150 G.
Geotechnical centrifuges are used to subject
small-scale models of geotechnical situations
to high accelerations. Due to the stress-strain
behaviour of soils being highly non-linear,
it is necessary to increase the stresses in a
model to be analogous to the stress distri-
bution in the full-scale situation. This is
Centrifuge modelling of a soil nail retaining wall
S W Jacobsz
This paper describes a physical model of a soil nail retained excavation face which was tested in the new geotechnical centrifuge at the University of Pretoria. As centrifuge modelling is new in South Africa, a short introduction to this technique is presented. The mobilisation of soil nail forces and their maximum values in response to excavation in the model were compared to measurements recently made in an instrumented 10 m high soil nail retaining structure for the Gautrain system in Pretoria. Results were also compared to predictions made using a simple failure wedge analysis and a database of eleven full-scale instrumented soil nail walls from the literature. The centrifuge model data compared well with both full-scale situations and theoretical analyses. The results suggest that soil nail forces measured in the centrifuge are conservative due to the mobilisation of a portion of the shear strength of the model soil during the acceleration of the centrifuge, leaving less un-mobilised shear strength available to resist loads resulting from the excavation.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201386
achieved using centripetal acceleration. As
such, a model with a scale of 1:50 has to be
accelerated to 50 times earth’s gravity (50 G)
to create the correct stress distribution.
Model dimensions scale linearly and
can be used to derive scaling laws for other
physical properties. Table 1 lists scaling laws
for a number of physical quantities. As an
example, the scaling law for force is derived:
According to Newton’s second law, force
(Fp) in the full-scale situation (the prototype)
can be expressed as Fp = mpap, where mp is
the mass and ap the acceleration of the pro-
totype. Assuming that the body to be scaled
is a cube with density ρ and side length lp
and that it is stationary on the earth’s sur-
face, Newton’s second law can be written as
Fp = ρl3p g (1)
where g is gravitational acceleration.
Newton’s second law for the model is
Fm = mmam (2)
where Fm is force at the model scale, mm the
mass of the model and am the acceleration at
model scale. In order to avoid problems with
different material properties, the same mate-
rial as that occurring in the full-scale situ-
ation is normally used to create the model.
The material density (ρ) therefore remains
the same. The model is N times smaller than
the prototype and is therefore accelerated to
N times earth’s gravitational acceleration to
create the correct stress distribution in the
model. Equation 2 therefore becomes
Fm = ρVmNg (3)
For a cube Equation 3 becomes
Fm = ρæççèlpN
æççè
3
Ng = ρl3
p g
N2 =
Fp
N2
which proves the scaling law for force.
In terms of scaling laws, particularly attrac-
tive is the fact that time-related problems,
e.g. consolidation, may be studied in a
fraction of the time that would be required
for a full-scale trial. Also, stiffnesses (e.g.
the Young’s and shear moduli) do not scale
because stresses and strains do not scale.
This enables the same material from the
full-scale prototype to be used to construct
the model.
Jacobsz & Phalanndwa (2011) described
a case study in which three instrumented
soil nails were installed in a retained face
along a cutting for the Gautrain railway line
in Pretoria. The structure was excavated in
residual andesite which increased in strength
and stiffness with depth. The wall was
10 m high with six rows of nails installed
at vertical spacings of 1.5 m and horizontal
spacings of 2 m, and at a downward angle of
10°. The shotcrete facing was 175 mm thick,
reinforced with two layers of mesh. The
retained face and the locations of the instru-
mented couplings are illustrated in Figure 1.
Axial forces in three of the soil nails were
measured as the excavation in front of the
retained face was deepened.
Although the survival rate of the soil nail
instrumentation was poor, it showed that
the maximum axial forces in the top soil nail
stabilised at approximately 50 kN, approxi-
mately two thirds of the load calculated
using a simple failure wedge analysis. It was
Figure 2 Axial load variation in the top instrumented soil nail (Jacobsz & Phalanndwa 2011)
Ax
ial
loa
d (
kN
)
100
75
50
25
002/26 03/26 04/23 05/21 06/18 07/16 08/13 09/10 10/08 11/05
Date
Figure 1 The full scale soil nail retaining structure modelled in the first centrifuge test
(Jacobsz & Phalanndwa 2011)
Nail horizontal spacing is 2 m
10 m
1.5 m
1.5 m 3 m 6 m 9 mInstrumented couplings
Soil nail length
12 m
12 m
12 m
9 m
9 m
6 m10°
Excavation floor
Table 1 Scaling laws for various physical
properties
Property Scale factor
Model scale
Accelerations
Linear dimensions
Stress
Strain
Density
Mass
Force
Bending moment
Moment of area
Time (consolidation)
Time (dynamic)
Time (creep)
Pore fluid velocity
n
n
1/n
1
1
1
1/n3
1/n2
1/n3
1/n4
1/n2
1/n
1/n
n
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 87
found that soil nail loads were not mobilised
gradually, but in distinct load increments.
It appeared that the material behind the
excavation remained stable to a point as
the excavation advanced and, only when a
certain excavation depth was reached, did
the retained soil exert more load on the soil
nails, as it depended on the nails for stability.
Soil nail loads were mobilised in a number of
such load steps as the excavation advanced,
as illustrated in Figure 2.
The aims of the centrifuge model study
were:
■ to measure the load mobilisation in the
soil nails over time during and after
excavation, and
■ to compare the mobilised soil nail loads
in the model with those from the Jacobsz
& Phalanndwa (2011) case study, and with
those calculated from conventional wedge
theory.
CENTRIFUGE MODEL
A centrifuge model was set up to model
the soil nail wall described in the Gautrain
retaining wall case study. The model was
constructed at a scale of 1:50 and was there-
fore tested at an acceleration of 50 G. The
scale factor was chosen taking into account
the dimensions of the model container,
referred to as a strong-box, in relation to the
dimensions of the full-scale situation being
modelled. The model is illustrated diagram-
matically in Figure 3.
The model retaining wall was construct-
ed from a 0.6 mm thick galvanised steel
plate. The calculated bending stiffness (EI) of
the shotcrete facing, assuming an un-cracked
panel, was approximately 9.4 x106 Nm2/m
(assuming a Young’s modulus for concrete
of 20 GPa and 200 GPa for steel). Bending
stiffness scales with the fourth power of the
scale factor. The bending stiffness of the
plate used to model the shotcrete face was
calculated at 3.6 Nm2/m, which was there-
fore approximately 2.4 times stiffer than the
scaled-down retaining wall value.
The model soil nails were made from
5 mm wide brass strips, 0.2 mm thick,
which were bolted to the wall using 2 mm
diameter nuts and bolts. The reason for
using flat metal strips was so that the model
soil nails could easily be instrumented with
strain gauges. For ease of installation during
model preparation, the nails were installed
horizontally.
The purpose of the model was to
investigate the mobilisation of axial
loads along the length of the nails during
excavation, i.e. to simulate normal
operational conditions and not to fail the soil
nail wall. Disregarding the effects of dilation,
the design pull-out capacity of the soil nails,
calculated purely from interface friction
between the nails and the soil, therefore
exceeded the imposed load estimated from
active pressure on the wall by approximately
one third, providing a safety margin. The
pull-out load (Qu) of the flat strip model soil
nails was calculated from σv An tan, where
σv is the vertical stress acting at the depth
of the nail, An the surface area of the nail
(top and bottom) and the interface friction
angle between the sand and the brass strips,
measured in a shear box test at 26°. A total
pull-out force of 1272 kN (full-scale) was
calculated for a column of six nails. The
predicted active pressures to be resisted per
column of nails were 932 kN.
The calculated axial stiffness of the
full-scale nails is approximately 100 MN.
Axial stiffness scales with the square of the
scale factor. The required stiffness of the
model nails was therefore 40 kN. The brass
strips were 2.7 times stiffer than the scaled
requirement. It was, however, not practical to
use narrower strips due to instrumentation
difficulties.
Three model nails were instrumented
with three strain gauges each, connected
in quarter Wheatstone bridge circuits. The
strain gauges were positioned with the first
gauge close to the wall and the second gauge
close to the position where the maximum
tensile force was expected, i.e. where an
active failure wedge is expected to be mobil-
ised (roughly at an angle of 45° + ’/2 with
the horizontal) (e.g. Lazarte et al 2003). The
third gauge was mounted approximately
halfway between the second gauge and the
end of the soil nail (see Figure 3).
The soil used in the model was a fine
alluvial silica sand sourced from a com-
mercial source near Cullinan. It was found
that particles larger than approximately
200 μm were relatively well rounded, but
the finer fraction tended to be more angular
with a description of angular to sub-angular
being appropriate. The grading curve for the
sand is presented in Figure 4. The friction
angle of the sand was measured at 37° using
a conventional shear box. During model
preparation the sand was placed by pluvia-
tion during which a constant drop height
Figure 3 The centrifuge model (not to scale)
Soil nail length
Stain gauges (offset fron retaining wall and gauge number)
200 mm
240 mm
240 mm
240 mm
180 mm
180 mm
15 mm
15 mm
15 mm
75 mm 140 mm
105 mm 195 mm
1 2 3
1 2 3
1
60 mm 125 mm
2 3
Enlarged section showing strain gauge positions
Nail 2
Nail 1
Nail 3
30 mm
Water filled Latex mould
Section
45° + φ'/2 = 64°
0.6 mm thick steel plate
Failure wedge
Nail 1
Nail 2
Nail 3
120 mm
Pot 1 Pot 2 Pot 3 Pot 4 Pot 5
50 mm 50 mm50 mm50 mm20 mm
Displacement transducers (potentiometers
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201388
and flow rate were maintained. The sand was
pluviated in layers of about 30 mm thickness,
i.e. the vertical spacing between rows of soil
nails. The placed relative density of the sand
was approximately 55% (1566 kg/m3), i.e. a
medium dense sand. The mass of sand was
determined by weighing the model before
and after placing the sand.
The deepening of the excavation was
modelled using a water-filled Latex rubber
mould in which the water level was reduced
during the test. This method was also used
by Tei (1993) (see also Tei et al 1998). During
the acceleration of the centrifuge to 50 G, the
water level in the rubber mould was main-
tained at the correct level using a standpipe
with a fixed overflow level into which water
was continuously fed. This procedure was
followed because it was expected that during
acceleration of the centrifuge some move-
ment of the system would have occurred,
possibly affecting the water level in the
rubber mould which would disturb the stress
regime. After accelerating to 50 G, the water
supply to the standpipe and rubber mould
was stopped. A solenoid valve was opened to
release the water from the rubber mould to
model the excavation of soil in front of the
retained face. In the first test the water level
was allowed to drop without interruption
from 200 mm to 0 mm depth. In the second
test the water level reduction took place in
steps over 2 000 seconds, and in the final
test over 3 000 seconds. After every step in
water level reduction, some horizontal wall
movement took place, which took some time
to stabilise. The next drop in water level was
only initiated after this wall movement had
stabilised.
During the tests the vertical movement
of the sand surface and the horizontal
movement at the top and mid-height of
the retaining wall were monitored using
potentiometer-based displacement transduc-
ers. The water level in the rubber mould
was monitored using a pressure transducer
mounted near the base of the standpipe. A
number of photos of the model are presented
in Figure 5.
CENTRIFUGE MODEL TEST RESULTS
Surface settlement
Surface settlements were recorded with
potentiometers with a resolution of approxi-
mately 0.001 mm during the lowering of the
water level. During the acceleration of the
centrifuge to 50 G the upper surface of the
sand settled between 1 mm and 2 mm in
response to the stress increase acting on the
model. Once at 50 G, the settlement data was
zeroed so that the surface settlements caused
Figure 4 Sand grading
100
90
80
70
60
50
40
30
20
10
0
Pa
ssin
g (
%)
Particle size (mm)
0.01 0.1 1
Figure 5 Sequence of photos illustrating model preparation
(a) Model soil nail wall (b) Model container before placement of sand and retaining structure
(c) Brass soil nails being placed into position during model preparation
(d) Top view of model
(e) Side view over model surface showing displacement transducers and data acquisition system
(f) Model in position on centrifuge ready for testing
Strain gauge electrical connectionsStrain gauge electrical connections
Model Model soil nailssoil nails
Standpipe with Standpipe with solenoid valve solenoid valve
and pressure and pressure transducertransducer
Model Model retaining wallretaining wall
Model soil nailsModel soil nails
StandpipeStandpipe
Model Model retaining wallretaining wall
Water-filled Water-filled latex mouldlatex mould
Displacement Displacement transducerstransducers
Data acquisition Data acquisition systemsystem
StandpipeStandpipe
Centrifuge Centrifuge modelmodel
Model Model retaining retaining
wallwall
Model Model compartmentcompartment
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 89
by the lowering of the water level behind the
retaining wall could be measured. Figure 6
shows the settlement of the soil surface
behind the retaining wall in response to the
lowering of the water level.
A maximum settlement of approximately
1.5 mm occurred immediately (20 mm)
behind the wall and reduced with distance
away from the wall. This translates to 75 mm
at the full scale (1:50).
Horizontal wall movement
Figure 7 presents the horizontal movement
measured at the top and mid-height of the
retaining wall in response to lowering of the
water level, modelling the excavation. The
results of the three tests show good repeat-
ability between tests and illustrate that the
rate of water level reduction did not have a
significant effect on the wall movement.
It can be seen from the figure that as
the water level began to be lowered, wall
movement immediately began to occur at the
top of the wall. When the water level in the
model excavation had dropped to below the
depth of the first row of soil nails (30 mm),
the rate of movement decreased as the nails
began to restrain wall movement. The rate of
wall movement then remained approximately
constant as the excavation advanced.
Little horizontal movement was observed
at the mid-height position on the wall until
the water level had reduced to that height.
Thereafter, horizontal movement occurred at
approximately the same rate as the horizon-
tal movement at the top of the wall.
Once the model excavation had been
emptied completely, a maximum horizontal
movement of about 2.5 mm was observed at
the top of the wall, equating to 125 mm for
the full-scale wall. The wall remained stable
after excavation.
Mobilisation of soil nail forces
The development of axial loads in the soil
nails in response to the deepening excavation
is presented in Figure 8. During acceleration
of the centrifuge to 50 G some settlement of
the model wall relative to the sand occurred
so that the parts of the nails close to the wall
were subjected to a small amount of bending.
This affected the zero offsets of force read-
ings registered by the instrumented nails.
Soil nail readings were therefore zeroed prior
to the water level in the model excavation
being reduced, to give loads mobilised due to
the reduction in the water level only. Loads
prior to zeroing were generally small (less
than 10 N at model scale), except where
bending of the nails occurred. The loads
measured in the model are shown on the
left-hand axis, with full-scale (prototype)
loads on the right-hand axis. The calculated
loads for the model from the wedge analysis
based on friction angles of 30° and 37° are
also shown in Figure 8; the comparison is
discussed later.
The evolving axial load distributions in
the instrumented nails, as the excavation
was deepened, are presented in Figure 9.
Initially, the highest loads were mobilised
immediately behind the wall in response to
active pressure behind the wall, but soon the
location of maximum force migrated back-
wards from the wall as a failure mechanism
began to mobilise.
DISCUSSION
Comparison of model results
with analytical methods
Wedge analysis
The equilibrium of a simple triangular active
failure wedge behind the excavation face was
examined to estimate the development of
axial soil nail forces in response to the deep-
ening excavation (Figure 10). This approach is
commonly used for soil nail design, although
the complexity of the mechanisms varies
(SAICE 1989). For the problem modelled in
the centrifuge, only three forces were consid-
ered: the self-weight of the failure wedge (W),
the resisting force mobilised on the failure
plane (R) and the sum of the individual soil
nail forces (T). For a fully mobilised failure
mechanism the resisting force R would act
at an angle as shown in Figure 10, where
is the soil friction angle. The soil nails were
assumed to carry only axial loads, disregard-
ing any bending or shear stiffness they might
possess. The failure wedge was assumed to
Figure 7 Horizontal wall movement in response to increasing excavation depth
Ho
riz
on
tal
pla
te m
ove
me
nt
(mm
)
2.5
3.0
1.5
2.0
0.5
1.0
0200150100500
Excavation depth (mm)
Test 1 Test 2 Test 3
Movement at the top of the wall
Movement at mid-height
Figure 6 Surface settlement in response to “excavation”
Offset from wall (mm)
0
Mo
de
l su
rfa
ce s
ett
lem
en
t (m
m)
–1.6
–1.4
–1.2
–1.0
0
–0.8
–0.6
–0.4
–0.2
50 100 150 200 250
Fu
ll-s
ca
le s
urf
ace
se
ttle
me
nt
(mm
)
80
70
60
50
30
20
10
0
40
0 11 21 28 37
48 72 136 200
Excavation depth (mm):
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201390
mobilise at a slope angle . This slope angle
was varied to find the maximum axial soil
nail force (T). For a horizontal soil surface
and smooth vertical retaining wall, the wedge
analysis provides the same solution as the
active Rankine earth pressure case.
The soil nail loads were calculated for vari-
ous depths of excavation by simply dividing
the total calculated soil nail force (T) by the
number of nails intersecting the failure wedge.
The calculated forces (based on horizontal
soil nails) are plotted with the observed loads
in Figure 8. As no failure wedge intersects soil
nails for excavation depths of up to 30 mm
(1.5 m at prototype scale), zero soil nail force
was assumed up to this depth.
Soil nail forces
Figure 8 illustrates that the loads in the soil
nails initially increased approximately linearly
with increasing excavation depth, but the rate
of increase reduced with further excavation.
The trend in the measured soil nail forces
compares well with the predictions from the
wedge analysis, although the latter generally
tends to underestimate the loads. This is
somewhat in contrast with Shen et al (1982),
Tei et al (1998), Lazarte et al (2003) and
others who stated that average nail forces are
generally smaller than those calculated by
considering full active earth pressures. The
most significant underestimation occurred
on the second soil nail.
During the acceleration of the centrifuge
to 50 G it was attempted to balance the
earth pressures behind the model retaining
wall by maintaining a constant water level
in the rubber mould as described. However,
some vertical and horizontal movements
of the various components of the model
were unavoidable during acceleration. The
imperfect method of balancing the earth
pressures as described, in combination with
the movements that occurred during accel-
eration, resulted in a certain amount of load
mobilising in the soil nails prior to reducing
the water level in the rubber mould to model
excavation. This means that a portion of
the shear strength of the sand was already
mobilised prior to water level being reduced.
Because of zeroing of the soil nail reading
prior to reducing the water level, these loads
were ignored. The various disturbances
would most probably have resulted in the
amount of shear strength mobilisation in the
sand before excavation to be different from
the situation applicable to an actual soil nail
wall, probably resulting in less shear strength
being available to support the excavated face
than what would have been expected. The
implication of this is that the soil friction
angle used in analysing the model should
probably be reduced. When a friction angle Figure 8 Development of soil nail forces with increasing excavation depth
Mo
de
l lo
ad
(N
)
60
200
Excavation depth (mm)
Fu
ll-s
ca
le l
oa
d (
kN
)
150
50
40
30
20
10
0
125
100
75
50
25
0150100500
Strain 1 Strain 2 Strain 3 Wedge analysis 37° Wedge analysis 30°
(a) Soil nail 1
Mo
de
l lo
ad
(N
)
60
200
Excavation depth (mm)
Fu
ll-s
ca
le l
oa
d (
kN
)
150
50
40
30
20
10
0
125
100
75
50
25
0150100500
Strain 1 Strain 2 Strain 3 Wedge analysis 37° Wedge analysis 30°
(b) Soil nail 2
Mo
de
l lo
ad
(N
)
60
200
Excavation depth (mm)
Fu
ll-s
ca
le l
oa
d (
kN
)150
50
40
30
20
10
0
125
100
75
50
25
0150100500
Strain 1 Strain 2 Strain 3 Wedge analysis 37° Wedge analysis 30°
(c) Soil nail 3
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 91
of 30° is used instead of 37°, the correlation
between the measured soil nail forces and
those calculated using a wedge analysis
improves (see Figure 8).
A further factor contributing to the
difference between the measured and calcu-
lated loads is the fact that the actual stress
distribution behind the retained face is sig-
nificantly more complex than the simple tri-
angular distribution assumed by active earth
pressure theory (Tei 1993 and Tei et al 1998).
Tei (1993) states that the failure surfaces in
sand would resemble a logarithmic spiral
which would result in failure wedges that are
approximately 10% heavier than the assumed
triangular wedge. Also, Zhang et al (2001)
mentioned that the failure wedge in the pres-
ence of soil nails was deeper than without
reinforcement. The actual mobilised soil nail
forces are controlled by many factors, includ-
ing the flexibility of the facing wall and soil
nails and dilation on the soil-nail interface
(Tei et al 1998).
The magnitude of the scaled-up maximum
observed soil nail forces in the centrifuge
model are put into context by comparison
with normalised soil nail forces measured
at eleven sites presented in Figure 11 (Byrne
et al 1998). Observed maximum tensile nail
forces were normalised by KaHgShSv, where
Ka is the coefficient of active earth pres-
sure, H the wall height, the density of the
retained material and Sh and Sv the respective
horizontal and vertical nail spacing. The
figure shows that the general trend is for soil
nail forces to reduce somewhat with depth,
but very significant scatter occurs, probably
as a result of variations in soil strength and
stiffness between sites which were not taken
into account in the normalisation. The obser-
vations from the centrifuge tests plot well
within the data set presented in the figure.
Figure 10 Simplified wedge analysis used for
the estimation of soil nail forces
W R
T
Failure wedge
Failure plane
α
T
W
R
φ
β
Soil nails
Figure 9 The distribution of soil nail forces along their lengths as excavation depth increases
Mo
de
l lo
ad
(N
)60
300
Strain gauge position (mm)
Pro
toty
pe
loa
d (
kN
)
150
50
40
30
20
10
0
125
100
75
50
25
0150100500
(a) Soil nail 1M
od
el
loa
d (
N)
60
Strain gauge position (mm)
Pro
toty
pe
loa
d (
kN
)
150
50
40
30
20
10
0
125
100
75
50
25
0
(b) Soil nail 2
Mo
de
l lo
ad
(N
)
60
Strain gauge position (mm)
Pro
toty
pe
loa
d (
kN
)
150
50
40
30
20
10
0
125
100
75
50
25
0
(c) Soil nail 3
200 250
300150100500 200 250
250150100500 200
0 11 28 48 72 136 200
0 11 28 48 72 136 200
0 11 28 48 72 136 200
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201392
In the Jacobsz & Phalanndwa (2011) case
study, soil nail loads of just less than 50 kN
were measured in the top soil nail when the
system was at equilibrium. These are of the
same order of magnitude, albeit somewhat
lower than scaled loads from the model
(see Figure 8). They are also lower than the
prediction from a wedge analysis. Note that
a wedge analysis predicts soil nail forces that
are 12% higher when nails are installed at
10° compared to horizontal nails. The reason
for the scaled model loads being higher
can be ascribed to the fact that the model
soil profile comprised cohesionless sand in
which some shear strength had already been
mobilised during acceleration of the centri-
fuge, while the profile in the field comprised
residual andesite, possessing significant
cohesive strength, increasing with depth.
A further difference between the model
and the case study is the step-wise way in
which loads were mobilised in the case study
compared to a more gradual increase in load
in the model (compare Figure 2 with Figure
8). The reason for the step-wise load increase
was attributed to the fact that the excavation
could support itself to a certain depth and
then suddenly yielded, mobilising load in the
soil nails. With further excavation, it again
remained stable to a certain depth before
yielding again, applying another step-wise
load increase on the soil nails. The cohesion-
less sand did not possess any strength to
support any depth of excavation, so that axial
load had to be mobilised in the soil nails very
shortly after the water level in the model
excavation began to reduce.
The measured axial force distributions
along the length of the nails shown in
Figure 9 generally agreed with the pattern
typically observed in the field. A soil nail
normally carries a load at the retained face
which increases towards the intersection
with the failure plane and then reduces to
zero at the end of the nail (Lazarte et al
2003). The maximum load was measured
consistently at the second strain gauge on
each nail. They were purposefully installed
close to where the failure wedge was expect-
ed to intersect the soil nails.
Wall and ground movements
The vertical soil settlement behind the wall
amounted to approximately double the
amount of the expected settlement given by
the guideline of H/333 by Lazarte et al (2003)
for fine grained soils. However, the observed
settlement applies to a medium dense sand,
the material used in the model in which
some shear strength had already been mobi-
lised during centrifuge acceleration. The
maximum settlement of the full-scale wall
amounted to only 8 mm, illustrating that,
as expected, the residual andesite behaved
much stiffer than the sand in the model,
settling less. The residual andesite appears to
mobilise its strength at smaller strains than
cohesionless sand.
It is interesting to note that the settle-
ments above the active wedge, potenti-
ometers 1 and 2 (see Figure 3 and Figure
6) settled significantly more than the
potentiometers further away, reflecting the
mobilisation of the failure mechanism. An
active failure wedge is predicted to intersect
the sand surface at an offset of 100 mm
from the retained face. The zone behind the
wall where noticeable settlements occurred,
agrees well with the 140 mm (at model scale)
predicted by Lazarte et al (2003).
The horizontal wall movements are pre-
sented in Figure 7 and were recorded from
the onset of water level reduction until the
model excavation was complete. The largest
portion of horizontal movement took place
during the initial reduction in water level to
the depth of the first row of nails. Thereafter
the rate of movement slowed considerably.
In practice this initial movement would not
have been recorded, because the first shot-
crete panels still had to be constructed. The
horizontal movement that would be recorded
in practice corresponds to that associated
with a drop in water level from 30 mm to
the bottom of the excavation. In the tests
reported here, this movement amounted to
approximately 1 mm, or 50 mm at full scale.
As in the case of the vertical movement
behind the wall, this horizontal wall move-
ment also exceeded the guideline recom-
mended by Lazarte et al (2003) (also H/333,
or 30 mm at full scale). The maximum
horizontal movement observed at the top
of the full-scale wall was 34 mm (Jacobsz
& Phalanndwa 2011). The difference can
be explained due to the model comprising
medium dense sand in which some shear
strength had already been mobilised during
centrifuge acceleration, while the full-scale
Figure 11 Normalised maximum tensile forces measured in soil nail retaining walls (Byrne et al 1998)
Normalised maximum load (T/KaHγShSv)
0.2
Na
il h
ea
d d
ea
pth
/ w
all
he
igh
t
0
0.6
0.4
1.0
0.8
0.20 0.60.4 1.00.8 1.61.2 1.4
Byrne et al (1998) Centrifuge tests
Figure 12 Mode of horizontal deformation of model soil nail wall in centrifuge models
Ground surface
Excavation level
Model soil nail wall
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 93
situation comprised stiff residual andesite
mobilising strength at smaller strains.
Following each drop in the water level
in front of the model wall, it took some
time before the horizontal wall movement
stopped. This was also seen in the field,
where some movement continued to occur
for some time after completion of the exca-
vation (Jacobsz & Phalanndwa 2011).
Figure 7 illustrates that the top of the
wall deflected rapidly initially, but when the
water level reached the level of the first row
of soil nails, the rate of horizontal movement
reduced due to the restraining effect of the
soil nails. Virtually no horizontal movement
took place at mid-height initially, indicating
that the upper part of the wall bent above
the excavation level. Once the water level
reached mid-height, horizontal movement
there took place at approximately the same
rate as at the top of the wall, indicating that
the wall translated horizontally with little
further bending. This suggests that horizon-
tal wall deformation occurred as indicated in
Figure 12, with bending taking place at the
excavation level while the upper part of the
wall remains approximately planar.
Comparison between the full-
scale situation and the model
Soil
It is often questioned whether the particle
sizes of material used in a centrifuge model
need to be scaled. For example, could the
fine sand at model-scale therefore hypotheti-
cally behave as a gravel at the full-scale? In
practice it is common with a centrifuge
model to model the actual material occur-
ring in the field, or often, to use the actual
material from the field directly in the model.
The material is then viewed as a continuum
with the same stress-strain properties as
in the field. Whether this assumption is
reasonable depends on the ratio between
the particle size in the model and the size
of significant components in the model,
e.g. particle size versus the dimensions of
model piles, foundations or model soil nails
(Taylor 1995). A method that is often used to
investigate whether unrealistic scale effects
occur is the so-called method of “modelling
of models”. Models are tested at different
scales. If the scaled observations from dif-
ferent scale models are consistent, particle
size effects can be ignored and the material
can be assumed to behave as a continuum
at the accelerations tested. However, when
failure mechanism bounded by shear bands
begin to dominate, the ratios between shear
band widths, particle size and model element
dimensions can become important. In such
instances dilation effects within shear bands
are likely to scale-up unrealistically (Taylor
1995). Milligan & Tei (1998) mentioned
that relative size effects between model soil
nail diameter and particle size may tend to
increase the apparent strength and stiffness
of the model compared to the prototype in
the case of rough nails. This scale effect is
significant where the ratio D/D50 ranges
from 1 to 35 (where D is the nail diameter
and D50 the main particle size), but reduces
at higher values applicable in the field. Due
to the thickness of the brass strips (model
soil nails) relative to the means particle
size, scale effects would be expected in the
model. However, due to the smoothness of
the model nails, dilation effects as described
above should have been limited, although
probably not insignificant.
Soil nails
One important aspect in which the soil nail
retaining wall in the centrifuge differed from
the full-scale situation was that the wall and
soil nails were pre-installed prior to model-
ling of the excavation. Installation of soil
nails during a test would be difficult. Due
to the nails being pre-installed, loads could
mobilise before the excavation depth had
advanced to the depth of a particular row
of nails. Also, installation-induced soil nail
loads and soil stresses could not be modelled.
These are likely to differ from the situation
in the model (Milligan & Tei 1998).
CONCLUSIONS
A physical model, examining an instru-
mented soil nail retaining structure, was
tested successfully in three centrifuge tests.
The test yielded realistic and repeatable
data, comparing well with measurements
made in a full-scale case study in Pretoria
(Jacobsz & Phalanndwa 2011) and with a
database of eleven other case studies (Byrne
et al 1998).
In terms of soil nail forces, the model
showed somewhat higher nail forces
compared to those predicted by a simple
equilibrium analysis and when compared
with the case study discussed. This is likely
to be a consequence more of the shear
strength of the soil being mobilised during
acceleration of the model than what would
be applicable in a full-scale (K0) situation,
resulting in less strength being available to
resist excavation-induced loads than what
would have been expected. Information
from the literature suggests that soil nail
forces from a simple wedge analysis or limit
equilibrium analysis are conservative. The
results of these centrifuge tests suggest
that soil nail forces from centrifuge tests
may be even more conservative, due to the
mobilisation of some soil strength during
centrifuge acceleration.
The axial load distributions measured along
the length of the soil nails compared well with
the known distributions from the literature.
The trend in axial load mobilisation in
the soil nails differed from the full-scale case
study reported. In the model, axial load was
mobilised gradually in response to excava-
tion, while in the full-scale field study a step-
wise mobilisation was observed. The reason
for this is that the soil in the model only pos-
sessed frictional strength, while the residual
andesite in the field had some “cohesive”
strength and a fissured structure, enabling it
to remain stable up to a certain depth.
Although differences between the full
scale situation and a model are unavoid-
able, physical modelling in the geotechnical
centrifuge is a valuable technique to model
complex three-dimensional problems. An
advantage is that a physical event can be
observed and realistic results obtained using
the same materials as in the field.
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Tei, K, Taylor, R N & Milligan, W E 1998. Centrifuge
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Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201394
TECHNICAL PAPER
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 94–103, Paper 829 Part 1
PROF DR SAEED-REZA SABBAGH-YAZDI is
professor in the Civil Engineering Department
of the KN Toosi University of Technology,
Tehran, Iran. He obtained his PhD from the
University of Wales, Swansea, United Kingdom.
He has more than twenty years’ academic and
professional experience in management,
design, computation, hydraulics, structural
engineering, computer simulation of fl uid fl ow and heat transfer, and stress
analysis of hydraulic structures.
Contact details:
Civil Engineering Department
KN Toosi University of Technology
Valiasr St Mirdamad Cross
Tehran, Iran
T: +98 21 88 77 9623
F: +98 21 88 77 9476
TAYEBEH AMIRI-SAADATABADI is a PhD student
in the Department of Civil Engineering at the
KN Toosi University of Technology. She obtained
her MSc in hydraulic structures from the
KN Toosi University of Technology and started
her PhD research in 2010. Currently she is
developing software to analyse concrete
structures. Her main research interest is in fi nite
volume numerical methods, cracking and creep.
Contact details:
Civil Engineering Department
KN Toosi University of Technology
Valiasr St Mirdamad Cross
Tehran, Iran
T: +98 21 88 77 9623
F: +98 21 88 77 9476
PROF DR FALAH M WEGIAN has more than 20
years’ academic experience, including the
research work for his Masters and Doctorate.
Prof Wegian is currently chairman of, and
professor in, the Civil Engineering Department
at the College of Technological Studies, Public
Authority for Applied Education and Training
(PAAET), Kuwait. His wide range of research
interests includes the use of Fiber Optic Bragg Grating Sensors embedded in
concrete structures to evaluate strains and cracks and the performance of
bridge structures. Prof Wegian has published numerous research papers and
has also authored two textbooks on concrete structures.
Contact details:
Chairman: Civil Engineering Department
College of Technological Studies
PAAET, Kuwait
PO Box: 42325
Shuwaikh
70654 Kuwait
T: +965 9 975 2002
F: +965 2 489 0767
Keywords: variable thermal property, mass concrete, Galerkin fi nite volume
solution, unstructured meshes of triangular elements
INTRODUCTION
Gradual setting of concrete layers during
construction of mass concrete structures
may give rise to drastic temperature gra-
dients due to the cement hydration and
heat conduction properties of the concrete.
Cement is a basic ingredient of concrete
which, by the process of hydration, mixes
with aggregates and water and produces
concrete. This process is exothermal and
causes the concrete temperature to rise.
After achieving maximum temperature,
the temperature decreases until it reaches
the ambient temperature. Predicting
the temperature field resulting from
the concrete hydration process during a
particular construction programme is an
important consideration in the design and
construction of mass concrete structures
like concrete dams. However, the thermal
properties of concrete (specific heat and
thermal conductivity) vary according to
the concrete temperature and the degree of
concrete hydration. These changes can be
considered in the thermal analysis of the
mass concrete structures by the adoption of
available empirical relationships.
The finite volume method has been
widely applied to heat transfer and fluid
dynamic problems through relatively
simple discretisation (Vaz Jr et al 2009). In
recent years the finite volume method has
been used for the solution of temperature
analysis, stress-strain computations and
thermal stress solutions of solid mechanical
problems, some of which are listed in the
following review.
For the computation of temperature
fields, an unstructured finite volume node-
centered formulation was implemented,
using an edge-based data structure for
the solution of two-dimensional potential
problems (Lyra et al 2002). Lyra et al used
an edge-based unstructured finite volume
procedure for the thermal analysis of steady
state and transient problems (Lyra et al
2004). Recently, a 2D finite volume method
to solve a heat diffusion equation was devel-
oped to predict the transient temperature
field in an RCC (roller-compacted concrete)
2D Linear Galerkin fi nite volume analysis of thermal stresses during sequential layer settings of mass concrete considering contact interface and variations of material properties Part 1: Thermal analysisS Sabbagh-Yazdi, T Amiri-SaadatAbadi, F M Wegian
In this research, a new explicit 2D numerical solution is presented to compute the temperature field which is caused due to hydration and thermal conductivity by the Galerkin finite volume method on unstructured meshes of triangular elements. The concrete thermal properties vary, based on the temperature variation and the age of the concrete in the developed model. A novel method for imposing natural boundary conditions is introduced that is suitable for the Galerkin finite volume method solution on unstructured meshes of triangular elements. In addition, the thermal contact is considered at the concrete-rock foundation interface to achieve more realistic simulations in this section. In this work we present the comparison of the thermal analysis numerical results of a plane wall, which had different thermal boundary conditions applied to its edges, with its analytical solution to assess the accuracy and efficiency of the developed model. The applicability of the developed numerical algorithm for thermal analysis is presented by the solution of thermal fields during gradual construction of a typical mass concrete structure.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 95
dam wall during concreting of sequential
layers, taking into consideration the constant
thermal properties during concrete setting
(Sabbagh–Yazdi et al 2007).
The variation in concrete properties
significantly influences the prediction of
the temperature history of mass concrete
structures. Much research has been done to
calculate temperature fields, and different
numerical models have been used in the
various solution methods to simulate the
temperature field in mass concrete structures.
For example, a 2D finite difference method for
predicting the hydration-induced temperature
profile in mass concrete was developed,
considering a sinusoidal function for the sur-
rounding air changes (Ballim 2004).
A 3D finite element solution was pro-
posed for thermal analysis by Kim et al
(2001) who considered the effect of pipe
cooling systems. Ilc et al (2009) also devel-
oped a numerical model for the thermal
analysis of young concrete structures, based
on the finite element method. Considering
the constant thermal properties of con-
crete, the NASIR (Numerical Analyzer for
Scientific and Industrial Requirements)
concrete temperature solver, a 2D finite
volume method solver for heat generation
and transfer equation, was developed to
predict the transient temperature field in an
RCC dam wall during sequential layers of
concrete setting (Sabbagh–Yazdi et al 2001).
The accuracy and efficiency of the proposed
model were assessed by comparing the
numerical results from the analysis with ana-
lytical solutions for problems with constant
concrete properties and various boundary
conditions (Sabbagh–Yazdi et al 2007). In
this research, the variation in the heat con-
duction properties of concrete that occurs
due to changes in concrete temperature and
the ageing process is considered in terms of
the NASIR concrete temperature solver. For
this purpose, a 2D matrix-free Galerkin finite
volume solution is utilised for computing the
temperature fields in mass concrete struc-
tures on unstructured meshes of triangular
elements. In the developed numerical model,
the heat generation and transfer equation is
explicitly solved to compute the temperature
field. For the cases where the boundary
normal vector is parallel to the direction of
the grid in the coordinate system, it is easy to
impose the natural gradient boundary condi-
tion. To overcome the difficulties that may
appear when imposing such a boundary con-
dition at inclined boundaries of unstructured
meshes of triangular elements, a technique is
applied in this work to modify the gradient
flux vectors at the centre of the boundary
elements. This method is adopted for the
implementation of the natural gradient
boundary condition for the solution of heat
generation and transfer equation using the
Galerkin finite volume method.
HEAT GENERATION AND TRANSFER
MATHEMATICAL MODEL
Heat transfer mathematical model
The heat generation and transfer equation
is produced from different thermodynamics
and heat transfer references (Sabbagh–Yazdi
et al 2007).
éêêë
δ
δx
æççèkx
δT
δx
æççè + δ
δy
æççèky
δT
δy
æççèéêêë + Q = ρCT (1)
where k(J/m.h.°C) is the thermal conductivity
of concrete, T(°C) is concrete temperature,
Q(J/m3.h) is the rate of heat generation per
volume, ρ(kg/m3) is the density of con-
crete, and C(J/kg.°C) is the specific heat of
concrete.
The two main boundary conditions at the
external surfaces are:
T = Tair, k.dT
dN = –q (2)
where Tair(°C) and q(w/m2) are the air tem-
perature and the rate of heat exchange.
q = ±qc +qr – qs
qc = hc (Tsurface – Tair), hc = hn + hf,
hn = 6(w/m2.°C), hf = 3.7V(w/m2.°C)
qr = hr(Tsurface – Tair)
qs = γ.IN (3)
where qc, qr and qs are heat flux by convec-
tion, long wave radiation and solar radiation,
respectively; hn, hf and hr are natural, forced
and radiation convection; and γ,IN (w/m2)
and V(m/s) are surface absorption, incident
normal solar radiation and wind speed,
respectively.
In this research, the effects of long wave
radiation and solar radiation in heat flux
have been disregarded and the wind speed
has been supposed to be zero.
Cement hydration heat generation
Cement is a basic ingredient of concrete
which gains its cementitious property after
mixing with water. This chemical reaction
called hydration causes the paste to harden
and gain strength. Because of its significance,
several research efforts into the concrete
heat of hydration field and the appropriate
mathematical models, have already been pre-
sented (Noorzaei et al 2006; Riding 2007).
In general, hydration is a thermo-activated
reaction, and temperature primarily affects
the rate of hydration. Hence, the equivalent
age parameter and maturity function are used
to consider this feature. Through the maturity
function, the effect of concrete temperature
on the rate of hydration is regarded.
Equation 4 is used to calculate the heat of
hydration.
Q(te) = A + E.exp(–b.(te)–n) (4)
where A, E, b, n are variables which are cal-
culated by appropriate fitting of Equation 4
to experimental data, and te(hr) is the
equivalent age.
By adopting the Rastrup maturity func-
tion, the following equation is used to calcu-
late the equivalent age:
H(T) = 20.1(T–Tref), te = ∫H(T)dt (5)
where H(T), T, Tref(°C), are the relative
speeds of hydration reaction, concrete
temperature and reference temperature,
respectively.
Finally, Equation 6 is used to calculate the
rate of concrete hydration (Sabbagh–Yazdi et
al 2007):
Q(te) = n.b.E.(te)–n–1.exp(–b.(te)–n).20.1(T–Tref)
(6)
The hydration process is a long-term reac-
tion, with different hydration products
developing over time as a result of the chem-
ical reaction of water with the cement com-
ponents. Through this process, a skeleton of
hardened cement paste is formed. Due to the
ageing process, therefore, the concrete prop-
erties (thermal and mechanical) may change
during the hydration reaction. The degree of
hydration is equivalent to the amount of heat
liberated at any point during the hydration
stage to the total heat corresponding to the
end hydration. Many different relationships
are presented to calculate the degree of
concrete hydration. One of these models is
the Schindler model, in which the degree of
hydration is calculated by the mixture pro-
portions and the concrete age, as presented
in Equation 7.
αcon(te) = αu.expæççè–
æççèτ
te
æççè
β æççè (7)
where αu(unitless) is the ultimate degree of
hydration, τ is hydration time parameter,
te(hr) is the equivalent age, and β is the
hydration slope parameter. The fit param-
eters (αu, τ, β)are specified according to the
mixture proportions (Schindler 2004).
Using Equation 7, the rate of heat genera-
tion due to the concrete heat of hydration can
be represented by the source terms, heat gen-
eration and transfer equation. In addition, the
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201396
variation of concrete thermal properties (such
as specific heat and thermal conductivity)
during the ageing process can be considered
in the computational thermal analysis.
Ageing effects on thermal
properties of concrete
The concrete temperature and degree of con-
crete hydration affect the thermal properties
of the concrete. The relationships below,
which are related to change in the thermal
properties of concrete over time, are used in
the present thermal analysis.
Specific heat
The specific heat of concrete, which is equal
to the required heat for 1°C increase of
concrete temperature per unit mass of the
concrete, depends on the mixture propor-
tions, the degree of hydration, concrete
temperature and the relative humidity of
concrete.
The following equation is used for
changes in the specific heat of concrete over
time, as provided by Van Breugel (1998):
C = 1
ρ (wc.αcon.cref + wc(1– αcon)cc + wa.ca + ww.cw
Cref = 8.4 T + 339 (8)
where C(J/kg.K) is the specific heat of con-
crete; ρ(kg/m3) is the density of concrete;
wc, wa, ww(kg/m3) are the weight of cement,
aggregate and water per unit volume;
cc, ca, cw(J/kg.K) are the specific heat of
cement, aggregate and water respectively;
αcon is the degree of concrete hydration; and
T(°C) is the concrete temperature.
Thermal conductivity
The thermal conductivity of concrete, which
is the concrete’s ability to conduct heat,
represents the amount of heat transition
through a unit thickness of concrete in a
direction normal to a surface area at the unit
time. This parameter is dependent on the
relative humidity, type and amount of aggre-
gate, porosity and the density of the concrete.
Schindler (2002) stated that a higher
degree of hydration decreases the thermal
conductivity of concrete. The following
equation was proposed by Schindler:
k(αcon) = kue(1.33 – 0.33αcon) (9)
where k(w/m.K) is the transient thermal
conductivity, kue(w/m.K) is the ultimate
thermal conductivity of concrete, and αcon is
the degree of concrete hydration.
NUMERICAL SOLUTION
Galerkin finite volume formulations
The heat generation and transfer Equation 5
can be written as:
æççèδ
δxi Fi
Hæççèn
+ æççèα
k Q
æççèn
= æççèδT
δt
æççè (i = 1,2) (10)
where FiH is diffusive flux in i direction.
FiH = αn
δT
δxi , αn =
æççèk
ρC
æççèn
(11)
In each time step, the values of thermal
properties (k, C) are updated considering the
concrete temperature and degree of concrete
hydration. Then the source term (Sn) is
computed for every node (n) of the concrete
body.
By application of the Galerkin weighted
residual method, after multiplying the
residual of Equation 10 by a weight function
(which can be considered as the nodal shape
function of a linear triangular element, φn)
and integrating over a subdomain Ωn (which
Figure 1 Triangular element within the subdomain Ωn
dly n
dlxm = 3m = 2
m = 1
n
n
l = 1
l = 2
l = 3
l = N
Figure 2 Triangular elements of the boundary edge
Heat flux
G
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 97
is formed by gathering all the elements shar-
ing node n), the weighted integral form of
Equation 10 is written as Equation 12:
∫Ω
æççèδFi
d
δxi
æççè
φndΩ + ∫Ω
æççèα
k Q
æççèn
φndΩ
= ∫Ω
æççèδT
δt
æççèn
φndΩ (12)
The weak form of Equation 12, after
the omission of zero boundary terms, is
expressed as:
–∫Ω(FiH. φn)dΩ + ∫Ω
æççèα
k Q
æççèn
φndΩ
= ∫Ω
æççèδT
δt
æççèn
φndΩ (13)
The approximate ratio given in Equation 14
can be used to calculate the spatial derivative
term of Equation 13:
∫Ω(FiH. φn)dΩ ≈
1
2 ∑3
k=1(FiH.Δli)k (14)
Here (Δli)k is the i direction component of
the normal vector of edge k of the subdo-
main Ωn which is opposite to its central
node n (Figure 1).
The source term of the Equation 13 can
be approximated as:
∫Ω
æççèα
k Q
æççèn
φndΩ ≈ Ωn
3
æççèα
k Q
æççèn
(15)
Using the forward differencing method,
the discrete form of the transient term of
the governing equations can be written as
follows:
∫Ω
æççèδT
δt
æççèn
φndΩ = æççè
Tnt+Δt – Tn
t
Δt
æççèn
Ωn
3 (16)
The explicit form of the heat generation
and transfer equation for subdomain Ωn is
expressed as Equation 17:
Tnt+Δt = Tn
t + (Δt)tn
éêêë
3
2Ωn ∑N
l=1
æççèFiH.Δli
æççèt
1
+ æççèα
k Q
æççèt
n
éêêë (17)
where Tnt+Δt is temperature of node n at
time t+Δt, and N is the number of edges sur-
rounding the subdomain Ωn (Figure 1).
Computation of heat flux
vector components
The components of the heat flux vector
FiH = αn
δT
δxi must be calculated at the centre
of the elements corresponding to the bound-
ary edges of the subdomain Ωn (Figure 1).
The integration over an element can be
converted to a boundary integral using the
Gauss divergence theorem:
∫ΩE δT
δxi dΩ = o∫1T.dli (18)
where ΩE is the area of a triangular element.
The discrete form of the line integral can be
written as:
o∫1T.dli ≈ 1
ΩE ∑3
m=1(T.Δli)m (19)
where Δli is the component of the mth edge
normal vector of a triangular element which
is perpendicular to the i direction, and T is
the average temperature at the same edge
(Figure 1).
Hence, diffusive flux at each triangular
element for both directions can be calculated
using the following equation:
(FxH) =
æççèαn
δT
δy
æççè @ 1
ΩE ∑
3
m=1
(T.Δly)m
(FyH) =
æççèαn
δT
δx
æççè @ 1
ΩE ∑3
m=1(T.Δlx)m (20)
Boundary conditions
Two types of boundary conditions, known as
essential and natural boundary conditions,
are usually applied in thermal analysis.
The essential and natural boundary condi-
tions are used for certain temperature and
temperature gradient flux at boundaries,
respectively.
Figure 3 Schematic illustration of plane wall
100°C
b
xy
50°C
Q = 7.2E7 (W/m3)
Isola
tion
Isola
tiona
Figure 4 Unstructured meshes of triangular elements for thermal analysis (with 940 nodes and
1 718 elements)
Y (
m)
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0–0.005 0 0.005
X (m)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 201398
For the cases where the boundary normal
vector n = (nx,ny) is parallel to the direc-
tion of the grid in the coordinate system,
the given normal gradient due to heat flux
by convection, G, can simply be inserted,
but the computational difficulties arise for
inclined or curved boundaries. To solve this
problem, the computed gradient flux vector
(Equation 20) at the centre of the boundary
elements (hatched elements in Figure 2) at
the end of each computational step may be
modified as Equation 23.
FH = (FxH)i + (Fy
H)j = æççèαn
δT
δx
æççèi + æççèαn
δT
δy
æççèj (21)
(G)normal = æççè
qc
k nx
æççè i + æççè
qc
k ny
æççèj (22)
(Fd)modify = αn
æççèδT
δx +
qc
k nx
æççè i + αn
æççèδT
δy +
qc
k ny
æççèj
(23)
where k is thermal conductivity and qc is
heat flux by convection, which was defined
previously.
Time integration
If the propagation speed of heat is considered
proportional to αn, the critical time step size
solution of the heat generation and transfer
equation can be written as Equation 24:
Δt < M æççèΩn
αn
æççè (24)
where M is a coefficient that is less than
unity.
In order to maintain the stability of the
explicit solution, the minimum time step size
of the computational domain must be used
in the computation of the unsteady prob-
lems. For the steady state cases, the concept
of local time stepping can be used where
every node has a special time step which
reduces the programme execution time.
THERMAL CONTACTS
When two solids, of initially different tem-
peratures, are brought into contact, thermal
coupling must be considered within the
contact analysis. Heat normally flows from
one solid to another one at the interface
between the two solids; this affects the
temperature distribution near the contact
surfaces. A constitutive equation is required
for the determination of heat flux in the
contact zone. In addition, the heat conduc-
tion is dependent on contact pressure in the
contact area. The following equation is often
assumed to be the constitutive equation for
heat flux:
q = h(T2 – T1) (25)
Where T2 is the temperature of the slave
node and T1 is the temperature of the closest
point in the master surface to the slave node.
The heat transfer coefficient (h) depends on
the temperature of the contact surfaces and
the contact pressure. The heat transfer can
be accomplished in three possible ways, i.e.
heat conduction through spots (hs), gas (hg)
and radiation (hr). The following equation is
obtained when one assumes that the above-
mentioned mechanisms act in parallel:
h = hs +hg +hr (26)
In this research, the heat conduction through
gas and radiation has been disregarded and
Equation 27 is used to determine the heat
conduction through the spots in the contact
interface.
hs = hræççè
P
Hv
æççèξ (27)
where P is the contact pressure and coef-
ficients hr, Hv and ξ are the thermal resist-
ance coefficient, Vickers hardness and an
Table 1 Specifications of plane wall
Height b = 1 cm
Thickness a = 1 cm
Thermal conductivity k = 18(w/(m.°C))
Internal heat generation Q0 = 7.2 * 107(w/m3)
Figure 5 Computed temperature contours
Y (
m)
0.014
0.012
0.010
0.008
0.006
0.004
0.002
0–0.005 0 0.005
X (m)
220
60
20018016014012010080
°C T
220
220
200
200
180160
160
140120
100
100
80
80
60
60
Figure 6 Convergence of logarithm of root mean square of temperature
RM
S (
Te
mp
era
ture
)
–7
–6
–5
–4
–3
–2
–1
100 00080 00060 00040 00020 0000
Iteration
0
10 000 30 000 50 000 70 000 90 000
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 99
Figure 8 Schematic illustration of a typical mass concrete structure on a natural foundation
4.35
30
.00
15.00
30.00
Foundation
Contact surface
exponent, respectively, which are given as
hr = 1.0, Hv = 3.0 and ξ = 1.5.
The thermal boundary condition is
applied by the following equations for each
node in the contact interface:
T2 = T1 , K.dT
dn + q =0 (28)
where T1 and T2 are the temperature of
solids 1 and 2, respectively, and dT
dn and q
are the thermal conductivity, normal tem-
perature gradient and heat flux, respectively
(Wriggers 2002).
VERIFICATION AND APPLICATION
Verification test
In this section, the solution for a steady
state problem with inclined boundary is
presented. Using the developed solver, the
time stepping limit of the formulation is
utilised to maintain the stability of itera-
tive computation from the assumed initial
condition towards the steady state condition.
Furthermore, use of the local time stepping
method speeds up the computation towards
equilibrium. Consider a plane wall with
specifications as presented in Table 1.
The boundary at y = 0,b of the domain
is assumed to be insulated. The boundary
at x = 0 is maintained at T0 = 50°C, and the
boundary at x = a is exposed to ambient
temperature Tc = 100°C (Figure 3). The film
coefficient is hc = 200(w/m2°C). The assump-
tion of an insulated boundary condition at
y = 0,b of the domain results in the 1D heat
flowing along the x direction. In this case,
the analytical temperature field is given as
Equation 29 (Reddy et al 2000).
T(x) = 50 + 5x
a +200
æççè1.9 – x
a
æççèx
a (29)
where x(m) is the distance from the edge,
which is held at a constant temperature of
50°C, and a(m) is the dimension of the plate.
Unstructured meshes of triangular ele-
ments are shown in Figure 4, and computed
temperature contours are illustrated in
Figure 5.
Using the Dell Vostro 1500 with an Intel
Core 2 Duo T7100 CPU with 1.8 GHz, 2 GB
main memory, the CPU time measured 44.6
seconds.
The root mean square of the computed
temperature during iterations, which is cal-
culated by Equation 30, is shown in Figure 6.
In Figure 7 the temperature changes along
the x direction are compared with the ana-
lytical results. The good correlation between
the computed results and the analytical solu-
tion is promising.
RMS = Logæççè
∑Ni=1(Ti
t+Δt – Tit)2
N
æççè (30)
Application case
In this section, the developed algorithm is
utilised to analyse the transient temperature
field during the gradual construction of a
typical mass concrete structure. The dam
is 30 m high, while the base and crest are
30 m and 4.35 m wide, respectively. The left
and right slopes are 0.1:1, 0.8:1 respectively
(Figure 8). Layer thickness at every concreting
is 0.5 m, and the interval between consecutive
concrete placing lasts 48 hours. The portion
of the dam foundation that is considered for
thermal analysis is shown in Figure 8.
The far field boundary of the foundation
is treated as a zero gradient boundary condi-
tion, and the Newman thermal boundary
condition is used for the external surfaces of
the dam wall and ground surface (Figure 8).
Figure 7 Comparison of computed temperature with analytical solution (along the x-axis)
RM
S (
Te
mp
era
ture
)0
50
100
150
200
250
0.010.0080.0060.0040.0020
Distance (m)
Theory Computational
Error Max = 0.96Error Average = 0.36
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013100
The use of unstructured meshes of
triangular elements for the geometric
modelling of the foundation media (Figure
9) facilitates simulation of the geo-structure
layers with irregular formation and material
variation. Likewise, application of structured
meshes of triangular elements for the dam
wall (Figure 9) provides the development
of concrete media in the vertical direction
(proportional to the construction stage and
concrete layer). The sinusoidal function is
utilised for air temperature changes.
The thermal properties and mixture pro-
portions of concrete are presented in Tables
2 and 3. The specific heat of materials, which
is needed to calculate the specific heat of
concrete, is presented in Table 4.
As mentioned, thermal properties of
concrete vary with the ageing process. In
the present analysis, the relationships as
presented above are used for the simulation
of the changes in the thermal properties of
concrete over time. The thermal properties
of the mass concrete structure are summa-
rised in Table 2.
Using the presented relationships, the
thermal properties of concrete can be deter-
mined according to concrete ageing over
time, as shown in Figures 10 and 11. Having
the transient changes of the thermal proper-
ties, these properties are assigned to each
node considering the temperature and age of
every concrete layer during thermal analysis.
The simulation results for the various stages
of gradual construction of a typical mass
concrete dam are presented in terms of the
transient temperature contour in Figure 12
(see page 102).
CONCLUSION
A 2D matrix-free Galerkin finite volume
solution is presented to compute the tran-
sient temperature field, considering the vari-
able thermal properties on the developing
linear triangular elements due to the heat of
hydration and thermal conduction through
boundary surfaces during gradual concret-
ing of concrete structures. The represented
explicit solution is a computationally effi-
cient algorithm which can achieve results of
time-dependent heat generation and transfer
problems with considerably low computa-
tional effort and CPU time consumption.
However, for the steady state problems, the
time stepping of the formulation may be uti-
lised for iterative stable computation towards
equilibrium, and using the local time step-
ping method, the programme execution time
can be reduced.
Due to the hydration progress of con-
crete and the ageing process, the thermal
properties of concrete vary over time. In
the present transient thermal analysis of
the concrete media, the proposed relation-
ships by previous researchers, as mentioned
above, are used for the simulation of the
transient changes in the thermal properties
of concrete according to concrete tempera-
ture and the degree of concrete hydration.
The method presented in this research
resolves the problem of imposing a normal
temperature gradient at the inclined bound-
aries of unstructured meshes of triangular
elements. In the developed algorithm, the
temperature gradient boundary condition is
applied by the modification of the gradient
flux vector at the centre of the boundary
elements.
In addition, the geometry of the dam
wall and foundation is not considered
integrated anymore, so the thermal contact
is considered at concrete-rock foundation
interface to achieve more realistic simula-
tions in this part. In this work we present
the comparison of the thermal analysis
numerical results of a plane wall, where
different thermal boundary conditions are
imposed at its edges, with its analytical
solution to assess the accuracy and efficien-
cy of the developed model. The computed
Figure 9 The triangular elements of a typical RCC dam wall
Y (
m)
20
30
0
10
–20
–10
–30
X (m)
20 300 10 40–10 50
Table 2 Thermal properties of concrete
Material property Value
Concrete
Coefficient of thermal expansion Variable (asymptote value = 10–5/°C)
Specific heat Variable (asymptote value = 827 J/kg.°C)
Thermal conductivity Variable (asymptote value = 10 326 J/m.h.°C)
FoundationThermal conductivity 9 360 J/m.h.°C
Thermal diffusivity 0.0038 m2/s
Table 3 Mixture proportions of concrete in a
unit volume
Material Value (kg/m3)
Cement 150
Aggregate 1 936
Water 163
Table 4 Specific heat of materials
MaterialSpecific heat
(J/kg°C)
Cement 1 000
Aggregate 800
Water 2 080
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 101
results presented promising correlation with
the analytical solution. In order to present
the applicability of the developed solver to
simulate real-world problems, the developed
model was used for transient thermal analy-
sis of a typical mass concrete structure on
a natural foundation in which the concrete
media were gradually developed via sequen-
tial setting of fresh concrete layers.
The concrete temperature module of
the NASIR Galerkin finite volume solver
can be applied as a useful modelling means
for the prediction of transient temperature
profiles during the desired sequential setting
construction programme of a mass concrete
structure, considering variations in thermal
properties.
NOTATION SECTION
k : Thermal conductivity of concrete
kuc : Ultimate thermal conductivity of
concrete
C : Specific heat of concrete
ρ : Density of concrete
Sn : Source term
te : Equivalent age of concrete
T : Concrete temperature
Tref : Reference temperature
Tsurface : Concrete surface temperature
Tair : The air temperature
Tnt+Δt : Temperature of node n at t + Δt
time
T : Average temperature of edge
Q : Heat of hydration
Q : Rate of heat generation per
volume
Q0 : Internal heat generation
αcon : Degree of concrete hydration
αu : Ultimate degree of hydration
A,E,b,n : Fit parameters
τ : Hydration time parameter
β : Hydration slope parameter
q : Rate of heat exchange
qc : Heat flux by convection
qr : Heat flux by long wave radiation
qs : Heat flux by solar radiation
hn : Natural convection
hf : Forced convection
hr : Radiation convection
γ : Surface absorption
IN : Incident Normal Solar Radiation
V : Wind speed
Ω : Subdomain
Δli : Normal component of boundary
edge at the i direction for the
subdomain Ω
N : Number of control volume out-
side faces
n→ : Normal vector of the boundary
edges
ΩE : Area of the triangular element
Δl : Edge of triangular element
FiH : Diffusive flux in i direction.
G : Given normal temperature
gradient
Δt : Time step size for heat generation
and transfer equation
M : Coefficient that can be consid-
ered less than unity
wc,wa,ww : Weight of cement, aggregate and
water, respectively
cc,ca,cw : Specific heat of cement, aggregate
and water, respectively
hc : Film coefficient
x : Distance
a : Dimension of plate
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Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013102
Figure 12 Computed results of temperature distribution for various construction heights, considering variations of thermal properties according to
the age of each concrete layer
(f) Temperature field at 120 days (construction height = 30 m)(e) Temperature field at 100 days (construction height = 25 m)
(b) Temperature field at 40 days (construction height = 10 m)
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16
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21
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Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013104
TECHNICAL PAPER
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 104–113, Paper 829 Part 2
PROF DR SAEED-REZA SABBAGH-YAZDI is
associate professor in the Civil Engineering
Department of the KN Toosi University of
Technology, Tehran, Iran. He obtained his PhD
from the University of Wales, Swansea, United
Kingdom. He has more than twenty years’
academic and professional experience in
management, design, computation, hydraulics,
structural engineering, computer simulation of fl uid fl ow and heat transfer,
and stress analysis of hydraulic structures.
Contact details:
Civil Engineering Department
KN Toosi University of Technology
Valiasr St Mirdamad Cross
Tehran, Iran
T: +98 21 88 77 9623
F: +98 21 88 77 9476
TAYEBEH AMIRI-SAADATABADI is a PhD student
in the Department of Civil Engineering at the
KN Toosi University of Technology. She obtained
her MSc in hydraulic structures from the
KN Toosi University of Technology and started
her PhD research in 2010. Currently she is
developing software to analyse concrete
structures. Her main research interest is in fi nite
volume numerical methods, cracking and creep.
Contact details:
Civil Engineering Department
KN Toosi University of Technology
Valiasr St Mirdamad Cross
Tehran, Iran
T: +98 21 88 77 9623
F: +98 21 88 77 9476
PROF DR FALAH M WEGIAN has more than 20
years’ academic experience, including the
research work for his Masters and Doctorate.
Prof Wegian is currently chairman of, and
associate professor in, the Civil Engineering
Department at the College of Technological
Studies, Public Authority for Applied Education
and Training (PAAET), Kuwait. His wide range of
research interests includes the use of Fiber Optic Bragg Grating Sensors
embedded in concrete structures to evaluate strains and cracks and the
performance of bridge structures. Prof Wegian has published numerous
research papers and has also authored two textbooks on concrete structures.
Contact details:
Chairman: Civil Engineering Department
College of Technological Studies
PAAET, Kuwait
PO Box: 42325
Shuwaikh
70654 Kuwait
T: +965 9 975 2002
F: +965 2 489 0767
Keywords: variable mechanical property, mass concrete, Galerkin fi nite
volume solution, unstructured meshes of triangular elements
INTRODUCTION
The volume changes in concrete that take
place during the hydration process and cool-
ing phase will cause tensile stress develop-
ment. The external and internal constraints
often exist simultaneously and will limit the
thermal strains corresponding to the tem-
perature changes. Therefore, critical thermal
stresses may appear in the concrete members.
The concrete has a relatively low tensile
strength (compared to other building materi-
als) and is susceptible to cracking. Therefore,
if thermal stresses exceed the tensile strength
of concrete, they could cause visible crack-
ing in the concrete members. Hence, mass
concrete structures such as concrete dams,
nuclear reactor containments and bridges may
be subject to thermal cracking due to thermal
stresses. Thermal cracking can influence the
durability and serviceability of concrete dams,
and should therefore be studied in detail.
Calculating the temperature and stress
distribution is one of the most important
considerations in solid mechanics. These
phenomena have therefore been modelled by
various numerical techniques, such as the
finite difference method (FDM), the finite
element method (FEM), the finite volume
method (FVM), etc. Traditionally, solid body
problems were addressed by the FEM. The
FDM has, however, become one of the most
popular methods in the area of computa-
tional fluid mechanics, and recently some
problems in continuum mechanics have been
solved successfully by FVM (Demirdžić et
al 1993). The FDM is the oldest method and
is based on the application of a local Taylor
expansion to approximate the differential
equations, which are truncated usually after
one or two terms. The number of terms
determine the accuracy of the solution
(the more there are, the more accurate the
2D Linear Galerkin fi nite volume analysis of thermal stresses during sequential layer settings of mass concrete considering contact interface and variations of material properties Part 2: Stress AnalysisS Sabbagh-Yazdi, T Amiri-SaadatAbadi, F M Wegian
In this research, a 2D matrix-free Galerkin finite volume method on the unstructured meshes of triangular elements is utilised to compute thermal stress fields resulting from the predefined transient temperature distribution in a mass concrete structure (dam wall). In the developed numerical model, the convergence of the force equilibrium equations are achieved via some iterative solutions for each given computed temperature field. Since the mechanical properties of concrete may vary over time due to concrete ageing, the presented numerical model considers the variation of mechanical properties corresponding to the degree of concrete hydration and concrete temperature. In addition, the geometry of the dam wall and foundation is not considered integrated any longer, so the mechanical contact is considered at concrete-rock foundation interface to achieve more realistic simulations of the strain-stress fields in this part. In this work we present the comparison of thermal stress analysis numerical results (of a clamped plane which is exposed to constant temperature) with the results of finite element-based ALGOR software to assess the accuracy and efficiency of the developed model, and prove that the results correlate well. As an application of the developed model for a real-world problem, thermal stress analysis of a mass concrete structure which is gradually constructed on a natural foundation is performed with regard to variable mechanical properties.
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 105
solution), but this is a complex matter (Yip
2005). The FDM is suitable for structured
grids associated with regular boundaries, and
is not as accurate for complex geometries
as the FVM is. However, for dealing with
irregular boundaries, the use of unstructured
meshes provides considerable flexibility and
accuracy for modelling projects (Sabbagh–
Yazdi et al 2009).
This is a potential bottleneck of the FDM
when hand ling complex geometries in mul-
tiple dimensions. The issue motivated the use
of an integral form of the governing equations
(PDE), and subsequently the development of
the FEM and FVM (Yip 2005). Both methods
have surpassed the FDM and other numerical
methods, and researchers typically use one of
them for numerical simulations of all types of
physical phenomena. The FEM has become
very popular in structural analysis due to the
great practical value of the results, especially
in cases where deformations are limited to
elastic ones (Demirdžić et al 1993).
The FEM is based on the variational
principle and uses the predefined shape
functions dependent on the topology of
the element, easily extends to higher order
discretisation, produces large block-matrices,
usually with high condition numbers, and
as a consequence relies on direct solvers.
The FVM is usually second-order accurate,
based on the integral form of the governing
equation, uses a segregated solution proce-
dure, where the coupling and non-linearity
are treated in an iterative way, and creates
diagonally dominant matrices well suited for
iterative solvers.
The question here is a trade-off between
the high expense of the direct solver for a
large matrix in FEM or the cheaper iterative
solvers in FVM. The reason for this may be
the fact that the FVM is inherently good at
treating complicated, coupled and non-linear
differential equations, widely present in fluid
flows. By extension, as the mathematical
model becomes more complex, the FVM
should become a more interesting alterna-
tive to the FEM. Another reason to consider
the use of the FVM in structural analysis
is its efficiency. In recent years industrial
computational fluid dynamics has been
dealing with meshes of high order which are
necessary to produce accurate results for
complex mathematical models and full-size
geometries (Jasak et al 2000).
It is well known that the numerical analy-
sis of solids in incompressible limit could
lead to difficulties. For example, fully inte-
grated displacement-based lower-order finite
elements suffer from volumetric locking.
Also, some difficulties are experienced pro-
ducing a stiffness matrix and shape function
in order to increase the convergence rate.
From the results of several benchmark
solutions, the FVM appeared to offer a
number of advantages over equivalent finite
element models. For instance, unlike the
FDM solution, the FVM solution is conserva-
tive, and incompressibility is satisfied exactly
for each control volume of the computational
domain. In principle, because of the local
conservation properties, the FVMs should
be in a good position to solve such problems
effectively. Furthermore, numerical calcula-
tion with meshes consisting of triangular
cells showed excellent agreement with ana-
lytical results (Sabbagh–Yazdi et al 2009).
The presented results show that both local
and global norms of error for the FVM are
similar to the FEM. Using the constant strain
triangles leads to a similar stiffness matrix
and consequently a comparable level of accu-
racy in both the FVM and FEM. It is interest-
ing that the execution time for the FVM is
less than that of the FEM for sufficiently fine
mesh (Ekhteraei–Toussi et al 2007).
As mentioned before, the FVM is a
popular method in thermal analysis, while
the FEM is a conventional technique in
the solid mechanics field. The use of both
methods would inevitably necessitate the
transferring of data. However, the trans-
formation of results between the FVM and
FEM is time-consuming. By using the FVM
for the analysis of solids and temperature,
the time-consuming transfer of data can be
avoided, while the method is also more stable
when simulating complicated problems
(Suvanjumrat et al 2011).
For determining the displacement fields
and elastic stress distribution in structures,
Wheel (1996) introduced an implicit finite
volume method for axisymmetric geometries
using structured meshes. Wenke et al (2003)
presented a finite volume-based discretisation
method for determining displacement, strain
and stress distributions in two-dimensional
structures on unstructured meshes. They
incorporated rotation variables in addition to
the displacement degrees of freedom. Slone
et al (2003) evaluated the dynamic structural
response of solids on unstructured meshes. In
this work, a three-dimensional vertex-based
method with a Newmark implicit scheme was
presented and the neutral frequency was pre-
dicted accurately by employing viscous damp-
ing. Demirdžić et al (2000) extended their
numerical technique for the stress analysis in
isotropic bodies subjected to hygro-thermo-
mechanical loads. In this research, the tem-
perature, stress, displacement and humidity
fields were calculated using the fully implicit
time differencing, whereas the source term
and diffusion fluxes were treated explicitly.
Fainberg et al (1996) performed similar work
for thermo-elastic material.
In one of the numerical research efforts,
ANSYS software was used for 2D and 3D
thermo–structural analyses of roller-com-
pacted concrete (RCC) (Malkawi et al 2003).
Both thermal and mechanical properties of
the concrete were considered constant dur-
ing the analysis. In this research, a 2D finite
element programme was used to simulate
the construction process of a mass concrete
structure. A computer code for thermo-struc-
tural analysis of the mass concrete structures
was also implemented by these researchers.
They predicted the time of crack occur-
rence via the crack index with regard to the
constant mechanical properties of concrete
over time. Noorzaei et al (2006) and Jaafar et
al (2007) implemented a 2D computer code
based on the finite element method for the
thermal analysis of a mass concrete structure.
In this research the thermal properties of
concrete were assumed to be constant during
analysis. Azenha & Faria (2008) proposed a
2D numerical method for the prediction of
temperature and stress distribution consider-
ing the evolution of mechanical properties
during the early ages of concrete.
It should be noted that, as the reactions
proceed, the products of the cement hydration
process gradually grow to form the skeleton of
hardened cement paste as a solid mass which
bears the applied loads. Hence, the mechani-
cal properties of concrete change with respect
to concrete age. This process is known as
concrete ageing and must be considered in
precise thermal stress analysis. Luna & Wu
(2000) predicted the temperature and stress
distribution during RCC dam construction
considering the temperature effect on the
elastic modulus and creep behaviour of con-
crete, but the other concrete properties were
assumed to be constant over time. Cervera et
al (2000) implemented a numerical simula-
tion for construction of the mass concrete
structure with regard to the ageing effects.
In that work the numerical analyses were
performed under different scenarios of dam
construction. Chen et al (2001) developed
the finite element relocating mesh method
for stress analysis of RCC dams during the
construction period. The ageing effects on the
elastic modulus of concrete were considered
by Chen et al.
Another module of NASIR (Numerical
Analyzer for Scientific and Industrial
Requirements) solver, which uses a matrix-
free Galerkin finite volume method on
the unstructured meshes of triangular
elements, was recently introduced for strain-
stress analysis of plane-strain problems
under external loads considering constant
mechanical properties (Sabbagh–Yazdi et
al 2008). In Part I of this two-part paper, a
new explicit 2D numerical solution has been
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013106
presented to compute the temperature field
which is caused due to the hydration and
thermal conductivity by the Galerkin finite
volume method on the unstructured meshes
of triangular elements with respect to the
variation of temperature and age of concrete.
In this research, NASIR plane-strain
solver, the finite volume method solver of
Cauchy equations for plane-strain problems,
is developed to predict the strain-stress fields
during multi-layer concrete setting of a mass
concrete structure considering the variations
of mechanical properties. For this purpose,
a strain-stress solver based on the Galerkin
finite volume method for plane-strain prob-
lems is developed for stress analysis during
the various stages of gradual construction of
mass concrete structures. In this modelling
strategy, the convergence of 2D force equilib-
rium equations is achieved via some iterative
matrix-free solutions for a given (previously
computed in Part I of this two-part paper)
temperature field at each stage of the gradual
construction of the mass concrete struc-
ture. The thermal stresses are computed
considering the effect of concrete ageing
on the mechanical properties of concrete.
The variations of mechanical properties are
considered corresponding to the concrete
temperature, the time dependent degree of
hydration and the concrete age.
After the detailed description of the
numerical modelling, the accuracy of the
introduced numerical model is assessed
by comparison of the computed principle
thermal stress contours of a clamped plate
due to a uniform temperature field with the
finite element method solution which has
been reported by Logan (2000). Finally, the
thermal stress solution during the multi-layer
construction of a mass concrete structure on
a natural foundation is performed consider-
ing the variable mechanical properties of
concrete
FORCE EQUILIBRIUM AND STRESS
FIELD MATHEMATICAL MODEL
Force equilibrium equations
It is well known that the Cauchy equa-
tions are the predominant equations of
solid mechanics. The following equation
is attained from the equilibrium equations
which can be used on each body with any
material (Sabbagh–Yazdi et al 2008).
δσx
δx +
δτxy
δy = ρüx
δτxy
δx +
δσy
δy = ρüy (1)
where ρ (kg/m3) is the material’s density and
üi (m/s2) is the acceleration of the body.
Strain-stress relations
The stress field for plane-strain problems is
expressed as:
σx = D11εx + D12εy
σy = D21εx + D22εy
τxy = D33γxy
D = E(1 – ϑ)
(1 + ϑ)(1 – 2ϑ)
éêêêêêë
1 ϑ
1 – ϑ 0
ϑ
1 – ϑ 1 0
0 0 1 – 2ϑ
2(1 – ϑ)
éêêêêêë
(2)
where σx,σy,τxy are the normal stresses in the
x and y directions and shear stress, respec-
tively; εx,εy,γxy are the normal strains in the
x and y directions and shear strain, respec-
tively; and E, ϑ denote the elastic modulus
and Poisson’s Ratio coefficient.
The strain field is expressed as:
εx = δux
δx + εEth
εy = δuy
δy + εEth
εxy = δux
δy +
δuy
δx (3)
where (εEth)n is the external thermal strain of
node n which is calculated from Equation 4:
(εEth)n = αΔT = α(Tt+Δt – Tt)n (4)
where
α(l/°C) : coefficient of thermal expansion
Ttn(°C) : temperature of node n at time (t)
Ageing effects on
mechanical properties
The changes of concrete properties dur-
ing the hydration reaction are called the
concrete ageing. The evolution of elastic
Figure 1 Control volume node n with triangular elements
dx
m = 3
m = 2
m = 1
n
l = 1
l = 2
l = 3
l = N
dy
k
j
i
Ux
Uy
Figure 2 Clamped constraint
v
u
Figure 3 Sliding constraint
v
u
un ut
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 107
modulus and strength of concrete must
be considered for a precise thermal stress
analysis.
Elastic modulus
The elastic modulus is defined as the
ratio between the constrained strains and
stresses. The elastic modulus of concrete
relates to the hydrated cement paste of
concrete, which is able to support the
applied loads. The hydrated cement paste
of concrete grows with time and causes
considerable increase of the concrete
elastic modulus. Equation 5 may be used
for the evolution of the concrete elastic
modulus over time (Noorzaei et al 2006).
Ec(t) = Ec.eatb , Ec = 4 750 f ’c (5)
where Ec(MPa) is the elastic modulus of
concrete at time (t), Ec(MPa) is the ultimate
elastic modulus of concrete, t(day) is the
equivalent age of concrete, f ’c is the char-
acteristic cylinder strength of concrete,
and a, b are the fit parameters which were
determined for one mass concrete structure
as follows: a = –0.5, b = –0.63.
Poisson’s Ratio
The Poisson’s Ratio coefficient is required
for stress modelling in multi-dimensional
structures. This coefficient is defined as
the ratio of transverse strain to longitu-
dinal strain under uniform axial stress.
De Schutter & Taerwe (1996) presented
a model to calculate the variation in the
Poisson’s Ratio of concrete over time based
on the degree of concrete hydration.
ϑ(αcon) = 0.18sinπαcon
2 + 0.5e–10αcon (6)
where ϑ(αcon) is the Poisson’s Ratio of con-
crete at the degree of hydration (αcon).
Coefficient of thermal expansion
Coefficient of thermal expansion is one of
the most important parameters of thermal
stress analysis. The mixture proportions,
type of aggregate, degree of saturation and
concrete age are the effective parameters
on the coefficient of thermal expansion
of concrete. The coefficient of thermal
expansion is dependent on the coefficient
of thermal expansion of the concrete com-
ponents. Since the aggregate content of
concrete is relatively high, the coefficient
of thermal expansion of the aggregate has
the greatest effect on the coefficient of
thermal expansion of concrete.
The Loukili model expresses the evolu-
tion of the coefficient of thermal expan-
sion of concrete over time (Equation 7).
According to this relationship, the
coefficient of thermal expansion of con-
crete decreases over time and converges to
10–5(1/°C).
α(t) = 77e
0.75–t
2.5 + 10 (7)
where α(10–6/°C) is the coefficient of thermal
expansion of concrete, and t(hr) is the equi-
valent age of concrete (Loukili et al 2000).
NUMERICAL SOLUTION
Galerkin finite volume formulations
The compact form of Cauchy equations can
be expressed as:
æççèδσij
δxi
æççè = æççèρ
δ2ui
δt2
æççèn (i = 1,2) (8)
For j = 1,2 the stress vector can be defined
as F→
i = σi1i + σi2j = F1i + F2j where ui(m) is
displacement in the i direction.
By application of the Galerkin weighted
residual method, after multiplying the residual
of the above equation by a weight function
(which can be considered as the nodal shape
function of a linear triangular element φn)
and integrating over a subdomain Ω (which is
formed by gathering all the elements sharing
node n), the weak form of Equation 8, after
omitting zero boundary terms, is expressed as:
∫Ωφn.( .FiS)n = ∫Ωφn.
æççèρδ2ui
δt2
æççèn dΩ (9)
The first term on the right-hand side of
Equation 9 can be written as Equation 10:
∫Ωφn.( .FiS)n = [φn.nFi
S]Γ – ∫Ω(FiS. φn)dΩ
→ ∫Ωφn.( .FiS)dΩ = –∫Ω(Fi
S. φn)dΩ (10)
The approximate relationship given in
Equation 11 can be used to calculate the
spatial derivative term of Equation (10):
∫Ω(FiS. φn)ndΩ ≈
1
2 ∑3
m=1(FiS.Δli)m (11)
Here (Δli)m is the i direction component of
the normal vector of edge m of the subdo-
main Ωn.
The weighting function φ has a value of
unity at the desired node n, and zero at the
other neighbouring nodes k of each triangu-
lar element.
For an equilibrium condition in which
time stepping can be considered as a strat-
egy to perform the iterative computation
until the desired convergence is achieved,
the transient term of the equation can be
expressed as:
ρΩn
3
æççèδ2ui
δt2
æççèn = ρ
æççèui
k+1 – 2uik + ui
k–1
Δt2
æççèn
Ωn
3 (12)
The discrete form of the Cauchy equation for
a node n is written as Equation 13:
(ui)nk+1 = (Δt)n
kéêêë
3
2ρΩn ∑N
i=1
æççèFiS.Δli
æççèk
1
éêêë
+ 2(ui)nk – (ui)n
k–1 , (i = 1,2) (13)
where (ui)nk+1 is the displacement of node n at
k+1 iteration in the i direction (Figure 1).
Computation of stress vector
components
The stress field can be calculated using the
following equations:
σx = ìïíïî
D11
æççèδux
δx + εEth
æççè + D12
æççèδuy
δy + εEth
æççèìïíïî
σx ≈ ìïíïî
1
ΩE ∑3
m=1
æççèD11uxΔy – D12uyΔx
+ εEth(D11 + D12)æççèm
ìïíïî (14)
σy = ìïíïî
D12
æççèδux
δx + εEth
æççè + D11
æççèδuy
δy + εEth
æççèìïíïî
σy ≈ ìïíïî
1
ΩE ∑3
m=1
æççèD12uxΔy – D11uyΔx
+ εEth(D12 + D11)æççèm
ìïíïî (15)
τxy = τyx = ìïíïî
D22
æççèδux
δy +
δuy
δx
æççèìïíïî
τxy = τyx ≈ ìïíïî
1
ΩE ∑3
m=1
æççèD22uyΔy – D22uxΔx
æççèm
ìïíïî (16)
where
εEth : the external thermal strain which is
the average strain of each edge
ΩE : the area of triangular element
n : the external edges number of control
volume
Boundary conditions
The boundary conditions of the force equi-
librium equation are presented as follows:
Clamped constraint
In this boundary condition, not only the
displacement, but also the rotation must be
limited (Figure 2).
ux = 0, uy = 0, θ = 0 (17)
Sliding constraint
This boundary condition provides only the
tangential displacement, and the normal
displacement is prevented (Figure 3).
un = 0, θ = 0 (18)
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013108
Iterative computation
The iterative computations are resumed until
the steady state condition and desired con-
vergence are achieved. In order to maintain
the stability of the iterative computations, the
time stepping size must be limited. Using the
local time stepping method can reduce the
run-time required to reach equilibrium. In
order to have the stable explicit solution, the
Courant’s number must be less than unity.
According to the proposed relation
(Sabbagh–Yazdi et al 2008), the time step size
must be limited to the following equations:
Δtn < rn
C (19)
rn = Ωn
Pn , Pn = ∑
k=1Nedge(Δl)k (20)
where Ωn and Pn are the area and perimeter
of the control volume, respectively.
C is the speed of information transition
which is calculated from Equation 21:
C = E
ρ(1 – ϑ2) (21)
Every node has its own time step size.
Using the concept of the local time step-
ping method accelerates the convergence to
the equilibrium condition for steady state
problems.
CONTACT ANALYSIS
Contact mechanics involves the study of
forces transmitted from one solid to another
and the consequent stresses in those solids.
Contact mechanics has widespread applica-
tion in many engineering problems and
no one can disregard its importance. The
general goals of contact analysis are to deter-
mine the contact stresses transmitted across
the contact interfaces of the solids that are
brought into contact. Nowadays computa-
tional mechanics is a useful tool to simulate
contact problems numerically so that one
is able to analyse large-scale problems. One
of the interesting applications of contact
mechanics is the modelling of dam-rock
foundations interface. Interface may not only
affect the mechanical behaviour of the dam
and foundation system, but also the diffusion
properties, such as moisture transmission.
The safety against sliding has to be assessed
for the interface between the dam and the
foundation, especially in dynamic analysis.
In the contact area, the constraint equa-
tions for normal and tangential contact have
to be formulated. Let us assume that two
solids are brought into contact (Figure 4).
In this case, the non-penetration condition
(constraint equation) is given by the follow-
ing equation:
g = [x1 – x2].n ≥ 0 or g = Cu on Γc = Γ1 + Γ2 (22)
where Γc denotes the contact surface; n is
the normal to solid 2; x1,x2 are the deformed
positions of solids 1 and 2, respectively; u is
the displacement matrix; and g = æççègn
gt
æççè is the
Figure 4 Contact forces
Contactor
Target segment
C
i j
time = t
time = t + dt
gt
gn
ft
fn
(a) Before contact (b) Possible normal and tangential gaps
Figure 5 Schematic illustration of plate
clamped at left and subjected to
uniform temperature
50 cm
Free edge
50
cm
Cla
mp
ed c
on
stra
int
A50°C
Fre
e ed
ge
A
Free edge
Table 1 Plate specifications
Plate Specification Value
Length * Height 50 * 50 cm
Elastic modulus 210 GPa
Poisson’s Ratio ϑ = 0.3
Coefficient of thermal expansion
α =1.2E – 5/°C
Temperature difference 50°C
Figure 6 Unstructured meshes of triangular elements for thermal stress analysis (with 940 nodes
and 1 718 elements)
Y (
m)
0.5
0.4
0.3
0.2
0.1
0
X (m)
0 0.1 0.2 0.3 0.4 0.5
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 109
relative motion in normal and tangential
direction, respectively.
If the above relationship isn’t exactly
satisfied, we have some penetration in the
contact surface which could be interpreted
as the g function:
g = Cu – Q (23)
In this research, the penalty method is con-
sidered for enforcing a constraint condition
in contact analysis. The stiffness equation of
a constrained problem is determined by min-
imising the total potential energy (Equation
24). As is clear from this, the stiffness matrix
and force vector are modified to incorporate
the impenetrability constraint stiffness.
[K + CTαC]u = R + CTαQ (24)
where α is the penalty number.
The contact force vector is calculated
from the following equation:
æççèfn
ft
æççèCon
= éêêë αn 0
0 αt
éêêë
æççègn
gt
æççè (25)
where fn, ft are the normal and tangential
contact forces, respectively, and αn, αt are
the normal and tangential contact stiffness,
respectively.
One has to distinguish two cases which
are called stick state and slide state in the
tangential direction of the contact surface. In
the first situation (stick state) a point which
is in contact cannot move in the tangential
direction, but in the slide state situation
relative slip between two solids occurs and
friction law is applied to the contact surface.
A slip criterion is used to indicate whether
stick or slip state occurs, which is stated as in
Equation 26:
φ = |τ| – τcrit = ìïíïî
< 0 stick state
= 0 slip state (26)
where |τ| denotes the norm of the tangential
traction and τcrit is determined by the fric-
tion law.
The Coulomb friction law, which is
adequately applicable to common frictional
contact problems, is adopted in this research
as (Mohammadi 2003):
τcrit = μ|σn| (27)
where μ is the friction coefficient and σn
denotes the normal stress. The value of the
friction coefficient for mass concrete on
sound rock is considered to be 0.7 so that the
stick state always occurs (ETL 1110-3-446
1992).
VERIFICATION AND APPLICATION
Verification test
External thermal stresses are induced in
concrete structures because the coefficients of
Figure 7 Maximum principal stress contours computed by developed model (Pa)
Y (
m)
0.5
0.4
0.3
0.2
0.1
0
X (m)
0 0.1 0.2 0.3 0.4 0.5
4.4E+064.4E
+06
8.8E
+06
8.8E+06
1.3E+07
1.3E+07
1.3E+07
1.8E+07
1.8E
+07
2.2E+07
8E+073.1E
+07
3.1E+072.8E+07
4.4E+06
1.3E+078.8E+06
2.2E+071.8E+07
S1
Figure 8 Maximum principal stress contours computed by ALGOR finite element method
software (Logan 2000)
Y (
m)
500
400
300
200
100
0
X (m)
0 100 200 300 400 500
450
350
250
150
50
50 150 250 350 450
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013110
thermal expansion of the body and adjacent
structures are different. When the tem-
perature difference between the body and its
adjacent structures is the same, the thermal
strains in the body and its adjacent structures
due to the difference between their coef-
ficients of thermal expansion are different,
which cause thermally induced stress.
A plate specimen is clamped at the left
and is subjected to a uniform temperature
of 50°C as shown in Figure 5 (Logan 2000).
The properties of the material are given in
Table 1.
The unstructured mesh of triangular
elements, as shown in Figure 6, is used to
perform the Galerkin finite volume method
solution. In order to assess the computed
results of the present solver with other
developed methods, the results of the finite
element-based ALGOR commercial software
(presented in the previous literature review)
are used to compare the computed results.
Under a uniform temperature, the thermal
stresses are induced by the restraint bound-
ary conditions. The computational stress
field is the same as the results from the
ALGOR software (Logan 2000), as are shown
in Figures 7 and 8.
Application case
The applicability of the developed solver to
simulate real-world problems is shown in
this section. Using the developed software,
the simulation of a thermally-induced stress
field of a typical mass concrete structure is
performed with regard to the variations of
mechanical properties of the material. The
mechanical properties of the concrete and
foundation are tabulated in Table 2. For more
geometrical details please refer to Part I of
this two-part paper.
Using the presented relationships, the
mechanical properties of concrete can be
determined according to concrete ageing
during analysis. Their variation diagrams
over time are shown in Figures 9–11.
The numerical analysis of a typical
mass concrete structure is performed using
the above-mentioned relationships of the
mechanical properties and the computed
results of both simulations (constant and
variable properties of concrete), as demon-
strated in Figure 12 (see page 112) in terms
of the transient principal stress contours in a
concrete dam wall during the different stages
of construction.
In order to provide a better understand-
ing of the effects of the gradual load impos-
ing technique and to ensure the convergence
of the presented results, the root mean
square of the computed displacements is
shown in Figure 13.
CONCLUSION
Considering the temperature and time-
dependent mechanical properties of concrete
is an essential task for the precise thermal
stress analysis of mass concrete structures.
In this research, a plane-strain matrix-free
Galerkin finite volume method was used
to develop a numerical solver which is able
to predict the temperature-induced stress-
strain fields in mass concrete structures due
to concrete heat of hydration and thermal
conduction between the concrete and sur-
rounding air through the boundary surfaces,
considering the concrete ageing dependent
mechanical properties.
Figure 9 Variation of Poisson’s Ratio with respect to concrete ageing
Po
isso
n's
ra
tio
0.6
0.5
0.4
0.3
0.2
0.1
0
Variable Constant
Time (hour)
120967248240
Figure 10 Variation of coefficient of thermal expansion with respect to time
Co
eff
icie
nt
of
the
rma
l e
xp
an
sio
n (
1/°
C)
0.000070
Variable Constant
Time (hour)
24181260
0.000060
0.000050
0.000040
0.000030
0.000020
0.000010
0
Table 2 Mechanical properties
Material propertyValue
Concrete Foundation
Final elastic modulus 21 GPa 22 GPa
Characteristic cylinder strength 20 MPa …………
Elastic modulus Variable Constant
Poisson’s Ratio Variable (asymptote value = 0.16) 0.3
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 111
Building on the computed transient
temperature field from the similar solver in
Part I of this two-part paper, stress analysis
was performed on the same mesh, and
the converged stress–strain fields were
achieved via some iterative solution of
Cauchy equilibrium equations. The time
step of the Cauchy equation formulation
was used for the iterative solution of the
equilibrium equation at each desired time
step of the thermal analysis. The thermal
stresses were computed using the previously
computed displacements and the thermal
strains which had been accumulatively
calculated from the results of performed
thermal analyses between the two sequen-
tial stress-strain computation stages. In
addition, dam wall and foundation geometry
were not considered integrated anymore,
so the mechanical contact was considered
at concrete-rock foundation interface to
achieve more realistic simulations of stain-
stress fields in this area. The accuracy of
the developed model was evaluated by
the comparison of thermal stress analysis
numerical results of a clamped plane, which
was exposed to constant temperature
(constant mechanical properties), with the
results of finite element-based ALGOR
software. The calculated results correlated
well with the finite element results. Then
the applicability of the developed numerical
solver was demonstrated by the simulation
of the transient stress-strain field during
the gradual construction of a concrete dam
wall on a natural foundation. The numerical
computations were performed for a typi-
cal mass concrete structure on a natural
foundation for the variable mechanical
properties. The simulation results showed
that significant tensile stresses may develop
at the concrete surfaces due to the severe
temperature gradient.
The thermal stress module of the NASIR
Galerkin finite volume solver can be used
as a helpful simulation tool to predict the
thermal stresses of the multi-layer construc-
tion programme of a mass concrete struc-
ture considering the variable mechanical
properties.
NOTATION SECTION
bi : Body force
ρ : Material density
üi : Acceleration of body
D : Stiffness matrix
εEth : External thermal strain
α : Coefficient of thermal expansion
Ttn : Temperature of node n at time t
F→
i : Stress vector in the direction
Ω : Subdomain
φ : Test function
(un)it+Δt : Displacement of node n at k itera-
tion number
ΩE : Area of the triangular element
n : External edges number of control
volume
Ωn : Area of the control volume
Pn : Perimeter of the control volume
C : Speed of information transition
Δtn : Virtual time step of node n
Ec : Ultimate elastic modulus of
concrete
t : Equivalent age of concrete
f ’c : The characteristic cylinder
strength of concrete
a,b : Fit parameters
ϑ : Concrete Poisson’s Ratio
αcon : Degree of concrete hydration
Ec(t) : Elastic modulus of concrete at
time (t)
(Δli)m : The i direction component of the
normal vector of edge m of the
subdomain Ωn
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Figure 11 Variation of elastic modulus with respect to concrete ageing
Ela
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Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013112
Figure 12 2D distribution of maximum principle stress for different construction heights (MPa) considering variations of mechanical properties
according to the age of each concrete layer
-0.10
0
0
0
0
0
0
0.1
0.1
0.1
0.1
0.2
0.2
0.30.40.6
-0.1
0
0
00
0.1
0.1
0.1
0.2
0.2 0.2
0.3 0.4
0.40.
5
-0.2
0
0
0.2
0.2
0.2
0.4
0.6
0.8
0
0.2
0.4 0.4
0.8
1
1.2
1.4 S1
1.41.210.80.60.40.20
-0.2
(Mpa)
-0.2
0
0
0
0.2
0.2
0.40.6
0.6
0.8
1.21.4
0
0
0.2
0.2
0.20.4
0.4
0.6
0.6
0.81
1.2
1.4
1.6
(f) Stress field at 120 days(e) Stress field at 100 days
(b) Stress field at 40 days
(d) Stress field at 80 days
(a) Stress field at 20 days
(c) Stress field at 60 days
Y (
m)
X (m)
10
–30
–20
0
–10
–10 403020100
20
50
30
Y (
m)
X (m)
10
–30
–20
0
–10
–10 403020100
20
50
30
Y (
m)
X (m)
10
–30
–20
0
–10
–10 403020100
20
50
30
Y (
m)
X (m)
10
–30
–20
0
–10
–10 403020100
20
50
30
Y (
m)
X (m)
10
–30
–20
0
–10
–10 403020100
20
50
Y (
m)
X (m)
10
–30
–20
0
–10
–10 403020100
20
50
1.81.6
–0.2–0.4
0.20
0.60.4
1.00.8
1.41.2
S1Mpa
1.21.0
0–0.2
0.40.2
0.80.6
S1Mpa1.41.2
–0.2
0.20
0.60.4
1.00.8
S1Mpa
0.60.5
–0.2–0.3
0–0.1
0.20.1
0.40.3
S1Mpa
1.61.4
0–0.2
0.40.2
0.80.6
1.21.0
S1Mpa
0.60.5
–0.2
0–0.1
0.20.1
0.40.3
S1Mpa
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Suvanjumrat, C & Chaichanasiri, E 2011.
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Wenke, P & Wheel, M A 2003. A finite volume method
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Wheel, M A 1996. A finite-volume approach to the
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Yip, S 2005. Handbook of Materials Modeling, Volume
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Figure 13 Convergence of the results for the computed displacements
Lo
g (
RM
S)
–4
–5
–6
–7
–8
–9
0 0.5 1.51.0 2.0 2.5 3.53.0 4.0
Iterations (millions)
X Direction Y Direction
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013114
DISCUSSION
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Pages 114–116, Discussion Paper 762-1
Publishing particulars of paper under discussionVol 54 No 1, April 2012, Pages 32–42, Paper 762-1
COMMENT
The paper states the following: “A strongly
cemented layer might show signs of car-
bonation, but the strength of the carbonated
material is still adequate for its use and
purpose in the pavement. This could be
described as ‘non-deleterious’ carbonation
(or simply carbonation), whereas when
carbonation causes the properties of the
material to deteriorate to the extent that the
layer cannot fulfil its intended function it is
known as ‘deleterious’ carbonation, in the
context of this set of papers.” (pp 34–35)
Some of the causes for the formation of
weak interlayers listed in the paper are the
following:
■ Detrimental carbonation of chemically
stabilised layer from below or from sides
after construction. (p 38)
■ Some materials perform well in labora-
tory tests, but have a tendency to form
a soft surface or soft base in the field
(Bergh 1979). (p 38)
■ Weakening due to detrimental car-
bonation, dry out and/or wet-dry cycles is
probably the most common cause of sur-
face weake ning of chemically stabilised
layers. (p 39)
■ Note that in chemical soil stabilisation,
carbonation almost invariably weakens
the stabilised material. (p 39)
■ If a chemically stabilised layer has
been badly cured – even allowed to dry
partially only once – the upper layer has
probably been weakened. (p 39)
■ Most weak layers, interlayers, laminations
and/or interfaces can be prevented by
good construction practices. (p 40)
■ In order to prevent the formation of weak
interlayers the specifications specify the
following:
■ Curing of a chemically stabilised layer
for at least seven days is carefully
specified and it is stated that drying
out or wet-dry cycles may be the cause
for rejection if the layer is damaged
thereby (para 3503(h)). (p 40)
■ No priming shall be carried out on a
base which is visibly wet or which is at
moisture content in excess of 50% of
the OMC (para 4104). (p 40)
■ Before priming, the base shall be
broomed and cleaned of all loose
material (para 4105). (p 40)
■ Asphalt shall not be placed if free
water is present on the working
surface or if the moisture content of
the underlying layer, in the opinion
of the engineer, is too high, or if the
moisture content of the upper 50 mm
of the base exceeds 50% of the OMC
(para 4205(b)). (p 40)
■ Before applying a tack coat or asphalt,
the surface shall be broomed and
cleaned of all loose or deleterious
material (para 4205(c)(ii)). (p 40)
■ Before applying a seal, the moisture
content of the upper 50 mm of base
shall be less than 50% of the OMC
(par 4304(d)(i)). (p 40)
■ Additional precautions may be
required when utilising marginal or
substandard materials (Netterberg et al
1989). (p 40) [These additional precau-
tions are not mentioned in the paper.]
The paper concludes that weak layers,
interlayers and laminations have more than
one cause, but most can be prevented simply
by application of known good construction
practices. (p 41)
From these remarks it is clear that the
paper sees the main cause of ‘deleterious’
carbonation as construction-related and
therefore the contractor’s responsibility.
I would like to refer to Dr P Paige-Green’s
TREMTI paper of 2010 to show that, even if
the true cause of ‘detrimental carbonation’
was the carbonation of the surface layer by
the carbon dioxide in the air, that it is still a
water-driven reaction. Allow me two quotes
from Paige-Greene’s 2010 TREMTI paper:
“During the early 1980s a number of prob-
lems related to the loss of stabilisation and
disintegration of stabilised layers in roads
(lime and cement) were reported in South
Africa. This led to many comprehensive
investigations and it was shown without
any doubt that the problems were related
to carbonation of the stabilised materials.
A paper was presented at the TREMTI
conference in Paris in 2005 indicating
that many of the problems in South Africa
that were attributed to carbonation, were
actually caused by ‘water driven reactions’
and were thus material related and not
construction related. This paper assesses
the fundamental principles of each of the
processes and draws conclusions as to their
likelihood and the increasing occurrence of
stabilisation problems. It is concluded that,
although there is indubitable proven field
and laboratory evidence for carbonation of
stabilised layers, there is no solid scientific
evidence for the occurrence of ‘water driven
reactions’ in soil stabilisation in roads.”
“The carbonation reaction depends on
the solubility and diffusion of the compo-
nents. The diffusion is controlled by the
concentration differences and is an inward
diffusion of CO2 gas and carbonate ions
(Lagerblad 2005). The gas diffusion is much
faster than ion diffusion. Thus the rate of
reaction is controlled by the humidity in the
material, i.e. how much liquid fills the con-
nected pore system. In dry material the CO2
can penetrate well, but there is insufficient
water for the reaction to take place. In the
saturated condition, only the carbonate ions
move and carbonation is slow. Typically, the
reaction is most likely and rapid at humidi-
ties of 40 to 70% (Lo & Lee 2002; Ballim &
Basson 2001; Gjerp & Oppsal 1998).”
However, Ballim & Basson also state that no
carbonation takes place when the pores are
completely dry or when they are fully saturated
and that the rate of carbonation also increases
with increasing ambient temperature (Fulton
2002 p 150). Neither of these conditions is
normally found in chemically stabilised layers.
In actual fact, the moisture regime of the stabi-
lised layer is usually closer to 50% of the OMC
as can be seen from the above quotes.
Encyclopaedia Britanica states:
“The atmosphere is made up of a number
of gases of which water vapour is in
many respects the most important. This
importance arises from the fact that water
vapour is the only constituent of air whose
state changes at the temperatures encoun-
tered in the atmosphere. Water substance
occurs as vapour (invisible), as liquid (fog,
cloud and rain droplets) and as a solid (ice
crystals, hail and snowflakes). The subject
Weak interlayers in fl exible and semi-fl exible road pavements: Part 1
F Netterberg, M de Beer
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013 115
of atmospheric humidity deals only with
water in its vapour state.”
Relative humidity gives the amount of water
vapour present in a volume of air as a per-
centage of the maximum possible amount
of water vapour in that volume at the same
temperature. The relative humidity depends
on the temperature, as well as the water
vapour content.
Wikipedia states the following about the
effect of carbonation on phenolphthalein:
“The acid-base indication abilities of
phenolphthalein also make it useful for
testing for signs of carbonation reactions in
concrete. Concrete has naturally high pH
due to the calcium hydroxide formed when
Portland cement reacts with water. The
pH of the ionic water solution present in
the pores of fresh concrete may be over 14.
Normal carbonation of concrete occurs as
the cement hydration products in concrete
react with carbon dioxide in the atmo-
sphere, and can reduce the pH to 8½ – 9,
although that reaction usually is restricted
to a thin layer at the surface. When a 1%
phenolphthalein solution is applied to
normal concrete it will turn bright pink. If
the concrete has undergone carbonation,
no colour change will be observed.”
Therefore, the carbonation of cement-
stabilised layers cannot take place without a
certain amount of water vapour being present.
Therefore it is a water-driven or water-
activated reaction. However, the pink colour
of the phenolphthalein on the loose powdery
interlayer shows that the cement-stabilised
layer is not carbonated. Furthermore, the
contractor has no permanent control over the
moisture regime in the stabilised layer, which
is specified to be close to 50% OMC and thus
in the active carbonation humidity range.
Therefore the problem is material related.
The fact that performance of the stabi-
lised material on site sometimes differs from
the performance in the laboratory is due to
the fact that laboratory design tests pres-
ently do not simulate specified construction
conditions on site. It is not possible for the
contractor to simulate laboratory conditions
on site during construction. The laboratory
tests should simulate site constraints.
Dr CJ Semelink
RESPONSE FROM AUTHORS
The additional precautions which may be
required when utilising marginal or substan-
dard materials were discussed by Netterberg
et al (1989) referred to in our paper.
Carbonation is inevitable in the long term
as both Portland-type cements and lime are
unstable, both under normal atmospheric
conditions and those in the road and soil.
However, it can be prevented or delayed in
engineering time by means of suitable design,
e.g. a sufficiently high stabiliser content and/
or a high density (used as a proxy for low
permeability to air) and construction precau-
tions, e.g. good stabiliser control, compac-
tion and curing. Obviously, only the latter
aspects are under the contractor’s control
and therefore his responsibility. Most of these
factors are specified and/or regarded as good
engineering practice. The prevention of ‘del-
eterious’ carbonation is thus the responsibility
of both the designer and the contractor.
It is correct that carbonation is most rapid
under conditions of intermediate humidity of
about 40 – 70% and very slow under very dry
or saturated conditions, and in that sense it
does require water, as do many other chemical
reactions. However, it is driven more by the
difference between the partial pressure of
carbon dioxide in the atmosphere, pavement
air or soil air, and that in the stabilised layer
and only requires water vapour or minute
amounts of water as a carrier. During curing
the upper part of the layer is exposed to the
humidity of the atmosphere when it is allowed
to dry, as is often the case. As southern African
conditions are usually warm and at such
intermediate humidities, they are in fact often
at an optimum for carbonation. Moreover, it
has been shown that carbonation is accelerated
by wet-dry cycles, which are worse than doing
nothing (Netterberg et al 1987).
If the upper base dries to 50% of
MAASHO OMC before priming, and to
less than this before sealing, the whole base
will not necessarily remain exactly at this,
but will in time equilibrate to something of
this order – on average about 0.6 OMC in
the base as a whole and 0.75 OMC in the
sub-base (Emery 1992). Whilst published
(Netterberg &Haupt 2003) and unpublished
measurements of suction and humidity show
that the relative humidity in the base as a
whole is mostly over 99%, this varies during
the daily temperature cycle and can be much
lower in the upper base. The combination
of suitable and varying humidities and high
temperatures in the base, but probably
especially the high partial pressures of
CO2 in the underlying layers and roadbed
air – which latter can easily exceed 10 or 20
times that of the atmosphere – constitute
an environment suitable for carbonation in
the medium to long term (e.g. Netterberg
1987, 1991; Sampson et al 1987). In spite of
the apparently unfavourably high average
humidity in the pavement layers, it has been
known since at least 1984 that complete
carbonation of a lime or cement-stabilised
pavement layer from the bottom upwards
can occur (Netterberg 1987, 1991; Sampson
et al 1987; Paige-Green et al 1990).
Contrary to Dr Semmelink’s opinion
then, the conditions in a pavement are actu-
ally conducive to carbonation and, as the
above-mentioned authors have shown, it
does indeed occur and it does also weaken
the layer. However, it does not always lead
to distress or failure of the pavement, and in
this sense only is not always deleterious.
Regarding the phenolphthalein test, it is
important to note that a deep red (or purple)
only indicates a pH of more than about 10 and
that phenolphthalein starts to turn pink at a
pH of about 8.3, is pale pink by 8.5 and a dark
pink or light red by 9. A pink colour therefore
only indicates the presence of very little (prob-
ably less than about 0.2%) lime or cement, and
a deep red more than about 1%, whereas only
a pH of more than about 12.4 can be taken as
indicating the more or less complete absence
of carbonation. This is a very old test, and
Netterberg’s (1984) main contribution was to
use diluted hydrochloric to confirm that the
stabiliser had indeed been added and that it
was therefore carbonation.
A pink – and in some cases even a red
– colour therefore usually indicates either
partial carbonation or that very little stabi-
liser was present in the first place, the acid
test usually providing the answer.These tests
are of course only indicative and qualitative,
and a chemical or mineralogical analysis is
required for confirmation and quantitative
determination of the degree of carbonation.
Whilst it is correct to say that the contrac-
tor has no permanent control over the moisture
regime, it is only specified to be less than 50%
of OMC in the upper 50 mm of the layer before
sealing. Fifty percent of OMC does not equate
to a relative humidity of 50% – in fact it is likely
to be much higher than this, but is dependent
on the material, as well as other factors.
Premature drying out is of course deleterious
in the sense that it both promotes carbonation
and prevents hydration of the cement. In this
case there may be a conflict between the speci-
fication requirement to dry out and the need to
keep it moist to promote proper curing.
However, it is only correct to state that
the problem is material related insofar as the
material properties affect the equilibrium
moisture content, compactability and perme-
ability. It is also only correct to state that
some laboratory design tests (such as UCS)
do not simulate site conditions, as these are
simulated by the wet-dry test (wet-dry cycles
and, effectively, surface carbonation) and the
UCS and PI tests before and after accelerated,
complete carbonation of the whole briquette.
Dr Frank Netterberg Dr Morris de Beer
Journal of the South African Institution of Civil Engineering • Volume 55 Number 1 April 2013116
COMMENT
I was very interested to read this useful con-
tribution to the practical aspects of concret-
ing on site, specifically for bored piles. The
information given is very helpful in assessing
the influence of ingressing water into such
pile holes during concreting operations, and I
would like to commend the authors on their
contribution.
It reminds me of a case I dealt with about
30 years ago, on exactly the same problem.
Unfortunately we did not have this paper
to refer to then, because it could have saved
quite some difficulties. The case involved a
series of deep (20 m) bored piles for a very
large cement silo. I was privileged to work
with the late Dr Ross Parry-Davies on the
problem–I as a young and somewhat green
engineer and academic, he as an already
well-experienced and knowledgeable geo-
technical engineer of substantial reputation.
There had been a lot of water ingress
into some of the pile holes before and dur-
ing concreting. While the piling contractor
had taken all the necessary precautions,
there was concern that the water may have
compromised the integrity of the piles.
Consequently, cores were taken through the
full depth of some piles. The appearance
of the cores was remarkably similar to the
photographs given in the cited paper. It was
obvious that water had created lenses in the
concrete at certain points.
The client and his engineer were of
the opinion that the contractor had been
negligent in the piling operation. It was our
contention that all reasonable precautions
had been taken, but that in spite of these, the
ingressing water had caused problems in the
piles – problems that would have been very
difficult to avoid. I recall having to defend
my theory of how the ingressing water had
affected the piles before a very critical and
somewhat caustic senior engineer, which
was certainly intimidating! After consider-
able argument, the client and the engineer
eventually accepted our explanation, and it
was decided to remedy the piles by grouting
of the voids. I am happy to report that the
cement silo has operated quite successfully
for the last 30 years, and continues to do so!
Prof Mark Alexander
The eff ects of placement conditions on the quality of concrete in large-diameter bored piles
G C Fanourakis, P W Day, G R H Grieve
REFERENCES
Emery, S J 1992.The prediction of moisture content
in untreated pavement layersand an application
to design in southern Africa. NTRR, Pretoria:
CSIR, National Institute for Transport and Road
Research.
Netterberg, F 1984. Rapid field test for carbonation of
lime or cement treated materials. NITRR Research
Report RS/2/84, Pretoria: CSIR, National Institute
for Transport and Road Research.
Netterberg, F 1987. Durability of lime and cement
stabilization.NITRR ReportTS/9/87, Pretoria: CSIR,
Revision of July 1987 of TRH 13 Symp.
Netterberg, F 1991. Durability of lime and cement
stabilization. In: Concrete in Pavement Engineering.
Halfway House, South Africa: Portland Cement
Institute.
Netterberg, F, Paige-Green, P, Mehring, K & Von Solms,
C L 1987. Prevention of surface carbonation of lime and
cement stabilized pavement layers by more appropriate
curing techniques. Proceedings, Annual Transportation
Convention (ATC), Pretoria, Paper 4A/X.
Netterberg, F, Van der Vyver, I C & Marais, C P 1989.
Some problems experienced during the construc-
tion of a substandard base course for a very low
volume surfaced road. Proceedings, 5th Conference
on Asphalt Pavements for South Africa, Mbabane,
Session 1X, pp 28–31.
Netterberg, F & Haupt, F J 2003. Diurnal and seasonal
variation of soil suction in five road pavements and
associated pavement response. Proceedings, 13th
Regional Conference for Africa on Geotechnical
Engineering, Marrakech, pp 427–438, Megamix,
Marrakech.
Sampson, L R, Netterberg, F & Poolman, S F 1987. A
full-scale road experiment to evaluate the efficacy
of bituminous membranes for the prevention of
in-service carbonation of lime and cement stabilized
pavement layers. Proceedings, Annual Transportation
Convention (ATC), Paper 4A/IX.
Paige-Green, P, Netterberg, F & Sampson, L R 1990.
The carbonation of chemically stabilised road con-
struction materials: guide to its identification and
treatment. Research Report DPVT 123, Pretoria:
CSIR Division of Roads and Transport Technology.
DISCUSSION
JOURNAL OF THE SOUTH AFRICAN INSTITUTION OF CIVIL ENGINEERING
Vol 55 No 1, April 2013, Page 116, Discussion Paper 806
Publishing particulars of paper under discussionVol 54 No 2, October 2012, Pages 86–93, Paper 806
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