Integrating Traditional Characterization Techniques in Mechanistic Pavement

Design Approaches

A.A. Araya1, M. Huurman

2 and A.A.A. Molenaar

3

1Road and Railway Engineering, Delft University of Technology, P.O. Box 5048, 2600 GA,

Delft, Tel: +31 15 278 4008, Fax: +31 15 278 3443, email: a.a.araya@tudelft.nl 2Road and Railway Engineering, Delft University of Technology, P.O. Box 5048, 2600 GA,

Delft, Tel: +31 15 278 1525, Fax: +31 15 278 3443, email: m.huurman@tudelft.nl 3Road and Railway Engineering, Delft University of Technology, P.O. Box 5048, 2600 GA,

Delft, Tel: +31 15 278 4812, Fax: +31 15 278 3443, email: a.a.a.molenaar@tudelft.nl

ABSTRACT

Although widely applicable and useful, the traditional CBR test does not provide the

mechanical behaviors such as resilient and permanent deformation characteristics of

granular road materials. A relatively simple testing technique is developed to

characterize the resilient modulus of granular materials based on the traditional CBR

test using repeated load cycles. The Finite Element Method (FEM) analysis has been

attempted for the purpose of modeling the Repeated Load CBR and derives an

equivalent resilient modulus of the sample as a bulk. Strain gauges were used to

measure the lateral deformation of the CBR mould from which the confining stress

can be estimated to determine a stress dependent resilient modulus. Furthermore, a

large scale cyclic load triaxial test was carried out to validate the result of the

repeated load CBR on coarse granular materials from South Africa and Ethiopia. The

repeated load CBR test is quite useful to estimate the resilient modulus of unbound

granular materials that can be used as an input in mechanistic pavement design

analysis in the absence of triaxial testing facilities.

INTRODUCTION

An examination of the history of pavement design reveals an evolutionary process

that began with rule-of-thumb procedures and gradually evolved into empirical

design equations based on experience and road test pavement performance studies.

As Elliott and Thompson (1985), Monismith (2004), de Beer (1990) stated this

evolution and transformation has been accompanied by the development of an

understanding of material behavior, load-pavement distress relationships and

environment interactions. Through the years, much of the development has been

hampered by the complexity of the pavement structural system both in terms of its

indeterminate nature and in terms of the changing and variable conditions to which it

is subjected.

The advent of the powerful digital computers and their penetration even to

the remote places has created, these days, the possibility of the practical use of

analytical solutions to determine stresses and strains in pavements. Today, much

effort is spent on further developing of mechanistic design procedures, both

improving the existing analytical tools for determination of pavement responses and

by performing extensive long-term pavement performance studies. Many countries,

particularly developing countries, however still rely on empirical design methods,

realizing that more sophisticated mechanistic design procedures often require too

many assumptions regarding material behavior and too complicated material testing

techniques to be of direct practical use (Molenaar 2004).

In flexible pavements, especially when the surface is a thin asphalt layer or

chip seal, the role of granular layers is very important in the general performance of

the structure since the load is distributed to the subgrade mainly through these layers.

Over the last four decades, many researchers have been investigating the resilient

behavior of granular materials as the shift from the empirical to the mechanistic

design of pavement gained popularity. Many factors were determined to have an

effect on the resilient modulus of granular materials. The state of stress was found to

have the most influence on the resilient behavior. Hicks (1970); Smith and Nair

(1973); Sweere (1990) and Huurman (1997) have shown that the resilient modulus

increases with an increase in confining pressure. On the other hand, Brown (1974)

reported a significant effect of the deviator stress, especially at high stress levels.

Many other factors such as density, moisture content, stress history, number of load

cycles, particle shape and mineralogy, and load characteristics (frequency, and load

sequence) have been found to impact the resilient behavior of granular materials. A

detailed discussion of these parameters can be found in LeKarp et al. (2000).

Most of these investigations have been carried out using facilities such as the

Repeated Load Triaxial (RLT) test and Hollow Cylinder Apparatus (HCA) etc.

However such specialist tests are considered too complex and unaffordable to

implement in routine road construction projects particularly in developing countries.

Even in the industrialized countries such tests are implemented mainly for research

purpose but hardly used in day to day engineering practice. The existence of the gap

between research and industry based practice reveals the absence of appropriate

characterization techniques. These characterization techniques developed for

research purposes have economical and practical limitations that prevent their

widespread use. Edward (2007) reports these barriers include level of complexity,

skills or trainings required prior to use, availability and affordability. On the other

hand despite their worldwide acceptance and existence for long time index testing

such as California Bearing Ratio (CBR), being too empirical, have technical

limitations to be used in the Mechanistic design methods.

A new characterization technique, a repeated load CBR (RL-CBR) test, is

developed in this research to characterize mechanical properties such as resilient

modulus of unbound granular road materials. This intermediate testing mechanism,

which is based on the traditional CBR testing equipment, can bring mechanistic

design method into practice. The advantage of integrating the traditional CBR

characterization technique in to mechanistic pavement deign approach through the

development of the repeated load CBR testing is that the RL-CBR can be carried out

in most standard non-sophisticated road engineering laboratories. This paper presents

the characterization techniques of the RL-CBR and the results for the South African

ferricrete granular subbase material compared to the well accepted triaxial test

results.

THE REPEATED LOAD CBR

The principle of the RL-CBR test is similar to the standard CBR test but repeated

loads are applied. Upon multiple repetitions of the same magnitude of loading

granular materials comes to a state in which almost all strain under a load application

is recoverable. The permanent (plastic) strain ceases out to exist or becomes

negligible and the material behaves basically elastic i.e. with stable recoverable

deformation (Araya et al. 2010). From the applied stress and the measured strain an

elastic modulus can be estimated. By recording the load and displacement and plot in

x-y axes, similar to Figure 1 are obtained from which load levels and total, resilient

(elastic) and permanent (plastic) deformations under the penetration plunger can be

determined.

Deformation

Lo

ad

Standard CBR Repeated Load CBR

Time

Defo

rmatio

n .

1.27 mm/min

Cummulative

permanent deformation

permanent deformation

resilient deformation

Figure 1. Repeated load CBR test principle and load-deformation pattern

Test setup. The intention of the repeated load CBR tests setup is to estimate the

resilient modulus from a standard CBR testing facility by repeating the loading and

unloading cycle. The tests in this research were performed using large mould having

a diameter of 250 mm and a height 200 mm to accommodate the full 0/45 gradation.

Proportionally a bigger penetration plunger of 81.5 mm diameter is used instead of

the standard CBR 49.64 mm diameter plunger.

To simulate the repeated load application in the standard CBR the test is

performed in the displacement controlled mode at a constant displacement rate of

1.27 mm/min (0.05 inch/min) = 0.021 mm/sec for both loading and unloading. The

specimen is first loaded at the rate of 1.27 mm/min to a predetermined deformation

(for e.g. 2.54 mm) or a target load level. The load is recorded and unloaded with the

same rate (1.27 mm/min) to a minimum contact load of 0.5 to 1 KN (0.1 to 0.2 MPa)

to keep the plunger in contact with the specimen. The loading and unloading cycles

are generally repeated for about 50 – 100 load cycles at which the permanent

deformation due to the last 5 loading cycles will be less than 2% of the total

permanent deformation at that point.

The RL-CBR test is carried out with strain gauges. Strain gauges were used

to measure the lateral deformation of the CBR mould to get the feeling of the

confining stress developed by the steel mould. Four strain gauges capable of

measuring in micro-strains are glued at the external surface of the mould which

measures the mould lateral deformation during the loading and unloading cycles. The

four strain gauges are positioned in such a way that the variation in lateral

deformation (if any) along the height and circumference of the mould can be

observed. Two of the strain gauges are position at the mid-height of the mould in

opposite diametric side of the mould and the other two near to the top edge of the

mould (40 mm below the top edge). The schematic diagram of the RL-CBR mould

and the strain gauges are shown in Figure 2.

load cell

plunger

collar

mould

magnetic

stand

LVDT

75 mm

200 mm

81.5 mm

250 mm

specimen

surcharge

load

strain

gauge

mid-height

strain gauge

near top

strain gauge

14.5 mm

Figure 2. Repeated load CBR test with strain gauges schematic diagram

Material. The material tested was a South African subbase granular material

ferricrete (FC). The ferricrete are natural gravel obtained from a borrow pit in South

Africa. It is natural coarse aggregate relatively week to crushing where its particles

are characterized with porous spherical shape and rough surface texture with grading

0/45, Table 1 shows the wet sieve gradation of the material. The iron-rich (sub)

tropical ferricrete is characterized as a mineral conglomerate consisting of surficial

sand and gravel cemented into a hard mass by iron oxide derived from the oxidation

of percolating solutions of iron salts. The RL-CBR test is carried out at varying

moisture content (MC) and degree of compaction (DOC). The molding moisture

varies as dry (5%), moderate (7.5%), wet (9.5%) and the DOC varies from 95% -

100% of the maximum modified Proctor dry density (MPDD).

Table 1 Gradation of the ferricrete Sieve size 45 31.5 22.4 16 8 4 2 0.5 0.18 0.063

% passing 100 99.1 88.8 75.2 50.0 33.3 27.3 23.0 16.9 10.7

Finite Element Method. A Finite Element (FE) analysis has been attempted to

model the RL-CBR test using ABAQUS. As the loading and boundary conditions of

the test are symmetric with respect to the central axis an axisymmetric approach is

adopted in the modeling. A linear elastic material property is assumed for the steel

mould and the granular material with 210 GPa elastic modulus, E, and 0.2 Poisson’s

ratio, for the steel mould and varying E and for the granular material as shown in

Table 2. The plunger is assumed as a rigid body and a contact surface property was

defined between the plunger and the granular as hard contact; and the mould and the

granular with exponential pressure-overclosure relationship defined in ABAQUS.

Table 2 Granular material properties used in the FE analysis

Poisson’s ratio [-] 0.15, 0.25, 0.35, 0.45

Elastic modulus E [MPa] 100, 200, 300, 400, 500, 600, 800, 1000

For a given material property of the granular material a strain controlled is used to

simulate the test i.e. a vertical displacement is applied on the rigid plunger. Stresses,

strains and deformations through out the granular material and steel mould; and total

load on the plunger has been recorded for each granular material property

combination and applied vertical plunger displacement. This data set can be recorded

for each node or element of the mesh shown in Figure 3.

By using non linear multidimensional least square regression fitting on the FE

analysis data transfer functions have been developed that relate material properties

and the bulk stresses components of the specimen with the laboratory measurable test

parameters i.e. the plunger load, plunger deformation and the lateral or tangential

mould exterior strain at mid height. The vertical and radial stresses of the bulk

sample are approximated by weighted average of vertical and radial stresses along

the central axis (the axisymmetry) using the vertical deformation in each element

along the depth of the sample as weighing factor, equation1. This is based on the

assumption that the granular material under the plunger is carrying the load most,

thus the stress and strains along the central axis are considered as representative of

the bulk. An illustrative stress and strain distribution along the depth of the specimen

at the axis of symmetry is shown in Figure 4.

, ,

,

v i v i

V

v i

u

u

, ,

,

h i v i

h

v i

u

u

(1)

Where V = vertical stress of the sample as a bulk [kPa]

h = horizontal or radial stress of the sample as a bulk [kPa]

,v i = vertical stress of each element along the axisymmetry [kPa]

,h i = horizontal stress of each element along the axisymmetry [kPa]

,v iu = vertical deformation of each element along the axisymmetry [mm]

granular

mould

plunger axis of symmetry

LVDT

strain gauge

125 mm

22 mm 20 mm

200 mm

25 mm

14.5 mm

40.75 mm

Figure 3. RL-CBR Finite Element model mesh (left) and its test setup (right)

0

20

40

60

80

100

120

140

160

180

200

-0.03 -0.02 -0.01 0.00

Vertertical strain [mm/mm]

Depth

[m

m]

E=200 v=0.45E=400 v=0.45E=600 v=0.45E=200 v=0.35E=400 v=0.35E=600 v=0.35E=200 v=0.25E=400 v=0.25E=600 v=0.25

0

20

40

60

80

100

120

140

160

180

200

-20 -15 -10 -5 0

Radial stress [MPa]

Depth

[m

m]

E=200 v=0.45E=400 v=0.45E=600 v=0.45E=200 v=0.35E=400 v=0.35E=600 v=0.35E=200 v=0.25E=400 v=0.25E=600 v=0.25

Figure 4. Illustrative stress and strain distribution along the axisymmetry for a

2.5 mm plunger deformation

Based on linear elastic theory for axisymmetric condition the following transfer

functions were developed from the regression for the vertical and radial bulk stresses,

the Poisson’s ratio and elastic modulus. Note that in equation 2 below common soil

mechanics sign convention is adopted with compressions as positive and tensile

negative.

41 3

5

2

exp

2

V p h tt

V htt

p v

kk k

kk E

u

(2)

Where p = vertical plunger stress = total plunger load/ plunger area [kPa]

= Poisson’s ratio [-]

E = Elastic or stiffness modulus [MPa]

tt = tangential strain at mid height of mould exterior [micro-strain]

vu = vertical plunger deformation [mm]

k1 to k5 = model parameters where: k1 = 0.368 [-] k2 = -120.927 [kPa]

k3 = 43.898 [kPa] k4 = -0.072 [-] k5 = 0.144 [mm]

The regressions for the above four relations in equation 2 show a good fit with

determination of correlation r2 > 0.99 see Figure 5; this fit is of course an indication

of relations of the parameters presented in the Finite Element model through the

stiffness matrix (force and displacement relation), the kinematic compatibility (strain

and displacement relation) etc under the given boundary conditions.

0

10

20

30

40

0 10 20 30 40

FE data v [MPa]

Pre

dic

tion m

odel

v [M

Pa]

R2 = 0.999

line of equality

0

250

500

750

1000

0 250 500 750 1000

FE data E [MPa]

Pre

dic

tion m

odel E

[M

Pa] .

R2 = 0.997

line of equality

Figure 5. Model prediction fit for illustrative transfer functions v and E

RL-CBR Equivalent modulus. The equivalent stiffness modulus, Eequ, of the

sample as a bulk is estimated, the same as the elastic modulus of the finite element

analysis, as a function of the vertical (axial) stress, horizontal (radial) stress, the

Poisson’s ratio and exterior strain at mould mid-height as shown in equation 2. The

advantage of such a model is that it is based from basic theory of elasticity Hooke’s

law where the model parameters are related to boundary conditions. Moreover it is

express as stress dependent modulus similar to resilient modulus of cyclic load

triaxial test models such as the Mr- models, thus can be compared and validated

with such model of triaxial results. For such purpose a cyclic load triaxial testing has

been carried out for the same material.

CYCLIC LOAD TRIAXIAL TEST

A large scale triaxial setup with a diameter of 300 mm and a height of 600 mm

specimen was used in the study for testing the full 0/45 mm coarse material. The

triaxial apparatus is equipped with a hydraulic loading system actuator and MTS

controller capable of cycling the axial stress and with a partial vacuum constant

confining pressure (CCP). The test is carried out according to the European Standard,

EN13286-7 (CEN 2004) test protocol. The cyclic load signals used are a haversine at

a loading frequency of 10 Hz for the first 20,000 load cycles of conditioning phase

and 1 Hz for the series of short loadings 100 cycles each. The stress range used is a

ratio of axial stress to their respective failure axial stress, 1/1,f = 0.05 to 0.6, where

the monotonic shear failure triaxial tests are carried out prior to the cyclic load

triaxial tests.

The objective of the cyclic conditioning is to stabilize the permanent strains

of the material and attain a practically elastic behavior. Generally the conditioning is

performed with a stress level corresponding to the maximum cyclic and confining

stresses applied in the test. The triaxial cell is equipped with transducers measuring

the axial and radial strains on the middle third, 200 mm, of the specimen as shown in

Figure 6. The resilient modulus (Mr) is defined as the ratio of the cyclic deviatoric

stress (d) to the recovered strain (r):

dr

r

M

(3)

Time

Load

1 Sec.

Cyclic

Load

Maximum

Load

Contact Load (3-5 kPa)

Haversine Shape

Figure 6. Haversine triaxial cyclic loading curve (left) and instrumented triaxial

specimen ready for testing (right)

Similar to the RL-CBR test cyclic load triaxial testing were carried out for the

ferricrete subbase material with varying the moisture content (MC) and degree of

compaction (DOC as % MPDD) conditions. However for comparison with the RL-

CBR test with strain gauges the cyclic load triaxial test result of the ferricrete

material compacted with moderate (7%) MC at 98% DOC will be presented.

RESULT AND DISCUSSION

Cyclic triaxial test result. The stress dependency of the resilient modulus was

analyzed using the simple and well known isotropic non-linear Mr – model for

comparison with the result of the RL-CBR tests with strain gauge. For the ferricrete

compacted at moderate MC and 98% DOC the Mr- in log-log scale is presented in

Figure 7.

2

1

k

rM k (4)

Where Mr = resilient modulus [MPa]

= bulk stresses = 1+2+3 [kPa]

k1 & k2 = model parameters

100

1000

100 1000 [kPa]

Mr [M

Pa]

20

35

50

65

80

3

[kPa]

Mr- model

k1 = 12.301

k2 = 0.569

r2 = 0.926

Figure 7. Resilient modulus variation with bulk, , and confining stress, 3

RL-CBR test result. To obtain stress dependent behavior from the RL-CBR test

with strain gauges, large numbers of tests have been carried out at various plunger

load levels. For the ferricrete with similar compaction conditions eight tests at

different load level is conducted. From the RL-CBR laboratory test setup described

earlier three parameters were measured the average plunger stress, p, the plunger

deformation, uv, and the exterior strain at mould mid-height, tt. The equivalent

modulus (Eequ) is then computed using the transfer functions in equation 2,

developed from the finite element analysis, with deviator values of p, uv and tt

between the maximum of loading and minimum of unloading of the last 5 cycles of

the 100 cycles. The equivalent modulus is plotted verses the bulk stress i.e. v +

2h where v and h are in absolute values of a stress state of a specimen under

testing. Although mould strain measurements have been recorded at mid-height and

near the top of the mould at different locations as shown in Figure 2, the average of

the two mid-height strain gauges is considered for the computation of the transfer

function. The hoop strain at the mid-height gauges is higher than the gauges near the

top of the mould which is in agreement with the result obtained from the FE analysis

too. On the other hand, small variation strain measurement is observed among the

gauges at the same height but in different vertical direction. However an average of

the strain measurement is considered to compute the stress state for the entire bulk

sample.

In Figure 8A the Eequ- model is presented along with the Mr-model of the

triaxial test result from Figure 7. It can be recognized that the equivalent modulus

from the RL-CBR test with strain gauge provides the stress dependent resilient

behavior of the material. The stress state of a RL-CBR test specimen is uncontrolled

and generally at a very high stress level due to the high confinement from the steel

mould which results higher equivalent modulus compared to the resilient modulus of

the triaxial. In addition the Eequ- model shows less stress dependent, or a gentle

slope, than the Mr-. However, when granular materials loaded at much higher stress

levels close to failure, the resilient modulus tends to decrease its stress dependency.

Figure 8B shows the equivalent modulus of the RL-CBR test appears as a

continuation of the resilient modulus of the triaxial data with more scatter and at high

stress level. This indicates that the RL-CBR test is a more complex form of a triaxial

test that can provide a good estimate of the stiffness modulus.

100

1000

10000

100 1000 10000

Θ [kPa]

Mr

& E

equ [

MP

a]

Eequ

Eequ-Θ

Mr-Θ

A

100

1000

10000

100 1000 10000

Θ [kPa]

Mr

& E

equ [

MP

a]

Mr

Eequ

B Figure 8. Cyclic triaxial test resilient modulus, Mr, and RL-CBR test with strain

gauges equivalent modulus, Eequ, as a function of bulk stress, .

CONCLUSIONS

In this paper, an intermediate (between the fundamental cyclic triaxial test and the

traditional standard CBR test) method of characterization of unbound granular

materials, the RL-CBR test, was discussed. It was shown that a good estimate of

stress dependent modulus of the ferricrete granular subbase can be obtained with this

characterization technique. The method can thus be used to characterize and estimate

the resilient modulus of unbound granular materials, which can be used as an input in

mechanistic design procedures, in the absence of fundamental test results.

It should be clear that non-linear finite element models may be developed, as

unbound granular materials have a non-linearity behavior. However the intension of

the study is to investigate an alternative simple way of characterization technique

that can be implemented in common road engineering laboratories than assessing and

modeling advanced material behaviors. Indications are that such advanced models

will strongly contribute to the understanding of the stress-strain development in the

complex CBR specimen and may provide a more fundamental material behavior.

It is to be noted that in the RL-CBR the granular arrangement or grain pattern

in specimen preparation of the coarse particles, the big ratio between the bigger

particle size and plunger diameter have a significant effect on the test result.

Moreover the very slow rate of load application in the RL-CBR testing, comparing to

wheel loading and the cyclic triaxial load, will have an effect on the relationship with

the triaxial modulus and the field practice.

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