articulo modelo estadistico v1

8/10/2019 Articulo Modelo Estadistico V1

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Statistical model to predict the maximum

lateral pressure exerted by Self-Compacting

Concrete on vertical formworks.

ABSTRACT:

In construction practice, an accurate model to predict the lateral pressure exerted by SCC is needed in

order to design vertical formwork. In this work, an empirical model to predict lateral pressure for SCC

was developed. A total of 128 experimental data compiled from the literature were used in the

formulation of the model.

The model considered seven of the variables that affect fresh concrete lateral pressure: placement rate,

slump flow, the height of the concrete piece, concrete temperature, minimum form dimension and cross

section size. Due to the formulation of the model, the prediction obtained is always lower than the

hydrostatic distribution.

The model is developed for all experimental data. However, the principal objective of the model is to

obtain an accurate prediction of the maximum lateral pressure exerted by SCC on vertical formwork for

high placement rates (over 6 m/hr), which is a common practice today.

The results show that, the model presents a very good approximation to the experimental data, being

better for high placement rates.

KEYWORDS:Lateral pressure; Self-compacting concrete; Formwork design; Experimental model

HIGHLIGHTS:

An empirical model to predict the lateral pressure exerted by SCC on vertical formworks has beendeveloped.

Predictions are always under hydrostatic distribution

Principal objective: predicting lateral pressure for high placement rates.

The model developed does not require the determination of a rheological parameter.

The model presents very good approximation to the experimental data.

1

INTRODUCTION

The use of SCChas grown in recent years due to the interest in reducing or eliminating vibration duringplacement, and also to facilitate the casting of densely reinforced sections and areas of restricted access.

Despite the fact that the SCChas been well established in the precast concrete industry, current effort is

directed towards casting on site.

The rheological behavior of SCC, the structural changes governing thixotropy and structural breakdown

are determining parameters on the quality of SCC [1]. According to Barnes et al. [2], the definition of

thixotropy is . A gradual decrease of the viscosity undershear stress followed by a gradual recovery of

structure when the stress is removed .


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Thixotropy has the largest influence on the casting process, but one of its main applications is to

determine the envelope of formwork pressure. Roussel [3] presented a method to model and measure

the thixotropy of fresh concrete. The author also concluded that the variation in formwork pressure

between a non-thixotropic SCC, a thixotropic SCCand a highly thixotropic SCCis very high; the maximum

lateral pressure is higher for a lower thixotropy. The magnitude of the maximum lateral pressure is

needed for designing formworks, since its overestimation would increase construction costs. According

to Hanna and Senouci [4] this increase can amount to as much as 60% of concrete structure cost, a fact

reaffirmed by Hurd [5].

Assaad et al. [6] show that the lateral pressure exerted by the SCCis directly related to thixotropy. Since

the thixotropy is not an easy parameter to measure, it is characterized indirectly by several parameters

that require a rheological study. Researchers perform tests developed by themselves or use laboratory

devices to measure these parameters, but this makes it difficult to measure in real practice.

Furthermore, it is noteworthy that in neither case the methods proposed by the authors are normalized.

The methods proposed by Roussel [3] and Billberg [7] are examples in this regard.

Despite the high influence of thixotropy in the development of lateral pressure on formwork, there are

several factors that also affect the value of maximum lateral pressure. The literature classifies thosefactors into three categories: formwork characteristics, concrete characteristics and placing method.

Several researchers have studied these variables [8][11]. Each category contains a large number offactors, which explains the complexity of the problem. Therefore, experimental models are frequently

used for predicting fresh concrete lateral pressure.

Nowadays, there is no universally accepted model for predicting fresh concrete lateral pressure for SCC.

Therefore, this work compiles the experimental data published over the last ten years, with the

objective of determining a statistical model to predict the maximum lateral pressure exerted by SCCon

vertical formworks, which can be used in situ and does not require the use of a rheometer or a

laboratory test to determine a rheological parameter.

2

EXPERIMENTAL MODELS

While there are many authors who study the maximum lateral pressure exerted on vertical formwork,

this work considers the models developed solely for SCC. Firstly, the most conservative case, the

hydrostatic distribution, was considered. Lastly, models developed to predict lateral pressure exerted by

SCCon vertical formworks were described.

2.1

HYDROSTATIC DISTRIBUTION

The hydrostatic model is the most conservative as it considers SCCa fluid, establishing that the lateral

pressure on the formwork follows a hydrostatic distribution, with concrete density.

2.2

VANHOVE ET AL (2004)

Vanhove et al. [12], based on analogy of Janssens theory [13], determined the lateral pressure of

concrete on formwork. The authors considered concrete as a continuous material and assumed that the

horizontal pressure is proportional to the vertical one, where the proportionality factor (K) is constant

along the entire height and depends on the materials internal friction angle (). The model also


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considers that Coulombs law with a constant friction coefficient () governs the friction betweenconcrete and formwork. As a result, they proposed Eq.1to determine fresh concrete lateral pressure.

Eq. 1 (

)Where:

Pmaxis the maximum lateral pressure.

is the density of the material.

gis acceleration of gravity.

Ais the area of formwork pressure.

0 is the yield shear stress. An equation given by the authors [12] has to be used to determine this

parameter.

eis the formwork thickness.

Lis the formwork width.

Kis a reduction factor of the hydrostatic pressure.

His the formwork height.

is a coefficient that considers the physical phenomenon of the problem and that controls theimperfections.

is the friction coefficient, whose value is determined by a tribometer. It considers the movement

between concrete and formwork, thus being able to determine the static and dynamic friction

coeficient.

The study considers concrete as a two-phase medium (intersticial paste + aggregates).The principle

adopted by the tribometer involves sliding a metal plate between two samples of concrete, and moved

at a given velocity.

The concrete is placed in two 120 mm diameter sample holders with a gasket system to prevent any

water leakage. A mobile bottom is placed at the back of the sample to transmit the pressure deliveredby the pneumatic jack to the material. To reduce the gravity force, the plate was moved horizontally.

The schematic representation of a sample holder against a plate can be seen inFigure 1.a.

The friction coefficient can be obtained from the ratio between friction force (F) and normal force (N)

delivered by the pneumatic jack. The resultant friction force (2F) is easily measurable since the

interchangeable plate was being moved at a given velocity (V), while the normal force (N) is calculated

according to the pressure exerted by the pneumatic jack. The resultant friction force is 2F as it was

considered that the two samples have similar friction. The measurement principle can be shown in

Figure 1.b

The authors conclude that the dynamic coefficient should be used in cases that concrete is pumped

from the bottom of the formwork, and the static coefficient when the concrete is poured from the top;

since the friction force is relatively weaker.

As can be seen above and is shown by the authors, the test, despite its great precision, has a certain

complexity that makes it almost impossible to use on real construction.


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2.3

OVARLEZ AND ROUSSEL (2005)

Ovarlez and Roussel [14] proposed a theoretical model that characterizes the SCCby its yield stress (0)as a function of resting time. As a simplification, they consider Trescas plasticity criterion, meaning that

0is the maximum sustainable shear stress for an internal plane. Furthermore, the authors assume that

for stresses with values below 0, SCC behaves as an elastic material, and the friction against theformwork walls could take a value between 0 and 0. The lateral pressure may be determined from Eq.2for rectangular formwork and from Eq.3for circular one.

Eq. 2 Eq. 3 Where:

PHis the lateral pressure during casting at a depth H.

is the density of the material.

gis the acceleration of gravity.

His the formwork height.

eis the formwork width.

ris the formwork radius.

Ris the casting rate (m/hr).

Kis the ratio of lateral to vertical pressure.

Athixis a flocculation coefficient, which is determined experimentally according to the yield stress taken

by the rheometer at different times.

The authors assume a linearly increasing yield stress over time, as is shown in Eq.4

Eq.4

Where:

0is the yield stress.

The authors performed experimental tests of the evolution of yield stress with a device called BTRHEOM

[16-17], which allows the quantitative determination of the yield stress. The main feature of this

rheometer is that it allows a quantitative determination of the yield stress and viscosity of concrete

mixtures. Unlike rheometers with concentric cylinders, this instrument is a parallel plate rheometer. The

concrete sample is placed between a fixed and a rotating plate, which has a known angular velocity of W.

The yield stress in this type of rheometer is imposed by geometry. The shear stress can be calculated

through the relation between the moment and the angular velocity. Figure 1.c. shows the shear

distribution in BTRHEOM and its schematic representation.

The major difference between this instrument and the tribometer (used by Vanhove et al. [12]) is its

parallel plate geometry, since the tribometer has a jack rod rotating in a cylindrical container. The

parallel plate geometry allows a mathematical description of the velocity field, which permits analytical

calculation of yield stress and plastic viscocity in terms of rheometer measurements.


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2.4

KHAYAT AND OMRAN (2009)

Khayat and Omran [16] determined the maximum value of the lateral pressure using a statistical model,

based on experimental data obtained from a PVC column of 200 mm diameter and 0.7 m high. In the

tests, the column was filled with 0.5 m of concrete, and by injecting pressurized air, the authors

simulated different heights up to 13 m.The authors expressed Pmaxas a function of: concrete height, casting rate, concrete temperature and the

structural build up. The latter is expressed in terms of static yield stress after 15 minutes of rest. The

authors described two possible empirical methods to determine the yield stress values of SCCat rest:

the portable vane method [17] and the inclined plane method [18]. The procedures for performing

these tests are described in [17] and [18], respectively. If the first method employed,Pmaxis determined

by Eq.5The model also considers the influence of the maximum size aggregate (MSA) and the effect of

waiting time (WT) between successive lifts.

Eq. 5 * +

Where:Pmaxis the maximum lateral pressure against the formwork (kPa)

is the specific weight of concrete (kN/m3) .

His concrete height (m).

Ris casting rate (m/hr) .

Tis concrete temperature (C).

Dminis the minimum formwork dimension (mm).

fMSAis a correction factor for MSAother than 14 mm.

fWTis a correction factor that reflects the effect of the waiting time between successive lifts.

PV0rest15minsis the static yield stress measured by the portable vane after 15 min of rest (Pa).

The portable vane test consists on four-bladed stainless steel vanes of different sizes arranged in a crossshape around a shaft (as is shown inFigure 1.e.), to shear the material at different rest times.

The SCC is placed in four containers up to a given height (h), where the four vanes are introduced

vertically in the center of each one. The containers are covered to prevent drying. The plastic cover has a

central hole of 2 mm, a greater diameter than the vanes shaft diameter, to help maintain the vane in acentral and vertical position.

The testing procedure consists on imposing a rotational speed to the vane immersed in the fresh sample

of concrete subjected to a certain rest period and the increase in resulting torque will be saved as a

function of time. The accuracy of the torque measurement can improve when the container is placed

on a flat surface, when the vane is set in a vertical position, and when the torque meter is turned at a

constant speed of 10 to 15 seconds per quarter turn. The shear growth test involves the determination

of the maximum yielding torque before torque decayed toward a steady-state region. Thus, themaximum torque for breaking down the interstructural bonds and overcoming the yield stress of the

material is determined. This torque is employed to obtain the static shear stress (0rest) of concrete as

shown by the authors [17]

The authors also developed another way to measure the static yield stress after 15 min of rest: the

inclined plane. This test, like the PV, is not standardized in the case of concrete mixtures. The

consolidation of the concrete determines that with increasing rest time; the mixture develops greater


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shear strength due to internal friction between particles. Therefore, the longer the rest time, the greater

is the value of 0.

The test consists on placing the concrete on PVC specimens of 60 mm diameter and 120 mm high. After

leaving the mixture at rest for fifteen minutes, the specimen is removed slowly to allow the mixture to

flow evenly. The average settled height (h)of the mixture is then determined. The plane is afterwards

slowly raised until the mixture begins to flow. At that time, the angle of the plane when the flow starts

(c) is measured. Once this is obtained, the value of 0 is calculated as established by the authors

[18] .The schematic of inclined plane test can be observed inFigure 1.d.

2.5 ANALYSIS OF PREVIOUS MODELS

According to Billberg et al. [19] models that require the determination of a rheological parameter

(Vanhove et al. [12], Ovarlez and Roussel [14], and Khayat and Omran [16]) accurately predict maximum

lateral pressure. However, the use of a laboratory device for its determination makes their application

more difficult in real construction.

Despite the good results obtained by the use of the btrheom, the tribometer, the PVor the PI; their use

in a real construction would be highly complex.

In the first two cases, the devices are very delicate, expensive and they require qualified laboratories

with the softaware needed for their use. The software allows to analyze the compiled data and set the

parameters that could vary in each case. In the case of the tribometer, a set of mechanisms that depend

on the properties of the interface has to be determinated: roughness of the plate, the sliding velocity

against the plate, the pressure or normal stress, the nature of the demoulding agent on the

concrete/wall, among others. Additionally, the tractive strengths compiled by the sensor must be

processed to calculate the friction coefficient.

On the other hand, to use the rheometer a mathematical description of the velocity field is necessary for

the analytical calculation of yield stress and plastic viscosity.

For the devices developed by Khayat and Omran: the portable vane [17] and the inclined plane [18], it is

necessary both the construction of the devices, as well as a skilled person to carry out the different

assays in a special place in construction site.

As a result of the preceding arguments, it would be practically impossible to apply one of these models

in situ, considering also that none of these tests are standardized.

The project developed by Billberg et al. [19] in Stockholm, Sweden in May 2012 gathered experts who

represented the models to carry out such field evaluation. The objective of this work is to validate these

models with experimental results. For the validation, eight instrumented walls with various geometries

were casted with SCCusing different mix designs as well as various casting rates. Pressure transducers at

panel surfaces were used to determine lateral pressure. All necessary parameters for the respective

models were characterized simultaneously from samples taken from the same batch. Each expert

performed the appropriate test for the model that each one represented. This shows the impracticality

to carry out the tests for determining the rheological parameter. While the castings resulted in a wide

range of formwork lateral pressures, and the evaluation of the ten evaluated models indicates that all of


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them predict the lateral form pressure satisfactorily, the work represented the difficulty of determining

the rheological parameter in real construction.

Although in the literature there are some authors who determine the rheological parameter in their

works, this does not occur in all cases. Leeman and Hoffman [20], Tejeda-Dominguez et al. [21], Leeman

et al. [22], and Giammatteo et al. [23] are examples of authors who do not determine the rheological

parameter to determine the maximum lateral pressure. Therefore, it is easy to conclude that if some

researchers cannot determine this parameter in their works, it would be less likely that this could be

determined in situ.

Wallevik [24] affirms this by stating that if rheometers are hard to find in the laboratory, it would be

more difficult to find one in situ. This is why a statistical model, which does not requires the use of a

rheometer and can be used in situ for determining the maximum lateral pressure is proposed, based on

the model proposed by Santilli and Puente [25] for vibrated concrete.


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|

||

|

Specimen

Bottom plane

Inclined plane

Z

X

Y

r

a) b)

e)c)

d)

Fixed plate

Rotating plate, which

has a known angular

velocity of W

Shaft

Cross shape

Four-bladed vanes of

different sizes

Sample holder

Mobile bottom

Fresh

concrete

Pressure delivered by

the pneumatic jack

Plate moved at a given velocityV

N

Direction of displacement

Plate

N

N, normal force

V, velocity of displacement

2F ,friction force

Material sample

Figure 1 Laboratory devices for the determination of rheological parameters.

3 STATISTICAL MODEL FORMULATION.

Santilli and Puente [25] developed a statistical model based on experimental data from vibratedconcrete, some of which were carried out by the author and others collected from the literature.

The authors proposed a bilinear distribution of lateral pressure exerted by the SCC against the

formwork, with hydrostatic distribution to the maximum pressure and constant until the bottom of the

formwork. The maximum value of lateral pressure is determined using Eq.6and it may never be higher

than the hydrostatic distribution of a liquid with concrete density.


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Eq. 6 Where:

Pmaxis the maximum lateral pressure against the walls of the formwork.

is the specific weight of concrete.

His the height of the piece to be formed.

The authors determined a value of Kthat would always be equal or less than one, thereby ensuring that

the model prediction is never greater than the hydrostatic distribution.

The model was developed considering each of the variables separately and progressively, as expressed

in Eq.7

Eq. 7 Where:

K is the coefficient to be applied in Eq.6.

KRis a coefficient of correction by the casting rate.

Kis a coefficient of correction by the slump cone.

KHis a coefficient of correction by the height of the concrete piece.KTis a coefficient of correction by the concrete temperature.

Kdis a coefficient of correction by the minimum dimension of the cross section.

KC is a coefficient of correction by the cement type.

KSTis a coefficient of correction by the cross section type (columns or large volumes of concrete).

The coefficients Ki are determined in an arbitrary manner. The determination of each of the Ki

coefficients are carried out from the prediction confidence intervals of a new observation, considering

simple linear regressions. Montgomery et al. [36] define a simple linear regression as a model in which a

single regressor x has a linear relationship with a response y. Based on Montgomery et al. [36] the

estimation of the linear regression (y00), for a new observation x0is detailed in Eq.8.

Eq. 8 Montgomery et al. [36] states that a future observation (y0) is independent of y00. Therefore, the authors

state that if y00is used to estimate y0, the standard error (y0- y00) is an appropriate statistic to measure

the prediction interval. Therefore, the upper bound of the prediction confidence interval (1 - i)100 for afuture observation x0is calculated as expressed by Eq.9.

Eq. 9

Where Ki is the factor K associated to the variable i, y00 is the estimation of the linear regression for a

new observation, t/2,n-2 is the tStudentdistribution for a level /2 and with n-2 degree of freedom. MSRESisthe estimation of the variance of the errors from the sample data, n is the sample size, x0 is the

regressor of the new observationxand are defined in Eqs.10and11respectively.

Eq. 10


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Eq. 11

Eq.9 determines all the Ki coefficients, with exception of KC and KST. Table 1 summarizes the results

obtained by Santilli and Puente [25] for the statistical parameters needed to determine those

coefficients. In all cases, the coefficients have to be less than or equal to one and higher than theminimum value, which are also shown inTable 1. Table 2 andTable3 show the values for KCand KST,

respectively. The correspondent groups are described by the authors [25].

Ki Regressor X0 (unit) 00 11 t/2,n-2 MSRES n x Sxx Minimum value

Kr 1-(1/(R+1), R(m/h) 0.12 0.56 0.96 0.028 226 0.75 6.02 0.64

K (mm) 0.43 0.002 1.96 0.026 213 107.45 584.88 0.81

Kh H(m) 0.865 -0.047 1.65 0.032 226 4.28 478.64 0.77

Kt T(C) 0.835 -0.007 1.65 0.034 214 17.95 7923.75 0.92

Kd d(mm) 0.641 0.002 1.46 0.034 190 32.3 28.499 0.94Table 1 Statistical parameters for the determination of coefficients Ki

Group Coefficient KC

Group A 0.9

Group B 0.95

Group C 1

Table 2 Coefficient KC

Group Coefficient KST

Column 1.00

Wall 0.95

Table 3 Coefficient KST

Thus, an experimental database of lateral pressures exerted by SCCon vertical formwork was compiled

in this paper. Based on the procedure described above and on the methodology proposed by Santilli and

Puente [25], a new model to predict the maximum lateral pressure exerted by SCC on vertical

formworks was developed.

4

EXPERIMENTAL BASE CONSIDERED TO PERFORM THE MODELThe experimental data that considers the SCCbeing poured from the top of the formwork were those

supplied by CEBTP [26], Proske and Graubner [27], Leeman and Hoffman [20], Khayat et al. [28] Assaad

et al. [6], Khayat and Assaad [30, 31], Khayat [31], Billberg et al. [32], Tejeda-Dominguez et al. [21],

Assaad and Khayat [33][37], Leeman et al. [22], Giammatteo et al. [23] Kwon et al.[38], Beitzel [39], Mc.Carthy et al [40], Gardner et al. [41] and Billberg et al. [19]


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CEBTP [26] (from Khayat et al. [28]) studied formwork pressure exerted by SCCon experimental columns

12.0 m high, 2.0 m long, and 0.34 m wide. The concrete had a slump flow consistency of 700 mm and a

water to cement ratio (w/c) equal to 0.46.

Proske and Graubner [27] studied the pressure of fresh SCCin eleven experimental square columns 4.0

m high and 30 cm wide. Ten of them had steel reinforcement. The authors divided the tests into three

series where the parameters to be varied were casting rate, slump flow and reinforcement.

Leeman and Hoffman [20] studied the vertical distribution of the lateral pressure caused by three SCCs

with different workability, when filling a form 2.7 m high, 0.75 m wide and 0.2 m thick, with a casting

rate of 8 m/hr.

Khayat et al. [28] used two types of experimental columns 3.6 m high and 92 cm in diameter, and the

second 2.1 m high and 20 cm in diameter to evaluate the influence of formwork dimensions and the

casting rate on fresh concrete lateral pressure. For the latter, the concrete was placed at two different

casting rates; one of 10 m/hr and the other of 25 m/hr. However, for the formwork with a height of 3.6

m the lateral pressure was evaluated at a casting rate of 10 m/hr.

Assaad et al. [6], investigated the influence of thixothropy on lateral pressure in a cylindrical formwork

2.1 m high and 20 cm in diameter. For this, the authors incorporated a set-retarding agent or an

accelerator agent in the different mixtures, which were prepared with three different types of

cementitious materials and had an initial slump flow of 650 10 mm and the w/c ratio was fixed at 0.42.

Khayat and Assaad [29] , analyzed the effect of mixture parameters on thixotropy and lateral pressure

exerted by SCC. Experimental PVC columns with a 20 cm diameter and 2.8 m high were used to

determine lateral pressure. The mixtures were prepared with three different w/c ratios: 0.36, 0.40, and

0.46. Depending on the w/c ratio, the dosage of viscosity-enhancing admixture (VEA) was adjusted to

eliminate bleeding and reduce the risk of segregation. In the case of SCCwith a low w/c ratio no VEA

was used.

Khayat and Assaad [30] studied the pressure of fresh SCC in experimental PVC columns with the same

formwork dimensions mentioned above. The authors evaluated and compared seventeen different

mixtures prepared with combinations of thixotropy-enhancing agents (TEA) and/or VEA with various

types of high-range water-reducing admixtures (HRWRA). All of the mixtures were prepared with 450

kg/m3 of cementitious material and the sand-to-total aggregate ratio was fixed at 0.46. The w/c was set

at 0.36 for the mixtures made without any VEA, and 0.4 for those incorporating TEA and/or conventional

VEA. The lateral pressure was determined using five pressure sensors mounted at 50, 250, 450, 850 mm

and 1.55 m from the base.

Khayat [31] analyzed fresh concrete lateral pressure in columns with the objective of showing how

different casting rates affect maximum lateral pressure. The author used three different mixtures of SCC

and varied the casting rate between 2 and 22 m/hr.

Billberg et al. [32] studied seven full scale walls filled with SCC. The walls were 3.0 m high; 3.38 m longand 0.3 m wide. The authors filled the formwork with different casting rates between 0.8 and 2.3 m/hr.

The authors tested two different mixtures. In all cases, the cement content was fixed at 400 kg/m3, so

they had to vary the quantity of limestone filler to compensate for the different w/c ratios.

Tejeda-Dominguez et al. [21] studied the lateral pressure exerted by concrete in 3 different walls; the

first one, 8.53 m high, 24.38 m long and 1.52 m wide, the second one, 3.96 m high and with the same


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cross section as the first one, and the third one 6.6 m high, 24.3 m long and 0.3 m wide. The authors also

tested one column 3.26 m high with a diameter of 0.609 m.

Assaad and Khayat [33] evaluated the effect of coarse aggregate concentration on lateral pressure of

seven mixtures with different values of sand-to-total aggregate ratio (S/A), by weight. Values between

0.3 and 1.0 were used. The column used by the authors was the same one used by Khayat and Assaad

[29].

Assaad and Khayat [34] analyzed the effect of the proportion of binder type on the pore water pressure

development, and on kinetics of lateral pressure decay early in the process. The authors made ten

different mixtures with binary, ternary or quaternary cements. In all of them, the authors determined

the initial slump flow, air content, temperature, unit weight, h2/h1 of the L-box test [42] and surface

settlement. They used an experimental column 1.1 m high and with 20 cm of diameter, with three

sensors to measure the lateral pressure mounted at 50, 250, and 450 mm from the base.

Assaad and Khayat [35] studied the effect of the temperature and casting rate on the pressure exerted

by SCC. Similary to the previous case, the authors used an experimental column 1.1 m high and with 0.2

m of inner diameter. The authors also used another 2.8 m high, with the same diameter. In this case, the

authors used 5 pressure sensors mounted at 50, 250, 450, 850 and 1450 mm from the base. Thedifferent mixtures were made with ternary cement, and cast at temperatures of 10, 22, and 30C, while

the velocity varied between 5 and 25 m/hr.

Assaad and Khayat [36] used the same formwork used by Assaad and Khayat [18] to study the effect of

mixture consistency on the lateral pressure developed by SCC. They used six different mixtures, varying

the contents of HRWRA, and with a slump flow between 220 mm and 750 mm. All the mixtures had the

same S/A ratio, fixed at 0.46, and a w/c ratio of 0.4.

Assaad and Khayat [37] studied the effect of incorporating VEAs along with HRWRA on variations in

thixotropy and formwork pressure developed by SCC, using the same experimental columns used in

Assaad and Khayat [35]. For this, the authors prepared twelve different mixtures.

Leeman et al. [22] investigated the influence of casting method, workability, and mixture proportion.

Three walls 2.7 m high, 0.75 m long and 0.2 m wide, were cast from the top, with three SCCmixtures

with different w/c ratio.

Giammatteo et al. [23], evaluated the effect on lateral pressure due to different structural shapes. The

authors evaluated lateral pressure in a wall and a column. The wall was 2.5 m large, 0.3 m wide and 9.0

m high; and the column 6.0 m high, 0.5 m wide and 0.3 m thick

Kwon et al. [38] studied the lateral pressure on circular columns of three different diameters (13, 18,

and 28 cm) and of the same height (1.8 m), to find out how friction stress affects the interface, and how

it varies over time.

Beitzel [39] studied the lateral pressure exerted by SCCin two different columns with different castingrates. The columns were 3.0 m high; 1.25 m long and 0.3 m wide. The first one was filled at a casting

rate of 15 m/hr and in the second one the casting rate was of 30 m/hr.

Mc. Carthy et al [40]study the effect of using a fast rate of concrete rise in formwork (80 m/h). The

authors tested two different mixtures. The formwork was 8.0 m high, 0,5 m wide and 0,5 m long.


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Gardner et al. [41] studied formwork pressure exerted by SCCon experimental columns with different

casting rate at four different sites. Four different formworks were used and the SCChad a slump flow

between 600 and 700 mm.

Billberg et al. [19] made an evaluation of existing models for predicting the maximum lateral pressure

exerted by SCC on vertical formworks. Eight different walls with different sections were tested at

different casting rates. All these values along with the values of the slump flow and T50 for each SCCs

used in each walls are detailed in their work.

5

ANALYZED VARIABLES

Seven of the variables that can affect fresh concrete lateral pressure have been considered in the

determination of K:rate of placement (R), slump flow (), the height of the concrete piece (H), concrete

temperature (T), minimum form dimension (d), cement type (C) and cross section size (ST). The model

considered each of the variables separately and progressively. That is, the hydrostatic pressure is

calculated and each coefficient is afterwards applied, in the order detailed in Eq.7

. Once the firstcoefficient is applied, the result is the new variable considered for the application of the following

coefficient and so on.

5.1 HYDROSTATIC PRESSURE

Firstly, the hydrostatic model is considered, establishing that the lateral pressure on the formwork has

an hydrostatic distribution, with concrete density.

Based on the experimental data, the hydrostatic model presents a mean value (M/C), of the ratiobetween measured pressure (M) and calculated pressure (C), equal to 86.4%. Figure 3.a. shows the

experimental data for the maximum pressure exerted by the SCC vs. the lateral pressure obtained froma hydrostatic distribution.

5.2

CASTING RATE

Following the hydrostatic pressure, the coefficient of correction by casting rate () was considered. Inthis way the model (considering only the correction by casting rate) is expressed according to Eq.Eq. In the empirical model, at every step, the regressor is the studied variable, or a function which contains

this variable. The literature shows an influence of placement rate on maximum lateral pressure that isnot linear. While a proportional relationship for low rate of placement is shown, this relation gets

weaker for high placement rates. Due to the variable influence of this parameter on fresh concrete

lateral pressure, the function expressed in Eq.is considered as the regressor for this parameter.

Eq.


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Where:

R is the rate of placement (m/hr)

Casting rates are noticeably higher in case of SCC, as no compaction is required and the concrete

behavior is more like a fluid than in the case of VC. So it can be filled at greater casting rates without any

problems, like segregation. Therefore in this case a new regression, different than the one presented in

the model proposed by Santilli and Puente [43] for VC, was performed considering different casting

rates present in the experimental data base.

The response of the model which only considers casting rate (M/HKR) presents a M/Cequal to 88,5%.Figure 3.b. shows the experimental data vs. the prediction made by the model considering only the

reduction of the maximum lateral pressure according to the SCCrate of placement. For high placement

rates the coefficient KR tends to one. However, for low placement rates, the value of this coefficient

decreases, thereby decreasing the maximum lateral pressure prediction. The lowest rate of placement

considered in the experimental data is 1.5 m/hr, which corresponds to a KRcoefficient equal to 0.62.

This value was considered as the lower limit for this parameter, as is shown inTable 4.

5.3

SLUMP FLOW

As in the previous case, the result of the hydrostatic pressure with the correction due to the rate of

placement of the SCCinto the formwork is considered when applying the coefficient of correction by the

slump flow (). In this way the partial result of the model (considering corrections by casting rate andslump flow) is shown inEq. 14

Eq. 14

In the model proposed by Santilli et al the slump cone () was considered as a regressor to determinethe factor . For SCCthis parameter is not valid, since according to the type of concrete, the slump testand its result are different. While in VCthe slump cone is measured, in the case of SCCit is the slump

flow. After filling the cone with SCC, it is lifted. The SCCspreads out and the slump flow is measured as

the final diameter attained by SCC. This is why in this case,Eq.15 shows the function considered as a

regressor to determine the factor K, being different than that of VC.

Eq.15 Where:

is the slump flow (mm)

The response of the model considering the influence of casting rate and slump flow (M/HKRK)

presents a M/Cequal to 89.5%.Figure 3.c. shows the experimental data vs. the prediction made by themodel considering the reduction of the maximum lateral pressure according to slump flow and rate of

placement. Therefore, the coefficient Kis considered equal to 1 for slumps flows greater than 660 mm.But the lowest slump flow analyzed in the experimental data was 540 mm, which corresponds to a Kcoefficient equal to 0.93. This value is considered as a lower limit for K.


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5.4

HEIGHT,CONCRETE TEMPERATURE,MINIMUM SIZE,CEMENT TYPE AND CROSS-SECTION.

For the remaining parameters (height, temperature, minimum size and cross-section), the procedure to

be followed is the same as in the case of correction by casting rate and slump flow, resulting inEq. 16

Eq. 16 In this case, the regressions determined by Santilli and Puente [43] were considered, since there are no

differences between SCCand VCfor these parameters, as neither of them depend on the dosage. In all

cases, the regressors are considered as the value of the parameter.

This occurs because SCCexperimental data tend to approach to a ratio (M/C) equal to 1.0, while for VC,

the experimental data group has a ratio (M/C) lower than the ratio resulting in SCC. Furthermore,

experimental data obtained with SCC, for each analyzed variable, have very little variation because the

group of authors working in this type of concrete is always the same. For example, in the case of the

minimum dimension, 76% of the data have a minimum dimension of 0.2 meters, almost not showingvariation with the rest. This justifies the best adaptation of the statistical parameters proposed by

Santilli and Puente [43] to determine the corresponding of these five variablesFromFigure 3.c. toFigure 3.h it can be seen how the addition of each parameter in the model (height,

concrete temperature, minimum size, cement type and cross section) affects the value of maximum

lateral pressure, respectively.

5.4.1 Height

The height of the concrete piece (m) was considered as a regressor to determine the factor KH.

Therefore, the coefficient KHis considered equal to 1 for heights lower than 2.0; and the greatest height

analyzed in the experimental data is 8.6 m, which corresponds to a KH coefficient equal to 0.77. This

value is considered as a lower limit for this parameter, as is shown inTable 4.The response of the modelconsidering the influence of casting rate, slump flow and concrete height (M/HKRKKH) presents a M/Cequal to 91.4%. Figure 3.d. shows the experimental data vs. the prediction made by the model

considering the reduction of the maximum lateral pressure according to casting rate and slump flow.

5.4.2 Temperature

Concrete temperature (C) was considered as a regressor to determine the factor KT. KThas a value of 1

at a concrete temperature of 27.2 C, and since this is considered conservative, this factor is going to beconsidered equal to 1 for lower temperatures. The highest temperature analyzed in the experimental

data is 30 C, whichcorresponds to a KT

coefficient equal to 0.92, which is considered as the minimum

value of KT as shown inTable 4.The response of the model considering the influence of casting rate,

slump flow, concrete height and the temperature of concrete (M/HKRKKHKT) presents a M/Cequal to

91.7%.Figure 3.e. shows the experimental data vs. the prediction made by the model considering thereduction of the maximum lateral pressure according to these variables.

5.4.3 Minimum size

The minimum cross section dimension (cm) was considered as a regressor to determine the factor Kd.

The lowest minimum form dimension analyzed in the experimental data is 12.2 cm, which corresponds

to a Kd coefficient equal to 0.94. This value has been established as the minimum value of Kdas shown in


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Table 4. The response of the model considering the influence of casting rate, slump flow, concrete

height, concrete temperature and minimum cross section dimension (M/HKRKKHKTKd) presents a M/Cequal to 95.9%. Figure 3.f. shows the experimental data vs. the prediction made by the model

considering the reduction of the maximum lateral pressure according to these variables.

5.4.4

Cement type

As cement type cannot be considered as a continuous function, the correction factor KC has been

determined in an arbitrary manner, as shown in Table 2, where three different groups have been

established. Santilli and Puente [43] describe the differences between each groups. For all the SCC

experimental data base that was mentioned above, the KCis equal to 1 due to the composition of SCCin

each case.Figure 3.g. shows the experimental data vs. the prediction made by the model considering

the reduction of the maximum lateral pressure according to these variables.

5.4.5

Cross-section

The correction factor KST was also determined in an arbitrary manner, as shown inTable 3.In order to

establish this division, the authors [43] defined two different groups: walls and columns. A wall is

defined as sections where either the width or the breadth exceeds 2 m, while for a column both

magnitudes are less than 2 m. The experimental database comprises 115 experimental values of

columns and 13 for walls and bases. The response of the model considering the influence of casting rate,

slump flow, concrete height, concrete temperature, minimum cross section dimension, cement type and

the type of cross section (M/HKRKKHKTKdKCKST) presents a M/Cequal to 96.3%.Figure 3.h. shows theexperimental data vs. the prediction made by the model considering the reduction of the maximum

lateral pressure according to these variables.

The lines which represent the ratio (M/C) of measured pressure (M) to calculated pressure (C)equal to

1.0; 1.075 and 1.15 are also drawn with the objective of clarifying the division between the different

recommendations proposed by Santilli and Puente [44]. The different recommendations according to

the control levels in situ, are based on the quartile of 95% of the ratio distribution (M/C95%). A saferecommendation should be used for formworks that are going to have low control levels (M/C95% higher

than one must be discarded), a less conservative recommendation should be used for formworks that

are going to have extensive control (M/C95% lower than 1.15). Finally, a medium recommendation,

halfway between the previous two, should be used for formworks that are going to have medium level

of control (M/C95% lower than 1.075 are acceptable).

5.5 HIGH RATES OF PLACEMENT

The principal objective of the model is to obtain an accurate prediction of the maximum lateral pressure

exerted by SCC on vertical formworks for high placement rates (over 6 m/hr), which is a common

practice today. As established by Leemann et al. [22], one of the most important advantages of SCCareits high rates of placement, since it does not need vibration and can behave as a fluid without any

segregation; resulting in shorter construction times and lower costs. Based on that, the model was

carried out only for experimental data where SCChas rate of placement higher than 6 m/h.

As can be seen in the development of the model, for high placement rates the coefficient KR tends to

one. However, for low placement rates, the value of this coefficient decreases, thereby decreasing the

maximum lateral pressure. This is why in this case the model for rates of placement greater than 6 m/h


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will be studied, as these are the most common values in real practice. In the experimental database,

there are some experimental results in which casting rate are lower than 6 m/h, but these are mostly

laboratory studies and there are not feasible in situ.

Figure 2 details the result of the model considering only experimental data with rate of placement over

6 m/h; concluding that the proposed model improves when casting rates greater than 6 m/h are

considered.

When all experimental data are considered (also experimental data with casting rates lower than 6m/h)

the model presents an average of 96.3%. However, the proposed model presents an average of 98.8%

when casting rates are greater than 6 m/h.

In this way, it is easy to establish that the model fits better, even for the case of experimental data

provided by real practice. This is one of the most important advantage for the application of this model,

in addition to not requiring the determination of a rheological parameter.

0

20

40

60

80

100

120

140

160

180

0 20 40 60 80 100 120 140 160

Measuredpressure(KPa)

Calculated limiting pressure (Kpa)

Casting rates over 6 m/hM/C=1,15

M/C=1,075

M/C=1,00

Figure 2 Resulting model for casting rates over 6 m/hr

5.6

SUMMARYAn empirical model with a bilinear envelope useful for formworks higher than 2 m was developed to

predict the maximum lateral pressure exerted by SCCon vertical formworks. Eq.6 determines the value

of the maximum lateral pressure and Eq.9determines all the Kicoefficients, with exception of KCand

KST.

Figure 3.a. shows the experimental data vs. the prediction made by a hydrostatic distribution. Then,

Figure 3.b. to 3.h. show experimental data plotted against the prediction made by the model, factoring

in progressively all the Ki factors.


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Table 4 shows the statistical parameters needed to determine all the Kicoefficients using Eq.9., with

exception of KCand KST, which are determined inTable 2 andTable 3,respectively. In all cases, these

coefficients have to be less than or equal to one and higher than the minimum value, which is also

shown in Table 4. In the case of VC, the model considers the same equation but Table 1,Table 2 and

Table 3.

Figure 3 shows the influence of each coefficient on the prediction of maximum lateral pressure. At the

same time, it can be observed how the points move to the left as the different coefficients are

considered. FromFigure 3.a. toFigure 3.h it can be seen how the different points are grouped near the

straight line which represent M/C = 1.0, which means the model accurately predicts actual pressure.

The proposed model presents a M/C equal to 96.3%. The resultant M/C95% is equal to 1,074; whichallows the use of the model in the medium recommendation, since it is lower than 1.075. Based on

these results, it is possible to establish that the model presents a good approximation to the SCC

experimental data. The model also presents an advantage compared to other models used to predict

maximum lateral pressure exerted by SCC, because it does not require the determination of any

rheological parameters. Other models for SCCneed this type of parameters for its use, as mentionedabove.

Ki Regressor X0 (unit) 00 11 t/2,n-2 MSRES N x Sxx Minimum value

Kr 1-(1/(R+1)); R(m/hr) -0,250 1,241 1,28 0,0090 120 0,90 0,58 0,62

K log(SF); Slump Flow (mm) -1,462 0,834 1,17 0,0090 114 2,82 0,0620 0,93

KH H(m) 0,865 -0,047 1,65 0,0320 226 4,28 478,6 0,77

Kt Temeprature (C) 0,835 -0,007 1,65 0,0340 214 17,95 7923,8 0,92

Kd Dmin (cm) 0,641 0,002 1,46 0,0340 190 32,30 28499 0,94

Table 4 Statistical parameters for the determination of coefficients Ki.


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0

3060

90

120

150

180

210

240

0 20 40 60 80 100 120 140 160 180 200

Meas

uredpressure(KPa)


Model considering KR

0

3060

90

120

150

180

210

240

0 20 40 60 80 100 120 140 160 180 200



Hydrostatic

0

30

60

90

120

150

180

210

240

0 20 40 60 80 100 120 140 160 180 200



Model considering KR and K

0

30

60

90

120

150

180

210

240

0 20 40 60 80 100 120 140 160 180 200



Model considering KR, Kand KH

0

30

60

90

120

150

180

210

240

0 20 40 60 80 100 120 140 160 180 200Measuredpressure(KPa)


Model considering KR, K,

KH and KT

0

30

60

90

120

150

180

210

240




KH, KT and Kd

0

30

60

90

120

150

180

210

240




KH, KT, Kd, KC and KST

0

30

60

90

120

150

180

210

240




KH, KT and Kd

HKRKKHKTKdKCKST(KPa)HKRKKHKTKdKC(KPa)

HKRKKHKTKd(KPa)HKRKKHKT(KPa)

HKRKKH(KPa)HKRK(KPa)

HKR(KPa)H(KPa) b)a)

c)

e)

d)

f)

h)g)

M/C=1,15

M/C=1,075

M/C=1,00

M/C=1,15

M/C=1,075

M/C=1,00

M/C=1,15

M/C=1,075

M/C=1,00M/C=1,15

M/C=1,075

M/C=1,00

M/C=1,15

M/C=1,075

M/C=1,00

M/C=1,15

M/C=1,075

M/C=1,00

M/C=1,15

M/C=1,075

M/C=1,00

M/C=1,15

M/C=1,075

M/C=1,00

Figure 3 Experimental data plotted vs. 7 different predictions which range from the

hydrostatic distribution to the complete model considering one by one the coefficients Ki.

6

APPLICATION OF THE MODEL

The application of the model requires the calculation of seven parameters Ki. If some of the data are

unknown, then the corresponding parameter Ki has to be considered equal to one. In the worst case (all

the parameters equal to one), the model matches the hydrostatic distribution. For example, applying


20/24

the model to a sample wall 4,0 m high with a rectangular cross section 0.30 m wide, a slump flow of 750

mm, rate of placement 19 m/h and a concrete density of 2400 kg/m3, produces the following result:

As the rate of placement (19 m/h), height of concrete piece (4.0 m), slump flow (750 mm) and minimum

form dimension (30 cm) are known parameters, the coefficients are determined by Eq. 9 using the

statistical parameters shown inTable 4.The results obtained are: KR= 0.99, KH= 0.97, K= 1,01 and Kd=

0.97.

As Kis greater than one, for the application of the model this parameter has to be considered equal to

one. Temperature and cement type are unknown parameters, therefore the values of KTand KCare also

equal to one. On the other hand, the coefficient KST is determined fromTable 3,and in this case it is

equal to 1.0, because the sample is a wall.

Summarizing, the value of Kis 0.93 as showEq. Eq. The maximum lateral pressure is then determined by Eq. 6 obtaining a value of 89.3 kPa, and the

distribution can be seen inFigure 4.

PmaxPmax

Hydrostatic

distribution

Presin lateralLateral pressure

Heightofconcrete

(H=4,0mts)

Pmax = 0,93*4*2400= 89.3 Kpa.

Figure 4 Bilinear distribution resulting from the application of the proposed model

7

CONCLUSIONS AND RESUME

This work presented an empirical model to predict the lateral pressure exerted by SCC on vertical

formworks. The model has a bilinear envelope, in which pressure follows a hydrostatic distribution up

to a maximum value, which remains constant until the end of the formwork, and is based on the

empirical model proposed by Santilli et al [45] to calculate the maximum lateral pressure exerted by VC

on vertical formworks. The value of maximum lateral pressure is determined by Eq.18


21/24

Eq. 18

The determination of each of the Ki coefficients is carried out from the prediction confidence intervals of

a new observation considering simple linear regressions. KR and K are determined according to theexperimental database for SCC, while regressions for KH, KT and Kd match those found for vibrated

concrete. KC and KSTare determined in an arbitrary manner.

The model presents a very good approximation to the experimental data, which is reflected in a value of

M/C equal to 96.3%, and when rates of placement are greater than 6 m/h this value increases to 98.8%.

The results show that the proposed model has a very good prediction of the maximum lateral pressure

exerted by SCC on vertical formworks, considering that this prediction improves when casting rates are

greater than 6 m/h. In addition, it is noteworthy that in comparison with other models, this does not

require the determination of a rheological parameter.

8

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