Numerical Simulation of MSE Wall Behavior Induced by Surface-Water Infiltration

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TITLE: Numerical simulation of MSE wall behavior induced by surface water

infiltration

Wan Soo Kim1, Ph.D., P.E., M.ASCE and Roy H. Borden2, Ph.D., P.E., M.ASCE

1 Soils Engineer, Virginia Department of Transportation, Materials Division, 1401 East Broad

Street, Richmond, VA 23219; email: [email protected]; (Formerly Research

Assistant, Department of Civil, Construction, and Environmental Engineering, North

Carolina State University, Campus Box 7908, Raleigh, NC 27695-7908)

2 Professor, Department of Civil, Construction, and Environmental Engineering, North

Carolina State University, Campus Box 7908, Raleigh, NC 27695-7908; email:

[email protected]

Journal of Geotechnical and Geoenvironmental Engineering. Submitted October 13, 2011; March 20, 2013; posted ahead of print March 22, 2013. doi:10.1061/(ASCE)GT.1943-5606.0000927

Copyright 2013 by the American Society of Civil Engineers

J. Geotech. Geoenviron. Eng.

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ABSTRACT

A series of numerical simulations including transient seepage analyses and stress deformation

analyses were performed in order to predict the behavior of a MSE wall subjected to surface-

water infiltration. In this research, two mechanisms to cause the deformation due to wetting

were considered: (1) the deformation induced by shear strength decreases and (2) the

volumetric deformation (swell or collapse) due to wetting. The effects of a low as-

compacted water content and a low-quality compaction zone behind the wall face on the wall

behavior were investigated. As result of the simulations, the wall deformations (face

deflections and reinforced-soil settlements) and reinforcement tensions (maximum tensions)

are presented at the end of construction and after periods of surface water infiltration.

Key words: MSE wall, unsaturated soil mechanics, compaction, water infiltration, numerical

analysis




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INTRODUCTION

Prediction of MSE wall behavior due to surface water infiltration is a complicated problem

which includes seepage, shear strength, and volume change based on unsaturated soil

mechanics principles. Several researchers (Ng and Pang, 2000 and Yoo and Jung, 2006) have

showed the failure mechanism of an earth structure due to rain infiltration using unsaturated

shear strength based on limit equilibrium analysis. However, there are still several existing

limitations for performing stress-deformation analyses based on unsaturated soil behavior.

This is mainly due to the complexities of analysis utilizing the unsaturated soil constitutive

law and the increased difficulties of performing experimental studies on unsaturated soils.

Most numerical simulation programs were, for this reason, developed assuming saturated soil

mechanics and therefore adopted one stress state variable (either total stress or effective

stress) to predict soil behavior. However, unsaturated soil behavior is better explained using

two stress state variables (Fredlund and Rahardjo, 1993). These two stress state variables are

net normal stress, ( -ua), and matric suction, (ua–uw), where is total normal stress, ua is

pore-air pressure and uw is pore-water pressure.

A 5.4-m high MSE wall constructed with marginal fills in the Research Triangle Park

(RTP) of North Carolina experienced a localized collapse in March, 2001 during a rainy

period a few months after completion of wall construction. In this study, numerical

simulations with unsaturated soil properties (elastic modulus and shear strength) were

performed to provide better understanding of the behavior of the MSE wall both at the end of

construction and during rainfall. However, it must be clearly stated that these analyses cannot

provide conclusive proof as to why the wall failed, as detailed as-compacted material

properties are not available in the project records. Nevertheless, the analyses presented are

believed to be very instructive, even if taken as a parametric study of potential conditions.

PROJECT DESCRIPTION

The RTP MSE wall geometry and cross section are shown in Figure 1. The wall was built

with 11 layers of 4.75m long polyester geogrid reinforcement (Fortrac 35/20-20 Geogrid,

Huesker Inc.). Vertical spacings of reinforcements varied from 0.2m to 0.6m throughout the

wall height. Commercially available Rockwood blocks (Classic 8, Rockwood retaining walls

Inc.) were used as the facing system unit. The blocks were 300mm deep, 200mm high, and




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450mm wide, and had a mass of 35 kg per unit. The facing batter of the wall was

approximately 7 degrees from vertical, and the 2m-high back-slope portion (18 degrees)

extended from the wall face. Crushed gravel (No. 57 stone) was used to infill the spaces

between adjoining modular block units and to create a 300-mm thick gravel column behind

the wall facing. The connection between blocks relied on the friction between the contact

block material and gravel material filled in the blocks.

Post-Failure Investigation

The post-failure site investigation of the MSE wall included the following:

1. A review of QA/QC testing and field reports, which revealed that none of the QC/QA

compaction testing performed during wall construction was done within 2m of the

wall face, therefore the as-built condition cannot be known with certainty.

2. Within one week after the wall failure, drive-tube samples obtained from this 2m-

zone directly behind the failed zone and off to the sides behind unfailed-portions of

the wall, revealed in-place dry densities less than 90% of dmax with moisture contents

on the order of 20%.

3. Laboratory tests on bulk samples obtained from a test pit within this zone, determined

the low plasticity clayey soil (CL according to USCS) to have a Liquid limit = 29 and

Plastic limit = 19. Standard density tests (ASTM D 698-00) yielded a maximum dry

density of 1.90g/cm3 with an optimum water content of 11.7%. The grain size

distribution curve is shown in Fig. 2.

4. Double-oedometer tests on specimens recompacted under various compactive efforts

and at various moisture contents were used to define the shrink-swell behavior of the

material. Only materials compacted significantly dry of optimum with low

compactive effort demonstrated magnitudes of compression upon soaking consistent

with the field-measured settlement in the undisturbed areas of the wall adjacent to the

failed section and between layers of grids.

5. Based on interviews with those involved in construction, the soil that was being used

for wall construction was very dry (due to drought conditions and the time of year).




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NUMERICAL MODELING

Efforts were made to investigate the behavior of a MSE wall using unsaturated soil properties

as a function of soil suction. Similar efforts were found in Yoo and Jung (2006) performing a

numerical simulation for the failure of a MSE wall during a rainfall period. In this study,

special attention was given to modeling the effect of a relatively dry, low density zone behind

the wall face. This may or may not have been the case of the wall that failed in the RTP, and

the subsequent analyses should be viewed as prompted by the wall failure and not possessing

all of the critical information required to be an investigation that shows why the wall failed.

Nevertheless, as the soils that were used in the construction of this wall are typical of those in

the area, values obtained from lab tests on the site materials are incorporated where possible.

The backfill is assumed to be compacted very dry of optimum (w = 4.8%, -7% of OMC) and

using the compaction data developed from bulk samples obtained from a test pit after the

wall failure, dry densities of 1.79 g/cm3 (R.C.= 94%) and 1.60 g/cm3 (R.C.= 84%) were used

to simulate well- and poorly- compacted backfills, respectively. These higher density and

lower density zones are designated as soil H and soil L. Also, for the purposes of this

simulation, it was assumed that a poorly compacted zone exists behind the wall face (1.6m

wide).

FLAC model

The finite difference code, FLAC (Itasca, 2000), was used to simulate the response of the

reinforced wall during wall construction. Figure 1 shows the numerical grids used for the

MSE wall. The simulation modeled the sequential bottom-up construction of the wall facing,

soil and reinforcement. The backfill and facing units of the wall model were elevated in lifts

of 0.2 m, which was the same as the height of the modular block units, and the reinforcement

layers were placed in the model as each reinforcement elevation was reached.

Lee (2000) developed a FLAC numerical model that was able to predict the behavior

of a geosynthetic reinforced retaining wall at the end of construction. This model was

incorporated into the FLAC model developed in this study. Elastic material elements were

used to represent modular blocks, and Mohr-Coulomb material elements were used to

represent the gravel column and the MSE wall backfill. The hyperbolic model with plain

strain soil properties was used to simulate the gravel column response (Table 1). The




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behavior of the geosynthetic reinforcements was simulated using cable elements (Table 2).

The Young’s modulus (E) of reinforcement was determined from published wide width

strength test results at 5% strain. This modulus was then reduced in order to consider the

effect of the faster strain rate used in laboratory tests; 20% reduction for polyester woven

reinforcement, as suggested by Lee (2000). Different interface properties of reinforcement

elements were assigned to simulate the reinforcements located within the block elements and

within the soil (backfill) elements. The interface properties of the cable located within blocks

were determined from connection test data. Within the soil elements, the reinforcement

(cable) elements were attached to the nodes of the soil elements assuming that there was no

slippage between the soil and the geosynthetic reinforcement. This technique was

successfully used by Lee (2000) and Hatami and Bathurst (2003). The interface elements

were used for (1) the interface between structural blocks and (2) the interface between

modular block and gravel. The interface input properties are summarized in Table 3.

Additional efforts have been made to improve the FLAC model for MSE walls by

Hatami and Bathurst (2005, 2006). In their FLAC model, a hyperbolic model was adopted to

better model the non-linear behavior of geosynthetic reinforcement, and the influence of

backfill compaction effects and reinforcement type on end of construction and surcharge

loading response was investigated. However, it should be noted that the FLAC models found

in the literature were developed and calibrated based on the measured displacements and

reinforcement strains from instrumented walls constructed with coarse-grained fills. As this

study was trying to focus on developing a model that utilized unsaturated soil properties,

Lee’s model was chosen as the base for our model, as it was simpler and we were not

convinced that the use of these advanced FLAC numerical modeling techniques would

guarantee better results for a wall that was constructed with marginal fill.

Method of analysis

A series of numerical simulations with unsaturated soil properties were performed in order to

investigate the MSE wall behavior during construction and during subsequent water

infiltration. Rorie (2006) performed the pressure plate test (ASTM D 6836-02), filter paper

test (ASTM D 5298-03), collapse potential test (ASTM D 5333-03), and falling head

permeability test using an oedometer on reconstituted samples of actual backfill and the




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results of these tests were used as input values for these numerical simulations. Figure 3

shows the procedural flow chart that was used in this study. Details of each step of analysis

are described as follows.

Step 1: Numerical simulation of the MSE wall behavior during construction

The behavior of the MSE wall at the end of construction was predicted using the developed

FLAC model that accounted for unsaturated soil properties (elastic modulus and shear

strength) and the staged construction of the wall. The matric suction change due to loading

(lifts of backfill) was computed in the model, and the properties of construction materials

such as reinforcement, interfaces, and backfills were updated by the developed FISH

subroutines based on changes in total normal stress and matric suction. The matric suction

distribution within the backfill at the end of construction was stored in a data file and used as

initial values in the subsequent flow analysis.

Based on the measured SWCC (Fig. 4) and assumed saturated strength parameters (c’

and ’), shear strength under zero net normal stress (total cohesion, c) was first predicted

using the equation 1 (Fig. 5). Total cohesion and effective friction angle along with dilation

angle ( =10°) were then used to characterize the shear strength behavior of soils H and L.

Kim and Borden (2011) performed comprehensive studies on the prediction of unsaturated

shear strength using three commonly used empirical procedures. From the findings of their

studies, and because the subject soils are low plasticity clays, Vanapalli et al.’s procedure

(1996) with residual suction value of 3000 kPa was adopted as a prediction method (Eq. 1).

'' ( ) tan ' ( )[(tan ) ]100

rf n a a w

r

S Sc u u u

S (1)

where c’= effective cohesion of saturated soil;

’= effective friction angle of saturated soil;

S = degree of saturation; and

Sr = residual degree of saturation

It should be noted that drying SWCCs were used to predict unsaturated shear strength

in this paper. Although it is well known that the use of wetting SWCCs would be more




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appropriate for the condition of water infiltration, drying curves still have been measured

widely, mainly because it is more difficult, time consuming, and expensive to measure the

wetting curves. More research is needed to investigate the incorporation of the effect of

hysteresis on estimating unsaturated soil strength by empirical methods.

As shown in Fig. 6, the undrained constitutive relation was determined from the

predicted pore pressure parameter, B’ (= ua / y) and the drained constitutive relation that

was measured from the conventional oedometer test. The prediction of the pore pressure

parameter was accomplished by modifying Hilf’s equation (1948) as follows;

0 0 0

0

1'

(1 )1

( )a a as

BS hS n

u u m

(2)

where, ua = change in pore pressure;

ua0 = initial absolute air pressure ( = initial gauge pressure + atmospheric pressure);

S0 = initial degree of saturation;

h = the volumetric coefficient of solubility;

n0 = initial porosity; and,

mas = compressibility of as-compacted specimen measured from an oedometer test

The undrained modulus was then estimated by computing the slope of the undrainded

constitutive relation. Figure 7 shows undrained modulus functions with respect to mean

stress for soils H and L. The computed B’ values for soils H and L were 0.06 and 0.1,

respectively. The initial values of matric suction for soil H and L measured by filter paper

method were 783 kPa (Rorie, 2006). In this research, the volume change due to changes in

matric suction, which would result from the change in degree of saturation produced by the

strain during loading, was ignored based on the assumption that it is relatively small

compared to the volume change due to change in net normal stress. The assumption seems to

be reasonable because the changes in matric suction during loading are very small for the

backfills (H and L) compacted very dry of optimum and in general compressive index with

respect to matric suction is much smaller than compressive index with respect to net normal




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stress (Fredlund and Rahardjo, 1993).

Step 2: Transient seepage analysis for water infiltration

Transient seepage analysis using unsaturated permeability was conducted in order to estimate

changes of matric suction within the backfill due to water infiltration. The van Genuchten

equation (1980), which is built into a two phase flow option in FLAC, was used in the model

to predict coefficient of permeability functions with respect to matric suction (Figure 8). The

saturated permeability values were laboratory determined (Rorie, 2006).

The matric suction distribution at the end of wall construction, which was computed

in the previous step (step 1), was used as the initial condition for the seepage analysis. When

the desired infiltration period (3, 6, 9, and 12days) was reached during the simulation, the

matric suction distribution was stored in a data file. These stored values of matric suction

were recalled and used in the following stress-deformation analysis.

Step 3: Numerical simulation for the MSE wall behavior during water infiltration

Post-construction wetting of compacted backfill is known to produce wall deformations. Two

factors that induce the wall deformation due to wetting were considered in this study. These

two factors are described as follows:

a) Shear induced deformation

For materials existing in an unsaturated state, wetting generally results in loss of shear

strength, which can be significant, as well as increases in total unit weight. These adverse

changes induce yielding of soil, and, in turn, plastic deformations.

Figure 9 shows the FLAC-predicted matric suction and total cohesion profiles during

water infiltration along section-I, located 1.1 m behind the back face of the block (Fig 1; in

the middle of the poor quality backfill zone). The “day 0” designation in the figure indicates

the point in time when the wall construction was completed. It is seen from Fig.4 that the

suctions of 783kPa measured by filter paper method do not lie on the SWCCs and much

higher suctions are estimated at the given degree of saturations (for as-compacted condition)

from the drying curves due to hysteresis effect. These higher suctions would produce

unreasonably high shear strength of backfill at end of construction. In this paper, the suction




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value of 783kPa along with the adjusted degree of saturation as shown in Fig.4 was used to

estimate unsaturated shear strength (equation 1). Total cohesion of 93kPa was estimated at

“day 0”. It is significant to note that for this wall height and a soil friction angle of 25 degrees,

the wall would have a FS of 1.2 (using a Stability Number of 6) without any reinforcement

with a cohesion on the order of 15 kPa (ignoring the 57 stone in the front). Significant

decreases in total cohesion (from 93kPa to 0kPa) are observed in the upper portion of the

wall, and the depth of this shear strength-decreased zone is seen to increase as the duration of

the infiltration period increases.

b) Volumetric deformation

Matric suction changes due to wetting also cause volumetric deformation (expansion or

collapse). Figure 10 shows the results of double oedometer tests that measured wetting

induced deformation for soils H and L. Noorany et al. (1999) developed a model for slope

response analysis to compute wetting-induced slope deformation using FLAC. In their model,

the wetting stresses were calculated from the wetting strain using the incremental form of

Hooke’s law (Eq.3).

4 2( ) ( )( )

3 3xx xx yy zzK G K G

4 2( ) ( )( )

3 3yy yy xx zzK G K G (3)

4 2( ) ( )( )

3 3zz zz xx yyK G K G

where K = bulk modulus

G = shear modulus;

xx yy and yy wetting stresses in the x, y, and z directions, respectively; and

xx yy and zz wetting strains in the x, y, and z directions, respectively.

In the current research, wetting vertical strains measured from the double oedometer tests

were used as input to the FLAC model, assuming there were no lateral displacements. The

wetting stresses were then added to the initial stresses within the soil elements and the FLAC




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model was cycled to equilibrium. In addition, several advanced features were added to the

model developed by Noorany et al. First, the changes in degree of saturation due to water

infiltration were smoothly defined from unsaturated flow analysis, as intermediate values

between initial and saturated conditions were evaluated, rather than defined as one of two

extreme conditions (either initial or saturated) by the prescribed wetting front. Second, the

amount of volumetric strain in the process of wetting (between initial and saturated

conditions) was estimated from the SWCC assuming the wetting strain magnitude is

proportional to the amount of moisture gain (0% of volumetric strain at initial condition and

100% at saturated condition) (Rodrigues, R. A. and Vilar, O. M., 2006). Lastly, both lateral

and vertical displacements were restricted at the grids of the “non-wetting zone” and very

large values for the cohesion and tensile strength were assigned to the backfill, forcing the

material to behave elastically. Therefore, shear induced deformation could not occur in this

phase of the simulation.

Step4: Superposition of the results

As a final step, the results (lateral and vertical displacements within the solution domain and

axial strain in the reinforcement) from the two numerical simulations described in step 3

were combined.

RESULTS

Cases used for numerical analysis

Four different backfill conditions were considered for numerical simulation. Table 4 lists the

compaction conditions and permeabilities of backfill soils used for each case. Cases 1 and 2

were chosen to represent the wall constructed without and with the poorly compacted backfill

zone(1.6m-wide) behind the wall face, respectively. Additionally, Cases 3 and 4 were

introduced to consider possible variation of the backfill permeability. A saturated coefficient

of permeability two times higher than that measured in the lab (ksat) was adopted for Cases 3

and 4. Until surface water infiltration is included in the analysis, there is no difference

between the responses of Cases 1 and 3 and 2 and 4.




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Wall behavior at the end of Construction

Figures 11(a) and 11(b) show contours of stresses and displacements within the MSE wall at

the end of construction for the walls constructed without a low-quality compaction zone

(Case 1) and with a low-quality compaction zone (Case 2), respectively. Distinct differences

between the vertical stress distributions for each wall are observed. Compared to the vertical

stress distribution for Case 1, relatively low vertical stress is developed in the poorly

compacted zone behind the wall face for Cases 2. This is because some of the vertical stress

induced during construction within this zone is transmitted to the adjacent high stiffness

materials (gravel column and well compacted backfills). The lateral stress contour for Case 2

reaches deeper than that for Case 1 within a 1.6m-wide zone behind the wall face. Distinct

difference between the vertical displacement distributions is also observed showing that

relatively high vertical displacements occur within the poorly compacted zone. As expected,

higher lateral displacements are predicted for Case 2.

Figure 12(a) shows the distributions of lateral displacements along the wall face and vertical

displacements within the reinforced soil mass at section- I. For Case 1, with the well

compacted backfill, the maximum lateral displacement of the wall face is 19mm (at a height

of 0.43H above the wall base) and the maximum vertical displacement at section I is 36mm.

For the analyses performed with the 1.6m wide poorly compacted zone (Case 2) both the

wall-face lateral displacement and reinforced soil mass vertical displacement were seen to

increase to values of 29 mm and 55 mm, respectively, and the location of max. lateral

displacement increases to 0.5H. The existence of the 1.6m-wide poorly-compacted zone

behind the wall face increased both wall face deflection and settlement by approximately

52 %.

The maximum tension force in a reinforcement layer, Tpeak, is plotted along the wall

elevation as shown in Fig. 12(b). The results show that Tpeak for Case 2 are higher than those

for Case 1. Tpeak increases with increasing depth in the upper half of the wall but do not tend

to decrease in the lower half. The maximum values of Tpeak in all layers for the walls without

and with a poorly-compacted zone were 3.1kN/m and 3.7kN/m, respectively. The possible

reason for these small reinforcement tensions at the end of construction, which are well

below the yield strength of 35 kN, is that the shear-induced deformations are small due to

high shear strength of backfills that result from relatively high suction values in the backfill




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soils used.

Transient seepage analysis

The matric suction distributions for Cases 2 and 4 during surface water infiltration periods

from the seepage analysis are shown in Figs. 13(a) and 13(b), respectively. It is clearly shown

that there is a substantial difference between the infiltration depths in the poorly compacted

zone. Also, it is observed that the transition zone between the wetting zone and the non-

wetting zone is very sharp and distinct because of the high initial matric suction. From the

results of Case 2 as shown in Fig. 13(a), the infiltration depth in the poor quality compaction

zone is about 3m after the 12-days period of infiltration, while a relative shallow advancing

“wetting front” (less than 1m) is developed in the well compacted zone, as most of the

surface water cannot infiltrate into the soil because of relatively low water permeability. The

matric suction distribution of Case 4 that was performed using the higher coefficients of

permeability (2 times) is shown in Fig. 13(b). The matric suctions almost disappear in the

low quality compaction zone after 12 days of infiltration. However, the depth of the wetting

front is still only about 1m below the ground surface in the well compacted zone. Although

the matric suction distributions for Cases 1 and 3 are not presented in this paper, one might

approximate them by extending the wetting fronts in the good quality compaction zones,

which were determined from Cases 2 and 4, across the low quality compaction zone.

Wall behavior during water infiltration

For the wall behavior during water infiltration, the results of Case 2 are presented first and

then the effect of varying permeability on the behavior of the wall is investigated through

comparison between the results of Cases 2 and 4. Finally, the behaviors of the walls that were

modeled to be constructed with high density backfill using two different values of

coefficients of permeability are presented (Cases 1 and 3).

Results for Case 2

a. Shear induced deformation

Figure 14 illustrates the development of lateral and vertical displacements in the MSE

wall that result from the decrease in backfill shear strength due to wetting. It should be noted




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that only the “change” in the displacements after the initiation of infiltration is shown in the

figures (not the cumulative displacements from the construction of the wall). It is clearly seen

from the figures that the wall movement tends to increase as the water infiltrates into the wall

system. No significant increases in lateral and vertical displacements are observed during the

first 3-days of infiltration. The displacements, however, start to gradually increase with

increasing infiltration. Most displacements occur within the poorly compacted zone.

b. Volumetric deformation (Case 2)

Figure 15 shows the wetting-induced changes in lateral and vertical displacements as

a result of the volumetric strains. It is seen from these figures that the vertical displacements

are dominant in the wall behavior since only the vertical wetting strain, which was

determined from the one-dimensional oedometer test, was used as an input in the simulation.

c. Total deformation –Combined results (Case 2)

The “total” displacements are estimated by summing the displacements induced by

(1) decreases of shear strength due to loss of suction and (2) volumetric strain of backfill

soils due to wetting. Figure 16 (a) shows the face-deflection and vertical-displacement

profiles along section I during the 12-day infiltration period from the end of the construction

condition. It can be seen that the magnitude of the increased displacements become larger

from the top of the wall (ground surface), and that the zone of significant displacement

increases in depth with time. After 12-days of infiltration, the maximum values of the wall-

face deflection and vertical displacements are predicted to be 33 mm and 74 mm,

respectively. The locations of these maximum values are found at 0.6H and 0.8H,

respectively, which are higher than those at the end of construction (approximately 0.5H).

Figure 17 illustrates the variation of reinforcement tension distribution along the

length of each layer (layers 8-11) during water infiltration. In the simulation, the compressive

axial force in the reinforcement is restricted by assigning the compressive yield strength to be

a very small number (ycomp = 0.01kN). This implies that the axial forces cannot be

superimposed once the reinforcement meets the compressive yield criteria. Therefore, the

axial strains of reinforcements for each simulation are superimposed and then converted to

the tension force using the reinforcement cross-sectional area and stiffness. The




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reinforcement tension of the layers within the wetting zone are seen to increase significantly

near the wall facing because of the increasing differential settlements between the block and

backfill during the infiltration period. The increases in reinforcement tension observed at the

boundary of poorly compacted zones (at 2.2m behind the wall face) also can be explained by

the differential settlement between poorly and well compacted backfill soils. The maximum

tension forces, Tpeak, for each layer along the wall height are shown in Fig. 16(b). After the

12-day infiltration period, the maximum value of Tpeak of all layers inside the MSE wall

(defined as Tpeak_max) is computed to be 5.1kN, and is found in layer nine (third from the top).

Results for Case 4

Figure 18 shows the simulation results for Case 4 that were obtained using values of

ksat two times higher than those used for Case 2. The simulation results are only presented for

the “total” displacements and reinforcement tensions after the 12-day infiltration period. The

results for Case 2 are also presented in the graphs for comparison. As expected, the results for

Case 4 show higher values of displacements and reinforcement tensions than those for Case 2

because of the extended wetting zone. The maximum values of 47mm and 107mm are

observed for the wall face deflection and vertical displacements along the wall height (Fig.

18a). The maximum values of 47mm and 107mm indicate a 42% and 44% increase,

respectively, compared to those values of Case 2. However, these values are found at the

same locations as were observed for Case 2 (at 0.6H and 0.8H, respectively). The value of

Tpeak_max is predicted to be 7.7 kN (increases over 45% compared to Case 2) and is still found

in layer nine(Fig. 18b).

Results for Cases 1 and 3

Due to the shallow depths of water infiltration observed for Cases 1 and 3, there are only

small changes in displacements and reinforcement forces after the 12-day period. Therefore,

these results are not presented in this paper.

DISCUSSION

Influence of infiltration zone on wall behavior

Figure 19 shows the magnitudes of increases in wall displacements and reinforcement forces




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after 12 days of water infiltration for all four cases. The wetting fronts in the low quality

compaction zone are 1.0, 3.2, 1.3 and 4.8m below the ground surface for Cases 1, 2, 3, and 4,

respectively. The depth of the wetting front for each case is shown for reference in each of

the figures (WF). It is clearly seen from Figs. 19 (a) and (b) that the displacements become

much more significant as the infiltration depth increases. As an example, when the wetting

front reached 1.3m below the ground surface (Case 3), a very small increase of the wall face

deflection (less than 2 mm) is observed. However, as the wetting front reached 3.2 m and

4.8m from the ground surface, the wall face deflections increased greatly, reaching maximum

values of 12mm and 24mm, respectively. The same trends are shown for the maximum

tension force in the reinforcement, as shown in Figs. 19(c).

Comparison with measured settlements

Although the simulation results did not show that the wall would fail under the conditions

used in this study, it was clearly seen that the behavior of the wall would be significantly

influenced by surface water infiltration, showing significantly increased magnitudes of

displacements and reinforcement tensions.

During the site investigation of the RTP wall failure previously described, a test pit

was dug behind a portion of the adjacent wall that had not failed. It was seen that the fill

behind the wall face had settled more than 102 mm at 1.6m above the wall base and 229 mm

at 3.5m above the wall base. It was also observed that some portion of the grid at the back

face of the block had been ruptured, and that the reinforcement was in a state of distress (Fig.

20). The measured settlements are far in excess of the predicted settlements for Case 4, which

provided the largest values among the cases investigated. The large settlement behind the

facing blocks would have caused an even more significant increase in the reinforcement

tension near the wall face; therefore, it could be a one of the possible factors that caused the

wall failure.

Based on analysis of the predicted results and observations made during the site

investigation, one could suggest that some of the possible factors that could have contributed

to the wall failure include:




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(1) Wetting zone

The wetting zone in the backfill (especially for the well compacted zone) due to

infiltration might be larger than that predicted from the simulation. The permeability of the

compacted soil may vary over several orders of magnitude depending on compaction

conditions. This implies rather large changes in permeability may accompany very small

changes in as-compacted water content (Mitchell et al., 1965). In addition, the field

permeability tends to be higher than that measured in the lab. Furthermore, if there is a weak

portion in the backfill where surface water infiltrates into the wall more easily (i.e. crack), the

wetting zone could be significantly deeper than predicted.

(2) Collapse potential

The collapse potential results for the backfill materials (Rorie, 2006) showed that the

magnitude of collapse increased significantly when the dry density of the material decreased

from 1.60 g/cm3 (used in the simulation) to 1.53 g/cm3. If the properties of more

compressible backfill were used as an input in the simulation, the results would show worse

wall performance.

(3) Lateral forces

Several types of lateral forces, which have not been simulated in the model, could have

been acting behind the wall face. For a low permeability soil, a perched water table could be

developed during the infiltration period (Cho and Lee, 2001). Positive pore water pressure is

then generated and could be applied behind the wall face. Also, some amount of radial

swelling could occur within the backfill behind the wall face during infiltration (Lawton et al.,

1991).

(4) Length of the geogrid embedded within the blocks

Another possible reason for the wall failure could be found in the embedded length of

reinforcement between the blocks. If the reinforcement was not embedded the full length of

block (as is called for in design), it could be pulled out from the blocks when the upper

portion of the wall moved out and the reinforcement was pulled down vertically due to the

settlement of the fill behind the wall face.




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It is also true that compaction of fill to below the intended the top-of-block elevations

could have contributed to some of the observed grid “sag.” And the actual wall failure could

have been associated with piping thru the wall face, although no evidence of this was seen in

adjacent areas.

CONCLUSIONS

A series of numerical analyses with unsaturated soil properties were performed in

order to better understand a 5.4 m high MSE wall in North Carolina that experienced a

localized collapse during a rainy season. As the end-of-construction material properties are

uncertain, the simulations are based on properties estimated from laboratory testing. As such,

the analyses are not presented as an exact representation of field conditions. From the results

of the numerical simulations presented, the following conclusions can be drawn:

1) The existence of a 1.6m-wide poorly-compacted zone behind the wall face in the analyses

performed significantly increased the wall displacements and reinforcement tensions at the

end of construction and during infiltration.

2) For an MSE wall constructed with backfill compacted very dry of optimum (and with 1.6

m wide poorly compacted zone behind the wall face), the results showed good wall

performance during wall construction, with small displacements and reinforcement tensions.

However, during the surface water infiltration, the results showed large increases in lateral

wall face, vertical soil deformation and reinforcement tensions. This behavior was caused by:

- Shear strength decrease: The backfill shear strength at the end construction was

predicted to have been very high (more than 90kPa) due to the high initial suction, but

decreased significantly when water infiltrated into the soils.

- Settlements behind the wall face: The settlements behind the wall induced high

tension in the grids at the back face of the blocks making up the wall face. Since the soil

compacted to a low density showed higher compressive behavior due to wetting, the wall

was shown to perform more poorly when an improperly compacted zone (low quality

compaction zone) existed behind the wall face.




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REFERENCES

ASTM Standard D698-00, 2000: Standard Test Methods for Laboratory Compaction

Characteristics of Using Standard Effort (12,400 ft-lbf/ft3(600 kN-m/m3)), Annual Book of

ASTM Standards, ASTM International, West Conshohocken, PA.

ASTM Standard D5298-03, 2003: Standard Test Method for Measurement of

Measurement of Soil Potential (Suction) Using Filter Paper, Annual Book of ASTM

Standards, ASTM International, West Conshohocken, PA.

ASTM Standard D5333-03, 2003: Standard Test Method for Measurement of

Collapse Potential of Soils, Annual Book of ASTM Standards, ASTM International, West

Conshohocken, PA.

ASTM Standard D6836-02, 2002: Standard Test Methods for Determination of the

Soil Water Characteristic Curve for desorption Using a Hanging Column, Pressure Extractor,

Chilled Mirror Hygrometer, and/or Centrifuge, Annual Book of ASTM Standards, ASTM

International, West Conshohocken, PA.

Cho, S. E., and Lee, S. R., 2001. Instability of unsaturated soil slope due to

infiltration, Computers and Geotechnics, Vol. 28, pp. 185-208.

Fredlund, D. G., and Rahardjo, H., 1993. Soil mechanics for unsaturated soils, New

York: Wiley

Fredlund, D. G., and Xing, A., 1994. Equations for the soil-water characteristic curve,

Canadian Geotechnical Journal, 31, pp. 521-532.

Hatami, K., and Bathurst, R. J., 2003. A calibrated FLAC model for geosynthetic

reinforced soil modular block walls at end of construction, FLAC and Numerical Modeling

in Geomechanics, pp. 223-231.

Hatami, K., and Bathurst, R. J., 2005. Development and verification of a numerical

model for the analysis of geosynthetic-reinforced soil segmental walls under working stress

conditions, Canadian Geotechnical Journal, 42, pp. 1066–1085.

Hatami, K., and Bathurst, R. J., 2006. Numerical model for reinforced soil segmental

walls under surcharge loading, Journal of Geotechnical and Geoenvironmental Engineering,

Vol.132, No.6, pp. 673-684.

Hilf, J. W., 1948. Estimating construction pore pressures in rolled earth dams, Pro.

2nd Int. Conf. Soil Mech. Found. Eng. Rotterdam, The Netherlands, vol. 3, pp. 234-240.




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Itasca consulting group., 2000. FLAC-Fast Lagrangian Analysis of Continua, Version 4.0,

Minnesota.

Kim, W. S., and Borden, R. H., 2011. Influence of soil type and stress state on

predicting shear strength of unsaturated soils using the soil-water characteristic curve,

Canadian Geotechnical Journal, 48, pp. 1886–1990.

Lawton, E. C., Fragaszy, R. J., and Hetherington, M. D., 1991. View of wetting-

induced collapse in compacted soil, Journal of Geotechnical Engineering, 118(9), pp. 1376-

1394.

Lee, W. F., 2000. Internal stability analysis of geosynthetic reinforced retaining walls,

Ph.D. dissertation, University of Washington, Seattle.

Mitchell, J. K., Hooper, D. R., and Campanella, R. G., 1965. Permeability of

compacted clay, Journal of Soil Mechanics and Foundations, ASCE, 91(4), pp. 41-65.

Ng, Charles, W. W., and Pang, Y. W., 2000. Influence of stress state soil-water

characteristics and slope stability, Journal of Geotechnical and Geoenvironmental

Engineering, Vol.126, No.2, pp. 593-622.

Noorany, I., Frydman, S., and Detournay, C., 1999. Prediction of soil slope

deformation due to wetting, FLAC and Numerical Modeling in Geomechanics, pp. 101-107

Rorie, D., 2006. Investigation of soil suction in a compacted low-plasticity clay. MS

thesis, North Carolina State University, Raleigh. 246 pp.

Rodrigues, R. A., and Vilar, O. M., 2006. Relationship between collapse and soil-

water retention curve of a sandy soil, Proceedings of the fourth international conference on

unsaturated soils, Geotechnical Special Publication No. 147, Vol.1, pp. 1025-1036.

van Genuchten, M. Th., 1980. A closed-form equation for predicting the hydraulic

conductivity of unsaturated soils, Soil Science Society of America Journal, 44, pp. 892-898.

Vanapalli, S. K., Fredlund, D. G., Pudahl, D. E., and Clifton, A. W., 1996. Model for

the prediction of shear strength with respect to soil suction, Canadian Geotechnical Journal,

33, pp. 379–392.

Yoo, C., and Jung, H., 2006. Case History of Geosynthetic Reinforced Segmental

Retaining Wall Failure, Journal of Geotechnical and Geoenvironmental Engineering, Vol.132,

No.12, pp. 1538-1548.




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Fig. 1 MSE wall geometry and numerical model used in FLAC

Fig. 2 Grain size distribution curve (after Rorie, 2006)

Fig. 3 Analysis algorithm flow chart

Fig. 4 SWCC fits for the entire suction range (after Rorie, 2006)

Fig. 5 Total cohesion intercepts with matric suction

Fig. 6 Determination of constitutive relation for undrained loading from drained loading

(after Fredlund and Rahardjo, 1993)

Fig. 7 Undrained modulus functions with respect to mean stress

Fig. 8 Coefficients of permeability with respect to matric suction

Fig. 9 Variation of (a) matric suction and (b) total cohesion for Case 2

Fig. 10 Measured collapse potentials (soils H and L) and the best fit functions (after Rorie,

2006)

Fig. 11 FLAC results at the end of construction for (a) Case 1 and (b) Case 2; where yy =

vertical stress, xx= lateral stress, ydisp = vertical displacement, and xdisp = lateral

displacement

Fig. 12 Profile of (a) lateral wall movement and vertical displacement within reinforced soil

mass at section I (Fig. 1), (b) tension force distributions at the end of construction

Fig. 13 Matric suction contours during surface water infiltration; (a) Case 2 and (b) Case 4

Fig. 14 Shear-induced deformation due to wetting for Case 2; (a) lateral displacement and (b)

vertical displacement

Fig. 15 Wetting-induced volumetric deformation for Case 2; (a) lateral displacement and (b)


Fig. 16 Variation of (a) “total” lateral wall movements, vertical displacements at Section I

and (b) “total” reinforcement tension along wall height for Case 2

Fig. 17 Variation of reinforcement tension during water infiltration for Case 2 (where B:

block, G: gravel Column, H: soil H, L: soil L)

Fig. 18 Variation of (a) Wall face lateral movements, Section I vertical displacements and (b)

Reinforcement tensions after the 12-days infiltration period for Case 4

Fig. 19 Increases of (a) wall face deflections (b) vertical displacements and (c) maximum

tension force, Tpeak, after 12-days infiltration period (all Cases)

Fig. 20 Condition of the grid behind the block

Figure Caption List




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Fig. 1 MSE wall geometry and numerical model used in FLAC

Fig 1.pdf

Accepted Manuscript Not Copyedited




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Fig. 2 Grain size distribution curve

0

10

20

30

40

50

60

70

80

90

100

0.0010.010.1110100

particle diameter,d (mm)

% P

assi

ng

Fig 2.pdf





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Fig. 3 Analysis algorithm flow chart

Fig 3.pdf





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Fig. 4 SWCC fits for the entire suction range

Fig 4.pdf





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Fig. 5 Total cohesion intercepts with matric suction

0

30

60

90

120

150

0 200 400 600 800 1000Matric suction (kPa)

Tota

l coh

esio

n, c

(kP

a)

soil L ( c' = 0 kPa, ' =26° )

d = 1.60 g/cm3, w = 4.8 %

soil H ( c' = 3 kPa, ' =30° )

d = 1.79 g/cm3, w = 4.8 %

Fig 5.pdf





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Fig. 6 Determination of constitutive relation for undraind loading from drained loading

Fig 6.pdf





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Fig. 7 Undrained modulus functions with respect to mean stress

02

468

10

121416

1820

0 20 40 60 80 100Mean stress, m (kPa)

Ela

stic

mod

ulus

, E (M

Pa)

Emin = 4.1 MPa

Emin = 1.2 MPa

soil H

d = 1.79 g/cm3

w = 4.8 %

soil L

d = 1.60 g/cm3

w = 4.8 %

Fig 7.pdf





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Fig. 8 Coefficients of permeability with respect to matric suction

1.E-11

1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

0.1 1 10 100 1000Matric suction (kPa)

Coe

ffici

ent o

f per

mea

bilit

y (c

m/s

ec)

Soil H ( ksat = 3.62 x10-6 cm/sec )

d = 1.78 g/cm3

Soil L ( ksat = 7.75 x10-5 cm/sec )

d = 1.60 g/cm3

Fig 8.pdf





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Fig. 9 Variation of (a) matric suction and (b) total cohesion for Case 2

0

1

2

3

4

5

6

0 200 400 600 800 1000Matric suction (kPa)

Pos

ition

abov

e ba

se o

f wal

l (m

)

day 0day 3day 6day 9day 12

T.O.W

(a)

0

1

2

3

4

5

6

0 20 40 60 80 100 120Total cohesion (kPa)

Posi

tion

abov

e ba

se o

f wal

l (m

)


T.O.W

(b)

Fig 9.pdf





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Fig. 10 Measured collapse potentials (soils H and L) and the best fit functions

-0.08

-0.06

-0.04

-0.02

0

0.02

1 10 100 1000

Overburden pressure (kPa)

Ver

tical

stra

n (×

100,

%)

Soil H

d = 1.78 g/cm3

Soil L

d = 1.60 g/cm3

Swell

Collapse

Fig 10.pdf





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Fig. 11 FLAC results at the end of construction for (a) Case 1 and (b) Case 2; where yy =

vertical stress, xx= lateral stress, ydisp = vertical displacement, and xdisp = lateral displacement

Fig 11.pdf





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Fig. 12 Profile of (a) lateral wall movement and vertical displacement within reinforced soil

mass at section I (Fig. 1), (b) tension force distributions at the end of construction

0

1

2

3

4

5

6

0204060Displacement (mm)

Pos

ition

abo

ve b

ase

of w

all

(m)

Case 1

Case 2

T.O.W

Wall face

Vertical

(a)

0

1

2

3

4

5

6

01234Maximum tension force,Tpeak (kN/m)

Pos

ition

abov

e ba

se o

f wal

l (m

) Case 1Case 2

T.O.W(b)

Fig 12.pdf





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Fig. 13 Matric suction contours during surface water infiltration; (a) Case 2 and (b) Case 4

Fig 13.pdf





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Fig. 14 Shear-induced deformation due to wetting for Case 2; (a) lateral displacement and (b)


Fig 14.pdf





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Fig. 15 Wetting-induced volumetric deformation: (a) lateral displacement and (b) vertical

displacement for Case 2

Fig 15.pdf





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Fig. 16 Variation of (a) “total” lateral wall movements, vertical displacements at Section I and (b)

“total” reinforcement tension along wall height for Case 2

0

1

2

3

4

5

6


Pos

ition

abov

e ba

se o

f wal

l (m

)


Vertical

Wall face

T.O.W(a)

0

1

2

3

4

5

6


Posi

tion

abov

e ba

se o

f wal

l (m

)


T.O.W

(b)

Fig 16.pdf





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0.01.02.03.04.05.06.0

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5Distance from wall face (m)

Axi

al fo

rce

(kN

/m)

day 0 day 3day 6 day 9day 12

Layer 11

0.01.02.03.04.05.06.0


Axi

al fo

rce

(kN

/m)


Layer 10

0.01.02.03.04.05.06.0


Axi

al fo

rce

(kN

/m)


Layer 9

0.01.02.03.04.05.06.0


Axi

al fo

rce

(kN

/m)


Layer 8

Fig. 17 Variation of reinforcement tension during water infiltration for Case 2 (where B:

block, G: gravel Column, H: soil H, L: soil L)

B G HL

Fig 17.pdf





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Fig. 18 Variation of (a) Wall face lateral movements, Section I vertical displacements and (b)

Reinforcement tensions after the 12-days infiltration period for Case 4

0

1

2

3

4

5

6


Posi

tion

abov

e ba

se o

f wal

l (m

)

day 0day 12 (Case 2)

day 12 (Case 4)

Wall faceVertical

T.O.W(a)

0

1

2

3

4

5

6


Posi

tion

abov

e ba

se o

f wal

l (m

)

day 0day 12 (Case 2)day 12 (Case 4)

T.O.W(b)

Fig 18.pdf





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Fig. 19 Increases of (a) wall face deflections (b) vertical displacements and (c) maximum tension

force, Tpeak, after 12-days infiltration period (all Cases)

0

1

2

3

4

5

6

0102030Wetting-induced wall face deflection (mm)

Posi

tion

abov

e ba

se o

f wal

l (m

)Case 2

Case 4Case 1

Case 3T.O.W

W.F

W.F

W.FW.F

(a)0

1

2

3

4

5

6

020406080Wetting-induced vertical displcement (mm)

Pos

ition

abov

e ba

se o

f wal

l (m

)

T.O.WCase 4

Case 2Case 3

Case 1

W.F

W.F

W.FW.F

(b)0

1

2

3

4

5

6

0246Wetting-induced tension force, Tpeak (kN/m)

Pos

ition

abo

ve b

ase

of w

all

(m) T.O.W

Case 4Case 2

Case 3 Case 1

W.F

W.F

W.FW.F

(c)

Fig 19.pdf





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Fig. 20 Condition of the grid behind the block

Fig 20.pdf





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Table 1 Input properties (plane strain properties) for gravel column (extracted from Lee,

2000)

Properties ValuesPlane strain friction angle ( ) 55°

Dilation angle ( ) 20°Modulus number, K 4000

Failure ratio, Rf 0.73Modulus exponent, n 0.5

Table 2 Summary of reinforcement input properties

Reinforcement Input properties Within blocks Within backfills

E (kN/m2) 84 84Yield (kN) 35 35

ycomp (kN) 0.01 0.01kbond (kN/m/m) 110.5× (normal stress)+3302 -

sbond (kN/m/m) 6.8 (if normal stress < 34.3 kPa)28 (if normal stress >= 34.3 kPa) -

sfric (degree)20.5(if normal stress < 34.3 kPa)

48.7(if normal stress >= 34.3 kPa) -

Table 3 Summary of interface input properties

Interface input properties Block-Block Block-Soilkn (kN/m/m) 10.95×107 1×106

ks (kN/m/m) 8500 8500fric (degrees) 55° 55°

coh 0 0

Table 4 Cases used for numerical simulations

(1.6m wide zone) (Beyond 1.6m) PermeabilityCase 1 Soil H Soil H ksat*Case 2 Soil L Soil H ksat

Case 3 Soil H Soil H 2 times ksat

Case 4 Soil L Soil H 2 times ksat

* ksat = saturated permeability obtained from laboratory tests

Acc

epte

d M

anus

crip

t N

ot C

opye

dite

d




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Documents

Numerical Simulation of MSE Wall Behavior Induced by Surface-Water Infiltration