A new method for remediation of sandy slopes susceptible to seepage flow using EPS-block geofoam

Bartlettc, David Arellanod a Department of Civil Engineering, Okan University, Tuzla Campus, Istanbul 34959, Turkey b Department of Biosystems and Agricultural Engineering, Oklahoma Stat

A new method for remediation of sandy slopes susceptible to seepage

flow using EPS-block geofoam

A Tolga Özera,*, Onur Akaya, Garey A Foxb, Steven F Bartlettc, David Arellanod

a Department of Civil Engineering, Okan University, Tuzla Campus, Istanbul 34959, Turkey

b Department of Biosystems and Agricultural Engineering, Oklahoma State University, 120 Ag Hall Stillwater, OK 74078-6016, USA

c Department of Civil and Environmental Engineering, University of Utah, 110 Central Campus Dr., Salt Lake City, UT 84112, USA

d Department of Civil Engineering, The University of Memphis, 104 Engineering Science Building, Memphis, TN 38152-3180, USA

a r t i c l e i n f o

Article history:

Received 31 July 2013

Received in revised form

5 December 2013

Accepted 24 January 2014

Available online 4 March 2014

Keywords:

EPS-block geofoam

Slope stability

Slope remediation

Hydrostatic sliding

Seepage

a b s t r a c t Using expanded polystyrene (EPS) geofoam (geofoam block) in slope remediation projects has drawn interest from the civil engineering sector for its ease of application and budget saving features According

to design precedence, all slope remediation applications that use geofoam blocks should incorporate permanent drainage systems to prevent instability of the lightweight geofoam blocks due to hydrostatic and seepage pressures In this study, a new method for slope remediation using geofoam blocks was tested through physical laboratory experiments For this purpose, a total of 24 lysimeter (dimensions of

60 cm height, 20 cm width, and 200 cm length) experiments (including duplicates) were conducted in which seepage through a geofoam block slope system were generated with three different constant water levels in the water reservoir of the lysimeter Geofoam blocks (dimensions of 2.5 cm height, 5 cm width, and 15 cm length) were assembled to form embankment type configuration at the toe section of the sandy slopes This study also included coupled numerical model simulations that were comprised of variably saturatedflow modeling and slope stability modeling which could be implemented successfully for the global static failure analysis of the geofoam block slope system comprised of two mediums with different geotechnical characteristics In addition to global static stability failure analysis, which involved conventional limit equilibrium analysis for the geofoam block slope system, hydrostatic sliding mech-anism was investigated which provided insight into using an overburden concept to increase the resistance against horizontal driving forces Experimental and numerical modeling results showed that the geofoam block slope system was stable even though the phreatic surface was above the bottom of the geofoam block assemblage For this reason, the embankment type configuration tested in this study can

be considered a viable remediation technique where seepage induced deep-seated global stability and hydrostatic sliding failures are a concern

Ó 2014 Elsevier Ltd All rights reserved

1 Introduction

There are several factors that can trigger slopes to fail Steep

slopes, low strength slope materials, weak foundation conditions,

and earthquakes are major factors affecting slope instability

Seepage is another primary cause of slope instability for both

manmade and natural slopes (Fox and Wilson, 2010) Leaky pipes,

irrigation, snowmelt, thawing ice lenses, runoff from uphill sources,

the clogging of a drain, or shutting off a near-surface well might

produce mounding of the phreatic surface within the slope above

its steady-state position (Schmertmann, 2006) When this

infiltrated water enters a slope faster than the excess pore-water pressures can dissipate, stability will be significantly reduced Pore-water pressure accretion is the most prevalent of failures on natural hillslopes (Sidle and Ochiai, 2006)

The cause and nature of a slope failure must be understood before designing slope remediation systems (Duncan and Wright,

2005).Fay et al (2012)listed the essential elements of slope sta-bilization as proper planning and site investigation, understanding the soil, and knowing the surface and subsurface water conditions Since every slope repair project has unique causes, numerous types

of remediation techniques have been developed (Dronamraju, 2008; Shah, 2008; Fay et al., 2012) These remediation techniques can be categorized in four different groups: mechanical stabiliza-tion techniques, earthwork techniques, erosion control techniques, and bioengineering techniques (Fay et al., 2012)

* Corresponding author Tel.: þ90 216 6771630x1978; fax: þ90 216 6771486.

E-mail addresses: tolga.ozer@okan.edu.tr (A.T Özer), onur.akay@okan.edu.tr

(O Akay), garey.fox@okstate.edu (G.A Fox), bartlett@civil.utah.edu (S.F Bartlett),

darellan@memphis.edu (D Arellano).

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Geotextiles and Geomembranes

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Geotextiles and Geomembranes 42 (2014) 166e180

In addition to these listed slope stabilization categories,

reducing the driving force is a viable alternative (Elragi, 2000)

However, since the resisting forces along the failure surface are also

dependent on the weight of the slope (resisting forces are

pro-portional to normal stresses), the factor of safety against global

stability failures (instability along rotational failure surfaces) can

only be increased if the reduction of the driving forces is greater

than the reduction in the resisting forces In order to reduce the

driving forces in slopes, engineers have used several lightweightfill

solutions (e.g., pumice, shredded tires, expanded polystyrene (EPS)

geofoam (geofoam block), and tyre bales) Among these lightweight

fill materials, a geofoam block has high strength to density ratio

(Elragi, 2000; Stark et al., 2004) Due to this property, durability and

ease of installation in thefield, geofoam block has been gaining

popularity since it wasfirst used as a lightweight embankment fill

by Norwegian Public Roads Authorities in 1972 (Aabøe, 2011)

In addition to its application as a lightweight embankmentfills

for roadways, geofoam blocks were used for slope stabilization

projects in Japan largely in the mid-1980’s to the mid-1990’s

(Tsukamoto, 1996) Geofoam blocks have been used byReuter and

Rutz (2000), Reuter (2001), Mann and Stark (2007) in slope

remediation projects in United States Even though geofoam blocks

have experienced wide-spread use in slope stabilization and

rehabilitation projects, there were no formal design guidelines or

procedures until 2011.Arellano et al (2011)developed a design

guideline, which was funded by the National Cooperative Highway

Research Program (NCHRP), to use geofoam blocks for slope

sta-bilization and repair projects In this design guideline, Arellano

et al (2011)presented design procedure algorithms which were

based on conceptual failure modes This design guideline is based

on the recommendation that all geofoam block slope systems

incorporate a drainage system since many of the geofoam block

slope case histories evaluated as part of the NCHRP 24-11(02)

research included use of underdrain systems below geofoam blocks

to prevent water from accumulating above the bottom of the

geofoam block assemblage Also, in some cases, drainage systems

were incorporated between the adjacent upper slope material and

geofoam blocks to collect and divert seepage water and thereby

alleviate seepage pressures

Even though the design procedure recommends permanent

drainage systems, the groundwater table may rise in the long-term

due to clogging of the drainage pipe as a result of improper design

and/or poor construction in thefield As a result, the groundwater

table may rise above the bottom of the geofoam blocks which may

cause global stability failure of the slope and/or hydrostatic sliding

failure of geofoam block assemblage The behavior of geofoam

block slope systems for remediation of sandy slopes with seepage

wasfirst studied byAkay et al (2012, 2013)using scaled physical

slope experiments for marginally stable sand slopes Based on an

extensive laboratory testing program,Akay et al (2013)concluded

that in comparison with the results obtained from the

non-remediated slope (“Matrix” configuration), the geofoam block

configurations (“One Row” and “One Row Partial Bottom”) could be

considered as a viable alternative remediation technique for

shallow-seated failures; however, they seemed to be ineffective to

prevent deep-seated global stability failures of a marginally stable

steep sandy slope under seepage Therefore, Akay et al (2013)

recommended that various geofoam block configurations be

investigated to evaluate the use of geofoam block for remediation

of sandy slopes that experience deep-seated global stability failures

under seepage

The overall objective of this study was to evaluate a geofoam

block configuration in order to remediate a 1:1 sandy slope with a

deep-seated slip surface with seepage In general, geosynthetic

reinforcements are used to remediate/construct 1:1 or even steeper

sandy slopes (Benjamim et al., 2007; Portelinha et al., 2013) In this study, the possible use of geofoam blocks as a remedial geo-synthetic alternative for steep sandy slopes subjected to seepage was investigated For this purpose, a small scale (1:20) laboratory, physical-slope modeling techniques (1-g model test) were utilized This laboratory method has been successfully performed to model not only the behavior of geofoam block slope systems with seepage forces (Akay et al., 2012, 2013), but also to model various geotechnical systems such as stone columns (Deb et al., 2011), geogrid reinforced foundations (Latha and Somwanshi, 2009), footing on geogrid reinforced clay slope (El Sawwaf, 2007a), geo-grid and geotextile reinforced sand slopes (Lee and Manjunath, 2000; Yoo, 2001), geogrid reinforced flyash slope (Choudhary

et al., 2010), horizontal anchor plates (El Sawwaf, 2007b), and geocell reinforced foundations (Dash et al., 2003) When compared

to thefield prototype, the main drawback of the 1-g small scale laboratory model is the differences in the stress levels between the 1-g model andfield prototype (Akay et al., 2013; Choudhary et al., 2010; Latha and Somwanshi, 2009) However, the results of this research are relevant to revealing insights of using the proposed geofoam block configuration for remediation of sandy slopes sus-ceptible to seepage forces at 1:20 scale

This study also included numerical model simulations that were comprised of variably saturatedflow modeling and slope stability modeling The model results were utilized in the determination of the factor of safety against prevailing failure mechanisms observed during laboratory lysimeter experiments Therefore, the factor of safety against global stability failure (FSGL) of the slope and the factor of safety against hydrostatic sliding of the geofoam block assemblage along the interface of the bedding level and the bottom

of the embankment (FSSL) were calculated for the quantification of the performance of the geofoam block configuration

2 Materials and methods 2.1 Laboratory lysimeter studies

A total of 24 lysimeter experiments (including duplicates) were performed in this study FollowingFox et al (2006),Wilson et al (2007), andAkay et al (2013), the lysimeter was constructed us-ing 1-cm-thick Plexiglas and had the dimensions of 200 cm length,

20 cm width, and 60 cm height (Fig 1a) In addition to the soil compartment, the lysimeter had a water reservoir located at one end that generated the necessary hydraulic gradient for seepage to occur through the constructed slope The constant water level in the reservoir was adjusted to be higher than the base of the slope (25 cm, 38 cm, and 50 cm water pressure head) A stainless steel mesh having an opening size of 0.063 mm (equivalent to No 230 sieve size) and a perforated 1-cm-thick Plexiglas plate with 8-mm-diameter holes was placed between the reservoir and the soil compartment of the lysimeter The back-slope was uniformly compacted into the soil compartment of the lysimeter in 2.5 cm lifts

to obtain a homogeneous domain with a dry density of 14 kN/m3 The constructed slope had a side-hill with a 45angle (1:1 hori-zontal:vertical) In order to mimic field conditions in which the failed mass of the slope displaced at the toe provides resistance to subsequent failures, the slope was packed only to a length of

100 cm The slope height and width was 55 cm and 20 cm, respectively (Fig 1a)

Data collection during an experiment included the pore-water pressures (h) developed inside the slope that were measured by

22 pencil-size tensiometers (Soil Measurement Systems, Tucson,

AZ, USA) which were found to be successful at monitoring water pressure dynamics during previous soil column and lysimeter studies (Akay and Fox, 2007; Akay et al., 2013) The numbering and

the coordinates of the tensiometers with respect to the toe of the

slope are given in Fig 1b Bi-directional pressure transducers

(ASDXRRX005PDAA5, Honeywell Sensing and Control, Golden

Valley, MN, USA) were attached to the tensiometers to transmit

pore-water pressure heads to datalogger (CR1000 w/multiplexer,

Campbell Scientific, Logan, UT) in the range from 345 cm-H2O

toþ345 cm-H2O (5 psi) at 10 s intervals In addition, cumulative

discharge measurements of the seepageflow were recorded by a

digital scale located at the outlet section of the lysimeter Specific

time measurements were recorded during an experiment which

included the“time of seepage” (elapsed time from the start of an

experiment to seepage initiation at the slope face),“time of final

failure” (the time the slope becomes stable because of the failed soil

resistance at the toe), and“end of the experiment”

The soil used in the construction of the slope was selected to be

similar to that of sand used by Akay et al (2013) Geotechnical

properties of soil used in this study are given inTable 1 Particle size

distribution (ASTM D 6913, 2009), specific gravity (ASTM D 854,

2010), and triaxial shear strength (ASTM D 4767, 2011) tests were

conducted on randomly selected undisturbed core samples (20-cm

long, 7.26-cm diameter) extracted from the compacted slope after

completion of the experiments Similarly, the hydraulic properties

of the soil were determined from nine undisturbed core samples on

which constant head permeability (ASTM D 2434, 2006) tests were

conducted that resulted in an average saturated hydraulic

con-ductivity, Ksat, of 0.0295 cm/s (standard deviation,s¼ 0.0035 cm/s)

The average dry density of the core samples was equal to 13.93 kN/

m3(s¼ 0.11 kN/m3)

Retention characteristics of the soil were determined by

col-lecting pore-water pressure and water content pairs using

undis-turbed core samples (6.4-cm long, 7.26-cm diameter) following the

procedure given by Akay et al (2013) In this study, three core

samples were extracted for this purpose which resulted in a total of

147 pairs including the data from Akay et al (2013) The van Genuchten-Mualem model (van Genuchten, 1980) was used to represent the retention curvefitted by the RETC (RETention Curve) computer code (van Genuchten et al., 1991):

qðhÞ ¼

8

<

:

qrþ qs qr

½1þjaj n

m h< 0

9

=

Fig 1 (a) Laboratory setup included lysimeter, tensiometer, pressure transducer, and datalogger; (b) Location of tensiometers installed on one side of the lysimeter with coordinates (x, y) referenced to the toe of the slope (0, 0).

Table 1 Material properties of soil and geofoam blocks used in the laboratory lysimeter experiments.

Material: sand Classification Unified soil classification system SP Particle size distribution Sand (%), Silt þ Clay (%) 98.0, 2.0

Angle of internal friction f0 (degrees) 33.7

Material: EPS-block geofoam

Corrected initial Young modulus E (MPa) 4.2e4.8

A.T Özer et al / Geotextiles and Geomembranes 42 (2014) 166e180 168

KðhÞ ¼ KsatSl

e

h

m ¼ 1 1

where h is the pore-water pressure head [L];qsis the saturated

water content;qris the residual water content;a[L1] is the

in-verse of the air-entry pressure (bubbling pressure); n is the

pore-size distribution index; l is the pore-connectivity parameter

(taken as 0.5); and S ¼ (qq)/(q q) is the effective saturation

Based on the curvefit (R2¼ 0.92), the van Genuchten parameters

of the soil were: qs ¼ 0.45, qr ¼ 0.0, a ¼ 0.0928 cm1, and

n¼ 2.3579

While the soil was compacted to construct the back-slope, geofoam blocks were placed in a certain configuration as a lightweight remediation material (dry unit weight¼ 0.2 kN/m3)

at the toe of the slope The compressive resistance of geofoam block was determined using a series of three standard 50-mm cube samples according to ASTM D1621 (2010) The geofoam block strength parameters used in this study are summarized in

Table 1

Fig 2 Embankment type configuration with four different heights of geofoam block assemblages: (a) 10 cm, (b) 15 cm, (c) 22.5 cm, and (d) 30 cm.

2.2 Geofoam block configuration

As stated earlier, the configurations tested byAkay et al (2013)

were ineffective to remediate deep-seated failures For this reason,

the new configuration was expected to withstand earth and

hy-drostatic pressures exerted by the backslope in order to remediate

the slope (FSGL> 1.0 and FSSL> 1.0) However, due to their

light-weight nature, geofoam blocks are vulnerable against hydrostatic

sliding.Stark et al (2004)summarized remedial procedures to

in-crease factor of safety against hydrostatic sliding and overturning

under four main categories for geofoam block embankments: use

separation material between EPS blocks and foundation soil which

can provide higher interface friction angle then EPS/foundation soil,

increase overburden stress on EPS blocks (i.e heavier pavements),

implement a drainage system, or use anchorage system to keep the

blocks intact Using a separation layer to increase the interface

shear resistance along the geofoam blocksefoundation interface

and implementing anchorage plates can bring additional cost to the

projects In addition, the use of anchorage system is not a typical

field application Therefore, the overburden concept was

imple-mented to design a configuration that can resist hydrostatic forces

that can occur if the subsurface drainage system malfunctions

In order to account for the previously mentioned overburden

concept to resist hydrostatic forces, embankment type con

figura-tion was implemented for remediafigura-tion of marginally stable steep

sandy slopes in which geofoam blocks were placed at the toe of the

compacted sandy slope (Fig 2) As shown in Fig 2, compacted

sandy slope applies overburden along the portion of the geofoam

block assemblage which remains inside the slope Geofoam block

assemblages were rested on the 2.5 cm thick bedding level (Fig 2)

Geofoam blocks used in the lysimeter tests were: 2.5-cm high, 5-cm

wide, and 15-cm long These dimensions were selected to ensure

1:20 scale of geofoam block which relates to a common

manufac-tured size As shown in the previous study byAkay et al (2013),

final failure surface entered at the face of the initial 1:1 slope

(shallow-seated failure) for the 25 cm-H2O boundary condition,

whereas final failure surface entered at the crest (deep-seated

failure) for the 38 cm-H2O and 50 cm-H2O boundary conditions for

the“Matrix” configuration They concluded that that replacement

of the soil mass that is typically dislodged during a shallow-seated

failure with the lightweight geofoam blocks, could remediate the

slope However, it seemed to be ineffective to prevent

“deep-seated” failures For this reason, embankment type configuration

with four different heights (10 cm, 15 cm, 22.5 cm, and 30 cm) of

geofoam block assemblages were tested against three different

constant water levels in the reservoir to quantify the effect of the

overburden stress on both FSGLand FSSL All of the 24 lysimeter

experiments (including duplicates) were conducted in 2012, and

the complete list can be found inTable 2 The title of an experiment

included the geofoam block assemblage, constant water head level

at the reservoir, and the date (ddmm), respectively

2.3 Numerical model simulations

Numerical model simulations involved variably saturatedflow

modeling coupled with slope stability modeling for each geofoam

block assemblage Thefirst step in variable saturated flow modeling

included a calibration process to match the cumulative seepage

discharge computed by the variably saturatedflow modeling to the

cumulative seepage discharge recorded at the outlet section of the

lysimeter during laboratory experiments This was achieved by the

inverse estimation of saturated hydraulic conductivity, Ksat, a

pre-vailing soil parameter affecting the time of seepage and magnitude

of the seepage discharge (Akay et al., 2008) HYDRUS, a

finite-element computer model which solves the Richards equation for

saturated-unsaturated waterflow (Simunek et al., 2012), was used

To access the predictive ability of the calibration model of HYDRUS, NasheSutcliffe model efficiency coefficient (NS) was calculated, where a value of 1 indicates a perfect match between modeled and observed discharge:

NS ¼ 1 

2

6Pni¼1



Yobs

i  Ysim i

2

Pn

i¼1



Yobs

i  Ymean2

3

where Yobs

i is the ith observed cumulative discharge, Ysim

i is the ith simulated cumulative discharge, and Ymeanis the mean of observed cumulative discharge

Once the observed hydrological response of the laboratory lysimeter experiments matched the simulated response of the numerical models after calibration of Ksat, the next step included a coupled analysis of variable saturated flow modeling and slope stability modeling by using SEEP/W, afinite-element model solving Richards equation for two-dimensional variably saturated flow (Geo-Slope International, 2012a) and SLOPE/W, a conventional limit equilibrium analysis to determine slope stability (Geo-Slope International, 2012b), respectively

The initial pressure head conditions needed for the start of the numerical models were obtained from the tensiometer-pressure transducer-datalogger setup used during the laboratory lysimeter experiments Instead of prescribing 22 different pressure heads at tensiometer locations, a single averaged value was input as an initial condition for the entire computational domain since the variance between recordings were minimal at the start of the lab-oratory lysimeter experiments (initial water content of the soil was constant during compaction of the slope)

The boundary condition of the computational domain was prescribed as“hydrostatic pressure head boundary” for the inlet boundary simulating the water reservoir of the laboratory lysim-eter The prescribed pressure heads referenced to the base of the slope were 25 cm-H2O, 38 cm-H2O, and 50 cm-H2O, respectively A

“seepage face boundary” condition was prescribed to the outlet boundary simulating the exfiltration from the 45hill-side of the

compacted slope A no-flux boundary was selected for the bottom

of the computational domain to simulate the impervious base of the lysimeter Numerical simulations were terminated at times equal to the end of the laboratory lysimeter experiments

The Spencer method (Spencer, 1967), a limit equilibrium model, was utilized during slope stability analysis by SLOPE/W to estimate

FSGL Evaluation of geofoam block slope systems by using conven-tional limit equilibrium analysis required assigning appropriate strength parameters not only to soil but also to geofoam blocks

Table 2 List of the laboratory lysimeter tests including “Matrix a ” and “Embankment” type configuration.

Configuration Height of geofoam

block assemblage

Constant water head level

a “Matrix” configuration refers to a non-remediated slope that no geofoam blocks placed at the toe ( Akay et al., 2013 ).

A.T Özer et al / Geotextiles and Geomembranes 42 (2014) 166e180 170

FollowingAkay et al (2013), both cohesion and internal friction

angle was defined for the geofoam blocks, where a cohesion value

equal to one-quarter of the compressive strength of the geofoam

used in this study (Table 1) The dry unit weight of geofoam blocks

was 0.2 kN/m3 However, during design of geofoam block slope

systems, potential weight gain from long-term water absorption is

taken into account While an increase in the unit weight due to

water absorption increases the driving forces, it also increases the

resisting forces since normal stresses along the failure surface

in-creases In order to discern which unit weight value is more

con-servative, stability analysis should be performed using both the dry

unit weight and water absorbed unit weight (Arellano et al., 2011)

For this reason, this study used the water absorbed value of 1.0 kN/

m3as suggested byStark et al (2004), which generated lower FSGL

during stability analysis

2.4 Hydrostatic sliding

Lightweight geofoam blocks are mainly used in slope

remedia-tion works to reduce the driving forces that cause global stability

failure However, seepage flow may trigger hydrostatic sliding

failure of the geofoam block assemblage since the resisting force, a

function of normal stress, is reduced by the lightweight geofoam

blocks For this reason, stability analyses have not only been

per-formed against global stability but also against hydrostatic sliding

failures Hydrostatic sliding mechanisms werefirst considered for

stand-alone geofoam block embankments byStark et al (2004)

along the interface of bedding level and bottom of the

embank-ment as a part of external stability analysis In this study, analysis of

horizontal sliding of the geofoam block slope system at the

inter-face between the bottom of the geofoam block embankment and

the underlying foundation soil was conducted For this purpose,

coupled seepage and stress modeling were performed to calculate

total horizontal driving forces and total resisting forces acting on

the geofoam block embankment to calculate FSSLas follows:

FSSL ¼

P

Horizontal Resisting Forces

P

Horizontal resisting and driving forces along with vertical forces

acting on the geofoam block configuration are shown inFig 3 Total

resisting force against hydrostatic sliding is comprised of only the

shear resistance along the EPS/foundation soil interface (FF):

X

where cais the interface cohesion along the EPS/foundation soils, A

is the area resisting horizontal sliding,SN is the total normal forces

acting along the interface, WEPSis the weight of the geofoam block

assemblage, FT,Vis the total vertical earth force (comprised of

ver-tical hydrostatic and verver-tical effective earth pressures), anddis the

interface friction angle between the geofoam blocks and the

foundation soil

The total horizontal driving force is the summation of the

effective horizontal earth force (FE,H), and horizontal component of

the hydrostatic force (FH,H) As a result, by neglecting the weight of

the geofoam blocks, FSSLcan be defined as:

FSSL ¼ caAþ FT;Vtand

After evaluating the EPS/sand interface test results reported by

Jutkofsky (1998), Bartlett et al (2000), andJutkofsky et al (2000),

Stark et al (2004) recommended an EPS/sand interface friction angle,d, of 30to use in design.Xenaki and Athanasopoulos (2001)

performed a series of direct shear tests to determinedof the EPS/ sand interface and discussed the effects of geofoam block density, the mean grain size, void ratio and grain shapes of sand particles on the test results They concluded that the failure envelope at the EPS/ sand interface is a non-linear curve, and may be approximated by a piecewise linear curve Under low normal stress range (0e35 kPa) a

dvalue of 32for geofoam blocks with a density of 20 kg/m3were recommended Within this low normal stress range,dis approxi-mately equal to the friction angle of the sand and the apparent interface adhesion, ca, is zero.Xenaki and Athanasopoulos (2001)

indicated that by increasing normal stress acting at the interface, the interaction behavior becomes progressively adhesional; therefore, while the value ofddecreases, the value of caincreases until it becomes equal to the shear resistance of geofoam block Based on the interface shear testing results reported in the litera-ture, and considering the stress ranges acting on the geofoam blocks in the lysimeter, adof 30and caof 0 kPa were selected to use for the calculation of FSSLas follows:

FSSL ¼ FT;Vtan 30

In order to calculate the forces in the above equation, coupled seepage and stress modeling were performed using SEEP/W and SIGMA/W SIGMA/W is a stress-deformation computer program which includes six different analysis types: in-situ, stress redistri-bution, load/deformation, coupled stress-pore pressure, volume change, and dynamic deformation analysis (Geo-Slope International, 2009) As shown in the free body diagram (Fig 3), both the resisting and the driving forces due to earth and hydro-static pressure acting on geofoam blocks are related with the gravity (self weight) of the variably saturated sand In-situ analysis (gravity turn-on analysis) converts the weight of the soil into stresses (Geo-Slope International, 2005) In-situ analysis uses the unit weight which simulates the effect of gravity, and Poisson’s ratioðyÞ which simulates the earth pressure at rest ðKo ¼y=1 yÞ In-situ analysis ignores stiffness related parameters (Geo-Slope International, 2012a,b) since there is no need to calculate strains

at this stage Poisson’s ratios used to calculate Koin the models for both sand and geofoam block are presented inTable 1 Once the stress distributions acting on the geofoam block assemblage were obtained for both horizontal and vertical directions, the related forces were calculated as the total areas of these distributions

Fig 3 Free-body diagram of geofoam block embankment located at the toe of the slope indicating the prevailing forces taken into account during the calculation of the Factor of Safety against sliding (FS SL ).

3 Results and discussion

3.1 Model calibration

Inverse estimation of Ksat required the use of cumulative

seepage discharge measurements recorded during laboratory

lysimeter experiments However, not all experiments were eligible

for calibration due to change in their physical condition during the

experiment While the physical condition of the geofoam block

slope system may change due to global failure and/or hydrostatic

sliding during laboratory lysimeter experiments, the computational

domain of the HYDRUS calibration model remains unchanged

(time-invariant mesh structure) during simulations For this reason,

model calibration involved experiments with 25 cm-H2O constant

pressure head boundary condition during which the physical

con-dition of the constructed slope remained unchanged as shown in

the upcoming sections Moreover, since the sediment entrainment

by the seepageflow was negligible for these experiments, direct

conversion of digital scale weight measurements to seepage

cu-mulative discharge (volumes of water) was possible

The calibration routine of HYDRUS iteratively improved the initial estimation of the Ksat to match the simulated cumulative seepage discharge to the laboratory measured cumulative seepage discharge For each calibration model, laboratory measured value of 0.0295 cm/s (average of nine samples) was used as the initial es-timate of the Ksat The calibrated Ksathas a value of 0.02647 cm/s, 0.04510 cm/s, 0.04791 cm/s, and 0.04398 cm/s for geofoam block assemblages “10 cm Embankment”, “15 cm Embankment”,

“22.5 cm Embankment”, and “30 cm Embankment”, respectively These calibrated values of Ksatwere utilized by the coupled analysis

of SEEP/W and SLOPE/W Using the calibrated values of Ksat, the numerical model revealed an acceptable level of performance for the prediction of the cumulative discharge with high values of NS (NS 0.94) for all selected experiments

3.2 Geofoam block assemblage: 10 cm embankment The physical conditions formed at the end of the duplicate ex-periments of the“10 cm Embankment” geofoam block assemblage are given in Fig 4 As in the case of “Matrix” configuration

Fig 4 Slope physical conditions and hypothesized failure surfaces at the end of the duplicate experiments of “10 cm Embankment” assemblage under (a) 25 cm-, (b) 38 cm-, and (c)

50 cm-H 2 O pressure head boundary conditions (d) Representative failure surfaces for each boundary condition.

A.T Özer et al / Geotextiles and Geomembranes 42 (2014) 166e180 172

experiments byAkay et al (2013), the experiments were

termi-nated when the steady-state conditions were well established in

terms of pore-water pressures measured by the tensiometers

(Fig 5a) Steady-state condition refers to the horizontal portion of

the soil pore-water pressure versus time graph (Fig 5) For

example, the experiment “10cmEmb25cmHead1705”, for which

the physical condition at the end of the experiment was shown in

Fig 4a, reached steady-state condition near the water reservoir

section of the slope (tensiometer 5) at 1330 s, coinciding with the

time of seepage (Fig 5b) The experiment was terminated at 3600 s soon after all tensiometers in the slope reached steady-state con-dition at approximately 2400 s Pore-water pressures measured by tensiometers located along the bottom of the slope during exper-iment“10cmEmb25cmHead1705” were given inFig 5b

Considering thefinal slope surfaces obtained at the end of the experiments, hypothesized global failure surfaces (entering from the crest and exiting at the toe of the slope) were indicated for each experiment with 38 cm-H2O and 50 cm-H2O constant water level in

the reservoir (Fig 4 ed) One exception was the

“10cmEmb38cmHead0908” experiment which did not show any

indication of change in physical shape with 38 cm-H2O boundary

condition, and hence slope failure was not evident (Fig 4b) In

contrast to the non-remediated slope (“Matrix” configuration)

which showed a shallow-seated type global stability failure with

25 cm-H2O boundary condition in the earlier study byAkay et al

(2013), the geofoam block slope system experienced only a small

crack formation due to sliding on the slope face for experiment

“10cmEmb25cmHead1705” (Fig 4a) On the other hand, its

dupli-cate experiment “10cmEmb25cmHead1707” showed no signs of

either global stability failure or hydrostatic sliding (Fig 4a)

By taking into account the hypothesized failure surfaces

indi-cated at the end of experiments, a representative failure surface

was drawn (Fig 4d) Experiments showed that global static failures

took place along the failure surface immediately behind the

geo-foam block assemblage Consequently, the representative failure

surface shown inFig 4d was used to calculate FSGLby the coupled

analysis of SEEP/W and SLOPE/W FSGLvalues remained above 1.0 at

all times during the simulation with 25 cm-H2O boundary

condi-tion confirming the laboratory observations that no global static

failure took place with this boundary condition (Figs.4a and6a) On

the other hand, it is obvious that considering the strength

param-eters of the sand (f0¼ 33.7, c’ ¼ 0 kPa inTable 1), the 1:1 slope face

above the geofoam block assemblage is inherently unstable This

has also been quantified by the slope stability analysis for the

hy-pothesized failure surface given inFig 4a Even though, the FSGL

value was below 1.0, no shallow-seated global stability failure

above geofoam block assemblage was observed during the

exper-iments (Fig 4a) This can be attributed to the apparent cohesion of

the partially-saturated sand which clearly acted as an additional

resisting force (Fox and Wilson, 2010)

It can be noticed that FSGLvalues tend to decrease with time

during the simulation as the seepageflow progress into the failure

zone and phreatic surface rises above the toe of the geofoam block slope system (Fig 6a) The effect of seepage on FSGLwas even more severe for the cases with 38 cm-H2O and 50 cm-H2O boundary conditions (Fig 6a) The FSGLvalue decreased from 1.3 at the start of the simulation to 0.9 and 0.7 at the end of the simulation with

38 cm-H2O and 50 cm-H2O boundary conditions, respectively (Fig 6a) The FSGL value of 0.9 at steady-state condition, being slightly under the critical value of 1.0, indicated a marginally stable slope with 38 cm-H2O boundary condition This situation could be observed during laboratory testing that its duplicate, experiment

“10cmEmb38cmHead0908”, did not show any indication of change

in physical shape (Fig 4b)

Failure due to hydrostatic sliding was observed with 25 cm-H2O boundary condition (experiment “10cmEmb25cmHead1705” in

Fig 4a) Hydrostatic sliding was induced by seepage progressing into geofoam block assemblage only 590 s after the time of seepage (Fig 5b) At this time of crack formation, almost all tensiometers reached steady-state condition The in-situ stresses (total vertical stress, effective horizontal stress, and pore-water pressure) devel-oped at three time intervals (beginning of the test, time of seepage, end of experiment) is presented inFig 7 The magnitudes of the resultant forces (kN/m) and computed FSSL values are given in

Table 3 The FSSLvalue of 1.0 at steady-state (end of experiment) with a 25 cm-H2O boundary condition reveals a critical condition in term of hydrostatic sliding type of failure This situation was experienced in the laboratory that only one of the duplicates formed a crack on the slope (experiment “10cmEmb25cm-Head1705” inFig 4a) while the other showed no signs of hydro-static sliding Due to higher levels of the phreatic surface at steady-state, the FSSL value decreased to 0.9 and 0.8 with 38 cm-, and

50 cm-H2O boundary conditions, respectively Nevertheless, the geofoam block system experienced global static failures due to lower FSGL(Figs.4and6a) In addition, the effect of seepage on FSSL

was not severe as compared to its effect on FSGL The FSSLvalue

A.T Özer et al / Geotextiles and Geomembranes 42 (2014) 166e180 174

decreased from 1.0 at the start of the experiment to 0.8 at steady-state with 50 cm-H2O boundary condition whereas the decrease was from 1.3 to 0.7 for FSGL(Table 3)

3.3 Geofoam block assemblage: 15 cm embankment The final slope surfaces of the duplicate experiments of the

“15 cm Embankment” geofoam block assemblage are given inFig 8 Contrary to“10 cm Embankment” geofoam block assemblage, the slope showed no indication of a tension crack on the slope face at the end of the experiment with a 25 cm-H2O boundary condition; hence no hydrostatic sliding occurred In addition, calculated FSSL

values throughout the test were greater than 1.0 which confirmed the laboratory slope model results (Table 3) Since the laboratory physical slope model tests showed no global stability failure at the end of the duplicate experiments (Fig 8a), a failure surface located immediately behind the geofoam blocks was selected (Fig 8d) to compute the magnitude of FSGLwith a 25 cm-H2O boundary con-dition FSGLvalues were reported for this deep-seated global sta-bility failure surface inFig 6b Considering the change in FSGLwith time during the experiment for this failure surface, it can be seen that the FSGLvalue remained above 1.0 throughout the experiment (Fig 6b), where steady-state conditions were well established (Fig 5c)

The FSSL with 38 cm-H2O pressure head boundary condition decreased from 1.1 at the beginning of the experiment to 0.8 at the end of the experiment which demonstrated unstable condition against hydrostatic sliding (Table 3) This unstable condition for hydrostatic sliding was observed during only one of the duplicate experiments as a crack formed on the slope face of the experiment

“15cmEmb38cmHead2905” (Fig 8b) As in the case of 25 cm-H2O pressure head, deep-seated global stability failure was not observed under 38 cm-H2O pressure head boundary condition (Fig 8b) Therefore, a failure surface located behind the geofoam blocks (Fig 8d) was selected to calculate the FSGLby SLOPE/W The FSGL

value calculated by SLOPE/W for this representative failure surface

at the end of the experiments was 0.9 which showed unstable condition against global failure (Fig 6b) However, the duplicate experiments showed no global stability failure (Fig 8b)

The representative failure surface resulting from the 50 cm-H2O pressure head boundary condition was“deep-seated” type global stability failure (Fig 8c and d) The FSGLvalue decreased from 1.5 at the beginning of the experiment to 0.8 at the end of the experiment (Fig 6b), whereas FSSL value decreased from 1.1 to 0.8 (Table 3) Simultaneous reduction of both FSGLand FSSL below the critical value of 1.0 during the experiment (at the time of seepage;

Fig 7 Insitu stress [kPa] contours generated for “10 cm Embankment” assemblage

under 25 cm-H 2 O pressure head boundary condition by SIGMA/W (a) Total vertical

stress; (b) Effective horizontal stress; (c) Pore-water pressure.

Table 3

The magnitude of total vertical earth force (F T,V ), effective horizontal earth force (F E,H ), and horizontal component of hydrostatic force (F H,H ), all in [kN/m], acting on the geofoam block embankment computed by using SIGMA/W stress contours at three time intervals under boundary conditions (BC) of 25 cm-, 38 cm-, and 50 cm-H 2 O.