Prediction of lateral swelling pressure behind retaining structure with expansive soil as backfill

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Prediction of lateral swelling pressure behind retaining structure with expansive soil as backfill Yunlong Liu, Sai K. Vanapalli ⇑ Department of Civil Engineering, University of Ottawa, Ottawa, Ontario, Canada Received 10 January 2018; received in revised form 12 September 2018; accepted 6 October 2018 Available online 8 December 2018

Abstract Lateral swelling pressure (LSP) develops in expansive soil when the volume expansion associated with water infiltration is restrained in the horizontal direction due to a rigid infrastructure. Various types of testing techniques, used to determine the LSP from both laboratory and field studies, are critically reviewed by focusing on two key factors, namely, the boundary conditions and the saturation path. Most testing techniques are capable of reasonably simulating the stress state of a soil element behind a retaining structure by applying a fixed boundary condition in the horizontal direction and a stress boundary condition in the vertical direction. However, they are only used to determine the LSP following a simple path, which is from an initially unsaturated state to a fully saturated state. In other words, these tests fail to provide information on the variation in LSP with respect to changes in the degree of saturation, the water content or the matric suction during the infiltration process. Furthermore, the literature review suggests that a reliable model for the prediction of the LSP during the infiltration process is not available. For this reason, a model is proposed in this paper to estimate the lateral earth pressure (LEP) considering the variation in LSP behind fixed rigid retaining structures with respect to the matric suction during the infiltration process. The proposed model is simple and only requires information, which includes the soil water characteristic curve (SWCC) and a limited number of soil properties. Data from one large-scale model test and two field case studies from published literature are used to illustrate and verify the proposed model. Reasonable comparisons are made between the predictions and the measured data. The proposed model will be a valuable tool for use in conventional engineering practice for the quick prediction of the increasing LEP behind retaining structures with expansive soils as backfill due to the development of LSP associated with water infiltration. Ó 2018 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/) Keywords: Expansive soils; Unsaturated soils; Matric suction; Lateral swelling pressure

1. Introduction and background Expansive soils are susceptible to significant increases or decreases in volume with changes in the water content. For this reason, geotechnical engineers encounter various challenges in the rational design of geotechnical infrastructures in expansive soils. The volume expansion of soils that are expansive by nature typically arises upon water infiltration.

Peer review under responsibility of The Japanese Geotechnical Society. ⇑ Corresponding author. E-mail address: [email protected] (S.K. Vanapalli).

However, if this is restricted in the horizontal direction, lateral swelling pressure (LSP) will develop. The LSP that acts on an infrastructure is in addition to the lateral earth pressure (LEP) that is associated with the self-weight and/or the surcharge effects of the soil. The effects of LSP are common in rigid infrastructures (for example, retaining walls and cantilever sheet pile walls) with expansive soils as backfill and other geotechnical infrastructures constructed within expansive soils (for example, basements, sewer lines, pipe lines and deep foundations). In several scenarios, LSP can significantly influence the stability and safety of geotechnical infrastructures. For fixed retaining structures

https://doi.org/10.1016/j.sandf.2018.10.003 0038-0806/Ó 2018 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society.

This is an open access article under CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Y. Liu, S.K. Vanapalli / Soils and Foundations 59 (2019) 176–195

(i.e., in the at-rest condition), the LEP is typically less than the vertical pressure (i.e., the self-weight and surcharge effects of the soil). However, from an investigation conducted by Richards and Kurzeme (1973), the LEP was found to be 1.3 to 5.0 times the overburden pressure considering the influence of the LSP behind a 7.5-m retaining wall. Moza et al. (1987) also suggested that the LSP value in certain scenarios can be ten times greater than the overburden pressure. Joshi and Katti (1980) conducted a largescale model test and showed that at a depth of 0.28 m, the LSP was ten times greater than the vertical swelling pressure (VSP). More recently, Mohamed et al. (2014) monitored the LSP behind a basement wall and found it to be seven times the LEP calculated assuming active conditions. The increased LEP associated with the LSP can contribute to the development of cracks in basement walls, tunnels and sewers. In certain scenarios, the failure of these structures is also likely (for example, Kassiff and Zeitlen, 1962). Moreover, it reduces the factors of safety against overturning and sliding failure for retaining walls or slopes and may contribute to the possibility of failure during periods of rainfall (Ng et al., 2003). For underground structures in expansive soils, such as the pile foundations, an increased level of LEP may contribute to the development of uplift friction along the pile shaft in the active zone. After analyzing several case studies of pile failures in expansive soils, Chen (1988) pointed out that additional design checks are necessary to take into account the tension capacity of piles as well as the stability of superstructures with respect to ground heave. Damage to structures constructed within (for example, pile foundations), adjacent to (for example, retaining structures) or on (for example, pavements) expansive soils typically poses significant problems. For this reason, government agencies, contractors, owners, consultants and insurance companies are forced to invest significant financial resources to deal with the problems induced by expansive soils (Day, 1994). More recently, Adem and Vanapalli (2016) summarized losses associated with expansive soils in various countries of the world. For example, losses associated with expansive soils to various infrastructures in the United States of America have increased from $2.3 billion (Jones and Holtz, 1973) to $13 billion (Puppala and Cerato, 2009) over the last five decades. The annual cost of damage due to expansive soils is typically twice that of damage associated with floods, hurricanes and earthquakes (Holtz, 1984). The failures of or repairs to the various infrastructures induced by LSP can account for a considerable proportion of these losses. One of the major reasons for the failure of infrastructures constructed in/on expansive soils may be the lack of a proper understanding of the mobilization of LSP. In this paper, a critical review of laboratory and field investigations related to the determination of the LSP in different scenarios is provided. Various factors that influence the LSP mobilization are sorted and summarized in the form of a flow chart. In addition, models that are capable of predicting LSP mobilization are compared and

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discussed. Furthermore, a simple model is proposed for predicting the variation in LEP considering the LSP behind retaining structures with respect to the variation in matric suction extending unsaturated soil mechanics. Research studies summarized in this paper will be useful for practicing geotechnical engineers in the rational design of retaining structures in expansive soil regions where LSP mobilization is of concern. 2. Literature review The literature review on the LSP in expansive soils is summarized in three different sections, namely, testing techniques, a flow chart illustrating the mobilization of LSP and prediction models. 2.1. Testing techniques Laboratory and field tests (including large-scale model tests) have been undertaken by various researchers over the past half century to study the LSP in expansive soils. The laboratory tests were conducted based on simple operational principles using relatively small cubic or cylindrical specimens. The experimental data acquired from the laboratory tests can provide valuable information on the mechanical behavior of expansive soil elements under different test conditions. Compared to laboratory tests, large-scale model and in-situ tests usually require extensive planning, instrumentation and the assistance of trained personnel. Furthermore, a longer period of time is required for the water to infiltrate the in-situ expansive soil due to its low coefficient of permeability. However, large-scale model and in-situ test results are more representative and provide valuable information; they can be used with a greater degree of confidence when applied in engineering practice. These advantages outweigh the difficulties associated with their testing methods and limitations. 2.1.1. Laboratory testing techniques The various laboratory testing devices, available for the determination of the LSP, can be categorised into three types, namely, modified oedometer, modified hydraulic triaxial apparatus and 3-D swelling-shrinkage apparatus (see Table 1). The typical configurations for these three types of testing apparatuses are shown in Fig. 1. The stress-strain boundaries applied in each of the three testing apparatuses are also highlighted. Table 1 summarizes the details of the different combinations of boundary conditions for the three testing methods to study the swell behavior of a soil element under different stress states. Among the various testing apparatuses, the modified odeometer is widely used because of its simplicity with respect to the equipment and the testing technique. The three different oedometer test methods are summarized in Table 1. One of these methods, known as the swell under surcharge method, is widely used since it can simulate well the stress state of a soil’s elementary volume behind retaining structures in engineering

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Table 1 Various types of laboratory tests used for the measurement of LSP. Type of apparatus

Apparatus

Reference

Testing method

Saturation path

Remarks

Modified odeometer

Fig. 1(A) and (B)

Komornik and Zeitlen (1965), Ofer (1981), Edil and Alanazy (1992), Windal and Shahrour (2002), Sapaz (2004), Azam and Wilson (2006), Agus and Schanz (2008) and Saba et al. (2014)

From initial water content to fully saturated condition

Test is easy and can be conducted using conventional laboratory equipment with minor modifications

Modified hydraulic triaxial apparatus

Fig. 1(C)

Fourie (1988), Yesßil et al. (1993), Puppala et al. (2007) and AlShamrani (2004)

Fig. 1 (D) and (E)

Xie et al. (2007) and Ikizler et al. (2012)

From initial water content to fully saturated condition From initial water content to fully saturated condition

Trained operator is required for performing swell and load back tests

3-D swelling shrinkage apparatus

Three types of tests can be conducted with different boundary conditions: (1) constant volume swell test, (2) swell under surcharge test and (3) swell and load back test. In all these tests, vertical stress is applied on the specimens Two types of tests can be conducted: (1) swell under different axial and radial stress conditions and (2) swell and load back test under fixed vertical boundary and different radial stress conditions Xie et al. (2007): swell test can be conducted under different strain boundary conditions in vertical and horizontal boundaries; Ikizler et al. (2012): swell test can be conducted at constant volume condition

practice. The soil specimen swells under a surcharge load that is representative of the overburden pressure associated with the self-weight of the upper layer soil and/or the load from the superstructure. To date, no experimental method has been reported in literature that can precisely determine the variation in the LSP with respect to the degree of saturation, matric suction or water content changes. The focus of various tests in the literature has been to measure the LSP only at the fully saturated condition. In other words, the presently available laboratory testing methods have limitations in their direct application to or use in engineering practice. This is because in many scenarios, significant problems arise in the infrastructure due to the reduction in matric suction associated with water infiltration prior to the soil reaching the saturated condition. 2.1.2. Large-scale model and field-testing techniques Table 2 summarizes relatively large-scale model tests and field tests that have been conducted over the past half century. The configurations of these tests are illustrated in Fig. 2. Although the specific configurations of these largescale model tests and field tests vary from case to case, because of the differences in soil types, testing site dimensions, experiment objectives and other criteria used for measuring the LEP considering LSP, the large-scale model tests and field tests can be classified into two categories based on how the LSP was monitored or measured. In the first category, the LEP development was monitored by a pressure measuring system attached to a large-scale model or real retaining structure [as shown in Fig. 2(A)–(E)]. In the second category, a pressure sensor was buried vertically inside the soil to monitor the LSP development [as shown in Fig. 2 (F)–(H)]. One outstanding merit of this testing technique is its simple configuration. However, for in-situ tests, special measures are usually required to keep the pressure sensor in the same position throughout the testing process.

Specially designed apparatus required for the measurement of LSP

The total LEP measured from the large-scale model tests or field tests for expansive soils is the sum of the measured LSP and LEP. In other words, the LEP for large-scale model tests and field tests has to be interpreted based on the swell under surcharge tests considering the influence of the self-weight of the upper soil layer and/or the surcharge. It is important to note that the LSP can only be fully mobilized against fixed rigid retaining walls. Studies on model retaining walls in expansive soils have suggested that there will be a significant reduction in the LSP if some movement or minor strain is allowed (Ofer, 1981; Katti et al., 2002; Xie et al., 2007). The model tests and field studies were performed on similar soil specimens in laboratory tests. In other words, the expansive soil behind the model or real retaining structure was fully saturated from its initial unsaturated state. The saturation process usually requires a long time due to the low coefficient of permeability of expansive soils. In order to accelerate the infiltration process, various approaches have been developed, which include providing sand drains or conducting these studies in a centrifuge. One of the most comprehensive field tests reported in the literature was conducted by Brackley and Sanders (1992). Their study simulated infiltration activity associated only with natural precipitation, it lasted for a period of close to 10 years and both the LEP and soil suction variations were measured. The results of this study suggest a strong correlation between the mobilization of the LSP and the reduction in soil suction. 2.2. Flow chart summarizing the mobilization of LSP Fig. 3 summarizes experimental investigations from the literature in the form of a flow chart to highlight how LSP develops. The swelling potential within unsaturated or compacted expansive soils is stored as internal stress. Expansive soils experience a reduction in matric suction

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Load

(A) Vertical pressure sensor Strain gauge

(C)

Porous stone

LVDT

Soil sample Soil sample Bottom plate

Vertical pressure sensor Lateral pressure sensor Water inlet

(B) (D)

Soil sample

Counterforce beam Soil sample

Seating cylinder Pressure Porous To pressure sensor stones panel Membrane Pressure measuring system

(E) Soil sample inside the chamber

Fixed boundary Stress boundary Strain boundary

Fig. 1. Various apparatus for measurement of LSP in lab [(A) Modified odeometer with strain gauge (modified after Ofer, 1981); (B) Modified odeometer with pressure sensor (modified after Saba et al., 2014); (C) Modified hydraulic triaxial apparatus (modified after Puppala et al., 2007); (D) 3-D swelling shrinkage apparatus presented by Xie et al. (2007) (Modified after Xie et al., 2007); (E) 3-D swelling shrinkage apparatus presented by Ikizler et al. (2012) (Modified after Ikizler et al., 2012)].

when water infiltrates and triggers volume expansion. As discussed earlier, once the volume expansion is restricted in the horizontal direction, LSP mobilizes. In Fig. 3, the various factors affecting the swelling potential of expansive soils prior to water infiltration are summarized (Seed et al., 1962; Nagaraj et al., 2010; Sapaz, 2004; Schanz and AlBadran, 2014; Lambe, 1958; Gokhale and Jain, 1972; Komornik and Livneh, 1968; Nelson et al., 2015). Most laboratory and field-testing techniques follow a path along which the soil specimens are fully saturated to determine the maximum LSP. However, in-situ LSP that develops can be different from that occurring from the initial unsaturated state to a subsequent unsaturated state. The swell under surcharge test can simulate well the stress state of a soil element that is typically encountered in engineering practice. In such tests, fixed boundary conditions are applied in the horizontal direction to simulate fixed rigid retaining structures. Different levels of stress boundary conditions are applied in the vertical direction to simulate the vertical load due to the soil self-weight and the superstructure load. Stress relaxation contributes to decreases in LSP based on some experimental investigations, and fatigue is associated with wetting and drying cycles (Clayton et al., 1991; Brackley and Sanders, 1992; Symons and Clayton, 1992; Windal and Shahrour, 2002; Xie et al., 2007; Mohamed et al., 2014; Dif and Bluemel, 1991; Estabragh et al., 2015; Al-Homoud et al., 1995; Basma et al., 1996). 2.3. Prediction models Laboratory and field tests are direct methods that provide reliable information on the mobilization of LSP. However, these tests are complex and require the assistance of professionally trained personnel. Their services are expen-

sive, and hence, these tests cannot be used in routine engineering practice. In addition, the data collection is usually time-consuming due to the low coefficient of permeability of expansive soils. As shown in Table 2, field tests require a long period of time; for example, Brackley and Sanders (1992) gathered data for 10 years. Based on experimental and theoretical studies, some investigators have proposed models for predicting LSP or LEP considering LSP that is based on experimental and/or theoretical studies. Table 3 summarizes the widely used prediction models from the literature along with their advantages and limitations. All these models are capable of predicting the LSP mobilized under swell under surcharge boundary conditions, which corresponds to the stress state of the soil’s elementary volume in engineering practice. There are two models proposed by Jiang and Qin (1991) and Hong (2008) in the literature that consider the mobilization of LSP from an initial unsaturated state to another different unsaturated state. Both these models require parameters which can only be determined from complex experiments instead of basic soil properties. In some scenarios, these experiments can be more complicated than the direct measurement of the LSP. Recent studies suggest that the volume change characteristics of expansive soils can only be better explained by taking account of the hydromechanical behavior considering the attributes of soil, such as the matric suction and clay mineralogy information (Puppala et al., 2016). However, the presently available models do not incorporate the influence of matric suction for the LSP mobilization, thereby leading to poor or erroneous characterization practices. Besides the theoretical models summarized in Table 3, there are also various constitutive relationships and numerical models that are capable of reasonably simulating the mobilization of LSP due to restricted volume changes even

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Table 2 Measurement of LEP considering LSP from large-scale model and field tests. Soil type

Testing time

Testing type

Apparatus

Saturation path

Remarks

Katti et al. (1983) Gu (2005)

Black cotton soil/Malaprabha right bank canal, India Expansive clay/Nanning, China

LM

Fig. 2(A)

A

C

Fig. 2(B)

A

Influence of different thickness cohesive non-swelling (CNS) soil layers as backfill placed on top of expansive clay as surcharge was studied for understanding the mobilization of LEP Centrifuge test terminates when the LEP measurement is stabilized; Video technique was used to monitor ground heave

Symons et al. (1989) Yang et al. (2014) Wang et al. (2008) Ofer (1980)

London clay/London, England

LM

Fig. 2(C)

A

Sand drains were installed to accelerate the infiltration process

Expansive clay/Baise, China

Average 60 days Around 45– 80 min Over 20 months 5 days

LM

Fig. 2(D)

A

Sand drains were installed to accelerate the infiltration process

Expansive clay/Nanjing, China

100 days

F

Fig. 2(E)

A

PVC infiltration pipes were used to accelerate the infiltration process

Expansive clay/ South Africa

More than 7 days 10 years

F

Fig. 2(F)

A

In-situ probe with ingenious design enables simultaneous infiltration and measurement of LEP

F

Fig. 2(G)

B

Around 10 months

F

Fig. 2(H)

A

Long term measurement; Detailed measures were introduced to ensure the soil was disturbed as little as possible during the placement of the pressure cell. Sand drains were installed to accelerate the infiltration process; LEP and VSP measurement conducted by conventional pressure cells inserted in the testing pit

Brackley and Sanders (1992) Robertson and Wangener (1975)

Leeuhof clay (lacustrine clay)/ Vereeniging, South Africa Remoulded compacted expansive clay/Newcastle South Africa

Testing apparatus details: Fig. 2(F) shows the LEP sensors used by Ofer (1980), Fig. 2(G) shows the configuration of pressure sensor borehole used by Brackley and Sanders (1992). Details of testing type: F represents field test; LM represents large-scale model test; C represents centrifuge test. Saturation path details: A represents manual irrigation from initial water content to fully saturated conditions; B represents environmental factors variation, which shows soil suction fluctuations.

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Reference

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181

Top

(E)

0.9-1.35m

Expansive soil Dry density=1.60g/ cm3

Expansive soil Dry density=1.45g/cm3 2.5m

1.25-2.45m

Backing Expansive soil

Fixed or Moveable concrete retaining wall

(A) PVC infiltration pipes Earth pressure cell 10m

Reaction jacks Pertinent rings Pressure Sensors 3m 3m

Blocked Model retaining wall Expansive soil

(G) Ground level Porous ring

20m

3m

(F) Water supply

14m

Recompacted soil

Rubber fill Transducer

3m

(B)

3m

Epoxy resin Porous ring Cutting Edge

34.25m Horizontal Moveable metal retaining wall load cells 5m (50kN)

Pressure cell Side view

Front view

1m

3m

2m

0.75m

Compacted clay fill

Jacks

Sand drains

Reference Pressure standard cell

Polyethylene sheet

Ponding wall

(C)

2.2m

Vertical load cells (25kN) Timber packing

(H)

Reinforced concrete trough Fixed reinforced concrete model retaining walls

Expansive soil

1.5m

Sand drains

(D) Earth pressure cell

2.5m 2.5m Clay compacted in 50mm layers with 5mm coarse sand between each layer

Outlet gravel drains

Fixed boundary Strain boundary

Reinforced concrete beams

Fig. 2. Large-scale model and field tests on measurement of LEP considering LSP [(A) Apparatus used by Katti et al., 1983 (modified after Katti et al., 1983); (B) Apparatus used by Gu (2005) in a centrifuge model using enlarged dimensions (modified after Gu, 2005); (C) Apparatus used by Symons et al., 1989 (modified after Symons et al., 1989); (D) Apparatus used by Yang et al. (2014) (modified after Yang et al., 2014); (E) Apparatus used by Wang et al. (2008) (modified after Wang et al., 2008); (F) In-situ probe (modified after Ofer, 1980); (G) Pressure cell (modified after Brackley and Sanders, 1992); (H) Field configuration using by Robertson and Wangener (1975) (modified after Robertson and Wangener, 1975].

under complex stress and hydraulic boundary conditions. Alonso et al. (1987) proposed an integrated elastoplastic framework for interpreting the shear strength and volumetric change behavior of unsaturated soils. This pioneering framework was extended by Alonso et al. (1990), which is referred in the literature as the Barcelona Basic Model (BBM). The BBM is a landmark contribution that provides a critical state-based model for non-expansive and lightly loaded expansive unsaturated soils. Later, Gens and Alonso (1992) further extended this approach to overcome

some limitations of the BBM to take into account the large strain behavior of expansive soils. A more comprehensive mathematical formulation of the modified BBM (named the Barcelona Expansive Model-BExM) was eventually presented in Alonso et al. (1999). Several other researchers have also contributed to the development of various numerical models for unsaturated expansive soils (Wheeler and Sivakumar, 1995; Wheeler et al., 2003; Sa´nchez et al., 2005; Pinyol et al., 2007; Sheng et al., 2008; Sheng and Zhou, 2011; Sun and Sun, 2011;

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Swelling potential Clay minerals: Amount of montmorillonite and illite.

Soil structures: Particle size distribution; Degree of compaction (remoulded soil); Stress history (natural soil); Initial water content, w0; Dry density, ρd; Soil particle orientation.

Triggers

Lateral swelling pressure

Saturation path: Matric suction reduction associated with water infiltration which determines the amount of LSP can be mobilized. Stress/strain boundary conditions: Maximum LSP can be monitored under fixed boundary conditions in all directions while swell under surcharge test best simulates the stress state of soil in engineering practice.

Stress relaxation: LSP gradually reduces from peak value to a stabilized final value due to changes in the microstructure and collapse of macrostructure. Fatigue phenomenon:The swelling ability of expansive soil decreases after wetting and drying cycles due to destruction of large aggregates and disorientation of structural elements.

Fig. 3. Flow chart summarizing factors influencing mobilization of LSP.

Guimara˜es et al., 2013, etc.). For example, Xing and Gang (2014) recently proposed a model for compacted expansive clays by incorporating the mathematical formulations of microstructure and macrostructure in the existing BBM. Wang and Wei (2015) presented a constitutive model capable of describing the volume changes of compacted expansive soils during wetting and drying cycles considering the double structure concept. Ahmed and Abduljauwad (2016) proposed a comprehensive nano-level constitutive model for natural and compacted clay soils containing parameters that control such swelling behaviors as moisture content, cation exchange capacity and non-clay minerals. A comprehensive review presented by Ahmed and Abduljauwad (2018) highlights the strengths and limitations of the presently available constitutive models for the expansive characteristics of clayey soils at macro, micro and nano levels. These numerical methods are powerful tools for the interpretation of unsaturated expansive soil behavior; however, they may not be widely employed in routine practice because of the high computational requirement and the need to gather several soil parameters from laboratory or field studies in order to use them. For the above-mentioned reasons, a simple model has been proposed in this study which can provide reliable predictions of the LEP considering the LSP against fixed rigid retaining structures from an initial unsaturated state to another unsaturated state based on variations in the matric suction profile and a limited number of soil properties. 3. Proposed model for the prediction of LEP considering LSP in the infiltration process Liu and Vanapalli (2017) proposed a model (Eq. (7)) for the estimation of the LEP considering the LSP upon free swelling (PL) according to constant volume VSP (Ps), extending unsaturated soil mechanics principles. However, no simple testing technique or model is available for the reliable prediction of constant volume VSP (Ps) from an initial unsaturated state to a subsequent unsaturated state (Fredlund, 1969; Brackley, 1973; Sridharan et al., 1986; Shuai, 1996; Azam and Wilson, 2006; Nagaraj et al., 2009; Rao, 2006; Vanapalli and Lu, 2012; C ¸ imen et al.,

2012). For this reason, Eq. (7) can only be applied to the most critical scenario of the LEP considering the fact that LSP arises when the matric suction decreases from a certain initial value to zero (i.e. the saturated condition). However, such a scenario is rare as backfill material is typically in an unsaturated state for most of its design life. For this reason, in the present study, a superposition approach is proposed to estimate the LEP considering the LSP against a fixed rigid retaining structure that arises due to a reduction in matric suction while the soil is still in an unsaturated state. PL ¼

ð1  l  2l2 ÞP s l rS þ 1  l2  EP as ð1 þ lÞð1  l  2l2 Þ 1  l

ð7Þ

where Ea is the average elastic modulus with the matric suction variation range, l is Poisson’s ratio and Ps is constant volume VSP. The elastic modulus of soil under an unsaturated condition can be estimated using the semi-empirical model (Eq. (8)) proposed by Oh et al. (2009) and Adem and Vanapalli (2014).
 ðua  uw Þ bE S ð8Þ Eunsat ¼ Esat 1 þ aE ðP a =101:3Þ where Eunsat is the modulus of elasticity under an unsaturated condition, Esat is the saturated modulus of elasticity and Pa is atmospheric pressure (i.e., 101.3 kPa). aE and bE are fitting parameters, namely, aE = 0.05–0.15 and bE = 2. As shown in Fig. 4, the soil’s elementary volume behind a fixed rigid retaining structure experiences a decrease in matric suction from (ua  uw)a to (ua  uw)b where (ua  uw)b is an intermediate matric suction value (i.e., not equal to zero) during the infiltration process. Therefore, the LSP mobilizes with a decrease in matric suction and adds an additional increment to the LEP associated with the soil self-weight and surcharge. In order to apply the superposition method, the soil’s elementary volume behind the retaining wall is assumed to experience a series of stress state changes following two different paths. In Path (I), the soil element experiences a reduction in matric suction

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Table 3 Models for predicting LEP considering LSP or LSP in expansive soils. Reference

Skempton (1961) Sudhindra and Moza (1987) Katti et al. (1983) Nelson et al. (2015) Jiang and Qin (1991) Hong (2008)

Equation/Description

=rs As Þ P L ¼ rs ðP Kð1A (1) sÞ

P SV

dz

P L ¼ ðaþbddz0z Þ (2) d z0

P L ¼ P CNS þ 0:2ðP SW  P CNS Þ (3) P L ¼ P 0 þ aN P SV 6 P 0 þ P p (4) P LS ¼ aJ bJ P LSðmaxÞ (5) P L ¼ ð32Þrim 10 (6)

c

2eh r ð1f H Þ

ch

ðhhfi Þcr  ct2zH

Stress/ strain boundary conditions

Saturation path

Remarks

Swell under surcharge test. Swell under surcharge test

From initial water content (i.e., unsaturated condition) to fully saturated condition From initial water content (i.e., unsaturated condition) to fully saturated condition

Semi-empirical equation involving parameter As which can be determined from triaxial tests

Swell under surcharge test Swell under surcharge test Swell under surcharge test Swell under surcharge test

From initial water content (i.e., unsaturated condition) to fully saturated condition From initial water content (i.e., unsaturated condition) to fully saturated condition From an unsaturated state to another unsaturated state associated with reduction in matric suction From an unsaturated state to another unsaturated state associated with reduction in matric suction

Empirical equation only suitable for certain cases with CNS material filled between expansive soil and the retaining wall Simple empirical equation involving an empirical parameter aN which is estimated from past engineering practice experience Empirical equation involving parameters aJ and bJ determined from complex experiments

Empirical equation deduced from limited case studies; two empirical parameters, a and b, need to be determined from complex experiments

Complex semi-empirical equation involving two parameters, cr and ch, determined from complex experiments and one empirical parameter, fH

where PL = LEP considering the influence of LSP; rs = vertical effective stress; PK = soil capillary pressure before test; As = pore pressure parameter which can be evaluated from triaxial testing; PSV = minimum stress required to prevent vertical swelling; dz = calculating depth; dz0 = unit depth; a and b = empirical parameters determined from experiment; PCNS = LEP of cohesive non-swelling (CNS) material for corresponding depth; PSW = LSP of oven-dried expansive soil at constant volume condition; P0 = at rest earth pressure; Pp = passive earth pressure; aN = parameter varying from 0.7 (Sapaz, 2004) to 1 (Katti et al., 2002); PL = LSP under partially saturated condition; aJ = coefficient of water content, which is the ratio of the LSP at the current water content to the water content at the maximum LSP; bJ = coefficient of deformation, which is the ratio of the current deformation to the deformation at the maximum LSP; PLS(max) = maximum LSP from laboratory tests; rim = initial values of mean principle stress; eh = horizontal swelling strain; cr = mean principle stress compression index; hi = initial matric suction; hf = final matric suction; ch = matric suction compression index; fH = factor ranging from 1/h to 1 depending on degree of saturation; h = volumetric water content; ct = unit weight of soil; zH = depth of calculating point.

directly from (ua  uw)a to zero. However, in Path (II), the soil element initially undergoes a reduction in matric suction from (ua  uw)a to (ua  uw)b. The matric suction (ua  uw)b subsequently decreases to zero. The stress state changes in the soil element in Path (I) and Path (II) (as shown in Fig. 5) are illustrated below. (i) Following Path (I), from the initial state to State (1), there is an increment in lateral pressure, rL(a-0), with the reduction in matric suction from (ua  uw)a to zero in the soil element. In the vertical direction, the vertical side length of the soil element increases from initial value c to b1. From State (1) to State (2), it is assumed that vertical stress Ps(a-0) compresses the expanding soil element back to its initial volume. (ii) Following Path (II), from the initial state to State (3), the soil element experiences a reduction in matric suction [(ua  uw)a  (ua  uw)b]. As a consequence, the soil element shown in State (3) gains a stress increment rL(a-b) in the horizontal direction. In addition, the side length increases from c to b2 in the vertical direction. From State (3) to State (4), vertical stress Ps(a-b) compresses the analytical element shown in State (3) back to its initial volume. From State (3) to State (5), after undergoing a

reduction in matric suction which is equal to [(ua  uw)a  (ua  uw)b], the soil element experiences a further reduction in matric suction from (ua  uw)b to zero, which means the soil element is fully saturated. For the soil element shown in State (5), in the horizontal direction, compared to the element shown in Stage (3), there is a stress increment rL(b-0) that arises due to the reduction in matric suction, while the vertical side length increases from b2 to b3. From State (5) to Stage (6), vertical stress Ps(b0) compresses the volume of the soil element shown in State (6) back to Stage (5). The soil element further gains a stress increment rrc, in the horizontal direction. To simplify the analysis, the soil element behind the retaining structure is considered to be isotropic, homogeneous and elastic in nature without any plastic deformation (such as collapse of the soil structure due to over-load) during the swelling process (Terzaghi’s, 1925, 1926, 1931). In addition, to extend the conservative approach, the horizontal displacement of the soil element is assumed to be strictly restricted. The constitutive relations (Eq. (9)) proposed by Fredlund and Morgenstern (1976) can be used to interpret the variation in the stress state of the soil element shown in Fig. 4.

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8 aÞ wÞ > e ¼ ðrx u  El ðry þ rz  2ua Þ þ ðua u > E H < x ðr u Þ wÞ ey ¼ y E a  El ðrx þ rz  2ua Þ þ ðua u H > > : aÞ wÞ ez ¼ ðrz u  El ðrx þ ry  2ua Þ þ ðua u E H

ð9Þ

where ex is the total strain in the x-direction, ey is the total strain in the y-direction, ez is the total strain in the zdirection, rx is the total normal stress in the x-direction, ry is the total normal stress in the y-direction, rz is the total normal stress in the z-direction, ua is the pore-air pressure, uw is the pore-water pressure, E is the elastic modulus with respect to the net normal stress and H is the elastic modulus with respect to the matric suction. The mathematical expressions corresponding to the stress states shown in Fig. 5 are summarized as Eq. (10) for Path (I), the initial state to State (1); Eq. (11) for Path (I), from State (1) to State (2); Eq. (12) for Path (II), from the initial state to Stage (3); Eq. (13) for Path (II), from State (3) to State (4); Eq. (14) for Path (II), from State (3) to State (5); and Eq. (15) for Path (II), from State (5) to State (6), respectively. Rearranging the above equations, the levels of LEP corresponding to the different decreases in matric suction are given as Eq. (16). 8 < b1cc ¼ E 2l rLða0Þ  ðuHa uw Þa ða0Þ ða0Þ ð10Þ : 0 ¼ l1 rLða0Þ  ðua uw Þa Eða0Þ H ða0Þ 8 < cb1 ¼ 2l rra  P sða0Þ Eða0Þ b1 Eða0Þ ð11Þ : 0 ¼  rra þ l ½P sða0Þ þ rra  Eða0Þ Eða0Þ where E(a-0) is the average elastic modulus over the range in matric suction from (ua  uw)a to zero, H(a-0) is the average elastic modulus over the range in matric suction from (ua -

 uw)a to zero and Ps(a-0) is the constant volume VSP generated from the reduction in matric suction from (ua  uw)a to zero. 8 < b2cc ¼ E 2l rLðabÞ  ½ðua uwHÞa ðua uw Þb  ðabÞ ðabÞ :0 ¼

l1 EðabÞ

rLðabÞ 

½ðua uw Þa ðua uw Þb  H ðabÞ

8 < cb2 ¼ 2l rrb  P sðabÞ EðabÞ b2 EðabÞ :0 ¼ 

rrb EðabÞ

l þ EðabÞ ½P sðabÞ þ rrb 

ð12Þ

ð13Þ

where E(a-b) is the average elastic modulus with respect to net normal stress over the range in matric suction from (ua  uw)a to (ua  uw)b, H(a-b) is the average elastic modulus with respect to matric suction over the range in matric suction from (ua  uw)a to (ua  uw)b and Ps(a-b) is the constant volume VSP generated from the reduction in matric suction from (ua  uw)a to (ua  uw)b. 8 < b3bb2 ¼ E 2l rLðb0Þ  ðuHa uw Þb 2 ðb0Þ ðb0Þ ð14Þ : 0 ¼ l1 rLðb0Þ  ðua uw Þb Eðb0Þ H ðb0Þ 8 < b2 b3 ¼ 2l rrc  P sðb0Þ Eðb0Þ b2 Eðb0Þ ð15Þ : 0 ¼  rrc þ l ½P sðb0Þ þ rrc  Eðb0Þ Eðb0Þ where E(b-0) is the average elastic modulus with respect to net normal stress over the range in matric suction from (ua  uw)b to zero, H(b-0) is the average elastic modulus with respect to matric suction over the range in matric suction from (ua  uw)b to zero and Ps(b-0) is the constant volume swell pressure generated from the reduction in matric suction from (ua  uw)b to zero.

Infiltration Matric suction Soil selfweight

Lateral earth pressure

Stress boundary

Fixed boundaries

(ua-uw)b

Passive earth pressure

(ua-uw)a

Soil's elementary volume behind the retaining wall

Depth

Stable zone

Depth

Active zone

σL(b-0) σL(a-b) Path (II) Path (I)

σL(a-0)

(A)

σL(a-b) σs·μ/(1-μ)

(B)

(C)

Fig. 4. Mobilization of LSP behind retaining structure associated with matric suction reduction [(A) Soil’s elementary volume; (B) Matric suction reduction; (C) LEP distribution changes].

Y. Liu, S.K. Vanapalli / Soils and Foundations 59 (2019) 176–195

Soil's elementary volume

185

Ps(a-0) σL(a-0)+σra

σL(a-0) c

Fixed boundaries

σL(a-0) b1

c

Path (I)

σL(a-0)+σra c

σL(a-0) (ua-uw)a σL(a-0)

σL(a-0)+σra σL(a-0)+σra c

c

State (1)

Ps(a-0)

State (2)

Soil's elementary volume

Ps(a-b) σL(a-b)

c

Fixed boundaries

σL(a-b) b2

c

Path (II)

σL(a-b)+σrb

σL(a-b) (ua-uw)a-(ua-uw)b σL(a-b)

σL(a-b)+σrb c

σL(a-b)+σrb σL(a-b)+σrb c Ps(a-b)

c

State (3)

State (4)

Ps(b-0) σL(a-b)+σL(b-0) σL(a-b)+σL(b-0) b3

(ua-uw)b σL(a-b)+σL(b-0)

σL(a-b)+σL(b-0)

σL(a-b)+σL(b-0)+σrc σlb+σlc+σrc b2

σL(a-b)+σL(b-0)+σrc σL(a-b)+σL(b-0)+σrc c Ps(b-0)

c

State (5)

State (6)

Fig. 5. Stress states variations of the soil’s elementary volume following different matric suction reduction paths.

8 ð1l2l2 ÞP sða0Þ > rLða0Þ ¼ P sða0Þ > > 2 1l  E ð1þlÞð1l2l2 Þ > > ða0Þ > > < ð1l2l2 ÞP sðabÞ rLðabÞ ¼ P sðabÞ 2 1l  E ð1þlÞð1l2l2 Þ > ðabÞ > > > > ð1l2l2 ÞP sðb0Þ > > P sðb0Þ : rLðb0Þ ¼ 1l2  E

ðb0Þ

ð16Þ

ð1þlÞð1l2l2 Þ

Since the soil element following Path (I) and Path (II) experiences the same reduction in matric suction from (ua  uw)a to zero, under the same boundary conditions (fixed boundaries in the horizontal direction and free boundary in the vertical direction), the LSP in State (1) and State (5) generated due to the reduction in matric suction should also be the same, as well (Eq. (17)). The LSP induced by the reduction in matric suction [(ua  uw)a  (ua  uw)b] can be expressed as Eq. (18). A general equation can be summarized as Eq. (19) considering the influence of the LEP due to the soil self-weight and surcharge. The Ps(a-0) and Ps(b-0) values in Eq. (19) represent the constant volume VSP generated from the initial condition to the fully saturated condition, which can be acquired from simple laboratory tests according to ASTM, D4546. If there are no experimental data, the semi-empirical prediction model (Eq. (20)), proposed by Tu and Vanapalli (2016), is suitable for use with compacted expansive soils. This equation can also be extended for expansive soils

behind retaining structures as they are disturbed during construction and then compacted to function as backfill material. Employing Eqs. (19) and (20), the LEP considering the LSP behind a fixed rigid retaining structure from an initial unsaturated state to a subsequent unsaturated state can be predicted based on variations in the matric suction profile or water content profile using soil properties. They include the soil water characteristic curve (SWCC), saturated elastic modulus Esat, plasticity index Ip, maximum dry density qd,max and Poisson’s ratio l. rLða0Þ ¼ rLðabÞ þ rLðb0Þ rLðabÞ ¼

ð1  l  2l2 ÞP sða0Þ 1  l2  

rLðabÞ ¼

ð17Þ

P sða0Þ Eða0Þ

ð1 þ lÞð1  l  2l2 Þ

ð1  l  2l2 ÞP sðb0Þ 1  l2 

P sðb0Þ Eðb0Þ

ð1 þ lÞð1  l  2l2 Þ

ð18Þ

ð1  l  2l2 ÞP sða0Þ 1  l2   þ

P sða0Þ Eða0Þ

ð1 þ lÞð1  l  2l2 Þ

ð1  l  2l2 ÞP sðb0Þ 1  l2  l rS 1l

P sðb0Þ Eðb0Þ

ð1 þ lÞð1  l  2l2 Þ ð19Þ

186

Y. Liu, S.K. Vanapalli / Soils and Foundations 59 (2019) 176–195



Sr P s ¼ P s0 þ bc  w  100

2 ð20Þ

rhp3 ¼ rs

where Sr is the degree of saturation, Ps0 is the intercept on the Ps axis at zero suction value (Ps0 = 55 kPa is suggested for compacted expansive soils), bc is a fitting parameter, bc = (0.011e0.107Ip  7.872qd,max + 13.706)/2, qd,max is the maximum dry density of the soil, IP is the index of plasticity and w is the soil suction. As shown in Fig. 4(C), the increased LEP considering the LSP cannot exceed the passive earth pressure (PEP) to alleviate the failure conditions with respect to the shear strength of the soil (Pufahl et al., 1983). Fig. 6 provides a better illustration of the mobilization of LSP using Mohr circles. Prior to water infiltration, the LEP (rL1) can be considered to be at the at rest condition, which is less than the vertical pressure. With a reduction in matric suction, the LEP keeps increasing due to the mobilization of the LSP from the initial condition (rL1), which is lower than the vertical pressure to (rL2), which is higher than the vertical pressure and further to (rL3), which is approximately equivalent to the PEP. Considering the influence of both matric suction and soil-structure interface roughness, the PEP for saturated soil against a rough surface (rhp1), saturated soils against a frictionless surface (rhp2), unsaturated soil against a rough surface (rhp3) and unsaturated soils against a frictionless surface (rhp4) are summarized in Eqs. (21)–(24), respectively. Information that is more detailed is available in Liu and Vanapalli (2017).



rhp1

0 1 þ sin/0 cos2ap 0 2cos/ cos2ap ¼ rs þ c þ p0 1  sin/0 cos2ap 1  sin/0 cos2ap

rhp2 ¼

rs ð1 þ sin/0 Þ 2c0 cos/0 þ 1  sin/0 1  sin/0

rhp4 ¼

1 þ sin/0 cos2ap þ ½c0 þ ðuaf  uwf Þtan/b  1  sin/0 cos2ap 2cos/0 cos2ap 1  sin/0 cos2ap

rs ð1 þ sin/0 Þ 2½c0 þ ðuaf  uwf Þtan/b cos/0 þ 1  sin/0 1  sin/0

ð23Þ ð24Þ

1 C 1 B ap ¼ arcsin pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  arctan 2 2 2 2 A A þB 8 > A ¼ rs sin/0 þ ½c0 þ ðuaf  uwf Þtan/b cos/0 > > > > > > > b 0 0 0 > 0 > < B ¼ ½ca þ ðuaf  uwf Þtand sin/  rs sin/ tand > > > > > > > > > > :

2½c0 þ ðuaf  uwf Þtan/b cos/0 tand0 C ¼ rs tand0 þ ½c0a þ ðuaf  uwf Þtandb 

where rs is the vertical stress due to the unit weight of the upper soil layers and the surcharge, p0 is the pore water pressure, c0 is the true cohesion of soil, ca0 is the interface cohesion, /0 is the effective internal friction angle of soil, /b is the angle of friction with respect to matric suction, d0 is the effective interface friction angle, db is the interface friction angle with respect to matric suction and (uaf  uwf) is the matric suction on the failure plane at failure. 4. Validation of the proposed model

ð21Þ ð22Þ

4.1. Large-scale model test results by Katti et al. (1983) Katti et al. (1983) conducted large-scale model tests in a laboratory environment to monitor the variation in the

Fig. 6. Variation in LEP considering LSP with matric suction variations in Mohr cycle.

Y. Liu, S.K. Vanapalli / Soils and Foundations 59 (2019) 176–195

LEP of compacted expansive soil against a fixed model retaining wall [as shown in Fig. 7(A)]. The expansive soil used in this experiment was collected from Malaprabha Right Bank Canal km No. 76 (MRBC-76) from Karnataka State, India. The properties of MRBC-76 (i.e., the expansive clay) are summarized in Table 4. A thin coat of grease was applied to the tank walls and covered with polythene paper to minimize the tank wall friction. In the test, airdried soil was compacted to an average density of 1.32 g/ cm3 at a void ratio of 1.0 in the test tank. The compacted expansive soil was then soaked with water for a period of 70 days to achieve a fully saturated condition (Katti et al., 1983). The LEP on the rigid wall was measured using reaction jacks and proving rings, which were placed at depth intervals of 0.6 m. The matric suction profile for the soil in the test tank was not available in Katti et al. (1983). For this reason, commercial software SEEP/W from Geo-slope was used to simulate the variation in the matric suction profile in the infiltration process. Aytekin (1992) proposed a finite element estimation model to predict the LEP behind the retaining wall to simulate the experimental studies of Katti et al. (1983) by assuming the initial suction and SWCC. As good comparisons were achieved between the simulations by Aytekin (1992) and the large-scale model experimental results of Katti et al. (1983), key assumptions made by Aytekin (1992) in the simulation are extended in the present study. Assumptions of 10,000 kPa (5 pF) for the initial suction at the air-dried compaction condition and zero soil suction at a fully saturated condition, respectively, in the test tank were used by Aytekin (1992). In addition, in order to estimate the SWCC, Aytekin (1992) made three assumptions. Firstly, the soil suction value in the driest state was assumed to be around 6.0 pF

187

Table 4 Properties of expansive soil (MRBC-76) (summarized from Katti et al., 1983). Physical property

Expansive soil

Liquid limit, % Plastic limit, % Plasticity index Shrinkage limit, % Specific gravity Maximum dry density, g/cm3 Optimum moisture content, % Coefficient of permeability, m/sec

71.4 42 29.4 10.4 2.64 1.46 29 1  109

(100,000 kPa) (Russam and Coleman, 1961; Vanapalli et al., 1999). Secondly, the soil suction value of 3.3 pF was considered for the water content value of the plastic limit. Thirdly, the soil suction value of 0.1 pF was assumed for the water content value of the liquid limit (Croney and Coleman, 1954). The saturated volumetric water content of the expansive soil has been estimated to be 50% (calculated based on the void ratio, e = 1.0 at saturated soil condition from Katti et al., 1983). Based on above information, the SWCC was estimated with SEEP/W using the information from the discussed data points. Fig. 8 shows the estimated SWCC as well as the SWCC data points from the study presented by Aytekin (1992) for comparison purposes. Katti et al. (1983) reported that the soil inside the testing tank was fully saturated in 70 days. However, as per the coefficient of permeability (1  109 m/sec) information provided by Katti et al. (1983), a fully saturated condition cannot be achieved in the suggested short period of time from theoretical considerations for the large soil tank used in the study. For this reason, it is postulated that infiltration may have been accelerated in the compacted expansive soil of the test tank due to the likely presence of tension a= 1. m

0.6m

35

Expansive soil

0kPa

b=2.45m

0.6m

-10000kPa

h=3.2m

0.6m 0.6m

No-flow boundary

0.6m

Reaction jacks

Proving rings

Test tank (A)

(B)

Fig. 7. (A) Model retaining wall tested by Katti et al. (1983) (modified after Katti et al., 1983); (B) Boundary conditions in numerical simulation.

Y. Liu, S.K. Vanapalli / Soils and Foundations 59 (2019) 176–195 100

Degree of saturation (%)

Points from Aytekin (1992) 80

60

40

20

10 0

SWCC K-function (Van Genutchen 1980) Ksat=7.5e-7 m/sec 10 1

10 2

10 3

10 4

10 5

10 -5 10 -6 10 -7 10 -8 10 -9 10 -10 10 -11 10 -12 10 -13 10 -14 10 -15 10 -16 10 -17 10 -18 10 -19 10 -20 10 -21 10 -22

Coefficient of permeability (m/sec)

188

10 6

Suction (kPa)

Fig. 8. SWCC and coefficient of permeability function for expansive clay in Katti et al. (1983) test.

Esat ¼ 140sc

0.0

0.0

0.5

0.5

1.0

1.0

1.5 2.0 Initial condition After 20 days

2.5

1.5 2.0

3.0

-12000-10000 -8000 -6000 -4000 -2000

0

2000

-12000-10000 -8000 -6000 -4000 -2000

Pore water pressure (kPa)

0

2000

0

2000

Pore water pressure (kPa)

(A)

(B) 0.0

0.0

0.5

Initial condition After 60 days

1.0

Depth (m)

Depth (m)

Initial condition After 40 days

2.5

3.0

0.5

ð25Þ

where sc is the shear strength of soil, sc = kcv, cv is the vane shear strength and k is a correction factor, which is a function of the plasticity index (k = 0.92 for MRBC-76). Fig. 10 summarizes estimations using Eq. (19) and the experimental data. There is a good comparison between

Depth (m)

Depth (m)

cracks associated with volume expansion. In the simulation, in order to saturate the expansive soil within the tank in 70 days, a saturated coefficient of permeability value of 7.55  107 m/sec has been used. This assumption is more realistic and consistent with the coefficient of permeability values of laboratory specimens rather than the large-scale models and field studies. Several investigators have suggested that the coefficient of permeability for in-situ and large-size specimens is approximately two orders greater than that for laboratory specimens (Daniel, 1984; Elsbury et al., 1990). The variation in the coefficient of permeability with respect to suction is illustrated in Fig. 8. For the hydraulic boundary conditions shown in Fig. 7(B), variations in the suction profile during the infiltration simulated

with SEEP/W from Geo–Slope are shown in Fig. 9. The wetting front advances at a relatively slow rate along the depth as the initial suction is relatively high (i.e., 10,000 kPa). It should be noted that the variations in the suction profiles shown in Fig. 9 represent the total suction values. However, at high suction (i.e., greater than about 1500 kPa), matric suction and total suction can typically be assumed to be equivalent (Fredlund and Xing, 1994). The elastic properties of the expansive soil (i.e., saturated elastic modulus Es and Poisson’s ratio l) were not available in Katti et al. (1983). For this reason, they were estimated from known soil properties using the relationships proposed by Skempton and Henkel (1957) (Eq. (25)) between the shear strength and elastic modulus of London clay which had a plasticity index of around 50 percent (Cooling and Skempton, 1942). This relationship (Eq. (25)) was also employed by Aytekin (1992) to estimate the elastic modulus of saturated expansive soil for analyzing the results of Katti et al. (1983). In this study, the average saturated modulus of elasticity is estimated to be 5 MPa. A typical value for Poisson ratio, l = 0.3, used in Aytekin (1992)’s numerical simulation has been adopted in present study.

1.5 2.0

Initial condition After 70 days

1.0 1.5 2.0 2.5

2.5

3.0

3.0 -12000-10000 -8000 -6000 -4000 -2000

Pore water pressure (kPa)

(C)

0

2000

-12000-10000 -8000 -6000 -4000 -2000

Pore water pressure (kPa)

(D)

Fig. 9. Simulated variations in suction profiles during infiltration process in Katti et al. (1983) test.

Y. Liu, S.K. Vanapalli / Soils and Foundations 59 (2019) 176–195

and provides a good comparison with the experimental data in Katti et al. (1983). As discussed earlier, PEP is the upper limit of LEP. The PEP was not measured by Katti et al. (1983); however, this information can be estimated using the LEP distribution curve. From Fig. 10, it can be seen that the measured

0.0

0.0

0.5

0.5

1.0

1.0

Depth (m)

Depth (m)

the estimations and the measured data from the summarized results including the development of the LSP associated with the gradual increase in the degree of saturation upon water infiltration. In Fig. 10(D), after 70 days, the soil within a depth of 2.8 m has been fully saturated. For this reason, the LEP profile increases linearly with depth

1.5 2.0 Initial condition After 20 days

2.5

1.5 2.0 Initial condition After 40 days

2.5

3.0

3.0 0

50

100

150

200

250

0

Lateral earth pressure (kPa)

50

100

150

200

250

Lateral earth pressure (kPa)

(A)

(B) 0.0

0.0 0.5

0.5

Initial condition After 60 days

1.0

Depth (m)

Depth (m)

189

1.5 2.0 2.5

1.0 Initial condition After 70 days Experimental data after 70 days (Katti et al. 1983) Passive earth pressure

1.5 2.0 2.5

3.0

3.0 0

50

100

150

200

250

300

Lateral earth pressure (kPa)

0

50

100

150

200

250

300

Lateral earth pressure (kPa)

(C)

(D )

Fig. 10. Comparison between estimation and in-situ measurement of LEP in Katti et al. (1983) test.

Wood frame with pressure cells

0kPa

1m Clayey silt 2.5m

No-flow boundary

0.5m 0.5m 0.5m Retaining wall

-268.3kPa

Position of pressure cells

1m

(A)

(B)

Fig. 11. (A) Position of pressure cells in project by Mohamed et al. (2014); (B) Boundary conditions in numerical simulation.

190

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LEP increases linearly with an increasing depth due to the influence of water infiltration. However, beyond a depth of around 1.4 m, this increase slows down. Once the soil achieves a saturated condition, both LEP values, including the LSP and the PEP, should exhibit a linear increase with respect to the depth. The measured LEP is bi-linear in nature, which can be attributed to the mobilization of the LEP because the LSP is limited by the PEP in the shallow depth zone (0 to around 1.4 m). However, below 1.4 m, the LSP can be fully mobilized without any limitation.

Table 5 Parameters used in the estimation of SWCC. Physical property

Clayey silt

Liquid limit, % Saturated volumetric water content, m3/m3 Diameter at 10% passing, mm Diameter at 60% passing, mm

27.2 0.3146 0.0025 0.013

Initial condition After 1 hour After 24 hours After 48 hours After 72 hours After 96 hours

4.2. In-situ test results by Mohamed et al. (2014)

10-7 10-8 10-9 10-10 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19

Degree of saturation (%)

100 80 60 40 20

100

SWCC K-function (Van Genutchen 1980) Ksat=1e-7 m/sec 101

102 103 104 Suction (kPa)

105

Coefficient of permeability (m/sec)

106

Fig. 12. Soil water characteristic curve and coefficient of permeability function for clayey silt in Mohamed et al. (2014) project.

0.0 0.5

Depth (m)

Mohamed et al. (2014) measured the development of LSP against a retaining wall, which forms one of the Assiut el gadida city projects in Assiut, Egypt. The backfill behind the retaining wall was compacted to achieve a bulk density of 1.43  103 kg/m3 in several layers with the thickness of each layer being equal to 0.25 m. Five strain gauges were placed at different positions, as shown in Fig. 11(A) for the measurement of the LEP. Water was added at the soil surface when the soil showed signs of drying. The soil used in this investigation was clayey silt, which consisted of 9.6% clay and 84.4% silt. A maximum LSP of around 173 kPa was measured from the field investigations. Due to the lack of data, the Atterberg limits of the soil were estimated based on the soil type and the clay content. This was achieved using the relationship for fine-grained soils provided by Wu and Liu (2008) which only requires information on the clay content. The liquid limit and the plastic limit of the clayey silt are estimated to be 17.8% and 27.2%, respectively. The maximum dry density is estimated as 1.21  103 kg/m3 assuming that the soil was compacted at the optimum water content. The suction profile variation in the infiltration process was not available in the study presented by Mohamed et al. (2014). For this reason, similar to the approach used earlier for interpreting Katti et al. (1983)’s case study, a finite element program (SEEP/W from Geo-Slope 2012) was used as a tool to estimate the changes in suction over time. The boundary conditions used in the simulation are

1.0 1.5 2.0 2.5 3.0 -300

-250

-200

-150

-100

-50

0

Pore water pressure (kPa) Fig. 13. Simulated variations in suction profiles during infiltration process in Mohamed et al. (2014) project.

shown in Fig. 11(B). Using SEEP/W, the SWCC (Fig. 12) was estimated from the grain size distribution presented by Mohamed et al. (2014). Detailed parameters are listed in Table 5. The coefficient of permeability value of 107 m/sec has been assumed for clayey silt for simulation studies following guidelines from Sarsby (2000). The simulated suction profile variation is presented in Fig. 13. Mohamed et al. (2014) considered that the soil was initially in an active state and negative values of the active earth pressure were reported. These results suggest that there should be a tension crack between the retaining wall and the soil. For this reason, the LSP contribution increased the active earth pressure from a negative value to a positive one. The maximum value of the LSP, however, was limited by the PEP. In this study, the PEP is calculated using the shear strength parameters (/0 = 6° and c0 = 20 kPa) provided by Mohamed et al. (2014). Since there were no data available in Mohamed et al. (2014), a saturated elastic modulus and Poisson’s ratio values for a typical silt of 5 MPa and 0.3, respectively, were assumed from the studies summarized by Ranjan and Rao (2000) for the calculation of Eq. (19). Fig. 14 summarizes the comparisons between the estimated (Eq. (19)) and the measured LEP at different periods. Estimations based on Eq. (19) illustrate well the development of the LSP with the variation in suction [see Fig. 14(A)–(D)]. However, there are

1.0

1.0

1.5

1.5 Depth (m)

Depth (m)

Y. Liu, S.K. Vanapalli / Soils and Foundations 59 (2019) 176–195

after 24 hours In-situ measurement Prediction Passive earth pressure

2.0

2.5

after 48 hours In-situ measurement Prediction Passive earth pressure

2.0

2.5

3.0

3.0 0

100

200

300

400

0

Lateral earth pressure (kPa)

100

200

300

400

Lateral earth pressure (kPa)

(A)

(B)

1.0

1.0

1.5

1.5 Depth (m)

Depth (m)

191

after 72 hours In-situ measurement Prediction Passive earth pressure

2.0

2.5

after 96 hours In-situ measurement Prediction Passive earth pressure

2.0

2.5

3.0

3.0 0

100

200

300

400

0

Lateral earth pressure (kPa)

100

200

300

400

Lateral earth pressure (kPa)

(C)

(D)

Fig. 14. Comparison between estimation and in-situ measurement of LEP in Mohamed et al. (2014) project.

some differences in the comparisons between the estimated values and the in-situ measurements. For example, in Fig. 14(D), the calculated PEP is less than the measured LEP. The reasons for these differences can be attributed to following: (i) the idealized boundary conditions described by Mohamed et al. (2014); (ii) the assumed coefficient of permeability used for the numerical simulations may be different from the actual value; (iii) the in-situ infiltration of water into soils can be affected by minor cracks, and the initial natural water content within the soil may be also influenced by in-situ factors; and (iv) manual operation such as the installation of the pressure measuring system, and any inclination of the earth pressure cells during the installation can considerably influence the LEP measurement.

might cause a large amount of pressure on the wall. In order to investigate the behavior of the retaining wall, the earth pressure and the soil suction in the stiff clay were monitored by Richards and Kurzeme (1973), using psychrometers and pressure cells, respectively. Fig. 15 shows Readout cabinet

A 7.5-m-deep basement of the Gouger Street Mail Exchange (Adelaide, Australia) required construction of a reinforced concrete retaining wall, supporting over most of its depth in stiff Hindmarsh clay. As free water was present in the clay from precipitation sources, there was concern that subsequent wetting and heaving of the clay

Timber panels

Earth pressure cells

Psychrometer borehole Fill

1.8m

Marl

1.7m

4m 0300 0301

2m

4.3. In-situ test results by Richards and Kurzeme (1973)

0.62m×0.19m Beam

0.8m

0302 0303

Hindmarsh clay

Retaining wall

Around 3.5m

Fig. 15. Locations of earth pressure cells and psychrometer borehole at Adelaide test site (modified after Richards and Kurzeme, 1973).

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Table 6 Atterberg limits of Hindmarsh clay. Hindmarsh clay layer

No. of tests

Liquid limit, %

Plastic limit, %

Plastic index

Cox (1970) Sheard and Bowman (1996)

11 14

16–30 17–42 (average 26.9)

55–100 46–100 (average 72.4)

40–70 27–66 (average 45.5)

Bowman (1996) reported the Atterberg limit results of Hindmarsh clay from laboratory test results. In this study, the average values reported by Sheard and Bowman (1996) were used (see Table 6). To predict the variation in the LEP in this study (considering the influence of the LSP) with respect to changes in the suction profile using the proposed model (Eq. (19)), the SWCC, saturated soil elastic modulus and Poisson’s ratio were also necessary. The SWCC equation proposed by Fredlund and Xing (1994) is used to fit the in-situ measurement database reported by Jaksa (1995). The predicted SWCC along with the fitted parameters of the SWCC and the position of in-situ measurements are illustrated in Fig. 16. From the database provided by Jaksa (1995), the average water content of the Hindmarsh clay along the depth is around 27% and the water content of the soil at a saturated condition is around 34%. An average modulus of elasticity of 43.1 MPa was estimated corresponding to the water content of 27%. Using Eq. (8), the saturated elastic modulus was back calculated as 1.36 MPa. A value of 0.3 was assumed for Poisson’s ratio in the calculation. The levels of LEP recorded by cells 0302 and 0303 in the middle of the Hindmarsh clay layer (as shown in Fig. 15) are used to validate the proposed model. The in-situ test conducted by Richards and Kurzeme (1973) lasted from August 1971 to September 1973. Fig. 17(A) summarizes the variation in vertical pressure with respect to depth measured using the earth pressure cells. Fig. 17(B) summarizes the variations in the suction profile on the soil samples at different depths. Fig. 18 shows comparisons between the

80 60 40

SWCC of Hindmarsh clay (Fredlund and Xing 1994, a=199.0201; n=299.4268; m=0.056)

20 0 100

Information from the database (Jaska 1995)

101

102 103 104 Suction (kPa)

105

106

Fig. 16. Fitted SWCC for Hindmarsh clay.

the positions of the pressure cells on the retaining wall, the distance between the pressure cells and the psychrometer borehole as well as the soil profile behind the retaining wall. The Hindmarsh clay layer that underlies the Adelaide city area belongs to a very stiff to hard, high plastic silty clay (USCS symbol CH). The soil properties of Hindmarsh clay were not presented by Richards and Kurzeme (1973). For this reason, the soil properties of Hindmarsh clay reported by other investigators were used in the present study (Jaksa, 1995; Cox, 1970; Sheard and Bowman, 1996). From the database summarized by Jaksa (1995), the dry density of the Hindmarsh clay at the test site region varies from 1.38  103 kg/m3 to 1.82  103 kg/m3. In this study, an average value of 1.6  103 kg/m3 is employed for simplicity reasons. Cox (1970) and Sheard and Pressure (kPa) 200 300 400

100

500

600

Suction (kPa) 500 1000

100

0

0

0

Degree of saturation (%)

100

5000

4

5 3

0302

6 4

5

2

6

6 2 4

1

4

2

Probe 0340

3 52

6

0341

1

0342

5 3 41

0303

6

64

Vertical pressure distribution changes

8

8

1 2

0301

6

4

1253 4

5

6

Cell 0300 Depth (m)

4 6

Depth (m)

2

Borehole 008 23465

5

21

0343

Soil suction profile changes

Legend: 1=AUG 1971, 2=SEPT 1971, 3=NOV 1971, 4=MAY 1972, 5=SEPT 1972, 6=SEPT 1973. (A)

(B)

Fig. 17. Variation in (A) Vertical pressure with respect to depth. (B) Suction profile (summarized from Richards and Kurzeme, 1973).

Y. Liu, S.K. Vanapalli / Soils and Foundations 59 (2019) 176–195

300 Cell 0302 at the depth of 6.6m In-situ measurement Prediction

200 150 100 50 0 1 2 3 4 5 6 Legend: 1=AUG 1971; 2=SEPT 1971; 3=NOV 1971; 4=MAY 1972; 5=SEPT 1972; 6=SEPT 1973.

Lateral earth pressure (kPa)

Lateral earth pressure (kPa)

300 250

193

250

Cell 0303 at the depth of 7.4m In-situ measurement Prediction

200 150 100 50 0 1 2 3 4 5 6 Legend: 1=AUG 1971; 2=SEPT 1971; 3=NOV 1971; 4=MAY 1972; 5=SEPT 1972; 6=SEPT 1973.

Fig. 18. Comparison between estimated LEP using proposed approach and in-situ measurement of LEP at Adelaide site from Richards and Kurzeme (1973).

prediction using the proposed model and the in-situ measurement data. Reasonably good comparisons can be observed between the estimation and the in-situ measurements in cells 0302 and 0303. The undrained shear strength parameters from field tests were presented by Richards and Kurzeme (1973) and Jaksa (1995); however, no information on the effective shear strength parameters was available. For this reason, the variations in PEP could not be summarized for this example. 5. Conclusions LSP mobilizes as water infiltration triggers swelling potential characteristics in expansive soils under confined conditions in the horizontal direction and contributes to serious problems in geo-infrastructures. For this reason, the LSP should be considered as a key factor in the rational design of geotechnical infrastructures such as retaining structures. In this study, a critical review of various testing techniques (laboratory, large-scale model and in situ tests), that are conventionally used for the determination of the LSP, has been presented. The LSP mobilization of an expansive soil is dependent on both the boundary conditions and the saturation path. Among the various laboratory-testing techniques that are presently available in the literature, the swell under surcharge test is mostly used because it simulates well the stress state of a soil’s elementary volume behind the retaining wall. However, the conventionally applied techniques are only useful for determining the LSP at a fully saturated condition. This is inconsistent with the scenarios typically encountered in engineering practice, in which the soil is still in an unsaturated state even after a certain amount of water infiltration. The review of LSP prediction models also highlights that there is no simple and reliable model presently available in the literature for predicting LSP mobilization during the infiltration process.

A model has been proposed in this study to predict the LEP considering the LSP against a fixed rigid retaining structure taking account of the variation in matric suction associated with water infiltration, extending the mechanics of unsaturated soils. The proposed model has been verified using the experimental data from a large-scale model retaining wall test by Katti et al. (1983) along with the in-situ measurements from Mohamed et al. (2014) and Richards and Kurzeme (1973) on retaining structures. The proposed model has been found capable of reasonably predicting the LSP mobilization from an initial unsaturated state to a subsequent unsaturated state during the infiltration process employing only a limited number of soil properties, which include the SWCC, saturated elastic modulus Esat, plasticity index Ip, maximum dry density qd,max and Poisson’s ratio, l. The proposed simple model will be valuable in geotechnical engineering practice for assisting geotechnical engineers in quickly estimating the increasing LEP due to the LSP mobilization behind retaining structures during the infiltration process, thus contributing to the rational design or construction decisions. Acknowledgements The authors gratefully acknowledge the research funding and financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) and China Scholarship Council - University of Ottawa Joint Scholarship. References ASTM (American Society for Testing and Materials), 2014. Standard Test Methods for One-Dimensional Swell or Collapse of Soils. ASTM D4546 – 14, ASTM International, West Conshohocken, PA. Alonso, E.E., Gens, A., Hight, D.W., 1987. Proceedings of 9th European Conference on Soil Mechanics, pp. 1087–1146. Alonso, E.E., Gens, A., Josa, A., 1990. A constitutive model for partially saturated soils. Ge´otechnique 40 (3), 405–430.

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