Draft - TSpace Repository: Home...2018) change the matric suction, stress state, and stress history in the surface soil on the earth. Although soil mechanics was initiated from the

Draft

HYDROMECHANICAL BEHAVIOUR OF OVERCONSOLIDATED UNSATURATED SOIL IN UNDRAINED CONDITIONS

Journal: Canadian Geotechnical Journal

Manuscript ID cgj-2018-0323.R2

Manuscript Type: Article

Date Submitted by the Author: 06-Nov-2018

Complete List of Authors: Wu, Shengshen; RMIT University, School of EngineeringZhou, Annan; RMIT University, School of EngineeringLi, Jie; RMIT University, School of EngineeringKodikara, Jayantha; Monash UniversityCheng, Wen-Chieh; Xi’an University of Architecture and Technology, School of Civil Engineering

Keyword: Unsaturated soil, overconsolidated ratio, hydromechanical behaviour

Is the invited manuscript for consideration in a Special

Issue? :Not applicable (regular submission)

https://mc06.manuscriptcentral.com/cgj-pubs

Canadian Geotechnical Journal

Draft

- 1 -

HYDROMECHANICAL BEHAVIOUR OF OVERCONSOLIDATED UNSATURATED SOIL IN

UNDRAINED CONDITIONS

Shengshen Wu, Annan Zhou*, Jie Li, Jayantha Kodikara and Wen-Chieh Cheng

Name: Shengshen Wu (PhD candidate)Affiliation: School of Engineering, Royal Melbourne Institute of Technology (RMIT), Melbourne,

Vic 3001, Australia

Email: [email protected]

Name: Annan Zhou (PhD, Senior Lecturer, *Corresponding author)

Affiliation: School of Engineering, Royal Melbourne Institute of Technology (RMIT), Melbourne,

Vic 3001, Australia


Name: Jie Li (PhD, Associate Professor)

Affiliation: School of Engineering, Royal Melbourne Institute of Technology (RMIT), Melbourne,

Vic 3001, Australia


Name: Jayantha Kodikara (PhD, Professor)

Affiliation: Department of Civil Engineering, Monash University, Vic 3800, Australia


Name: Wen-Chieh Cheng (PhD, Professor)Affiliation: School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an

710055, China


Manuscript submitted toCanadian Geotechnical Journalfor consideration for publication

Ms. No.: cgj-2018-323.R2

Page 1 of 39



Draft

- 1 -

HYDROMECHANICAL BEHAVIOUR OF OVERCONSOLIDATED UNSATURATED SOIL IN


Shengshen Wu†, Annan Zhou*†, Jie Li†, Jayantha Kodikara ‡, Wen-Chieh Cheng§†School of Engineering, Royal Melbourne Institute of Technology (RMIT), Melbourne, Vic 3001, Australia

‡Department of Civil Engineering, Monash University, Vic 3800, Australia§School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China

*Corresponding author: Dr Annan Zhou ([email protected])

ABSTRACT

Hydromechanical behaviour of an unsaturated silt with various suctions and different

overconsolidated ratios (OCRs) was investigated through a series of undrained triaxial tests

(constant water contents, CW). All the samples were prepared from the slurry state. Different

OCRs (= 1, 2, 4, and 8 in net stress) were achieved by unloading the samples to 400, 200, 100,

and 50 kPa from an initial confining net pressure of 400 kPa. Then the samples were dried to

various suctions (0, 100, 200, 300, and 400 kPa). Unsaturated samples with different OCRs

then were sheared at constant water content conditions following the conventional triaxial

compression (CTC) paths. Full hydromechanical responses including the changes on deviator

stress, stress ratio, volumetric strain, suction and degree of saturation with axial strain were

monitored and presented in this paper. Some key findings include: (1) the critical state for

unsaturated soils with different OCRs can be well defined by Bishop’s effective stress; (2) the

peak strength in Bishop’s effective stress increases with increase of OCR but decreases with

increase of suction in the undrained condition; and (3) the volume change of unsaturated soils

in undrained conditions is related to OCRs and the volume of pore air.

KEYWORDS

Unsaturated soil, OCR, suction, constant water contents, hydromechanical behaviour

Page 2 of 39



Draft

- 2 -

1 INTRODUCTION

Most of soils in the natural environment are partially saturated with water. Unsaturated soils

are generally near the ground surface and are commonly overconsolidated due to

environmental effects (Nishimura et al. 1999). Furthermore, the varying climatic environment

(Power et al. 2017; Lyu et al. 2018) and human activities like excavation, tunnelling and

dewatering (Shen and Xu 2011; Shen et al. 2014; Wu et al. 2015; Wu et al. 2017; Xu et al.

2018) change the matric suction, stress state, and stress history in the surface soil on the earth.

Although soil mechanics was initiated from the study on saturated soil behaviour, some

significant advances in understanding of unsaturated soil behaviour have been seen in the last

thirty years, both in laboratory testing and in the development of constitutive models (Alonso

et al. 1990; Bolzon et al. 1996; Cui and Delage 1996; Fredlund et al. 1996; Wheeler 1996;

Khalili and Loret 2001; Gallipoli et al. 2003a; Sun et al. 2007b; Sheng et al. 2008; Lu et al.

2010; Kodikara 2012; Zhou et al. 2012b; Zhou et al. 2012c; Zhou et al. 2016; Zhou et al.

2018). However, as reviewed recently by Gens (2010) and Sheng (2011), unsaturated soil

mechanics is still at an early stage and there are still a number of fundamental questions

unanswered. For example, regarding the laboratory testing, compacted unsaturated soils are

overwhelmingly studied but the reconstituted unsaturated soils are rarely investigated in the

literature. Compared with unsaturated soils prepared from compaction, unsaturated soils

prepared from the initial slurry state show more clear stress and suction histories which are of

benefit for understanding the fundamental behaviour of unsaturated soils and for establishing

constitutive models (Gao et al. 2015; Zhang et al. 2015). In addition, the stress history (or

over-consolidation) is a key factor in saturated soil mechanics, but seldom investigated in the

context of unsaturated soil mechanics. One of the reasons is that the stress history cannot be

clearly identified for compacted unsaturated soils.

The experimental study on mechanical behaviour of overconsolidated unsaturated soils is very

limited but has been initiated. To study the dependence of the shear strength parameters on

Page 3 of 39



Draft

- 3 -

the stress history, Nishimura et al. (1999) conducted a series direct shear tests by using a

modified direct shear apparatus on a statically compacted unsaturated soil subjected to various

total stress ratios (TSR, the ratio of the static compaction pressure and current confining

pressure) with controlled matric suction. The critical state and Hvorslev state surfaces have

been investigated for an overconsolidated unsaturated silty soil through a set of controlled

suction triaxial laboratory experiments (Estabragh and Javadi 2008; Estabragh and Javadi

2014). The soil used in their study consists of 5% sand, 90% silt, and 5% clay. The liquid

limit and plasticity index are 29% and 19%, respectively. The suctions are 0, 100, 200 and

300kPa and the OCRs are estimated from 1.38 to 11. The definition of the OCR used in their

study was not well defined because the stress history for a compacted unsaturated soil was

naturally vague (Nishimura et al. 1999). In addition, regarding the previous experimental

study on unsaturated soils with different OCRs (Nishimura et al. 1999; Estabragh and Javadi

2008; Estabragh and Javadi 2014), only the mechanical responses were monitored but no

hydraulic and hydromechanical data were recorded, which restricted the application of their

results especially when the coupling behaviour has to be emphasised recently (Sheng 2011;

Sheng and Zhou 2011; Zhou et al. 2012b; Zhou and Sheng 2015). For the compacted

unsaturated soils, the stress history can also be reflected by the different densities

approximately, and the effect of density on the hydromechanical behaviour of the compacted

unsaturated soils has been studied in the literature. For example, compacted pearl clay at

different densities were tested in suction-controlled oedometer and triaxial to study its

hydromechanical behaviour, especially the wetting-collapse behaviour (Sun et al. 2007a; Sun

et al. 2007b). However, to highlight the collapse behaviour, the densities were set to be

relatively low. According to Li and Yang (2018), the OCR for the tested pearl clay was

relatively low (= 1.45 ~ 2.67). Furthermore, very limited test results were reported for

overconsolidated unsaturated soils in undrained conditions, especially when the change of

both mechanical and hydraulic variables was measured during the tests.

The theoretical progress in modelling the mechanical or hydromechanical behaviour of

overconsolidated unsaturated goes beyond the progress in experiments. For example, Yao et

Page 4 of 39



Draft

- 4 -

al. (2014) extended the UH model from the saturated condition to unsaturated conditions to

consider the influence of OCRs on the mechanical behaviour of unsaturated soils. The UH

model (Yao et al. 2009) was originally developed for describing the shear-dilation and post-

peak softening behaviour for overconsolidated saturated soils (Yao and Zhou 2013; Yao et al.

2015) by employing a novel unified hardening parameter (Yao et al. 2008a; Yao et al. 2008b).

Based on the sub-loading surface plasticity, Zhou and Sheng (2015) extended their fully-

coupled hydromechanical model for normally-consolidated unsaturated soils (Zhou et al.

2012b; Zhou et al. 2012c) to overconsolidated unsaturated soils. Very recently, based on the

framework proposed by Zhou et al. (2012c), Li and Yang (2018) proposed a new

hydromechanical model for overconsolidated unsaturated soils by introducing a new state

variable related to the stress history. It is noted that, for the model validation, these

mechanical or hydromechanical models (Yao et al. 2014; Zhou and Sheng 2015; Li and Yang

2018) employ the very limited experimental data (Sun et al. 2007b; Sun et al. 2007c;

Estabragh and Javadi 2008; Estabragh and Javadi 2014) mentioned previously. It clearly

shows a shortage and a demand on the high quality experimental data for unsaturated soils

with different stress histories

Considering the shortage of the experimental data on hydromechanical behaviour of

overconsolidated unsaturated soils in undrained conditions (especially prepared from slurry

state with a clear stress history), we performed a series of triaxial tests in undrained conditions

on an unsaturated silt prepared from the slurry state with different initial suctions (0, 100, 200,

300, and 400 kPa by axis-translation technique) and OCRs (OCR in terms of net stress = 1, 2,

4, and 8, confining net pressure = 400, 200, 100, and 50 kPa and maximum net stress in

isotropic compression stage = 400 kPa for all specimens). The OCR in net stress is defined as

the ratio between the maximum net mean stress in the history and the current net mean stress

(i.e., OCR = pmax/p). Hydromechanical responses including the changes on deviator stress,

stress ratio, volumetric strain, suction and degree of saturation with axial strain were presented

and discussed in this paper. The major novelties of the paper include that (1) the

comprehensive and precise measurements of hydraulic (such as changes on suction and degree

Page 5 of 39



Draft

- 5 -

of saturation) and mechanical responses (such as changes on deviator stress and volumetric

strain) with joint suction and OCR control, and (2) the extension of existing knowledge on

unsaturated soils from normally consolidated state to over-consolidated states by solid and

innovative experimental data. The experimental results can be employed to develop or validate

advanced hydromechanical models for unsaturated overconsolidated soils. The experimental

results and conclusions can be also used to guide the design of excavation, slope, pavement,

footing and other earthworks related to unloading/reloading cases on unsaturated

overconsolidated soils.

2 EXPERIMENTAL TESTS

2.1 Soil properties and sample preparation

The soil used in the testing program is a silty soil obtained from a testing site established for

studying the potential damage caused by climate change on urban pavements and residential

buildings (Sun et al. 2017a; Sun et al. 2017b). The site chosen for field instrumentation is

located in Glenroy East, approximately 13 km north of Melbourne CBD and about 500 meters

north of the Northern Golf Club. It lies within the City of Moreland council boundary. The

Glenroy site was selected for this study because the geology is typical of many existing and

new residential housing estates to the west and north of Melbourne and the silt in the Glenroy

area is a typical top soil distributed wide in the Great Melbourne Region.

The X-ray diffraction analysis showed that the main minerals in the Glenroy silt were 75%

quartz, 10% sodium feldspar, 7.5% micro line, 4% illite and 3.5% montmorillonite. The soil

was obtained from about 1.0~1.5 meter below the ground surface and the particle distribution

curve is shown in Figure 1. The soil was refined, and the coarse particles were removed by

0.425mm sieve. For the Glenroy silt, the specific gravity is 2.70, the plastic limit is 24%, the

liquid limit (LL) is 35% and the plasticity index (PI) is 11%. According to the Unified Soil

Classification System (USCS), it can be classified as silty soil with low plasticity (ML). The

Page 6 of 39



Draft

- 6 -

soil was prepared in slurry form with water content around 1.5LL (Burland 1990; Burton et al.

2014; Gao et al. 2015). The slurry soil was then reconsolidated in four consolidometers

(diameter = 25cm, height = 30cm) under a pressure of about 50 kPa for 21days

(consolidometer was sealed with water) to prepare reconstituted fully saturated samples for

tests. The samples prepared in the consolidometer were trimmed to 76 mm in height and 38

mm in diameter for triaxial tests, and 20 mm in height and 50 mm in diameter for water

retention tests.

2.2 Experimental apparatus

The Fredlund SWCC device was employed for water retention testing under different vertical

net stresses (10, 200, and 400kPa) and the GDS unsaturated triaxial test system (double cell

with differential pressure transducer) was employed for testing hydromechanical behaviour of

the Glenroy silt.

The layout of the Fredlund SWCC device is presented in Figure 2a. The axis-translation

technique (Hilf 1956) was used for creating the desired suctions in the samples. The pore air

pressure (ua) was applied at the top of the sample and the pore water pressure (uw) was applied

at the base of the sample through a saturated ceramic disk with a high air entry value (HAVE)

of 1500 kPa. The pore water pressure used for water retention test was very low and can be

ignored (10 cm water head, ~1kPa). The air pressure was supplied by a Kaeser Aircenter SM9

air compressor with a stable pressure output of 1500 kPa. Two sets of air pressure regulators

(0~200kPa and 200~1500kPa) were used to control the air pressure applied onto the soil

samples. Vertical net stress can also be applied separately by the air pressure as well. Sample

was confined by steel ring and volume change can be measure by LVDT. The flow of water

out of the sample was measured by a standing pipe.

The layout of the GDS-UNSAT device is presented in Figure 2b. The axis-translation

technique was used for controlling the suction in the soil samples. The pore air pressure (ua)

Page 7 of 39



Draft

- 7 -

was applied by the GDS pneumatic pressure controller at the top of the sample through a filter

with low air entry value and a hydrophobic membrane (Cai et al. 2013; Gao et al. 2015; Zhang

et al. 2015) that only allows air to pass but stops water. The cell pressure ( ) was controlled 𝜎3

by the GDS pneumatic pressure controller. The pore water pressure (uw) was applied by the

advanced GDS pressure-volume controller at the base of the sample through a saturated

ceramic disk with an air entry value of 1500 kPa. The axial force was applied by the lower-

chamber pressure controller. In terms of the measurement, the axial displacement was

measured by the LVDT and axial stress force was measured by the inner-cell force transducer.

The pore water pressure (uw) was measured by the pore-water pressure transducer for

undrained scenarios and the drained water from the sample was measured by the advanced

GDS pressure-volume controller. The most important feature of this system is that the volume

change of the sample is measured through the change of the inner-cell water level to the

reference water level by the differential pressure transducer (DPT).

2.3 Experimental procedure

In this study, twenty CW (constant water contents) tests with four different stress histories

(OCR = 1, 2, 4, and 8) and five different initial suctions (0 kPa, 100 kPa, 200 kPa, 300 kPa,

and 400 kPa) were performed. The loading paths in terms of net stress, suction and deviator

stress are shown in Figure 3 and the details for each test are presented in Table 1. In general,

the experimental procedure (triaxial tests) can be divided into the following three stages, i.e.,

isotropic loading/unloading, drying and shearing.

Insert Table 1 here.

2.3.1 Isotropic loading/unloading

After preparing the slurry sample in the consolidometer at a vertical pressure of 50kPa with 21

days, soil sample was cut by sampling tube and trimmed to standard triaxial specimens

Page 8 of 39



Draft

- 8 -

(diameter = 38mm and height = 76 mm). The fully saturated specimens were set up in the

triaxial, loaded isotropically to a net mean stress of 400kPa after the saturation check by the

back pressure, and then left to deform and drain until the equilibrium (ASTM-D2435). After

the equilibrium, the specimens were then unloaded to preselected net mean stress (50, 100,

200, and 400kPa) to create desired OCRs (= 8, 4, 2, and 1) in net stress. At the end of

unloading, the samples were left to deform and drain until the equilibrium (ASTM-D2435).

The equilibrium was also judged by both the drainage volume and volume change measured

by the DPT, both of which were monitored and recorded by a computer during the isotropic

loading/unloading process. In particular, the comparison between the measured drainage

volume by back volume/pressure controller (BVC) and the volume change measured by the

DPT can be employed to evaluate the accuracy of the DPT. As shown in Figure 4, the void

ratio change calculated by the drainage volume for different isotropic loading/unloading paths

are presented by dots and the void ratio change calculated by the direct volume measurement

by DPT for different isotropic loading/unloading paths are presented by curves. The

comparison in Figure 4 indicates that the DPT measurements have a good agreement for both

compression (loading) and swelling (unloading) processes. Figure 4 also shows clear

equilibrium processes for different isotropic loading/unloading paths.

2.3.2 Drying

The fully saturated specimens with different OCRs were dried to different suctions by using

axis-translation technique. During this stage, the drainage valve was open and the net

confining stress kept as a constant. To introduce the unsaturation to the soil specimens, the air

pressure was ramped to the preselected values (100, 200, 300, and 400 kPa) according to the

previous work (Sivakumar 1993; Wheeler and Sivakumar 1995). Then, the volume change

measured by the DPT and the drainage volume were monitored by the BVC. Figure 5a shows

the volume of pore water discharged from the specimens with different OCRs along with the

time when a suction of 400 kPa was imposed. Figure 5b shows the volume change of the

specimens with different OCRs along with the time when a suction of 400 kPa was imposed.

Page 9 of 39



Draft

- 9 -

According to the previous research (Toyota et al. 2001; Sun et al. 2007c), the equalization

time for dehydration process was set to be one week for the tests. Form Figure 5, we can also

find one week (10080 min) was enough for achieving equilibrium in terms of both volume

change and drainage.

2.3.3 Shearing

After the drying stage, the drainage valve was closed and undrained triaxial shear tests were

conducted on the samples with different initial suctions and OCRs. During the shearing stage,

the confining pressure, air pressure and the rate of axial strain keep constant. Although

undrained condition was employed, to ensure the internal suction equilibrium (Toyota et al.

2001; Oka et al. 2010), the rate of 0.76mm/h (1%/h) was used in the shear tests. The selected

strain rate ensured the stabilized states can be achieved in constant water content conditions.

During shearing, the change of pore water pressure was measured by pore water pressure

transducer and the volume change of specimen was measured by the DPT only. The axial

strain, volumetric strain, void ratio, suction, degree of saturation, net stress, deviator stress,

and stress ratio were calculated from the recorded data. Moreover, membrane effects were

corrected when estimating the volume strain and deviator stress by using ASTM D-4767. This

was important for the shear-dilatancy behaviour particularly at higher OCRs. According to

ASTM D-4767, all the samples were tested to critical state at the end of the shearing stage

with an axial strain of ~20% (Toyota et al. 2001; Oka et al. 2010).

2.3.4 Water retention tests

In addition to the triaxial tests listed in Table 1, three water retention tests (drying branch only)

were conducted with different net vertical pressures (=10kPa, 200kPa and 400kPa) by using

the Fredlund SWCC device (see Figure 2a). The specimen size for water retention tests is

50mm in diameter and 20mm in height. The specimens were cut from the sample extracted

from the consolidometer by using a steel cutting ring that was used to confine the specimen

during the drying test. Because of the applied vertical stress and the long drying process by

Page 10 of 39



Draft

- 10 -

several steps, the separation between the specimen and cutting ring during the drying process

was not observed. Suction was applied step by step (10, 50, 200, 400 and 800kPa) and the

total drying time was about 6~8 weeks. The vertical displacement was measured by vertical

LVDT and the volume change can be calculated by assuming constant diameter of the

specimen. The volume of the drained water during drying was measured by a standpipe, as

shown in Figure 2a.

3 EXPERIMENTAL RESULTS

3.1 Water retention behaviour

The measured water retention curves (drying branches) of the Glenroy silt at different vertical

net stresses (v) have been presented in Figure 6. Along with the increase of the vertical net

stresses, the initial void ratio before drying decreases (i.e., e = 0.63, 0.58, 0.54 when v = 10,

200, 400kPa, respectively). As shown in Figure 6, a clear ‘shift’ phenomenon of the water

retention curve can be observed due to the increase of vertical stress (or the decrease of initial

void ratio), which has been reported and discussed in the literature (Gallipoli et al. 2003b;

Tarantino 2009; Sheng and Zhou 2011; Zhou et al. 2012a). In this paper, as shown in Figure 6,

the 3-parameter VG model (van Genuchten 1980) has been adopted to reproduce the test data.

The 3-parameter VG model can be written as follows.

𝑆r = [ 11 + (𝑠/𝑎)𝑚]𝑛

(1)

where a, m and n are there fitting parameters. The values of parameter a that is closely related

to the air-entry value are set to be 120, 210 and 300 kPa when v = 10, 200 and 400 kPa,

respectively. The values of parameter m and n for the VG model are set to be 1.3 and 0.6,

which implies the curvature of the water retention curves is identical for all different net

stresses. The values of R2 are equal to 0.995, 0.998 and 0.997 for the fitting curves, when v =

10, 200 and 400 kPa, respectively.

Page 11 of 39



Draft

- 11 -

3.2 Changes of void ratio and saturation for the entire testing processes

The measured change of void ratio and the change of degree of saturation of the Glenroy silt

with different initial suctions have been presented in Figure 7 (s = 0, tests CW-0-1, CW-0-2,

CW-0-4, and CW-0-8 in Table 1), Figure 8 (s = 100kPa, tests CW-100-1, CW-100-2, CW-

100-4, and CW-100-8), Figure 9 (s = 200, tests CW-200-1, CW-200-2, CW-200-4, and CW-

200-8), Figure 10 (s = 300kPa, tests CW-300-1, CW-300-2, CW-300-4, CW-300-8), and

Figure 11 (s = 400kPa, tests CW-400-1, CW-400-2, CW-400-4, CW-400-8). As shown in

Figure 7 ~ Figure 11, the changes of void ratio are presented in the space of void ratio versus

net confining stress , and the changes of degree of saturation are presented in the space of

degree of saturation versus net confining stress. The void ratio and degree of saturation have

been monitored for the entire testing processes, including (1) initial state, (2) isotropic loading

to a confining stress of 400 kPa, (3) unloading to different initial confining stresses (50, 100,

200kPa), (4) drying to different suctions (suction = 0, 100, 200, 300, 400kPa), and (5) critical

state after undrained shearing. Numbers 1~5 are adopted to indicate above 5 different states.

As shown in Figure 7, the elastoplastic compressibility index for saturated soil (λ0) can be

determined to be 0.048 and elastic compressibility (κ) is equal to 0.01. For saturated samples,

the undrained triaxial tests do not produce volume change and degree of saturation is always

equal to 1.

As shown in Figure 8, for unsaturated samples at a suction of 100kPa with different OCRs, the

void ratios range from 0.507 (see □4 in Figure 8a) to 0.532 (see ◊4 in Figure 8a), and the

degree of saturation ranges from 93.3% (see □4 in Figure 8b) to 78.9% (see ◊4 in Figure 8b)

before the undrained shearing. After undrained shearing, the void ratio ranges from 0.475 (see

□5 in Figure 8a) to 0.583 (see ◊5 in Figure 8a) and the degree of saturation ranges from 99.5%

(see □5 in Figure 8b) to 71.8% (see ◊5 in Figure 8a). The water contents before shearing and

after shearing for different OCRs are identical to each other by re-checking the value of 𝑒𝑆r/

. The water contents at a suction of 100kPa range from 17.8% (OCR=1) to 15.8% (OCR=8). 𝐺s

Page 12 of 39



Draft

- 12 -

For unsaturated samples at a suction of 200kPa with different OCRs, the void ratios range

from 0.492 (see □4 in Figure 9a) to 0.527 (see ◊4 in Figure 9a), and the degree of saturation

ranges from 67.9% (see □4 in Figure 9b) to 60.3% (see ◊4 in Figure 9b) before the undrained

shearing. After undrained shearing, the void ratio ranges from 0.455 (see □5 in Figure 9a) to

0.610 (see ◊5 in Figure 9a) and the degree of saturation ranges from 74.4% (see □5 in Figure

9b) to 52.2% (see ◊5 in Figure 9b). The water contents before shearing and after shearing for

different OCRs are identical to each other. The water contents at an initial suction of 200kPa

range from 12.7% (OCR=1) to 12.0% (OCR=8).

As shown in Figure 10, for unsaturated samples at a suction of 300kPa with different OCRs,

the void ratios range from 0.489 (see □4 in Figure 10a) to 0.520 (see ◊4 in Figure 10a), and the

degree of saturation ranges from 60.4% (see □4 in Figure 10b) to 48.5% (see ◊4 in Figure 10b)

before the undrained shearing. After undrained shearing, the void ratio ranges from 0.417 (see

□5 in Figure 10a) to 0.610 (see ◊5 in Figure 10a) and the degree of saturation ranges from 71.3%

(see □5 in Figure 10b) to 41.2% (see ◊5 in Figure 10b). The water contents before shearing

and after shearing for different OCRs are identical to each other. The water contents at an

initial suction of 300kPa range from 11.2% (OCR=1) to 9.5% (OCR=8).

For unsaturated samples at a suction of 400kPa with different OCRs, the void ratios range

from 0.485 (see □4 in Figure 11a) to 0.510 (see ◊4 in Figure 11a), and the degree of saturation

ranges from 48.4% (see □4 in Figure 11b) to 39.3% (see ◊4 in Figure 11b) before the

undrained shearing. After undrained shearing, the void ratio ranges from 0.377 (see □5 in

Figure 11a) to 0.583 (see ◊5 in Figure 11a) and the degree of saturation ranges from 62.4%

(see □5 in Figure 11b) to 34.5% (see ◊5 in Figure 11b). The water contents before shearing

and after shearing for different OCRs are identical to each other. The water contents at an

initial suction of 400kPa range from 8.9% (OCR=1) to 7.6% (OCR=8).

Page 13 of 39



Draft

- 13 -

For all unsaturated samples, as shown in Figure 8 ~ Figure 11, the shear contraction was

observed when OCR = 1, and shear dilation when OCRs = 4 and 8, for undrained conditions.

During undrained shearing, increase of degree of saturation was observed together with shear

contraction and decrease of saturation together with shear dilation. When OCR =2, the

changes of void ratio and degree of saturation are less distinct at four different suctions.

3.3 Hydro-mechanical behaviour during undrained triaxial shearing

The measured stress-strain behaviour ( versus , and versus ), volume change 𝑞/𝑝′ 𝜀1 𝑞 𝜀1

behaviour ( versus ), saturation change behaviour ( versus ), and suction-strain 𝜀v 𝜀1 𝑆r 𝜀1

behaviour ( versus ) for the Glenroy silt at different initial suctions and OCRs during the 𝑠 𝜀1

undrained triaxial shearing are presented in this section. For the data analysis here, both

Bishop’s effective stress (i.e., ) and net stress ( ) are adopted for unsaturated 𝑝′ = 𝑝 + 𝑆r𝑠 𝑝

samples. For saturated samples, Terzaghi’s effective stress (i.e., ) is adopted here.𝑝′ = 𝑝 ― 𝑢w

3.3.1 Mechanical behaviour for saturated samples

The saturated Glenroy silt with different OCRs were tested and employed to benchmark the

fundamental mechanical behaviour of the Glenroy silt. The measured stress-strain behaviour

( versus ), and pore water pressure ( versus ), are presented in Figure 12a, and Figure 𝑞/𝑝′ 𝜀1 𝑢 𝜀1

12b respectively.

As shown in Figure 12a, the ~ curves for different OCRs clearly merge into the critical 𝑞/𝑝′ 𝜀1

state, which can be reached when the axial strain goes beyond 8%. The effective stress ratio at

the critical state is about 1.3 and the peak effective stress ratio ( ) is about 1.72. The heavily 𝑀f

overconsolidated sample (e.g. OCR=8) shows a distinct peak strength and a clear post-peak

softening behaviour. The development of pore water pressure for samples with different

OCRs during shearing is presented in in Figure 12b. For heavily overconsolidated sample (e.g.

OCR = 8), a negative pore water pressure (equivalent to suction) of about 40kPa was

developed during undrained shearing. For the normally consolidated sample (OCR = 1), a

positive pore water pressure of about 290kPa was produced during the test.

Page 14 of 39



Draft

- 14 -

3.3.2 Stress-strain behaviour for unsaturated samples

The stress-strain behaviour for unsaturated samples with different initial suctions (100, 200,

300, 400kPa) and different OCRs (=1, 2, 4 and 8) is presented in Figure 13 (in the space of

versus ), and in Figure 14 (in the space of versus ).𝑞/𝑝′ 𝜀1 𝑞 𝜀1

As shown in Figure 13, the stress-strain curves that are presented in the space of effective

stress ratio and axial strain show well convergence in terms of critical state. For different

initial suctions and different OCRs, all the stress-strain curves converge to critical state at an

effective stress ratio of 1.3 that is identical to the effective stress ratio at critical state for

saturated soils. For unsaturated soils, the peak strength for a high OCR becomes less distinct,

along with the increase of initial suction. For example, the peak effective stress ratios (Mf) for

100kPa, 200kPa, 300kPa and 400kPa initial suction are equal to about 1.53, 1.50, 1.47, and

1.38, respectively, which are all less than the Mf for the saturated counterpart (Mf =1.72).

The measured relationships for the deviator stress versus the axial strain for unsaturated

Glenroy silt with different OCRs and different initial suctions are presented in Figure 14. At

the same suction level, the stress-strain curves are related to the net confining stresses and

OCRs. The high net confining stress (e.g., 3 = 400kPa when OCR=1) leads to high deviator

stress. For same OCR value, high initial suction leads to high deviator stress. For

overconsolidated samples with different suctions, peak in deviator stress and post-peak

softening can be observed. For the samples with OCR=1, the monotonic increase in deviator

stress can be observed along with the shearing.

3.3.3 Volume change behaviour for unsaturated samples

The volumetric strain for unsaturated samples with different initial suctions (100, 200, 300,

400kPa) and different OCRs (=1, 2, 4 and 8) during the undrained triaxial tests are presented

in Figure 15. For each sub-figure, Volume change variations are presented with same initial

suctions.

Page 15 of 39



Draft

- 15 -

As shown in Figure 15, the overconsolidated samples show shear dilation and normally

consolidated samples show shear contraction. This general phenomenon has been observed

for all samples with different initial suctions. Since the drainage valve is closed for the

undrained condition, the volume change is partially (not fully) restricted. The volume of pore

water cannot be changed but the volume of pore air is allowed to change. Therefore, the

potential (i.e., the cap value) of the volume change for unsaturated soils is dependent on the

volume of pore air. If the volume of pore air is equal to zero, the potential of volume change

is equal to zero. For the cases when suction is equal to 100kPa, see Figure 15a, the volume

change is highly restricted because the degree of saturation is high (78.9%~93.3%, see Figure

8b). Especially when OCR = 1, the volume change stops when the degree of saturation

increases to fully saturated (99.5%, see Figure 8b). For the cases when suction is equal to

400kPa, the volume change can behave more freely with less restriction since the quantity of

pore water is low (Sr = 39.3%~48.4%, see Figure 11b). Therefore, the volumetric stains, no

matter if dilation or contraction, for the samples with a higher initial suction level behave more

distinct than the samples with a lower initial suction level.

3.3.4 Saturation change behaviour for unsaturated samples

The saturation change for unsaturated samples with different initial suctions (100, 200, 300,

400kPa) and different OCRs (= 1, 2, 4 and 8) during the undrained triaxial tests are presented

in Figure 16. For each sub-figure, saturation variations are presented with constant OCRs.

The saturation change for unsaturated samples is highly related to the volume change, or verse

versa. For example, as shown in Figure 16a unsaturated soils (OCR = 1) with different initial

suctions show increase in degree of saturation because of shear contraction is observed for

normally consolidated unsaturated samples. The decrease in degree of saturation was observed

for all the overconsolidated unsaturated samples (OCR= 2, 4 and 8). The magnitude of

saturation decrease becomes more distinct along with the increase of the OCR. For example,

when OCR = 2, the volume change (dilation) is weak for all samples with different suctions

and therefore the curve of degree of saturation along with the axial strain is also flat (see

Page 16 of 39



Draft

- 16 -

Figure 16b). When OCR = 8, as shown in Figure 16d, more distinct decrease in degree of

saturation can be observed since the volume dilation is more significant, compared with other

cases (e.g., OCR = 2).

3.3.5 Suction-strain behaviour for unsaturated samples

The suction variations for unsaturated samples with different initial suctions (100, 200, 300,

400kPa) and different OCRs (=1, 2, 4 and 8) during the undrained triaxial tests are presented

in Figure 17. For each sub-figure, suction variations are presented with constant OCRs. In

general, we observed a decrease of suction for all the samples. Since the air pressure keeps

constant for all the tests, the decrease of suction implies an increase of the pore water pressure.

Suction change can be very complicated for unsaturated soil during undrained tests, since the

volume change is only partially (not fully) restricted and the degree of saturation is also

changing during the tests. Both volume change and degree of saturation affect the change of

suction during the undrained triaxial tests. In general, as shown in Figure 6, either volume

contraction or decrease of degree of saturation leads to suction increase, and either volume

dilation or increase of degree of saturation results in suction decrease.

As shown in Figure 17a, the decrease of suction was observed for normally consolidated

unsaturated samples (OCR = 1), which is corresponding to the increase of degree of saturation

(see Figure 16a). For example, the suction decreases to zero (degree of saturation increases to

one) for the normally consolidated sample with a suction of 100kPa during the undrained

shearing. For heavily overconsolidated samples (OCR=8), as shown in Figure 17d, the

decrease of suction was observed, which can be attributed to volume dilation. Although

degree of saturation increased for heavily overconsolidated samples (OCR=8), the suction can

also be decreased due to distinct volume dilation. Comparison between samples with different

OCRs shows that, in general, the suction variation becomes less distinct along with the

increase of OCRs for the same initial suctions.

Page 17 of 39



Draft

- 17 -

4 DISCUSSIONS

4.1 Critical effective stress ratio and critical net stress ratio

The relationships between the critical effective stress ratio (M) and the OCR for different

suctions are presented in Figure 18(a). The critical effective stress ratio (Sheng et al. 2011;

Zhou et al. 2012b) is defined as at the critical state, where is the deviator stress and is 𝑞/𝑝′ 𝑞 𝑝′

the Bishop’s mean effective stress ( ). The critical effective stress ratio is slightly 𝑝′ = 𝑝 + 𝑆r𝑠

increasing along with the increase of OCR at the same suction levels. The convergence of the

critical effective stress ratio is very well. The average value of the critical effective stress

ratios for total 20 tests is about 1.3, with an upper boundary of 1.4 and a lower boundary of 1.2.

The critical net stress ratio is defined as at the critical state. The relationships between the 𝑞/𝑝

critical net stress ratio (Mnet) and the OCR for different suctions are presented in Figure 18(b).

In general, the critical net stress ratio increases along with the increase of suction and OCR.

The critical net stress ratios for different OCRs and different suctions are scattered with a

range of 0.5~2.7, while the range of the critical effective stress ratios for different OCRs and

different suctions is 1.2~1.4. Compared with Mnet (see Figure18(b)), the result shows that the

effective stress ratio (M, see Figure18(a)) can provide more unified description to the shear

strength for unsaturated soils with different OCRs and suctions. The effective stress represents

the contact stress between the particles which is directly related to the frictional behaviour

(strength) of unsaturated soils.

4.2 Peak effective stress ratio

The relationships between the peak effective stress ratio (Mf) and the OCR for different

suctions are presented in Figure 19. The peak effective stress ratio is almost linearly increasing

along with the increase of OCR at the same suction levels. The ratio of the increase Mf over

the increase of OCR becomes less when suction increases. In addition, for the same OCRs,

the effect of suction on the value of Mf becomes distinct along with increases of the suction.

For example, the range of Mf is between 1.2 and 1.3 for a suction range of 0~400kPa when

Page 18 of 39



Draft

- 18 -

OCR=1. While, when OCR=8, the range of Mf is between 1.38 and 1.72 for the same suction

range.

4.3 Degree of saturation at failure

The relationships between the degree of saturation at failure and the OCR for different

suctions are presented in Figure 20. For saturated samples, the degree of saturation at failure

state keep constant (Srf = 1). For unsaturated samples, the degree of saturation at failure state

nonlinearly decrease along with the increase of OCR at the same suction levels. For example,

when suction is equal to 100kPa, the value of Srf decreases from 99.8% to about 73% if OCR

increase from 1 to 8. This mainly can be attributed to the volume dilation that becomes more

distinct along with the increase of OCR. In addition, for the same OCRs, the effect of suction

on the value of Srf becomes more distinct for the same suction range. For example, when OCR

= 1, the range of Srf is between 100% and about 61% for a suction range from 0 to 400kPa. For

the same suction range (0~400kPa), the range of Srf becomes between 100% and about 35%

when OCR = 8.

4.4 Suction at failure

The relationships between the suction at failure (sf) and the OCR for different initial suctions

are presented in Figure 21. The negative pore water pressure for saturated samples can be

equivalent to the suction for unsaturated samples. As shown in Figure 21, the suction

(negative pore water pressure) at failure (sf) increases distinctly along with the increase of

OCR when s = 0 kPa. For unsaturated soils (s = 100~400kPa), the value of sf is also slightly

increase with OCR.

4.5 Volumetric strain at failure

The relationships between the volumetric strain at failure (vf) and the OCR for different initial

suctions are presented in Figure 22. As shown in Figure 22, the volumetric strain for saturated

samples is always equal to zero, which can be used as the dividing line for positive

(contraction) and negative (dilation) volumetric stains. The samples with a OCR of 2 almost

Page 19 of 39



Draft

- 19 -

do not show the volumetric strain at failure at different suctions. The normally consolidated

samples at the failure states show contractions for different suctions and the value of positive

volumetric strain is increasing with the increase of the initial suction. The heavily

overconsolidated samples (OCR=4 and 8) at the failure states show dilations for different

suction. The absolute value of average dilation when OCR = 8 for 4 different suctions is larger

than that when OCR = 4. For the heavily overconsolidated samples (OCR=4 and 8), the

absolute value of negative volumetric strain at the failure states with same OCR values is

increasing with the increase of the initial suction.

5 CONCLUDING REMARKS

Hydromechanical behaviour of an unsaturated silt with various suctions and different stress

histories was investigated through a series of undrained triaxial tests. Some main concluding

remarks can be drawn as follows.

1. The critical state for saturated and unsaturated soils with different OCRs can be well

defined by employing Bishop’s effective stress.

2. The peak strength in terms of Bishop’s effective stress is increasing with increase of

OCR but decreasing with increase of suction in the undrained condition.

3. Volume change for unsaturated soils with different OCRs can be observed in the

undrained condition. In the undrained condition, the volume change is related to the

stress history (OCRs) and the volume of pore air (i.e., the potential of the volume

change). The volumetric stains in undrained conditions, no matter if dilation or

contraction, for the samples with a higher initial suction level behave more distinct

than the samples with a lower initial suction level.

4. For unsaturated soil, the degree of saturation varies correspondingly to the volumetric

strain. The volume dilation usually leads to the decrease in degree of saturation, and

the contraction leads to the increase in degree of saturation.

5. Suction change in the undrained conditions is jointly affected by the volumetric strain

and the variation of the degree of saturation.

Page 20 of 39



Draft

- 20 -

ACKNOWLEDGEMENTS

The financial support from ARC Linkage Project (LP160100649), ARC Industrial

Transformation Research Hubs (IH180100010) and NSFC (Project No.51679004) is

appreciated.

REFERENCE

Alonso, E.E., Gens, A., and Josa, A. 1990. A constitutive model for partially saturated soils. Geotechnique 40, 405-430.

Bolzon, G., Schrefler, B.A., and Zienkiewicz, O.C. 1996. Elastoplastic soil constitutive laws generalised to partially saturated states. Geotechnique 46, 279-289.

Burland, J. 1990. On the compressibility and shear strength of natural clays. Géotechnique, 40, 329-378.

Burton, G.J., Sheng, D. and Airey, D. 2014. Experimental study on volumetric behaviour of Maryland clay and the role of degree of saturation. Canadian Geotechnical Journal, 51, 1449-1455.

Cai, G., Zhou, A., and Sheng, D. 2013. Permeability function for unsaturated soils with different initial densities. Canadian Geotechnical Journal 51, 1456-1467.

Cui, Y.J., and Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Geotechnique 46, 291-311.

Estabragh, A.R., and Javadi, A.A. 2008. Critical state for overconsolidated unsaturated silty soil. Canadian Geotechnical Journal 45, 408-420.

Estabragh, A.R., and Javadi, A.A. 2014. Roscoe and Hvorslev Surfaces for Unsaturated Silty Soil. International Journal of Geomechanics 14, 230-238.

Fredlund, D.G., Xing, A., Fredlund, M.D., and Barbour, S.L. 1996. Relationship of the unsaturated soil shear strength to the soil-water characteristic curve. Canadian Geotechnical Journal 33, 440-448.

Gallipoli, D., Gens, A., and Sharma, R. 2003a. An elastoplastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Geotechnique 53, 123-135.

Gallipoli, D., Wheeler, S.J., and Karstunen, M. 2003b. Modelling of variation of degree of saturation in a deformable unsaturated soil. Geotechnique 53, 105-112.

Gao, Y., Sun, D.A., and Zhou, A.N. 2015. Hydromechanical behaviour of unsaturated soil with different specimen preparations. Canadian Geotechnical Journal 53, 909-917.

Gens, A. 2010. Soil-environment interactions in geotechnical engineering. Geotechnique 60, 3-74.

Hilf, J.W. 1956. An investigation of pore water pressure in compacted cohesive soils, Technical Memorandum, No. 654. US Department of Interior, Bureau of Reclamation.

Page 21 of 39



Draft

- 21 -

Khalili, N., and Loret, B. 2001. An elasto-plastic model for non-isothermal analysis of flow and deformation in unsaturated porous media: formulation. International Journal of Solids and Structures 38, 8305-8330.

Kodikara, J. 2012. New framework for volumetric constitutive behaviour of compacted unsaturated soils. Canadian Geotechnical Journal 49, 1227-1243.

Li, W., and Yang, Q. 2018. Hydromechanical Constitutive Model for Unsaturated Soils with Different Overconsolidation Ratios. International Journal of Geomechanics 18, 04017142.

Lu, N., Godt, J.W., and Wu, D.T. 2010. A closed-form equation for effective stress in unsaturated soil. Water Resources Research 46, W05515.

Lyu, H.M., Sun, W.J., Shen, S.L., and Arulrajah, A. 2018. Flood risk assessment in metro systems of mega-cities using a GIS-based modeling approach, Science of the Total Environment 626, 1012-1025.

Nishimura, T., Hirabayashi, Y., Fredlund, D.G., and Gan, J.K.M. 1999. Influence of stress history on the strength parameters of an unsaturated statically compacted soil. Canadian Geotechnical Journal 36, 251-261.

Oka, F., Kodaka, T., Suzuki, H., Kim, Y. S., Nishimatsu, N. and Kimoto, S. 2010. Experimental study on the behavior of unsaturated compacted silt under triaxial compression. Soils and foundations, 50, 27-44.

Power, S.B., Delage, F.P.D., Chung, C.T.Y., Ye, H., and Murphy, B.F. 2017. Humans have already increased the risk of major disruptions to Pacific rainfall. Nature Communications 8, 14368.

Shen, S.L., and Xu, Y.S. 2011. Numerical evaluation of land subsidence induced by groundwater pumping in Shanghai. Canadian Geotechnical Journal 48(9),1378-1392.

Shen, S.L., Wu, H.N., Cui, Y.J., and Yin, Z.Y. 2014. Long-term settlement behavior of metro tunnels in the soft deposits of Shanghai. Tunneling and Underground Space Technology 40(12), 309-323.

Sheng, D. 2011. Review of fundamental principles in modelling unsaturated soil behaviour. Computers and Geotechnics 38, 757-776.

Sheng, D., Fredlund, D.G., and Gens, A. 2008. A new modelling approach for unsaturated soils using independent stress variables. Canadian Geotechnical Journal 45, 511-534.

Sheng, D., and Zhou, A.N. 2011. Coupling hydraulic with mechanical models for unsaturated soils. Canadian Geotechnical Journal 48, 826-840.

Sheng, D., Zhou, A.N., and Fredlund, D.G. 2011. Shear strength criteria for unsaturated soils. Geotechnical and Geological Engineering 29, 145-159.

Sivakumar, V. 1993. A critical state framework for unsaturated soils. University of Sheffield, Sheffield.

Sun, D.A., Sheng, D., Cui, H.B., and Sloan, S.W. 2007a. A density-dependent elastoplastic hydro-mechanical model for unsaturated compacted soils International Journal for Numerical and Analytical Methods in Geomechanics 31, 1257-1279.

Sun, D.A., Sheng, D., and Sloan, S.W. 2007b. Elastoplastic modelling of hydraulic and stress-strain behaviour of unsaturated soils. Mechanics of Materials 39, 212-221.

Page 22 of 39



Draft

- 22 -

Sun, D.A., Sheng, D., and Xu, X.F. 2007c. Collapse behaviour of unsaturated compacted soil. Canadian Geotechnical Journal 44, 673-686.

Sun, X., Li, J., and Zhou, A.N. 2017a. Assessment of the impact of climate change on expansive soil movements and site classification. Australian Geomechanics Journal 52, 39-50.

Sun, X., Li, J., and Zhou, A.N. 2017b. Evaluation and comparison of methods for calculating thornthwaite moisture index Australian Geomechanics Journal 52, 61-75.

Tarantino, A. 2009. A water retention model for deformable soils. Geotechnique 59, 751-762.

Toyota, H., Sakai, N., and Nishimura, T. 2001. Effects of stress history due to unsaturation and drainage condition on shear properties of unsaturated cohesive soil, Soils and Foundations, 41(1), pp. 13-24

van Genuchten, M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44, 892- 898.

Wheeler, S.J. 1996. Inclusion of specific water volume within an elsto-plastic model for unsaturated soil. Canadian Geotechnical Journal 33, 42-57.

Wheeler, S.J., and Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Geotechnique 45, 35-53.

Wu, Y.X., Shen, S.L., Wu, H.N., Xu, Y.S., Yin, Z.Y., and Sun, W.J. 2015. Environmental protection using dewatering technology in a deep confined aquifer beneath a shallow aquifer, Engineering Geology 196, 59-70.

Wu, H.N., Shen, S.L., and Yang, J. 2017. Identification of tunnel settlement caused by land subsidence in soft deposit of Shanghai. Journal of Performance of Constructed Facilities ASCE 31(6), article no. 04017092.

Xu, Y.S., Shen, S.L., Lai, Y., and Zhou, A.N. 2018. Design of sponge city: Lessons learnt from an ancient drainage system in Ganzhou, China. Journal of Hydrology 563, 900-908.

Yao, Y., Hou, W., and Zhou, A. 2008a. Constitutive model for overconsolidated clays. Science in China, Series E: Technological Sciences 51, 179-191.

Yao, Y.P., Hou, W., and Zhou, A.N. 2009. UH model: three-dimensional unified hardening model for overconsolidated clays. Geotechnique 59, 451-469.

Yao, Y.P., Kong, L.M., Zhou, A.N., and Yin, J.H. 2015. Time-dependent unified hardening model: three-dimensional elastoviscoplastic constitutive model for clays. Journal of Engineering Mechanics 141, 04014162.

Yao, Y.P., Niu, L., and Cui, W.J. 2014. Unified hardening (UH) model for overconsolidated unsaturated soils. Canadian Geotechnical Journal 51, 810-821.

Yao, Y.P., Sun, D.A., and Matsuoka, H. 2008b. A unified constitutive model for both clay and sand with hardening parameter independent on stress path. Computers and Geotechnics 35, 210-222.

Yao, Y.P., and Zhou, A.N. 2013. Non-isothermal unified hardening model: a thermo-elastoplastic model for clays. Geotechnique 63, 1328-1345.

Page 23 of 39



Draft

- 23 -

Zhang, J., Sun, D.A., Zhou, A.N., and Jiang, T. 2015. Hydro-mechanical behavior of expansive soils with different suctions and suction histories. Canadian Geotechnical Journal 53, 1-13.

Zhou, A., Huang, R.-Q., and Sheng, D. 2016. Capillary water retention curve and shear strength of unsaturated soils. Canadian Geotechnical Journal 53, 974-987.

Zhou, A.N., and Sheng, D. 2015. An advanced hydro-mechanical constitutive model for unsaturated soils with different initial densities. Computers and Geotechnics 63, 46-66.

Zhou, A.N., Sheng, D., and Carter, J.P. 2012a. Modelling the effect of initial density on soil-water characteristic curves. Geotechnique 62, 669-680.

Zhou, A.N., Sheng, D., Sloan, S.W., and Gens, A. 2012b. Interpretation of unsaturated soil behaviour in the stress-saturation space, I: Volume change and water retention behaviours. Computers and Geotechnics 43, 178-187.

Zhou, A.N., Sheng, D., Sloan, S.W., and Gens, A. 2012c. Interpretation of unsaturated soil behaviour in the stress-saturation space, II: Constitutive relationships and validations. Computers and Geotechnics 43, 111-123.

Zhou, A., Wu, S., Li, J., and Sheng, D. 2018. Including degree of capillary saturation into constitutive modelling of unsaturated soils. Computers and Geotechnics 95, 82-98.

Page 24 of 39



Draft

- 24 -

Figure CaptionsFigure 1 Particle distribution curve for the Glenroy silt

Figure 2 Testing apparatuses

Figure 3 Loading paths for CW tests

Figure 4 Void ratio change during the isotropic loading/unloading processes: the measurement

by the BVC versus that by the DPT.

Figure 5 Drainage volume measured by the BVC and the sample volume change measured by

the DPT when dried to a suction of 400kPa.

Figure 6 Water retention curves of the Glenroy silt at different net vertical pressures.

Figure 7 Void ratio change for the saturated samples

Figure 8 Void ratio and saturation changes for samples with an initial suction of 100kPa




Figure 12 Mechanical responses of the saturated Glenroy silt with different OCRs

Figure 13 Stress-strain behaviour in the space of versus of the unsaturated Glenroy silt 𝑞/𝑝′ 𝜀1

with different OCRs

Figure 14 Stress-strain behaviour in the space of versus of the unsaturated Glenroy silt 𝑞 𝜀1

with different OCRs

Figure 15 Volume change behaviour of the unsaturated Glenroy silt with different OCRs

Figure 16 Saturation variation of the unsaturated Glenroy silt with different OCRs in

undrained shearing tests

Figure 17 Suction variation of the unsaturated Glenroy silt with different OCRs in undrained

shearing tests

Figure 18 The relationship between the stress ratio at critical state (in effective stress and net

stress) and the OCR for different initial suctions

Figure 19 The relationship between the peak effective stress ratio and the OCR for different

initial suctions

Figure 20 The relationships between the degree of saturation at failure and the OCR for

different initial suctions

Figure 21 The relationships between the degree of saturation at failure and the OCR for

different initial suctions

Figure 22 The relationships between the volumetric strain at failure and the OCR for different

initial suctions

Page 25 of 39



Draft

Table 1 Summary of test conditions

Test no. Stress path OCR in net stress

Confining pressure before

shearing(kPa)

Suction before shearing(kPa)

1 CW-0-1 B-E-E′ 1 400 02 CW-0-2 B-E-D-D′ 2 200 03 CW-0-4 B-E-C-C′ 4 100 04 CW-0-8 B-E-B-B′ 8 50 0

Page 26 of 39



Draft

- 1 -

Ms. No.: cgj-2018-323.R2 HYDROMECHANICAL BEHAVIOUR OF OVERCONSOLIDATED UNSATURATED SOIL IN


Shengshen Wu†, Annan Zhou*†, Jie Li†, Jayantha Kodikara ‡, Wen-Chieh Cheng§

†School of Engineering, Royal Melbourne Institute of Technology (RMIT), Melbourne, Vic 3001, Australia

‡Department of Civil Engineering, Monash University, Vic 3800, Australia §School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an 710055, China

*Corresponding author: Dr Annan Zhou ([email protected])

Figures

0

20

40

60

80

100

0.001 0.01 0.1 1

Particle size (mm)

Figure 1 Particle distribution curve for the Glenroy silt

Page 27 of 39



Draft

- 2 -

Figure 2 Testing apparatuses

Page 28 of 39



Draft

- 3 -

Figure 3 Loading paths for CW tests

Figure 4 Void ratio change during the isotropic loading/unloading processes: the measurement

by the BVC versus that by the DPT.

Page 29 of 39



Draft

- 4 -

0 2000 4000 6000 8000 10000Time, t (min)

-20000

-15000

-10000

-5000

0

0 2000 4000 6000 8000 10000-2500

-2000

-1500

-1000

-500

0

OCR=1 OCR=2 OCR=4 OCR=8

s=400kPa


s=400kPa

Time, t (min) Figure 5 Drainage volume measured by the BVC and the sample volume change measured by

the DPT when dried to a suction of 400kPa.

Deg

ree

of s

atur

atio

n, S

r (-)

Suction, s (kPa)

0

0.2

0.4

0.6

0.8

1

1.2

1 10 100 1000 10000

sv = 10kPasv = 200kPasv = 400kPa

VG modela=120 kPa, m=1.3, n=0.6a=210 kPa, m=1.3, n=0.6a=300 kPa, m=1.3, n=0.6

Figure 6 Water retention curves of the Glenroy silt at different net vertical pressures.

Page 30 of 39



Draft

- 5 -

Figure 7 Void ratio change for the saturated samples



Page 31 of 39



Draft

- 6 -



0 5 10 15 20Axial strain, (%)

0

0.4

0.8

1.2

1.6


s=0kPa

(a)

0-50

0

100

200

300


s=0kPa

1 Axial strain, (%)1

Pore

wat

er p

ress

ure,

u (k

Pa)

(b)

5 10 15 20

M=1.3

Eff

ectiv

e st

ress

rat

io/

qp

(-)

Figure 12 Mechanical responses of the saturated Glenroy silt with different OCRs

Page 32 of 39



Draft

- 7 -

/q

p/

qp

/q

p/

qp

Figure 13 Stress-strain behaviour in the space of 𝑞/𝑝′ versus 𝜀 of the unsaturated Glenroy silt

with different OCRs

Page 33 of 39



Draft

- 8 -

Dev

iato

r st

ress

, q(k

Pa)

Dev

iato

r st

ress

, q(k

Pa)

Dev

iato

r st

ress

, q(k

Pa)

Dev

iato

r st

ress

, q(k

Pa)

Figure 14 Stress-strain behaviour in the space of 𝑞 versus 𝜀 of the unsaturated Glenroy silt

with different OCRs

Page 34 of 39



Draft

- 9 -

Figure 15 Volume change behaviour of the unsaturated Glenroy silt with different OCRs

Page 35 of 39



Draft

- 10 -

Figure 16 Saturation variation of the unsaturated Glenroy silt with different OCRs in undrained shearing tests

Page 36 of 39



Draft

- 11 -

Suct

ion,

s(k

Pa)

Suct

ion,

s(k

Pa)

Suc

tion,

s(k

Pa)

Suct

ion,

s(k

Pa)

Figure 17 Suction variation of the unsaturated Glenroy silt with different OCRs in undrained

shearing tests

Figure 18 The relationship between the stress ratio at critical state (in effective stress and net stress) and the OCR for different initial suctions

Page 37 of 39



Draft

- 12 -

0 2 4 6 8 10OCR (-)

1

1.2

1.4

1.6

1.8

s = 0 kPas = 100kPas = 200 kPas = 300 kPas = 400 kPa

Figure 19 The relationship between the peak effective stress ratio and the OCR for different initial suctions

Figure 20 The relationships between the degree of saturation at failure and the OCR for different initial suctions

Figure 21 The relationships between the degree of saturation at failure and the OCR for different initial suctions

Page 38 of 39



Draft

- 13 -

Figure 22 The relationships between the volumetric strain at failure and the OCR for different initial suctions

Page 39 of 39



Documents

Draft - TSpace Repository: Home...2018) change the matric suction, stress state, and stress history in the surface soil on the earth. Although soil mechanics was initiated from the