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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)
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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
Email: [email protected]
Name: Jie Li (PhD, Associate Professor)
Affiliation: School of Engineering, Royal Melbourne Institute of Technology (RMIT), Melbourne,
Vic 3001, Australia
Email: [email protected]
Name: Jayantha Kodikara (PhD, Professor)
Affiliation: Department of Civil Engineering, Monash University, Vic 3800, Australia
Email: [email protected]
Name: Wen-Chieh Cheng (PhD, Professor)Affiliation: School of Civil Engineering, Xi’an University of Architecture and Technology, Xi’an
710055, China
Email: [email protected]
Manuscript submitted toCanadian Geotechnical Journalfor consideration for publication
Ms. No.: cgj-2018-323.R2
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HYDROMECHANICAL BEHAVIOUR OF OVERCONSOLIDATED UNSATURATED SOIL IN
UNDRAINED CONDITIONS
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
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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
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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
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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
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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
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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)
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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
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(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.
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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
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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.
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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
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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).
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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.
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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.
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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
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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.
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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
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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
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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.
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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
https://mc06.manuscriptcentral.com/cgj-pubs
Canadian Geotechnical Journal
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
https://mc06.manuscriptcentral.com/cgj-pubs
Canadian Geotechnical Journal
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
https://mc06.manuscriptcentral.com/cgj-pubs
Canadian Geotechnical Journal
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.
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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 9 Void ratio and saturation changes for samples with an initial suction of 200kPa
Figure 10 Void ratio and saturation changes for samples with an initial suction of 300kPa
Figure 11 Void ratio and saturation changes for samples with an initial suction of 400kPa
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
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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
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Ms. No.: cgj-2018-323.R2 HYDROMECHANICAL BEHAVIOUR OF OVERCONSOLIDATED UNSATURATED SOIL IN
UNDRAINED CONDITIONS
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
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Figure 2 Testing apparatuses
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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.
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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
OCR=1 OCR=2 OCR=4 OCR=8
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.
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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 9 Void ratio and saturation changes for samples with an initial suction of 200kPa
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Figure 10 Void ratio and saturation changes for samples with an initial suction of 300kPa
Figure 11 Void ratio and saturation changes for samples with an initial suction of 400kPa
0 5 10 15 20Axial strain, (%)
0
0.4
0.8
1.2
1.6
OCR=1 OCR=2 OCR=4 OCR=8
s=0kPa
(a)
0-50
0
100
200
300
OCR=1 OCR=2 OCR=4 OCR=8
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
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/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
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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
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Figure 15 Volume change behaviour of the unsaturated Glenroy silt with different OCRs
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Figure 16 Saturation variation of the unsaturated Glenroy silt with different OCRs in undrained shearing tests
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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
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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
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Figure 22 The relationships between the volumetric strain at failure and the OCR for different initial suctions
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