Long term cyclic behavior of unsaturated granular soils

Transportation Geotechnics 17 (2018) 48–55
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Transportation Geotechnics
journal homepage: www.elsevier.com/locate/trgeo
Long term cyclic behavior of unsaturated granular soils
a
c,⁎
b
a
Jingyu Chen , Eduardo E. Alonso , Chuan Gu , Zhigang Cao , Yuanqiang Cai
a
b
c
T
a
Key Laboratory of Soft Soils and Geoenvironmental Engineering, Ministry of Education, Zhejiang University, Hangzhou 310027, PR China
Department of Geotechnical Engineering and Geosciences, Building D2, Technical University of Catalunya, 08034 Barcelona, Spain
College of Civil Engineering and Architecture, Wenzhou University, Wenzhou 325035, PR China
A R T I C LE I N FO
A B S T R A C T
Keywords:
Unsaturated granular soils
Large-scale triaxial tests
Matric suction
Axial strain accumulation model
The road base and subbase materials are normally situated in unsaturated conditions, and are subject to traffic
loadings over a long period of time. To study the influences of matric suction on the long-term deformation of
road base and subbase materials, the large-scale cyclic tri-axial apparatus, equipped with unsaturated system,
was adopted to conduct tests on these unsaturated coarse granular materials. Four matric suction and three
cyclic stress amplitudes were applied on the specimens through the apparatus. The axis-translation technique
was used to control the matric suction in the specimen. The test results indicate that with the increase of matric
suction, the axial accumulated strain decreases at the declining rate, and larger cyclic stress amplitude will
strengthen the influence of matric suction. An improved cyclic model containing a new exponential function to
describe the influence of matric suction was then proposed. By comparing the experimental results and the
calculated results, the improved model was validated to be effective to predict the long-term deformation of
unsaturated granular soils.
Introduction
Road base and subbase layers are normally constructed by coarse
granular soils, and regarded as the key structural elements for supporting upper loads and transferring the traffic loadings to the subgrade
layers. With the increase of loading cycles and the variation of environment, the road base and subbase layers gradually deteriorate,
which threatens the transportation safety and causes great economic
loss. Therefore, the long-term characteristics of road base and subbase
materials have attracted more and more attention of many researchers
(e.g. [9,16,17,25,10,7,8]. Generally, road base and subbase layers are
situated above the water table, and thus the base and subbase materials
are usually in the unsaturated state. The moisture content is easily affected by environmental factors such as rainfall, freezing and thawing,
and it varies with seasons. Since the base and subbase materials are
compacted to be close to the maximum dry density, small changes in
moisture content can lead to considerable changes in the degree of
saturation, which affects the serviceability and life of pavements
[16,17]. Therefore, the moisture content is an important consideration
in the actual road design.
Due to sample size effects, large-scale cyclic tri-axial test systems
have been developed to study the long-term mechanical characteristics
of coarse granular materials considering the effects of moisture content
(e.g. [9,28,5,25,8,7]). Most researchers [9,28,5] concluded that the
⁎
Corresponding author.
E-mail address: single_k@163.com (C. Gu).
https://doi.org/10.1016/j.trgeo.2018.06.001
Received 28 March 2018; Received in revised form 16 May 2018; Accepted 5 June 2018
Available online 07 June 2018
2214-3912/ © 2018 Elsevier Ltd. All rights reserved.
increase of moisture content increased the permanent deformation and
reduced the resilient modulus, while Rahman et al. [25] indicated that
when moisture content was less than optimum moisture content, resilient modulus increased with the increase of moisture content, and
when the moisture content was larger than optimum moisture content,
resilient modulus presented the opposite trend. These above researches
have revealed the effects of moisture content on the long-term behavior
of the coarse granular materials to some extent. However, due to the
limitation of their test devices, the matric suction in the samples could
not be controlled and measured during the tests. It is hard to make deep
analysis of the test results under the framework of unsaturated soil
mechanics.
Heath et al. [14] pointed out that matric suction existed in unsaturated base and subbase materials indeed, and it had significant
impacts on strength and stiffness of these materials. Some researchers
have improved the original large-scale test apparatus with unsaturated
control module, which realized the control of the matric suction by
axis-translation method [12,11,17]. These researches further confirmed
that higher matric suction (lower moisture content) led to lower accumulated deformation and larger resilient modulus, and the influence
degree depended on the stress state. Although these above researches
have explained the influence of matric suction on the long-term behavior of the unsaturated base and road base materials based on the unsaturated soil mechanics, they mainly focused on the improvement of
Transportation Geotechnics 17 (2018) 48–55
J. Chen et al.
apparatus, and less test results were presented. More detailed test
programs were needed to study the on the long-term behavior of the
unsaturated base and road base materials.
Based on the test results, some empirical models have been developed to predict the long-term deformation of the pavements. The most
commonly formulas usually gave the permanent strain accumulation as
an exponential function of the number of cycles (e.g. [32,15,9]. To
consider the influence of stress paths, some empirical models in more
complicated forms have been proposed (e.g. [13,30,29]. Azam et al. [5]
concluded that permanent strain presented a better correlation with
suction than that with moisture content, and established a model considering the influence of matric suction. However, the models above are
empirical, and cannot be applied to complicated conditions.
Some theoretical models were established for unsaturated soil under
cyclic loadings. For example, Yang et al. [33,34] proposed an elastoplastic model for unsaturated soils under cyclic loadings from microscopic and macroscopic views, respectively. In their model, the Barcelona basic model (BBM), proposed by Alonso et al. [1,2] was adopted to
consider the effects of suction, and then integrated into a bounding
surface plasticity framework to predict model strain accumulation
under cyclic loadings. Pedroso et al. [24] extended the BBM by using
two-yield surfaces and adding a smooth transition between the elastic
and elastoplastic states, which realized the prediction of cyclic mechanical and hydraulic behavior at the same time. Bian et al. [6] developed the cyclic elastoplastic constitutive model (MODSOL) within
the framework of the theory of Biot and the formulation of Coussy,
which could reflect the influence of soil saturation on the response of a
sandy soil under both monotonic and cyclic undrained loading paths.
Although these models were equipped with theory basis, they were
proved to cause higher computation effort due to a large number of
iterative steps and are only suitable for small number of cycles.
To avoid a step-by-step calculation of the entire loading history,
Suiker et al. [27] proposed a long term constitutive model for ballast
materials based on the shakedown theory. The model described the
envelope of permanent deformation generated during the cyclic loading
process, considering two separate mechanisms, namely frictional
sliding and volumetric compaction. However, the model made no explicit distinction between the static and cyclic stress contributions,
where the cyclic loading amplitude should be relatively large with respect to the static part [18]. Niemunis et al. [23] and Wichtmann et al.
[31] formulated an accumulation model for granular materials, named
as the Bochum accumulation model, where the influences of the strain
amplitude, the number of cycles, the average mean pressure, the
average stress ratio, the void ratio, and the change of the polarization of
the strain loop were expressed as multiplication forms. However, the
accumulation of deformation was non-vanishing and no shakedown
behavior was encountered [18]. Base on the models of Suiker et al.
[27,23], Karg et al. [18] proposed another elasto-plastic long-term
model considering the dependency of the deformation on the stress
state, the void ratio, and the dynamic loading amplitude under small
cyclic loading amplitudes. In this model, it was assumed that the dynamic part of the stresses was small with respect to the static part, and
only the accumulation of the average plastic deformation was considered. However, matric suction, as an important influence factor, was
not considered in the model.
In the present study, the large-scale unsaturated triaxial tests were
conducted on crushed tuff aggregate mixtures considering the influence
of matrix suction under different cyclic stress amplitudes. The axistranslation technique was adopted to control the suction in the specimens. The axial accumulated strain were emphatically analyzed. Based
on Karg et al. [18], an improved model considering the influence of
matrix suction was proposed. The model parameters were obtained
based on the experimental results.
Fig. 1. The overall system of LDCTTS.
Test samples and programs
Test apparatus
The large-scale cyclic tri-axial test system (LDCTTS), developed by
the British company GDS, has been successfully used to study the longterm behavior of saturated coarse granular materials [7,8]. To conduct
tests on unsaturated coarse granular mixtures, the LDCTTS is upgraded
with the following devices: a dual-channel pneumatic control system to
simultaneously control the internal gas pressure within the sample and
confining pressure; a ceramic plate with low air-entry value of 100 kPa
to control the matric suction; a large-scale double cell to calculate the
volume change during the tests; a matric suction probe with a high airentry value of 500 kPa to measure the matric suction inside the sample
directly. All the upgraded equipment is controlled by the unsaturated
control module embedded in the original control system. It should be
emphasized that the axial strain is measured by the axial displacement
transducers installed on the top cap. The overall upgraded apparatus is
shown in Fig. 1.
Test Materials
The test materials are crushed tuff aggregates, which are taken from
a quarry near Wenzhou City in China. Tuffs are typical soft rock, which
are widely distributed in the southeast coast of China. Due to its easy
exploitation and good geotechnical characteristics, the crushed tuff
materials are usually used as the major source of road base and subbase
materials in this area. Through the cleaning, drying and sieving process,
the gradation curve of these materials is shown in Fig. 2, which is
classified as GW groups according to the unified soil classification
system [4]. The detailed material parameters of crushed tuff aggregates
are as followed: the specific gravity Gsb = 2.72, the maximum particle
diameter dmax = 30 mm,the average particle diameter d50 = 6.3 mm,
the coefficient of uniformity Cu = 6.1 and the coefficient of curvature
Cc = 2.2. To stimulate the characteristics of the fouled base and subbase materials invaded by fines from the soft soil sublayers, crushed tuff
aggregates are incorporated with Kaolin at the mass ratio of 3%. The
detailed material parameters of Kaolin are as followed: the specific
gravity Gsk = 2.61, the plastic wp = 23.5%, and the liquid limit
wl = 42.6%.
For the mixtures, shaking table test was conducted to obtain the
maximum and minimum void ratios. Preliminary modified Proctor
compaction test was conducted to determine the maximum dry density
and optimum moisture content. The compaction energy works out to be
2693.3 kJ/m3. The compaction curve is shown in Fig. 3. The index
properties are given in Table 1.
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J. Chen et al.
preparation procedure was adopted. Firstly, the crushed tuff aggregates
and the corresponding mass of Kaolin were mixed under the optimum
moisture content. Then the mixed materials were sealed with plastic
wrap and stored in an airtight container for at least 48 h for moisture
homogenization. The specimens were prepared in a spilt mold by moist
tamping method under the optimum water content. The specimens
were tamped layer-by-layer (six layers), and the height and weight of
each layer were controlled to be the same. During the tamping procedure, the drop height of miniature hammer was set the same to ensure
the same compaction energy, and each layer’s surface was scratched to
ensure better interlocking with the next layer. The relative density ID is
approximately 70% for all the specimens, and the corresponding compaction degree is approximately 95.4%, which satisfies the requirements of Chinese road specifications [20]. After the specimen tamping,
rubber membrane was placed to enclose the specimen.
Prior to transferring the specimen to the base plate of the large-scale
tri-axial apparatus, the ceramic base plate was required to be fully saturated. The saturation of ceramic base plate was realized by the following steps. Firstly, all pore-water pressure lines of the base plate were
flushed with de-ionized and de-aired water. Then, three stages of increasing water pressures (25 kPa, 50 kPa, 75 kPa) were applied on
ceramic base plate in the sealed pressure chamber. Each stage of water
pressure was kept for 2 h to dissolve the bubbles in the ceramic base
plate, and then the valve of the base plate was opened for drainage
before applying the next stage of water pressure. Finally, when the
reading of confining pressure transducer was the same as that of back
pressure system connecting to the base plate, the ceramic base plate
was considered to be saturated fully [21,11,17].
Fig.2. Gradation curves of the tested materials.
Matric suction initialization
The initialization of matric suction enables the control of an initial
stress state. For the saturated samples (s = 0 kPa), those samples were
saturated with reference to the methods by Cai et al. [7] and Cao et al.
[8]. For the unsaturated samples (s = 30 kPa; 60 kPa; 90 kPa), the initialization of matric suction was achieved by axis-translation method,
which has been used successfully in unsaturated tests [21,11,17]. For
all the tests, the matric suction was applied in drying path. The detailed
process was as follows:
(a) Firstly, the specimen needed to be basically saturated to eliminate
the influence of matric suction path. After applying a initial confining pressure σ3 = 20 kPa on the specimen, de-aired water was
injected into the specimen from the valve at the bottom, and the air
inside the specimen was excluded from the valve at the top. The
basic saturation of the specimen could be estimated when the
drainage of water was stable without air bubbles.
(b) Subsequently, the specimen was isotropically consolidated under
the net confining pressure σnet = 40 kPa by applying a confining
pressure σ3 = 240 kPa, pore air pressure ua = 200 kPa, and pore
water pressure uw = 200 kPa. Here, σnet = σ3 − ua. Since matric
suction s = ua − uw, matric suction was kept constant 0 kPa during
the consolidation process.
(c) After isotropic consolidation, pore water pressure was decreased to
the prescribed value based on formula s = ua − uw. The decrease of
pore water pressure led to the drainage of water from the specimen,
which was collected and recorded by the back pressure system
connected to the ceramic base plate. When the water volume
change rate was less than 200 mm3/h, specimens were regarded to
attain the equilibrium condition [11]. Normally, the equilibrium
durations were more than 5 days.
Fig. 3. Compaction curve.
Table 1
Index properties of mixtures.
Index properties
value
Initial void ratio, e0
Maximum void ratio, emax
Minimum void ratio, emin
Maximum dry density, ρd,max (g/cm3)
Optimum water content, ωop(%)
Grain shape
0.323
0.518
0.271
2.02
5.2
Subangular
Sample preparation
The cylindrical sample with a diameter (D) of 150 mm and a height
(H) of 300 mm was adopted in this study. The aspect ratio of H/D was 2.
The maximum particle diameter dmax was 30 mm. Considering that
larger particle diameter relative to specimen diameter leads to inaccuracy and poor productivity of tests due to size effects of the specimens, the ratio between specimen diameter and maximum particle
diameter was controlled to be 5, which satisfied the requirements of test
standards ASTM D3999-91 [31,9,7,8].
To guarantee the consistency of the specimens, a standard routine
Test programs
To reflect the stress state of actual road base and subbase materials,
all the tests were isotropically consolidated under a low confining
50
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J. Chen et al.
cyclic loadings were applied in a load-controlled fashion with compression wave form. The loading cycles N was set to 50,000, and the
loading frequency was 1 Hz. During the cyclic loading process, data
storage occurred for every 10th cycle, and in every storage cycle, the
data were recorded at 50 points.
Test results and model
Accumulated axial strain
Accumulated axial strain is an important factor to evaluate the longterm performance of base and subbase materials under traffic loading.
Fig. 4(a)–(c) show the accumulated axial strain, εacc 1 as the function
of the number of cycles N, subjecting to three cyclic stress amplitudes
(qampl = 60 kPa, 100 kPa and 150 kPa) under four matric suctions
(s = 0 kPa, 30 kPa, 60 kPa and 90 kPa), respectively. In general, the
axial strain develops rapidly at compaction stage, and then accumulates
at decreasing rate with the number of loading cycles for all the tests. It
can be found that with the increase of matric suction, the accumulated
axial strain will decrease under all cyclic stress amplitudes. Compared
to the saturated specimen, unsaturated specimens will present obviously smaller deformation. This is due to that when specimens are in
unsaturated condition, an air-water interface occurs inside the specimens, inducing a normal inter-particle contact force. When the matric
suction increases, the radius of the air-water interface decreases,
leading to the increase of the inter-particle contact force [19,22].
Fig. 5 gives the relationship between the accumulated axial strain,
εacc 1 at N = 50,000 and matric suction, s under three cyclic stress
amplitudes (qampl = 60 kPa, 100 kPa and 150 kPa). It can be found that
with the increase of matric suction, the accumulated axial strain reduces at decreasing rate. The ratios of εacc 1 at s = 90 kPa to that at
s = 0 kPa are roughly 29.29% 45.38% and 56.50% for the tests of
qampl = 60 kPa, 100 kPa and 150 kPa respectively. It illustrates that the
stress amplitude can enlarge the influences of the matric suction on the
accumulated axial strain obviously.
Model improvement
The model considering the influence of matric suction is necessary
to predict the deformation of unsaturated road base and subbase materials subjecting to traffic loadings. In the shakedown range, the axial
strain increases rapidly at the beginning of loading cycles, and then the
development rate decreases to be a relative small value or even zero
with the increase of loading cycles [30]. Based on this, Karg et al. [18]
Fig. 4. Axial strain accumulation versus the number of cycles.
pressure σnet = 40 kPa. Three cyclic stress amplitudes (qampl = 60 kPa,
100 kPa and 150 kPa) and four different matric suctions (s = 0 kPa,
30 kPa, 60 kPa and 90 kPa) were applied on each specimen. The selection of matric suction is based on the field conditions [11]. During
the test process, the matric suction in the specimen was always kept
constant by controlling the inside air pressure and water pressure. The
Fig. 5. The accumulated axial strain at N = 50,000 versus matric suction.
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J. Chen et al.
put forward a phenomenological law to describe the shape of the deformation curve, which is characterized by the sum of an initial logarithmic growth of the accumulated axial strain as the function of the
cycle numbers at the beginning of tests and a linear growth after a
certain number of load cycles. Hence, the accumulated axial strain ε1acc
is expressed as:
ε1acc = c1 ln(1 + c2 N ) + c3 N
(1)
where c1, c2 and c3 are constants. To differentiate both sides of Eq. (1),
the accumulated axial strain rate can be found as:
dε1acc
c1 c2
=
+ c3
dN
1 + c2 N
(2)
Compared to the deformation at the beginning of tests (c1ln(1 + c2)
in Eq. (1), the later deformation (c3N in Eq. (1) is relatively small. To
get the equation reflecting the relationship between the rate of accumulated axial strain during one loading cycle and the accumulated axial
strain, where the cycle numbers N is removed, it is assumed that only
the first term on the right hand side of Eq. (1) is important, and neglect
the term c3N, considering that c3N is much smaller compared to c1ln
(1 + c2). Therefore, the Eq. (1) can be further expressed as [18]:
ε1acc ≈ c1 ln(1 + c2 N )
Fig. 6. The schematic diagram of the variables.
(3)
fs = a exp(−s / sref ) + b
Combine Eqs. (2) and (3), the rate of accumulated axial strain as the
function of the accumulated axial strain can be presented as:
ε acc
dε1acc
= c1 c2 exp ⎛− 1 ⎞ + c3
dN
⎝ c1 ⎠
⎜
where s0 is reference matric suction, a and b are constant parameters.
Similarly, the accumulated axial strain rate can be also expressed as:
ampl
dε1acc (N , η0 , p0 , ε0
dε1acc (N , η , pav , ε ampl, s )
= fη fp fampl fs
dN
dN
⎟
(4)
For simplification , the Eq. (4) is rewritten as:
dε1acc
= αf exp(−θf ε1acc ) + βf
dN
(11)
αf exp(−θf ε1acc (N , η , pav , ε ampl, s ) + βf =
(5)
fη fp fampl fs αf0 exp(−θf0 ε1acc (N , η0 , p0 , ε0ampl, s0)) + fη fp fampl fs βf0
1
where αf0 , θf0 and
0
αf = αf (η0 , p0av , ε0ampl, s0) ,
θf (η0 , p0av , ε0ampl, s0) .
(8)
fη = exp(Cη η)
(9)
parameters,
and
θf0 =
(13)
Comparing left and right sides of Eq. (13), it can be concluded that:
αf = αf0 fη fp fampl fs
θf =
(14)
θf0
fη fp fampl fs
βf = βf0 fη fp fampl fs
(15)
(16)
Integrate both sides of Eq. (13) with N, the expression of the accumulated axial strain ε1acc can be obtained that:
Campl
av
fp = exp[−Cp (pav / pref
−1)]
reference
αf exp(−θf ε1acc (N , η , pav , ε ampl, s ) + βf =
where p the average mean stress, η is the ratio of the average
deviatoric stress (qav) to the average mean stress pav, η = qav/ pav, and
ε ampl is the strain amplitude during one loading cycle. The detailed
explanation of these variables is shown in Fig. 6. η0 , p0av , q0ampl and s0 are
reference variables, and the functions fη , fp and fampl describe the influences of the average stress ratio η, the average mean pressure pav,
and cyclic strain amplitude ε ampl on accumulated axial strain ε1acc , respectively. In this paper, only the axial strain is considered. Thus, ε ampl
only represents the axial strain amplitude. The functions of fη , fp and
fampl are expressed as follows[23,31,18]:
(7)
are
θf0 = θf (η0 , p0av , ε0ampl, s0) ,
(12)
fη fp fampl fs αf0 exp(−θf0 ε1acc (N , η , pav , ε ampl, s )/ fη fp fampl fs ) + fη fp fampl fs βf0
(6)
⎛
⎞
fampl = ⎜ ampl ⎟
ε
⎝ ref ⎠
βf0
Substituting Eq. (6) into Eq. (12), it yields that:
av
ε ampl
, s0 )
Substituting Eq. (5) into Eq. (11), it can be obtained that:
where αf = c1 c2 and θf = c , describing the initial exponential decrease
1
of the accumulated axial strain rate, and βf = c3 , describing the stable
accumulated axial strain rate after a large number of cycles.
Based on Sawicki et al. [26], Niemunis et al. [23] and Wichtmann
et al. [31], it is assumed that the shape of the deformation curve is
invariant with respect to different parameters. Therefore, the accumulated axial strains in cyclic triaxial tests can be expressed as follows:
ε1acc (N , η , pav , ε ampl, s ) = fη fp fampl fs ε1acc (N , η0 , p0av , ε0ampl, s0)
(10)
ε1acc =
1 ⎛
⎛ αf
⎞ αf ⎞
ln exp(θf βf N ) ⎜ + exp(θf ε1acc (N , η0 , p0 , ε0ampl, s0))⎟ θf ⎜
βf
βf ⎟
⎝
⎠
⎠
⎝
(17)
Model calibration
ampl
av
is the reference stress amplitude, pref
is the reference
where εref
average mean pressure. Campl , Cp , Cη are model parameters.
As shown in Fig. 5, an exponential relationship exists between the
accumulated axial strain ε1acc and the matric suction s. Based on this, a
new function fs considering the influence of matric suction s on the
accumulated axial strain ε1acc is proposed, and the exponential function
fs can be described as:
To obtain the expression of function fs , it is necessary to eliminate
the influences of the average stress ratio η, the average mean pressure
pav and cyclic strain amplitude .. Fig. 7 presents the accumulated axial
strain ε1acc , normalized by functions fη , fp and fampl , ε1acc/(fη fp fampl ) versus
ampl
is 0.1, and
the number of cycles, N. The reference stress amplitude εref
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Transportation Geotechnics 17 (2018) 48–55
J. Chen et al.
Fig. 7. Axial strain accumulation (divided by the stress ratio function, mean pressure function and strain amplitude function) versus the number of cycles.
av
the reference average mean pressure pref
is 60 kPa. The model parameters Campl = 1.05, Cp = - 1.08 and Cη = 1.85, which are obtained by
fitting methods from some basic cyclic triaxial tests on the same test
material, subjected to different qampl, η and p values [8]. To simplify the
expression, the fitting processes are not given here. Due to different test
materials, the parameter values are a little different from the values
given by Wichtmann et al. [31]. It can be seen that the curves under the
same s subjecting to different qampl coincide well with each other, indicating that the function fη , fp and fampl are effective in this study.
The differences between Fig. 7(a)–(d) indicate the influence of fs
obviously. To eliminate the influence of fs , the accumulated axial strain
ε1acc normalized by functions fη , fp , fampl and fs , expressed as
ε1acc/(fη fp fampl fs ) , versus the number of cycles N for all the tests are
shown in Fig. 8. By the fitting method, the reference matric
suctionsref = 38.4 kPa, and the model parameters, a = 0.65, b = 0.81 in
fs are obtained. It can be found that all the curves coincide well with
each other, indicating that the function fs can represent the influence of
matric suction s on the accumulated axial strain ε1acc .
Based on Eq. (6), the reference accumulated axial strain
ε1acc (N , η0 , p0 , ε0ampl, s0) can be expressed as:
ε1acc (N , η0 , p0av , ε0ampl, s0) = ε1acc (N , η , pav , ε ampl, s )/ fη fp fampl fs
Fig. 8. Axial strain accumulation (divided by the stress ratio function, mean
pressure function strain amplitude function and matric suction function) versus
the number of cycles.
(18)
Therefore, the fitting curve in Fig. 8 can represent the curve of
Thus,
the
reference
parameters
ε1acc (N , η0 , p0 , ε0ampl, s0) .
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J. Chen et al.
results and calculated results are shown in Fig. 9. It can be seen that two
results agree well with each other, which indicates that the unsaturated
cyclic model can effectively predict the accumulated axial strain considering the influence of matric suction.
Conclusion
This paper mainly focuses on the influence of matric suction on the
vertical deformation of road base and subbase materials. Large-scale
triaxial tests were firstly conducted under four matric suction subjecting
to three cyclic stress amplitudes. The control of matric suction is the key
problem during the tests, and the initialization of matric suction needs a
significant amount of time to ensure the water-air equilibrium. Based
on the cyclic model proposed by Karg et al. [18], a new function considering the influence of matric suction on the axial accumulated strain
was then established. The function is in a exponential form, which
conforms to the experimental phenomenon. Finally, the model parameters are calibrated, and the calculated results are compared with the
experimental results. The mainly conclusion are as follows:
(a) qampl = 60 kPa
1. With the increase of matric suction, the axial accumulated strain
decreases at declining rate, and the influence of matric suction on
vertical deformation of road base and subbase materials cannot be
neglected.
2. The influence degree of matric suction depends on the stress state of
the materials. Larger cyclic stress amplitude will strengthen the influence of matric suction.
3. An improved cyclic model containing a new exponential function to
describe the influence of matric suction is proposed, and proved to
be effective by comparing the experimental results and the calculated results.
Acknowledgements
The authors wish to acknowledge the support of the National Key
Research and Development Plan of China (Grant No.
2016YFC0800200), the National Natural Science Foundation of China
(Grant Nos. 51238009, 11372274, 51578500, 51578426), Program of
International Science and Technology cooperation (Grant No.
2015DFA71550), the Natural Science Foundation of Zhejiang Province
(Grant No. LY15E080009) and the Fundamental Research Funds for the
Central Universities (Grant No. 2015QNA4024).
(b) qampl = 100 kPa
Appendix A. Supplementary data
Supplementary data associated with this article can be found, in the
online version, at https://doi.org/10.1016/j.trgeo.2018.06.001.
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(a) qampl = 150 kPa
Fig. 9. Comparison between experimental results and calculated results.
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