第 31 卷
2009 年
岩
第1期
1月
土
工 程
学 报
Chinese Journal of Geotechnical Engineering
Vol.31 No.1
Jan. 2009
Modeling rate-dependent behaviors of soft subsoil under embankment loads
YIN Zhen-yu1, 2, 3, HUANG Hong-wei3, UTILI Stefano1, HICHER Pierre-Yves2
(1. Department of Civil Engineering, University of Strathclyde, Glasgow, G4 0NG, UK; 2. Research Institute in Civil and Mechanical
Engineering, Ecole Centrale de Nantes, Nantes 44321, France; 3. Key Laboratory of Geotechnical and Underground Engineering of
Ministry of Education, Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China)
Abstract: The paper aims to model the rate-dependent behaviors of subsoil under embankment loads using a simple
elasto-viscoplastic model, based on the modified Cam-clay model and Perzyna’s overstress theory, coupled with Biot’s
consolidation theory. A geotextile reinforced embankment is studied. An inverse analysis procedure is proposed to identify the
viscosity parameters of subsoil from the settlements due to the first few loading phases. In order to assess the performance of
the proposed model, numerical predictions using the determined parameters are then compared with those obtained by four
other models. Special attention is given to the effect of reinforcement on delayed deformations and on the stability of the
embankments and foundations. The performance of the proposed inverse analysis procedure is also assessed. Finally, according
to the simulation runs, it can be concluded that the proposed model is easy to be calibrated and suitable for geotechnical projects.
The proposed model can describe the rate-dependent behaviors of soft soil compared with the modified Cam-clay model, with
accuracy using the simple constitutive equations compared with other viscoplastic models.
Key words: clay; embankment; geotextile; rate dependence; elasto-viscoplasticity
CLC number: TU43
Document code: A
Article ID: 1000–4548(2009)01–0109–09
Biography: YIN Zhen-yu(1975– ), male, research fellow in geotechnical engineering. E-mail: zhenyu.yin@gmail.com.
模拟堤坝荷载作用下软土的速率效应特性
尹振宇
1,2,3
，黄宏伟 ，UTILI Stefano1, HICHER Pierre-Yves2
3
(1.英国斯特莱斯克莱德大学，格拉斯哥 G4 0NG 英国；2.法国南特中央大学，南特 44321 法国；3.同济大学地下建筑与工程系
教育部重点实验室，上海 200092)
摘 要：用基于 Perzyna 超应力理论与修正剑桥模型的简单的弹黏塑性本构模型，耦合比奥固结理论，来模拟堤坝荷载
作用下的软土的速率效应特性。以土工织布加固的堤坝为实例，提出从最初几个加载阶段下的沉降数据来确定黏性参
数的反分析法。根据反分析的参数值来模拟，同实测值予以比较，并同文献中使用其他四个不同本构模型的模拟结果
进行比较，比较研究表明：本文建议的模型具有优越性。特别研究了土工织布加固对堤坝下软土的滞后变形和稳定性
的影响。良好的模拟结果反应了所提出的反分析法的可用性，同时展示了所使用的弹黏塑性本构模型在岩土工程中的
实用性：弥补了修正剑桥模型不能模拟速率效应特性的缺点；跟其他黏塑性本构模型比较, 本模型参数确定方法简单，
模拟结果准确。
关键词：软土；堤坝；土工织布；速率效应特征；弹黏塑性
0
Introduction
The construction of embankments on soft natural
soil deposits has become increasingly important in the
last decades, as development occurs more and more on
areas previously considered unsuitable for construction.
Stability of embankments is a major consideration in the
design and construction, while consideration of the
duration of construction is also required. Geosynthetic
reinforcement has been widely used to improve the
bearing capacity of subsoil and then to fasten the
construction, as reported by researchers [1-4]. To simulate
the rate-dependent behaviors of embankments, a suitable
and simple constitutive model is required. This study is
an attempt to use a simple but robust elasto-viscoplastic
───────
Foundation item: Supported by a grant from “Conseil Regional des Pays
de la Loire” in France
Received date: 2007–12–14
110
2009 年
岩 土 工 程 学 报
(EVP) model EVP-MCC, based on the framework of
Perzyna’s overstress theory and the elasto-plastic
modified Cam-clay model, with an inverse analysis
procedure for identifying soil parameters, in order to
describe the rate-dependent behaviors of compressible
subsoils under embankment loads.
The strain-rate-dependency behaviors of soft
compressible subsoil under a reinforced embankment
load at Sackville in Canada have been studied. Details of
Sackville embankment and field measurements were
reported by Rowe et al.[5-6] used a fully coupled Biot’s
consolidation theory with the modified Cam-clay model
(named MCC in this study) to analyze the reinforced
embankment showing that the elasto-plastic model was
not adequate for accurately predicting the different
features of the embankment behaviors. Rowe &
Hinchberger [7] demonstrated that an EVP model could
better reproduce the strain-rate-dependent behaviors of
the foundation soil using an EVP model with an elliptical
cap yield surface (named EVP-EC in this study).
However, the model has four additional parameters
compared to the Cam-clay model to be identified. A
comparison between different model predictions was
later carried out by Gnanendran et al.[8] Using the MCC,
an EVP model based on the original Cam-clay model and
Perzyna’ overstress theory by Adachi & Oka [9] (named
EVP-OCC in this study), and a constitutive model based
on the critical state theory and secondary compression
coefficient Cαε proposed by Kutter & Sathialingam[10]
(named CREEP in this study). However, their predictions
performed less well than those by EVP-EC model by
Rowe & Hinchberger[7]. Thereby the need for a new
model, the EVP-MCC, capable of taking into account the
rate-dependent behavior of soils with only two additional
parameters in comparison with the MCC model, is
adopted to simulate the subsoil behavior under the
embankment loads.
In the following, first, the EVP model and its
constitutive equations are briefly introduced. Then, the
Sackville reinforced embankment is illustrated. An
inverse analysis procedure is used to identify the
viscosity parameters from the several initial loading
phases.
Settlements,
vertical
and
horizontal
displacements, and excess pore pressures are calculated.
The obtained predictions are compared with field data
and predictions by four other constitutive models to
assess the performance of the models as well as the
performance of the inverse analysis procedure. The
effect of reinforcement is also numerically investigated.
1
Constitutive model
The constitutive model EVP-MCC developed by
Yin et al. (in press), is based on the framework of
Perzyna’s overstress theory[11-12] and the elasto-plastic
MCC[13] model. The elastic behavior in the proposed
model is given by the same expressions as in the MCC
model. The constitutive equations of the proposed model
for normally consolidated clays are derived as follows:
εij =
sij′
2G
+
δ ⎞
⎛ 3s ′
p ′
δ ij + µ φ ( F ) ⎜ ij2 + ( 2 p′ − pcd ) ij ⎟ ,(1)
3K
3 ⎠
⎝M
with
⎛
⎜
⎝
⎡ ⎛ pcd
⎞⎤ ⎞
− 1⎟⎥ − 1⎟ ,
s
⎠⎥⎦ ⎟⎠
⎣⎢ ⎝ pc
µ φ ( F ) = µ ⎜ exp ⎢ N ⎜
(2)
where sij′ is the deviatoric stress tensor ( sij′ = σ ij′ − p′δ ij ;
G is the elastic shear modulus, which is related to the
elastic bulk modulus (K=(1+e) p′ /κ) by assuming a
constant value of Poisson’s ratio ν(G=3(1-2ν)K/2(1+ν));
κ is the slope of the swelling line in the “ e − ln σ v′ ” plane;
δij is the Kronecker delta with δij=1 for i=j and δij=0 for
i≠j; pcs is the static preconsolidation pressure; pcd is the
dynamic preconsolidation pressure corresponding to the
current stress state; M is the slope of the critical state line;
N is the viscosity index; µ is the viscosity coefficient;
p′ is the effective mean stress; q is the deviatoric stress,
relating to the second invariant of deviatoric tensor; <
and > represent the MacCauley´s function.
The proposed model involves the parameters of the
MCC model {ν, κ, λ, e0, M, pc′0 }, and two additional
parameters of viscosity {N, µ}. Details can be found in
Yin et al.[14] and Yin & Hicher [15].
2
Sackville reinforced embankment
2.1 Embankment and soil conditions
A full scale test embankment was constructed on
organic silty clays and clayey silts in New Brunswick
(Canada), consisting of a 25 m long unreinforced section
and a 25 m long reinforced section connected by a
reinforced transition (Fig. 2). A number of instruments
was installed and readings taken during construction (see
Rowe et al.[5]).
第1期
YIN Zhen-yu, et al. Modeling rate-dependent behaviors of soft subsoil under embankment loads
The elasto-plastic Mohr-Coulomb model is adopted
for the embankment fill consisting of gravelly silty sand
and clay. The unit weight and parameters of fills are
listed in Table 1.
The geotextile reinforcement is modeled as a series
of linear elastic perfectly plastic bar elements. The
parameters adopted for the reinforcement were: axial
stiffness J = 1920 kN/m, and tensile strength Tf = 216
kN/m (see Rowe et al.[6]). The embankmentreinforcement-soil interface was modeled using nodal
compatibility joint elements, assumed to be rigid plastic
and nondilatant.
Table 1 Parameters of the embankment (after Rowe et al.[6])
Height
γ
E
-3
ν
c＇/kPa
ϕ/(°)
Ψ/(°)
kh=kv
/(m·s 1)
-
/m
/(kN·m )
/kPa
0.0~1.3
18.8
10000
0.35
0
43
8
1
1.3~9.6
19.6
15000
0.35
17.5
38
7
1
2.2
Parameter calibration
For the compressible subsoil, the time-dependent
behavior is taken into account by using the EVP-MCC
model. For all the soil layers, the Poisson’s ratio ν is
taken equal to 0.3 as for most clays; the slope of the
critical state line M is taken equal to 1.12 as proposed by
Rowe et al.[6] for the MCC model; the coefficients of
compressibility and the vertical and horizontal
permeabilities are taken by Rowe et al.[6] and Rowe &
Hinchberger [7]; the preconsolidation pressure pc′0 is
determined using the in-situ vertical effective stresses
′ , the coefficient of earth pressure at rest K 0′ and the
σ v0
ratio of overconsolidation OCR reported by Rowe et al.[5]
and Rowe & Hinchberger[6]:
⎡ 3 (1 − K ′ )2
(1 + 2 K0′ ) ⎤
0
⎥ σ v0
′ =⎢
′ OCR .
+
pc0
3
⎢ (1 + 2 K0′ ) M 2
⎥
⎣
⎦
(3)
The viscous index N is taken equal to 10 according to
111
Yin et al.[14]. The parameters adopted for the subsoil of
the embankment are summarized in Table 2.
2.3 Finite element analysis
Plain strain conditions are assumed in the finite
element method analysis (FEM). The modeled range in
vertical direction is 14 m deep and 65 m away from the
embankment centerline horizontally. The displacement
boundary conditions are as follows: at the bottom, both
vertical and horizontal displacements are fixed, while
along the left and right vertical boundaries, only the
horizontal displacements are fixed. The adopted drainage
boundary conditions are as follows: the ground surface is
kept drained while the other boundaries undrained. The
FEM mesh is constituted by 2519 nodes and 1204
triangular elements. Each element has 6 Gauss
integration points. The adopted mesh is proved to be
suitable since analyses run using 2 and 10 times denser
meshes gave rise to closely convergent results.
The construction of the embankment is simulated
by increasing the unit weight of each layer of the
embankment fills linearly over time. Eight phases of
construction are adopted according to the construction
sequence shown in Figure 1. The apparent viscosity is
then identified from the settlements measured during the
initial loading phases by performing inverse analysis.
2.4 Inverse analysis procedure to identify A procedure of inverse analysis is carried out to
obtain the value of µ. The parameter is calibrated by an
optimization procedure. According to this procedure, the
input values of the parameter are iteratively changed
until the calculated results matched the observed data.
The methodology of the inverse analysis is shown in
schematic form in Figure 2. In the optimization
procedure, the difference between the observed data and
the model predictions is expressed as follows:
Table 2 Values of MCC parameters and permeability for subsoil
Layer
Depth/m
κ
λ
e0
γ/(kN·m 3)
OCR
K′0
ν
M
kh/( m·s 1)
kv/(m·s 1)
Sol6
0~1.1
0.06
0.28
2.2
17.8
3.6
0.68
0.3
1.12
3.0 x10-6
3.0 x10-7
Sol5
1.1~2.7
0.02
0.12
1.31
17.8
3.6
0.70
0.3
1.12
2.0 x10-7
1.0 x10-7
Sol4
2.7~4.4
0.05
0.23
1.39
16.5
1.0
0.75
0.3
1.12
2.0 x10-7
5.1 x10-8
Sol3
4.4~5.8
0.06
0.28
2.3
17.2
1.0
0.80
0.3
1.12
1.0 x10-6
1.0 x10-7
Sol2
5.8~10
0.03
0.15
1.12
17.2
1.2
0.80
0.3
1.12
3.3 x10-8
8.2 x10-9
Sol1
10~14
0.03
0.15
1.12
17.2
1.2
0.80
0.3
1.12
3.3 x10-8
8.2 x10-9
-
-
-
112
岩 土 工 程 学 报
2009 年
Fig. 1 Section of embankment with instrumentation layout and construction sequence (after Rowe et al.[5])
iterative process.
The procedure of parameter identification by
inverse analysis, as presented in Figure 2, is used to
determine the parameter µ from the settlements
measured for plates 8S and 9A during the first loading
Fig. 2 Procedure of identifying parameter by inverse analysis
Fig. 3 Iterative process to identify soil viscosity parameter
Ln ( P ) =
1
tini − tfin
∫
R * ( t ) − R ( µ , t ) dt ,
(4)
where the notation ||…|| represents the scalar norm in the
space variable, tini-tfin is the time of observation, R is the
response of the system, and R*(t)-R(µ,t) is the difference
between experimental and numerical data. Since
measurements are taken at discrete moments, the integral
of the norm can be replaced by a summation and the
length of observation by the number of measurements.
The difference between measured and predicted data is
then expressed as follows:
Ln ( P ) =
1
Mn
Mn
∑(R
i
*
i
− Ri )
2
,
(5)
Ln(P)<ε (ε is a given tolerance) can be used as a
discriminate function to judge the convergence of the
phases up to 5.7 m, assuming that µ is identical for all
subsoil layers. The iterative process to update the
parameter is presented in Figure 3. The optimization
loops (Table 3) are carried out as follows:
(a) First, an interval of acceptable values for the
parameter µ is selected, as shown in the first two lines in
Table 3. The initial value of the parameteris then taken as
the average of the upper and lower bound values.
(b) This value is used in the FE analysis to calculate
the settlements of the points 8S and 9A. Then the
difference between the values determined by FE and the
observed data is calculated. The sign of the difference is
then used to half the range of the parameter for the
successive iteration according to a dichotomy procedure.
If the sign of the difference is positive, the value of the
parameter assumed in the FE simulation becomes the
new upper bound for the successive iteration and
conversely if it is negative, it becomes the new lower
bound. In the former case, the predicted curve will
overestimate the experimental one whereas in the latter
case it will underestimate it. The value adopted in the
successive iteration is taken as the average between the
bounds of the new range as shown in Table 3.
(c) The procedure is stopped when convergence is
achieved that is when the norm of the difference between
第1期
YIN Zhen-yu, et al. Modeling rate-dependent behaviors of soft subsoil under embankment loads
experimental data and predictions become smaller than a
predefined tolerance. In Table 3, the value of the
parameter at the end of the iterative process, µ = 1.07×
10 8 s 1kPa 1, is given.
The final value of the parameter µ is then used in
the FE analysis.
Table 3 Optimization loops for identifying viscosity parameter
Loop of µ
Iteration number
Logµ/(s-1·kPa-1)
Initial
-5
Up
Initial
-10
Low
1
-7.5
Up
2
-8.75
Low
3
-8.125
Low
4
-7.813
Up
5
-7.97
Converge
Final
10
-7.97
113
settlements for locations 10A and 11A from the first
loading phases until the embankment reaches 8.2 m can
be attributed to the presence of a soft zone of soil and the
auger being driven down in the foundation soil by the
surrounding soil as pointed out by Rowe &
Hinchberger [7]. On the other hand, it is found out that the
settlements of the foundation soil decrease with the depth
and the settlement-time responses at different depths are
very similar. This result is reasonable and in general
agreement with the field measurements.
= 1.07×10- 8 s- 1.kPa- 1
Remarks: up – Upper bound value; low – Lower bound value.
3
Results
3.1
Settlements at 6S, 7S, 8S, and 9A, 10A, 11A
The comparison between measured and calculated
settlements for different positions beneath the
embankment and at different depths in the subsoil is
shown in Figure 4. The evolution of the settlements with
time generally agrees with the field measurements. For
all positions investigated but 11A, settlements are
overestimated so long as the embankment height reaches
5.7 m. From that point of construction onwards, good
agreement is achieved so long as the embankment height
reaches 8.2 m except for positions 6S and 10A. But, in
the last phase of the embankment construction, a
significant
discrepancy between analysis and
observations is found. Rowe et al.[5] reported that a large
increase of settlements was observed at location 8S
during this phase of construction because of the rupture
of the geotextile, perhaps due to horizontal
non-uniformity of the foundation shear strength. On the
contrary, the geotextile does not reach the failure
condition because of the assumptions of soil
homogeneity made in the FE analysis. The calculated
settlement at location 6S is greater than the measured
one. This may be due to the presence of a zone of soft
soil that is not spotted by soil investigations. The
difference between the measured and calculated
Fig. 4 Measured and predicted settlements
In the following, the predictions obtained by the
selected five models for locations 7S and 8S are
compared with the field observations as shown in Figure
5. Considering the first construction phases of the
embankment, up to the height of 4.2 m, the predictions
by the EVP-EC model capture well the settlements
whereas other models overestimate them. Considering
the subsequent two loading phases, the predictions by the
proposed model, EVP-MCC, result to be better than the
others. Finally considering the last phase, from end of
construction onwards, the settlements predicted by the
elasto-plastic model (MCC) become stable after a while
whereas those predicted by the four elasto-viscoplastic
models increase indefinitely over time as observed in the
field.
A similar comparison is carried out for plates 9A
and 11A, as shown in Figure 6. For 9A (Fig. 6(a)),
considering the first construction phases of the
embankment up to the height of 5.7 m, the predictions by
EVP-MCC overestimate the settlements while the other
four models give better results. For the subsequent
114
岩 土 工 程 学 报
loading phases, the predictions by EVP-EC and the
proposed model are closer to the field observations than
those by MCC, EVP-OCC and CREEP models. For 11A
(Fig. 6(b)), all predicted settlements are lower than the
field observations, whereas predictions by EVP-MCC
are better than those obtained by the other models.
2009 年
deformation at the embankment toe, as noted by Rowe &
Hinchberger[7].
Fig. 5 Settlements by different models for (a) 7S and (b) 8S
Fig. 7 Vertical displacements by different models
Fig. 6 Settlements by different models for 9A and 11A
3.2 Vertical displacements at 1H, 2H, 3H and 4H
The comparison between the measured and
calculated vertical displacements at the heave plates 1H,
2H, 3H and 4H is shown in Figure 7. A good agreement
is achieved up to an embankment height of 5.7 m.
However, for the last two loading phases, the calculated
displacements are greater than the measured ones. Rowe
et al.[4] observed significant “thrust faulting” in the heave
zone at a fill height of 8.2 m, while the present method of
analysis does not account for this type of discontinuous
Figure 7(b) shows a comparison between
predictions by the EVP-EC and the proposed EVP-MCC
model for plates 1H and 4H. Both of them well capture
the evolution of vertical displacements up to the fill
height of 5.7 m. Considering the subsequent phase, the
rate of displacements calculated by EVP-EC is different
from that by the proposed model, while the final
displacements predicted by the two models are close to
each other.
Figure 7(c) shows a comparison of predictions by
the five models for plate 2H. The proposed model and
EVP-EC can well reproduce the evolution of vertical
displacements as long as the embankment height of 5.7
m is reached, while the other models overestimate the
displacements. For the subsequent phase, the predicted
第1期
YIN Zhen-yu, et al. Modeling rate-dependent behaviors of soft subsoil under embankment loads
displacements by EVP-EC are higher than those
predicted by other models. Concerning 3H (Fig. 7(d)),
the predictions by MCC, EVP-OCC and CREEP models
are better than those by the proposed model as long as
the embankment reaches the height of 5.7 m, and much
lower than those by the proposed model for the
subsequent phase. The lack of agreement in this case can
be attributed to the “thrust faulting” described by Rowe
et al.[4] and Rowe & Hinchberger[7].
3.3 Horizontal displacements
A good agreement between the measured and
calculated horizontal displacements at the embankment
toe by the proposed model and EVP-EC is achieved as
long as an embankment height of 8.2 m is reached, as
shown in Figure 8.
Fig. 8 Horizontal displacements by different models
Figure 9 presents the comparisons of horizontal
displacements at inclinometers 22I and 23I for different
models with observations. For both inclinometers,
considering t = 449 h, the predictions by the proposed
model are close to the field data and to the predictions by
other models up to a depth of 5 m, whereas they
overestimate displacements at greater depth. Considering
22I at t = 473 h (Fig. 9(b)), the proposed model
underestimates displacements until a depth of 2 m and
115
then overestimates them resulting to be less accurate than
the other ones. However, the predictions are quite similar
for all models. Based on the simulation run, it can be
stated that any model is able to well predict some
features of the horizontal displacements at some times,
but none of them can capture all the curves. Rowe &
Hinchberger [7] indicated the many difficulties associated
with the prediction of lateral deformations beneath
embankments due to: difficult estimation of Poisson’s
ratio for the foundation soil, anisotropy and
non-homogeneity
of
the
foundation
soil,
three-dimensional effects, etc. In conclusion, the general
magnitude and profile of lateral displacements beneath
the embankment can be determined with reasonable
accuracy using the proposed EVP-MCC model.
3.4 Excess-pore pressure in the foundation soil
Figure 10 presents the comparison between the
measured and predicted excess pore pressure for
different positions and depths (from 2 to 10 meters) in
the foundation soil. The predictions by the proposed
model are in reasonable agreement with the measured
values for all phases of construction. It is worth noting
that the predictions for locations 12 (Fig. 10(b)) and 19
(Fig. 10(c)) by MCC, EVP-OCC and CREEP models are
overestimated.
3.5 Reinforcement effect
A calculation for the case of embankment without
reinforcement is carried out. In this case, the pore
pressure dissipation is a little faster but similar to the
case of reinforced embankment (Fig. 11). Settlements
and displacements are much greater than in case of
Fig. 9 Horizontal displacements by different models
116
岩 土 工 程 学 报
2009 年
Fig. 10 Excess-pore pressures in the foundation soil
Fig. 11 Comparison of the calculated results at different loading phases for the embankment with and without reinforcement
reinforced embankment as shown in Figure 11 for a fill
height of 9.5 m; therefore the reinforcement can increase
the stability of the embankment. As described by
Leroueil & Rowe[2], the reinforcement serves two
primary functions: it resists some or all of the earth
pressure that develops with the embankment; it also
resists the lateral deformations of the foundation that
would otherwise occur in response to the applied vertical
load.
Figure 12 presents the comparison of settlements at
plates 7S, 8S, 9A, 10A and 11A with and without
reinforcement. The settlement increases far more rapidly
and more significantly at lower depths for un-reinforced
embankments, while for deep depths (for plate 10A), the
effect of reinforcement is small. It is worth remarking
that the reinforcement by geotextile makes it possible to
reduce the construction duration of an embankment on
compressible soils.
4
Conclusions
The rate-dependent behaviors of the foundation soil
under an embankment reinforced by geotextile are
simulated using an elasto-viscoplastic model, EVP-MCC,
coupled with the Biot´s consolidation theory, with an
inverse analysis procedure to identify the viscosity
parameter.
The soil parameters are determined from laboratory
tests with the value of µ identified by the inverse
analysis from the settlement curves of several initial
phases of embankment loads. The predictions by
theproposed model are compared with the field data, as
well as with the predictions by other four constitutive
models:a good performance is achieved for the proposed
model and for the proposed procedure of inverse analysis.
Based on the simulations performed for both cases of
reinforced and unreinforced embankment, it is possible
to conclude that the use of reinforcement with geotextile
can significantly reduce the creep deformation of the
foundation soil and therefore improve the stability of the
embankment and underlying foundation. It is found that
the reinforcement affects the effective stress state, thus
affects the velocity field of subsoil. The presence of the
第1期
117
YIN Zhen-yu, et al. Modeling rate-dependent behaviors of soft subsoil under embankment loads
reinforcement significantly delays both horizontal and
vertical displacements in the part of the embankment
opposite to the berms.
[4] ROWE R K, LI A L. Behavior of reinforced embankments on
soft rate-sensitive soils[J]. Géotechnique, 2002, 52(1): 29–
40.
[5] ROWE R K, GNANENDRAN C T, LANDVA A O,
VALSANGKAR A J. Construction and performance of a
full-scale geotextile reinforced test embankment, Sackville,
New Brunswick[J]. Can Geotechnical J, 1995, 32(3): 512–
534.
[6] ROWE R K, GNANENDRAN C T, LANDVA A O,
VALSANGKAR A J. Calculated and observed behavior of
reinforced embankment over soft compressible soil[J]. Can
Geotechnical J, 1996, 33(2): 324–338.
[7] ROWE R K, HINCHBERGER S D. Significance of rate
effects in modeling the Sackville test embankment[J]. Can
Geotechnical J, 1998, 35(3): 500–516.
[8] GNANENDRAN C T, MANIVANNAN G, LO S C R.
Fig. 12 Comparison of the calculated settlements for the
embankment with and without reinforcement
A good agreement between the measured and
predicted settlements, displacements and excess pore
pressures is achieved. So it can be concluded that FE
analyses with fully coupled EVP-MCC model and the
Biot’s consolidation theory can adequately describe the
rate-dependent behaviors of the foundation soil under a
reinforced embankment compared with the modified cam
clay, with accuracy using the simple constitutive
equations compared with other viscoplastic models. All
the simulation runs demonstrate that the proposed model
can be easily calibrated and used in geotechnical
projects.
Influence of using a creep, rate, or an elastoplastic model for
predicting the behavior of embankments on soft soils[J]. Can
Geotechnical J, 2006, 43(2): 134–154.
[9] ADACHI T, OKA F. Constitutive equations for normally
consolidated clay based on elasto-viscoplasticity[J]. Soils and
Foundations, 1982, 22(4): 57–70.
[10] KUTTER B L, SATHIALINGAM N. Elastic-viscoplastic
modeling of the rate-dependent behavior of clays[J].
Géotechnique, 1992, 42(3): 427–441.
[11] PERZYNA P. The constitutive equations for work-hardening
and rate sensitive plastic materials[C]// Proc Vibration
Problems, 1963, 3: 281–290.
[12] PERZYNA P. Fundamental problems in viscoplasticity[M].
Advances in Applied Mechanics, Academic Press, 1966: 243
–377.
[13] ROSCOE K H, BURLAND J B. On the generalized
References:
[1] HUMPHREY D N, HOLTZ R D. Reinforced embankments: a
review of case histories[J]. Geotextiles and Geomembranes,
[2] LEROUEIL S, ROWE R K. Embankments over soft soil and
Geotechnical
535–609.
[14] YIN Z Y, ZHANG D M, HICHER P Y, HUANG H W.
1987, 6(4): 129–144.
peat.
stress-strain behavior of wet clay[J]. Engrg Plasticity, 1968:
and
geoenvironmental
engineering
handbook[M]. Springer Kluwer Academic Publishers, 2001:
463–500.
Modeling of the time-dependent behavior of soft soils using a
simple
elasto-viscoplastic
model[J].
Chinese
J
of
Geotechnical Engrg, 2008. (in Chinese)
[15] YIN Z Y, HICHER P Y. Identifying parameters controlling
[3] LI A L, ROWE R K. Combined effects of reinforcement and
soil delayed behaviour from laboratory and in situ
prefabricated vertical drains on embankment performance[J].
pressuremeter testing[J]. International Journal for Numerical
Can Geotechnical J, 2001, 38(6): 1266–1282.
and Analytical Methods in Geomechanics. (in press).