Three-dimensional generalization and verification of structured bounding surface model for natural clay
As the proposed structured bounding surface model can only be used to solve planar strain problems of natural soft clay, a three-dimensional adaptive failure criterion is adopted to improve the model to capture the three-dimensional behaviors of natural soft clay. The three-dimensional adaptive fail...
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| Цитувати: | Three-dimensional generalization and verification of structured bounding surface model for natural clay / Cui Yunliang, Wang xinquan, Zhou lianying // Functional Materials. — 2018. — Т. 25, № 1. — С. 138-143. — Бібліогр.: 13 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1544642025-02-23T18:07:36Z Three-dimensional generalization and verification of structured bounding surface model for natural clay Cui Yunliang Wang xinquan Zhou lianying Modeling and simulation As the proposed structured bounding surface model can only be used to solve planar strain problems of natural soft clay, a three-dimensional adaptive failure criterion is adopted to improve the model to capture the three-dimensional behaviors of natural soft clay. The three-dimensional adaptive failure criterion incorporated in this model can cover the Lade-Duncan criterion and the Matsuoka-Nakai criterion as its special ones. The structured bounding surface model is generalized into three-dimensional stress space by using the three-dimensional adaptive failure criterion. After improved with the three-dimensional adaptive failure criterion, the model can be seen as a modified bounding surface model which considers the destructuration and three-dimensional behaviors and neglects the anisotropy of natural soft clay. The simulations of undrained compression and extension tests of K0 consolidation state Bothkennar clay shows the unimportance of neglecting anisotropy in this model. It was validated on Pisa clay that the improved model can simulate well the three dimensional behaviors of natural soft clay under true triaxial conditions. The support of National Natural Science Foundation of China(Grant no. 51508507), Zhejiang Provincial Natural Science Foundation of China (Grant no. LQ16E080007), and Zhejiang Provincial Transportation Bureau Scientific Research Plan (Grant no. 2017004) are gratefully acknowledged. 2018 Article Three-dimensional generalization and verification of structured bounding surface model for natural clay / Cui Yunliang, Wang xinquan, Zhou lianying // Functional Materials. — 2018. — Т. 25, № 1. — С. 138-143. — Бібліогр.: 13 назв. — англ. 1027-5495 DOI:https://doi.org/10.15407/fm25.01.138 https://nasplib.isofts.kiev.ua/handle/123456789/154464 en Functional Materials application/pdf НТК «Інститут монокристалів» НАН України |
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Modeling and simulation Modeling and simulation |
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Modeling and simulation Modeling and simulation Cui Yunliang Wang xinquan Zhou lianying Three-dimensional generalization and verification of structured bounding surface model for natural clay Functional Materials |
| description |
As the proposed structured bounding surface model can only be used to solve planar strain problems of natural soft clay, a three-dimensional adaptive failure criterion is adopted to improve the model to capture the three-dimensional behaviors of natural soft clay. The three-dimensional adaptive failure criterion incorporated in this model can cover the Lade-Duncan criterion and the Matsuoka-Nakai criterion as its special ones. The structured bounding surface model is generalized into three-dimensional stress space by using the three-dimensional adaptive failure criterion. After improved with the three-dimensional adaptive failure criterion, the model can be seen as a modified bounding surface model which considers the destructuration and three-dimensional behaviors and neglects the anisotropy of natural soft clay. The simulations of undrained compression and extension tests of K0 consolidation state Bothkennar clay shows the unimportance of neglecting anisotropy in this model. It was validated on Pisa clay that the improved model can simulate well the three dimensional behaviors of natural soft clay under true triaxial conditions. |
| format |
Article |
| author |
Cui Yunliang Wang xinquan Zhou lianying |
| author_facet |
Cui Yunliang Wang xinquan Zhou lianying |
| author_sort |
Cui Yunliang |
| title |
Three-dimensional generalization and verification of structured bounding surface model for natural clay |
| title_short |
Three-dimensional generalization and verification of structured bounding surface model for natural clay |
| title_full |
Three-dimensional generalization and verification of structured bounding surface model for natural clay |
| title_fullStr |
Three-dimensional generalization and verification of structured bounding surface model for natural clay |
| title_full_unstemmed |
Three-dimensional generalization and verification of structured bounding surface model for natural clay |
| title_sort |
three-dimensional generalization and verification of structured bounding surface model for natural clay |
| publisher |
НТК «Інститут монокристалів» НАН України |
| publishDate |
2018 |
| topic_facet |
Modeling and simulation |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/154464 |
| citation_txt |
Three-dimensional generalization and verification of structured bounding surface model for natural clay / Cui Yunliang, Wang xinquan, Zhou lianying // Functional Materials. — 2018. — Т. 25, № 1. — С. 138-143. — Бібліогр.: 13 назв. — англ. |
| series |
Functional Materials |
| work_keys_str_mv |
AT cuiyunliang threedimensionalgeneralizationandverificationofstructuredboundingsurfacemodelfornaturalclay AT wangxinquan threedimensionalgeneralizationandverificationofstructuredboundingsurfacemodelfornaturalclay AT zhoulianying threedimensionalgeneralizationandverificationofstructuredboundingsurfacemodelfornaturalclay |
| first_indexed |
2025-11-24T06:34:14Z |
| last_indexed |
2025-11-24T06:34:14Z |
| _version_ |
1849652469477408768 |
| fulltext |
138 Functional materials, 25, 1, 2018
ISSN 1027-5495. Functional Materials, 25, No.1 (2018), p. 138-143
doi:https://doi.org/10.15407/fm25.01.138 © 2018 — STC “Institute for Single Crystals”
Three-dimensional generalization and verification of
structured bounding surface model for natural clay
Cui Yunliang, Wang xinquan, Zhou lianying
School of Engineering, Zhejiang University City College, Hangzhou,
Zhejiang, 310015, China
Received December 1, 2017
As the proposed structured bounding surface model can only be used to solve planar strain
problems of natural soft clay, a three-dimensional adaptive failure criterion is adopted to im-
prove the model to capture the three-dimensional behaviors of natural soft clay. The three-
dimensional adaptive failure criterion incorporated in this model can cover the Lade-Duncan
criterion and the Matsuoka-Nakai criterion as its special ones. The structured bounding surface
model is generalized into three-dimensional stress space by using the three-dimensional adap-
tive failure criterion. After improved with the three-dimensional adaptive failure criterion, the
model can be seen as a modified bounding surface model which considers the destructuration
and three-dimensional behaviors and neglects the anisotropy of natural soft clay. The simula-
tions of undrained compression and extension tests of K0 consolidation state Bothkennar clay
shows the unimportance of neglecting anisotropy in this model. It was validated on Pisa clay
that the improved model can simulate well the three dimensional behaviors of natural soft clay
under true triaxial conditions.
Keywords: natural soft clay, bounding surface, three-dimensional behavior, adaptive failure
criterion
Рассмотрен трехмерный адаптивный критерий отказа трехмерного поведения
естественной мягкой глины, в котором использованы критерий Ладэ-Дункана и критерий
Мацуока-Накаи. Структурная модель ограничивающей поверхности обобщается на
трехмерное пространство напряжений с использованием трехмерного адаптивного критерия
отказа. После его учета модель может рассматриваться как модифицированная модель
ограниченной поверхности, которая учитывает разрушающее и трехмерное поведение
и пренебрегает анизотропией естественной мягкой глины. Проведено моделирование
недренированных грунтов на сжатие и растяжение, а также состояния консолидации.
Подтверждено, что предложенная модель может хорошо имитировать трехмерное поведение
естественной мягкой глины при истинных трехосных условиях воздействия нагрузок.
Тривимірне узагальнення та перевірка структурованої моделі граничної
поверхні для природної глини. Cui Yunliang, Wang xinquan, Zhou lianying.
Розглянуто тривимірний адаптивний критерій відмови тривимірної поведінки природної
м’якої глини, в якому використано критерій ладе-дункана і критерій мацуока-накаї.
Структурна модель обмеженої поверхні узагальнюється на тривимірний простір напружень
з використанням тривимірного адаптивного критерію відмови. Після його обліку модель
може розглядатися як модифікована модель обмеженої поверхні, яка враховує руйнівну і
тривимірну поведінку і нехтує анізотропією природної м’якої глини. Проведено моделювання
недренованих грунтів на стиск і розтяг, а також стану консолідації. Підтверджено, що
запропонована модель може добре імітувати тривимірну поведінку природною м’якої глини
при істинних тривісних умовах впливу навантажень.
Functional materials, 25, 1 2018 139
Cui Yunliang et al. / Three-dimensional generalization ...
1. Introduction
Experimental results [1, 2] indicate
that the stress-strain relationship curve of
natural clay has a softening after peak stress
in triaxial compression with low confining pres-
sure, and the compression rate of one-dimen-
sional compression becomes faster when the
compression pressure exceeds the structure
yielding stress. To capture the structured be-
haviors of natural soft clay, many advanced
constitutive models [3, 4] had been proposed.
Based on the bounding surface concept initi-
ated by Dafalias [5], AI-tabbaa and Wood [6]
set a kinematic hardening yield surface, called
‘bubble surface’, inside the bounding surface to
formulate a bubble model for soil. Rouainia and
Wood [7] presented a structured bounding sur-
face model, using the structure surface as the
bounding surface and incorporating a structure
measure of the bounding surface. The structure
measure allows the size of the bounding sur-
face to decay with plastic straining, so that the
proposed model can describe the loss of struc-
ture. Taiebat et al. [8] suggested a destructura-
tion law to address both isotropic and frictional
destructuration and applied it on SANICLAY
model. The frictional destructuration is proved
to have significant effect on the loss of structure
[8]. Literature [9] proposed a simple bounding
surface model incorporating the destructura-
tion law with some modifications. The proposed
model can be seen as a simplified model of the
existing structured bounding surface models
[6-7], because it neglected some complex prop-
erties of soil, such as the kinematic hardening
and anisotropy but considered the frictional de-
structuration. However, the model proposed by
work [9] is two-dimensional constitutive model.
it can only be used to solve planar strain prob-
lems of natural soft clay. It should be extended
to be three-dimensional to capture the three-
dimensional problems of natural soft clay. In
order to describe the three-dimensional defor-
mation of natural soft clay more precisely, the
proposed model is generalized in three-dimen-
sional principal stress space with a three-di-
mensional adaptive failure criterion [10, 11].
The adopted criterion can cover the Lade crite-
rion as well as the Matsuoka-Nakai criterion.
The performance of the proposed model is veri-
fied by typical experimental results on intact
samples of natural soft clay.
2. Generalization of bounding surface
model
The yielding surface of bounding surface
has the same elliptical shape with the Modified
Cam-Clay model [7, 8]:
F p p p q Mc= - +* *2 2 2/ (1)
where, p and q are the mean effective stress
and the generalized shear effective stress of
the mapping point on the bounding surface of
the current stress point, respectively; pc
* is the
intersection point of the bounding surface and
the axial of p , which denotes the size of the
bounding surface; M* is the critical state stress
ratio that is the slope of the critical state line.
By definition:
p =
+ +σ σ σ1 2 3
3
(2)
q = - + - + -
1
2
1 2
2
2 3
2
3 1
2( ) ( ) ( )σ σ σ σ σ σ (3)
where σ σ σ1 2 3, , are principal stresses in three-
dimensional stress.
In the classical plastic theory, the basic con-
stitutive equation can be expressed as follows:
d C dp
pε σ= × (4)
wherein d pε is incremental plastic strain, dσ
is incremental stress, and Cp is the plastic flex-
ibility matrix.
According to the associated flow rule, the
plastic flexibility matrix can be presented as
[10]
C
F F
Kp
T
p
=
¶
¶
¶
¶
æ
è
ççç
ö
ø
÷÷÷÷σ σ (5)
wherein Kp is the plastic hardening modulus.
It is necessary to define the plastic hardening
modulus in constitutive model. Work [9] pro-
posed a structured bounding surface model. As
presented in [9],
K Kp p= +ζ ψP
F
p
F
q
ba (( ) ( ) )( )
¶
¶
+
¶
¶
-2 2 1 (6)
The expression of Kp in eq. (6) can be seen
in Ref. [9]. b is the measure of the distance
between the loading surface which has been
defined in work [9]. ζ andψ are interpolation
parameters, reflecting the affect of the stress
level on the modulus. Their values can be de-
termined based on experimental curve fitting.
Pa denotes the initial size of the bounding sur-
face on axial of p in p q- stress space.
The model proposed by work [9] is proved to
be efficient and accurate for simulating the deg-
radation of structure of natural clay. However,
this model can only predict the two-dimension-
al stress-strain relationship of natural for it is
only a two-dimensional constitutive model. It
can only be used to solve planar strain prob-
lems. As we know, engineering problems are of-
140 Functional materials, 25, 1, 2018
Cui Yunliang et al. / Three-dimensional generalization ...
ten three-dimensional problems, which should
be solved with three-dimensional constitutive
models. Thus, in order to simulate the three-
dimensional behaviors of natural soft clay, a
reasonable three dimensional adaptive failure
criterion [10, 11] will be introduced to revise
the proposed model in [9]. An adaptive crite-
rion adopted here almost covers all the crite-
ria between the Lade-Duncan criterion and the
Matsuoka-Nakai criterion in principal stress
space by adjusting the adaptive parameter m
, including the Lade-Duncan criterion and the
Matsuoka-Nakai criterion as its special cases.
So, it is more adaptive compared with conven-
tional criteria. The function of the three-dimen-
sional adaptive failure criterion [10, 11] can be
expressed as
I I I
I
c c c
c c
1
3
1 2
3
3 2
2
3 9 1
1
+
=
=
- + - -
- -
m
f m f f
f f
( sin ) ( sin )( sin )
sin sin ++ sin3 fc
(7)
where m is a material constant which is deter-
mined by true triaxial test; fc is the critical
state internal friction angle for triaxial com-
pression; I1, I2 and I3 are the first, second and
third effective stress invariants, respectively.
I
I
I
1 1 2 3
2 1 2 2 3 3 1
3 1 2 3
= + +
= + +
=
ü
ý
ïïïï
þ
ïïïï
s s s
s s s s s s
s s s
(8)
I1, I2 and I3 can be expressed as:
I p
I p
q
I p pq q
1
2
2
2
3
3 2 3
3
3
3
1
27
27 9 2 3
=
= -
= - +
ü
ý
ïïïïïïïï
þ
ïïïïïï( cos )θ ïïï
(9)
wherein
θ
σ σ
σ σ σ
=
-
- -
arctan
( )3
2
2 3
1 2 3
(10)
Substituting (10) into (8), equation (8) can
be written as
p L q p L q3
2
2
3
3 0- + = (11)
wherein L and L2 3 and L2 are as follows:
L
c c c
c c
2
3 2
2
3 1 9
3 1
=
-( ) + - -é
ëê
ù
ûú
-
- -
sin ( sin )( sin )
( sin sin
ϕ µ ϕ ϕ
µ ϕ ϕ ++
ì
í
ïïï
î
ïïï
ü
ý
ïïï
þ
ïïï
-( ) + - -
sin )
sin ( sin )( sin
3
3 23 3 1 9
ϕ
ϕ µ ϕ ϕ
c
c c c))
( )( sin sin sin )
é
ëê
ù
ûú
-
+ - - +é
ëê
ù
ûú
ì
í
ïïïï
î
ïïïï
ü
ý
27 3 1 2 3µ ϕ ϕ ϕc c c
ïïïïï
þ
ïïïï
=
-( ) + - -é
ëê
ù
ûúL
c c c
3
3 22 3 1 9 3sin ( sin )( sin ) cos( )ϕ µ ϕ ϕ θ
227 3 1 9
729 243 1
3 2-( ) + - -é
ëê
ù
ûú
-
+ -
sin ( sin )( sin )
( )( sin
ϕ µ ϕ ϕ
µ ϕ
c c c
cc c c- +
ì
í
ïïï
î
ïïï
ü
ý
ïïï
þ
ïïï
ü
ý
ïïïïïïïïïïïïïïïïï
þ
ïïï
sin sin )2 3ϕ ϕ
ïïïïïïïïïïïïïïï
(12)
It should be noted that L2 and L3 are only
used to denote complex expressions, and they
have no physical meanings.
Derived from mathematical calibration, the
shaping function of the criterion can be defined
as [10,11]
g
L
L
( )
cos arccos
cos
/
q =
-
é
ë
ê
ê
ê
ù
û
ú
ú
ú
ì
í
ïïï
î
ïïï
ü
ý
ïïï
þ
ïïï
1
3
3 3
2
3
2
3 2
11
3
3 3 3
2
3
2
3 2
arccos
cos
/
-
é
ë
ê
ê
ê
ù
û
ú
ú
ú
ì
í
ïïï
î
ïïï
ü
ý
ïïï
þ
ïïï
L
L
q
(13)
Bounding surface revised by the three-di-
mensional adaptive failure criterion can be ex-
pressed as
Fig. 1. Comparison of prediction (solid lines) and experimental data (symbols) for undrained stress paths
and stress-strain curves of triaxial compression and extension tests on Bothkennar clay following the K0
state at point A. (a) Comparison of stress-strain curves;(b) Comparison of stress paths.
Functional materials, 25, 1 2018 141
Cui Yunliang et al. / Three-dimensional generalization ...
F p p p
q
M gc= - +2
2
2 2
*
* ( )q
(14)
where p S pc i c
* = and M S Mf
* = . Si is an iso-
tropic destructuraion factor and Sf is a fric-
tional destructuraion factor.
Solving the partial derivatives of Eq. (15)
with respect to p , q and q , respectively, it
comes that
¶
¶
= -
F
p
p S pi c2 (15)
¶
¶
=
F
q
q
S g Mf
2
2 2 2( )q
(16)
¶
¶
=
- ¢F q g
S M gfq
q
q
2 2
2 2 3
( )
( )
(17)
In Eq. (17), ¢g ( )q is the derivative of g( )q
with respect to q .
Work [9] has already presented the expres-
sion of plastic modulus at the bounding surface
Kp . To generalize the expression of Kp into
three-dimensional stress space, it can be re-
vised by multiplying M by g( )q in the expres-
sion of Kp in work [9]. M is the critical state
stress ratio which is determined by the slope of
the critical state line. Thus Kp can be written
as,
K S p
e p F
p
p p
S F
p
p i
c
c
i
mi
=
+( )
-
¶
¶
-
-
-( )
-
( ) ¶
¶
æ
è
çççç
ö
ø
÷÷÷÷
1
1
0
λ κ
λ κ
β1-
22 2
+
¶
¶
æ
è
çççç
ö
ø
÷÷÷÷
-β
F
q
(18)
-
-( )
-
-
¶
¶
æ
è
çççç
ö
ø
÷÷÷÷
+
¶
¶
æ
è
ççç
2 1
1
2
2 2 3
2
q
g M S
S F
p
F
qf
f
mf
( )
( )
q l k
b b
çç
ö
ø
÷÷÷÷
2
where [9]
S
S
i
i
m
d
p
i
= -
-
-
( )1
l k
e (19)
S
S
f
i
m
d
p
f
= -
-
-
( )1
l k
e (20)
ε β ε βεd
p
v
p
q
p= - +( )1 2 2 (21)
In eq. (18)-(21), λ and κ are the slopes of
the compression line and the swelling line in
a volumetric strain-logarithmic mean stress
plane, respectively. mi and mf are material
constants which are determined by fitting the
stress-strain curve of triaxial compression. εv
p
is volumetric plastic strain rate and εq
p is de-
viatoric plastic strain rate. β is a material con-
stant distributing the effect of volumetric and
deviatoric plastic strain rates to the value of εd
p
. β could be set to 0.5 as a default value. Si Sf
The initial values of Si and Sf are needed in
calculating with the proposed model. The initial
isotropic destructuraion parameter Si0 is deter-
mined by one-dimensional compression test
and initial frictional destructuraion parameter
Sf0 is determined by triaxial compression test.
e0 is the initial void ratio.
The plastic modulus at the current stress
point, that is pK , can be derived by substitut-
ing Eq. (18) into Eq. (6).
3. Model verification
Natural soft clays are mainly in the state of
K0 state which is an anisotropic state. To keep
the proposed model simple, the anisotropy fea-
ture of natural soft clay is neglected. However,
this model is believed to be able to well capture
the behaviors of natural anisotropic clay when
structure is the main feature of the clay. In or-
der to prove this statement and show the unim-
portance of neglecting anisotropy, the proposed
model is used to simulate the undrained triaxial
compression and extension tests on intact sam-
ples of Bothnennar clay following the in-situ
K0 state. The mechanical response and stress-
strain relationship of Bothkennar clay have
been studied by Smith et al. [12] and Taiebat
et al. [8], respectively. The samples were tak-
en with Laval and Sherbrooke samplers from
depths of 5.3-6.2 m and only the experimen-
tal data of Laval samples is used in this work.
The samples were reconsolidated to in-situ K0
state before shear test. The K0 state stresses
are σ1 46= kPa , σ σ2 3 28= = kPa . Then, the
initial mean effective stress p kPain = 34 .
Fig. 2. Stress paths and failure points of true
axial tests of Pisa soft clay
142 Functional materials, 25, 1, 2018
Cui Yunliang et al. / Three-dimensional generalization ...
The stress-strain data of the undrained tri-
axial compression and extension tests on intact
samples of Bothnennar clay following the in-
situ K0 state is shown in Figure 1 by discrete
points. To simulate the experiments, the pro-
posed constitutive model proposed in this work
is coded in FORTRAN. The parameters for the
proposed model are obtained according to the
study of Smith et al. [12] and Taiebat et al.
[8] and shown in Table 1. The lines in Figure
1 show the stress-strain curve obtained by the
simulation.
In Figure 1, pin is the initial mean effective
stress which equal to 34 kPa, ε1 is the axial
strain in compression or extension test. It can
be seen in Figure 1 that the simulation stress-
strain curves of the triaxial compression and
extension tests both show good match to the ex-
perimental data. Thus, The proposed model is
accurate for simulating the destructuration of
natural clay. From a practical point of view, it
is acceptable to neglect the anisotropy feature
in the proposed model for natural soft clay to
keep the model simple.
The samples of the true triaxial compression
tests performed by Callisto [2, 13] were sampled
under the Pisa tower. All of them were recon-
solidated to the in-situ stress state at point O of
Figure 2 (σ1 113 5= . kPa , σ σ2 3 75 5= = . kPa ).
From point O, drained compression tests were
performed along rectilinear stress paths with
different orientations in the stress space. Tests
are labeled with the prefix ‘T’, followed by a rel-
evant value of angle α . In Figure 2, the rect-
angular points are failure stress point normal-
ized in plane π . Choosing an appropriate value
for the adaptive parameter µ and fitting the
failure points with the three-dimensional adap-
tive failure criterion gives the optimized fitting
curve in Figure 2 with µ =1.5. Adaptive crite-
Table 1. Parameters of the model for Bothkennar clay
l k n M Si0
Sf0 mi mf b V y
0.255 0.03 0.2 1.4 6.0 1.3 1.0 1.0 0.5 15.0 0.8
Fig. 3. Comparisons of experimental and simulation curves of the relationships of LSP versus following
the T0, T60, T90 and T150 stress paths for Pisa clay.
Functional materials, 25, 1 2018 143
Cui Yunliang et al. / Three-dimensional generalization ...
rion in Figure 2 means the three-dimensional
adaptive failure criterion expressed by eq.(7).
It can be seen in Figure 2 that the adaptive cri-
terion can fit the failure points better compared
with the lade criterion, except of the failure
point of test T150. The inaccuracy in fitting the
failure point of test T150 is caused by the limit
of the adopted three-dimensional adaptive fail-
ure criterion that this criterion is isotropic but
natural soils are always anisotropic. It seems
that the anisotropy of soil should be considered
in later research.
To verify the proposed constitutive model
generalized by the three-dimensinal failure
criterion, the model is computed in FORTRAN
and used to simulate the true triaxial compres-
sion tests on natural Pisa clay. The optimized
values of the parametersmi , mf , ς and ψ are
obtained by adjusting the values to fit the ex-
perimental curve of test T0 with the proposed
model. The simulation of other tests takes the
same model parameters with test T0. The model
parameters are listed in Table 2. The compari-
sons of simulation (heavy line) and observa-
tion (thin line) of tests T0, T60, T90 and T150
are shown in Figure 3. LSP and εs denote the
lengths of stress path and the deviatoric strain
invariant, respectively. The expressions are
LSP = - + - + -( ) ( ) ( )σ σ σ σ σ σ1 2
2
1 3
2
2 3
2
and
ε ε ε ε ε ε εs = - + - + -2 3 1 2
2
1 3
2
2 3
2 1 2/ [( ) ( ) ( ) ] /
where ε1,2,3 are axial strains in true triaxial
compression respectively. It can be seen that
the simulation curves can well fit the experi-
mental curves. Therefore, the proposed model
is demonstrated to be able to well capture the
behaviors of natural soft clay under general
stress conditions.
4. Conclusions
The three dimensional adaptive failure
criterion incorporated in this model can cover
the Lade-Duncan criterion and the Matsuoka-
Nakai criterion as its special ones. It is a good
choice to use this failure criterion to generalize
the bounding surface model into three-dimen-
sional space.
The proposed model improved with the three
dimensional adaptive failure criterion can cap-
ture the three-dimensional behaviors of natural
clay, but neglect the anisotropy of natural soft
clay. However, it can be proved by simulations
of undrained compression and extension tests
of K0 consolidation state Bothkennar clay, that
it is not important to neglect anisotropy in this
model.
It can be verified by simulating the true tri-
axial tests of Pisa clay, that improved model
can simulate the three dimensional behaviors
of natural soft clay under true triaxial condi-
tions.
Acknowledgements
The support of National Natural Science
Foundation of China(Grant no. 51508507), Zhe-
jiang Provincial Natural Science Foundation of
China (Grant no. LQ16E080007), and Zhejiang
Provincial Transportation Bureau Scientific
Research Plan (Grant no. 2017004) are grate-
fully acknowledged.
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Table 2. Parameters of the model for Pisa clay
l k n M Si0
Sf0 mi mf b V y µ
0.110 0.024 0.2 0.983 3.0 1.4 0.9 0.9 0.5 12.0 1.1 1.5
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