Download ErosLab 2017-en

EROSLAB 2017
User’s Guide
by GeoInvention Studio
30 June 2017
User’s guide of ErosLab2017
E
INVENTION
2
E
INVENTION
User’s guide of ErosLab2017
Table of contents
1
Introduction to ErosLab.......................................................................................... 9
2
Installation and operating environment ................................................................ 10
3
Stress and strain .................................................................................................... 12
4
5
3.1
Stress analysis ................................................................................................................ 12
3.2
Strain analysis ................................................................................................................ 14
Introduction of test types ...................................................................................... 16
4.1
Oedometer test ............................................................................................................... 16
4.2
Triaxial test .................................................................................................................... 18
4.3
Simple shear test ............................................................................................................ 20
Constitutive models .............................................................................................. 22
5.1
Introduction to constitutive models ................................................................................ 22
5.2
Elastic constitutive relation ............................................................................................ 24
5.3
3D strength criterion ...................................................................................................... 28
5.4
Nonlinear Mohr-Coulomb model - NLMC .................................................................... 30
5.5
Modified Cam-Clay model - MCC ................................................................................ 32
5.6
Critical state based simple sand model - SIMSAND ..................................................... 34
5.7
Anisotropic structured clay model - ASCM ................................................................... 38
5.8
Anisotropic creep model for natural soft clays - ANICREEP ........................................ 41
5.9
User defined material ..................................................................................................... 43
6
Operating instructions .......................................................................................... 46
7
Examples .............................................................................................................. 50
7.1
Example of simulating an oedometer test ...................................................................... 50
7.2
Example of simulating a triaxial test .............................................................................. 57
7.3
Example of simulating a simple shear test ..................................................................... 64
Reference .................................................................................................................... 68
3
User’s guide of ErosLab2017
E
INVENTION
4
User’s guide of ErosLab2017
E
INVENTION
List of symbols
Symbol
Definition
a
Constant of fines content effect in silty sand (SIMSAND+fr)
a
Target inclination of yield surface related to volumetric strain (ASCM)
Ad
Constant of magnitude of stress-dilatancy (0.5~1.5)
b
Constant controlling the amount of grain breakage (SIMSAND+Br)
b
Target inclination of yield surface related to deviatoric plastic strain
Caei
Intrinsic secondary compression index (remoulded clay)
D
Stiffness matrix of material
E
Young's modulus
e, e0
Void ratio and initial void ratio
E0
Referential Young’s modulus (dimensionless)
ec0
Initial critical state void ratio (SIMSAND); Virgin initial critical state void ratio before
breakage
ecuf
Fractal initial critical state void ratio due to breakage
ed
General shear strain
Eh, Ev
Horizontal and vertical Young’s modulus
ehc,c0
Initial critical state void ratio of pure fine soils (fc=0%)
ehf,c0
Initial critical state void ratio of pure coarse soils (fc=100%)
emax
Maximum void ratio
Eu
Undrained Young's modulus
fth
Threshold fines content from coarse to fine grain skeleton (20~35%)
f
Fines content
G
Shear modulus
G0
Referencial shear modulus
5
User’s guide of ErosLab2017
E
INVENTION
Gvh
Shear modulus
I1, I2, I3
The first, second and third invariants of the stress tensor
I1', I2', I3'
The first, second and third invariants of the strain tensor
J1, J2, J3
The first, second and third invariants of the deviatoric stress tensor
J1', J2', J3'
The first, second and third invariants of the deviatoric strain tensor
K
Bulk modulus
K0
the coefficient of earth pressure at rest
kp
Plastic modulus related constant in SIMSAND; Plastic modulus related parameter in
ASCM
Kw
Bulk modulus of water
M
Constraint modulus in elasticity; Slope of critical state line in p'-q plane
m
Constant of fines content effect in sandy silt
Mc
Slope of critical state line in triaxial compression in p'-q plane
n
Porosity of soil; Elastic constant controlling nonlinear stiffness
nd
Phase transformation angle related constant (≈1)
np
Peak friction angle related constant (≈1)
p'
Mean effective stress
pat
Atmosphere pressure
pb0
Initial bonding adhesive stress
pc0
Initial size of yield surface; Initial size of yield surface of grain breakage
(SIMSAND+Br)
pexcess
Excess pore pressure
psteady
Steady pore pressure
q
Deviatoric stress
Rd
Ratio of mean diameter of sand to silt D50/d50
R
Stress relaxation coefficient
6
User’s guide of ErosLab2017
E
INVENTION
sij
Deviatoric stress tensor
ux, uy, uz
Displacements
k0
Initial inclination of yield surface

Rate-dependency coefficient
0
Initial bonding ratio
ij
Kronecker symbol
1, , 
Principle strains
 a,  r
Axial strain and radial strain
ij
Strain tensor
m
Mean strain
v
Volumetric strain
xy, yx, yz,
zy, zx, xz
Engineering shear strains

Friction angle

Swelling index of the isotropic compression test (in e-lnp’ plane)
i
Intrinsic swelling index (of remoulded soil, in e-lnp’ plane)

Lame constant in elasticity; Compression index (in e-lnp’ plane); Constant controlling
the nonlinearity of CSL in SIMSAND
'
Compression index under the plane of loge-logp′
i
Intrinsic compression index (of remoulded soil, in e-lnp’ plane)
u
Undrained Poisson's ratio
vh'
Horizontal Poisson’s ratio
vv'
Vertical Poisson’s ratio

Lode angle

Constant controlling the movement of CSL
7
User’s guide of ErosLab2017
E
INVENTION
a, r
Axial stress and radial stress
ij
Stress tensor
m (p)
mean stress
n, h
Vertical and horizontal stresses
p0
Preconsolidation pressure
w
Pore water pressure
x, y, z
Normal stresses
, , 
First, second and third principle stresses

Reference time (Oedometer test  = 24h) (ANICREEP)
xy, yx, yz,
zy, zx, xz
Shear stresses

Poisson's ratio

Absolute rotation rate of the yield surface
d
Rotation rate of the yield surface related to the deviatoric plastic strain

Constant controlling the nonlinearity of CSL (SIMSAND); Absolute rate of bond
degradation
b
Degradation rate of the inter-particle cohesive bonding
d
Constant controlling the deviatoric strain related bond degradation rate

Dilatancy angle
8
E
INVENTION
User’s guide of ErosLab2017
1
Introduction to ErosLab
ErosLab is a practical and simple software for simulating laboratory tests, which gathers three
common test types and five constitutive models. It can be used for all kinds of numerical simulations of
laboratory tests and it offers the comparison between simulations and experimental data, which is
helpful on selecting the best model with relevant parameters. ErosLab is one of GeoInvention’s latest
software.
GeoInvention Studio was created by Dr. Zhen-Yu YIN who is also in charge of all the
development. Dr Yin-Fu JIN is in charge of technical part. In the studio there are still some software
developers and senior researchers of geomechanics and geotechnics, making it rapid to response to
clients’ demand and help solving practical engineering problems. The studio aims to share latest
scientific achievements in geomechanics and geotechnics, to promote the application of these
achievements, and thus to realize the scientific innovation of geotechnics.
9
User’s guide of ErosLab2017
2
E
INVENTION
Installation and operating environment
The main program of ErosLab is an executable file, which can run directly in most Windows
Systems with minor request for operating environment. The results can be obtained directly by using
the ErosLab platform. Note that the system needs a version of Microsoft .NET Framework 4.0 or newer.
If the version of Microsoft .NET Framework is older than 4.0, the user can download the advanced
version from https://www.microsoft.com/en-hk/download/details.aspx?id=17851. To guarantee the
normal operation of ErosLab without installing the FORTRAN program, three FORTRAN environment
files “libifcoremd.dll”, “libmmd.dll” and “msvcr100.dll” are provided in the installation package. Note
that the current version needs the installation of “Intel Fortran” (it is recommended to install
Visual_studio_2010 and Intel.Visual.Fortran.Composer.XE.2011).
The MATLAB environment is needed for plotting the results. The version of MATLAB
environment adopted is ‘MCR_R2016b_win64_installer.exe’, which is free to download from the
official website and free for use. For convenience, this program named ‘Matlab_env.exe’ is already
provided in the installation package.
The start interface of the installation of MATLAB environment is shown in Figure 2-1. By
clicking ‘Next’ step, the program will automatically download required files and install. During the
installation, it is important to keep the network connected. The completed interface is shown in Figure
2-2.
Figure 2-1 Start interface of the MATLAB environment installation
10
User’s guide of ErosLab2017
E
INVENTION
Figure 2-2 Completed Interface of the MATLAB environment installation
11
E
INVENTION
User’s guide of ErosLab2017
3
Stress and strain
3.1 Stress analysis
Taking an infinitesimal cubic cell on an arbitrary point from a soil element and putting it in a
3-dimensional coordinate system with three mutually orthogonal axis, the stress state can be shown in
Figure 3-1. There are 3 normal stress components (x, y, z) and 6 shear stress components (xy, yx, yz,
zy, zx, xz) on the six faces of the cubic cell. In soil mechanics, the normal stress is positive for
compression while negative for extension. For the shear stress, on the face which is in accordance with
axial directions, it is positive when contrary to the positive axial direction, while negative in the other
direction. As shown in Figure 3-1, both normal and shear stresses are positive. The magnitude of these
9 stress components is not only related to stress state, but also to the direction of the coordinate axis,
which is called the stress tensor:
 x  xy  xz   xx  xy  xz   11  12  13 

 

 ij   yx  y  yz    yx  yy  yz    21  22  23 
           
 zx zy z   zx zy zz   31 32 33 
(3.1)
z
z
zx
xz
x
zy
yz
xy
y
yx
y
O
x
Figure 3-1 Schematic diagram for the stress state at a point
It can be derived from moment equilibrium that xy=yx, yz=zy and xz=zx. Therefore, the stress
state of a single element can be described by using 6 independent stress components. In constitutive
model programing, the stress tensor is usually expressed as
 ij   xx  yy  zz  xy  xz  yz 
T
(3.2)
12
E
INVENTION
User’s guide of ErosLab2017
If m (or p) is defined as the average normal stress or mean effective stress:
m 
1
 xx   yy   zz 
3
(3.3)
Then, the stress tensor can be transformed to:
 xx   m
 xy

 ij    yx
 yy   m
 
 zy
 zx
 xz
  m 0 0 

 yz   0  m 0
 zz   m  0 0  m 
(3.4)
The first tensor in the equation is called deviatoric stress tensor, while the second one is called spherical
stress tensor. Spherical stress tensor can be abbreviated to  m ij or p ij , where ij is the Kronecker
symbol ( when i  j,ij  1; when i  j,ij  0 ).
The deviatoric stress tensor can be expressed as:
 xx   m
 xy

sij   ij   m ij    yx
 yy   m
 
 zy
 zx
 xz
  sxx sxy sxz   s11 s12 s13 
 

 yz  =  s yx s yy s yz  =  s21 s22 s23 
 zz   m   szx szy szz   s31 s32 s33 
(3.5)
The first, second and third invariants of the stress tensor are:
I1   xx   yy   zz
I2 
 xx  xy

 yx  yy
 yy  yz
 zy  zz

 zz  zx
  xx yy   yy zz   zz xx   xy2   yz2   zx2
 xz  xx
(3.6)
 xx  xy  xz
I 3   yx  yy  yz   xx yy zz  2 xy yz zx   xx yz2   yy zx2   zz xy2
 zx  zy  zz
While the three invariants of the deviatoric stress tensor are:
 J1  sxx  s yy  szz  0

1
1 2

2
2
2
2
2
 J 2  sij s ji   sxx  s yy  szz  2 xy  2 xz  2 yz 
2
2

 J 3  sxx s yy szz  2 xy yz xz   xx yz2   yy xz2   zz xy2
(3.7)
It can be shown that the invariants of the deviatoric stress tensor J1, J2 and J3 are related to the
invariants of the stress tensor I1, I2 and I3 through the following relations:
13
E
INVENTION
User’s guide of ErosLab2017

 J1  0

1 2

 J 2   I1  3I 2 
3

1

3
 J 3  27  2 I1  9 I1 I 2  27 I 3 
(3.8)
where the deviatoric stress q can be calculated by using the second invariant of the deviatoric stress
tensor J2.
q  3J 2
(3.9)
In a triaxial test, the deviatoric stress q can be simplified to q=|a-r|, or q=a-r to distinguish the
compression or the extension conditions.
The Lode angle  can be calculated by using the invariants of deviatoric stress tensor as:
cos 3 
3 3 J3
3
2
J 22
(3.10)
For a conventional triaxial compression test with 2=3, b=0 and =0°; for a conventional triaxial
extension test with 2=1, b=1 and =60°; and when  2 = 1   3  2 , b=0.5 and =30°. Note that b is
the parameter of intermediate principal stress and defined as b   2   3  1   3  ).
3.2 Strain analysis
Under small deformation condition, the strain state at a point can be described by the strain tensor:

 x

1
 ij    yx
2

 1  zx
 2
1
 xy
2
y
1
 zy
2
1 
 xz
2  
 xy  xz  11 12 13 
xx



1

 yz   yx  yy  yz    21  22  23 

2
  zx  zy  zz   31  32  33 


z 

(3.11)
where  is engineering shear strain. The strain tensor can be divided into deviatoric strain tensor and
spherical strain tensor as follows,
14
E
INVENTION
User’s guide of ErosLab2017

 x   m

1
 ij    yx
2

 1  zx
 2
1
 xy
2
 y  m
1
 zy
2
1 
 xz
2  
0 0

m
1


 yz  0  m 0 

2
 0 0  m 
z  m 

(3.12)
where the mean strain  m is defined as  m   x   y   z  3 .
Similar to stress tensor, the invariants of strain tensor are:

 
 I1   x   y   z

2
2
2
  xy    yz    zx 
 
I












 2

 
 
x y
y z
z x

 2   2   2 

2
2

2
 I       2   xy   yz    zx      yz      zx      xy 







x y z
y 
z

 x 2

 3
 2 
 2  2   2 


 2 

(3.13)
The invariants of deviatoric strain tensor are:


 J1 '  ( xx   m )  ( yy   m )  ( zz   m )  0

2
2
2
  xy    yz    zx 

J
'

(



)(



)

(



)(



)

(



)(



)



 2

 
 
xx
m
yy
m
yy
m
zz
m
zz
m
xx
m
 (3.14)
 2   2   2 

2
2

2
 J '  (   )(   )(   )  2   xy   yz    zx      yz      zx      xy 




xx
m
yy
m
zz
m
y 
z 
 x 2 

 3
 2 
 2  2   2 


 2 

The general shear strain  d is defined as:
d 
2
(1   2 )2  ( 2   3 )2  ( 3  1 )2
3
(3.15)
For a triaxial test (  2   3 ), the general shear strain  d can be reduced to:
2
3
 d  (1   3 )
(3.16)
The volumetric strain  v is (under small deformation assumption):
v 
V
 (1  1 )(1   2 )(1   3 )  1  1   2   3
V
(3.17)
15
E
INVENTION
User’s guide of ErosLab2017
4
Introduction of test types
There are three test types available in the platform: Oedometer test, Triaxial test and Simple shear
test (more test types like biaxial test, true triaxial test and HCA test will be available in later advanced
versions), as shown in Figure 4-1. The schematic diagram picture of the selected test below will change
according to the user’s selection, in order to further clarify the test type.
Figure 4-1 Three test types available in ErosLab
In this section, the three test types with their loading path will be introduced. Then, the operation
for each test in the ErosLab platform will be also introduced.
4.1 Oedometer test
In the platform, the oedometer test is simulated as one-dimensional compression test, where the
lateral deformation is constrained to be zero and only the vertical deformation is allowed,
(  2   3  0 & 1  0 ), as shown in Figure 4-2. The lateral stress necessarily keeps changing during the
loading process because of the restriction of lateral deformation. Therefore, it is convenient that the test
can be controlled by pure strain loading (  2   3  0 & d1  0 ), or by strain and stress mixed loading
16
E
INVENTION
User’s guide of ErosLab2017
(  2   3  0 & d1  0 ).
v (v)
h = 0
Figure 4-2 Schematic diagram of an oedometer test
The interface of the Oedometer test in ErosLab is shown in Figure 4-3. Both stress-control and
strain-control are optional, and the specific loading values must be entered. For the selected control, the
values of loading and the duration time are needed for each loading stage. If the value of time is
negative, the loading process will be stopped.
For stress-control loading, the default loading is 25-50-100-200-400-50-400-800-1600 kPa and the
duration time for each loading process is 24 h. For the strain-control loading, the default loading is
0.05-0.1-0.15-0.145-0.2-0.3-0.35-0.4-0.45 and the duration time for each loading process is also 24 h.
The users can change the value of default loading and the duration time according to their requirements.
Note that the effect of duration time can be taken into account only when the time-dependent
constitutive model is selected, e.g. ANICREEP in this platform.
Figure 4-3 Loading condition of the oedometer test
17
E
INVENTION
User’s guide of ErosLab2017
4.2 Triaxial test
Only the consolidated drained and undrained triaxial tests are available in this version. For
conventional consolidated drained triaxial compression test, the soil sample is first consolidated to a
given confining pressure, then the axial load is increased up to the failure of the sample ( d a  d1  0
or d a  d1  0 ) while keeping the confining pressure constant ( d r  d 2  d 3  0 ). The slope of
this loading path in the p′-q plane is dq dp  3 , which is noted as the conventional triaxial
compression path (CTC). Another approach to conduct this test is reducing the axial load till the sample
reaches failure ( d a  d 3  0 或 d a  d 3  0 ) while keeping the confining pressure constant
( d r  d1  d 2  0 ). The slope of this loading path is dq dp  3 , which is the conventional
triaxial extension path. The above stress schematic diagrams are shown in Figure 4-4(a).
In conventional consolidated undrained triaxial compression test (Figure 4-4(b)), the increment of
total confining stress is kept constant ( d r  0 ). Thus, the slope of the loading path on the p-q plane is
still 3 ( dq dp  3 ). In p(p′)-q plane, the horizontal distance between the total stress path and the
effective stress path is excess water pore pressure. The excess water pore pressure is always positive for
the normal consolidated soil during the loading process, thus the effective stress path is to the left of the
total stress path in p′-q plane. Whilst for over-consolidated soil, the excess water pore pressure is
negative during the post loading process. Therefore, the effective stress path is to the right of the total
stress path. Under the conventional confining pressure, both the soil particle and the water are
considered to be incompressible, which makes it possible to fulfill the undrained condition by keeping
the volumetric strain constant ( d v  0  d a  2d r ). In this way, the compression or extension
depends on the increasing or decreasing of the axial strain. In this program, all undrained simulations
(except for the creep simulation using ANICREEP model) are performed by keeping the volumetric
strain constant.
a (a a)
a (a)
r =cst
(a)
r u = 0
(b)
r
u
r (r)
Figure 4-4 Schematic diagram of triaxial test for: (a) drained test, and (b) undrained test
The interface of the loading condition for triaxial tests is shown in Figure 4-5. The consolidation
process before the shear loading stage is optional. If the consolidation process is selected, the confining
18
User’s guide of ErosLab2017
E
INVENTION
pressures r and a should be filled in (r=22=33). If not, the confining pressures r and a would be
equal to initial stress state. The shear loading is divided into two types of control: (a) strain control and
(b) stress control. The triaxial test is simulated by choosing either mode or giving a proper load value.
Furthermore, if ANICREEP model is selected, the time effect will be controlled by ‘loading time’.
Besides, for convenience, a multistage setting is provided: select the button “Multistage” and click the
button “Settings” to complete the multistage simulation.
19
User’s guide of ErosLab2017
E
INVENTION
Figure 4-5 Interface of the loading condition for triaxial tests
Apart from the monotonic loading, the cyclic loading is also available for triaxial tests, as shown
in Figure 4-6. The user can set the number of cycles, loading mode and the amplitude of loading. Then,
the load is generated as a sinusoidal function for the calculations.
Figure 4-6 Settings of the cyclic loading for triaxial tests
4.3 Simple shear test
When the soil subjected to shear stress reaches the critical state, the soil will slide along a surface
which leads to the failure. In order to study such phenomena, a simple shear test (shown in Figure
4-7(a)) has been developed and used (equivalent to direct shear and ring shear in Figure 4-7(b-c)). In
this simple shear test, the shear strain (γ) is defined as the ratio of the horizontal displacement to the
sample height. Under the loading of vertical shear strain, the shear stress, vertical stress and vertical
displacement can be obtained from a simple shear test. There are two ways to conduct this simple shear
test: (1) keeping a constant vertical load, which is the drained simple shear test, and (2) keeping the
volume of the sample constant, which can be regarded as the undrained simple shear test.
20
E
INVENTION
User’s guide of ErosLab2017
n ,
n
n
,
n
,
(a) 单剪
(a)
(b) 直剪
(b)
(c) 环剪
(c)
Figure 4-7 Three typical shear tests: (a) simple shear test; (b) direct shear test; (c) ring shear test
In ErosLab, the simple shear test is controlled by σn and γ, as shown in Figure 4-8. The sample is
first K0-consolidated under a vertical stress σn, and then a tangential strain γ is applied at the bottom of
the sample after consolidation. In this version, the multistage loading is also available. It the input time
of a loading stage is less than zero, the loading will stop up to the previous stage.
Figure 4-8 Loading conditions of the simple shear test
21
E
INVENTION
User’s guide of ErosLab2017
5 Constitutive models
5.1 Introduction to constitutive models
In this software, we provide five different constitutive models (Figure 5-1): Non-Linear
Mohr-Coulomb model (NLMC), Modified Cam-Clay model (MCC), critical state based SIMple SAND
model (SIMSAND), Anisotropic Structured Clay Model (ASCM), and natural soft clay Anisotropic
Creep model (ANICREEP). Moreover, the platform also provides an open access for user defined
models (UMAT), which may be useful for users to develop and test their own models (note that the
micromechanics based model —MicroSoil— and unsaturated model —Unsat— will be open in next
version).
Figure 5-1 Five constitutive models available in current version of the software
Similar to the test type in the previous chapter, the user can select here one model. Then, the figure
representing the principle of the model will be displayed below the selection window. Then, the user
22
User’s guide of ErosLab2017
E
INVENTION
can click the “Parameters” button to give values to the parameters of the selected model (Figure 5-2).
Additional options included in some models can be set in the “Advanced” button, e.g. SIMSAND
model.
Figure 5-2 An example of selecting model and opening the window of parameters (e.g. SIMSAND model)
Before introducing all adopted constitutive models, we will first introduce briefly the elastic
23
E
INVENTION
User’s guide of ErosLab2017
stress-strain relationship and the three dimensional strength criterion, which are common for the
different models.
5.2 Elastic constitutive relation
（1）Isotropic elasticity
Due to the nonlinearity of the stress-strain behaviour of soils, the elastic constitutive relation is
normally expressed in incremental form using generalized Hooke’s law:
1

d ij  d kk  ij
E
E
(5.1)
E
E
d  ij 
d 
1
1   1  2  kk ij
(5.2)
d  ij 
or
d ij 
where two parameters are needed: Young’s modulus E and Poison’s ratio .
In order to calculate the stress-strain relationship, we need to define a stiffness matrix for the
material D. In most finite element codes, the engineering shear strain (  xy   xy   yx  ux y  u y x )
is used. Then, the elastic stiffness matrix with the stress-strain relationship in incremental form can be
expressed as follows:

0
0
0   d  xx 
 d xx 
1   
 d  
  1 
0
0
0   d  yy 
 yy 

 d zz 
 
 1
0
0
0   d  zz 
E





0
0
0.5  
0
0   d  xy 
 d xy  1  2 1     0
 d yz 
 0
0
0
0
0.5  
0   d  yz 





0
0
0
0
0.5     d  zx 
 0
 d zx 
(5.3)
which can also be written in the inverse way with an elastic flexibility matrix:
1
 d  xx 
 
d 

 yy 
 d  zz  1  

 
 d  xy  E  0
0
 d  yz 



 d  zx 
 0


0
0
1

0
0

1
0
0
0
0
2 1   
0
0
0
0
2 1   
0
0
0
0
  d xx 
0   d yy 


0   d zz 


0   d xy 
0   d yz 


2 1      d zx 
0
(5.4)
According to experimental observations, for clays we can directly adopt the swelling index of the
isotropic compression test (=-e/lnp′) as the input parameter to calculate the Young’s modulus. Note
that the swelling index from the oedometer test is slightly different, but acceptable as the value of this
24
E
INVENTION
User’s guide of ErosLab2017
parameter.
K
1  e0

p, E  3K 1  2 
(5.5)
For sand, the shear modulus is usually adopted as the input parameter to calculate the Young’s
modulus. In the case that the isotropic compression curve is available, the bulk modulus can be directly
measured to be an input parameter:
G  G0  pat
 2.97  e 
1  e 
2
n
 p 

 , E  2G 1   
 pat 
(5.6)
where e is the void ratio, pat is the atmospheric pressure (pat = 101.325 kPa)，G0 is the reference shear
modulus, n is the parameters controlling the nonlinearity of the modulus with the applied mean
effective stress. In the case of the lack of measurement of shear modulus, it is suggested to use the bulk
modulus as input parameter from the isotropic compression test (which is easy to perform in
laboratory). Then a typical value of Poisson’s ratio = 0.25 can be adopted to complete the input
setting for elasticity.
Different elastic constants (E, G, K, , , M) are related to each other. If we know two of them, we
can calculate the others, as summarized in Table 5-1.
（2）Elasticity under undrained condition
Pore pressure includes steady pore pressure psteady and excess pore pressure pexcess:
 w  psteady  pexcess
(5.7)
Steady pore pressure is just generated data according to the depth of water. Thus, the differential
of steady pore pressure by time is zero. Then, we have:
 w  pexcess
(5.8)
It can then be obtained by Hooke’s law:
 xxe 
0
0
0   xx 
 1    
 e 
   1  
 
0
0
0   yy
 yy 


  zze  1      1
0
0
0   zz 
 e  
 
0
0 2  2 
0
0   xy 
 xy  E   0
 e 
 0
0
0
0
2  2 
0   yz 
 yze 

 
0
0
0
0
2  2   zx 
 0
 zx 
(5.9)
Substituting into Eq.(5.9) with the relationship between effective stress and total stress
25
E
INVENTION
User’s guide of ErosLab2017
(  ij   ij   w ij ), we get:
 xxe 
0
0
0   xx   w 
 1    
 e 
   1  
0
0
0   yy   w 
 yy 

  zze  1      1
0
0
0   zz   w 
 e  




0
0 2  2
0
0    xy 
 xy  E  0
 e 
 0
0
0
0
2  2 
0    yz 
 yze 



0
0
0
0
2  2    zx 
 0
 zx 
(5.10)
Considering slight compressibility of water, the pore pressure rate can be expressed as:
w 
Kw e
 xx   yye   zze 
n
(5.11)
where Kw is the bulk modulus of water, and n is the porosity of the soil.
Then, Hooke’s law can be expressed by using the total stress increment with the undrained
Young’s modulus Eu and the undrained Poisson’s ratio u:
K 
 xxe 
 1
 e 
 
 yy 
 u
  zze  1  u
 e 

 xy  Eu  0
 e 
 0
 yze 

 0
 zx 
1  e0

p, E   3K  1  2  
u
u
0
0
1
u
0
0
u
1
0
0
0
0
2  2u
0
0
0
0
2  2u
0
0
0
0
(5.12)
  xx 
0   yy 
0   zz 
 
0   xy 
0   yz 
 
2  2u   zx 
0
(5.13)
in which
Eu =2G 1  u  

    1    
1  2 1    
E
1 Kw
, K 
3 1  2  
3n K 
(5.14)
(5.15)
Thus, according to previous equations, the consideration of undrained behavior results in the
parameters of effective stress G and  replaced by the undrained constants Eu and u. Note that this
part is only used in the software when we use the ANICREEP model to simulate the undrained
creep test.
The u=0.5 represents the full incompressibility of water. However, this will result in the
singularity of the stiffness matrix. In fact, the water is slightly compressible with a very high value of
the bulk modulus ( Kw  nK  ). In order to avoid this computational problem, u=0.495 is adopted.
26
E
INVENTION
User’s guide of ErosLab2017
Then, for the undrained soil behavior, the bulk modulus of water is automatically added in the
stiffness matrix, expressed by:
3 u    
Kw
0.495   

K   300 
K   30 K 
n
1
1  2u 1   
(5.16)
For the undrained elastic constitutive law, more information can be found in the material manual
of PLAXIS [1].
Table 5-1 Summary of elastic constants
Shear
G
Young’s
E
G, E
G
E
G, M
G
G, K
G
G, 
G
G, 
G
2G 1   
E, K
3KE
9K  E
E
E, 
E
2 1   
E
3 K   
9K  K   
K, 
K, M
K, 
G  3M  4G 
3G  E
GE
9G  3E
M G
4
M G
3
9GK
3K  G
4
K G
3
K
G  3  2G 
 G
3K  
3 M  K 
9K  M  K 
4
3K  M
2 1   
G  4G  3
Bulk
K
M
2
3K 1  2 
Constraint
M
2 K 1  2 
  2G
2G 1   
1  2
K  9 K  3E 
9K  E
E 1   

2G
3
2G 1   
3 1  2 
K
Lame
Poisson’s


G  E  2G 
E  2G
2G
3G  E
M  2G
M  2G
2M  G
2G
3
3K  2G
2  3K  G 
K

2G
1  2
K  9 K  3E 
9K  E
E

2   G 

3K  E
6K
1   1  2 
E
3 1  2 
1   1  2 
3K  2
K

M
K
3K  M
2
3K / M  1
3K / M  1
K
3 K
1

3K 1   
1


3K  
27
E
INVENTION
User’s guide of ErosLab2017
（3）Cross-anisotropic elasticity
During the natural sedimentation, soil exhibits a significant cross-anisotropy in elastic stiffness,
friction angle and even critical state line. In this software, we consider the cross-anisotropic elasticity of
Graham and Housley[2] for users to choose, expressed by:
  11   1 / Ev
     / E
 22   vv v
 33   vv / Ev


 12   0
 23   0

 
 13   0
vv / Ev
vv / Ev
0
0
1 / Eh
vh / Eh
0
0
vh / Eh
1 / Eh
0
0
0
0
1 / 2Gvh
0
0
0
0
1     / E
0
0
0
0
vh

0 

0 

0 
0 

1 / 2Gvh 
0
h
  11 
  
 22 
 33 


 12 
 23 


 13 
(5.17)
where Eh  nEv , vh  nvv with Ev and Eh representing vertical and horizontal Young’s modulus;
vv and vh are vertical and horizontal Poisson’s ratio; Gvh is shear modulus. For a convenient
utilization, the modification of the elastic modulus increment was obtained based on the
stress-controlled isotropic compression test as follows,

2
 v  11   22   33  1  4vv  
n

2vv   p

n  Ev
(5.18)
According to K=p'/v, the vertical Young’s modulus Ev can be calculated by,
2 2   1  e0

Ev  1  4vv   vv 
p
n
n  

(5.19)
Then the shear modulus becomes
Gvh 

nEv
2 1  nvv

(5.20)
Thus, for cross-anisotropic elasticity, we need three input parameters Ev, ’vv and n. Comparing to
the isotropic elasticity, one extra parameter n is added for the cross-anisotropic elasticity. The K or 
can be obtained from the curve of isotropic compression test.
5.3 3D strength criterion
Two methods for modifying the strength in the stress space are introduced herein. This two
methods are widely adopted in the models under the macro-mechanics framework.
（1）Modification of the Lode angle
This method mainly works for some soil models which take the slope of the critical state line in
28
E
INVENTION
User’s guide of ErosLab2017
p′-q plane as the main parameter. This method modifies the yield strength of different Lode angles by
using M=Mcg(), namely g() method. E.g. the modification proposed by Sheng et al. [3] as follows:
1

4
2c 4
M  Mc 

4
4
1  c  1  c  sin 3 
(5.21)
where c=Me/Mc is the ratio of the critical state line in compression and extension conditions. For a
friction angle independent of the Lode angel, c  3  sin   3  sin   .
（2）Transformation of stress space method
Yao et al. [4-6] proposed a new method by transforming the strength failure plane in the principle
stress space to the circular conical surface using a transformed stress tensor Figure 5-3).
(a)
(b)
Figure 5-3 3D strength criterion： (a) g() modification；(b) transformation of stress space method
The equivalent relationship between the transformed stress tensor  ij and the Cauchy stress tensor
ij is:
 ij  p ij 
q
 ij  p ij 
q
(5.22)
The expression of strength has been obtained for two different typical strength criteria,
2 I1
q
3

 1
q  3 p 1 
 2
 I1I 2  I3   I1I 2  9I3   1
SMP criterion 

I3   1
I  
cos  cos 1   33   
3

p   3
p   



1




 Lade criterion 
(5.23)
(5.24)
29
E
INVENTION
User’s guide of ErosLab2017
To conveniently adopt the above two equations in the programming, we have modified them by
defining M  q p ,
6
M
3

 1
M  3 1 
 2
(5.25)
SMP criterion 
 I1I 2  I3   I1I 2  9I3   1

I3   1
I  
cos  cos 1   33   
3
p   3
p   



1




(5.26)
 Lade criterion 
In the current version of ErosLab platform, the Eq.(5.25) is adopted in the constitutive model to
modify the strength. Therefore, no extra parameter is needed as input.
5.4 Nonlinear Mohr-Coulomb model - NLMC
Nonlinear Mohr-Coulomb model was developed under the framework of Mohr-Coulomb,
implementing nonlinear elasticity, nonlinear plastic hardening, and a simplified three-dimensional
strength criterion (Jin et al., 2016a)[7]. The model is similar to the shearing part of the Hardening Soil
model (HS). The principle of the model is illustrated in Figure 5-4. The basic constitutive equations are
summarized in Table 5-2. Model parameters with their definitions are summarized in Table 5-3.
Table 5-2 Basic constitutive equations of NLMC
Components
Constitutive equations
 ije 
Elasticity
1

 ij   kk  ij
E
E
 2.97  e 
E  E0 pat
1  e 
f 
Yield surface
Potential surface
 p  pb 


 pat 
n
q
H 0
p  pb
g
q
g
 M pt 
and
 1 1 1 1 1 1
p '
p ' pb
sij
M pt =
6sin  pt
3  sin  pt
H
Hardening rule
2
with  pt   
M p  dp
k p   dp
with M p =
6sin 
3  sin 
 pb   pbb dp
30
E
INVENTION
User’s guide of ErosLab2017
Table 5-3 Model parameters and definitions of NLMC
Parameters
Definitions
e0
Initial void ratio

Poisson’s ratio
E0
Referential Young’s modulus (dimensionless)
n
Elastic constant controlling nonlinear stiffness

Friction angle
kp
Plastic modulus constant

Dilatancy angle
emax
Maximum void ratio (limit of dilation)
pb0
Initial bonding adhesive stress
b
Constant controlling the degradation rate of bonding
Figure 5-4 Principle of nonlinear Mohr-Coulomb model
Figure 5-5 Model parameters of NLMC in ErosLab
31
E
INVENTION
User’s guide of ErosLab2017
Note that, it is generally considered the coefficient of earth pressure at rest K0=1-sin. According
to this assumption, the Poisson’s ratio can be obtained as a function of the friction angle since there is
only elastic deformation in 1D compression:
 v  p K G 1  2 K 0  



 d  q 3G K 1  K 0  
Oedometer:

G 3 1  K 0  3
sin 

 
K
2
1

2
K
2
3


 2sin  
0

K 0  1  sin  


 v 3

 d 2
G
K  1  sin 

G  2  sin 

23  
K

(5.27)
3 2
(5.28)
This formulation provides a reference value of the Poisson’s ratio. In fact, for most soils =
0.2-0.3 is the suggested value to be used.
5.5 Modified Cam-Clay model - MCC
Modified Cam-Clay model was developed by researchers of the University of Cambridge
according to the mechanical behaviour of remoulded clay (Roscoe & Burland[8]), and is widely
adopted in geotechnical analysis. The principle of the model is illustrated in Figure 5-6. The basic
constitutive equations are summarized in Table 5-4. Model parameters with their definitions are
summarized in Table 5-5. Note that, to keep the original modified Cam-Clay model, the adopted
strength criterion is Von-Mises criterion.
Table 5-4 Basic constitutive equations of MCC
Components
Elasticity
Yield surface
Constitutive equations
 eij 
1

 sij 
 p ij
2G
3 1  e0 
f 
q2
 p2  ppc
M2
Potential surface
g f
Hardening rule
p
0
 pc  pc 
  v





 1 e 
32
E
INVENTION
User’s guide of ErosLab2017
Table 5-5 Model parameters and definitions of MCC
Parameters
Definitions
e0
Initial void ratio

Poisson’s ratio

Swelling index

Compression index
Mc
Slope of the critical state line in the p’-q plane
pc0
Initial size of the yield surface
q
M
f=g
pc
p’
Figure 5-6 Principle of Modified Cam-Clay model
Figure 5-7 Model parameters of MCC in ErosLab
Note that the Modified Cam-Clay model assumes a value for K0 according to its stress-dilatancy
(bigger than that of Jack):
33
E
INVENTION
User’s guide of ErosLab2017
 vp M 2   2

2
 dp


9  4M c2  3
9  9  4M c2
3 K 0

 K0 

  K 0 
2
3  2 K 0

3
2 9  4M c2
Oedometer: v  
 d 2 
(5.29)
Thus, when we use the Modified Cam-Clay model, the relationship between the preconsolidation
pressure from the oedometer test and the initial size of the yield surface can be established as follows:

q2
 p 
2

M p

 3 1  K 0 2
1  2 K0  

q  1  K 0   p 0

p



  p0

c0
2
3
 1  2 K 0  M


p   1  2 K 0   p 0 3



f K 0  0  pc 0 
(5.30)
Alternatively, p0 can also be an input parameter instead of pc0.
5.6 Critical state based simple sand model - SIMSAND
The critical state based simple sand model was developped based on the nonlinear Mohr-Coulomb
model through implementing the critical state concept, the cap mechanism (Jin et al., 2016a, 2016b) [7,
9]. The principle of the model is illustrated in Figure 5-8. The basic constitutive equations are
summarized in Table 5-6. Model parameters with their definitions are summarized in Table 5-7.
Table 5-6 Basic constitutive equations of SIMSAND
Components
Constitutive equations
 ije 
1

 ij 
 kk  ij
3K 1  2 
3K 1  2 
Elasticity
 2.97  e 
K  K 0 pat
1  e 
Yield surface in shear
fs 
Potential surface in shear
 p 


 pat 
n
q
H
p
g s

q  g s
 Ad  M pt   ;
 1 1 1 1 1 1
p
p  sij

H
Hardening rule for shear
Critical state line and
inter-locking effect
2
M p  dp
k p   dp
  p  
ec  ec 0 exp   
 
  pat  
n
p
e 
e 
tan  p   c  tan ； tan  pt   c 
e
e
 nd
tan 
34
E
INVENTION
User’s guide of ErosLab2017
Table 5-7 Parameters of SIMSAND
Parameters
Definitions
e0
Initial void ratio

Poisson’s ratio
K0
Referential bulk modulus (dimensionless)
n
Elastic constant controlling nonlinear stiffness

Friction angle
ec0
Initial critical state void ratio

Constant controlling the nonlinearity of CSL

Constant controlling the nonlinearity of CSL
Ad
Constant of magnitude of the stress-dilatancy (0.5~1.5)
kp
Plastic modulus related constant (0.01~0.0001)
np
Peak friction angle related constant (≈1)
nd
Phase transformation angle related constant (≈1)
Figure 5-8 Principle of SIMSAND
35
E
INVENTION
User’s guide of ErosLab2017
Figure 5-9 Parameters of SIMSAND in ErosLab
Based on the SINSAND model, the grain breakage effect has been further considered. The grain
breakage can result in the increase of the compressive plastic strain, the change of grain size
distribution and the transformation of the critical state line (Hu et al. [10] and Yin et al. [11]). The
related equations and corresponding parameters are defined in Table 5-8 and Table 5-9.
Table 5-8 Additional constitutive equations considering the grain breakage effect
Components
Constitutive equations
3
1 q 
fc  
 p  p  pc 0
2  M p p 
Yield surface in compression
gc  f c
Potential surface in compression
 pc  pc
Hardening rule in compression
Kinematics of CSL
 vp
n
2

2.97  e   p  




  1  e0  p  K0 pat
1  e   pat  

Br * 
Grain breakage related formula
1 e
      e
wp
b  wp

with wp =  p  vp  q dp

F (d )  1  Br*  F0  d   Br* Fu  d 
  p  

ec  ec 0 exp   
 
  pat  
ec0  ecuf   ec 0  ecuf  exp    Br* 
36
E
INVENTION
User’s guide of ErosLab2017
Table 5-9 Additional parameters related to grain breakage effect
Parameters
Definitions
'
Compression index under the plane of loge-logp’
pc0
Initial size of the yield surface of grain breakage
b
Constant controlling the amount of grain breakage

Constant controlling the movement of CSL
ec0
Virgin initial critical state void ratio before breakage
ecuf
Fractal initial critical state void ratio due to breakage
Figure 5-10 Additional parameters relating to grain breakage effect in ErosLab
Based on the SINSAND model, the fines content effect has been further considered. The fines
content effect can result in the change of the relative density, the change of the grain size distribution
and the transformation of the critical state line (Yin et al. 2014, 2016 [12, 13]). The related equations
and the corresponding parameters are defined in Table 5-10 and Table 5-11. Definitions of fines content
effect related parameters and calibration method are shown in Figure 5-11.
Note that the small strain stiffness and the inter-particle bonding will be available in the next
version.
37
E
INVENTION
User’s guide of ErosLab2017
Table 5-10 Additional constitutive equations considering the fines content effect
Components
Constitutive equations
  p  
ec  ec0 exp   
 
  pat  
Fines content effect
related CSL
ec0  ehc ,c 0 1  fc   af c 

1  tanh 20  fc  fth 
1  fc  1  tanh 20  f c  fth 

 ehf ,c 0  fc 
m

2
2
 Rd  

Definitions
ehc,c0
Initial critical state void ratio of pure fine soils (fc=0%)
ehf,c0
Initial critical state void ratio of pure coarse soils (fc=100%)
a
Constant of fines content effect in silty sand
m
Constant of fines content effect in sandy silt
Rd
Ratio of mean diameter of sand to silt D50/d50
fth
Threshold fines content from coarse to fine grain skeleton
f
Current fines content
0.8
0.6
a =0
a = -0.4
0.4
0.2
m = 0.55
 = 20
f th = 28%
a = -0.8
0.8
m = 0.2
0.6
m = 0.55
0.4
m = 0.8
0.2
Foundry sand
0
0
(a) Effect of a
0.6
0.8
0.6
f th = 28%
0.4
0.2
f th = 15%
f th = 40%
Foundry sand
0
0.3
a = -0.4
 = 20
f th = 28%
Minimun void ratio
Parameters
Minimun void ratio
Minimun void ratio
Table 5-11 Additional parameters related to fines content effect
0.9
1.2
0
Fines content, fc
(b) Effect of m
a = -0.4
m = 0.55
 = 20
Foundry sand
0
0.3
0.6
0.9
1.2
0
Fines content, fc
(d) Effect of f th
0.3
0.6
0.9
1.2
Fines content, fc
Figure 5-11 Definitions of fines content effect related parameters and calibration method
5.7 Anisotropic structured clay model - ASCM
Anisotropic structured clay model was developed under the framework of the Modified Cam-Clay
model and considering the behaviour of intact clays due to its structure (Yang et al.[14]). The model
can be used to predict the mechanical behaviour of soft structured clay, stiff clay and artificial
reinforced clay. The principle of the model is illustrated in Figure 5-12 Principle of ASCM. The basic
constitutive equations are summarized in Table 5-12. Model parameters with their definitions are
38
E
INVENTION
User’s guide of ErosLab2017
summarized in Table 5-13.
q
Initial surface
Mc
K0
 K0
p’
pc0
pci0
pb0
Disturbed surface
Me Initial intrinsic
yield surface
Figure 5-12 Principle of ASCM
Table 5-12 Basic equations of ASCM
Components
Constitutive equations
 ije 
E  3K (1  2 )
Elasticity
K
Yield surface
1

 ij   kk  ij
E
E
f 
1  e0
i
 p  pb0 (1  Rb )  ( pc0  pci0 )(1  Rc )
3  sij  ( p  pb ) ij  :  sij  ( p  pb ) ij 
+( p  pb )( p  pc )
2
 2 3

 M   ij :  ij 
2


g f
Potential surface
 pci  pci
pc 
Hardening rule
1  e0
 vp
i   i

pci
pc 0 1  Rc   pci Rc with Rc  1  exp c  ijp ijp
pci 0

pb  pb0 1  Rb  with Rb  1  exp  b dp 
 asij


ij   
 ij   vp  ij 0 1  R  d  dp  with R  1  exp    dp 
 p  pb


 ij   ij
Bounding surface rule
Kp  K p  kp
1  e0
1
3
  p   1  
 



39
E
INVENTION
User’s guide of ErosLab2017
Table 5-13 Parameters of ASCM
Parameters
Definitions
e0
Initial void ratio

Poisson’s ratio
i
Intrinsic swelling index (of remoulded soil)
i
Intrinsic compression index (of remoulded soil)
Mc
Slope of the critical state line in the p′-q plane
pc0
Initial size of the yield surface
k0
Initial inclination of the yield surface
a
Target inclination of the yield surface related to the volumetric strain
b
Target inclination of the yield surface related to the deviatoric plastic strain

Absolute rotation rate of the yield surface
d
Rotation rate of the yield surface related to the deviatoric plastic strain
kp
Plastic modulus related parameter in the bounding surface
0
Initial bonding ratio（pci0=pc0/(1+0)）

Degradation rate of the bonding ratio related to the plastic volumetric strain
d
Degradation rate of the bonding ratio related to the plastic deviatoric strain
pb0
Initial inter-particle bonding
b
Degradation rate of the inter-particle bonding
Figure 5-13 Parameters of ASCM in ErosLab
40
E
INVENTION
User’s guide of ErosLab2017
Note that the anisotropy related parameters are directly calculated by using the Mc:
a  0.75, b  0
 K 0  K 0 
d 
M c2  K2 0
3M c
with K 0 
3
6  Mc
3  a K 0   K 0 
2  b K 0   K 0 

(5.31)
(5.32)
3  M c 2   K2 0  3 1  a K 0 
  2
2  K 0  M c 2  3 1  b  K 0 
(5.33)
1  e0
10M c2  2 K 0d
ln
 i  i  M c2  2 K 0d
(5.34)
5.8 Anisotropic creep model for natural soft clays - ANICREEP
The anisotropic creep model for natural soft clays is developed under the framework of the
modified Cam-Clay model, the overstress theory and the different time-dependent behaviors of natural
soft clays (see Yin et al. [15, 16]). The ANICREEP can be applied to different soft clays, stiff clays and
artificial soils. Figure 5-14 and 5-15 shows the principles it's the interface of parameters. Table 5-14
shows the basic equations. The model parameters are shown in Table 5-15.
q
Mcc
Dynamic loading surface
σ’pi0
pi0
1
00σ’pi0
pi0
1
B
Reference surface

ii
1
Intrinsic surface
11
pmi
pmmrr
pmi
ln(σ’vv))
ln(σ’
Knc
nc-line
A
O
σ’p0
σ’
p0
pmmdd
p’
f dd
 ijij
Intact sample
sample
Intact
Reconstituted sample
sample
Reconstituted
(a)
1
Mee
(b)
(b)
e
Figure 5-14 Yield surface of ANICREEP:(a) p'- q; (b) 1D condition

41
E
INVENTION
User’s guide of ErosLab2017
Figure 5-15 Parameters of ANICREEP in ErosLab
Table 5-14 Basic equations of ANICREEP
Components
Constitutive equations
 ije 
Elasticity
1

 ij   kk  ij ，  ije   ije t
E
E
E  3 p(1  2 )
Reference yield surface
Potential surface
fr 
1  e0

r
r
r
r
3  sij  p  ij  :  sij  p   ij 
+pr  pcr (reference stresses)
2
 2 3
 r
 M   ij :  ij  p
2


fd 
3  sij  p ij  :  sij  p ij 
+p  pcd (current stresses)
2  2 3
 
 M   ij :  ij  p
2



Viscous plastic strain rate
 pmd  f d
，  ijvp   ijvp t
r 



p
ij
 m
 ijvp   
 pci  pci
Hardening rule
1  e0
 vp
i   i

pc  pci 1    with     vp  d  dp

 sij


 sij

 ij   vp  d  b  ij   dp 
 p


 p

ij    a
42
E
INVENTION
User’s guide of ErosLab2017
Table 5-15 Parameters of ANICREEP
Parameters
Definitions
e0
Initial void ratio

Poisson’s ratio

Swelling index
i
Intrinsic compression index (of remoulded soil)
Mc
Slope of the critical state line in the p′-q plane
p0
Initial reference preconsolidation pressure
Cei
Intrinsic secondary compression index (remoulded clay)

Reference time (Oedometer test  = 24h)
k0
Initial inclination of the yield surface

Absolute rotation rate of the yield surface
d
Rotation rate of the yield surface related to the deviatoric plastic strain
0
Initial bonding ratio (0≈St-1)

Absolute rate of the bond degradation
d
Relative rate of the bond degradation
Note that the involved anisotropy related parameters are directly calculated using the slope of the
critical state line Mc. The detailed information can be found in Yin et al. [15, 16].
Two parameters andd controlling the degradation rate of the bond can be calculated by
combining the isotropic compression test and the oedometer test:

    d
 1  e0 
evp*
2    
M
2
 2 




 v
1 
ln 

 *
 evp*  *  0* 
  0 exp 

  pi 0

 i   





 f
 1  e0  
1

ln


0 
evp
 evp 
  0 exp 

  vi 0


 i   
(5.35)
(5.36)
5.9 User defined material
In order to enrich the database of constitutive models, and to make ir easier for users to write their
own model, the ErosLab platform provides an interface module of user defined material. The interface
43
E
INVENTION
User’s guide of ErosLab2017
module is written in FORTRAN language. A .dll file is compiled by adopting the Intel Fortran 32 bit in
Visual studio as the compiler tool. After finishing the compilation, the .dll file should be renamed to
“Umat.dll” and should be put into the same directory with the main program of ErosLab. Then, the user
defined material can be found in the platform and the user can use the UMAT to simulate different
types of tests. The interface of UMAT is as follows:
Figure 5-15 Interface of the user defined material
where the name of the subroutine must be “Umat” (changing this name will produce errors). IDtask is
task number. IDtask=1, is the initialization of the state variables; IDtask=2, calculates the elastic matrix;
44
User’s guide of ErosLab2017
E
INVENTION
IDtask=3, updates the stress and state variables. cm is a vector with the material parameters; deps is the
strain increment; sig is stress; hsv are the state variables; CC is the elastic matrix tensor.
“!DEC$ ATTRIBUTES DLLEXPORT, DECORATE, ALIAS:"Umat" :: Umat”, is the statement
of the subroutine name. Other parameters and state variables are defined by the user. The total number
of parameters in the platform is 20, as shown in Figure 5-16.
Figure 5-16 Parameters of the user defined material
45
E
INVENTION
User’s guide of ErosLab2017
6
Operating instructions
When using the ErosLab platform, it is recommended to operate in the following sequence:
a)
Choose a test type and set the initial stress state
First, a test type is chosen and the initial stress state is set (the default value is set as σ1=σ2=σ3=1
kPa, σ4=σ5=σ6=0 kPa ), as shown in Figure 6-1. If the user wants to skip the consolidation stage, the
initial stress state corresponding to the stress after consolidation should be filled. If the “Oedometer test”
is selected, the selected box “Drainage condition” can’t be used, and the drained condition is preset.
Furthermore, the “suction” option is only available for the triaxial test and only for unsaturated soil
model in the next advanced version.
Figure 6-1 Selecting test type and set the initial stress state
46
E
INVENTION
User’s guide of ErosLab2017
b)
Choose the constitutive model and set its parameters
Once the test type has been selected, the constitutive model can be selected. Then, the model
parameters should be set.
Figure 6-2 Selection of the constitutive model and parameters setup
c)
Choose drainage condition
A proper drainage condition needs to be selected for most test types, as shown in Figure 6-3.
Figure 6-3 Choosing drainage condition
d)
Select loading condition
Either monotonic or cyclic (only for triaxial test and simple shear test) loading should be chosen,
as shown in Figure 6-4. The details have been introduced in previous sections.
Figure 6-4 Selecting the loading condition
47
E
INVENTION
User’s guide of ErosLab2017
e)
Run the simulation by clicking the ‘Run’ button
Figure 6-5 Run command in the platform
f)
(optional) Import experimental data, export simulated results and generate simulation
report
Figure 6-6 Data management module
As shown in Figure 6-6, in order to compare the simulated results with the experimental data, an
interface of importing data is provided by ErosLab. By clicking the ‘Import’ button, a window like
Figure 6-7 comes out to import data from an Excel file (.xlsx), and the specific sheet can be assigned.
In the data import window, clicking the ‘Import’ button makes the data plot in a figure. Figure 6-8
shows the format of the data required in the Excel file.
Figure 6-7 Data import window
48
E
INVENTION
User’s guide of ErosLab2017
Figure 6-8 Data input format (undrained test)
Furthermore, by clicking the ‘Export’ button, the simulated results in detail will be exported to an
Excel file (.xlsx). And by clicking the “Generate report”, a brief report written in a Microsoft Word file
with the test settings and the simulated results can be generated.
49
E
INVENTION
User’s guide of ErosLab2017
7
Examples
7.1 Example of simulating an oedometer test
(1) SIMSAND model
To simulate an oedometer test, it should be first selected the test type, and then set the initial stress
state. The default value of the initial stress is used in this example, as shown in Figure 7-2. Then the
selected soil model is ‘SIMSAND’, and the default parameters are also used, as shown in Figure 7-3. In
terms of the loading condition, the monotonic loading with stress control is selected. The default load
for each stage is used and the detailed load settings are shown in Figure 7-4. Figure 7-1 shows the
interface after finishing all settings. By clicking ‘Run’, the simulation starts, and a progress bar will
show the calculation process. The simulated results are shown in Figure 7-5.
Figure 7-1 Oedometer test
50
E
INVENTION
User’s guide of ErosLab2017
Figure 7-2 Setting the initial stress state
Figure 7-3 Parameters of the SIMSAND model
51
User’s guide of ErosLab2017
E
INVENTION
Figure 7-4 Settings of the loading condition for the oedometer test
Figure 7-5 Simulated results of the oedometer test using the SIMSAND model
(2) ANICREEP model
52
E
INVENTION
User’s guide of ErosLab2017
In order to show the time effect, the same oedometer test is simulated by using the ANICREEP
model. The used parameters of ANICREEP are shown in Figure 7-6. The user can select stress control
or strain control. The real loading time is needed for each stage in the simulation, as shown in Figure
7-7. The simulated results of the oedometer test using the ANICREEEP model are shown in Figure 7-8.
We can also simulate a creep test or a stress relaxation test by changing slightly the loading
settings, as shown in Figure 7-9. The results of a 1D creep test can be obtained, as shown in Figure
7-10. Similarly, the settings for a stress relaxation test are shown in Figure 7-11. The results of a 1D
relaxation test are shown in Figure 7-12.
Figure 7-6 Parameter settings of ANICREEP
53
User’s guide of ErosLab2017
E
INVENTION
Figure 7-7 Settings of the loading condition for a oedometer test (ANICREEP)
Figure 7-8 Simulated results of a 1D oedometer test using the ANICREEP model
54
User’s guide of ErosLab2017
E
INVENTION
Figure 7-9 Settings of the loading condition for a 1D creep test (ANICREEP)
Figure 7-10 Simulated results of a 1D creep test using the ANICREEP model
55
User’s guide of ErosLab2017
E
INVENTION
Figure 7-11 Settings of loading condition for 1D relaxation test (ANICREEP)
Figure 7-12 Simulated results of 1D relaxation test using ANICREEP model
56
E
INVENTION
User’s guide of ErosLab2017
7.2 Example of simulating a triaxial test
(1) SIMSAND model
To simulate a triaxial test, the test type ‘triaxial test’ is first selected. Similar to the oedometer test,
the initial stress state also keeps the default value in this example, as shown in Figure 7-2. The adopted
soil model is SIMSAND, and the default values for the parameters are used, as shown in Figure 7-3.
The drained condition is first examined and then followed by undrained condition. The loading way is
monotonic. The consolidation stage with 100 kPa confining stress is selected. The axial load is applied
by displacement. All settings are shown in Figure 7-13. Figure 7-14 shows the simulated results for
both drained and undrained tests, respectively.
Figure 7-13 Loading condition of triaxial test
57
E
INVENTION
User’s guide of ErosLab2017
(a)
Simulated results of a drained triaxial test
(b) Simulated results of an undrained triaxial test
Figure 7-14 Simulated results of triaxial tests (a) drained test; (b) undrained test
58
User’s guide of ErosLab2017
E
INVENTION
(2) ANICREEP model
Taking the undrained test as example, replacing the SIMSAND model by the ANICREEP model,
and giving three different loading times 1, 10 and 100 h, the settings are shown in Figure 7-15. Three
compression tests are first conducted and then followed by three extension tests. The simulated results
are shown in Figure 7-16.
Figure 7-15 Loading condition of triaxial test (ANICREEP)
59
User’s guide of ErosLab2017
E
INVENTION
Figure 7-16 Simulated results of undrained triaxial test using ANICREEP model
Similarly, selecting stress control, the undrained creep test can be successfully simulated. The
loading settings are shown in Figure 7-17. Three deviatoric stresses 5, 10 and 15 kPa are applied to
conduct the creep test. The results of the undrained creep tests are shown in Figure 7-18.
Note that the consolidation stage cannot be activated for simulating the undrained triaxial
creep test. The current stress can only be set in the “initial stress state”.
60
User’s guide of ErosLab2017
E
INVENTION
Figure 7-17 Loading settings for an undrained triaxial creep test
61
User’s guide of ErosLab2017
E
INVENTION
Figure 7-18 Simulated results of an undrained triaxial creep test using the ANICREEP model
Selecting the strain control and combining the relaxation, a drained triaxial relaxation test can be
successfully simulated. The loading settings are shown in Figure 7-19. The sample is first isotropically
consolidated to 100 kPa, and then time durations are given for different axial strain levels at 1, 3 and
5 %. The simulated results are shown in Figure 7-20. The stress relaxation under undrained condition
can also be simulated.
62
User’s guide of ErosLab2017
E
INVENTION
Figure 7-19 Loading settings for an undrained triaxial relaxation test
Figure 7-20 Simulated results of a drained triaxial creep test using the ANICREEP model
63
E
INVENTION
User’s guide of ErosLab2017
7.3 Example of simulating a simple shear test
(1) SIMSAND model
In the test type, the “simple shear test” is selected. The soil model and its parameters are the same
to those used in the simulation of the oedometer test and the triaxial test. Then, the “Monotonic”
loading is selected. The vertical stress σn is set to100 kPa with a default loading time. And the final
shear strain γ is set to 0.2 with five loading stages as shown in Figure 7-21. For each stage, the loading
time is set to 1 h. If the time-dependent soil model is used, the loading time should be set to the real
loading time. After clicking the “Run” button, the simulated results of both drained and undrained
simple shear tests are shown in Figure 7-22.
Figure 7-21 load condition of simple shear test
64
User’s guide of ErosLab2017
E
INVENTION
(a) Simulated results of drained simple shear test
(b) Simulated results of an undrained simple shear test
Figure 7-22 Simulated results of a simple shear test (a) drained; (b) undrained
65
User’s guide of ErosLab2017
E
INVENTION
(2) ANICREEP model
Similarly, select the ANICREEP model and modify the loading time, then the time effect of
ANICREEP model in a simple shear test can be achieved. The loading settings are shown in Figure
7-23. The simulated results of an undrained simple shear test by ANICREEP model are shown in
Figure 7-24.
Figure 7-23 Loading settings of simple shear test for ANICREEP model
66
User’s guide of ErosLab2017
E
INVENTION
Figure 7-24 Simulated results of an undrained simple shear test using the ANICREEP model
67
User’s guide of ErosLab2017
E
INVENTION
Reference
[1] Manual P, Plaxis Material Models and Plaxis Reference Manuals, The Netherlands, (2010).
[2] Graham J, Houlsby G, Anisotropic elasticity of a natural clay, Geotechnique, 33 (1983) 165-180.
[3] Sheng D, Sloan S, Yu H, Aspects of finite element implementation of critical state models, Comput
Mech 26 (2000) 185-196.
[4] Yao Y, Hou W, Zhou A, UH model: three-dimensional unified hardening model for
overconsolidated clays, Geotechnique, 59 (2009) 451-469.
[5] Yao Y, Lu D, Zhou A, Zou B, Generalized non-linear strength theory and transformed stress space,
Sci China Ser E: Technol Sci 47 (2004) 691-709.
[6] Yao YP, Sun DA, Application of Lade's criterion to Cam-Clay model, Journal of engineering
mechanics, 126 (2000) 112-119.
[7] Jin Y-F, Yin Z-Y, Shen S-L, Hicher P-Y, Selection of sand models and identification of parameters
using an enhanced genetic algorithm, Int J Numer Anal Methods Geomech 40 (2016) 1219-1240.
[8] Roscoe KH, Burland J, On the generalized stress-strain behaviour of wet clay, in: Engineering
Plasticity, Cambridge, UK: Cambridge University Press, 1968, pp. 535-609.
[9] Jin Y-F, Yin Z-Y, Shen S-L, Hicher P-Y, Investigation into MOGA for identifying parameters of a
critical-state-based sand model and parameters correlation by factor analysis, Acta Geotech 11
(2016) 1131-1145.
[10] Hu W, Yin ZY, Dano C, Hicher PY, A constitutive model for granular materials considering grain
breakage, Science China-Technological Sciences, 54 (2011) 2188-2196.
[11] Yin Z-Y, Hicher P-Y, Dano C, Jin Y-F, Modeling Mechanical Behavior of Very Coarse Granular
Materials, Journal of engineering mechanics, (2016) C4016006.
[12] Yin Z-Y, Zhao J, Hicher P-Y, A micromechanics-based model for sand-silt mixtures, Int J Solids
Struct 51 (2014) 1350-1363.
[13] Yin Z-Y, Huang H-W, Hicher P-Y, Elastoplastic modeling of sand–silt mixtures, Soils and
Foundations, 56 (2016) 520-532.
[14] Yang J, Yin Z-Y, Huang H-W, Jin Y-F, Zhang D-M, Bounding surface plasticity model for
structured clays using disturbed state concept-based hardening variables, Chinese Journal of
Geotechnical Engineering, 39 (2017) 554-561. (in Chinese)
[15] Yin ZY, Chang CS, Karstunen M, Hicher PY, An anisotropic elastic-viscoplastic model for soft
clays, Int J Solids Struct 47 (2010) 665-677.
[16] Yin ZY, Karstunen M, Chang CS, Koskinen M, Lojander M, Modeling Time-Dependent Behavior
of Soft Sensitive Clay, Journal of geotechnical and geoenvironmental engineering, 137 (2011)
1103-1113.
68
User’s guide of ErosLab2017
E
INVENTION
69
User’s guide of ErosLab2017
E
INVENTION
ErosLab is a practical and simple software for simulating laboratory tests, which gathers
three common test types and five constitutive models. It can be used for all kinds of
numerical simulations of laboratory tests and it offers the comparison between simulations
and experimental data, which is helpful on selecting the best model with relevant
parameters. ErosLab is one of GeoInvention’s latest software.
GeoInvention Studio was created by Dr. Zhen-Yu YIN who is also in charge of all the
development. Dr Yin-Fu JIN is in charge of technical part. In the studio there are still
some software developers and senior researchers of geomechanics and geotechnics,
making it rapid to response to clients’ demand and help solving practical engineering
problems. The studio aims to share latest scientific achievements in geomechanics and
geotechnics, to promote the application of these achievements, and thus to realize the
scientific innovation of geotechnics.
Contact us
QQ number:
3532256048
Email:
[email protected]
[email protected]
Wechat:
GeoInvention
Website:
www.geoinvention.com
70