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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 & d1 0 ), or by strain and stress mixed loading 16 E INVENTION User’s guide of ErosLab2017 ( 2 3 0 & d1 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 d1 0 or d a d1 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 d1 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 2u 0 0 0 0 2 2u 0 0 0 0 (5.12) xx 0 yy 0 zz 0 xy 0 yz 2 2u 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 2u 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 2M 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 nvv 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 4vv n 2vv 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 4vv vv p n n (5.19) Then the shear modulus becomes Gvh nEv 2 1 nvv (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 pbb 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 23 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 p2 ppc 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 ec0 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 ec0 exp pat Fines content effect related CSL ec0 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 0d ln i i M c2 2 K 0d (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 +pr 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 Cei 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 andd 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

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