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Anisotropic Viscous ISA (AVISA)

Two versions of the AVISA model1 are available. 

*Mechanical = AVISA-2022
lambda [-], kappa [-], e_{i0} [-], nu [-], alpha [-], M_c [-], f_{b0} [-], I_v [-]
R [-], m_R [-], beta_0 [-], chi_0 [-], chi_{max} [-], C_a [-] , d [-], F^ISA [-] 

*Mechanical = AVISA
lambda [-], kappa [-], e_{i0} [-], nu [-], alpha [-], M_c [-], f_{b0} [-], I_v [-]
R [-], m_R [-], beta_0 [-], chi_0 [-], chi_max [-], C_a [-] , d [-], F^ISA [-]
K^w [F/A]

AVISA 2022

The material parameters of the AVISA-2022 model with intergranular strain are given in the following.

  • \(\lambda\) [-] is the compression index. This parameter has no unit. Typical range: \(10^{-6}-1\).

  • \(\kappa\) [-] is the swelling index. This parameter has no unit. Typical range: \(10^{-7}-0.6\).

  • The void ratio \(e_{i0}\) [-] correspond to the maximum void ratio at pressure \(p\) = 1 F/A. This parameter has no unit. Typical range: \(0.5-5\).

  • \(\nu\) is the Poisson's ratio. This parameter has no unit. Typical range: \(0-0.5\).

  • \(\alpha\) is the anisotropy factor. This parameter has no unit. Typical range: \(0-5\).

  • \(M_c\) is the slope of the critical state line. This parameter has no unit. Typical range: \(0.5-2\).

  • \(f_{b0}\) is the loading surface factor. This parameter has no unit. Typical range: \(1-3\).

  • \(I_v\) is the viscosity index. This parameter has no unit. Typical range: \(0-2\).

  • \(m_R\) and \(m_T\) govern the increase of the stiffness due to changes of the direction of the strain path. This parameter has no unit and is only used if the IGS model is used (\(F^{ISA}=1\)). Typical range: \(1-7\).

  • \(R\) is the radius of intergranular strain. This parameter has no unit. Typical range: \(10^{-6}-10^{-2}\).

  • \(\beta_{h0}\) and \(\beta_{hmax}\) are the hardening parameter of the intergranular strain and describes the evolution of the intergranular strain tensor along a strain path. These parameters have no unit. Typical range: \(0-2\).

  • \(\chi_0\) and \(\chi_{max}\) are the minimum and maximum intergranular strain exponent. These parameters have no unit. Typical range: \(1-10\) for \(\chi_0\) and \(20 - 50\) for \(\chi_{max}\).

  • \(C^{acc}\) is the accumulation rate factor. This parameter has no unit. Typical range: \(0-0.2\).

  • \(d\) is the intergranular strain bounding surface radius. This parameter has no unit. Typical range: \(1-10\).

  • \(F^{ISA}\) is a switch that decides whether the ISA (\(F^{ISA}=1\)) model should be used or not \(F^{ISA}=0\).

State variables

In addition to the (effective) stress, the 2022 version of the AVISA constitutive model takes additional state variables. Performing simulations with this model requires the prescription of those. The following state variables are contained in the model:

  • Void ratio \(e\), void_ratio OR Over consolidation ratio \(\text{OCR}_0\), OCR.

    • The prescription of either the initial void ratio or the initial overconsolidation ratio is mandatory, if the initialization is omitted or wrong values are prescribed the simulation will abort. Only one of the two state variables should be given.

    • Void ratio: \(e\), void_ratio: In general, assuming isotropic conditions, the initial void ratio should be prescribed using the following expression: \(e_0 = e_{i0}- \lambda \cdot ln(\text{OCR}_0\cdot p_0)\). Therein, \(\text{OCR}_0\) is the initial overconsolidation ratio and \(p_0\) is the initial mean effective stress.

    • Over consolidation ratio \(\text{OCR}_0\), OCR. By prescribing a value larger or equal to one to the initial overconsolidation ratio, the initial void ratio is calculated internaly satisfying the prescribed \(OCR_0\) at the given stress state of the element. This is the recommended way of initializing the AVISA model.

    .

  • Intergranular strain anisotropy: \(R_{ij}\), int_strain11, int_strain22, int_strain33, int_strain12, int_strain23, int_strain13. Only in combination with the intergranular strain extension. Prescribing \(R_0\) is not mandatory, if omitted, \(R_{ij}\) is assumed. \(R_{ii} = R_0 / \sqrt{3}\) corresponds to an isotropically consolidated state.

  • Sedimentation vector: \(m_i\), sedimentation1, sedimentation2, sedimentation3. Prescribing \(m_i\) is mandatory. If not known, it is advised to initialize \(m_1=1\) (sedimentation1).

The state variables can be initialized in two different ways:

  • Using the *Initial conditions, type = state variables command in the input file, e.g.

    *Initial conditions, type = state variables
    element_set_name, void_ratio, <value>
    **
    element_set_name, int_strain11, <value>
    element_set_name, int_strain22, <value>
    element_set_name, int_strain33, <value>

  • Using the interface for user-defined initial state variables. In this approach, the vector holding the state variables is filled directly in a fortran user routine. The position of the state variables in the associated vector are as follows: statev(1) = \(e\), statev(3) = \(R_{11}\), statev(4) = \(R_{22}\), statev(5) = \(R_{33}\), statev(6) = \(R_{12}\), statev(7) = \(R_{23}\), statev(8) = \(R_{13}\), statev(16) = OCR, statev(17) = \(m_1\), statev(17) = \(m_2\), statev(17) = \(m_3\) (m being the sedimentation vector)

Additional output variables

The following additional output variables are available in the *Output command (see here):

  • Void ratio: void_ratio

  • Intergranular strain: int_strain11, int_strain22, int_strain33, int_strain12, int_strain23, int_strain13.

  • Over consolidation ratio: ocr.

  • Sedimentation vector: sedimentation1, sedimentation2, sedimentation3.

AVISA

The material parameters of the AVISA model with intergranular strain are given in the following.

  • \(\lambda\) [-] is the compression index. This parameter has no unit. Typical range: \(10^{-6}-1\).

  • \(\kappa\) [-] is the swelling index. This parameter has no unit. Typical range: \(10^{-7}-0.6\).

  • The void ratio \(e_{i0}\) [-] correspond to the maximum void ratio at pressure \(p\) = 1 F/A. This parameter has no unit. Typical range: \(0.5-5\).

  • \(\nu\) is the Poisson's ratio. This parameter has no unit. Typical range: \(0-0.5\).

  • \(\alpha\) is the anisotropy factor. This parameter has no unit. Typical range: \(0-5\).

  • \(M_c\) is the slope of the critical state line. This parameter has no unit. Typical range: \(0.5-2\).

  • \(f_{b0}\) is the loading surface factor. This parameter has no unit. Typical range: \(1-3\).

  • \(I_v\) is the viscosity index. This parameter has no unit. Typical range: \(0-2\).

  • \(m_R\) and \(m_T\) govern the increase of the stiffness due to changes of the direction of the strain path. This parameter has no unit and is only used if the IGS model is used (\(F^{ISA}=1\)). Typical range: \(1-7\).

  • \(R\) is the radius of intergranular strain. This parameter has no unit. Typical range: \(10^{-6}-10^{-2}\).

  • \(\beta_{h0}\) and \(\beta_{hmax}\) are the hardening parameter of the intergranular strain and describes the evolution of the intergranular strain tensor along a strain path. These parameters have no unit. Typical range: \(0-2\).

  • \(\chi_0\) and \(\chi_{max}\) are the minimum and maximum intergranular strain exponent. These parameters have no unit. Typical range: \(1-10\) for \(\chi_0\) and \(20 - 50\) for \(\chi_{max}\).

  • \(C^{acc}\) is the accumulation rate factor. This parameter has no unit. Typical range: \(0-0.2\).

  • \(d\) is the intergranular strain bounding surface radius. This parameter has no unit. Typical range: \(1-10\).

  • \(F^{ISA}\) is a switch that decides whether the ISA (\(F^{ISA}=1\)) model should be used or not \(F^{ISA}=0\).

  • \(\bar{K}^w\) is the bulk modulus of pore water for locally undrained simulations (and only for those). The parameter is not mandatory and zero per default.

State variables

In addition to the (effective) stress, the AVISA constitutive model takes additional state variables. Performing simulations with this model requires the prescription of those. The following state variables are contained in the model:

  • Void ratio: \(e\), void_ratio. The prescription of the void ratio is mandatory, if the initialization is omitted or wrong values are prescribed the simulation will abort. In general, the initial void ratio should be prescribed using the following expression: \(e_0 = e_{i0}- \lambda \cdot ln(\text{OCR}_0\cdot p_0)\). Therein, \(\text{OCR}_0\) is the initial overconsolidation ratio and \(p_0\) is the initial mean effective stress.

  • Intergranular strain anisotropy: \(R_{ij}\), int_strain11, int_strain22, int_strain33, int_strain12, int_strain23, int_strain13. Only in combination with the intergranular strain extension. Prescribing \(R_0\) is not mandatory, if omitted, \(R_{ij}\) is assumed. \(R_{ii} = R_0 / \sqrt{3}\) corresponds to an isotropically consolidated state.

The state variables can be initialized in two different ways:

  • Using the *Initial conditions, type = state variables command in the input file, e.g.

    *Initial conditions, type = state variables
    element_set_name, void_ratio, <value>
    **
    element_set_name, int_strain11, <value>
    element_set_name, int_strain22, <value>
    element_set_name, int_strain33, <value>

  • Using the interface for user-defined initial state variables. In this approach, the vector holding the state variables is filled directly in a fortran user routine. The position of the state variables in the associated vector are as follows: statev(1) = \(e\), statev(3) = \(R_{11}\), statev(4) = \(R_{22}\), statev(5) = \(R_{33}\), statev(6) = \(R_{12}\), statev(7) = \(R_{23}\), statev(8) = \(R_{13}\)

Additional output variables

The following additional output variables are available in the *Output command (see here):

  • Void ratio: void_ratio

  • Intergranular strain: int_strain11, int_strain22, int_strain33, int_strain12, int_strain23, int_strain13.

  • Over consolidation ratio: ocr.

  1. M Tafili and T Triantafyllidis. AVISA: Anisotropic Visco ISA model and its performance at cyclic loading. Acta Geotechnica, 15:2395–2413, 2020. ↩