.. _SAniSandMS: SANISAND-MS Material ^^^^^^^^^^^^^^^^^^^^ **Code Developed by**: `Haoyuan Liu `_ (Norwegian Geotechnical Institute (NGI), formerly TUDelft), `José A. Abell `_ (UANDES, Chile), `Andrea Diambra `_ (University of Bristol), and `Federico Pisanò `_ (TU Delft). This command is used to construct a multi-dimensional SANISAND-MS (``SAniSandMS``) material, which is an extension of the Manzari-Dafalias (SAniSand) model with cyclic ratcheting control using the memory-surface (MS) concept. This allows capturing the ratcheting effects in sands that occur in high-cyclic loading in the presence of a static stress field or in the case of assymetric loading. .. figure:: SAniSandMS-fig0a.png :align: center :width: 400px :figclass: align-center .. admonition:: TCL command: nDMaterial SAniSandMS $matTag $G0 $nu $e_init $Mc $c $lambda_c $e0 $ksi $P_atm $m $h0 $ch $nb $A0 $nd $zeta $mu0 $beta $Den $fabric_flag $flow_flag $intScheme $TanType $JacoType $TolF $TolR Please report bugs as an issue on the main OpenSees repositoy and tag ``@jaabell`` Where, .. csv-table:: :header: "Argument", "Type", "Description" :widths: 10, 10, 40 $matTag, |integer|, unique tag identifying material $G0, |float|, dimensionless shear modulus constant $nu, |float|, Poisson ratio $e_init, |float|, initial void ratio $Mc, |float|, critical state stress ratio $c, |float|, ratio of critical state stress ratio in extension and compression $lambda_c, |float|, critical state line constant $e0, |float|, reference critical void ratio at p = 0 $ksi, |float|, critical state line constant $P_atm, |float|, atmospheric pressure $m, |float|, yield locus opening parameter (radius of yield surface in stress ratio space) $h0, |float|, hardening parameter $ch, |float|, hardening parameter $nb, |float|, bounding surface void ratio dependence parameter $nb ≥ 0 $A0, |float|, intrinsic dilatancy parameter $nd, |float|, dilatancy surface parameter $nd ≥ 0 $zeta , |float|, memory surface shrinkage parameter $mu0 , |float|, ratcheting parameter $beta , |float|, dilatancy memory parameter $Den, |float|, mass density of the material $fabric_flag , |integer|, (deprecated) $flow_flag , |integer|, (deprecated) $intScheme , |integer|, constitutive integration method (3: Runge-Kutta 4th order with error control (the only one currently implemented)) $TanType , |integer|, type of tangent stiffness to report (0: elastic stiffness | 1: continuum elastoplastic stiffness ) $JacoType , |integer|, placeholder (not used in explicit methods) $TolF , |float|, tolerance for yield surface intersection calculation (stress units) $TolE, |float|, (adimensional) relative error for explicit integrator The current implementation on SANISAND-MS uses fourth-order Runge-Kutta with error control for constitutive integration. The strain coming from a finite-element containing SANISAND-MS is applied incrementally by subdividing automatically to keep the constitutive integration error below the parameter ``$TolE``. The integration error :math:`e` is defined as: .. math:: e = \max\left\lbrace e_{\sigma},\, e_{\alpha} \right\rbrace \\ e_{\sigma} = \dfrac{\Vert \sigma^5 - \sigma^4 \Vert}{\Vert \sigma^4 \Vert} \\ e_{\alpha} = \dfrac{\Vert \alpha^5 - \alpha^4 \Vert}{\Vert \alpha^4 \Vert} And :math:`\sigma^p` is the stress prediction using a :math:`p`-th order integration formula, and likewise for the backstress :math:`\alpha^p`. Thus, in the code a 5-th order formula to approximate and bound the integration error, while integration advances using the fourth-order equation (RK45). .. figure:: SAniSandMS-fig0b.png :align: center :width: 640px :figclass: align-center The above equations differ from those in the main reference by Liu et al. (2019) in that the use of the yield back-stress ratio :math:`\alpha` is resumed here, as in Dafalias and Manzari (2004), to avoid certain numerical inconveniences. .. admonition:: Citation information If you use SANISAND-MS in your published research work, please cite the main reference ([SANISAND-MS]_) and also inform ``jaabell`` (*at* miuandes *dot* cl), to update the list of published articles and works that use the code. .. admonition:: Naming convention In text documents we use the spelling `SANISAND-MS`, but the OpenSees implementation uses ``SAniSandMS`` to accomodate coding conventions in OpenSees. .. admonition:: Available formulations The material formulations for the SAniSandMS object are "ThreeDimensional" and "PlaneStrain" .. admonition:: Recorder queries Valid Element recorder queries are: * ``stress`` returns stress tensor * ``strain``returns strain tensor * ``alpha`` for :math:`\mathbf{\alpha}`, the back-stress ratio tensor for the yield surface * ``alphaM`` for :math:`\mathbf{\alpha^M}`, the back-stress ratio tensor for the memory surface * ``alpha_in`` for :math:`\mathbf{\alpha_{in}}` * ``MM`` size of memory surface * ``estrain`` elastic strain tensor .. code:: tcl recorder Element -eleRange 1 $numElem -time -file stress.out stress #. Elastic or Elastoplastic response could be enforced by Elastic: updateMaterialStage -material $matTag -stage 0 Elastoplastic: updateMaterialStage -material $matTag -stage 1 .. admonition:: Example This example, provides an asymetric drained triaxial test of the constitutive model to show the effect of ratcheting. First the sample is compressed isotropically to 200KPa, then a cyclic deviator stress is applied. .. literalinclude:: SAniSandMS.tcl :language: tcl The script produces an output that can be visualized as follows. .. figure:: SAniSandMS-fig1.png :align: center :width: 600px :figclass: align-center .. figure:: SAniSandMS-fig2.png :align: center :width: 600px :figclass: align-center .. figure:: SAniSandMS-fig3.png :align: center :width: 600px :figclass: align-center **Main references** .. [SANISAND-MS] Liu, H. Y., Abell, J. A., Diambra, A., & Pisanò, F. (2019). `Modelling the cyclic ratcheting of sands through `_. Géotechnique, 69(9), 783-800. .. [PhDThesis] Liu, H.Y. (2020). `Constitutive modelling of cyclic sand behaviour for offshore foundations `_ (Doctoral dissertation, Delft University of Technology). **List of works using SANISAND-MS** .. [1] Liu, H. Y., & Pisano, F. (2019). `Prediction of oedometer terminal densities through a memory-enhanced cyclic model for sand `_. Géotechnique Letters, 9(2), 81-88. .. [2] Liu, H. Y., Kementzetzidis, E., Abell, J. A., & Pisanò, F. (2021). `From cyclic sand ratcheting to tilt accumulation of offshore monopiles: 3D FE modelling using SANISAND-MS `_. Géotechnique, 1-16. .. [3] Liu, H.Y., & Kaynia, A. M. (2021). `Characteristics of cyclic undrained model SANISAND-MSu and their effects on response of monopiles for offshore wind structures `_. Géotechnique, 1-39.