NorSand

{

    "materials": [
        {
            "id" : 0,
            "type" : "NorSand2D",
            "density" : 2000,
            "poisson_ratio" : 0.17,
            "reference_pressure" : 1.0E+5,
            "friction_cs" : 27.0,
            "N" : 0.3,
            "lambda" : 0.3,
            "kappa" : 0.08,
            "gamma" : 1.0,
            "chi" : 3.5,
            "hardening_modulus": 200,
            "void_ratio_initial" : 0.38,
            "p_image_initial" : 3000000,
            "bond_model" : true,
            "p_cohesion_initial" : 1.2E+4,
            "p_dilation_initial" : 2.0E+4,
            "m_cohesion" : 10,
            "m_dilation" : 1,
            "m_modulus" : 100,
            "tolerance" : 1.0E-15    
        }
    ]

}

• "id" is the material ID corresponding to a subset (or all) of the generated material points.
• "type" is either "NorSand2D" or "NorSand3D".
• "density" is material density.
• "poisson_ratio" is the constant elastic parameter Poisson's ratio.
• "reference_pressure" is set at atmospheric pressure of 100 kPa.
• "friction_cs" is the critical state friction angle in degrees.
• "N" is the volumetric coupling (dilatancy) parameter.
• "lambda" is the virgin compression index.
• "kappa" is the swell/recompression index.
• "gamma" is the void ratio at the reference pressure.
• "chi" is the dilatancy coefficient.
• "hardening_modulus" is the hardening modulus.
• "void_ratio_initial" is the initial void ratio. Initial void ratio be replaced with porosity.
• "p_image_initial" is the initial mean stress image (i.e., the intersection between the yield surface and critical state line).
• "bond_model" flag is set true for the bonded behavior.
• "p_cohesion_initial" is the initial cohesive pressure enhancement.
• "p_dilation_initial" is the initial dilation pressure enhancement.
• "m_cohesion" is the cohesive degradation term.
• "m_dilation" is the dilative degradation term.
• "m_modulus" is bonded modulus effects of the cohesion and dilation.
• "tolerance" is an optional tolerance value for computations such as yield condition, set default as machine epsilon.

General NorSand information is provided in [1,2,3]. Details on the bonded NorSand model are provided in [4].

References

[1] Jefferies, M. G. (1993). Nor-Sand: a simle critical state model for sand. Géotechnique, 43(1), 91-103.

[2] Jefferies, M., Been K. (2016). "Soil liquefaction: a critical state approach." Second Edition. CRC Press.

[3] Jefferies, M., Shuttle, D. (2011). "On the operating critical friction ratio in general stress states." Géotechnique, 61(8), 709-713.

[4] Setiasabda, Ezra Y. (2020). “Material point method for large deformation modeling in geomechanics using isoparametric elements.” Ph.D. dissertation, Berkeley, CA: Univ. of California, Berkeley.