NTUA – SAND – A Bounding surface plasticity model

The NTUA-SAND Model (Andrianopoulos et al 2010a, b, 2011) is a bounding surface plasticity model with a vanished elastic region, developed to accurately simulate the rate – independent dynamic response of non-cohesive soils under small, medium and large cyclic strain amplitudes. This is achieved using a single set of values for the model constants irrespective of initial stress and density conditions, as well as loading directions. The model is equally efficient in simulating the monotonic response.

The model builds on the constitutive efforts of Manzari & Dafalias (1997) and Papadimitriou & Bouckovalas (2002) and adopts three open cone-type non-circular surfaces, with their apex at the origin of stress space. These surfaces, named critical state surface, bounding surface and dilatancy surface, correspond to the deviatoric stress ratios at critical state, peak strength and phase transformation, respectively. The aperture of these surfaces is explicitly related to the state parameter ψ (Been and Jefferies, 1985), thus allowing the incorporation of the Critical State Theory of Soil Mechanics. The non-linear soil response under small to medium cyclic strain amplitudes is governed by a Ramberg-Osgood type hysteretic formulation, aiming at accurately simulating the shear modulus degradation and the hysteretic damping increase with cyclic shear strain. Furthermore, an empirical index of the directional effect of fabric evolution scales the plastic modulus, aiming at accurately simulating the rates of excess pore pressure build-up and permanent strain accumulation leading to liquefaction or cyclic mobility. To ensure numerical stability, the UDM employs the modified-Euler integration scheme with automatic error control and sub-stepping (Sloan et al. 2001).

The NTUA-SAND Model subroutine is freely available here

Relevant references

  1. Andrianopoulos K. I., Papadimitriou A., Bouckovalas G. (2010), “Explicit integration of bounding surface model for the analysis of earthquake soil liquefaction”, International Journal for Numerical and Analytical Methods in Geomechanics, DOI: 10.1002/nag. 875
  2. Andrianopoulos K. I., Papadimitriou A. G., Bouckovalas G. D. (2010), “Bounding surface plasticity model for the seismic liquefaction analysis of geostructures”, Soil Dynamics and Earthquake Engineering, doi: 10.1016/j.soildyn.2010.04.001
  3. Andrianopoulos K. I., Papadimitriou and G. D. Bouckovalas. (2011), “Applications of the NTUA-SAND Model for the Seismic Liquefaction Analysis of Geostructures, in Continuum and Distinct Element Modeling in Geomechanics” — 2011 (Proceedings, 2nd International FLAC/DEM Symposium (Melbourne, February 2011). Keynote Lecture, Paper 13-01, pp. 709-718, D. Sainsbury et al., Eds. Minneapolis: Itasca International Inc.
  4. Been K., Jefferies M. G. (1985), “A state parameter for sands”, Geotechnique, 35 (2): 99-112
  5. Papadimitriou A. G., Bouckovalas G. D., Dafalias Y. F. (2001), “Plasticity model for sand under small and large cyclic strains”, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 127(11): 973-983
  6. Papadimitriou A. G., Bouckovalas G. D. (2002), “Plasticity model for sand under small and large cyclic strains: a multiaxial formulation”, Soil Dynamics and Earthquake Engineering, 22: 191-204
  7. Manzari M. T., Dafalias Y. F. (1997), “A critical state two-surface plasticity model for sands”, Geotechnique, 47(2): 255-272
  8. Sloan S. W., Abbo A. J., Sheng D. (2001), “Refined explicit integration of elastoplastic models with automatic error control”, Engineering Computations, 18(1/2): 121-154