Experimental studies show that initial fabric and its evolution under different stress paths highly influence soil behaviour. Even though different sample preparation methods create different inherent anisotropies and cause different material responses, the same initial fabric structure under different stress paths also results in different material behaviours. In this paper, a simple state-dependent, bounding surface-based elastoplastic constitutive model, that can simulate the anisotropic nature of sands including the effect of principal stress rotation, is described. The model is developed based on a semi-micromechanical concept within the multilaminate framework and, to include the inherent anisotropy of sand, a deviatoric fabric tensor describing the initial microstructure is introduced. In addition, a fabric evolution rule compatible with anisotropic critical state theory (ACST) is employed to describe the evolving fabric structure and induced anisotropy towards the critical state (CS). In contrast to the classical strain-driven formulation for fabric evolution, a micro-level evolution rule is proposed. This paper presents concise theoretical aspects of the multilaminate framework and the anisotropic elastoplastic constitutive formulation. The model's capability under drained and undrained monotonic loading conditions at different stress states, relative densities and principal stress orientations is demonstrated by simulating experimental data for Toyoura sand.

This paper describes an MPM formulation using linear quadrilateral elements suitable for soil-structure-interaction problems. The volumetric locking and stress-oscillations are mitigated using a reduced integration technique and the Gauss integration scheme, respectively. The formulation can be used with both structured and unstructured computational meshes. In addition, an improved calculation scheme is proposed to obtain accurate contact reaction forces, especially for contacts between non-porous structures and soils with high liquid pressures. The formulation is validated by simulating a wide range of applications such as a water dam break, 1D large-strain consolidation, and the bearing capacity of a strip footing. Finally, the installation of a cone penetrometer in a centrifuge is successfully simulated in soft soils and compared with the experimental data for the entire range of drainage conditions.

Cone penetration tests (CPTs) are widely used in geotechnical engineering for soil characterization and parameter determination. Throughout the years, experimental data have been used to determine correlations between CPT data and soil properties, such as stiffness or strength. Recent progress in advance numerical methods allows the simulation of the full CPT penetration by overcoming the limitations related to extreme deformations. The use of these numerical techniques provides new prospective to the soil characterization and determination of soil parameters, especially for the settings where limited (or no) experimental data is available and existing correlations are not accurate, or absent. This paper presents a numerical framework based on the Material Point Method (MPM) to simulate CPT in dry sand. First, it is proven that the calculation scheme is stable and accurate. Then, the model results are validated against chamber test data in terms of both cone resistance and displacement field during the penetration. Finally, some considerations about the formulation of the constitutive models of soils are presented, specifically oriented for CPT applications.

Within the standard material point method (MPM), the spatial errors are partially caused by the direct mapping of material-point data to the background grid. In order to reduce these errors, we introduced a novel technique that combines the least squares method with the Taylor basis functions, called the Taylor least squares (TLS), to reconstruct functions from scattered data while preserving their integrals. The TLS technique locally approximates quantities of interest such as stress and density, and when used with a suitable quadrature rule, it conserves the total mass and linear momentum after transferring the material-point information to the grid. The integration of the technique into MPM, dual domain MPM, and B-spline MPM significantly improves the results of these methods. For the considered examples, the TLS function reconstruction technique resembles the approximation properties of highly accurate spline reconstruction while preserving the physical properties of the standard algorithm.