Modeling dynamic spherical cavity expansion in elasto-viscoplastic media

In this paper, we extend the dynamic spherical cavity expansion model for rate-independent materials developedin refs. [1, 2, 3] to viscoplastic media. For that purpose, we describe the material behavior with an isotropic Perzyna-type overstress formulation [4, 5] in which the material rate-dependence is controlled by the viscosity parameter\eta. The theoretical predictions of the cavity expansion model, which assumes that the cavity expands at constantvelocity, are compared with finite element simulations performed in ABAQUS/Explicit [6]. The agreement betweentheory and numerical simulations is excellent for the whole range of cavitation velocities investigated, and for different values of the parameter \eta. We show that, as opposed to the steady-state self-similar solutions obtained for rate-independent materials [1, 2, 3], the material viscosity leads to time-dependent cavitation fields and stress relaxation as the cavity enlarges. In addition, we also show that the material viscosity facilitates to model the shock waves that emerge at the highest cavitation velocities investigated, controlling the amplitude and the width of the shock front.

Undrained Cylindrical and Spherical Cavity Expansion in Elastic-Viscoplastic Soils

Various undrained cavity expansion solutions for elastic-plastic soil have been proposed previously. However, no solution has been presented for elastic-viscoplastic (EVP) soil until now. This paper presents a general solution method for solving the classical one-dimensional (1D) boundary value problem (BVP) for undrained cylindrical or spherical cavity expansion in EVP soil with an emphasis on the rate effect of soil. The solution method is summarized as three standard procedures: (a) obtaining the soil displacement and strain under incompressible conditions; (b) calculating the effective stress of soil through a suitable constitutive law; and (c) obtaining the pore pressure by numerically solving the stress equilibrium equation through the finite difference method (FDM) or other numerical solution techniques. The numerical algorithms for calculating the effective stress and pore pressure are very simple without any complex iteration processes, and they require little calculation time but provide high computational accuracy. In addition, some numerical results are given to investigate the influence of the cavity expansion velocity on the cavity expansion response. The proposed solution procedure is general and can be applied not only for the EVP model but also for other plasticity models, and the given EVP solution can be applied to interpret the rate effect of the CPT test and pile penetration.

Yield stress evaluation of Finnish clays based on analytical piezocone penetration test (CPTu) models

A well-established analytical model based on spherical cavity expansion and critical state soil mechanics theories is applied to piezocone soundings for profiling the yield stress and overconsolidation ratio of five soft sensitive test sites located in Finland. Yield stress is related to three piezocone parameters: net cone resistance, excess porewater pressure, and effective cone resistances. Input geoparameters include the effective stress friction angle, defined at both peak strength and at maximum obliquity, and the model directly provides the operational value of the undrained rigidity index. The piezocone-evaluated profiles compare favorably with results from laboratory constant-rate-of-strain consolidation tests for all the investigated sites. Based on the obtained experimental results, simplified correlations valid for Finnish soil conditions are derived. Their validity is assessed based on the bias factor, coefficient of variation, and coefficient of determination, showing a fairly good agreement between the predicted and the target values.