Enhancing the Bolzon–Schrefler–Zienkiewicz Constitutive Model for Partially Saturated Soil

Abstract

This paper presents an enhanced version of the elasto-plastic model for partially saturated soil first proposed by Bolzon, Schrefler and Zienkiewicz in 1996, "BSZ" model, which uses the effective stress tensor and suction as independent stress variables. It is recalled that the effective stress tensor proposed by Lewis and Schrefler in 1982 is thermodynamically consistent and, compared with other choices of stress tensors, results particularly suitable for partially saturated soil mechanics. A hydraulic constitutive relationship and a hydraulic hysteresis are introduced in the model, to take into account the irreversible deformation during cyclic drying and wetting until structural collapse. For this reason the plastic rate of strain is split into the sum of two components: one depending on the effective stress tensor and the other one on suction. This is the new feature of the BSZ model. This enhanced model is then cast into a thermodynamical framework at macroscopic level and it is shown that it is possible to derive the constitutive law from the Helmholtz free energy and a dissipation function, both for associative and nonassociative plasticity. Finally the model predictions have been compared with experimental data for Sion slime, with particular emphasis on the deviatoric part, and model predictions of hysteretic behaviour have been investigated in case of a wetting and drying cycle on compacted betonite-kaolin.

Hyperelastic Multiphase Porous Media with Strain-Dependent Retention Laws

“…Another application example is the successful simulation by Callari (2009a) of the typical response of partially saturated soft grounds to tunneling. Further elasto-plastic extensions could be based on yield criteria written also in terms of capillary pressures, in order to model eventual structural collapse of soils and hysteresis in the retention behavior (Bolzon et al 1996;Jommi 2000;Sheng et al 2004;Santagiuliana and Schrefler 2006). used to show the presence of second-order terms in products between current porosity and infinitesimal strain measures, that is, nε m = n 0εm + nε m = n 0εm + (1 − n 0 )(ε v − ε s )ε m n 0εm for m = v, s (72) Therefore, as a consequence of d v ε v ,ė s ε s and of (72), relation (69) readṡ…”

“…In recent years, there has been an increasing interest in the form proposed by Lewis and Schrefler (1982) for the effective stress equation by Bishop (1959). Examples can be found in Bolzon et al (1996), Sheng et al (2004), Tamagnini and Pastor (2005), Borja (2006), and Santagiuliana and Schrefler (2006). An alternative stress decomposition was obtained by Coussy (1995) using the thermodynamic framework by Biot.…”

“…An alternative stress decomposition was obtained by Coussy (1995) using the thermodynamic framework by Biot. We refer to Santagiuliana and Schrefler (2006) for a list of articles considering this latter effective stress equation.…”

A general framework for modeling long-term behavior of earth and concrete dams

“…It was further extended for partially saturated materials by Refs. [26,27]. The partial saturation conditions are described using Safai-Pinder's law [28].…”

Coupled solid‐fluid FE‐analysis of geotechnical problems involving partially saturated soils

“…Three basic features define the fundamental characteristics of the BBM: (i) the Modified Cam Clay Model [7] is used as reference constitutive law for the special case of p c = 0, (ii) the constitutive behavior is formulated in terms of net stress and capillary pressure, and (iii) the evolution of the preconsolidation pressure with increasing capillary pressure is explicitly defined and is denoted as loading collapse (LC) yield curve. One of the first models for partially saturated soils, formulated in terms of the generalized effective stress and capillary pressure, was proposed in [8] and enhanced in [9]. In recent years a number of constitutive models for partially saturated soils were proposed, which consider further features of unsaturated soil behavior, e.g., the irreversible volumetric behavior during wetting and drying cycles [10] or the swelling behavior of highly expansive soils [11].…”