Implicit integration of a chemo‐plastic constitutive model for partially saturated soils

Abstract

SUMMARYA chemo-plastic constitutive model for partially saturated soils is proposed in this paper based on the existing models developed in Hueckel (Int. J. Numer. Anal. Meth. Geomech. 1997; 21:43-72) and Gallipoli et al. (Geotechnique 2003; 53:123-135). The chemical softening effects due to the increase in contaminant mass concentration are considered based on Hueckel's chemo-plastic model. Gallipoli's model is used to simulate the effects of suction and degree of saturation on mechanical behavior of partially saturated porous materials. In order to implement the proposed model in a finite element code, a fully implicit backward-Euler integration algorithm is put forward. Numerical solutions for the tests at local level and the application of the algorithm to the real boundary value problem demonstrate the accuracy and convergence properties of the proposed integration scheme.

Review of fundamental principles in modelling unsaturated soil behaviour

“…In implicit schemes, all gradients and functions are estimated at advanced unknown stress states and the solution is achieved by iteration. This group of stress integration schemes include Vaunat et al [142], Borja [10], Hoyos and Arduino [46], Zhang and Zhou [153], and Tamagnini and De Gennaro [130]. They usually do not deal with the non-convex problem by avoiding the transition between saturated and unsaturated states.…”

A coupled two‐phase fluid flow and elastoplastic deformation model for unsaturated soils: theory, implementation, and application

“…A trial saturation S r,trial can be written as S r;trial ¼ S r;n þ ΔS r;n (43) As indicated by Hu et al [62], the updated soil hydraulic state {e n + Δe n , s t + Δs t , S e,trial } should be located in the zone bounded by the main drying surfaces S r,d and the main wetting surfaces S r,w . The main wetting/drying surfaces can be calculated by…”

“…An early and important contribution is the work of Simo and Taylor , who proposed a general return‐mapping algorithm, together with a general closest‐point projection method, for rate‐independent elastoplastic constitutive models. On this basis, various implicit integration methods were developed . Vaunat et al .…”

“…An early and important contribution is the work of Simo and Taylor [40], who proposed a general return-mapping algorithm, together with a general closest-point projection method, for rate-independent elastoplastic constitutive models. On this basis, various implicit integration methods were developed [41][42][43][44][45]. Vaunat et al [42] implemented the return-mapping method for the Barcelona Basic Model to analyze the hydromechanical behaviors of unsaturated soils.…”

Implicit integration under mixed controls of a breakage model for unsaturated crushable soils

“…A notable example is the study by Vaunat et al , who integrated the constitutive equations of the BBM through an implicit scheme able to cope with suction‐induced plastic strains. Similar schemes have been used in a number of other multiphysical contexts, especially in the presence of highly nonlinear models and non‐mechanical agents . The preference towards explicit or implicit algorithms depends on the balance between the advantages of a simple implementation typical of explicit schemes (which, however, must be combined with error control strategies), against the benefits of unconditional stability and faster convergence rates (often accompanied by the algebraic complexity typical of implicit implementations).…”