Numerical integration of the Glasgow Coupled Model (GCM)

Abstract

This paper presents the derivation of the incremental constitutive relations of the Glasgow Coupled Model (GCM), an established elasto-plastic model for unsaturated soils intended to represent their mechanical and water retention behaviour. The set of incremental equations derived defines an initial value problem (IVP) that needs to be solved at each integration step once the initial (or previous) state and theincrements of suction and strain are known. To solve this IVP effectively, a small reformulation of the GCM (not involving any modification of the model, but simply presenting it differently) has been adopted withthe aim to facilitate the development of a robust algorithm capable to identify unambiguously the correct model response activated by a given stress path (i.e. elastic, mechanical yielding, water retention yielding or simultaneous mechanical and water retention yielding). Subsequent to the description of this algorithm, the paper presents an explicit substepping integration scheme with automatic error control able to integrate the incremental constitutive equations of the model for each possible response, including unsaturated and saturated conditions. The numerical capabilities of the substepping scheme in terms of accuracy and efficiency are then demonstrated in the context of the performance maps proposed originally for saturated soil models.