Constitutive modelling of crushable soil behaviour by conjugating hyperelasticity and bounding surface plasticity: from theory to application

In this paper, a constitutive model for crushable soils is developed with two main objectives: first, the elastic formulation is described within a hyperelastic framework that ensures one-to-one stress–strain relations derived from an energy potential, where a closed strain loop results in a closed stress cycle with zero energy dissipation. The second is to derive the constitutive equations in the full tensorial domain rather than the triaxial plane, allowing the model to be implemented in three-dimensional finite-element codes. To achieve this, hyperelastic equations are derived from a modified energy potential and the concept of elastoplastic coupling is considered. In this context, the breakage index acts as a coupling variable that captures the influence of plastic strain on the elastic stiffness tensor of soils. The hyperelastic description of the material is then conjugated with a state-dependent bounding surface plasticity model to capture the soil response in a hyperelastic–plastic framework. The influence of particle breakage on the stress–strain response of soils is incorporated by adjusting the critical state void ratio with the change in grain size caused by crushing. The performance of the model in capturing the small-strain behaviour of soils at different initial stress ratios is first evaluated using the concept of response envelopes. Then, a series of monotonic and cyclic triaxial tests are simulated on three different soils and the predictions are compared with laboratory results. The comparative analysis of the results shows a satisfactory agreement between the model predictions and the experimental data. After validation of the model with element tests, the model is implemented in Abaqus as a user-defined material routine to analyse the behaviour of a monopile and a strip foundation under loading. The qualitative comparison between experimental results and simulations shows good agreement.