A thermodynamically consistent two surface/bubble thermo-mechanical model considering thermal and mechanical cyclic behaviour of fine-grained soils

The formulation of a two surface/bubble thermo-mechanical constitutive model consistent with the principles of thermodynamics is presented. This allows plastic deformations inside the outer yield surface, resulting in a smooth stress–strain prediction and progressive cyclic deformations. This is achieved by the translation of the inner yield surface (also known as the bubble surface) with the stress state of the soil, inside the outer yield surface, by using a kinematic rule. The constitutive equations, including the hardening rules, are derived by specifying a Gibbs-type energy potential and a rate of dissipation potential function, ensuring thermodynamic consistency. The kinematic rule is divided into isothermal and non-isothermal parts. With the isothermal component, the model is capable of capturing the hysteresis behaviour of soils during cyclic mechanical loading. With the non-isothermal part, the model is able to predict the shakedown behaviour of soils observed when they are subjected to heating–cooling cycles. The performance of the model is compared with various experimental data for isothermal and non-isothermal conditions, and is shown to be in good agreement.