Thermoplasticity of Saturated Soils and Shales: Constitutive Equations

Plastic behavior of soils and shales due to heating and loading under constant elevated temperature is discussed in terms of a thermoplastic version of the critical state model. Rules for dependence of the yield surface on temperature in the elastic states and at yielding are proposed. The elastic domain is assumed to shrink during heating (thermal softening) and to expand during cooling, when the stress state is elastic. In a plastic state thermal softening occurs simultaneously with the plastic strain hardening. At a constant stress state, thermal softening may entirely be compensated by plastic strain hardening leading to thermal consolidation. Loading and unloading criteria are given to determine whether the soil response is thermoelastic or thermoplastic. As opposed to isothermal plasticity, stress rate excursions inside the current yield surface are admissable plastic processes, when temperature grows, even if strain hardening occurs. Also, outside stress rate excursions at the softening side may generate plastic strain, when cooling occurs. Thermally induced plastic strain rate non-associativity is discussed as well. Direct and inverse incremental strain-stress-temperature relationships are formulated. An analysis of the experimental results of thermomechanical testing of saturated clays is given in a companion paper.