A fully coupled rate- and temperature-dependent viscoplastic damage model for rock-like materials within the consistency framework

Abstract

Civil structures in the deep lithosphere are frequently exposed to thermal environments resulting from geothermal gradients and dynamic disturbances caused by blasting, rockbursts, and earthquakes during construction and operation. In this paper, a novel thermo-viscoplastic damage model is proposed within the consistency framework to capture the rate- and temperature-dependent behavior of rock-like materials. By rationally designing the free energy and dissipation potential functions, all the constitutive formulations relating the coupled thermo-elasto-viscoplastic-damage processes can be derived following the thermodynamic principle. The main innovation of our study lies primarily in deriving a fully coupled Lagrange multiplier satisfying the classical form of rate-independent plasticity while still retaining the rate-dependent characteristics, thus enabling a consistent solution for the viscoplastic strain, temperature, and damage variables. To better improve the usability of our model, a hierarchical procedure is formulated for identifying all model parameters based on conventional laboratory experiments. By reproducing a series of uniaxial/triaxial compression, SHPB tests, and large-scale impact tests across a broad range of pressures, strain rates, and temperatures, the proposed consistency thermo-viscoplastic damage model is proven able to characterize realistically the coupled dynamic and thermal responses, as well as corresponding failure patterns of rock-like materials. Our calculations show that greater thermal damage intensifies the strain rate sensitivity of dynamic rock strength. Moreover, we have newly discovered the competitive relations among different dissipation processes during inelastic material deformation, highlighting the potential application of our model in predicting the temperature evolution in geological fault zones associated with distributed rock fracturing and pulverization.