Abstract:

The response of rocks to confining pressure and strain rate can change from very brittle to ductile. Capturing this transition is crucial for accurately predicting the rock mass failure induced by blasting, explosions, or drilling in mining.rock mass failureis crucial.In this work, a new constitutive model is proposed that accounts for the effects of confining pressure and strain rate on the nominal strength and post-peak behaviour of dry intact rocks and other similar geological materials.The main feature of this constitutive model is the adoption of a single loading function from initial yield to final failure and a rate-dependent enhancement, thereby enabling a realistic description of strain rate effects under different confining pressures. The model can well reflect the brittle and ductile responses of materials, as well as the brittle-ductile transition process with strain rate and confining pressure.

Introduction:

Understanding and simulating the behaviour of rocks will pave the way for safe and economical design in geotechnical and mining engineering. Like any other geological material, the behaviour of rocks depends on strain rate and pressure; that is, under extremely high confining pressure or high strain rate, the response of rocks can change from very brittle to ductile.In mining and geotechnical engineering operations in crustal rock strata, the effects of blasting, drilling, or tunnel excavation and/or tectonic and seismic forces can greatly alter the stress state. Therefore, the prediction of failure requires a model that can capture as accurately as possible the macroscopic response of rocks under rather complex stress states and different loading rates.

The mesoscopic inelastic deformation of rocks involves a series of mesomechanical processes that lead to the degradation of the material microstructure. These processes usually begin with the initiation of microcracks in the material matrix (at low pressure) and/or grains (at high pressure), followed by the localization of microcracks in a band of a certain thickness, where the microcracks eventually coalesce to form a macroscopic fracture.Throughout the entire inelastic deformation process, frictional sliding between the two faces of microcracks, roughness interlocking, granular flow and/or diffusive flow, crystal plasticity, and other processes may accompany microcracking and fracturing. These microscopic mechanisms of deformation are observed at the macroscopic scale, such as stiffness and strength reduction, inelastic dilation/compaction, and residual strain. From a phenomenological point of view, all mechanisms that lead to stiffness and strength reduction can be described as damage, and all phenomena that lead to the occurrence of residual strain can be interpreted as plastic deformation. In addition, the micromechanical processes of rock deformation are mostly time/rate dependent, which leads to the macroscopically observed rate-dependent behaviour of rocks. Examples of such time/rate-dependent microscopic mechanisms can be the time dependence of static friction, the evolution of frictional strength with loading rate, or time-dependent microcrack propagation. The rate-dependent macroscopic rock behaviour can be characterized by the increase in tensile and compressive strength of rocks at high strain rates. In addition, at higher strain rates, rocks show a more ductile tendency, whereas under quasi-static loading, at the same confining pressure, the behaviour of rocks may be completely brittle.

Phenomenological coupled damage-plasticity models with different levels of complexity and applicability have been proposed to simulate the mechanical behaviour of rocks. Generally, these models specify the interaction between damage and plastic processes in the model formulation in order to simultaneously account for the stiffness and strength reduction and residual strain observed during inelastic deformation.Various approaches can be adopted to establish coupled damage-plasticity models for rocks in order to reflect the influence of confining pressure on the mechanical behaviour of rocks. Examples of such approaches can be models with two loading surfaces, or models in which the damage evolution is defined as a function of the volumetric plastic strain rate. Although many coupled damage-plasticity models capable of describing the mechanical behaviour of rocks under different confining pressures have been found in the literature, the establishment of models that consider the combined effects of confining pressure and loading rate, especially the brittle-ductile transition of rocks, has not attracted much attention.

In this study, by adopting a combined yield-failure function, a new formulation is developed that does not require multiple loading surfaces and at the same time facilitates the implementation and application of the model to cover a wide range of responses under different pressures and strain rates.In this formulation, the initial yield surface evolves into a linear frictional failure envelope with the evolution of a damage variable defined as a function of the accumulated plastic strain rate. This is an important feature of the proposed model, because as the confining pressure increases, the brittle/softening and ductile/hardening responses and the transition between the two behavioural states can be automatically captured by the model without the need to separately define hardening or softening laws. By simulating the effect of microcrack closure on the mechanical response of rocks, the fundamental mechanism that determines the behaviour of rocks when transitioning from tensile loading to compressive loading is also explained. In addition, the strain rate dependence of the behaviour experimentally observed in rocks and other similar geological materials is incorporated into the model through Perzyna-type viscosity. It is worth noting that the rate dependence in the proposed model is treated as an intrinsic feature of the model rather than as a regularization technique in numerical implementation. Furthermore, the rate-dependent response caused by pore pressure in wet rocks has not been considered in this study, which is an issue that needs to be addressed in our future work. In the proposed model formulation, the pressure and rate dependencies are separated, allowing independent calibration of the model under quasi-static and dynamic loading conditions. We believe that this is beneficial for the development and calibration of the model.

This paper first describes the model formulation and provides the connection between the model formulation and the characteristics of rocks under different confining pressures and strain rates. Then, the numerical implementation algorithm is described, and numerical examples of rock behaviour under different confining pressures and strain rates are given to demonstrate the good features of the new model.

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Conclusions:

We have proposed a new model that simultaneously considers the effects of confining pressure and strain rate on rock properties. The proposed model is simple and general enough to capture a variety of behaviours under the combined action of confining pressure and strain rate.Its evolving yield function allows the description of brittle and ductile responses and their transition without the need for explicit softening/hardening laws, while the rate-dependent enhancement relies on a single viscosity parameter and is valid over a wide range of confining pressures. Experimental tests show thatthe model has good features in predicting the complex behaviour of rocks under different loading conditions. This is essential for analysing large-scale failure in mining and resource engineering.On the other hand, the current model still needs improvement to account for the rate dependence caused by pore pressure in wet rocks.