Energy evolution of brittle granite under different loading rates

Abstract

The mechanisms for rock failure involve instability, where an energy exchange and transformation occurs between the rock and an external energy source. Few studies have been conducted on rock failure characteristics in terms of the energy evolution under different loading rates. This study investigated the damage resulting from brittle granite failure under loading rates of 0.001, 0.005, 0.01, and 0.05 mm/s from the energy perspective. The results showed that the elastic and scattered strain energies absorbed in the initial compression phase were small. The elastic strain energy absorbed in the rock elasticity stage was mainly stored in the form of elastic energy, and the rate of increase for the scattered energy was less than those for the total strain energy and elastic strain energy. In the dilatation and breaking stage, the scattered energy increased sharply, elastic energy was rapidly released, and rock bursting accompanied the breaking. The loading rate increased from 0.001 mm/s to 0.05 mm/s, total strain energy increased by 91%, elastic energy increased by 48%, and spread energy increased by 184%. At the first stage of loading, the damage variable of the rock mass was small. With an increase in the loading rate, the damage variable of the rock sample gradually increased. When the stress reached its peak value, the damage variable rapidly increased. Under the same stress, a greater loading rate resulted in a greater change in the damage variable.

Introduction

In plastic deformation, stress–strain curves are generally used to represent the failure process of rock.¹ However, establishing appropriate failure criteria for rocks under different conditions is difficult because of the heterogeneity of a rock mass.² Rock failure is caused by external forces, and internal microcracks develop gradually through the process of energy release, which ultimately results in the process of macro-crack failure. According to the law of thermodynamics, material failure is accompanied by an energy exchange and transformation. A rock failure mechanism such as rock bursting can be revealed from the perspective of energy.^3,4

The loading rate effect refers to how a material's mechanical characteristics change with the loading rate. Scholars in China and abroad have conducted many studies on the loading rate effect on the mechanical characteristics of rock. Chos et al.⁵ investigated the effect of the loading rate on the dynamic tensile strengths of granite and tuff. They found that the dynamic tensile strengths of these two types of rock specimens increased sharply with an increase in the strain rate. Backers et al.⁶ found that a rock's fracture toughness and fracture surface roughness were related to the loading rate. Zhang et al.⁷ determined that the loading rate remarkably influenced the Kaiser effect. To accurately apply the Kaiser effect to in situ stress measurement, the Kaiser effect on rocks under different loading rates should be quantitatively analyzed. Lavro studied the evolution mechanism of rock fracture under different loading rates using acoustic emission technology.⁸ Yin et al.⁹ conducted unconfined compression tests on sandstone roof–coal pillar structure specimens using acoustic emissions and a scanning electron microscopy (SEM) system under different loading rates. They found that the macrofracture initiation stress, uniaxial compressive strength, and elastic modulus of the sandstone roof–coal pillar structure decreased with a decrease in the loading rate. Huang et al.¹⁰ carried out uniaxial compression tests on composite coal rocks at different loading rates. They found that with an increase in the loading rate, the strain increment of the composite coal rock during the elastic, plastic, and failure phases gradually increased. Fast loading enhanced the ability of the composite coal rock to convert external energy into its own elastic energy.

Studies on rock mechanics from the perspective of energy have attracted considerable attention in the engineering field. Thomas,¹¹ Pietro,¹² and Bratov¹³ et al. explored the relationship between energy dissipation and release in rocks, along with their fracture and constitutive behaviors. Giuseppe carried out compression tests on a large number of concrete specimens of different sizes and found that the size effect on the energy dissipation density is more obvious than that on the uniaxial compressive strength.¹⁴ Xie et al.¹⁵ established the strength and failure criteria for a rock mass from the perspective of energy. Zhang examined the confining pressure effect on the evolution and distribution of the elastic and dissipative energy of red sandstone.¹⁶ Meng considered the effects of the strain rate and size on the energy accumulation and dissipation of rocks.¹⁷ Zuo et al.¹⁸ analyzed the whole brittle failure process of rock from the energy perspective, and then enumerated and classified a variety of energy forms in the process of rock failure. They showed that the thermal energy and mechanical energy had to be distinguished when an energy method is used to analyze the failure process of rock. The energy theory has also been used in research on the triaxial compression of rocks, because underground rock masses normally exist in an uneven three-dimensional stress state.19, 20, 21, 22 Zhang et al.²³ used the true triaxial compressive strain energy analysis method to study the energy evolution processes of different types of hard rocks. They found that the mineral composition and microstructure of the rock affected its elastic and plastic deformation capacities. Tiwari et al.²⁴ performed experimental studies on three different sets of rock masses under uniaxial, triaxial, and true triaxial stress states. An empirical expression for the modulus under triaxial stress was suggested to predict the deformation behavior of the rock mass. Zong et al.²⁵ studied the mechanical and damage evolution properties of sandstone under triaxial compression. The macroscopic fracture models of sandstone samples in triaxial compression tests under different confining pressures primarily showed shear failure.

Rock, as a natural geological material, is formed by long geological changes. Because of the interference of many natural actions and human factors, its internal structure and mechanical properties are extremely complicated. It is difficult to use the existing theory to satisfactorily explain the mechanical behavior during the entire deformation process for such a material. The research on rock failure characteristics usually involves different loading rates or a single energy perspective.26, 27, 28, 29, 30 Few studies have been conducted from the perspective of energy evolution under different loading rates, and certain research results remain unclear. This paper primarily discusses the change characteristics and relations of the elastic energy, dissipative energy, and damage variable of rock during changes in the stress–strain curve. The originality and core objectives of this study involved an analysis of the energy evolution during the failure process of brittle granite via uniaxial compressive strength tests under different loading rates, which laid a foundation for follow-up triaxial compression and shear experiments. Studying rock damage from the perspective of the energy dissipation and release can avoid the analysis of complex deformation processes, which helps to simplify the problem and determine the cause of rock failure. Therefore, further research in this area should be carried out and used in practical rock engineering. The results of this study can provide a reference for describing the failure law of a rock mass under different strain rates.