Energy evolution of brittle granite under different loading rates
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.
Section snippets
Rock sample preparation and test scheme
Rock samples were obtained from the surrounding rocks of middle section 216 of a tungsten mine underground in southern Jiangxi Province. Cores were drilled using boreholes in situ. The average diameter was 50 mm, and the error was within the standard range. The rock samples of each group were cut with a JRDQ-1T program-controlled automatic rock-cutting machine and then polished with a JKSHM-200 double-end grinder to ensure that both ends were smooth and that the parallelism of the upper and
Thermodynamic energy calculation principle
The process of rock failure under load involves energy absorption and release. Assuming that a rock is in an ideal state without heat exchange during its physical deformation under external loads, the first law of thermodynamics has the following relationship31:
In this formula, U is the energy of the total work transformation of the specimen under an external load, and its expression is as follows:
Variables and are the axial strain and transverse strain,
Experimental physical and mechanical parameters
Table 1 lists the physical and mechanical properties of the surrounding rock under different loading rates. As shown in the table, the average compressive strength of the rock samples gradually increased with the loading rate. When the loading rates were 0.001 and 0.05 mm/s, the average compressive strengths were 156.39 and 200.17 MPa, respectively. When the loading rate was 50 times higher, the average compressive strength increased by 30.0%. The average modulus of elasticity increased by
Exploration of damage mechanism based on energy analysis
In summary, according to the thermodynamic law, the exchange and transformation of energy between a system and the outside is one of the main characteristics of the physical changes in matter. The mechanism of failure in a heterogeneous material such as rock is a kind of instability phenomenon under the influence of energy. For example, in the process of unidirectional compression, the pore closure, microcrack development, and propagation are accompanied by energy loss and accumulation, which
Conclusion
This study investigated the energy changes in the four failure stages of brittle granite under uniaxial compression at loading rates of 0.001, 0.005, 0.01, and 0.05 mm/s from the energy perspective. The main findings of the research following are drawn.
There are different forms of energy conversion in several stages of the rock deformation and failure process. In the early stage, the energy conversion is generally slow, whereas in the later stage, the energy is released violently. The elastic
Declaration of competing interest
No conflict of interest exits in the submission of this manuscript. All the authors listed have approved the manuscript that is enclosed.
Acknowledgement
The study has been supported by the National Natural Science Foundation of China (No. 51764013), by China Postdoctoral Science Foundation funded project (Grant No. 2019M652277), by Natural Science Youth Foundation Key Projects of Jiangxi Province of China (Grant No.20192ACBL21014), by Jiangxi Province Postdoctoral Science Foundation funded project (Grant No. 2018KY356).
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