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To investigate the energy evolution and storage characteristics of the rock during the mixed-mode fracture failure, several single loading-unloading tests under preset different unloading levels were conducted on the cracked straight-through Brazilian disc (CSTBD) red-sandstone specimen with crack inclination angles of 10° and 20°. The input energy, elastic energy, and dissipated energy parameters were obtained by calculating the area integral of the load-displacement curve. Test results display that the total input energy, elastic energy, and dissipated energy of rock specimens increase in quadratic function with the increase of unloading level at different unloading levels. It was found that there are significant linear energy storage and dissipation laws of rock during the mixed-mode fracture process. The concepts of fracture energy storage coefficient (FESC) and fracture energy dissipation coefficient (FEDC) were proposed to express the energy variation of rock in the prepeak stage. Under the same loading conditions, FESC and FEDC remain unchanged regardless of crack inclination angles, indicating that the linear energy storage and dissipation laws are an inherent property of the rock. Besides, the peak fracture elastic-dissipation index W ed (the ratio of peak elastic energy to peak dissipation energy) was obtained through quantitative analysis and demonstrated its invariant feature. [ABSTRACT FROM AUTHOR]

To investigate the internal mechanism of drilling pressure relief (DPR) to reduce the elastic strain energy of deep rock, SG4500 equipment that can realize real-time drilling under high stress was independently developed. Real-time drilled (RD) uniaxial compression experiments were conducted on red sandstone specimens under different stress levels, and then the influence of real-time drilling on the weakening of rockburst proneness was studied. For comparison purposes, uniaxial compression tests were also performed on non-drilled (ND) and prefabricated drilled (PD) rock specimens. The results demonstrate that both prefabricated drilling and real-time drilling under high stress can effectively weaken the mechanical behavior of rock and reduce the storage capacity of the elastic strain energy and rockburst proneness of rock. Compared with ND specimen, the energy storage coefficients of PD and RD specimens were reduced by 1.01% and 5.16%, and the rockburst proneness index was reduced by 5.15% and 19.32%, respectively. The failure intensity of PD and RD specimens was also weaker than that of ND specimen. However, compared with prefabricated drilling, real-time drilling under high stress can more accurately reflect the change in the rock energy state. The energy storage coefficient and rockburst proneness index of RD specimen were decreased by 3.8% and 14.9% compared to those of PD specimen, respectively. Furthermore, it is also found that drilling energy relief (DER) is a significant feature of real-time drilling under high stress to prevent rockburst, which further demonstrates the effectiveness of DPR in reducing rockburst proneness from an energy perspective. Highlights: Real-time drilling pressure relief experimental equipment SG4500 was developed autonomously. Real-time drilling pressure relief under high stress accurately reflects the change in the rock energy state. Drilling energy relief is a significant feature of drilling pressure relief to prevent rockburst. Real-time drilling pressure relief under high stress effectively reduces the rockburst proneness of rock. [ABSTRACT FROM AUTHOR]

To explore the mechanical behaviors and energy evolution characteristics of rock materials with hole defects, eight types of red sandstone specimens with different hole numbers and arrangements were subjected to a series of single-cycle loading-unloading uniaxial compression tests. The experimental result revealed that the mechanical behaviors and energy evolution characteristics of the red sandstone specimens are significantly influenced by hole defects. As the number of boreholes increases, the compressive strength of rock specimens decreases. When the angle between drilling hole arrangement and loading direction changes from 0° to 27° and then to 90°, the compressive strength first decreases and then increases, and shear-splitting, splitting, and shear failure modes appear respectively. The experimental results also show that the energy evolution characteristics (linear energy storage and dissipation laws) of the rock specimens with hole defects were basically consistent with that of intact rock specimens, while the energy storage coefficient is different in various cases. There was a good correspondence between the compressive strength and energy storage coefficient. The larger the energy storage coefficient is, the greater the compressive strength. The hole arrangement angle shows a stronger effect on energy storage coefficient and compressive strength than the number of holes. Among all the arrangements, the rock specimens containing three holes with an angle of 27° between borehole arrangement and loading direction have the lowest energy storage coefficient and compression strength. The above research results provide a scientific basis for rock fracturing induced by drilling. [ABSTRACT FROM AUTHOR]

The elastic energy stored in deep rock in three-dimensional stress environment is the energy source of rockburst. To investigate the energy storage characteristics of deep rock under different confining pressures, a series of triaxial single-cyclic loading-unloading compression tests were conducted on red sandstone specimens under eight confining pressures. The input energy density, elastic energy density, and dissipative energy density of the specimen in axial, circumferential, and total directions can be obtained by the area diagram integration method. The results show that the input energy density in the axial direction accounts for the largest logarithmic proportion of the total input energy density, and the relationship between all energy density parameters and unloading level can be described by quadratic function. In the axial direction, there is a linear function relationship among elastic energy density, dissipative energy density, and input energy density. In the circumferential direction, there is a quadratic function relationship among elastic energy density, dissipative energy density, and input energy density. For the total energy density parameters of the rock specimen, the relationship among elastic energy density, dissipative energy density, and input energy density conforms to the quadratic function. According to the above correlation function, the elastic energy stored in deep rock under different confining pressures can be accurately obtained, which provides a foundation for studying the mechanism of rockburst under three-dimensional unloading from the energy perspective. [ABSTRACT FROM AUTHOR]

To study the effect of excavation unloading on hard rock failure, a series of true-triaxial compression tests, biaxial compression tests, and true-triaxial unloading compression tests (two different unloading rates) at different confining pressures was conducted on red sandstone cube samples. The strength and failure characteristics and their relationship for red sandstone unloading at different unloading rates and confining pressures were analyzed. Based on the test results, the effects of the unloading rate and confining pressure on the strength and failure characteristics of hard rock were explored, and a reasonable explanation for unloading-induced spalling in hard rock tunnels was presented. The results show the stress-strain curve of highly stressed red sandstone exhibits a stress step during unloading, and the higher the unloading rate, the lower the stress level required for a stress step. The rock strength-weakening effect induced by unloading was confirmed. The mechanical properties of red sandstone become more unstable and complicated after unloading. After the red sandstone is unloaded to a two-dimensional stress state, with increasing confining pressure, the strength increases first and then decreases; the failure mode changes from a low-confining pressure tensile-shear failure to a high-confining pressure tensile failure; and the geometries of the slabs change from large thick plates and wedges to medium- and small-sized thin plates. At equal confining pressures, the higher the unloading rate, the lower the strength (i.e., the strength-weakening effect is more pronounced), the thinner the slab, and the lower the confining pressure required for the failure mode to change from tensile-shear failure to tensile failure. The unloading rate and confining pressure affect the strength and failure characteristics by affecting the crack initiation type and propagation direction in hard rock. For deep hard rock tunnels with high unloading rate and axial stress, neglecting the effects of unloading rate and axial stress will lead to a dangerous support design. For deep hard rock ore, if the maximal horizontal principal stress exceeds the critical confining pressure, the mining surface should be perpendicular to the direction of the minimal horizontal principal stress. The results of this study are of great engineering significance for guiding deep hard rock tunnel construction and mining. [ABSTRACT FROM AUTHOR]

To investigate the specimen shape effect on rockburst proneness of rock materials, a string of conventional and single-cycle loading-unloading uniaxial compression tests was performed with cylindrical and cuboid red sandstone specimens. Despite similar development paths on stress-strain curves for the specimens with two shapes, the cuboid specimens generally show a higher uniaxial compressive strength than the cylindrical specimens. The energy evolution laws inside the two shaped specimens were explored. The results show that the input energy density (IED), elastic energy density (EED), and dissipated energy density (DED) of the two shaped specimens increased in a quadratic relationship with the increment of unloading level. Moreover, the linear relationships between the EED, DED, and IED were further confirmed for two shaped specimens, which were defined as the linear energy storage and dissipation laws, respectively. The energy storage coefficients and energy dissipation coefficients (the slopes of the linear relationships between the EED, DED, and IED, respectively) are almost independent of the specimen shape. According to the linear energy storage and dissipation laws, the peak EED and peak DED of every specimen can be calculated accurately. Finally, combining the failure process of rock specimens recorded by a high-speed camera, the elastic energy index ( W ET ), the residual elastic energy index (AEF), and the far-field ejection mass ratio (MF) of each specimen were adopted to assess the rockburst proneness of the red sandstone sampled in cylindrical and cuboid. The results show that cuboid specimens exhibited stronger rockburst proneness than cylindrical ones, which favorably agreed with the actual failure phenomena. [ABSTRACT FROM AUTHOR]

In order to quantitatively investigate the energy dissipation characteristic during the dynamic tension failure of rock materials, the dynamic Brazilian disc tests on red sandstone were conducted using the split Hopkinson pressure bar (SHPB) setup. The states of the specimens after different incident energies can be divided into three forms (i.e., the unruptured state, the ruptured state, and the broken state), and the failure processes of the specimens were recorded by using a high-speed camera. The results show that the ruptured state of the specimen corresponds to the critical failure strain. Taking the critical incident energy as a turning point, two positive linear fitting relations between the dissipated energy and incident energy before and after the point are obtained, and the dynamic linear dissipation law is found. When the incident energy is less than the critical energy, specimens were unruptured after impact. When the incident energy is greater than the critical energy, specimens will be broken after impact. According to the obtained linear energy dissipation law, the dynamic tensile energy dissipation coefficient (DTEDC) was introduced for quantitatively describing the dynamic energy dissipation capacity of rock materials in the dynamic Brazilian disc test. When the specimen is in the unruptured state, the ideal DTEDC is a constant value. When the specimen is in a broken state, the DTEDC increases with the increase of incident energy. [ABSTRACT FROM AUTHOR]

To fully understand the influence of water on rockburst proneness from energy storage viewpoint of rock and to check the performance of energy-related rockburst proneness indexes, several groups of uniaxial compression tests at different stress levels are performed on three types of red sandstone specimens (i.e., the saturated, natural, and oven-dried specimens). The method of combining strain energy calculations and experimental observations is used to assess the rockburst proneness. The progressive failure of the three types of specimens is recorded by a high-speed (H-S) camera, and the rockburst proneness is comprehensively assessed by considering the failure features of the rock specimens (including the fracture sound, fragment ejection, fragment distribution, and far-field ejection mass ratio). The laboratory results reveal that the rockburst proneness of the natural and oven-dried sandstone specimens is similar. However, compared with the natural and oven-dried specimens, the water-saturated specimens exhibit a visible weaker rockburst proneness. It is also evident that the linear energy storage and dissipation laws are applicable to the saturated, natural, and oven-dried specimens. Most interestingly, the energy storage and energy dissipation coefficients are nearly immune to the presence of water in the red sandstone. Based on this, the definitions of absolute energy storage capacity and relative energy storage capacity are adopted to describe the influence of water on the energy storage performance of rocks. It is found that water dramatically weakens the absolute energy storage capacity, but has little and negligible effect on the relative energy storage capacity of sandstone. Considering the direct and indirect indexes, the accuracy of several representative energy-related rockburst proneness indexes is comprehensively compared in terms of the far-field ejection mass ratio, and their performance is discussed from the relative and absolute energy storage aspects. According to their performance, it is strongly recommended to use the direct index for determination of rockburst proneness when energy-related indexes are used. • The rockburst proneness of oven-dried, natural, water-saturated sandstone specimens is analyzed. • The linear energy storage and dissipation laws are applicable for the sandstone under different contained water conditions. • The concepts of relative energy storage and dissipation capacities are proposed. • The performance of several representative energy-related rockburst proneness indexes is discussed [ABSTRACT FROM AUTHOR]

Abstract To investigate the dynamic Mohr-Coulomb and Hoek-Brown strength criteria under the low confining pressures at high strain rates, the dynamic uniaxial and triaxial compression tests of sandstone were conducted with a conventional and modified triaxial SHPB system, respectively. The confining pressures are 5.0 MPa, 7.5 MPa, 10.0 MPa, 12.5 MPa and 15.0 MPa, and the strain rates varied from approximately 40 s−1 to 160 s−1. The results show that the cohesion is a linear positive correlation with the logarithm of strain rate, and the internal friction angle is a linear negative correlation with the logarithm of strain rate. The change of cohesion is more obvious than that of the internal friction angle. The rock parameter m also exhibits a linear positive correlation with the logarithm of strain rate. Furthermore, the relationships between cohesion, internal friction angle and rock parameter m and strain rate were obtained. On this basis, the unified dynamic Mohr-Coulomb and Hoek-Brown strength criteria at high strain rates were established. According to the established dynamic strength criteria, the strength of sandstone under high strain rates and low confining pressures can be estimated theoretically. By comparing the theoretical curve and test data, it can be concluded that established dynamic Mohr-Coulomb and Hoek-Brown strength criteria of sandstone are appropriate for both high strain rates and low confining pressures. [ABSTRACT FROM AUTHOR]

Aiming at the determination of the rational loading waveform for rock materials, the comparative impact tests under the loadings of rectangular and half-sine stress waves were performed on red sandstone using an Ø50 mm SHPB apparatus. Experimental results with the rectangular stress wave affirm that the waveform dispersion and stress-strain curve oscillation frequently exist during the test of rock materials, which signifies that the accuracy of test results derived from the rectangular stress wave loading cannot be guaranteed. Under the loading of the half-sine stress wave, the phenomenon of wave dispersion during the tests has been eliminated radically, and there is no oscillation in the stress-strain curves. To further demonstrate the rationality of the half-sine wave loading in the SHPB test, by utilizing the three-dimensional numerical simulation approach, the propagations of rectangular, triangular, and half-sine stress waves travelling in the axial and radial directions of the SHPB with four elastic bar diameter sizes are analyzed and compared. The results show that the waveform dispersion of the rectangular and triangular stress waves always exists and will be more and more serious with increasing diameter size and propagation distance. For the half-sine stress wave, the waveform dispersion effect is very weak and not affected by the bar diameter size and propagation distance. The half-sine stress wave is the rational loading waveform for rock SHPB tests with different bar diameters. [ABSTRACT FROM AUTHOR]

The investigation of rock damage behaviour is an important requirement for ensuring stability control and safety prediction in rock engineering. In this study, based on the linear energy dissipation law and energy dissipation coefficient, a theoretical method is introduced for characterising the damage of intact rocks under uniaxial compression conditions. The existing uniaxial compression test data of 14 kinds of rock materials (including 6 types of granite, 4 types of sandstone, 2 types of marble, 1 type of slate, and 1 type of limestone) were used to verify the effectiveness of the damage characterization method. The results indicate that the damage evolution process of rocks under uniaxial compression can be fully expressed by the proposed theoretical damage characterisation method, and the damage variable exhibits a quadratic functional relationship with the loading stress level. Moreover, with the linear energy storage law serving as a theoretical basis, the peak dissipated strain energy in a rock damage expression under uniaxial compression can be accurately calculated. The new theoretical damage characterisation method overcomes the shortcomings of conventional damage characterisation methods (e.g. estimating the peak dissipated strain energy through a hypothesis), and provides a new means for analysing rock damage from an energy viewpoint. [ABSTRACT FROM AUTHOR]

• The mechanical properties of red sandstone increase with the increase of pre-existing single crack angle. • The linear energy storage and dissipation laws of pre-existing single crack rock are obtained. • The peak strain energy densities are determined using the linear energy storage law. • The linear energy dissipation law is applied to express the damage of rock with single crack. To investigate the effects of the pre-existing single crack angle on the mechanical behaviors and energy storage characteristics of red sandstone, a series of uniaxial compression and single-cyclic loading–unloading uniaxial compression tests were conducted on red sandstone specimens with five crack angles. The relationships among the crack angle and the mechanical properties, failure modes, and energy storage characteristics of red sandstone were analyzed using the acoustic emission (AE), stress–strain curve and curvilinear integral. The results indicate that the peak compressive strength, peak strain, and elastic modulus of specimens increase with the crack angle increasing, and the specimens with five different angles all present "anti-N-type" shear failure. Throughout the loading process, the total input energy density, elastic strain energy density, and dissipated energy density of the red sandstone at five different crack angles exhibit significant quadratic growth in response to the actual unloading stress. Importantly, the elastic strain energy density and dissipated energy density of red sandstone with different crack angles all show highly linear relationships with the total input energy density, and the linear energy storage and dissipation laws of pre-cracked rocks are obtained. Based on the linear energy storage law, the energy densities at peak strength of red sandstone with different crack angles are determined quantitatively. In addition, the linear energy dissipation law is applied to the expression of rock damage, and the damage constitutive equations of uniaxial compression specimens with different crack angles are obtained. Finally, the effects of crack geometric parameters on the energy storage and dissipation characteristics were discussed. [ABSTRACT FROM AUTHOR]