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Rockburst is a kind of rock failure phenomenon during which the internal elastic strain energy of surrounding rock mass is released dynamically under external load, and the loading rate is an essential influencing factor of potential for bursting. To investigate the effects of loading rate on rockburst proneness from energy storage and surplus perspectives, conventional uniaxial compression tests are conducted on granite under four orders of magnitude loading rate. The failure process and mode of granite specimens were recorded in real time with a high-speed camera with microsecond shooting speed. The variation trend of the internal elastic strain energy of granite specimens under four loading rates was obtained by performing the single-cycle loading–unloading uniaxial compression test. The experimental results show that the elastic strain energy linearly increases as the input strain energy increases under each loading rate, which meet the linear energy storage law. Based on the linear energy storage law, the peak elastic strain energy of each granite specimen can be accurately obtained. According to the mass and range of ejected rock debris after specimen failure, the bursting liability of each specimen was evaluated by the far-field ejection mass ratio (MF) from a qualitative point of view. Meanwhile, the residual elastic energy index (AEF) and the other three criteria were used to evaluate the potential for bursting of granite specimens under different loading rates. The comparison results show the rockburst proneness of granite specimens increases with the loading rate and that the evaluation results of MF and AEF are unified from qualitative and quantitative aspects, respectively. The fundamental reason for the consistent results is that these two indexes have a common essence of elastic strain energy release. Highlights: The mechanical properties of granite are significantly influenced by loading rate. The loading rate does not affect the existence of linear energy storage law and the compression energy storage coefficient is independent of loading rate. The rockburst liability of granite increases with the loading rate. At different loading rates, the far-field ejection mass ratio and residual elastic energy index offer consistent qualitative and quantitative evaluations for the rockburst proneness of granite. [ABSTRACT FROM AUTHOR]

In practical engineering, rocks are often subjected to repeated loading and unloading caused by natural or artificial actions. In this study, a novel staged cyclic damage constitutive model for brittle rock is proposed and verified. Firstly, aiming at the pre-peak deformation characteristics, the damage variable of brittle rock defines as the ratio of dissipation strain energy to constitutive strain energy is developed. Based on the linear energy dissipation law, a new damage variable characterization including compressive energy dissipation coefficient and strain energy parameters is deduced. Secondly, a power function correction coefficient of strain is introduced to modify the traditional damage model based on the strain equivalence hypothesis. Finally, the novel staged cyclic loading–unloading damage constitutive model considering the accumulation effect of plastic strain is established by using the iteration relationship. The established model includes basic parameters such as compressive dissipation coefficient, strain energy and plastic strain, and the feasibility of this model are verified through the experimental data of three brittle rocks (including shale, green sandstone, and red sandstone). The comparison results show that the established model can accurately reflect the cyclic loading–unloading behaviours and hysteresis process of brittle rocks, which provide an important reference for studying rock damage and constitutive model for brittle rocks. Highlights: Damage variable characterization of brittle rock containing energy dissipation coefficient is deduced using the linear energy dissipation law. By introducing a power functional correction coefficient of strain, a novel staged cyclic damage constitutive model is established through iterative relationship, which reproduces the loading–unloading process of brittle rock. The applicability of established model is verified by comparing \ the test results of brittle rock subjected to different cycles of loading–unloading. [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 evaluate rock brittleness more accurately, a new rock brittleness index based on the peak elastic strain energy consumption ratio (PEECR) was proposed in this study. Considering the relationship between rock brittleness and energy evolution characteristics of rock materials under confining pressure, the PEECR was defined as the dissipated proportion of peak elastic strain energy relative to failure energy and residual elastic strain energy (the maximum value of PEECR is 1.0, which indicates the corresponding rock will fail immediately after reaching the peak strength). The evaluation accuracy of the PEECR was verified based on the conventional triaxial compression tests on shale under six confining pressures, and the universality of the PEECR was also analyzed according to test data of six types of rocks from previous studies. The results show that the PEECR continuously decreases with the increasing of confining pressures, and is suitable for various types of rocks and a wider range of brittleness degrees. Finally, the evaluation accuracies of the PEECR and 11 existing rock brittleness energy indexes were compared and analyzed, and the results indicate that PEECR can evaluate rock brittleness more accurately. Highlights: A new rock brittleness index based on peak elastic strain energy consumption ratio (PEECR) was proposed considering the relationship between the rock brittleness and energy evolution characteristics of rock materials under confining pressures. It is verified based on conventional triaxial compression tests that PEECR can accurately evaluate rock brittleness, and is suitable for various types of rocks and a wider range of brittleness degrees. The evaluation accuracy for rock brittleness of PEECR is higher than other existing indexes by comparison based on test results, and PEECR can be popularized in practical application. [ABSTRACT FROM AUTHOR]

To investigate the influence of water on stress-induced failure in D-shaped hard rock tunnels, a series of true triaxial tests were performed on naturally saturated red sandstone cube samples containing a D-shaped hole. A self-developed real-time monitoring device was used to observe and record hole failure in real time, and the process and characteristics of stress-induced failure in D-shaped holes were summarized. The influence of water on failure form, energy storage properties, surrounding rock stability, and axial stress on the stability of the surrounding rock was discussed, and the mechanism of water on stress-induced failure was revealed. The results show that the stress-induced failure in a water-bearing D-shaped tunnel can be divided into buckling deformation, tension cracking, macrocrack propagation and coalescence, and slab flaking. The dominant failure mode of the stress-induced changes from tension around the tunnel to shear of the surrounding rock in depth. A quiet period exists between two adjacent significant AE counts, and the length of the quiet period increases as the two horizontal principal stresses increase. Under the influence of water, the capacity of the surrounding rock to store elastic strain energy decreases, and the dissipated energy required for deformation and failure increases; the form of stress-induced failure changes from spalling accompanied by occasional rockburst to spalling. The increase in lateral stress can enhance the stability of the surrounding rock, and the influence of axial stress on the stability of the surrounding rock is related to the magnitude of lateral stress. [ABSTRACT FROM AUTHOR]

The excavation-induced weakening effect of rock mass parameters is detrimental to the stability of deep tunnels. This study presents a quantification method for the weakening effect of rock mass parameters. In this method, the weakening factor is introduced as a quantitative index of the weakening effect of rock mass parameters, which can be calculated by the acoustic P-wave velocity measured in the surrounding rock and the Hoek–Brown criterion. Taking three deep tunnels as examples, the weakening law of rock mass parameters is investigated. The results indicate that the weakening effect is most severe near the excavation outline and gradually decays with increasing distance. Significant differences in the weakening effect can be observed at different parts of the tunnel cross-section and under different excavation methods. The weakening effect can be further exacerbated by multiple excavation disturbances. Among the strength parameters of rock masses, the weakening effect of uniaxial compressive strength is the most obvious, followed by uniaxial tensile strength, cohesive strength, and equivalent internal friction angle. The FLAC3D software is utilized to reproduce different weakening effects and analyze the energy distribution around tunnels. It is found that as the weakening effect intensifies, the accumulated elastic strain energy within the surrounding rocks gradually diminishes, and the peak elastic strain energy is at the junction of damaged and undamaged rock masses. • A quantification method for the weakening effect of rock mass parameters is proposed. • The weakening effect is most severe near the tunnel contour and decays with increasing distance. • Multiple excavation disturbances could further exacerbate the weakening effect. • The energy distribution of surrounding rock with varied weakening effects is numerically reproduced. [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]

Judgement of rock burst proneness of rock materials is one of the basic problems in the field of rock burst research. In this study, a peak-strength strain energy storage index is proposed for estimating and classifying the rock burst proneness of rock materials. The method for determining this index is also introduced in this paper. The peak-strength strain energy storage index is defined as the ratio of the elastic strain energy density to the dissipated strain energy density corresponding to the peak compressive strength of rock specimen. In order to obtain the elastic strain energy density and the dissipated strain energy density at the peak strength, a series of single cyclic loading-unloading uniaxial compression tests on nine rock materials were conducted. The relationships between the total input energy density and the elastic strain energy density at different unloading stress levels were investigated. The results show that, for every rock material, the elastic strain energy density increases linearly with the increase of the total input energy density. Based on this linear storage energy law, the elastic & dissipated strain energy density at the peak strength can be calculated for each specimen, and the peak-strength strain energy storage index can be obtained accordingly. A new criterion for rock burst proneness of rock materials is proposed. The rock burst proneness of nine rock materials estimated with the proposed criterion agreed well with the laboratory test results. [ABSTRACT FROM AUTHOR]

To estimate the energy storage and release performances of rock pillars in high stress and gain insights into the prevention and control of rockburst hazards from an energy aspect, several series of single-cyclic loading-unloading uniaxial compression tests with different stress levels were conducted on five types of rocks sampled in standard cylinders and prisms. The concepts of relative energy storage potential and ultimate energy storage potential were proposed to evaluate the energy storage performance of the two shaped specimens, and the energy release potential was determined using the residual elastic strain energy index. The results showed that, under similar loading conditions, the relative energy storage potential of rocks was insensitive to the specimen shape, whereas the ultimate energy storage potential and energy release potential were sensitive to both the specimen shape and rock type. Based on the lab results, a theoretical approach of assessing the rockburst (or instability) risk of isolated rock pillars subjected to high geostress was illustrated by estimating its current energy state and ultimate energy storage potential. Importantly, the residual elastic energy of an isolated pillar can also be estimated based on the lab results, according to which the number of supporting devices such as the energy-absorbing bolts needed for scientific and sufficient support of pillar rockburst was quantitatively estimated. This study provides a new method for estimating the desired number of energy-absorbing bolts during rockburst support in engineering practice. [ABSTRACT FROM AUTHOR]

2, the "failure energy" should be "post-peak failure strain energy"; in the line 10, the "failure energy" should be "post-peak failure strain energy"; in line 14, the "input energy" should be "input strain energy". 2, the "peak elastic strain density" should be "peak elastic strain energy"; the "failure energy density" should be "post-peak failure strain energy"; in line 6, the "residual elastic strain energy density" should be "residual elastic strain energy"; in line 14, the "input energy" should be "input strain energy". Correction to Tables b In the line 1 of column "Energy parameters" of Table 1, the "additional input energy" should be "additional input strain energy"; the "total failure energy" should be "post-peak failure strain energy". [Extracted from the article]

Considering the linear energy dissipation law under uniaxial compression, a damage characterization of rocks including the compression energy dissipation coefficient is proposed, which can make the existing damage calculation formula more quantitative. Damage variables of brittle rocks can be directly calculated by using the compression energy dissipation coefficient and the input strain energy of rock under uniaxial compression. Furthermore, because the classical strain equivalence hypothesis has a large error in describing the constitutive relation of rock, a correction coefficient considering the compaction effect is introduced to modify the classical model. The modified model is extended to single-cyclic loading–unloading conditions, and the corresponding constitutive equation is established to further verify the applicability of the damage model and correction coefficient. The conventional uniaxial compression and single-cyclic loading–unloading uniaxial compression models are validated with experimental results of four typical brittle rocks. The results show that the theoretical curves are highly coincident with the actual stress–strain curves, indicating that the established damage constitutive model can accurately reflect the conventional uniaxial compression and single-cyclic loading–unloading processes of rocks. The new model in this paper considers the linear energy dissipation and compaction effect, which provides an insight for the study of brittle rock constitutive model from the perspective of energy. [ABSTRACT FROM AUTHOR]

• The u t , u e , and u d increase nonlinearly with the increase of the i. • The u e , and u d have a significant linear relationship with the u t. • The A E increase linearly with the increase of age, while A D is opposite. • A novel method was proposed to calculate the u d and u e at ultimate strength point. To investigate the influence of age on energy storage and dissipation laws, uniaxial compression (UC) and single–cyclic loading–unloading uniaxial compression (SCLUC) tests were conducted on C35 concrete specimens with ages of 3 d, 7 d, 15 d, 28 d. The experimental results showed that the input strain energy (ISE), elastic strain energy (ESE), and dissipated strain energy (DSE) increased nonlinearly with the stress level during the pre-peak loading stage. Analyzing the relationship between the three strain energies, both ESE and DSE increase linearly with the increase of ISE in the pre-peak loading stage at different ages, namely, linear energy storage and dissipation laws exist in every ages. Based on the linear energy storage and dissipation laws, a novel method was proposed to calculate the DSE and ESE at the ultimate strength point of the concrete at different ages. In addition, we found that the DSE was greater than the ESE of concrete in the loading stage, because the energy was mainly dissipated in forming cracks, grain dislocation, and producing plastic displacement during compression. The value of compression energy storage coefficient represents the capacity of the concrete to store ESE, whereas energy dissipation coefficient represents the strain energy dissipation capacity of concrete. In the future, based on the linear energy storage and dissipation laws of concrete, the new method for calculating the damage variable may be proposed. [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]