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In this work, a Minkowski difference‐based advancing front approach is proposed to generate convex and non‐circular particles in a predefined computational domain. Two specific algorithms are developed to handle the contact conformity of generated particles with the boundaries of the computational domain. The first, called the open form, is used to handle the smooth contact of generated particles with (external) boundaries, while the other, called the closed form, is proposed to handle the internal boundaries of a computational domain with a complex cavity. The Gilbert‐Johnson‐Keerthi (GJK) method is used to efficiently solve the contact detection between the newly generated particle at the front and existing particles. Furthermore, the problem of one‐sided particle lifting, which can cause some defects in the packing structure in existing advancing front methods during packing generation, is highlighted and an effective solution is developed. Several examples of increasing complexity are used to demonstrate the efficiency and applicability of the proposed packing generation approach. The numerical results show that the generated packing is not only more uniform, but also achieves a higher packing density than existing advancing front methods. [ABSTRACT FROM AUTHOR]

The elastic modulus of rock is an important parameter in rock engineering, but the common methods based on laboratory tests are laborious, especially for obtaining the probability distribution of the elastic modulus that is required in reliability-based design. Many scholars have studied the regression model between the elastic modulus and P-wave velocity; however, most previous reports have ignored the characterization of parameter variability and model uncertainty. To address this problem, a large number of granite samples are collected from the Yingliangbao hydropower station (YLB), compressive wave velocity (P-wave velocity) and uniaxial compression tests are carried out in the laboratory. Then, four different regression models based on the frequentist method and Bayesian method are established to estimate the elastic modulus, the normal priors are adopted by prior analysis and the widely applicable information criterion (WAIC) is used to select the most appropriate Bayesian regression model. Finally, the effects of sample size and sample selection on different methods are studied, the results obtained from different priors are compared. The results show that the Bayesian method provides estimations that are more consistent with the test data and has better robustness in given sets of different sample selections, especially in small sample size. [ABSTRACT FROM AUTHOR]

Investigation into rock damage is of great significance for evaluating and predicting the stability of underground rock applications, such as deep mining or tunneling structures. Considering the energy dissipation properties during rock deformation, this paper proposes a novel theoretical characterization of the damage induced by compressive-shear stress and its evolution in intact rocks. The linear energy dissipation (LED) law is derived from shear stress and deformation data of rocks resulting from the preset angle shear experiment. Based on the LED law, two damage variables are separately constructed from the theoretical and experimental aspects. Several sets of experimental data are subsequently utilized to validate the two constructed damage variables. Results show that both damage variables grow first slowly and then rapidly with shear displacement or shear stress in nonlinear relations. By comparison, however, it is found that the theoretical damage variable outperforms the experimental damage variable, which can accurately reflect the stress and deformation data during progressive rock damage with favorable continuity. This study contributes to a novel theoretical approach to quantifying the pre-peak damage in intact rocks subject to compressive-shear stress. [ABSTRACT FROM AUTHOR]

The mechanical behavior of deep rock pillars is closely related to the coupling effect of the initial high stress and the excavation-unloading process. In this study, the failure and strength characteristics of rock pillars are studied under triaxial unloading paths of three-dimensional (3D) initial high stress followed by two-dimensional (2D) stress unloading and one-dimensional (1D) stress adjustment. Two different 2D stress unloading paths were used: horizontal bidirectional sequential unloading path (YU test), and horizontal bidirectional simultaneous unloading path (TU test). The 3D initial high stresses were σ1 = 60 MPa, σ2 = σ3 = 10, 20, 30, 40, and 50 MPa, that were applied on cubic granite specimens (50 × 50 × 50 mm). Uniaxial compression tests are also conducted for comparison. Violent rockburst occurred in all specimens under the triaxial unloading paths. The results reveal that the peak strengths of the cubic granite specimens under the triaxial unloading paths are significantly lower than the uniaxial compressive strength, namely exhibiting a remarkable strength reduction effect, and the degree of strength reduction will increase with the increase of initial stress. Further, the specimen strengths in the TU tests are lower than those in the YU tests, which indicates that the weakening intensity effect of simultaneous unloading is greater than that of sequential unloading. The weakening mechanism of deep pillar under high-stress unloading can be expressed as that the 3D initial stress determines the strength level of the pillar, whereas the triaxial unloading path affects its weakening intensity. Highlights: The rockburst failure and strength characteristics of rock pillars under the high-stress condition were studied from the perspective of triaxial unloading of 3D initial high stress + 2D stress unloading + 1D stress adjustment. The pillar strength reduction effect was observed and the triaxial unloading path has a significant influence on the strength reduction effect. The initial 3D stress determines the strength level of the pillar, whereas the triaxial unloading path affects its weakening intensity. [ABSTRACT FROM AUTHOR]

The coupled discrete element and lattice Boltzmann method using an immersed moving boundary scheme was extended to simulate methane hydrate exploitation involving mass transport and particle dissolution. In this coupled DEM‐IMB‐LBM model, a new Dirichlet‐type thermal boundary condition is extended to simulate moving curved boundaries with constant concentration. A novel periodic boundary including an efficient searching algorithm for particle contact is proposed to reduce the computational cost and boundary effect. Then this model is validated by two numerical examples: a circular particle with concentration convection‐diffusion moving in a horizontal channel and mass transport from a cylinder particle in a simple shear flow. The numerical results obtained from the proposed model agree well with previous studies. To further demonstrate the capacity of the proposed model, simulations of methane hydrate exploitation including two formations in marine sediments are carried out. The numerical results indicate that the coupled DEM‐IMB‐LBM is not only capable of simulating the dissolution of hydrate particles at the grain level, but also recover the sand erosion and migration process in a fundamental perspective during the methane hydrate exploitation process. [ABSTRACT FROM AUTHOR]

The characteristic impedance of a rock is defined as the product of the sonic velocity and the density of the rock. Based on previous studies, this article finds that: (1) For an intact rock, its characteristic impedance is a comprehensive physical property, since it is closely related with strengths, fracture toughness, Young's modulus, and Poisson's ratio. (2) For rock masses, their characteristic impedances either increase markedly or slightly with increasing depth. (3) The bursts of intact rocks in laboratory are dependent on their characteristic impedances to a great extent, and strong rock bursts happen mostly in the rocks with large characteristic impedance. (4) Rock burst occurrence in tunnel and mines has a close relation with the characteristic impedances of the rocks. (5) Laboratory experiments on different rock samples show that seismic velocity increases as applied stress rises, and field monitored results from coal mines indicate that in the areas where rock bursts happened, the seismic velocity was increasing markedly before or during the bursts. (7) Drillability of rock depends on the characteristic impedance of the rock and the rock with larger impedance has lower drillability or lower penetration rate. (8) The potential applications of characteristic impedance include evaluation and classification of rock masses, and prediction of rock burst proneness and drillability. Highlights: Characteristic impedance of rock mass is related to the depth below ground surface. Rock bursts are dependent on characteristic impedance of rock. Characteristic impedance of rock is related to its strengths, fracture toughness, and Young's modulus. Burst proneness and drillability of rock can be predicted by its characteristic impedance. [ABSTRACT FROM AUTHOR]

This study aims to investigate the influence of length-to-diameter (L/D) ratio on the strain energy storage and evolution characteristics of rock materials during progressive rock failure under compression. Uniaxial compression tests and single-cycle loading–unloading uniaxial compression tests were conducted on four rock materials with two specimen L/D ratios. The uniaxial compressive strength (UCS) and peak strain of the rock specimens with L/D = 1 were significantly greater than those of the specimens with L/D = 2, thus exhibiting a strong size effect. In the single-cycle loading-unloading uniaxial compression tests, the total energy density, elastic energy density and dissipated energy density of the specimens with different L/D ratios increased nonlinearly with the actual stress level. The specimen L/D ratio had a significant impact on the nonlinear energy evolutions over various actual stress levels. Interestingly, regardless of the L/D ratio, failure pattern and type of material in the tests, highly linear relationships exist between the elastic energy, dissipated energy and total energy. Although the UCS is sensitive to the specimen L/D ratio, the energy storage coefficient (ESC) and energy dissipation coefficient (EDC) almost show a size-independent behaviour. The ESC and EDC are not affected by the L/D ratio and failure mode and can be used as physical parameters in geotechnical engineering design. [ABSTRACT FROM AUTHOR]

In this study, mode I fracture tests on cracked straight-through Brazilian disc (CSTBD) and notched semi-circular bend (NSCB) shale specimens with different sizes were conducted to investigate the difference between maximum tangential stress fracture criterion and the size effect law (SEL) model in predicting apparent fracture toughness (Ka) of shale. In addition, the effects of specimen size and geometry on the Ka and the selection of fracture criterion on the prediction of the inherent fracture toughness (KIc) were also studied. The results show that the Ka increases with the increase of specimen size, and the difference between KIc of shale specimens with different sizes predicted by the fracture process zone length determined by the further improved maximum tangential stress (FIMTS) criterion is the smallest. For the prediction of Ka of NSCB specimen, the results predicted by the FIMTS criterion are the closest to the tested fracture toughness. However, the effect of SEL model applied to the prediction of Ka of NSCB specimens is poor. The effective establishment of SEL model requires high accuracy for test data, especially for the configuration with large variation of the dimensionless stress intensity factor (Y*) with normalized crack length (α). Highlights: Fracture toughness is closely related to the size and configuration of the specimen, which is ultimately attributed to the inconsistent tangential stress distribution at the crack tip. The further improved maximum tangential stress criterion has the best effect on apparent fracture toughness prediction, and higher-order terms of the Williams expansion should be considered in apparent fracture toughness prediction of small-size specimens. The fracture criterion for determining the fracture process zone length should be consistent with the prediction criterion of apparent fracture toughness. The effective establishment of size effect law requires high accuracy tested data, especially for the configuration with large variation of the dimensionless stress intensity factor with normalized crack length. [ABSTRACT FROM AUTHOR]

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]

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]

The influence of rock mineral composition and mineral grain size on basic rock strength performance and AE characteristics have been studied, 13 different rocks microstructures are analyzed in an optical microscope thin section using petrographic image analysis, making it possible to determine the mineral composition and mineral texture characteristics of rocks. Then, the basic strength parameters of rock and AE signals generated during fracture propagation were obtained by UCT (uniaxial compression test) and BIT (Brazilian intension test). Finally, the relationship between basic strength parameters and AE characteristics of rock with mineral composition and grain size was analyzed. The results showed that different mineral constituents have significant effects on rock strength. The positive influence of plagioclase content on igneous strength was obtained. Sedimentary rocks strength increases initially and then decreases with the increase of plagioclase content. Besides, with the increase in quartz and K-feldspar content, the strength of the rock was weakened obviously. It is also found that the greater the dimensional deviation of mineral grain, the greater the strength of the rock. The strength of igneous rocks was inversely proportional to the mineral grain size, but there is no correlation between the sedimentary rocks strength and the mineral grain size. Furthermore, the tension–shear crack propagation of rock can effectively distinguish by judging that the data set of the AF–RA density graph was nearby the AF axis or RA axis and the peak frequency data sets of below 100 kHz or more than. Alterations in the rock nature are the main key reasons for the differences between AE hit rate, AE count rate, AE energy, and cumulative energy. The plagioclase content and grain size play a decisive role in AE signal characteristics and failure mode. Highlights: The relationship between basic strength parameters (i.e., σc, σt and E) and AE characteristics of rock with mineral composition and grain size was analyzed with 13 different rocks. The positive influence of plagioclase content on igneous strength was obtained. Sedimentary rocks strength increases initially and then decreases with the increasing plagioclase content. The strength of igneous rocks was inversely proportional to the mineral grain size, but there is no correlation between the sedimentary rocks strength and the mineral grain size. The AF–RA nuclear density map and AE peak frequency can effectively distinguish the shear and tensile failure of rocks The plagioclase content and grain size play a decisive role in AE signal characteristics and failure mode. [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]

Size effect is a project that cannot be ignored in rock mechanics. To investigate the size effect on the energy distribution and evolution laws, several groups of uniaxial compression tests and single-cycle loading–unloading uniaxial compression tests were performed on red sandstone specimens of different sizes (diameters of 25, 37, 50, 75, and 100 mm; a constant length-to-diameter ratio of 2.0) using the INSTRON 1346 test system. Experimental results show that mechanical properties are influenced by specimen size while failure mode has no significant variation for different diameter specimens. Strain energy parameters (input strain energy, elastic strain energy, and dissipated strain energy) under each unloading stress level were calculated by integration based on the stress–strain curves. The input strain energy, elastic strain energy, and dissipated strain energy nonlinearly increase with actual unloading stress levels, expressed as unified quadratic function relationships. Furthermore, the elastic strain energy and dissipated strain energy have linear relationships with the input strain energy. Through analyzing coefficients of variation of common parameters, it was found that the energy storage capacity of rock was not sensitive to the specimen size, and therefore, the energy storage coefficient could be considered an essential property of rock materials. [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]

The b value is a critical parameter that has been used to describe spatial and temporal size distribution characteristics in data from both natural seismicity and laboratory rock acoustic emission (AE) tests. However, unlike the magnitude used for b value estimation in earthquakes which corrects for hypocentral distance, the apparent amplitude of the AE, is most commonly used for b value estimation in the rock AE test. This ignores the effect of attenuation, which may modify the frequency–amplitude distribution and affect the b value results. Here, we investigate the attenuation effect on the estimate of b value from synthetic data generated by random sampling of a doubly truncated frequency–amplitude distribution and a known underlying b value from a statistical perspective. We generated AE source amplitudes that obey an exponential distribution with different theoretical b values and applied an attenuation operator to obtain apparent frequency–amplitude data for comparison with the true underlying distribution. The results show that the b value is unchanged within a specific interval of amplitude distribution after accounting for attenuation under the conditions examined here, and that data truncation is the primary cause of modification of the frequency–amplitude distribution in the presence of attenuation, rather than attenuation alone. In addition, we employed the same synthetic data simulation scheme to estimate the minimum data volume for accurate estimation of the underlying b value from the apparent amplitude distribution. We found that the determination of the minimum data volume is influenced by the theoretical b value of the underlying distribution: the higher the theoretical b value, the larger the minimum data volume required, varying from 200 events from b  < 1.5 to 300 for b  > 1.5. [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]

Understanding the shear damage evolution of natural rock joints is of key importance for the stability of rock slopes and underground tunnels. However, the shear damage evolution of natural joints is difficult to determine due to the ubiquitous features of natural rock joints and the invisibility of the shearing process. In this study, the combined technology of "3D scanning + 3D engraving" is used to produce three types of natural rock joint specimens with identical surface morphology characteristics, and AE monitoring is applied to direct shear tests to reveal the shear damage evolution of natural rock joints. A multi-aspect analysis (including shear damage characteristics, dynamic analysis of failure types, and the maximum percentage of microcrack length in the shearing process) is conducted to recognize the shear damage evolution of natural joints. The results indicate that the shear damage characteristics of natural joints are localized and inhomogeneous, the timing and type of main failure in the shearing process will change when normal stress increases, and the increase in normal stress will first suppress and subsequently promote the maximum percentage of microcrack length. These results will encourage a better understanding of the shear failure mechanism of natural joints and provide references for the precursor identification of shear disasters in geotechnical engineering. Highlights: New way of "3D scanning + 3D engraving" is presented to produce a natural rock joint. An improved identification method for failure types and crack length is proposed. Shear damage characteristics of rock joints in the shearing process are exposed. [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]

In deep mining and excavation of tunnels with high geothermal, the surrounding rock is not only subjected to high ground stress but also subjected to high temperature. Temperature will change mechanical characteristics and energy storage capacity of rocks, as well as increase the destructiveness and randomness of rockburst. To reveal the mechanism of high-temperature strain burst in deep rock, the rockburst tests from uniaxial compression to three-dimensional compression were reviewed, and the research results of the minimum principal stress rapid unloading, true-triaxial loading with one free face, and dynamic disturbance triggered pre-heated granite rockburst simulation tests were focused on. According to the occurrence state of country rock for deep high-temperature and stress state in the whole process during excavation, six development directions for high-temperature strain rockburst simulation tests were proposed: (1) constructing the damage constitutive models of high-temperature rocks according to linear energy dissipation law; (2) developing the true triaxial rockburst simulation testing system accomplishing the function of "real-time high temperature + unloading + dynamic disturbance"; (3) considering the true triaxial rockburst simulation test after microwave irradiation; (4) developing the real-time high-temperature rockburst simulation testing device for large-size specimens and internal unloading; (5) focusing on the energy actuating mechanism for deep high-temperature rock failure via rockburst simulation tests; and (6) implementing the three-dimensional rockburst simulation test on the basis of deep in situ coring. [ABSTRACT FROM AUTHOR]

The tensile strength of rock is a crucial parameter for the stability assessment and reinforcement design of rock engineering, which is commonly determined by indirect tension test or uniaxial direct tension test. However, the rock in slopes and underground caverns is often in a direct tension stress state under confining pressure, due to the stress redistribution induced by excavation or mining. In this study, the direct tension tests of granite samples under both different confining pressures and tensile loading rates were carried out by an auxiliary apparatus installed in pressure chamber, to investigate the confined tensile strength and fracture surface morphology. High-precision 3D laser scanning was used to obtain the morphology data and the geometrical statistics of asperities on fracture surface, containing the distributions of height, dip angle and dip direction of the asperities. The tensile strength first increases and then decreases with the increase in confining pressure, indicating that the maximum tensile strength of tested granite is not the uniaxial tensile strength and appears in the condition of a certain confining pressure. The tensile strength slightly increases with the increase in tensile loading rate. The fracture surface is smoother as confining pressure increases, while is rougher with the increase in tensile loading rate. As confining pressure goes up, from a micro-point of view, the friction force and the locking force between grains of granite have a similar changing rule to the tensile strength. The roughness of fracture is closely related with both micro-fracture pattern between grains and macro-fracture pattern concerning tensile and shear properties. These provide a reasonable explanation for the correlation of the tensile strength and fracture roughness with confining pressure and loading rate. [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 D-shaped cross section is a commonly used tunnel cross section in underground engineering. To simulate the failure process of a D-shaped hole under deep three-dimensional (3D) high-stress conditions, true-triaxial tests were conducted on cubic granite specimens with a through D-shaped hole, and the failure process of the hole sidewall was recorded in real time. Results show that the spalling failure process of the D-shaped hole sidewall can be divided into four periods: calm, fine particle ejection, crack generation and propagation, and rock slab gradually buckling and spalling. Afterwards, symmetrical V-shaped notches were formed on both sidewalls between the corner and arch springing. The spalling failure shows tensile failure characteristics. Under high vertical stress and constant horizontal axial stress, increasing the lateral stress reduces the severity of the spalling failure and the depth of the V-shaped notch. The initial failure vertical stress of the D-shaped hole sidewall is higher than that of circular hole sidewall, and the failure of D-shaped hole sidewall is mainly characterized by static failure. The failure of the circular hole sidewall is a more severe dynamic failure. When the vertical applied stress is the maximum principal stress, the position of the V-shaped notch tip is 0.20–0.25 h (h is the height of the D-shaped tunnel) from the tunnel floor, whereas that in the circular tunnel is 0.5 d (d is the diameter of the circular tunnel) from the tunnel floor. Specific support schemes should therefore be designed for tunnels with different cross sections according to the damage location, depth of failure zone, and severity of failure. [ABSTRACT FROM AUTHOR]

The deep high prestatically loaded rock is often subjected to low-frequency dynamic disturbance and exhibits unusual strength characteristics, and thus, it is important to investigate the strength characteristics under the coupling effect of prestatic load and low-frequency dynamic disturbance loading conditions. In this study, a series of point load tests were conducted on the high prestatically loaded marble subjected to low-frequency disturbance by the MTS system, focusing on exploring the role of prestatic load level and low-frequency disturbance frequency in the process of rock strength change. Based on the average static failure load (Fmax) of samples under the static point loading, the high prestatic load levels (Fp) were selected as 70%, 80%, and 90% of Fmax, the corresponding low-frequency dynamic disturbance was loaded by sinusoidal waves with amplitudes of 60%, 40%, and 20% of Fmax, and the low-frequency dynamic disturbance frequencies (f) are 1, 2, 5, and 10 Hz. The change curve of the point load strength with the prestatic load level or the disturbance frequency was analyzed, which indicates that the point load strength under the coupled high prestatic load and low-frequency dynamic disturbance load was significantly lower than that under the pure static loading, presenting a significant point load strength weakening effect. Only when Fp or f reaches a certain level, the point load strength decreases significantly as f or Fp increases. Moreover, the point load strength weakening rate was proposed to characterize the degree of strength weakening. The comprehensive analysis demonstrates that Fp has a greater effect on the point load strength weakening effect than f, which is mainly reflected in the point load strength weakening level dominated by the Fp, and the weakening degree is affected by f. [ABSTRACT FROM AUTHOR]

The quantitative determination of crack damage stress is of significant importance for investigating rock deformation and failure. In this study, a new quantitative method for determining the crack damage stress of rock materials was proposed based on acoustic emission (AE) signal detection. Ten rock materials were subjected to uniaxial compression testing, during which real-time AE signals and axial, lateral, and volumetric strain values were recorded. The AE cumulative count curves of the different rock materials were calculated based on the AE counts. These curves were divided into three stages as the axial stress increased: the slowly increasing stage, the steady stage, and the sharply increasing stage. The point where the sharply increasing stage began was defined as the PR point and could be accurately determined based on a fitting optimization method. Then, the damage stress was calculated by using the crack volumetric strain model. Finally, the relationship between the R stress (axial stress corresponding to the PR point) and the crack damage stress was investigated for the ten rock materials. The results showed that there was a good correspondence between the R stress and the crack damage stress. Hence, the R stress can be used to determine the crack damage stress and the starting point of the unstable crack growth stage in rock materials. [ABSTRACT FROM AUTHOR]

This special issue compiles seventy-six original papers covering the following topics: mechanical properties and fracture behavior of deep rock, rock failure behavior under multifield coupling and multiscale systems, dynamic failure characteristics and constitutive properties of deep rock, mechanical behaviours of rock fractures during shearing, energy evolution characteristics during rock fracturing, experimental or numerical simulation of rockbursts, failure mechanism of spalling in deep tunnels, rock and structure response under blast and impulsive loading, and prevention and control of disasters in deep rock engineering. G. Deng et al. numerically simulate the evolution of mining-induced fracture network in a coal seam and its overburden under the top coal caving method. Q. Ma et al. give the dynamic behavior and energy evolution characteristic of deep roadway sandstone containing weakly filled joint at various angles. [Extracted from the article]

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 investigate energy dissipation and particle size distribution of rock under dynamic loads, a series of dynamic compression tests of granite specimens were conducted using a conventional split-Hopkinson pressure bar (SHPB) device with a high-speed camera. The experimental results show that the dissipated energy increases linearly with an increasing incident energy, following two different inclined paths connected by a critical incident energy, and the linear energy dissipation law in the dynamic compression test has been confirmed. This critical incident energy was found to be 0.29–0.33 MJ/m3. As the incident energy was smaller than the critical incident energy, the rock specimens remained unruptured after the impact. When the incident energy was greater than the critical incident energy, the rock specimens were ruptured or fragmented after the impact. In addition, the experimental results indicate that the dissipated energy and energy consumption ratio of a rock specimen, either unruptured or fragmented, increase with an increasing strain rate. Furthermore, it was found that fragment sizes at each mesh decrease with an increasing incident energy; that is, fragmentation becomes finer as incident energy increases. [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 energy evolution and storage performances of rock under uniaxial cyclic compression, a series of uniaxial cyclic loading and unloading compression tests were conducted on Green sandstone and Yueyang granite. Two methods for calculating the total input energy of the specimen under each cycle were proposed. One is based on the actual stress-strain curve of the specimen (ASC method); the other is based on the stress-strain envelope curve during the loading process (SEC method). The experimental results show that, for those two methods, the total input energy, elastic energy, and dissipated energy of the specimen show a quadratic function increasing trend with the increase of stress levels. Besides, the elastic energy increases linearly with the increase of total input energy for both methods, which confirms that the linear energy storage law is also applicable to rock materials under uniaxial cyclic loading and unloading compression conditions. Moreover, the uniaxial compression energy storage coefficient calculated by the SEC method is highly close to that obtained based on the single cycle loading and unloading test, which indicates that the uniaxial compression energy storage coefficient of rock can also be calculated by multiple cyclic loading and unloading test. In conclusion, the linear energy storage law is a basic physical property of rock materials, and the uniaxial compression energy storage coefficient is a physical index reflecting the energy storage capacity of rock materials. [ABSTRACT FROM AUTHOR]

A series of dynamic fracture experiments on semicircular bend (SCB) marble specimens were conducted to characterize the loading rate effect using the INSTRON testing machine and the modified SHPB testing system. The fracture toughness of the marble specimens was measured from a low loading rate to a high loading rate (10-3~106 MPa·m1/2s-1). The results show that the fracture toughness will increase with the loading rate. Since the fracture toughness at a magnitude of 10-3 MPa·m1/2s-1 is regarded as the static fracture toughness, the specific value of DI F f (the dynamic increase factor of fracture toughness) can be obtained at the other loading magnitudes from dynamic fracture tests. To describe the variation in DI F f from low to high loading rates, a new continuous model of DI F f was put forward to express the quantitative relation between the loading rate and rock dynamic fracture toughness. It is shown that the new DI F f model can accurately describe the loading rate effect on the dynamic fracture testing data for rock materials. [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]

The processes of deformation and failure in rocks are unavoidably accompanied by the absorption, storage, dissipation, and release of energy. To explore energy allocation during rock shear fracturing, two series of single loading and unloading preset angle shear tests at inclined angles of 60° and 50° were performed on red sandstone and granite by varying the experimental unloading level. The area integral approach was employed to interpret the load–displacement responses of the rock specimens via calculation of the energy parameters (referring to the external input energy, internal elastic energy and internal dissipation energy). The interpretations of the results revealed that the increase in the experimental unloading level nonlinearly increases the internal elastic energy, internal dissipation energy and external input energy; these relationships can be described by quadratic functions. It was also realized that under different experimental unloading levels, not only the internal elastic energy but also the internal dissipation energy is closely proportional to the external input energy. The proportional energy relationship can be used to quantify the internal elastic energy and internal dissipation energy at any expected experimental unloading levels, and a real-time calculation model for the internal elastic energy and internal dissipation energy in the pre-peak duration (including the peak point) was introduced. Meanwhile, an invariable feature for the ultimate internal elastic index Wed (the ratio of ultimate internal elastic energy to peak internal dissipation energy) was captured via quantitative analysis. Additionally, the energy allocation manner and transfer mechanisms of rocks bearing varied loading forms (including uniaxial compression, Brazilian splitting, point load, semicircular bending, and preset angle shear) were also comprehensively compared considering three basic rock fracture modes: the tensile, shear, and hybrid failure (mixed tensile-shear) modes. Thus, the proportional distribution patterns of internal elastic energy and internal dissipation energy or the linear correlations among the three energy parameters can be universally observed during the failure of homogeneous rocks, despite distinct loading forms under one-dimensional stress conditions. [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]

Keywords: Preset angle shear; Direct shear; Triaxial compression; Cohesion; Internal friction angle; Shear strength parameters EN Preset angle shear Direct shear Triaxial compression Cohesion Internal friction angle Shear strength parameters 2505 2519 15 05/08/20 20200501 NES 200501 Introduction Estimation of shear strength parameters, which are generally known as the cohesion and internal friction angle ( I c i and I i ) in the Mohr-Coulomb (M-C) strength criterion, plays an essential role in rock mechanics and rock engineering (Zhao [34]; Kahraman et al. [14]; Alejano and Carranzatorres [1]; Gong et al. [7]). 6 Shear strength parameters of a marble and b red sandstone obtained by three different testing methods Comparison of Testing Methods for Rock Shear Strength Parameters Hereinbefore, data deviations were observed for marble and red sandstone under the three testing conditions. [Extracted from the article]

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]

Identifying Crack Compaction and Crack Damage Stress Thresholds of Rock Using Load-Unload Response Ratio (LURR)Theory To investigate the LURR value and stress thresholds of different rocks in USLUC conditions, ten rocks (the names and origins of ten rocks are shown in Table 1) were collected and used in this study. 4 Stress-strain curves in the uniaxial step load-unload compression test: a, b axial stress-strain curves of ten rocks; c-e axial stress-lateral strain curves, axial stress-volumetric strain curves, and volumetric strain-axial strain curves of nine rocks 6 Axial stress-strain curves, axial stress-volumetric strain curves, LURR curves, and LURR curves for ten rocks. [Extracted from the article]

To investigate the energy evolution characteristics of rock materials under uniaxial compression, the single-cyclic loading–unloading uniaxial compression tests of four rock materials (Qingshan granite, Yellow sandstone, Longdong limestone and Black sandstone) were conducted under five unloading stress levels. The stress–strain curves and failure characteristics of rock specimens under the single-cyclic loading–unloading uniaxial compression tests basically corresponded with those of under uniaxial compression, which indicates that single-cyclic loading–unloading has minimal effects on the variations in the loading–deformation response of rocks. The input energy density, elastic energy density and dissipated energy density of four rocks under five unloading stress levels were calculated using the graphical integration method, and variation characteristics of those three energy density parameters with different unloading stress levels were explored. The results show that all three energy density parameters above increased nonlinearly with increasing unloading stress level as quadratic polynomial functions. Meanwhile, both the elastic and dissipated energy density increased linearly when the input energy density increased, and the linear energy storage and dissipation laws for rock materials were observed. Furthermore, a linear relationship between the dissipated and elastic energy density was also proposed. Using the linear energy storage or dissipation law, the elastic and dissipated energy density at any stress levels can be calculated, and the internal elastic (or dissipated) energy density at peak compressive strength (the peak elastic and dissipated energy density for short) can be obtained. The ratio of the elastic energy density to dissipated energy density with increasing input energy density was investigated using a new method, and the results show that this ratio tends to be constant at the peak compressive strength of rock specimens. [ABSTRACT FROM AUTHOR]

The dynamic mechanical properties and behavior of transversely isotropic rock are vital in engineering applications. In this study, the dynamic compressive properties of a low anisotropy slate are investigated for five sample groups (θ = 0°, 30°, 45°, 60°, and 90°) using a split Hopkinson pressure bar (SHPB) with three loading levels. A cone-shaped striker is used for achieving a dynamic stress equilibrium. The test results illustrate that the failure patterns of slate at a low loading level can be divided into four major types and that bedding plays an increasingly dominant role in the failure of samples as the dip angle increases. The tensile splitting effect gradually begins to have a prominent influence on the failure patterns as the loading level increases. Moreover, the variations in the failure patterns may lead to a decrease in the strain rate effect when the dip angle increases from θ = 30° to θ = 60°. At θ = 90°, the measured dynamic critical strength is less than the static strength, possibly due to the anisotropic effect of bedding directivity. In addition, the dynamic strength of the slate exhibits a higher anisotropy under dynamic loading, and the strength anisotropy index first decreases and then increases as the loading level increases. [ABSTRACT FROM AUTHOR]

A series of experimental tests were conducted to investigate the effects of loading rate on the tensile strength of sandstone by using four test methods, including a direct tensile method and three typical Brazilian disc methods (plate loading, circular arc loading, and strip loading). The loading rates used in these tests varied from 10−2 MPa/s to 100 MPa/s. The results show that the rate effects are clear for these test methods, and the tensile strength of sandstone will increase linearly with the logarithm of the loading rate. At the same loading rate, it is found that the tensile strengths of the sandstone specimens under plate loading and arc loading are relatively similar and are much greater than the direct tensile strength, while the tensile strength under strip loading is less than the direct strength. A comprehensive comparison suggested that the strip loading method can be adopted for the Brazilian disc test, while the obtained strength should be modified with a coefficient of 1.37 to obtain the direct tensile strength. [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]

In order to investigate the high loading rate effect on the behaviour and mechanical properties of coal-rock combined body, the dynamic compressive tests were conducted by using the Split-Hopkinson Pressure Bar (SHPB) device under the loading rate range from 2.7×105 MPa/s to 4.0×105 MPa/s. The stress-strain curves, dynamic peak stress and strain, elastic modulus, and energy distribution law of coal-rock combined body under different loading rates were analyzed and discussed. The results show that the dynamic stress-strain curves of coal-rock combined body have a double-peak feature under high loading rate range, which can be divided into the initial bearing stage, the bearing decline stage, the bearing enhance stage, and the unstable stage. The first peak stress of the coal-rock combined body is independent of the loading rate, while the dynamic compressive strength (the second peak stress) and dynamic peak strain (the second peak strain) have a strong loading rate effect and will generally increase linearly with the loading rate. The first and second elastic moduli of coal-rock combined body are not sensitive to the loading rate. With the increase of the loading rate, the incident energy and reflective energy of coal-rock combined body increase rapidly, while the change of transmitted energy is very small. The absorption energy ratio of the coal-rock combined body shows a good linear law with the incident energy under different loading rates. [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]

Open joints have significantly different effects on stress wave propagation across them as compared to closed and filled joints. In the present study, a theoretical model is developed based on the analysis of interaction process between stress waves and a single open joint. The analytical solutions to the energy transmission coefficient are mathematically derived for stress waves across an open joint. Parametric studies are conducted to evaluate the effects of various parameters on the energy transmission coefficient. It is found that the energy transmission coefficient follows a similar trend for all types of stress waves, but stress waves with different waveforms have different values. The energy transmission coefficient increases with the increase in the wave amplitude and duration, but decreases with the gap width. It also increases at the outset, and then decreases gradually with the increase in the incident angle for rectangle, symmetric triangle and ascending triangle waves, but it decreases with the incident angle for sine and descending triangle waves. Furthermore, different-shaped stress waves have different critical gap widths for wave transmission. The optimal incident angle and the critical gap width increase as the wave duration increases, but the critical stress amplitude decreases. [ABSTRACT FROM AUTHOR]

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