To systematically assess the rockburst proneness considering specimen shape,multiple groups of laboratory tests were performed on 5 rock materials in cylindrical and cuboid shapes.The linear energy storage(LES)law of ...To systematically assess the rockburst proneness considering specimen shape,multiple groups of laboratory tests were performed on 5 rock materials in cylindrical and cuboid shapes.The linear energy storage(LES)law of both cylindrical and cuboid rock specimens under uniaxial compressive load was confirmed,and the energy storage coefficient was found to be unrelated to specimen shape.On the basis of LES law,two rockburst proneness indexes,namely the strain energy storage index(W_(et))and the potential energy of elastic strain(PES),were modified.Subsequently,the W_(et),PES,peak-strength strain energy storage index(W_(et))p,and peak-strength potential energy of elastic strain(PESp)were used to assess the rockburst proneness of the cylindrical and cuboid specimens.In addition,the fragment ejection course of specimens under test was recorded by a high-speed camera.Then,the rockburst proneness judgments obtained from the 4 indexes were compared with the qualitative data during rock destruction.The results show that,under similar stress conditions,specimen shape has an ignorable effect on the rockburst proneness as a whole.The judgment accuracy of the two modified indexes,especially that of the PESp,is favorably improved to evaluate the rockburst proneness of both cylindrical and cuboid specimens.However,misjudgment ofW_(et)^(p)and PESp may still occur in the assessment of rockburst proneness as these two indexes only consider the energy state before rock peak strength and the W_(et)^(p)is formulated in a ratio form.展开更多
The effect of the elastic strain energy on the core-shell structures was studied in an Al-0.06Sc-0.02Er （at.%） alloy. A theoretical model for the calculation of the elastic strain energy caused by core-shell precipi...The effect of the elastic strain energy on the core-shell structures was studied in an Al-0.06Sc-0.02Er （at.%） alloy. A theoretical model for the calculation of the elastic strain energy caused by core-shell precipitates, which is applicable to materials with weak elastic anisotropy, was adopted. It was demonstrated that the partitioning of Er to the precipitate core did not reduce the elastic strain energy as expected in the previous study. The resistance due to the elastic strain energy to form an Al3（Sc0.36Ero.64）-Al3（Sc0.8Er0.2） core-shell precipitate was quite small, and could be easily overcome by the decrease of the total interracial energy, which was consistent with the previous experimental results. On the other hand, the resistance due to the elastic strain energy to form an Al3Er-Al3Sc core-shell precipitate was much larger than that to form an Al3（Sc0.36Er0.64）-Al3（Sc0.8Er0.2） core-shell precipitate, thus the partitioning of all the Er atoms to the core was strongly hindered by the elastic strain energy and was not observed in the experiment of the previous study.展开更多
There is an urgent need to develop optimal solutions for deformation control of deep high‐stress roadways,one of the critical problems in underground engineering.The previously proposed four‐dimensional support(here...There is an urgent need to develop optimal solutions for deformation control of deep high‐stress roadways,one of the critical problems in underground engineering.The previously proposed four‐dimensional support(hereinafter 4D support),as a new support technology,can set the roadway surrounding rock under three‐dimensional pressure in the new balanced structure,and prevent instability of surrounding rock in underground engineering.However,the influence of roadway depth and creep deformation on the surrounding rock supported by 4D support is still unknown.This study investigated the influence of roadway depth and creep deformation time on the instability of surrounding rock by analyzing the energy development.The elastic strain energy was analyzed using the program redeveloped in FLAC3D.The numerical simulation results indicate that the combined support mode of 4D roof supports and conventional side supports is highly applicable to the stability control of surrounding rock with a roadway depth exceeding 520 m.With the increase of roadway depth,4D support can effectively restrain the area and depth of plastic deformation in the surrounding rock.Further,4D support limits the accumulation range and rate of elastic strain energy as the creep deformation time increases.4D support can effectively reduce the plastic deformation of roadway surrounding rock and maintain the stability for a long deformation period of 6 months.As confirmed by in situ monitoring results,4D support is more effective for the long‐term stability control of surrounding rock than conventional support.展开更多
The coherent elastic strain-induced morphological transformation of a binarycubic model alloy was simulated with different strain energy parameters. The microscopic diffusionequation was combined with the theory of mi...The coherent elastic strain-induced morphological transformation of a binarycubic model alloy was simulated with different strain energy parameters. The microscopic diffusionequation was combined with the theory of microscopic elasticity. The results show that when thestrain energy is neglected, the randomly distributed equiaxed particles are obtained with isotropiccharacteristic. It is coarsening that follows the Ostwald ripening mechanism: smaller particlesdwindle and larger particles grow; when the elastic strain is considered, plate precipitates tend toalign along the elastically soft directions <01> with anisotropic characteristic. The particlesgrow in the soft directions and coarsen further; particles dwindle in out of the soft directions.While the coarsening of the particles localized in the same row or column follows the rule: smallerparticles shrink and larger ones grow.展开更多
Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high c...Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.展开更多
Coal burst remains one of the gravest safety risks that will be encountered in mining in the future, because the stress conditions will become more complex as mining depths increase. Various influencing elements exist...Coal burst remains one of the gravest safety risks that will be encountered in mining in the future, because the stress conditions will become more complex as mining depths increase. Various influencing elements exist, and varied geological and mining circumstances might result in diverse coal burst phenomena. The impact propensity of coal has variations as a result of the distinct physical and mechanical qualities of each. To identify the impact propensity of coal and then understand the rules of coal burst occurrence, laboratory tests can be conducted to identify the physical and mechanical parameters affecting coal samples. The mechanical properties, energy absorption, and energy dissipation characteristics of coal samples were examined experimentally in this paper using coal samples that were taken from the mine. On the basis of the evaluation of the impact inclination parameters for four fundamental coal samples, novel impact inclination indicators and the relationship between the fractures in the coal sample and the impact inclination parameters were discussed. The following are the key conclusions: 1) On-site samples of No. 15 coal from the Qi yuan Coal Mine were taken (15 s) and processed in accordance with the guidelines for the coal specimen impact inclination test. The accuracy of the specimen was sufficient for the test. 2) Analysis is done on the mechanical relevance and calculation techniques of the four fundamental coal sample impact tendency characteristics, dynamic failure time (DT), elastic strain energy index (W<sub>ET</sub>), impact energy index (K<sub>E</sub>), as well as uniaxial compressive strength (R<sub>C</sub>). 3) Regarding the rock burst danger of rock samples, the potential use of the ratio of pre-peak and post- peak deformation modulus to Kλ and the residual elastic strain energy index C<sub>EF</sub> as the impact propensity indices of coal samples are discussed. It is possible to utilize two new impact propensity indices to evaluate the impact propensity of coal samples, according to test results that reveal a linear correlation between two new impact inclination indexes and four fundamental impact tendency indexes. 4) The statistical analysis of the crack ratio with the four impact propensity indicators after coal specimen failure, and the correlation among the crack ratio with the indicators, are both done. The findings indicate that the four impact propensity indicators have a linear relationship with the crack ratio of the coal sample surface cracks.展开更多
A number of rockburst accidents occurring in soft coal seams have shown that the rockburst mechanism involved in soft coal seams is significantly different from that involved in hard coal seams. Therefore, the method ...A number of rockburst accidents occurring in soft coal seams have shown that the rockburst mechanism involved in soft coal seams is significantly different from that involved in hard coal seams. Therefore, the method used to evaluate rockburst in hard coal seams is not applicable to soft coal seams. This paper established an energy integral model for the rockburst-inducing area and a friction work calculation model for the plastic area. If the remaining energy after the coal seam is broken in the rockburstinducing area is greater than the friction work required for the coal to burst out, then a rockburst accident will occur. Mechanisms of ‘‘quaking without bursting" and ‘‘quaking and bursting" are clarified for soft coal seams and corresponding control measures are proposed as the optimization of roadway layouts and use of ‘‘three strong systems"(strong de-stressing, strong supporting, and strong monitoring).展开更多
The anchoring properties of substrate with a grating surface are investigated analytically. The alignment of nematic liquid crystal （NLC） in a grating surface originates from two mechanisms, thus the anchoring energ...The anchoring properties of substrate with a grating surface are investigated analytically. The alignment of nematic liquid crystal （NLC） in a grating surface originates from two mechanisms, thus the anchoring energy consists of two parts. One originates from the interaction potential between NLC molecules and the molecules on the substrate surface, and the other stems from the increased elastic strain energy. Based on the two mechanisms, the expression of anchoring energy per unit area of a projected plane of this grating surface is deduced and called the equivalent anchoring energy formula. Both the strength and the easy direction of equivalent anchoring energy are a function of the geometrical parameters （amplitude and pitch） of a grating surface. By using this formula, the grating surface can be replaced by its projected plane and its anchoring properties can be described by the equivalent anchoring energy formula.展开更多
The acoustic emission （AE） features in rock fracture are simulated numerically with discrete element model （DEM）. The specimen is constructed by using spherical particles bonded via the parallel bond model. As a r...The acoustic emission （AE） features in rock fracture are simulated numerically with discrete element model （DEM）. The specimen is constructed by using spherical particles bonded via the parallel bond model. As a result of the heterogeneity in rock specimen, the failure criterion of bonded particle is coupled by the shear and tensile strengths, which follow a normal probability distribution. The Kaiser effect is simulated in the fracture process, for a cubic rock specimen under uniaxial compression with a constant rate. The AE number is estimated with breakages of bonded particles using a pair of parameters, in the temporal and spatial scale, respectively. It is found that the AE numbers and the elastic energy release curves coincide. The range for the Kaiser effect from the AE number and the elastic energy release are the same. Furthermore, the frequency-magnitude relation of the AE number shows that the value of B determined with DEM is consistent with the experimental data.展开更多
A method for fairing a surface composed of a set of discrete data points distributed in a nonrectangular topological mesh is presented.All curves are expressed by nonuniform cubic B-spline curves.The fairing method is...A method for fairing a surface composed of a set of discrete data points distributed in a nonrectangular topological mesh is presented.All curves are expressed by nonuniform cubic B-spline curves.The fairing method is minimizing the elastic strain energy of mesh curves and of springs at- tached to the data points.The fairing surface can be generated by interpolating through the mesh curves.The generation and fairing of a ship hull surface is given as an example.展开更多
By the aid of irreducible decomposition, the average Eshelby tensor can be expressed by two complex coefficients in 2D Eshelby problem. This paper proved the limitation of complex coefficients based on the span of ela...By the aid of irreducible decomposition, the average Eshelby tensor can be expressed by two complex coefficients in 2D Eshelby problem. This paper proved the limitation of complex coefficients based on the span of elastic strain energy density. More discussions yielded the constraints on the sampling of module and phase difference of complex coefficients. Using this information, we obtained that the maximum relative error is 65.78% after an ellipse approximation. These results, as a supplement to our previous paper, further implied that Eshelby＇s solution for an ellipsoidal inclusion could not be applied to non-ellipsoidal inclusions without taking care.展开更多
基金National Natural Science Foundation of China,Grant/Award Number:41877272Fundamental Research Funds for the Central Universities,Grant/Award Number:2242022k30054。
文摘To systematically assess the rockburst proneness considering specimen shape,multiple groups of laboratory tests were performed on 5 rock materials in cylindrical and cuboid shapes.The linear energy storage(LES)law of both cylindrical and cuboid rock specimens under uniaxial compressive load was confirmed,and the energy storage coefficient was found to be unrelated to specimen shape.On the basis of LES law,two rockburst proneness indexes,namely the strain energy storage index(W_(et))and the potential energy of elastic strain(PES),were modified.Subsequently,the W_(et),PES,peak-strength strain energy storage index(W_(et))p,and peak-strength potential energy of elastic strain(PESp)were used to assess the rockburst proneness of the cylindrical and cuboid specimens.In addition,the fragment ejection course of specimens under test was recorded by a high-speed camera.Then,the rockburst proneness judgments obtained from the 4 indexes were compared with the qualitative data during rock destruction.The results show that,under similar stress conditions,specimen shape has an ignorable effect on the rockburst proneness as a whole.The judgment accuracy of the two modified indexes,especially that of the PESp,is favorably improved to evaluate the rockburst proneness of both cylindrical and cuboid specimens.However,misjudgment ofW_(et)^(p)and PESp may still occur in the assessment of rockburst proneness as these two indexes only consider the energy state before rock peak strength and the W_(et)^(p)is formulated in a ratio form.
基金Project supported by National Natural Science Foundation of China (50731002, 51271027)
文摘The effect of the elastic strain energy on the core-shell structures was studied in an Al-0.06Sc-0.02Er （at.%） alloy. A theoretical model for the calculation of the elastic strain energy caused by core-shell precipitates, which is applicable to materials with weak elastic anisotropy, was adopted. It was demonstrated that the partitioning of Er to the precipitate core did not reduce the elastic strain energy as expected in the previous study. The resistance due to the elastic strain energy to form an Al3（Sc0.36Ero.64）-Al3（Sc0.8Er0.2） core-shell precipitate was quite small, and could be easily overcome by the decrease of the total interracial energy, which was consistent with the previous experimental results. On the other hand, the resistance due to the elastic strain energy to form an Al3Er-Al3Sc core-shell precipitate was much larger than that to form an Al3（Sc0.36Er0.64）-Al3（Sc0.8Er0.2） core-shell precipitate, thus the partitioning of all the Er atoms to the core was strongly hindered by the elastic strain energy and was not observed in the experiment of the previous study.
基金support from the National Key Research and Development Program of China(Nos.2023YFC2907300 and 2019YFE0118500)the National Natural Science Foundation of China(Nos.U22A20598 and 52104107)the Natural Science Foundation of Jiangsu Province(No.BK20200634).
文摘There is an urgent need to develop optimal solutions for deformation control of deep high‐stress roadways,one of the critical problems in underground engineering.The previously proposed four‐dimensional support(hereinafter 4D support),as a new support technology,can set the roadway surrounding rock under three‐dimensional pressure in the new balanced structure,and prevent instability of surrounding rock in underground engineering.However,the influence of roadway depth and creep deformation on the surrounding rock supported by 4D support is still unknown.This study investigated the influence of roadway depth and creep deformation time on the instability of surrounding rock by analyzing the energy development.The elastic strain energy was analyzed using the program redeveloped in FLAC3D.The numerical simulation results indicate that the combined support mode of 4D roof supports and conventional side supports is highly applicable to the stability control of surrounding rock with a roadway depth exceeding 520 m.With the increase of roadway depth,4D support can effectively restrain the area and depth of plastic deformation in the surrounding rock.Further,4D support limits the accumulation range and rate of elastic strain energy as the creep deformation time increases.4D support can effectively reduce the plastic deformation of roadway surrounding rock and maintain the stability for a long deformation period of 6 months.As confirmed by in situ monitoring results,4D support is more effective for the long‐term stability control of surrounding rock than conventional support.
基金National Natural Science Foundation of China (No.50071046).
文摘The coherent elastic strain-induced morphological transformation of a binarycubic model alloy was simulated with different strain energy parameters. The microscopic diffusionequation was combined with the theory of microscopic elasticity. The results show that when thestrain energy is neglected, the randomly distributed equiaxed particles are obtained with isotropiccharacteristic. It is coarsening that follows the Ostwald ripening mechanism: smaller particlesdwindle and larger particles grow; when the elastic strain is considered, plate precipitates tend toalign along the elastically soft directions <01> with anisotropic characteristic. The particlesgrow in the soft directions and coarsen further; particles dwindle in out of the soft directions.While the coarsening of the particles localized in the same row or column follows the rule: smallerparticles shrink and larger ones grow.
基金supports by National Natural Science Foundation of China(Grant Nos.51874351 and 52078495)Excellent Postdoctoral Innovative Talents Project of Hunan Province,China(Grant No.2020RC2001).
文摘Study on crack propagation process of brittle rock is of most significance for cracking-arrest design and cracking-network optimization in rock engineering.Phase-field model(PFM)has advantages of simplicity and high convergence over the common numerical methods(e.g.finite element method,discrete element method,and particle manifold method)in dealing with three-dimensional and multicrack problems.However,current PFMs are mainly used to simulate mode-I(tensile)crack propagation but difficult to effectively simulate mode-II(shear)crack propagation.In this paper,a new mixed-mode PFM is established to simulate both mode-I and mode-II crack propagation of brittle rock by distinguishing the volumetric elastic strain energy and deviatoric elastic strain energy in the total elastic strain energy and considering the effect of compressive stress on mode-II crack propagation.Numerical solution method of the new mixed-mode PFM is proposed based on the staggered solution method with self-programmed subroutines UMAT and HETVAL of ABAQUS software.Three examples calculated using different PFMs as well as test results are presented for comparison.The results show that compared with the conventional PFM(which only simulates the tensile wing crack but not mode-II crack propagation)and the modified mixed-mode PFM(which has difficulty in simulating the shear anti-wing crack),the new mixed-mode PFM can successfully simulate the whole trajectories of mixed-mode crack propagation(including the tensile wing crack,shear secondary crack,and shear anti-wing crack)and mode-II crack propagation,which are close to the test results.It can be further extended to simulate multicrack propagation of anisotropic rock under multi-field coupling loads.
文摘Coal burst remains one of the gravest safety risks that will be encountered in mining in the future, because the stress conditions will become more complex as mining depths increase. Various influencing elements exist, and varied geological and mining circumstances might result in diverse coal burst phenomena. The impact propensity of coal has variations as a result of the distinct physical and mechanical qualities of each. To identify the impact propensity of coal and then understand the rules of coal burst occurrence, laboratory tests can be conducted to identify the physical and mechanical parameters affecting coal samples. The mechanical properties, energy absorption, and energy dissipation characteristics of coal samples were examined experimentally in this paper using coal samples that were taken from the mine. On the basis of the evaluation of the impact inclination parameters for four fundamental coal samples, novel impact inclination indicators and the relationship between the fractures in the coal sample and the impact inclination parameters were discussed. The following are the key conclusions: 1) On-site samples of No. 15 coal from the Qi yuan Coal Mine were taken (15 s) and processed in accordance with the guidelines for the coal specimen impact inclination test. The accuracy of the specimen was sufficient for the test. 2) Analysis is done on the mechanical relevance and calculation techniques of the four fundamental coal sample impact tendency characteristics, dynamic failure time (DT), elastic strain energy index (W<sub>ET</sub>), impact energy index (K<sub>E</sub>), as well as uniaxial compressive strength (R<sub>C</sub>). 3) Regarding the rock burst danger of rock samples, the potential use of the ratio of pre-peak and post- peak deformation modulus to Kλ and the residual elastic strain energy index C<sub>EF</sub> as the impact propensity indices of coal samples are discussed. It is possible to utilize two new impact propensity indices to evaluate the impact propensity of coal samples, according to test results that reveal a linear correlation between two new impact inclination indexes and four fundamental impact tendency indexes. 4) The statistical analysis of the crack ratio with the four impact propensity indicators after coal specimen failure, and the correlation among the crack ratio with the indicators, are both done. The findings indicate that the four impact propensity indicators have a linear relationship with the crack ratio of the coal sample surface cracks.
基金Financial supports for this work by the National Program on Key Basic Research Project (No.210CB226800)the National Natural Science Foundation of China (Nos.51274022 and 51174016)
文摘A number of rockburst accidents occurring in soft coal seams have shown that the rockburst mechanism involved in soft coal seams is significantly different from that involved in hard coal seams. Therefore, the method used to evaluate rockburst in hard coal seams is not applicable to soft coal seams. This paper established an energy integral model for the rockburst-inducing area and a friction work calculation model for the plastic area. If the remaining energy after the coal seam is broken in the rockburstinducing area is greater than the friction work required for the coal to burst out, then a rockburst accident will occur. Mechanisms of ‘‘quaking without bursting" and ‘‘quaking and bursting" are clarified for soft coal seams and corresponding control measures are proposed as the optimization of roadway layouts and use of ‘‘three strong systems"(strong de-stressing, strong supporting, and strong monitoring).
文摘The anchoring properties of substrate with a grating surface are investigated analytically. The alignment of nematic liquid crystal （NLC） in a grating surface originates from two mechanisms, thus the anchoring energy consists of two parts. One originates from the interaction potential between NLC molecules and the molecules on the substrate surface, and the other stems from the increased elastic strain energy. Based on the two mechanisms, the expression of anchoring energy per unit area of a projected plane of this grating surface is deduced and called the equivalent anchoring energy formula. Both the strength and the easy direction of equivalent anchoring energy are a function of the geometrical parameters （amplitude and pitch） of a grating surface. By using this formula, the grating surface can be replaced by its projected plane and its anchoring properties can be described by the equivalent anchoring energy formula.
基金supported by the National Basic Research Program of China (2010CB731502)
文摘The acoustic emission （AE） features in rock fracture are simulated numerically with discrete element model （DEM）. The specimen is constructed by using spherical particles bonded via the parallel bond model. As a result of the heterogeneity in rock specimen, the failure criterion of bonded particle is coupled by the shear and tensile strengths, which follow a normal probability distribution. The Kaiser effect is simulated in the fracture process, for a cubic rock specimen under uniaxial compression with a constant rate. The AE number is estimated with breakages of bonded particles using a pair of parameters, in the temporal and spatial scale, respectively. It is found that the AE numbers and the elastic energy release curves coincide. The range for the Kaiser effect from the AE number and the elastic energy release are the same. Furthermore, the frequency-magnitude relation of the AE number shows that the value of B determined with DEM is consistent with the experimental data.
文摘A method for fairing a surface composed of a set of discrete data points distributed in a nonrectangular topological mesh is presented.All curves are expressed by nonuniform cubic B-spline curves.The fairing method is minimizing the elastic strain energy of mesh curves and of springs at- tached to the data points.The fairing surface can be generated by interpolating through the mesh curves.The generation and fairing of a ship hull surface is given as an example.
基金supported by the National Natural Science Foundation of China (Nos. 10872086 and 11072105)
文摘By the aid of irreducible decomposition, the average Eshelby tensor can be expressed by two complex coefficients in 2D Eshelby problem. This paper proved the limitation of complex coefficients based on the span of elastic strain energy density. More discussions yielded the constraints on the sampling of module and phase difference of complex coefficients. Using this information, we obtained that the maximum relative error is 65.78% after an ellipse approximation. These results, as a supplement to our previous paper, further implied that Eshelby＇s solution for an ellipsoidal inclusion could not be applied to non-ellipsoidal inclusions without taking care.
