Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a d...Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a deep circular tunnel in a rock mass with multiple weakness planes using a 2D combined finite element method/discrete element method(FEM/DEM).Conventional triaxial compression tests were performed on typical hard rock(marble)specimens under a range of confinement stress conditions to validate the rationale and accuracy of the proposed numerical approach.Parametric analysis was subsequently conducted to investigate the influence of inclination angle,and length on the crack propagation behavior,failure mode,energy evolution,and displacement distribution of the surrounding rock.The results show that the inclination angle strongly affects tunnel stability,and the failure intensity and damage range increase with increasing inclination angle and then decrease.The dynamic disasters are more likely with increasing weak plane length.Shearing and sliding along multiple weak planes are also consistently accompanied by kinetic energy fluctuations and surges after unloading,which implies a potentially violent dynamic response around a deeply-buried tunnel.Interactions between slabbing and shearing near the excavation boundaries are also discussed.The results presented here provide important insight into deep tunnel failure in hard rock influenced by both unloading disturbance and tectonic activation.展开更多
To reveal stress distribution and crack propagation of Brazilian discs under impact loads, dynamic tests were conducted with SHPB （split Hopkinson pressure bar） device. Stress states of specimens were monitored with...To reveal stress distribution and crack propagation of Brazilian discs under impact loads, dynamic tests were conducted with SHPB （split Hopkinson pressure bar） device. Stress states of specimens were monitored with strain gauges on specimen surface and SHPB bars. The failure process of specimen was recorded by ultra speed camera FASTCAM SAI.1 （675 000 fps）. Stress histories from strain gauges offer comprehensive information to evaluate the stress equilibrium of specimen in time and space. When a slowly rising load （with loading rates less than 1 200 N/s for d 50 mm bar） is applied, there is usually good stress equilibrium in specimen. The stress distribution after equilibrium is similar to its static counterpart. And the first crack initiates at the disc center and propagates along the load direction. But with the front of incident wave becoming steep, it is hard for specimens to get to stress equilibrium. The first crack may appear anywhere on the specimen together with multiple randomly distributed secondary cracks. For a valid dynamic Brazil test with stress equilibrium, the specimen will break into two halves neatly. While for tests with stress disequilibrium, missing strap may be found when broken halves of specimens are put together. For those specimens broken up neatly at center but having missing wedges at the loading areas, it is usually subjected to local buckling from SHPB bars.展开更多
Rock is more sensitive to tensile loading than compressive loading,since the tensile strength of rock is much lower than compressive strength.The fracture characteristics of rock in the tensile state are of great sign...Rock is more sensitive to tensile loading than compressive loading,since the tensile strength of rock is much lower than compressive strength.The fracture characteristics of rock in the tensile state are of great significance to the understanding of rock failure mechanisms.To this end,we have conducted numerical simulation researches on modeⅠcracking process of rock with varying homogeneity,using the Realistic Failure Process Analysis program.With the increase of homogeneity,cracks are concentrating to the ligament area with a decreasing number of crack bifurcations,and the main crack path is becoming smooth.Crack behaviors and mechanical properties are influenced significantly when the homogeneity index is in the range of 1.5 to 5.When the homogeneity index is greater than 30,they are not affected by rock homogeneity and the rock can be considered as essentially homogeneous.It is considered that the global and local strengths are affected by the distribution of rock mechanical properties at mesoscale,which influence the crack behaviors and mechanical characteristics.展开更多
Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolu...Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolution equation.展开更多
We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra E of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable mo...We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra E of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable model of the Giachetti-Johnson （G J） hierarchy whose Hamiltonian structure can also be derived by using the trace identity. This provides a much simplier construction method in comparing with the tedious variational identity approach. Furthermore, the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra gN. As an application, we apply the loop algebra E of the Lie algebra E to obtain a kind of expanding integrable model of the Kaup-Newell （KN） hierarchy which, consisting of two arbitrary parameters a and β, can be reduced to two nonlinear evolution equations. In addition, we use a loop algebra F of the Lie algebra F to obtain an expanding integrable model of the BT hierarchy whose Hamiltonian structure is the same as using the trace identity. Finally, we deduce five integrable systems in R3 based on the self-dual Yang-Mills equations, which include Poisson structures, irregular lines, and the reduced equations.展开更多
基金Projects(52004143,51774194)supported by the National Natural Science Foundation of ChinaProject(2020M670781)supported by the China Postdoctoral Science Foundation+2 种基金Project(SKLGDUEK2021)supported by the State Key Laboratory for GeoMechanics and Deep Underground Engineering,ChinaProject(U1806208)supported by the NSFC-Shandong Joint Fund,ChinaProject(2018GSF117023)supported by the Key Research and Development Program of Shandong Province,China。
文摘Natural geological structures in rock(e.g.,joints,weakness planes,defects)play a vital role in the stability of tunnels and underground operations during construction.We investigated the failure characteristics of a deep circular tunnel in a rock mass with multiple weakness planes using a 2D combined finite element method/discrete element method(FEM/DEM).Conventional triaxial compression tests were performed on typical hard rock(marble)specimens under a range of confinement stress conditions to validate the rationale and accuracy of the proposed numerical approach.Parametric analysis was subsequently conducted to investigate the influence of inclination angle,and length on the crack propagation behavior,failure mode,energy evolution,and displacement distribution of the surrounding rock.The results show that the inclination angle strongly affects tunnel stability,and the failure intensity and damage range increase with increasing inclination angle and then decrease.The dynamic disasters are more likely with increasing weak plane length.Shearing and sliding along multiple weak planes are also consistently accompanied by kinetic energy fluctuations and surges after unloading,which implies a potentially violent dynamic response around a deeply-buried tunnel.Interactions between slabbing and shearing near the excavation boundaries are also discussed.The results presented here provide important insight into deep tunnel failure in hard rock influenced by both unloading disturbance and tectonic activation.
基金Projects(50904079, 51274254, 50934006) supported by the National Natural Science Foundation of ChinaProject(2010CB732004) supported by the National Basic Research Program of ChinaProject(NCET-11-0528) supported by Program for New Century Excellent Talents in University of China
文摘To reveal stress distribution and crack propagation of Brazilian discs under impact loads, dynamic tests were conducted with SHPB （split Hopkinson pressure bar） device. Stress states of specimens were monitored with strain gauges on specimen surface and SHPB bars. The failure process of specimen was recorded by ultra speed camera FASTCAM SAI.1 （675 000 fps）. Stress histories from strain gauges offer comprehensive information to evaluate the stress equilibrium of specimen in time and space. When a slowly rising load （with loading rates less than 1 200 N/s for d 50 mm bar） is applied, there is usually good stress equilibrium in specimen. The stress distribution after equilibrium is similar to its static counterpart. And the first crack initiates at the disc center and propagates along the load direction. But with the front of incident wave becoming steep, it is hard for specimens to get to stress equilibrium. The first crack may appear anywhere on the specimen together with multiple randomly distributed secondary cracks. For a valid dynamic Brazil test with stress equilibrium, the specimen will break into two halves neatly. While for tests with stress disequilibrium, missing strap may be found when broken halves of specimens are put together. For those specimens broken up neatly at center but having missing wedges at the loading areas, it is usually subjected to local buckling from SHPB bars.
基金Project(BJJWZYJH01201911413037)supported by the Beijing Outstanding Young Scientist Program,ChinaProjects(51622404,41877257)supported by the National Natural Science Foundation of ChinaProject(2018SMHKJ-A-J-03)supported by Shaanxi Coal Group Key Project,China。
文摘Rock is more sensitive to tensile loading than compressive loading,since the tensile strength of rock is much lower than compressive strength.The fracture characteristics of rock in the tensile state are of great significance to the understanding of rock failure mechanisms.To this end,we have conducted numerical simulation researches on modeⅠcracking process of rock with varying homogeneity,using the Realistic Failure Process Analysis program.With the increase of homogeneity,cracks are concentrating to the ligament area with a decreasing number of crack bifurcations,and the main crack path is becoming smooth.Crack behaviors and mechanical properties are influenced significantly when the homogeneity index is in the range of 1.5 to 5.When the homogeneity index is greater than 30,they are not affected by rock homogeneity and the rock can be considered as essentially homogeneous.It is considered that the global and local strengths are affected by the distribution of rock mechanical properties at mesoscale,which influence the crack behaviors and mechanical characteristics.
文摘Using a polynomial expansion method, the general exact solitary wave solution and singular one areconstructed for the non-linear KS equation. This approach is obviously applicable to a large variety of nonlinear evolution equation.
基金Supported by a Research Grant from the CityU Strategic Research under Grant No. 7002564
文摘We develop in this paper a new method to construct two explicit Lie algebras E and F. By using a loop algebra E of the Lie algebra E and the reduced self-dual Yang-Mills equations, we obtain an expanding integrable model of the Giachetti-Johnson （G J） hierarchy whose Hamiltonian structure can also be derived by using the trace identity. This provides a much simplier construction method in comparing with the tedious variational identity approach. Furthermore, the nonlinear integrable coupling of the GJ hierarchy is readily obtained by introducing the Lie algebra gN. As an application, we apply the loop algebra E of the Lie algebra E to obtain a kind of expanding integrable model of the Kaup-Newell （KN） hierarchy which, consisting of two arbitrary parameters a and β, can be reduced to two nonlinear evolution equations. In addition, we use a loop algebra F of the Lie algebra F to obtain an expanding integrable model of the BT hierarchy whose Hamiltonian structure is the same as using the trace identity. Finally, we deduce five integrable systems in R3 based on the self-dual Yang-Mills equations, which include Poisson structures, irregular lines, and the reduced equations.
