To investigate the influence of loading rate on rockburst in a circular tunnel under three-dimensional stress conditions,the true-triaxial tests were conducted on 100 mm×100 mm×100 mm cubic sandstone specime...To investigate the influence of loading rate on rockburst in a circular tunnel under three-dimensional stress conditions,the true-triaxial tests were conducted on 100 mm×100 mm×100 mm cubic sandstone specimens with d50 mm circular perforated holes,and the failure process of hole sidewall was monitored and recorded in real-time by the microcamera.The loading rates were 0.02,0.10,and 0.50 MPa/s.The test results show that the rockburst process of hole sidewall experienced calm period,pellet ejection period,rock fragment exfoliation period and finally formed the V-shaped notch.The rockburst has a time lag and vertical stress is high when the rockburst occurs.The vertical stress at the initial failure of the hole sidewall increases with loading rate.During the same period after initial failure,the rockburst severity of hole sidewalls increased significantly with increasing loading rate.When the vertical stress is constant and maintains a high stress level,the rockburst of hole sidewall under low loading rate is more serious than that under high loading rate.With increasing loading rate,the quality of rock fragments produced by the rockburst decreases,and the fractal dimension of rock fragments increases.展开更多
In this study, it was assumed that three-dimensional penny-shaped cracks existed in deep rock masses. A new non-Euclidean model was established, in which the effects of penny- shaped cracks and axial in-situ stress on...In this study, it was assumed that three-dimensional penny-shaped cracks existed in deep rock masses. A new non-Euclidean model was established, in which the effects of penny- shaped cracks and axial in-situ stress on zonal disintegration of deep rock masses were taken into account. Based on the non-Euclidean model, the stress intensity factors at tips of the penny- shaped cracks were determined. The strain energy density factor was applied to investigate the occurrence of fractured zones. It was observed from the numerical results that the magnitude and location of fractured zones were sensitive to micro- and macro-mechanical parameters, as well as the value of in-situ stress. The numerical results were in good agreement with the experimental data.展开更多
Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under sat...Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit(ADE)scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in nonuniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourthorder finite difference(FD) approximation to the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps,giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua(FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%-50% that of FLAC’s basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%-1.8%.展开更多
Two-dimensional dynamic numerical analyses have been conducted,using FLAC 7.0,to evaluate the seismic response of underground structures located far from the seismic source,placed in either linear-elastic or nonlinear...Two-dimensional dynamic numerical analyses have been conducted,using FLAC 7.0,to evaluate the seismic response of underground structures located far from the seismic source,placed in either linear-elastic or nonlinear elastoplastic ground.The interaction between the ground and deep circular tunnels with a tied interface is considered.For the simulations,it is assumed that the liner remains in its elastic regime,and plane strain conditions apply to any cross section perpendicular to the tunnel axis.An elastoplastic constitutive model is implemented in FLAC to simulate the nonlinear ground.The effect of input frequency and relative stiffness between the liner and the ground,on the seismic response of tunnels,is evaluated.The response is studied in terms of distortions normalized with respect to those of the free field,and load demand(axial forces and bending moments)in the liner.In all cases,i.e.for linear-elastic and nonlinear ground models,the results show negligible effect of the input frequency on the distortions of the cross section,for input frequencies smaller than 5 Hz;that is for ratios between the wave length and the tunnel opening(k=D)larger than ten for linear-elastic and nine for nonlinear ground.Larger normalized distortions are obtained for the nonlinear than for the linear-elastic ground,for the same relative stiffness,with differences increasing as the tunnel becomes more flexible,or when the amplitude of the dynamic input shear stress increases.It has been found that normalized distortions for the nonlinear ground do not follow a unique relationship,as it happens for the linear-elastic ground,but increase as the amplitude of the dynamic input increases.The loading in the liner decreases as the structure becomes more flexible with respect to the ground,and is smaller for a tunnel placed in a stiffer nonlinear ground than in a softer nonlinear ground,for the same flexibility ratio.展开更多
基金Projects(11972378,41630642)supported by the National Natural Science Foundation of ChinaProject(2019zzts310)supported by the Fundamental Research Funds for the Central Universities,China。
文摘To investigate the influence of loading rate on rockburst in a circular tunnel under three-dimensional stress conditions,the true-triaxial tests were conducted on 100 mm×100 mm×100 mm cubic sandstone specimens with d50 mm circular perforated holes,and the failure process of hole sidewall was monitored and recorded in real-time by the microcamera.The loading rates were 0.02,0.10,and 0.50 MPa/s.The test results show that the rockburst process of hole sidewall experienced calm period,pellet ejection period,rock fragment exfoliation period and finally formed the V-shaped notch.The rockburst has a time lag and vertical stress is high when the rockburst occurs.The vertical stress at the initial failure of the hole sidewall increases with loading rate.During the same period after initial failure,the rockburst severity of hole sidewalls increased significantly with increasing loading rate.When the vertical stress is constant and maintains a high stress level,the rockburst of hole sidewall under low loading rate is more serious than that under high loading rate.With increasing loading rate,the quality of rock fragments produced by the rockburst decreases,and the fractal dimension of rock fragments increases.
基金supported by the 973 Project(No.2014CB046903)the National Natural Science Foundation of China(Nos.51325903 and 51279218)the Natural Science Foundation Project of CQ CSTC(Nos.CSTC2013KJRC-1JRCCJ30001 and CSTC2013JCYJYS0005)
文摘In this study, it was assumed that three-dimensional penny-shaped cracks existed in deep rock masses. A new non-Euclidean model was established, in which the effects of penny- shaped cracks and axial in-situ stress on zonal disintegration of deep rock masses were taken into account. Based on the non-Euclidean model, the stress intensity factors at tips of the penny- shaped cracks were determined. The strain energy density factor was applied to investigate the occurrence of fractured zones. It was observed from the numerical results that the magnitude and location of fractured zones were sensitive to micro- and macro-mechanical parameters, as well as the value of in-situ stress. The numerical results were in good agreement with the experimental data.
基金the support from the University Transportation Center for Underground Transportation Infrastructure at the Colorado School of Mines for partially funding this research under Grant No. 69A3551747118 of the Fixing America's Surface Transportation Act (FAST Act) of U.S. DoT FY2016
文摘Explicit solution techniques have been widely used in geotechnical engineering for simulating the coupled hydro-mechanical(H-M) interaction of fluid flow and deformation induced by structures built above and under saturated ground, i.e. circular footing and deep tunnel. However, the technique is only conditionally stable and requires small time steps, portending its inefficiency for simulating large-scale H-M problems. To improve its efficiency, the unconditionally stable alternating direction explicit(ADE)scheme could be used to solve the flow problem. The standard ADE scheme, however, is only moderately accurate and is restricted to uniform grids and plane strain flow conditions. This paper aims to remove these drawbacks by developing a novel high-order ADE scheme capable of solving flow problems in nonuniform grids and under axisymmetric conditions. The new scheme is derived by performing a fourthorder finite difference(FD) approximation to the spatial derivatives of the axisymmetric fluid-diffusion equation in a non-uniform grid configuration. The implicit Crank-Nicolson technique is then applied to the resulting approximation, and the subsequent equation is split into two alternating direction sweeps,giving rise to a new axisymmetric ADE scheme. The pore pressure solutions from the new scheme are then sequentially coupled with an existing geomechanical simulator in the computer code fast Lagrangian analysis of continua(FLAC). This coupling procedure is called the sequentially-explicit coupling technique based on the fourth-order axisymmetric ADE scheme or SEA-4-AXI. Application of SEA-4-AXI for solving axisymmetric consolidation of a circular footing and of advancing tunnel in deep saturated ground shows that SEA-4-AXI reduces computer runtime up to 42%-50% that of FLAC’s basic scheme without numerical instability. In addition, it produces high numerical accuracy of the H-M solutions with average percentage difference of only 0.5%-1.8%.
基金The financial support of the Colombia-Purdue Institute for Advanced Scientific Research(CPI),Universidad del Valle(Colombia)and Purdue University-United States is gratefully acknowledged.
文摘Two-dimensional dynamic numerical analyses have been conducted,using FLAC 7.0,to evaluate the seismic response of underground structures located far from the seismic source,placed in either linear-elastic or nonlinear elastoplastic ground.The interaction between the ground and deep circular tunnels with a tied interface is considered.For the simulations,it is assumed that the liner remains in its elastic regime,and plane strain conditions apply to any cross section perpendicular to the tunnel axis.An elastoplastic constitutive model is implemented in FLAC to simulate the nonlinear ground.The effect of input frequency and relative stiffness between the liner and the ground,on the seismic response of tunnels,is evaluated.The response is studied in terms of distortions normalized with respect to those of the free field,and load demand(axial forces and bending moments)in the liner.In all cases,i.e.for linear-elastic and nonlinear ground models,the results show negligible effect of the input frequency on the distortions of the cross section,for input frequencies smaller than 5 Hz;that is for ratios between the wave length and the tunnel opening(k=D)larger than ten for linear-elastic and nine for nonlinear ground.Larger normalized distortions are obtained for the nonlinear than for the linear-elastic ground,for the same relative stiffness,with differences increasing as the tunnel becomes more flexible,or when the amplitude of the dynamic input shear stress increases.It has been found that normalized distortions for the nonlinear ground do not follow a unique relationship,as it happens for the linear-elastic ground,but increase as the amplitude of the dynamic input increases.The loading in the liner decreases as the structure becomes more flexible with respect to the ground,and is smaller for a tunnel placed in a stiffer nonlinear ground than in a softer nonlinear ground,for the same flexibility ratio.
