A mechanical model for strain softening pillar is proposed considering the characteristics of progressive shear failure and strain localization. The pillar undergoes elastic, strain softening and slabbing stages. In t...A mechanical model for strain softening pillar is proposed considering the characteristics of progressive shear failure and strain localization. The pillar undergoes elastic, strain softening and slabbing stages. In the elastic stage, vertical compressive stress and deformation at upper end of pillar are uniform, while in the strain softening stage there appears nonuniform due to occurrence of shear bands, leading to the decrease of load-carrying capacity. In addition, the size of failure zone increases in the strain softening stage and reaches its maximum value when slabbing begins. In the latter two stages, the size of elastic core always decreases. In the slabbing stage, the size of failure zone remains a constant and the pillar becomes thinner. Total deformation of the pillar is derived by linearly elastic Hookes law and gradient-dependent plasticity where thickness of localization band is determined according to the characteristic length. Post-peak stiffness is proposed according to analytical solution of averaged compressive stress-average deformation curve. Instability criterion of the pillar and roof strata system is proposed analytically (using) instability condition given by Salamon. It is found that the constitutive parameters of material of pillar, the geometrical size of pillar and the number of shear bands influence the stability of the system; stress gradient controls the starting time of slabbing, however it has no influence on the post-peak stiffness of the pillar.展开更多
Considering the influence of strain softening, the solutions of stress, displacement, plastic softening region radius and plastic residual region radius were derived for circular openings in nonlinear rock masses subj...Considering the influence of strain softening, the solutions of stress, displacement, plastic softening region radius and plastic residual region radius were derived for circular openings in nonlinear rock masses subjected to seepage. The radial stress distribution curve, ground reaction curve, and relation curve between plastic softening region radius and supporting force in three different conditions were drawn respectively. From the comparisons among these results for different conditions, it is found that when the supporting force is the same, the displacement of tunnel wall considering both seepage and strain softening is 85.71% greater than that only considering seepage. The increase values of radial displacement at 0.95 m and plastic softening region radius at 6.6 m show that the seepage and strain softening have the most unfavorable effects on circular opening stability in strain softening rock masses.展开更多
Fast Lagrangian analysis of continua(FLAC) was used to study the influence of pore pressure on the mechanical behavior of rock specimen in plane strain direct shear, the distribution of yielded elements, the distribut...Fast Lagrangian analysis of continua(FLAC) was used to study the influence of pore pressure on the mechanical behavior of rock specimen in plane strain direct shear, the distribution of yielded elements, the distribution of displacement and velocity across shear band as well as the snap-back (elastic rebound) instability. The effective stress law was used to represent the weakening of rock containing pore fluid under pressure. Numerical results show that rock specimen becomes soft (lower strength and hardening modulus) as pore pressure increases, leading to higher displacement skip across shear band. Higher pore pressure results in larger area of plastic zone, higher concentration of shear strain, more apparent precursor to snap-back (unstable failure) and slower snap-back. For higher pore pressure, the formation of shear band-elastic body system and the snap-back are earlier; the distance of snap-back decreases; the capacity of snap-back decreases, leading to lower elastic strain energy liberated beyond the instability and lower earthquake or rockburst magnitude. In the process of snap-back, the velocity skip across shear band is lower for rock specimen at higher pore pressure, showing the slower velocity of snap-back.展开更多
文摘A mechanical model for strain softening pillar is proposed considering the characteristics of progressive shear failure and strain localization. The pillar undergoes elastic, strain softening and slabbing stages. In the elastic stage, vertical compressive stress and deformation at upper end of pillar are uniform, while in the strain softening stage there appears nonuniform due to occurrence of shear bands, leading to the decrease of load-carrying capacity. In addition, the size of failure zone increases in the strain softening stage and reaches its maximum value when slabbing begins. In the latter two stages, the size of elastic core always decreases. In the slabbing stage, the size of failure zone remains a constant and the pillar becomes thinner. Total deformation of the pillar is derived by linearly elastic Hookes law and gradient-dependent plasticity where thickness of localization band is determined according to the characteristic length. Post-peak stiffness is proposed according to analytical solution of averaged compressive stress-average deformation curve. Instability criterion of the pillar and roof strata system is proposed analytically (using) instability condition given by Salamon. It is found that the constitutive parameters of material of pillar, the geometrical size of pillar and the number of shear bands influence the stability of the system; stress gradient controls the starting time of slabbing, however it has no influence on the post-peak stiffness of the pillar.
基金Project(09JJ1008) supported by Hunan Provincial Science Foundation of ChinaProject(200550) supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China
文摘Considering the influence of strain softening, the solutions of stress, displacement, plastic softening region radius and plastic residual region radius were derived for circular openings in nonlinear rock masses subjected to seepage. The radial stress distribution curve, ground reaction curve, and relation curve between plastic softening region radius and supporting force in three different conditions were drawn respectively. From the comparisons among these results for different conditions, it is found that when the supporting force is the same, the displacement of tunnel wall considering both seepage and strain softening is 85.71% greater than that only considering seepage. The increase values of radial displacement at 0.95 m and plastic softening region radius at 6.6 m show that the seepage and strain softening have the most unfavorable effects on circular opening stability in strain softening rock masses.
基金Project(50309004) supported by the National Natural Science Foundation of China
文摘Fast Lagrangian analysis of continua(FLAC) was used to study the influence of pore pressure on the mechanical behavior of rock specimen in plane strain direct shear, the distribution of yielded elements, the distribution of displacement and velocity across shear band as well as the snap-back (elastic rebound) instability. The effective stress law was used to represent the weakening of rock containing pore fluid under pressure. Numerical results show that rock specimen becomes soft (lower strength and hardening modulus) as pore pressure increases, leading to higher displacement skip across shear band. Higher pore pressure results in larger area of plastic zone, higher concentration of shear strain, more apparent precursor to snap-back (unstable failure) and slower snap-back. For higher pore pressure, the formation of shear band-elastic body system and the snap-back are earlier; the distance of snap-back decreases; the capacity of snap-back decreases, leading to lower elastic strain energy liberated beyond the instability and lower earthquake or rockburst magnitude. In the process of snap-back, the velocity skip across shear band is lower for rock specimen at higher pore pressure, showing the slower velocity of snap-back.
