The state of roof collapse in tunnels is actually three-dimensional, so constructing a three-dimensional failure collapse mechanism is crucial so as to reflect the realistic collapsing scopes more reasonably. Accordin...The state of roof collapse in tunnels is actually three-dimensional, so constructing a three-dimensional failure collapse mechanism is crucial so as to reflect the realistic collapsing scopes more reasonably. According to Hoek-Brown failure criterion and the upper bound theorem of limit analysis, the solution for describing the shape of roof collapse in circular or rectangular tunnels subjected to seepage forces is derived by virtue of variational calculation. The seepage forces calculated from the gradient of excess pore pressure distribution are taken as external loading in the limit analysis, and it is of great convenience to compute the pore pressure with pore pressure coefficient. Consequently, the effect of seepage forces is taken as a work rate of external force and incorporated into the upper bound limit analysis. The numerical results of collapse dimensions with different rock parameters show great validity and agreement by comparing with the results of that with two-dimensional failure mechanism.展开更多
Doubly excited intrashell 2p 2 3P e state in heliumlike F 7+ ion is calculated by using the modified configuration interaction wave function. Using the modified Slater type wave function having up to 362 terms, the en...Doubly excited intrashell 2p 2 3P e state in heliumlike F 7+ ion is calculated by using the modified configuration interaction wave function. Using the modified Slater type wave function having up to 362 terms, the energy position of the discrete 2p 2 3P e state in F 7+ is determined to be -18.812 629 78 a.u., Several expectation values of r i,r -1 12 and r 12 are also given in the present work. The present results indicate that the modified Slater type wave function in which r < and r > coordinates are incorporated is effective and powerful for the description of the 2p 2 3P e state showing strong correlation effect in two electron systems.展开更多
基金Project(2013CB036004) supported by the National Basic Research Program of ChinaProject(51178468) supported by the National Natural Science Foundation of ChinaProject(2013zzts235) supported by Innovation Fund of Central South University of China
文摘The state of roof collapse in tunnels is actually three-dimensional, so constructing a three-dimensional failure collapse mechanism is crucial so as to reflect the realistic collapsing scopes more reasonably. According to Hoek-Brown failure criterion and the upper bound theorem of limit analysis, the solution for describing the shape of roof collapse in circular or rectangular tunnels subjected to seepage forces is derived by virtue of variational calculation. The seepage forces calculated from the gradient of excess pore pressure distribution are taken as external loading in the limit analysis, and it is of great convenience to compute the pore pressure with pore pressure coefficient. Consequently, the effect of seepage forces is taken as a work rate of external force and incorporated into the upper bound limit analysis. The numerical results of collapse dimensions with different rock parameters show great validity and agreement by comparing with the results of that with two-dimensional failure mechanism.
文摘Doubly excited intrashell 2p 2 3P e state in heliumlike F 7+ ion is calculated by using the modified configuration interaction wave function. Using the modified Slater type wave function having up to 362 terms, the energy position of the discrete 2p 2 3P e state in F 7+ is determined to be -18.812 629 78 a.u., Several expectation values of r i,r -1 12 and r 12 are also given in the present work. The present results indicate that the modified Slater type wave function in which r < and r > coordinates are incorporated is effective and powerful for the description of the 2p 2 3P e state showing strong correlation effect in two electron systems.
