This paper discusses the calculation of plastic zone properties around circular tunnels to rock-masses that satisfy the Hoek–Brown failure criterion in non-hydrostatic condition,and reviews the calculation of plastic...This paper discusses the calculation of plastic zone properties around circular tunnels to rock-masses that satisfy the Hoek–Brown failure criterion in non-hydrostatic condition,and reviews the calculation of plastic zone and displacement,and the basis of the convergence–confinement method in hydrostatic condition.A two-dimensional numerical simulation model was developed to gain understanding of the plastic zone shape.Plastic zone radius in any angles around the tunnel is analyzed and measured,using different values of overburden(four states)and stress ratio(nine states).Plastic zone radius equations were obtained from fitting curve to data which are dependent on the values of stress ratio,angle and plastic zone radius in hydrostatic condition.Finally validation of this equation indicate that results predict the real plastic zone radius appropriately.展开更多
The satisfiability(SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design efficient optimization algorithms for finding a solution for a satisfiable CNF ...The satisfiability(SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design efficient optimization algorithms for finding a solution for a satisfiable CNF formula. A new formulation, the Universal SAT problem model, which transforms the SAT problem on Boofean space into an optimization problem on real space has been developed. Many optimization techniques, such as the steepest descent method, Newton's method, and the coordinate descent method, can be used to solve the Universal SAT problem. In this paper, we prove that, when the initial solution is sufficiently close to the optimal solution, the steepest descent method has a linear convergence ratio β<1, Newton's method has a convergence ratio of order two, and the convergence ratio of the coordinate descent method is approximately (1-β/m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the Universal SAT problem is also presented in this paper.展开更多
文摘This paper discusses the calculation of plastic zone properties around circular tunnels to rock-masses that satisfy the Hoek–Brown failure criterion in non-hydrostatic condition,and reviews the calculation of plastic zone and displacement,and the basis of the convergence–confinement method in hydrostatic condition.A two-dimensional numerical simulation model was developed to gain understanding of the plastic zone shape.Plastic zone radius in any angles around the tunnel is analyzed and measured,using different values of overburden(four states)and stress ratio(nine states).Plastic zone radius equations were obtained from fitting curve to data which are dependent on the values of stress ratio,angle and plastic zone radius in hydrostatic condition.Finally validation of this equation indicate that results predict the real plastic zone radius appropriately.
基金NSERC Strategic Grant MEF0045793NSERC Research Grant OGP0046423.
文摘The satisfiability(SAT) problem is a basic problem in computing theory. Presently, an active area of research on SAT problem is to design efficient optimization algorithms for finding a solution for a satisfiable CNF formula. A new formulation, the Universal SAT problem model, which transforms the SAT problem on Boofean space into an optimization problem on real space has been developed. Many optimization techniques, such as the steepest descent method, Newton's method, and the coordinate descent method, can be used to solve the Universal SAT problem. In this paper, we prove that, when the initial solution is sufficiently close to the optimal solution, the steepest descent method has a linear convergence ratio β<1, Newton's method has a convergence ratio of order two, and the convergence ratio of the coordinate descent method is approximately (1-β/m) for the Universal SAT problem with m variables. An algorithm based on the coordinate descent method for the Universal SAT problem is also presented in this paper.
