Evaluating the Effects of the Magnitude of Pseudo-static Force on Reinforced Slopes base on the Nonlinear M-C Failure Criterion   Lianheng Zhao, Liang Li Road Engineering Department, school of Civil and Architectural Engineering, Central South University, Changsha 410075, Hunan, China e-mail: zlh8076@163.com Feng Yang Tunnel Engineering Department, school of Civil and Architectural Engineering, Central South University, Changsha 410075, Hunan, China e-mail: abc@tech.edu.com Jing Zhou College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, Hunan, China e-mail: jingzhchina@163.com
			ABSTRACT

A linear Mohr-Coulomb failure criterion is widely used in the conventional analysis of seismic stability of reinforced soil structures. However, the experimental results show that the strength envelopes of almost all geo-materials own the nature of nonlinearity, and that the linear failure criterion is a special case of failure criteria. Based on the nonlinear M-C failure criterion and the admissible failure mechanisms, the seismic stability of reinforcement slope subjected to the static and seismic loads is studied by means of the kinematical approach of the limit analysis theory. The uniform and triangular distribution modes of reinforcement strength in the slope are assumed for analysis and calculation in the paper as well. Both the translational and rotational fracture surfaces are employed in the formulation for calculating the critical height, the critical strength of reinforcement and the critical failure surfaces. Both the horizontal effects and the vertical effects of pseudo-static forces on reinforced soil slope by using a seismic coefficient concept has been adopted for seismic stability calculations in this paper. The nonlinear shear strength parameters (internal friction angle ft and cohesive force ct) are treated as variable parameters for the calculation schemes. The objective functions of critical height are obtained by equating the work rate of external force to internal dissipation, and then the upper bound solutions are presented by applying a nonlinear sequential quadratic programming algorithm. A comparative analysis between the proposed approaches and published analyses has been accomplished, and if the nonlinear M-C yield criterion turns into a linear M-C yield criterion, comparison of results shows good agreement. From the results of parameter sensitivity analysis, it can be seen that both horizontal and vertical seismic force and the nonlinear failure parameter has a significant effect on the seismic stability of reinforcement slope; and an underestimated design could be resulted from the ignorance the true characteristic of geo-materials and the vertical effects of pseudo-static forces.

Keywords: reinforced slopes; seismic stability; pseudo-static analysis; nonlinear M-C failure criterion; limit analysis; upper bound theorem.

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