Seismic Stability Limit Analysis For Earth-rockfill Dams

After the Wenchuan earthquake, the seismic design of hydropower projects is strengthened in our country. It is pointed out by "Temporary Regulations for seismic design of hydropower projects and special report formulation" that the limit aseismic capability should be studied for the particularly important water retaining structures, except for the design and check seismic conditions. At present, the study on the limit aseismic capability of earth-rockfill dams is only in the exploratory research stages. It is necessary and has great value in theory and practical engineering to develop some direct and effective methods to determine the limit aseismic capability of dams.According to seismic damage statistics and relative research status, it is indicated that the stability is a key influence factor on the limit aseismic capability of earth-rockfill dams. For this reason, the study on the limit aseismic capability aimed at the stability of earth-rockfill dams is carried out in this paper.The limit analysis method, which involves collapse load calculations using the lower and upper bound theorems of plasticity, has provided engineers with a powerful tool for bearing capacity and slope stability problems. Therefore, the seismic stability of earth-rockfill dams is studied using limit analysis method in this paper, and it includes:(1) A new approach based on the upper bound theorem of limit analysis is proposed here to assess the seismic stability of earth-rockfill dams. The dam slope is divided into horizontal slices with regarding the sliding surface as an arbitrary surface. Then, the internal work rate and dissipation rate of each slice are calculated. With the conditions of the energy-work balance equation, the limit aseismic capability of dam slopes can finally be optimized by an intelligent algorithm. Using the horizontal slice method, a more precise calculation of the pseudo-static loads can be obtained than the conventional vertical slice approach. With the calculation of the reinforcement and soil dissipation rate separately, the method is applied to the assessment of the seismic stability of a reinforced earth-rockfill dam and the influence of the distribution of reinforcement on limit aseismic capability.(2) An FEM based on the lower bound theorem of limit analysis is developed to study the limit aseismic capability of earth-rockfill dams. Considering the large internal friction angel and nonlinear shear strength parameters of rockfill materials, the proposed method formulates the limit analysis as a second-order cone programming (SOCP) problem with constraints based on the conditions of equilibrium, stress discontinuity, stress boundary and the native Mohr-Coulomb yield criterion. The lower bound of the limit aseismic capability of dam slope is then obtained by means of the interior-point algorithm. Regarded as the conservative solutions, the lower bounds of limit aseismic capability can be used in practice to give a safe design.(3) Based on six-node linear strain elements and SOCP, an upper bound FEM is proposed to analyze the seismic stability of earth-rockfill dams. However, the equivalent shear strength parameters of materials with a nonlinear criterion are expressed in terms of stress, which can’t be obtained directly by upper bound method. After formulating the upper bound analysis as the dual problem, which is regarded as a static form, the corresponding shear strength parameters can be determined iteratively in order to consider the nonlinear strength properties of rockfill materials. By using the high order element type and leading the pore water pressures into the energy-work balance equation, the method can handle the complicated cases efficiently and with relative ease.Combined with lower bound FEM, the limit aseismic capability of dams can be defined in a very narrow range. Therefore, the lower and upper bound limit analysis FEM provide powerful and versatile tools for determination of the limit aseismic capability of earth-rockfill dams.(4) The over-loading FEM is used here to determine the limit aseismic capability of earth-rockfill dams. The study is focused on the influence of yield criteria, flow rules, element type and size on the limit aseismic capability of dams.