Earthquake Stress Analysis in Earth Dams

The finite element method, which has been used extensively in the static analysis of elastic continua, is extended to the dynamic analysis of two-dimensional stress systems. The method involves calculation of vibration mode shapes and frequencies, making use of a stiffness matrix evaluated by the finite element method and a mass matrix formed by lumping the mass at the finite element nodal points. The dynamic response is then calculated by the mode-superposition method, the response of each mode being obtained by step-by-step integration. The method is demonstrated by the earthquake analysis of a triangular earth-dam cross section treated as an elastic plane-strain problem. Vertical and horizontal acceleration components of the 1940 El Centro earthquake are applied; results are presented in the form of plots showing the time history of stresses at selected points in the cross section and also plots of stress contours at selected instants of time.