On the marriage of fracture mechanics and mixed finite element methods: An application to concrete dams

The Federal Energy Regulatory Commission (FERC) requires that all dams owned by utility companies be relicensed every five years. The relicensing process involves an analysis of the dam to determine the factors of safety for overturning and sliding failures. These analyses are typically performed using simple hand calculation methods based on statics and strength of materials concepts. Provisions are made in the FERC Guidelines for analysis using the finite element method, but a strength of materials approach is still used to determine the factor of safety for overturning. In addition, a great deal of emphasis is placed on the evaluation of the analysis using the stresses along lines of nodes in the dam. However, most commerically available finite element programs are based on the displacement formulation, where the stresses are discontinuous across element boundaries.; A finite element program, MERLIN, incorporating both mixed finite element methods and fracture mechanics models has been developed explicitly for the analysis of dams. The discrete crack approach is used for both linear elastic and nonlinear fracture models. Stress intensity factors for linear elastic fracture mechanics (LEFM) are computed using contour integral methods based either on conservation laws or reciprocal work theorems, which have been modified to account for body forces, surface tractions, and seepage pressures. Nonlinear fracture is modeled using the fictitious crack model (FCM) with a strength criterion governing crack propagation. This implementation of the FCM uses a standard incremental solution strategy with an indirect displacement control algorithm that scales the applied loads based on the normal stress on the uncracked ligament at the crack tip and allows for the presence of hydrostatic pressure in the fracture process zone (FPZ). Hydrostatic pressures in the FPZ are defined as a function of the crack width, with the distribution of pressure being determined from experimental results. Nodal stresses are obtained from the mixed equations using both iterative and penalty approaches. With the mixed approach accurate values of nodal stresses are obtained for use in these fracture models. The models were verified using known analytical solutions for LEFM and experimental results for the FCM.; Analysis of a dam was performed using both LEFM and the FCM to demonstrate the applicability of these models to determine the factor of safety for overturning. For the LEFM analysis three different approaches were used to model the uplift pressure at the base of the dam to determine if the predicted crack length was sensitive to idealization of the flow conditions adopted in the finite element model.