The cohesive frictional crack model applied to the analysis of the dam-foundation joint

The mechanical behaviour of dam-foundation joints plays a key role in concrete dam engineering since it is the weakest part of the structure and therefore the evolutionary crack process occurring along this joint determines the global load-bearing capacity. The reference volume involved in the above mentioned process is so large that it cannot be tested in a laboratory: structural analysis has to be carried on by numerical modelling. The use of the asymptotic expansions proposed by Karihaloo and Xiao [13] at the tip of a crack with normal cohesion and Coulomb friction can overcome the numerical difficulties that appear in large scale problems when the Newton-Raphson procedure is applied to a set of equilibrium equations based on ordinary shape functions (Standard Finite Element Method). In this way it is possible to analyze problems with friction and crack propagation under the constant load induced by hydro-mechanical coupling. For each position of the fictitious crack tip, the condition K₁=K₂=0 allows us to obtain the external load level and the tangential stress at the tip. If the joint tangential strength is larger than the value obtained, the solution is acceptable, because the tensile strength is assumed negligible and the condition K₁=0 is sufficient to cause the crack growth. Otherwise, the load level obtained can be considered as an overestimation of the critical value and a special form of contact problem has to be solved along the fictitious process zone. For the boundary condition analyzed (ICOLD benchmark on gravity dam model), after an initial increasing phase, the water lag remains almost constant and the maximum value of load carrying capacity is achieved when the water lag reaches its constant value.