The present work aims at providing a numerical method to estimate the damage of a concrete structure, under the load of an avalanche-type natural event. Using the Francfort and Marigo damage model, we begin by validating the model in a 1--D configuration by analytical and numerical calculus. Moreover, as concrete has very different behaviour in tension and compression, we then introduce a tension-compression formulation in a 2--D configuration within the variational approach to damage. Considering a non-vanishing resulting Young modulus and minimizing the total energy, including the energy released by damage, provides us with the damage state during the load, without resorting to non-local formulation. We present some validation simulations such as three-point flexural test. Finally, we show realistic simulations of bending of the structure under the load of an avalanche and the resulting damaged state.