In this work we consider numerical implementation of the modified version of a coupled rate dependent damage-plasticity concrete model first proposed in [8]. We developed an explicit-implicit integration scheme, implemented it in LS-DYNA finite element code, with explicit part dealing with large global problem of equations of motion and implicit part treating local evolution equations. We also provide a detailed consideration of the numerical stability of this kind of scheme for ratedependent damage model. Several numerical tests, both simple ones and a complex problem of the large aircraft impact on a large concrete slab demonstrate the efficiency of the proposed numerical implementation. Comparison between simulations of impact of equivalent aircraft engine missiles and the tests carried out in Sandia laboratory [25] also demonstrates its efficiency.