Damage models, developed in the last decades, insure a continuous description of the fracture process zone in quasi-brittle materials but fail at representing fine information of the cracking features such as openings and spacings. Recently, the concept of displacement discontinuities embedded in to a standard finite element has been proved to be efficient in modeling fracture of quasi-brittle materials. The present paper aims at capturing crack openings in a natural way by using the Strong Discontinuity Approach (SDA). This later is coupled with a continuous anisotropic damage model accounting for different crack orientations and crack closure effects. A regularized version of the Dirac distribution and the hardening parameter provides+ the establishment of anenriched model compatible with the continuous one. Numerical simulations at the integration point level and a three-point bending test carried out on a single edge notched beam show the performances of the model.