## 1 Introduction  
The aim of this study is to investigate the behaviour of Lingulid sandstone rock, with percussive drilling as the main application of interest. Different testing methods were used in quasistatic and also dynamic loading regimes [1]. The fragmentation process generated in geomaterials under percussive loading corresponds to both (mode I and mode II) fracturing modes induced by tensile stresses and triaxial stress states. For this reason, it is necessary to consider different constitutive laws that are able to describe both tensile damage and the confined compression response. One possible candidate for such a constitutive law is the so-called KST-DFH model. The KST elastoplastic model [2, 3] can be considered to model the confined behaviour of geomaterials and the tensile behaviour can be described with the DFH probabilistic-damage model [4, 5] that takes into account the critical defects associated to the geomaterial. The KST-DFH model was previously used to simulate damage and deformation modes in concrete structures when subjected to impact loading [6; 7; 8] in which high-strain-rate tensile stresses and triaxial stresses were involved. The KST-DFH model was also successfully employed in a numerical study of granite rock fragmentation of percussive drilling [9]. As explained in these previous works, the main parameters of both models can be identified based on static experiments. As detailed in [5], the DFH multiscale model allows one to describe the probabilistic behaviour of brittle materials under low stress rates and the deterministic response at high stress rates. At low stress rates, a failure stress randomly drawn according to the Weibull model provides the ultimate strength of the considered elementary volume. At high stress rates, a damage variable is used to describe the fragmentation process involved in brittle materials at high strain rates in terms of crack inception, crack propagation, and obscuration of critical defects from propagating cracks (Figure 1a). Crack inception phenomenon can be described again according to a Weibull distribution where the density of critical defects is a power law of the applied stress \(\sigma(T)\) Equation (1). In this equation, the input parameters are \(m\), the Weibull modulus and \(\lambda_{0}(\sigma_{0})^{-m}\), the scale Weibull parameter. Both Weibull parameters can be identified from a series of bending tests (about 20 tests) [4; 5]. In the DFH model, a constant crack speed \(V_{crack}\) is usually assumed for crack propagation. The last mechanism, called the obscuration of critical defects, corresponds to a shielding process from propagating cracks. It results from release waves initiated on the lips of the crack. The release of stresses in the vicinity of the propagating cracks prevents the activation of other critical defects located in a zone called the \"obscuration zone\" that is assumed to grow in a self-similar way. Therefore, the size of the obscured volume \(V_{o}(T-t)\) can be expressed as function of Equation (2) (in a case of 3D volume) where \(V_{crack}\) is the crack speed (\(V_{crack}=0.38\sqrt{E/\rho}\)) is assumed with the \(E\) [PERSON]'s modulus and \(\rho\) the initial density), \(S\) is a shape parameter (equal to 0.38, cf. [4; 5]), \(T\) is the current time, and \(t\) is the crack inception time. Finally, a damage variable is proposed (Equation (3)) taking into account the distribution of critical defects (Equation (1)) and the growth of the obscuration zones (Equation (2)). Three damage variables are defined, one for each principal direction. This makes the DFH model an anisotropic damage model.