## 3 Methods  
The problem here analysed is sketched in Figure 4. A regolith covering is supposed to absorb the impact of meteoroids and prevent the buried structure from damages. In this work, a thickness of 5.4 m is assumed for the regolith layer [14], which would provide protection from radiation and meteoroids of maximum mass of 37 kg, or diameter of 52 cm or smaller [48], reducing the flux of a penetrating impact on the structure to between \(10^{-8}\) and \(10^{-7}\) impacts/km\({}^{2}\)/yr [13,15]. Lower thickness could be employed in case of composite shields, adopting regolith in combination with other materials. The Relative Density of the regolith shield is assumed to be \(D_{r}=79\%\). A second 50 cm thick layer immediately below the regolith cover identifies the vault of the habitat to be shielded. Assuming that the latter is manufactured by 3D-printing [5] using in-situ regolith, the parameters assigned to it in the numerical simulation (\"lunar\" unit weight, \(\gamma=3.6\) kN/m\({}^{3}\); Young modulus, E = 2,350,000 kN/m\({}^{2}\); Poisson ratio, \(\gamma=0.2\)) reflect a level of stiffness that could plausibly be imparted to the material for satisfying structural requirements. This layer has been modelled as Linear Elastic Non-Porous in the FEM code. Furthermore, the conventional bedrock condition under the entire model was adopted. The geotechnical characteristics of the regolith shield layer employed in the FEM calculation (Table 2) have been assumed to be constant with depth. They have been chosen based on the mechanical behaviour exhibited by DNA-1A lunar simulant during triaxial tests [30]. In particular, the shear behaviour of a dry specimen initially confined under isotropic pressure of about 20 kPa has been of reference. The Young modulus has been assumed to be equal to two different values, i.e., 33 MPa and 6 MPa, taken at two levels of axial strain during the triaxial compression test, i.e., 0.006% and 0.2%, respectively. These stiffness values have been here calculated by further interpretation of the experimental data from [PERSON] and [PERSON]. It is worth noting that the first value can be measured on a triaxial specimen using local transducers for the axial strain measurement (Figure 2), directly placed on the specimen membrane, that is, using not conventional devices for the triaxial test. Figure 3: (**a**) Crater resulting from low kinetic energy impact on DNA-1A; (**b**) sketch of the ray system (in yellow); the outer diameter of the crater (see the red bar) is about 7 cm. The numerical simulation has been performed by means of the FEM code Plaxis 2D CE V22 (@2022 Bentley Systems, Inc. 2022). In the geometrical model, the layer has length of 48 m laterally, viscous boundaries [50] have been adopted, to absorb the outgoing wave energy. The constitutive model adopted for the soil is the Mohr-Coulomb model. The unit weight assigned to the regolith layer in Plaxis has been calculated based on the lunar gravity, starting from density value. To assign initial stress state to the soil, the K\({}_{0}\)-procedure has been used. The estimate of K\({}_{0}\) could be made by several relations proposed in the literature. In this case, the value of the at-rest coefficient (Table 2) has been deduced using a relationship by [PERSON] [51], based on previous works by [PERSON] [52; 53] and [PERSON] [54], which expresses K\({}_{0}\) as a function of the Critical State friction angle, \(\varphi^{\prime}\), and the Relative Density, \(D_{r}\), of the soil. The [PERSON]'s ratio, \(\
u=0.2\), has been assumed