## 3 Methods
\begin{table}
\begin{tabular}{c c} \hline Friction angle & 54\({}^{\circ}\) \\ \hline Cohesion & 0 \\ \hline Dilatancy angle & 20\({}^{\circ}\) \\ \hline Earth pressure coefficient at rest & 0.3 \\ \hline [PERSON]’s ratio & 0.2 [49] \\ \hline Void ratio & 0.94 \\ \hline Density & 1.39 g/cm\({}^{3}\) \\ \hline Young modulus & 33 MPa; 6 MPa \\ \hline Rayleigh damping parameter \(\alpha\) & 0.1232 [20] \\ \hline Rayleigh damping parameter \(\beta\) & 0.6410 \(\times\) 10\({}^{-3}\)[20] \\ \hline \end{tabular}
\end{table} 
Table 2: Geotechnical parameters of the regolith layer employed in the FEM calculation. Figure 4: Geometrical model with mesh, punctual impact force and observation points (point A is on the loading vertical, point B is 2 meters from point A, at the same depth; “Bedrock” in the legend is the 50 cm thick layer below the regolith cover). based on the value indicated by [PERSON] [49] for lunar regolith (as mean value to the depth of 200 cm), consistent with the value obtained by the elastic relationship between K\({}_{0}\) and v.  
The numerical simulation has been carried out both without and with damping. Damping has been modelled using the Rayleigh parameters \(\alpha\) and \(\beta\) (Table 2) adopted by [PERSON] et al. [20] for modelling an impact problem involving DNA-1A. They deduced these parameters using data from [PERSON] et al. [55] concerning a different volcanic soil. Direct determination of these parameters on DNA-1A is desirable for future research. The impact of the meteoroid is modelled as a punctual force variable with time according to a triangular function. The impact force acts vertically. The 2D FE domain is discretized by 2108 elements under plane strain conditions. The plane-strain condition corresponds to negligible displacement in the \(z\)-direction, therefore, along the longitudinal axis, the strain is assumed to be zero (\(\varepsilon_{z}=0\)). To ensure that the waves propagating through the layer are not filtered at high frequencies, [PERSON] and [PERSON] [56] suggested a maximum size of the element equal to one-eighth of the wavelength associated with the highest frequency of the input signal. Furthermore, the time step should be smaller than the ratio of the distance between two nodes and the wave propagation velocity of the soil [57]. In the present study these suggestions have been considered: the average element area in the middle zone of the layer, that is the zone most influenced by the load diffusion, was about 0.04 m\({}^{2}\), and the time step was 1.5 \(\times\) 10\({}^{-4}\) s. The tolerated error for stress was 0.01 kPa. The impact momentum adopted for this calculation comes from an impactor velocity of 18 Km/s, consistent with data from literature [13, 14, 58], and a meteoroid mass of 1 Kg. For simplicity, in this work a perfectly inelastic collision has been assumed. In the dynamic FEM calculation, a triangular shape of the force-time function has been assumed and, consequently, the required input parameters are the maximum value of the impact force and the time interval taken by the impact. As mentioned in the Introduction, it has been investigated, for equal impact momentum, the effect of two different hypotheses on the collision time, i.e., 0.01 s and 0.1 s, leading to maximum forces of 3600 kN and 360 kN, respectively. Finally, soil melting and vaporization [59], although expected in case of high energy impacts, are phenomena ignored in this work.