## 4 Results  
### Incidence of the Strain Interval Adopted for Stiffness Determination  
The vertical stress with time at a depth of about 4.5 m along the impact vertical is shown in Figure 5, for the two values of Young modulus implemented in the FEM calculation, without (\(\alpha=0\); \(\beta=0\); Figure 5a) and with (Figure 5b) Rayleigh damping. The comparison has been made for equal collision time (0.1 s) and, thus, for equal maximum impact force (360 kN). The transient effect of the impact on vertical stress is evident in all cases, but differences in terms of maximum value of the vertical stress have been found (Table 3). For no damping, the maximum stresses calculated in the two stiffness options, i.e., 73 kPa and 124 kPa for the higher and the lower stiffness, respectively, give evidence of an important discrepancy related to the definition of the strain interval adopted for the soil stiffness measurement. For the assumed damping (see Rayleigh parameters in Table 2), the calculated maximum stresses are 66 kPa and 102 kPa for the higher and the lower stiffness, respectively. The discrepancy calculated from the average value is about 52% in case of no damping and 43% with damping: although relevant, discrepancies arising from this kind of uncertainty could be managed when designing the regolith shield, for example by devoted safety factors, provided that the elastic moduli decay with strains is experimentally deduced with accuracy and suitable measurement devices.  
In Figure 6a-d the stress evolution through the layer related to impact for the case of stiffer regolith is shown by means of stress contours, with reference to four different  
Figure 5: Vertical stress with time at a depth of about 4.5 m, along the loading vertical, for the two options of Young modulus, without (**a**) and with (**b**) damping. Collision time for this analysis: 0.1 s (maximum force: 360 kN). The vertical dashed line indicates the start of the impulse load.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Investigated Hypotheses of Young Modulus**} & \multicolumn{4}{c}{**Max Vertical Stress [kN/m\({}^{2}\)]**} \\ \cline{2-5}  & \multicolumn{2}{c}{**without Damping**} & \multicolumn{2}{c}{**with Damping**} \\ \cline{2-5}  & **Point A** & **Point B** & **Point A** & **Point B** \\ \hline
33 MPa (0.1 s\(\rightarrow\)360 kN) & 73.0 & 47.3 & 65.8 & 44.8 \\ \hline
6 MPa (0.1 s\(\rightarrow\)360 kN) & 123.8 & 98.6 & 102.3 & 74.5 \\ \hline
33 MPa (0.01 s\(\rightarrow\)3600 kN) & 1043.2 & 788.6 & 632.6 & 435.7 \\ \hline \hline \end{tabular}
\end{table}
Table 3: The results of the FEM calculation for the three combinations of Young modulus and collision duration (or maximum force).  
times. The plots give evidence of the propagation of the stress perturbation. A little stress perturbation with respect to the initial geostatic condition is detected even after the end of the impulsive force--time history (plot d).  
It has been also calculated (Table 3), at the same depth of about 4.5 m, the maximum impact-induced stress along a 2 m far vertical (point B in Figure 4), which is clearly expected to be lower even assuming an elastic continuum half-space. Based on the FEM results, looking just as an example at the case of 33 MPa Young modulus and 0.1 s collision time, the calculated vertical stress at the point B decreases to 65% of the maximum stress calculated along the loading vertical (point A) in case of no damping, and to 68% when implementing damping.