## 5 Results and Discussion  
The results of the sensitivity analysis of the studied phenomenological penetration model parameters presented by the CDFs for the predicted DoB in each soil type are shown in Figures 3-5. The four previously discussed statistical distribution approaches were applied in the contexts of MCSs using PRS. This resulted in the nine simulations shown in Table 2 for each soil, with a total of 27 simulations. Comparison between normal and lognormal distributions for COVs limited to less than 30% suggests that the two distributions provide comparable results. However, real soils may experience COVs above this threshold, so the use of the lognormal distribution in the simulation of the DoB is recommended to prevent the analysis from selecting physically inadmissible negative quantities for density, drag, and bearing resistance. This was necessary to accommodate the high COVs exceeding 30% expected for the soils under investigation (Table 1). For sands, with coefficients of variation (COVs) less than or equal to 28%, both normal and lognormal distributions for all random variables yielded identical results, as illustrated in Figure 3a. However, for high COVs, when the lognormal distribution is compared to the lognormal distribution with COVs less than 28%, deeper predictions for depth of burial (DoB) are observed for higher probabilities (above 50%), as evidenced in Figure 3b. Finally, Figure 3c,d further show that when any or all of the random variables are considered as lognormal distributions with COVs greater than 28%, deeper DoB predictions are consistently produced. The nine different distribution conditions applied to various random variables for clayey sand soils are presented in Figure 4. A similar behavior to that observed in the sand is evident, where lognormal distributions with COVs greater than 30% yielded deeper DoB predictions for higher probabilities exceeding 50%. However, Figure 4c,d indicate that considering the variable R as lognormal with COVs > 30% was particularly dominant in predicting higher DoBs. A different behavior was observed in clay. The nine different distribution conditions applied to various random variables for clay are illustrated in Figure 5. Unlike sand or clayey sand soils, in the case of clay all distribution conditions produced approximately the same results under all conditions. A comparison of the CDFs of all DoBs obtained using a variety of distribution combinations for (a) sand, (b) clayey sand, and (c) clay is presented in Figure 6. First, it is evident that the studied projectile penetrates deepest in clay and shallowest in sand. Also, there was a wider distribution of DoBs in clay than in sand, with clayey sand in between. Thus, the target material plays a far more important role than other parameters. Next, an analysis of variance (ANOVA) was carried out on each soil type to investigate the significance of variance between the nine obtained CDFs for each soil. One-way ANOVA was carried out using Igor software (Version: 9.0.5.1) and the results were summarized in Table 3 using a significance value, \(\alpha\), of 0.05. In ANOVA, the _F-statistic_ is a measure of the ratio of variance between groups to the variance within groups. The _Fc_ is the threshold that the _F-statistic_ must exceed to reject the null hypothesis. The _p_-value represents the probability of obtaining an _F-statistic_ as extreme as, or more extreme than, the observed value under the null hypothesis. The null hypothesis in this context states that there are no differences among  
Figure 3: CDFs of DoB in sand using: (**a**) Restrict Normal Distribution to COV Values Lower than 30%, (**b**) Restrict Lognormal Distribution to COV Values Lower than 30%, (**c**) Unrestrict Lognormal Distribution, and (**d**) Use of Mixed Normal and Lognormal Distributions. the CDFs for each soil type. The ANOVA results indicate that there are no statistically significant differences among the CDFs within each of the three soil types.