In order to investigate the effect of COV of the random variables and the lithological variability on the reliability of the system response related to safety. A parametric study is carried out using only the finite element method (FEM), considering, as before, the two hydrology conditions. For the two random variables, the values of COV (C’) and COV (Phi’) increase by a step of 05% for the first phase (05,10,15 and 20%), then by 10% for the second phase (20,30 and 40% ). Six values of each input parameter are considered, and their effects on the likelihood of slope failure are evaluated.
6.1. Effect on the PDF of Factor of Safety
Figures (11) and (12), illustrate the PDF curves associated with each parameter variation for the two cases, namely with and without groundwater using the FEM methods.
From the first examination of the PDF curves represented in Figures (11-a) and (11-b) , we can notice that the increase in COV(C’) has a significant increase on the PDF curves for the first step 5% but this effect diminishs until the variation becoming almost identical when COV(C’) varies between 20% and 40%, , these remarks are true for both hydrology conditions. Though this changes are more important for saturated soil.
On the other hand, Figures (12-a) and (12-b), reveal that the increase of COV(Phi’) has a trivial effect on the PDF curves with the same tendencies as for COV(C’), knowing that the differences in the mean value of PDF for the two cases with and without water table are approximately 7 and 5.80% respectively.
We can also conclude that the values of COV (C’) and COV (Phi’) between 5% and 20% have more influence on the variability of system response (FOS) and probability density for both hydrology conditions.
As shown Figure (13), and (14), the increase of COV(C’) induce a slight modification of the mean values of the FOS with a maximum difference around 1.6% and 0.9% with and without water table respectively. However, the variations of COV(Phi’) leads to a gradual decrease in the values of the mean safety factor (FOS) with a maximum percentage of 3.2% and 3.7% for both hydrology conditions.
6.2. Effect on the probability of failure (PF) and reliability index (RI).
The primary purpose of this section is to check the effect of variability of geotechnical input parameters on probability of failure (PF) and reliability index (RI) using FEM methods.
For both cases with and without water table, Figures (15), we can realize that by increasing COV(C’), the value of PF remains constant, whereas those of IR diminishes progressively, firstly drops rapidly by a proportions of 45% and 49%, when COV(C’) ranges between 10% and 20%, then, as the COV(C’) varies between 20 % and 40%, the reduction rates become irrelevant around 5% and 6.5%.
Figure (16) shows the effect of the variation of COV(Phi’) on the probability of failure of the slope PF and the associated reliability index RI. In the absence of water table, the increase of COV(Phi’) has no effect on the PF, it remains unchanged but the RI decreases, first significantly by a percentage of 50% when COV(Phi’) varies between 5% and 20%, and then by 10%. In the case of the presence of water table the increase of COV(phi’) has a large influence on PF, when it varies between 5% and 20% the PF increases linearly from 2.5% to 20% and then continues to rise moderately until reaching 31% for COV(Phi’) equals 40%. However, the associated reliability index RI undergoes minor reductions.
Owing to these results we can conclude that:
When COV(C’) augments, the probability of slope failure PF is unchanged, for both hydrology conditions. But, when COV(Phi’) increases, PF remains constant in the case of absence of water table, whereas an important augmentation is recorded for saturated conditions. Therfore the presence of water table increase the risque of slope faillure with the variation of friction angle.
Regarding the reliability index RI, we note the same evolution of this parameter (reduction), for both cases with and without water table, when COV(C’) increases and also in the case of the absence of water table, when COV(Phi’) varies. However, in the case of presence of water table, the RI undergoes slight changes associated with variations of COV(Phi’).
6.3. Impact of the variation of correlation between the soil properties (C’ and Phi’) on the PDF for both systems responses
The effect of the negative and positive correlations between the two soil properties (C’ and Phi’), on the PDFs and FOS, are considered in this section. The approximation of the system response is carried out through the Monte Carlo simulation (MCS) for both hydrology conditions, with and without groundwater table.
According to the results, as shown in Figures (17-a) and and (17-b). We can deduce that the PDF curves are largely affected by negative correlations between the two parameters of resistance C’ and Phi’, and leads to an increase of PDF values, this is true for both hydrology conditions. Whereas, we note that the positive correlations have minor effects on the PDF curves and they appear almost the same for both cases with and without water table. Regarding the FOS values, the positive and negative correlations have slight effects for both cases, with small increases of FOS values with negative correlations.