PSI - Issue 22

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0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 0 Factor of safety (FS)

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Unit weight of soil, γ (kN/m 3 )

(c) Unit weight of soil, γ (kN/m 3 )

(d) Safety factor

Mahdi Shadab Fara et al. / Procedia Structural Integrity 22 (2019) 345–352 Shadab Far and Huang / Structural Integrity Procedia 00 (2018) 000–000

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Safety Factor 0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000 4.500 5.000 5.500 6.000+

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Overall Slope Results FS (mean) = 1.049 PF = 26.060% RI (normal) = 0.415 RI (lognormal) = 0.371

Maximum water table level

Y max

Y w

W (max)

Distribution function for ground water level

W (mean)

Minimum water table level

W (min)

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(a) Uncertainty modeling of water table position

(b) Slip surfaces obtained from the Monte Carlo analysis

Fig. 5. Uncertainty modeling of water table level and resulting slip surfaces for Lodalen slope.

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Histogram of Ywn Cases where FS<1 Fitted distribution

Histogram of FS Cases where FS<1

Sample mean=0.4983 Sample std=0.167 Minimum=0.001892 Maximum=0.9979

Sample mean=1.049 Sample std=0.1173 Minimum=0.1448 Maximum=1.425

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Relative frequency

Relative Frequency

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Normalized water table location

Factor of safety (FS)

(a) Normalized water table location, Y wn

(b) The factor of safety, SF

Fig. 6. Histogram of the generated random samples for (a) Y wn and (b) FS.

in the form of a cumulative probability curve in Fig. 7a. Furthermore, the scatter plot of FS corresponding to each water table position is presented in Fig. 7b with a curve fitted to data. This result is of practical significance since the water table location corresponding to the target probability level can be estimated and utilized in the subsequent analysis and design process.

4. Di ff erent distribution functions for groundwater level modeling

One of the parameters that can influence the results of the analysis is the type of distribution function used in uncertainty modeling of groundwater level. The failure probability can be a ff ected depending on the estimate of the groundwater uncertainty. For this purpose, assuming di ff erent distribution functions for the groundwater level, new models are established and analyzed separately by the Monte Carlo simulation. The probability of failure obtained for each new case is shown in Table 3. Additionally, the failure probability against the safety factor is plotted in Fig. 8. As can be noticed, normal and triangular distribution functions o ff er relatively similar results. However, the uniform distribution function calculates a failure probability higher than the other cases. In other words, without having specific information about the potential position of groundwater level and corresponding probability distribution function, a