Evaluating reliability in geotechnical engineering - Risk and Reliability in Geotechnical Engineering - page 146

Table 3.3 Probabilities that the factor of safety is smaller than 1.0, based on a normal distribution of factor of safety
Coefficient of variation of factor of safety—COV F
F MLV 2% 4% 6% 8% 10% 12% 14% 16% 20% 25% 30% 40% 50% 60% 80%
1.05 0.9% 11.7% 21.4% 27.6% 31.7% 34.6% 36.7% 38.3% 40.6% 42.4% 43.7% 45.3% 46.2% 46.8% 47.6%
1.10 0.0% 1.2% 6.5% 12.8% 18.2% 22.4% 25.8% 28.5% 32.5% 35.8% 38.1% 41.0% 42.8% 44.0% 45.5%
1.15 0.0% 0.1% 1.5% 5.2% 9.6% 13.9% 17.6% 20.7% 25.7% 30.1% 33.2% 37.2% 39.7% 41.4% 43.5%
1.16 0.0% 0.0% 1.1% 4.2% 8.4% 12.5% 16.2% 19.4% 24.5% 29.1% 32.3% 36.5% 39.1% 40.9% 43.2%
1.18 0.0% 0.0% 0.6% 2.8% 6.4% 10.2% 13.8% 17.0% 22.3% 27.1% 30.6% 35.1% 38.0% 40.0% 42.4%
1.20 0.0% 0.0% 0.3% 1.9% 4.8% 8.2% 11.7% 14.9% 20.2% 25.2% 28.9% 33.8% 36.9% 39.1% 41.7%
1.25 0.0% 0.0% 0.0% 0.6% 2.3% 4.8% 7.7% 10.6% 15.9% 21.2% 25.2% 30.9% 34.5% 36.9% 40.1%
1.30 0.0% 0.0% 0.0% 0.2% 1.1% 2.7% 5.0% 7.5% 12.4% 17.8% 22.1% 28.2% 32.2% 35.0% 38.6%
1.35 0.0% 0.0% 0.0% 0.1% 0.5% 1.5% 3.2% 5.3% 9.7% 15.0% 19.4% 25.8% 30.2% 33.3% 37.3%
1.40 0.0% 0.0% 0.0% 0.0% 0.2% 0.9% 2.1% 3.7% 7.7% 12.7% 17.0% 23.8% 28.4% 31.7% 36.0%
1.50 0.0% 0.0% 0.0% 0.0% 0.0% 0.3% 0.9% 1.9% 4.8% 9.1% 13.3% 20.2% 25.2% 28.9% 33.8%
1.60 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 0.4% 1.0% 3.0% 6.7% 10.6% 17.4% 22.7% 26.6% 32.0%
1.70 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.2% 0.5% 2.0% 5.0% 8.5% 15.2% 20.5% 24.6% 30.3%
1.80 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 0.3% 1.3% 3.8% 6.9% 13.3% 18.7% 22.9% 28.9%
1.90 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.2% 0.9% 2.9% 5.7% 11.8% 17.2% 21.5% 27.7%
2.00 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 0.6% 2.3% 4.8% 10.6% 15.9% 20.2% 26.6%
2.20 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.3% 1.5% 3.5% 8.6% 13.8% 18.2% 24.8%
2.40 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.2% 1.0% 2.6% 7.2% 12.2% 16.5% 23.3%
2.60 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 0.7% 2.0% 6.2% 10.9% 15.3% 22.1%
2.80 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 0.5% 1.6% 5.4% 9.9% 14.2% 21.1%
3.00 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.4% 1.3% 4.8% 9.1% 13.3% 20.2%
Source: Duncan, J.M., 2000, Factors of safety and reliability in geotechnical engineering, Journal of Geotechnical Engineering , Vol. 126, No. 4, p. 307-316. Used with permission from ASCE.
F M LV = factor of safety computed using most likely values of parameters.