A probabilistic formulation to assess the slopes safety under the hazard of strong storms is presented and illustrated through a slope in Mexico. The formulation is based on the classical safety factor (SF) used in practice to appraise the slope stability, but it is introduced the treatment of uncertainties, and the slope failure probability is calculated as the probability that SF<1. As the main hazard is the rainfall on the area, statistics of rainfall intensity and duration are considered and modeled with an exponential distribution. The expected life-cycle cost is assessed by considering a monetary value on the slope failure consequences. Alternative mitigation measures are simulated, and the formulation is used to get the measures driving to the optimal one (minimum life-cycle costs). For the example, the optimal mitigation measure is the reduction on the slope inclination angle.
Water erosion is the most important problems of the soil in the Jabel Nefusa area located in northwest of Libya; therefore, erosion station had been established in the Faculty of Veterinary and dryfarming research Station, University of the Al-japel Al-gharbi in Zentan. The length of the station is 72.6 feet, 6 feet width and the percentage of its slope is 3%. The station were established to measure the amount of soil eroded and amount of surface water produced during the seasons 95/96 and 96/97 from each rain storms. The monitoring shows that there was a difference between the two seasons in the number of rainstorms which made differences in the amount of surface runoff water and the amount of soil eroded between the two seasons. Although the slope is low (3%), the soil texture is sandy and the land ploughed twice during each season surface runoff and soil eroded were occurred. The average amount of eroded soil was 3792 grams (gr) per season and the average amount of surface runoff water was 410 liter (L) per season. The amount of surface runoff water would be much greater from Jebel Nefusa upland with steep slopes and collecting of them will save a valuable amount of water which lost as a runoff while this area is in desperate of this water. The regression analysis of variance show strong correlation between rainfall depth and the other two depended variable (the amount of surface runoff water and the amount of eroded soil. It shows also strong correlation between amount of surface runoff water and amount of eroded soil.