Page - 866 - in Book of Full Papers - Symposium Hydro Engineering

foundations using Monte Carlo simulation and uncertainty parameters is calculated. Among input variables, the friction angle is considered as random variables and (ψ), (γ) and (B) are constant. The number of iterations to simulate is set to 200,000 times, also the coefficient of variation of soil friction angle is considered 15% [26, 27]. 5.1. NUMERICAL ANALYSIS In this section, to demonstrate the efficiency of the proposed model to analyze the bearing capacity of foundation, a numerical example is assumed. In the example a foundation with a width of 2 meters and granular soil with the unit weight of 19 kN/m3 are considered. Also The average of dilation angle (ψ) is assumed to be 6°. In calculating the definitive bearing capacity, the average friction angle is considered 25 degree. Safety factor in different iterations is calculated and the frequency graph of ultimate bearing capacity is shown in Figures 1 and 2. As can be observed the curve is continuous and follows the log-normal probability distribution function. In Figures 3 and 4 the procedure of calculating allowable bearing capacity with a confidence level of 90% are illustrated. Ultimate bearing capacity of foundation using Michalowski method is obtained 92.5 kN for smooth foundations and 176 kN for rough foundations. If the dam foundation with the assumed specifications is analyzed using Monte Carlo method, the cumulative distribution graph of bearing capacity could be as Figures 1 and 2. To select the allowable bearing capacity of foundation, regarding the desired confidence level, cumulative distribution graph of bearing capacity can be selected. it can be concluded that the confidence level required for structures is about 90 to 98%.For example, a confidence level of 90% indicates that 90% of simulated items have more bearing capacity than the allowable bearing capacity. According to Figures 3 and 4 allowable bearing capacity of smooth foundation due to the 90 percent of confidence level equals to 48.2 kN and for rough foundation this value is 95.9 kN. By comparing the allowable values and ultimate bearing capacity regarding confidence level of 90%, it can be pointed out that safety factors for smooth and rough foundations are obtained 1.92 and 1.83 respectively. According to the above explanation, it can be stated that the method of reliability analysis to calculate the bearing capacity of foundations is more reliable that certain methods, because in addition to reducing construction costs, this method handles the uncertainties that are also quantified. 6. CONCLUSIONS Reliability analysis methods, which consider uncertainties and estimate the probability of bearing capacity, can facilitate the engineering judgment. 866