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Homework_30 - CEEN 641 ADVANCED SOIL MECHANICS HOMEWORK...

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CEEN 641 – ADVANCED SOIL MECHANICS HOMEWORK ASSIGNMENT #30 1. A 0.6 m wide strip foundation is to be constructed with an embedment of 0.3 m into the ground. The soil is characterized as having the following properties: drained friction angle = 36 ° , cohesion = 0 kPa, and unit weight = 18.1 kN/m 3 . The water table is very deep. The total load on the foundation is 80 kN/m (where the “per meter” refers to the dimension along the longitudinal axis of the foundation (i.e., the direction “in-and-out of the page”)). Determine the factor of safety against bearing capacity failure based on the tradition bearing capacity formula with bearing capacity factors shown below. (Don’t forget to convert the applied load to a pressure when calculating the factor of safety). γ γ γ N B N D N c q q f c ult + + = 2 1 where: ) 2 / 45 ( tan 2 ) tan ( φ φ π + × = e N q ) cot( ) 1 ( φ × = q c N N ) 4 . 1 tan( ) 1 ( φ γ × × = q N N Comment on whether or not the factor of safety is typically acceptable. 2. Perform a limited probabilistic bearing capacity analysis using a Monte Carlo simulation for the scenario presented in the previous problem. Assume that the values provided previously are mean values, and that standard deviation for the applied load is 15 kN/m and that the coefficient of variation for the friction angle is 12%. Assume that both applied load and friction angle are normally distributed, independent variables and that the other parameters are constant. For the purposes of this assignment, use 5,000 random trials.
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