Exact Probability Equation for Friction Piles in Clay

Abstract

This paper presents exact probabilistic model as a complementary mathematicalbase for the traditional deterministic approach to quantify the selection of a factorof safety for each term of the load equation of friction piles in clay. The procedureof assigning a partial value of factor of safety for each clay layer using a quantifiedprobabilistic model instead of the use of a single global factor of safety for alllayers that based on arbitrarily judgments seems to introduce an enhancement toboth economical and safety consideration in the design procedure of the frictionpiles. it is suggested in this paper to derive probabilistic equation that describe eachlayer of the problem individually, each term of the pile load equation (clay layers) consists on a certain amount of uncertainty and each request assigning a certainvalue of factor of safety to eliminate this variability and to keep the probability offailure (which is more reliable risk index) at certain level. Exact probabilityequation is mathematically derived on the bases of the variability inherited in soilparameters (average un-drained shear strength and thickness of each clay layerinserted). The equation was verified using Monte carol simulation method andresults indicate excellent agreement in both, probability distribution shape andcalculated failure values. The relationship between factor of safety and probabilityof failure produced from the derived equation was inspected in addition to thesensitivity of the equation to the change of the variability of input parametersthrough a reference example.Keywords: Friction Pile, Load, Probability, factor of safety