Stochastic analysis of strip footings on elastic layered soil

In the present work, Monte Carlo simulation assisted analysis of strip footings resting on elastic layered soil has been carried out. The elastic modulii of soil layers have been treated as a stationary stochastic field characterized by mean, variance, Autocorrelation Function (ACF) and the Autocorrelation Distance (ACD). Realizations of elastic modulii (E), generated by solving a stochastic differential equation, have been fed to a deterministic distributed parameter model to generate realizations of dependent stochastic fields viz. settlement of footing and interfacial vertical stresses. Subsequently these realizations have been analyzed to evolve probability distribution functions, variance and ACF of the dependent stochastic fields. It is revealed that ACF of these fields are independent of the ACF of E. The variance of settlement has been found to increase as the ACD of E increases, implying requirement of a larger factor of safety when random soils display low frequency (macro level) variations. On the other hand variance of the vertical stress is larger at smaller ACD of E, indicating that for vertical stress, larger factor of safety is required when the random soils display high frequency (micro level) variations.