Probabilistic bearing serviceability of drilled shafts in randomly stratified rock using a geostatistical perturbation method

摘要

The bearing stiffness (i.e., the slope of load-displacement curve at the tip) of drilled shaft foundations is an important serviceability-design parameter, especially for rock-socketed application of shallow embedment depths. Numerical solution techniques, such as finite element analysis (FEA) models, provide useful tools for investigating the bearing (tip) stiffness under various boundary conditions both homogeneous and heterogeneous. However, for uncertain and spatially heterogeneous mechanical input parameters, computational costs are high when meaningful statistical parameters of tip stiffness are to be obtained from full Monte Carlo FEA simulations. In the present work, an analytical expression for a one-dimensional, linear load-displacement relationship is derived by making use of perturbation analysis on randomly-stratified rock layers and their effects in the development of the tip stiffness using two-dimensional axisymmetric FEA. Numerical results show that spatial variability in both elastic modulus and undrained shear strength (cohesion) of supporting rock layers affect tip stiffness. However, the influence of cohesion on expectation and uncertainty of tip stiffness may be safely neglected for serviceability design. The tip stiffness of a drilled-shaft foundation is found to be highly proportional to the harmonic average of elastic moduli with averaging weights decreasing exponentially from the shaft tip downward. Exponentially-weighted harmonic averaging of elastic moduli is then incorporated in Winkler models to reasonably predict the results of full Monte Carlo FEA for cases where (1) a depth profile of elastic modulus is available at the footprint of a shaft, and (2) only geostatistical characteristics (i.e., expectation, variance, correlation length) of elasticity of rock are known a priori at a construction site. The presented closed-form solution is in good agreement with predictions of Monte Carlo FEA, and thus, may offer a practical alternative tool for the serviceability design. (C) 2016 Elsevier Ltd. All rights reserved.