The Osterberg cell (O-cell) type of bidirectional pile load testing is a modern full-scale proofing method in the realm of performance-based pile design. It is done at considerable cost, not possible on small- to medium-size projects. An economical approach of utilizing the flexible and approximate analytical solution proposed by Randolph has frequently been adopted in the past for evaluating pile settlements under static, unidirectional, top-down axial compression loading. To extend this solution for O-cell loadings, the following adaptations are warranted: (i) appropriate modifications to handle the loadings in two directions and (ii) development of a nonlinear stiffness reduction model, derived from the back-analysis of O-cell pile load tests. Accordingly, a modified analytical solution is presented for the two common cases of O-cell loading arrangements. Using these modified sets of solutions and a well-documented database of O-cell load tests on drilled shaft foundations from different sites, two stiffness reduction models have been developed. The shear wave velocity readings obtained from the hybrid geophysical–geotechnical seismic piezocone tests afford the evaluation of fundamental shear stiffness modulus (Gmax) profiles. These profiles together with the re-arranged modified solution were applied to the axial loads versus displacements (Q–w) from the database of load tests to back-calculate the applicable operational shear stiffness (G) values. Additional sensitivity analyses indicate that pile geometry and soil stiffness profile are the two most significant factors affecting the outcome of this solution. A comprehensive set of step-by-step example calculations is included to explain the procedure for implementing the solution.
ANALYTICAL SOLUTION OF PARTIAL TASKS OF SHEAR WAVE IN A CYLINDRICAL LAYER (in the case of the constant values γ-α + 2 = 0 and α = β)
