Initiating at the small-strain shear modulus (G_(max)), the mechanical nonlinear stress-strain-strength behavior of soil manifests in the form of modulus reduction, typically expressed in normalized form as G_(op)/G_(max). Here, G_(op)is the operative shear modulus – a reduced stiffness value corresponding to strain levels that the soil is experiencing. Assessment of G_(op)is critical to reliable predictions of load-related deformations within the soil. Among the various categories of loading, deep foundations and pilings exhibit a typical mechanism of axial load transfer to the foundation soil. For friction type piles, the stiffness reduction mostly takes place along the pile shaft-soil interface. Within the framework of an analytical solution, the back analyses from the results of load tests on pile foundations, together with the knowledge of pile geometries and soil parameters, provide an outline for evaluation of G_(op)at different load increments. This paper explains the methodology employed to develop stiffness reduction curves (G_(op)/G_(max)) as a function of pseudo-strain (γp = w_(t)/d), where, w_(t)= settlement at the pile top, and d = pile diameter. Algorithms that integrate the plasticity characteristics of the soil are also presented. The results afford an improved evaluation of the complete nonlinear load-settlement (Q-w_(t)) response for pile foundations under axial loads.
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