Evaluation of shallow foundation displacements using soil small-strain stiffness
Elhakim, Amr F.
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Foundation performance is controlled significantly by the stress-strain behavior of the underlying soils. For geomaterials, the small-strain shear modulus Gmax is a fundamental stiffness applicable to both monotonic static and dynamic loading conditions, as well to both drained and undrained loading. Yet, Gmax is too stiff for direct use in computing foundation displacements. The main objectives of this research are to: (1) explore the scaled parallelism between the stress-strain-strength behavior of the single soil element response and the load-displacement-capacity of a shallow foundation system supported on soil; (2) develop a methodology for evaluating the performance of vertically-loaded footings using a rational framework based on the small-strain modulus Gmax, large-strain strength ( and #964;max or su) and strain at failure ( and #947;f); and (3) calibrate the proposed method using a foundation database of full-scale load tests under both undrained and drained conditions. In geotechnical practice, foundation bearing capacity is handled as a limit plasticity calculation, while footing displacements are evaluated separately via elastic continuum solutions. Herein, a hybrid approach is derived that combines these two facets into a closed-form analytical solution for vertical load-deflection-capacity based on numerical studies. Here, a non-linear elastic-plastic soil model was developed to simulate the stress-strain-strength curves for simple shearing mode (LOGNEP) for each soil element. The model was encoded into a subroutine within the finite difference program FLAC. A large mesh was used to generate load-displacement curves under circular and strip footings for undrained and drained loading conditions. With proper normalization, parametric foundation response curves were generated for a variety of initial stiffnesses, shear strengths, and degrees of non-linearity in the soil stress-strain-strength response. Soil stress-strain non-linearity is described by a logarithmic function (Puzrin and Burland, 1996, 1998) that utilizes a normalized strain xL that relates strain at failure and #947;f, shear strength ( and #964;max or su), and small-strain stiffness Gmax, all having physical meaning. A closed-form algorithm is proposed for generating non-linear load-displacement curves for footings and mats within an equivalent elastic framework. The proposed method was calibrated using a database of well-documented footing load tests where soil input parameters were available from laboratory and/or in-situ field test results.