Nonlinear analysis of reinforced concrete foundation plates

Abstract

A nonlinear analysis of reinforced concrete foundation plates resting upon ground, based on a finite element model, capable of simulating the evolutive behavior up to rupture of the soil and/or of the RC plate, as well as of evaluating both the serviceability and the ultimate loads, is proposed. The contact problem between an RC plate and soil is solved by a unilateral elastic-plastic Winkler type model, where the plate-soil bonds have tensile strength equal to zero and compressive behavior described by a nonlinear curve, which is a function of geomechanical properties, capable of simulating phenomena such as the softening after the pressure has reached the maximum strength, as well as the residual strength. Moreover, the model also takes into account friction forces which arise on the contact surface between plate and soil. The RC plate is modeled by materially nonlinear layered finite elements where an orthotropic incrementally linear relationship and equivalent uniaxial concept are used to represent the behavior of concrete under biaxial stresses, while a uniaxial bilinear elasto-plastic model with hardening is employed for rebar. After cracking, the smeared orthogonal coaxial rotating crack model is adopted and tension stiffening, reduction in compressive strength and stiffness along the crack direction, and strain softening in compression are accounted for. The fundamental equations of the plate upon unilateral Winkler type ground are reviewed and generalized. The problem is solved by adopting an incremental approach, and the modified Newton-Raphson iteration method is employed to ensure convergency of nonlinear solution. The proposed finite element model was tested by comparisons with another analytical model available in literature, showing a good agreement. Furthermore, parametric analysis was conducted in order to investigate the influence of reinforced concrete nonlinear behavior of friction forces between plate and soil, and of relative density or consolidation index of the soil, on the nonlinear response of foundation plates.