Nonlinear Analysis of Deep Beam Resting on Linear and Nonlinear Random Soil

The soil–structure interaction has often a significant effect on the nonlinear structures response especially when the soil is modeled as a random medium. In fact, to ensure the design of economical and safe structure and to obtain a more realistic behavior of a beam, deterministic and probabilistic analyses of large displacements of a beam resting on linear and nonlinear soil are investigated. However, finite element models of Euler–Bernoulli and Timoshenko beam resting on elastic linear and nonlinear soil (Winkler and Pasternak) have been developed. The geometric nonlinear analysis of the beam is based on the updated Lagrangian Euler–Bernoulli and Timoshenko Von Kàrmàn beam formulations, which are then combined with the random field theory of soil using Monte Calro simulations. A Matlab code has been developed to solve the nonlinear equations by using the Newton–Raphson method. Various coefficients of soils, boundary conditions, beam properties and load types are taken into account to assess their effect on beam response. Moreover, to quantify the shear deformation effects on the nonlinear analysis, a comparison between Euler–Bernoulli and Timoshenko beams has been made and the influence of different beam heights has been taken into account to illustrate the divergence and the importance of the geometric nonlinearity. The obtained results indicated that the geometric nonlinearity of beam combined to material nonlinearity and spatial variability of soil and by taking into account the shear deformation effects, allowed us to obtain a more realistic behavior of beam and demonstrate the efficiency and accuracy of the developed models.