Numerical Analyses of Plate Loading Test

A numerical simulation of plate loading test, in order to underlines the size effect on settlements and derived values of geotechnical parameters, is shown. The study is based on the comparison between the results obtained by Finite Element Method (FEM) using the Mohr-Coulomb soil model and by some observations from literature. The obtained numerical results revealed that the subgrade reaction coefficient is strictly dependent on parameters like size of the loaded area and loading magnitude, and thus completely general and generic, and not a fundamental material property of soil that can somehow be determined rationally, as often one claims to be

Beams on Elastic Foundation. The Simplified Continuum Approach

The key aspect in the design of flexible structural elements in contact with bearing soils is the way in which soil reaction, referred to qualitatively as soil’s reactive pressure (p), is assumed or accounted for in analysis. A magnitude and distribution of p might be preliminary assumed, or some mathematical relationships could be incorporated into the analysis itself, so that p is calculated as part of the analysis. In order to eliminate the bearing soil reaction as a variable in the problem solution, the simplified continuum approach is presented. This idealization provides much more information on the stress and deformation within soil mass compared to ordinary Winkler model, and it has the important advantage of the elimination of the necessity to determine the values of the foundation parameters, arbitrarily, because these values can be computed from the material properties (deformation modulus, Es, Poisson ratio, νs and depth of influence zone, H, along the beam) for the soil. A numerical investigatio proach is also presented

Beam Elements on Linear Variable Two-Parameter Elastic Foundation

The traditional way to overcome the shortcomings of the Winkler foundation model is to incorporate spring coupling by assemblages of mechanical elements such as springs, flexural elements (beams in one-dimension, 1-D, plates in 2-D), shear-only layers and deformed, pretensioned membranes. This is the class of two-parameter foundations ? named like this because they have the second parameter which introduces interactions between adjacent springs, in addition to the first parameter from the ordinary Winkler?s model. This class of models includes Wieghardt, Filonenko-Borodich, Hetényi and Pasternak foundations. Mathematically, the equations to describe the reaction of the two-parameter foundations are equilibrium, and the only difference is the definition of the parameters. In order to analyse the bending behavior of a Euler-Bernoulli beam resting on linear variable two-parameter elastic foundation a (displacement) Finite Element (FE) formulation, based on the cubic displacement function of the governing differential equation, is introduced

A Finite Element Study of the Bending Behavior of Beams Resting on Two-Parameter Elastic Foundation

Although the Winkler’s model is a poor representation of the many practical subgrade or subbase materials, it is widely used in soil-structure problems for almost one and a half century. The foundations represented by Winkler model can not sustain shear stresses, and hence discontinuity of adjacent spring displacements can occur. This is the prime shortcoming of this foundation model which in practical applications may result in significant inaccuracies in the evaluated structural response. In order to overcome these problem many researchers have been proposed various mechanical foundation models considering interaction with the surroundings. Among them we shall mention the class of two-parameter foundations -- named like this because they have the second parameter which introduces interactions between adjacent springs, in addition to the first parameter from the ordinary Winkler’s model. This class of models includes Filonenko-Borodich, Pasternak, generalized, and Vlasov foundations. Mathematically, the equations to describe the reaction of the two-parameter foundations arc equilibrium ones, and the only difference is the definition of the parameters. For the convenience of discussion, the Pasternak foundation is adopted in present paper. In order to analyse the bending behavior of a Euler-Bernoulli beam resting on two-parameter elastic foundation a (displacement) Finite Element (FE) formulation, based on the cubic displacement function of the governing differential equation, is introduced. The resulting effects of shear stiffness of the Pasternak model on the mechanical quantities are discussed in comparison with those of the Winkler’s model. Some numerical case studies illustrate the accuracy of the formulation and the importance of the soil shearing effect in the vertical direction, associated with continuous elastic foundation