Numerical model for the dynamic and seismic analysis of pile-supported structures with a meshless integral representation of the layered soil

This paper presents a three–dimensional linear numerical model for the dynamic and seismic analysis of pile-supported structures that allows to represent simultaneously the structures, pile foundations, soil profile and incident seismic waves and that, therefore, takes directly into account structure–pile–soil interaction. The use of advanced Green’s functions to model the dynamic behaviour of layered soils, not only leads to a very compact representation of the problem and a simplification in the preparation of the data files (no meshes are needed for the soil), but also allows to take into account arbitrarily complex soil profiles and problems with large numbers of elements. The seismic excitation is implemented as incident planar body waves (P or S) propagating through the layered soil from an infinitely–distant source and impinging on the site with any generic angle of incidence. The response of the system is evaluated in the frequency domain, and seismic results in time domain are then obtained using the frequency–domain method through the use of the Fast Fourier Transform. An application example using a pile-supported structure is presented in order to illustrate the capabilities of the model. Piles and columns are modelled through Timoshenko beam elements, and slabs, pile caps and shear walls are modelled using shell finite elements, so that the real flexibility of all elements can be rigorously taken into account. This example is also used to explore the influence of soil profile and angle of incidence on different variables of interest in earthquake engineering.

Stiffness matrix method for analysis of torsionally loaded piles in multi-layered soil

A new, simple, and practical method to investigate the response of torsionally loaded piles on homogeneous or non-homogeneous multi-layered elastic soil is developed. The soil non-homogeneity is accounted for by assuming for each layer a shear modulus distribution that fits a quadratic function. The analysis of piles in multi-layered soil is carried out by subdividing the pile, at the soil-soil layer and soil-air interfaces, into multiple elements, and then using conventional matrix methods -such as those commonly implemented in structural analysis- to connect them. The governing differential equation (GDE) of an individual structural element is solved using the Differential Transformation Method (DTM). Next, the stiffness matrix is derived by applying compatibility conditions at the ends of the element. Piles partially or fully embedded in multiple layers and subjected to torsion can be analyzed in a simple manner with the proposed formulation -a tedious endeavor with other available solutions. Finally, explicit expressions for the coefficients of the matrix are provided. Four examples are presented to show the simplicity, accuracy, and capabilities of the proposed formulation.

Energy-Based Approach for the Analysis of a Vertically Loaded Pile in Multi-layered Non-linear Soil Strata

Numerous studies have been reported in published literature on analytical solutions for a vertically loaded pile installed in a homogeneous single soil layer. However, piles are rarely installed in an ideal homogeneous single soil layer. This study presents an energy-based approach to obtain displacements in an axially loaded pile embedded in multi-layered soil considering soil non-linearity. A simple power law based on published literature is used where the soil is assumed to be nonlinear-elastic and perfectly plastic. A Tresca yield surface is assumed to develop the soil stiffness variation with different strain levels that defines the non-linearity of the soil strata. The pile displacement response is obtained using the software MATLAB R2019a and the results from the energy-based method are compared with those obtained from the field test data as well as the finite element analysis based on the software ANSYS 2019R3. It is observed that the results obtained from the energy-based method are in better agreement with the field measured values than those obtained from the FEA. The approach presented in this study can be extended to piles embedded in multi-layered soil strata subjected to different cases of lateral loads as well as the combined action of lateral and axial loads. Furthermore, the same approach can be extended to study the response of the soil to group piles.