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The traditional method for analysis and design of laterally loaded piles with non-circular cross-sections such as rectangular, H-shaped, and X-shaped piles involves the simplification of converting the non-circular pile to a circular pile with equivalent second moment of inertia. A rigorous semi-analytical method is developed for calculating the response for laterally loaded piles with arbitrary non-circular cross-sections in multi-layered elastic soil without using any simplification regarding the shape of the pile cross-section. The governing differential equations for the pile–soil system are obtained using the principle of virtual work. The soil displacements around the pile are described as products of separable functions that are compatible with horizontal pile movement. As a result, the three-dimensional (3 D) boundary value problem (BVP) is described by a fourth-order linear ordinary differential equation (ODE) governing horizontal pile displacement and second-order partial differential equations (PDEs) governing soil displacements. New solution techniques for the ODE and PDEs are proposed, and the accuracy of the present method is verified by comparing the predicted pile and soil responses with the corresponding results of equivalent 3 D finite element method. The effects of pile cross-section shape and lateral loading direction on the pile and soil responses are highlighted through a series of parametric analyses. [ABSTRACT FROM AUTHOR]

Short stubby piles like monopiles and large diameter drilled shafts undergo rigid body translation and rotation when subjected to a lateral force and/or a moment at the head. A method of analysis for these piles embedded in multi-layered elastic soil is developed using the variational principles of mechanics. Using this analysis, the soil resistance against pile movement can be rigorously related to the soil elastic constants, and the pile head displacement and rotation can be quickly calculated. The equilibrium equations for pile and soil displacements are obtained using the principle of virtual work and solved using an iterative algorithm. Pile responses obtained from the analysis match well with those obtained from three-dimensional finite element analyses in which the same inputs of loads, geometry, and material properties are given. Based on the new analysis, fitted equations for soil resistance parameters are developed, which can be used to directly calculate the pile head displacement and rotation without the use of the iterative algorithm. Numerical examples are provided that demonstrate how the method can be used to analyse practical problems. [ABSTRACT FROM AUTHOR]

A computationally efficient continuum-based model is developed for obtaining the nonlinear response of pile foundations subjected to a static horizontal force and/or moment at the pile head. In the analysis, the soil is modeled using nonlinear elastic constitutive relationships expressed as power-law or hyperbolic equations; these relationships relate the induced shear strain in soil to the secant shear modulus. The soil displacements in the horizontal plane are expressed as products of separable functions maintaining compatibility with the horizontal pile movement, and the principle of virtual work is applied to obtain the governing differential equations describing pile and soil displacements under equilibrium. These differential equations are solved using the one-dimensional finite-difference method following an iterative algorithm. The soil resistance parameters associated with the pile-displacement differential equation capture the effect of soil nonlinearity because these parameters are related to the secant shear modulus at different points in the soil. The accuracy and computational efficiency of the present analysis are established by comparing the pile and soil responses with those obtained from equivalent three-dimensional finite-element analysis which used the same soil constitutive relationships. The present analysis framework is further validated against the results of two full-scale field pile-load tests. Furthermore, monopile responses obtained from the present analysis are compared with those of three-dimensional finite-element analyses in which the soil is modeled as an elastoplastic material. It is shown that, for the purpose of design against lateral loads, elastoplastic approaches are not necessary because the present nonlinear elastic analysis can produce sufficiently accurate pile and monopile responses. [ABSTRACT FROM AUTHOR]

A semianalytical method is developed to obtain the dynamic response of laterally loaded piles in a multilayered soil. In the analysis, the soil is modeled as a three-dimensional viscoelastic continuum with frequency-independent hysteretic material damping and the pile as a circular elastic Timoshenko beam. Unlike the Euler-Bernoulli beam that is conventionally used to model laterally loaded piles in various analytical, semianalytical, and numerical studies, the Timoshenko beam theory accounts for the effect of shear deformation and rotatory inertia within the pile cross-section that might be important for modeling short stubby piles with solid or hollow cross-sections and piles subjected to high frequency of loading. In the analysis, the soil displacements in the horizontal direction are expressed as products of separable functions, and the extended Hamilton's principle in conjunction with the calculus of variations is used to obtain two sets of coupled differential equations governing pile and soil motions along with the relevant boundary conditions. The coupled equations are solved analytically and numerically following an iterative algorithm. The differential equation and boundary conditions governing pile motion are progressively reduced to model the pile as a Rayleigh beam and a Euler-Bernoulli beam; thus, a unified framework incorporating various beam theories for the dynamic soil-structure interaction of laterally loaded piles in a multilayered soil is developed. The accuracy of the present analysis is verified against the results of several analytical and numerical solutions available in the literature. It is shown from the solved example problems that rotatory inertia has practically no effect on the dynamic response of piles, whereas there is some effect of shear deformation on the response of piles with hollow cross-sections. [ABSTRACT FROM AUTHOR]

A continuum-based method is developed for the analysis of laterally loaded piles in multilayered, heterogeneous elastic soil. The analysis considers the soil as a layered elastic continuum in which the modulus varies linearly or non-linearly with depth within each layer. Rational soil displacement fields are assumed and differential equations describing the pile and soil displacements are obtained using the principle of minimum potential energy. The differential equations describing the pile and soil displacements are solved using the Ritz method and the finite difference method, respectively, following an iterative numerical scheme. The analysis is used to study different pile geometries embedded in layered soil deposits with heterogeneity in each layer. The pile displacement, rotation, and maximum bending moment obtained from the analysis were found to be in good agreement with those obtained from an equivalent three-dimensional finite element analysis and from other studies available in the literature. The analysis can be used to obtain the pile head displacement, rotation, and maximum bending moment that can then be used in design. [ABSTRACT FROM AUTHOR]

A new method for calculation of head displacement and rotation of laterally loaded rigid monopiles and poles in multilayered heterogeneous elastic soil is presented. The analysis considers the soil as a layered elastic continuum in which the modulus vary linearly with depth within each layer. Rational pile and soil displacement fields are assumed, and the interaction between the pile and soil is taken into account by using the principle of virtual work. Two sets of equilibrium equations, one describing the pile displacement and rotation and the other describing the displacements in the soil, are obtained and solved analytically and numerically following an iterative algorithm. The new method produces pile responses as accurate as those obtained from three-dimensional finite element analysis but does not require any elaborate input for geometry and mesh. [ABSTRACT FROM AUTHOR]

The conventional approach in the design of laterally loaded piles with rectangular cross section involves the simplification of converting the rectangular cross section of the pile to an equivalent circular cross section. An analysis to determine the response of laterally loaded rectangular or circular piles in elastic soil is presented in which this simplification is not required. The analysis is based on the solution of differential equations governing the displacements of the pile–soil system derived using energy principles. The pile geometry and the elastic constants of the soil and pile are the input parameters to the analysis. Using this analysis, comparisons are made between the response of rectangular and circular piles in elastic soil. Based on the proposed solution scheme, a user-friendly spreadsheet program (LATPAXL) was developed that can be used to perform the analysis. In addition, simple equations obtained by regression analysis of the pile head deflection and bending moment profiles are proposed. Examples illustrate the use of the analysis. [ABSTRACT FROM PUBLISHER]

Continuum-based analyses for laterally loaded piles with rectangular and circular cross sections are presented using solutions that can be obtained quickly without requiring any elaborate inputs for the geometry and numerical mesh. The analysis is developed by solving the differential equations governing the displacements of the pile-soil system derived using the variational principles of mechanics. Parametric studies are performed to investigate the influence of the pile cross-sectional shape, soil layering, pile slenderness ratio, and pile-soil modulus ratio on the response of laterally loaded piles in heterogeneous soil in which the soil shear modulus varies continuously or discretely with depth. The results show that piles with the same second moment of inertia have similar lateral-load response. The lateral responses of piles in two-layer systems were mainly affected by the thickness and stiffness of the top soil layer. Soil layering also influences the lateral response of piles in three-layer soil deposits consisting of two thin layers overlying the third layer. Algebraic equations for estimating the pile-head deflection and maximum bending moment are proposed that can be readily used in design. A user-friendly spreadsheet program is developed as a tool to perform calculations of pile response using the analysis. Numerical examples demonstrating the use of the analysis are provided. [ABSTRACT FROM AUTHOR]

Laterally loaded piles are analyzed using the Fourier FEM. The analysis is performed for piles embedded in single-layer elastic soil with constant and linearly varying modulus and in two-layer elastic soil with constant modulus within each layer. The pile responses were observed to be functions of the relative stiffness of pile and soil, and of the pile slenderness ratio. Based on the analysis, equations describing pile head deflection, rotation, and maximum bending moment are proposed for flexible long piles and stubby rigid piles. These design equations are developed after plotting the pile responses as functions of pile-soil stiffness ratio and pile slenderness ratio. These plots can also be used as design charts. Design examples illustrating the use of the analysis are provided. [ABSTRACT FROM AUTHOR]