1,721,164 research outputs found
"p-y" curves for piles in radially inhomogeneous soil
No full text“p-y” curves are used to simplify the pile response of laterally loaded piles at any given depth by describing the applied lateral soil reaction as a function of the lateral displacement. Simple analytical solutions in two-dimensions for system stiffness are available by modelling a segment of the pile surrounded by an annular zone of linear-elastic soil. Current solutions assume homogeneous soil conditions. However, installation of a bored pile in clay would result in a region of softened material immediately surrounding the pile-soil interface, which can be modelled using a function describing the variation of shear modulus with distance from the pile. Such functions are available in the literature using linear and power-law variations. This paper derives an improved solution for the system stiffness considering the effects of pile installation. The previously discussed annular zone of soil is split into multiple rings with each able to define an independent shear modulus. A solution for the overall system stiffness is provided. Three-dimensional and parameter effects are discussed
A simplified analytical model for developing “t-z” curves for axially loaded piles
No full textPile settlement estimation can be simplified using one-dimensional “t-z” curves to describe the relationship between shear stress and settlement at the pile-soil interface at a specific depth. This simplifies the two-dimensional continuum problem to that of a one-dimensional rod. Some analytical “t-z” curves are available in literature; however, to employ these solutions a suitable soil constitutive model, expressed in a flexibility form γ = γ(τ), must be chosen. This must be carefully calibrated against laboratory test data to accurately represent soil behaviour. This paper explores an alternative approach for piles in clay employing a direct similarity-based relationship between a shear stress-strain curve and a “t-z” curve. A linear-transformation factor is derived which can be applied to a representative soil test directly from the site to produce a “t-z” curve, thus removing the need to calibrate/integrate a suitable soil constitutive model. Suitable values for this factor have been obtained through comparison with existing analytical “t-z” curves
Axial kinematic response of end-bearing piles to P waves
Full text linkKinematic pile-soil interaction under vertically impinging seismic P waves is revisited through a novel continuum elastodynamic solution of the Tajimi type. The proposed model simulates the steady-state kinematic response of a cylindrical end-bearing pile embedded in a homogeneous viscoelastic soil stratum over a rigid base, subjected to vertically propagating harmonic compressional waves. Closed-form solutions are obtained for the following: (i) the displacement field in the soil and along the pile; (ii) the kinematic Winkler moduli (i.e., distributed springs and dashpots) along the pile; (iii) equivalent, depth-independent, Winkler moduli to match the motion at the pile head. The solution for displacements is expressed in terms of dimensionless transfer functions relating the motion of the pile head to the free-field surface motion and the rock motion. It is shown that (i) a pile foundation may significantly alter (possibly amplify) the vertical seismic excitation transmitted to the base of a structure and (ii) Winkler moduli pertaining to kinematic loading differ from those for inertial loading. Simple approximate expressions for kinematic Winkler moduli are derived for use in applications. © 2013 John Wiley & Sons, Ltd
Exact Winkler solution for laterally loaded piles in inhomogeneous soil
Full text linkA novel exact analytical solution is derived for the equation y(4)+xny=0 in the region x≥0, which is important for the analysis of piles in soil with stiffness varying with depth. To date, exact solutions for long piles are available only for the cases where n=−4, 0, and 1. For other values of the exponent n, solutions have formerly been obtained numerically, mainly by the finite-difference method or approximate analytical solutions. An inherent difficulty in obtaining solutions for long beams (which are used to model flexible piles) lies in the inability to isolate the regular, converging part of the solution over the singular part that diverges with increasing x. In this paper, an exact solution is derived for n>−4, focusing on the important case of semi-infinite beams. Key aspects of the problem such as the stiffness and flexibility matrices at the pile head, and the peak bending moments due to eccentrically acting lateral loads, are discussed. A novel approach for deriving Winkler spring moduli for combined force and moment loading is proposed and shown to provide good agreement with rigorous numerical continuum results
Analytical non-linear "m-θ" curves for monopiles in clay
No full textDependable predictions of monopile foundation response to lateral loads is crucial to the efficient design of offshore wind turbine foundations. For squat monopile foundations, it is important to incorporate the distributed non-linear moment-rotation response with depth, known as “m-θ” curves, in addition to traditional “p-y” curves and lumped force-displacement curves at the pile base. Recognising the limited number of “m-θ” curves available in the literature, this paper develops new theoretical “m-θ” curves using a rational two-dimensional horizontal pile/soil “slice” model to obtain improved representations of the stress and displacement fields in the soil around the pile. Firstly, this model undergoes validation through comparisons with available linear-elastic solutions. Subsequently, it is employed in conjunction with a numerical discretisation of the pile circumference to obtain non-linear “m-θ” curves accounting for both soil yielding and slippage between pile and soil. The resulting curves are compa
Simplified models for axial static and dynamic analysis of pile foundations
Full text linkIn this chapter, simplified methods for static and dynamic analysis of pile foundations under axial loads are discussed. Firstly, a number of analytical solutions for Winkler springs and dashpots are briefly reviewed. Secondly, exact and approximate solutions for stiffness of single piles are derived for both homogeneous and inhomogeneous soil profiles using the Winkler model. The approximate solutions are based on energy principles obtained my means of shape functions analogous to those used in finite-element formulations. Thirdly, solutions for grouped piles are derived using the superposition approach of Poulos and Davis. To this end, a family of interaction factors accounting for pile-soil-pile interaction is reviewed. It is shown that soil inhomogeneity and pile-to-pile interaction may have a profound impact on pile head stiffness and ensuing settlement. Results are presented in the form of dimensionless graphs and charts that elucidate critical aspects of the problem, and detailed comparisons with more rigorous numerical continuum solutions are provided. Application examples are presented and discussed
Size Limitations for Piles in Seismic Regions
Full text linkA novel theoretical study exploring the importance of pile diameter in resisting seismic actions of both the kinematic and the inertial type, is reported. With reference to a pile under a restraining cap, is shown analytically that for any given set of design parameters, a range of admissible pile diameters exists, bounded by a minimum and a maximum value above and below which the pile will yield at the top even with highest material quality and amount of reinforcement. The critical diameters depend mainly on seismicity, soil stiffness and safety factor against gravity loading, and to a lesser extent on structural strength. This scale effect is not present at interfaces separating soil layers of different stiffness, yet it may govern design at the pile head. The work at hand deals with both steel and concrete piles embedded in soils of uniform or increasing stiffness with depth. Closed-form solutions are derived for a number of cases, while others are treated numerically. Application examples and design issues are discussed.<br/
Similarity-Based Nonlinear Settlement Predictions of Circular Surface Footings on Clay
No full textThe similarity method, employed to obtain nonlinear settlement predictions in undrained conditions for rigid circular footings on deep clay deposits, was introduced more than 70 years ago. This approach is based on the premise that the pressure–settlement curve of the footing and a stress–strain curve from a characteristic point in the soil can be linearly scaled to collapse into a single master curve. The method has been extended to predict deflections of axially and laterally loaded piles and is widely used in the offshore industry. Despite the theoretical and practical appeal of the method as well as its wide application in a range of geotechnical problems, limited investigation and validation exists in the literature. In this work existing classical similarity methods are reviewed, including a Boussinesq solution for elastic soil and the mobilizable strength design (MSD) method. The similarity factors derived from these methods are compared with those obtained from a novel nonlinear cone model solution, and the resulting expressions are evaluated against rigorous numerical analyses undertaken by the authors in FLAC. These are based on two different nonlinear constitutive models (hyperbolic and tanh) calibrated against triaxial tests from three clay deposits. Two alternative families of similarity methods are also compared with classical similarity, namely, a two-part similarity technique (based on separate scaling factors for elastic and plastic strains) and a stiffness similarity approach (based on secant stiffness degradation). Finally, three field test results are evaluated as case studies to demonstrate the applicability of the method in real-life problems. It is concluded that similarity approaches offer a rational yet approximate tool for nonlinear settlement analysis of footings
Theoretical t-z curves for axially loaded piles
No full textEstimation of nonlinear pile settlement can be simplified using one-dimensional “t-z” curves that conveniently divide the soil into multiple horizontal “slices.” This simplification reduces the continuum analysis to a two-point boundary-value problem of the Winkler type, which can be tackled by standard numerical procedures. Theoretical “t-z” curves can be established using the “shearing-of-concentric-cylinders” theory of Cooke and Randolph-Wroth, which involves two main elements: (1) a constitutive model cast in flexibility form, γ=γ(τ); and (2) an attenuation function of shear stress with radial distance from the pile, τ=τ(r). Soil settlement can then be determined by integrating shear strains over the radial coordinate, which often leads to closed-form solutions. Despite the simplicity and physical appeal of the method, only a few theoretical “t-z” curves are available in the literature. This paper introduces three novel attenuation functions for shear stresses, inspired by continuum solutions, which are employed in conjunction with eight soil constitutive models leading to a set of 32 “t-z” curves. Illustrative examples of pile settlement calculation in two soil types are presented to demonstrate application of the method.<br/
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