Variational elastic solution for axially loaded piles in multilayered soil

Most analytical or semi‐analytical solutions of the problem of load‐settlement response of axially loaded piles are based on the assumption of zero radial displacement. These solutions also are only applicable to piles embedded in either a homogeneous or a Gibson soil deposit. In reality, soil deposits consist of multiple soil layers with different properties, and displacements in the radial direction within the soil deposit are not zero when the pile is loaded axially. In this paper, we present a load‐settlement analysis applicable to a pile with circular cross section installed in multilayered elastic soil that accounts for both vertical and radial soil displacements. The analysis follows from the solution of the differential equations governing the displacements of the pile–soil system obtained using variational principles. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. We compare the results from the present analysis with those of an analytical solution that considers only vertical soil displacements. The analysis presented in this paper also provides useful insights into the displacement and strain fields around axially loaded piles. Copyright © 2011 John Wiley & Sons, Ltd.     

Dynamic analysis of an axially loaded pile embedded in elastic-poroelasitc layered soil of finite thickness

This paper presents an analytical solution for determining the dynamic characteristics of axially loaded piles embedded in elastic-poroelastic layered soil of finite thickness. The interface between the elastic and poroelastic soil coincides with the groundwater table level, which is explicitly taken into account in the solution. The pile is modelled as elastic one-dimensional rod to account for the effect of its dynamic characteristics on the response of the soil-pile system. The solution is based on Biot's poroelastodynamic theory and the classical elastodynamic theory, which we use to establish the governing equations of the soil and pile. Accordingly, the pile base resistance, shaft reaction, and the complex impedance of soil-pile system are obtained using the method of Hankel integral transformation. Following the validation of the derived solution, we identify the main parameters affecting the vertical dynamic impedance of the pile via a parametric study. The presented method poses as an efficient alternative for quickly estimating the dynamic characteristics of axially loaded piles, without having to resort to complex numerical analyses.     

A simplified analysis method for piled raft foundations in non‐homogeneous soils

A simplified method of numerical analysis based on elasticity theory has been developed for the analysis of axially and laterally loaded piled raft foundations embedded in non‐homogeneous soils and incorporated into a computer program “PRAB”. In this method, a hybrid model is employed in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are approximated based on Mindlin's solutions for both vertical and lateral forces with consideration of non‐homogeneous soils. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups and capped pile groups in non‐homogeneous soils. Thereafter, the solutions from this approach for the analysis of axially and laterally loaded 4‐pile pile groups and 4‐pile piled rafts embedded in finite homogeneous and non‐homogeneous soil layers are compared with those from three‐dimensional finite element analysis. Good agreement between the present approach and the more rigorous finite element approach is demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

Method of initial parameters for laterally loaded piles embedded in layered soils

The method of initial parameters (MIP) was originally developed to solve the problem of a beam on an elastic foundation with applied concentrated forces along the span, which introduce discontinuities in the mathematical formulation of the problem. MIP is modified in this paper so that it can be used for solving the problem of a laterally loaded pile with discontinuities due to soil layering along the length of the pile. In this paper, the basis of MIP is outlined, and its use to find the deflection, slope, bending moment and shear force of laterally loaded piles is illustrated. Example problems of laterally loaded piles embedded in multi-layered soil media are provided.     

Axial and lateral response of pile groups embedded in nonhomogeneous soils

A numerical method of analysis based on elasticity theory is presented for the analysis of axially and laterally loaded pile groups embedded in nonhomogeneous soils. The problem is decomposed into two systems, namely the group piles acted upon by external applied loads and pile–soil interaction forces, and a layered soil continuum acted upon by a system of pile–soil interaction forces at the imaginary positions of the piles. The group piles are discretized into discrete elements while the nonhomogeneous soil behaviour is determined from an economically viable finite element procedure. The load–deformation relationship of the pile group system is then determined by considering the equilibrium of the pile–soil interaction forces, and the compatibility of the pile and soil displacements. The influence of soil nonlinearity can be studied by limiting the soil forces at the pile–soil interface, and redistributing the ‘excess forces’ by an ‘initial stress’ process popular in elasto-plastic finite element analysis. The solutions from this approach are compared with some available published solutions for single piles and pile groups in homogeneous and nonhomogeneous soils. A limited number of field tests on pile groups are studied, and show that, in general, the computed response compares favourably with the field measurements.     

Study on laterally loaded piles with rectangular and circular cross sections

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.     

Prediction of the shaft resistance of nondisplacement piles in sand

Using pile segment analysis, the mobilized shaft resistance of axially loaded nondisplacement piles in sand is investigated here. It is accepted that the shaft capacity of piles constructed in granular soils is highly influenced by the mechanical behavior of soil–structure interfaces forming adjacent the piles skin. Adopting the thin interface layer as a load transfer mechanism, a simple but accurate critical state compatible interface constitutive model is introduced. After evaluation, the interface model in conjunction with the pile segment analysis is applied for the prediction of the shaft resistance mobilized in nondisplacement piles. The proposed approach takes into account the influences of pile diameter and surface roughness together with the effects of the surrounding soil density and stiffness on the mobilized shaft resistance. The performance of the proposed method is verified by comparing its predictions with the experimental data of various model piles covering wide ranges of length, diameter, roughness, and surrounding soil properties. Copyright © 2012 John Wiley & Sons, Ltd.     

Discrete layer analysis of axially loaded piles and pile groups

This paper presents a simple discrete layer approach for the settlement analysis of axially loaded piles and pile groups. The soil profile may be arbitrarily layered and underlain by either a stiff or rigid stratum. The pile-soil-pile interaction is determined using a modified form of Mindlin's solution for finite soil depth. Good agreement between the present approach and more rigorous finite element and boundary element approaches is observed for the analysis of piles and pile groups embedded in finite soil layers. Settlement predictions obtained from the present approach also agree reasonably well with measurements from a number of published pile tests. Although the emphasis of this paper is on linear elastic solutions, it can easily be extended to include non-linear response.     

Piles under axial and torsional loads

An analysis of axially and torsionally loaded piles is presented in which the pile is treated as an elastic bar supported on two series of interacting non-linear axial and torsional springs. The characteristics of these springs depend on the soil properties and the diameter of the pile as well as on the interaction between the axial and torsional response. Predicted pile responses are compared to the results of model tests conducted on piles installed in a soft clay bed and loaded with combined axial and torsional loads. Both experimental results and theoretical predictions show that a torque applied to the pile head affects significantly the settlement and the axial bearing capacity of the pile.     

An analytical continuum model for axially loaded end-bearing piles in inhomogeneous soil

An approximate static solution is derived for the elastic settlement and load-transfer mechanism in axially loaded end-bearing piles in inhomogeneous soil obeying a power law variation in shear modulus with depth. The proposed generalised formulation can handle different types of soil inhomogeneity by employing pertinent eigenexpansions of the dependent variables over the vertical coordinate, in the form of static soil “modes”, analogous to those used in structural dynamics. Contrary to available models for homogeneous soil, the associated Fourier coefficients are coupled, obtained as solutions to a set of simultaneous algebraic equations of equal rank to the number of modes considered. Closed-form solutions are derived for the (1) pile head stiffness; (2) pile settlement, axial stress, and side friction profiles leading to actual, depth-dependent Winkler moduli, (3) displacement and stress fields in the soil; and (4) average, depth-independent Winkler moduli to match pile head settlement. The predictive power of the model is verified via comparisons against finite element analyses. The applicability to inhomogeneous soil of an existing regression formula for the average Winkler modulus is explored.     

A numerical approach to estimate shaft friction of bored piles in sands

A new approach to estimate shaft capacity of bored piles in sandy soils, based on numerical analysis, is presented. The topic is relevant as current design methods often largely underestimate the shaft capacity of piles in sands, thus resulting in an over-conservative design. The proposed approach is based on explicitly modelling the thin cylinder of soil surrounding the pile, where strain localization concentrates (shear band), and on the fundamental mechanic behaviour of sandy soils (e.g. dilatancy, softening). This approach is both simple and easy to apply. Results of a broad parametric study involving axially loaded single piles embedded in different sandy soils are presented, highlighting that relative density and grain size distribution mainly affect the shaft capacity. The capability of the procedure to predict shaft friction is checked against data from a well-documented full-scale axial load test on instrumented pile. Some suggestions for calibration and application of the method are also reported.     

层状地基中群桩水平振动

在考虑地基土分层的基础上,采用动力Winkler地基模型模拟桩土相互作用并运用传递矩阵,求解层状地基中的单桩和群桩的阻抗函数.在计算动力相互作用因子时考虑了被动桩与土的相互作用.最后将相互作用因子和群桩阻抗的本文解与精确解进行对比,验证了本文方法的有效性.     

Computerised processing of ground investigation data and use in predicting the load-settlement behaviour of piled foundations

A new computer program “PILESET” is developed for use in predicting the bearing capacity and load-settlement behaviour of axially loaded single piles. The program can analyse almost any soil profile and accommodates (a) displacement piles (b) replacement (c) friction piles, (d) end-bearing piles, (e) under-reamed piles and (f) partially sleeved piles. A variety of soil input data can be used, including: (i) standard penetration tests, (ii) cone/piezo-cone tests, (iii) pressure-meter tests and (iv) laboratory tests. The above data types can be combined, if desired, for pile analysis by PILESET. The program calculates the shaft and base capacities of a pile based on 23 methods published in design guides in over 10 European countries. PILESET also predicts the pile load-settlement curve using five published methods, which include two modified load transfer (t-z) approaches formulated by the author. To demonstrate the capabilities of the program, analysis is carried out for case study involving seven full-scale screw piles formed in sand and tested to failure. In each case, the load-settlement curve computed using the author’s modified method in PILESET is found to be in excellent agreement with the actual pile test results.     

Importance sampling based algorithm for efficient reliability analysis of axially loaded piles

In reliability analysis, the crude Monte Carlo method is known to be computationally demanding. To improve computational efficiency, this paper presents an importance sampling based algorithm that can be applied to conduct efficient reliability evaluation for axially loaded piles. The spatial variability of soil properties along the pile length is considered by random field modeling, in which a mean, a variance, and a correlation length are used to statistically characterize a random field. The local averaging subdivision technique is employed to generate random fields. In each realization, the random fields are used as inputs to the well-established load transfer method to evaluate the load–displacement behavior of an axially loaded pile. Failure is defined as the event where the vertical movement at the pile top exceeds the allowable displacement. By sampling more heavily from the region of interest and then scaling the indicator function back by a ratio of probability densities, a faster rate of convergence can be achieved in the proposed importance sampling algorithm while maintaining the same accuracy as in the crude Monte Carlo method. Two examples are given to demonstrate the accuracy and the efficiency of the proposed method. It is shown that the estimate based on the proposed importance sampling method is unbiased. Furthermore, the size of samples can be greatly reduced in the developed method.     

考虑加筋与遮帘效应计算群桩沉降的相互作用系数法

群桩中各基桩在地基土中的加筋与遮帘效应是客观存在的,然而,在目前的桩基沉降理论与实践中,相关的研究仍显不足。基于剪切变形法理论,考虑桩的加筋与遮帘效应,求得各基桩在自身桩顶荷载作用下产生的沉降以及其引起相邻桩的附加沉降量,由此提出群桩中任两桩的相互作用系数简化公式,同时,也得到各基桩桩侧及桩端桩-土接触等效弹簧刚度,并基于荷载传递法原理,建立了成层地基条件下各基桩在自身桩顶荷载作用下的桩身位移平衡方程,推导出各土层层顶处桩身沉降、轴力与层底处桩身沉降、轴力之间的递推关系,进而将公式推广到高、低承台群桩基础计算中。工程算例分析表明,用该方法计算有较高的精度,求得的荷载-沉降曲线及两桩相互作用系数与实测值吻合较好;相互作用系数要明显小于弹性理论计算结果。     

Numerical analysis of axially loaded vertical piles and pile groups

A numerical method, based on a simplified elastic continuum boundary element method, is presented for the settlement analysis of axially loaded vertical piles and pile groups. The soil flexibility coefficients are evaluated using the analytical solutions for a layered elastic half space. Results are presented and compared with existing published solutions for the following cases: (i) piles in homogeneous soil, (ii) piles in finite soil layer, (iii) piles end-bearing on stiffer layer, (iv) piles socketted into stiffer bearing layer, and (v) piles in Gibson soil. Reasonably good agreement is obtained between the present solutions and existing published solutions.     

碎石土斜坡水平受荷桩承载特性研究

斜坡上的桩基础的承载性能是复杂多变的。对于四川西部山地地形较广泛,且地基覆盖层多为特有的碎石土地层来说,水平受荷桩的相关研究还较少。为了研究碎石土地基斜坡上单桩基础的水平承载特性及桩土间的相互作用,通过现场水平静载荷试验在坡度为0°、15°、30°、45°的条件下,探讨桩身变形、桩身弯矩、土压力的变化。运用FLAC3D有限元分析软件得出水平荷载作用下,碎石土斜坡不同坡度的桩基础与桩周土之间的应力云图、位移云图的变化特点。将数值模拟结果与现场试验结果进行了对比,提出了单桩水平临界荷载和极限荷载在不同坡度区间内取值时的折减系数,为实际工程提供一定的参考。     

层状地基中轴向受荷单桩的边界元法分析

以层状地基内部作用一竖向集中力时的广义Mindlin解作为边界单元法的基本解,对层状地基中的轴向受荷单桩进行了分析,对基本解的奇异性处理方法进行了改进。考虑了桩的可压缩性和长径比对桩-土荷载传递规律和沉降特性的影响,编制了计算程序,并进行了数值分析和计算。结果表明,该方法具有较快的计算速度和良好的计算精度。     

General Analytical Solution for Laterally-Loaded Pile-Based Miche Model

Piles subjected to lateral loading can create problems in soil-structure interaction. Several differing methods of analysis have been proposed to solve the problem of laterally loaded piles, resulting in the determination of pile bending and the bending moment as a function of depth below soil surface. These piles are widely used to support laterally loaded piles, such as bridge pillars, offshore platforms, communication towers and others. This study presents an analytical solution to Miche’s problem as a continuous function of depth: deflection and moment, as well as a dimensional plots to be used in projects involving piles subjected to laterally loading only including data concerning laterally loading test and pile geometry. A new formula is presented to calculate the pile head displacement as well as an equation to determine maximum moment for a generalized Miche model and further analysis. In addition, this paper proposes an equation for the determination of constant horizontal subgrade reaction \((n_{h})\) based on the CPT in-situ test and the geometric characteristics of the pile. Calibration of the analytical model showed good fit and conservative results regarding inclinometer data from an bored pile and good agreement with the literature results.