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.     

Finite element analyses of soil plug response

Open-ended pipe piles are often used in offshore foundations. The response of the soil plug inside a pipe pile is poorly understood, and only limited work has been performed to quantify the response under the different loading conditions relevant to offshore platforms. This paper describes numerical analyses that have been carried out in order to assess the end-bearing capacity of the soil plug under loading conditions which range from undrained to fully drained. The soil plug has been modelled as either elastic, elastic–perfectly-plastic or elastoplastic. The soil–pile interface, an important aspect of the problem, has been examined critically. Comparison with experimental data from model test at laboratory scale indicates that the load–deformation behaviour of the soil plug is modelled well using an elastoplastic model for the soil plug, and an elastic–perfectly-plastic joint element to model the soil–pile interface. The finite element analyses show that, under typical loading conditions, adequate end bearing may be mobilized by the soil plug, largely by high effective stresses in the bottom 3–5 diameters of the soil plug.     

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.     

Analysis of vertically loaded pile groups

An approach is presented for the analysis of linear and non-linear responses of vertically loaded pile groups. The soil behaviour of individual piles in modelled using load-transfer curves and the pile-soil-pile interaction is determined based on Mindlin's solution. Good agreement between the present method of analysis and the rigorous boundary integral method is observed for the computation of the response of pile groups embedded in a homogeneous, isotropic elastic half-space. The computed non-linear response of pile groups compares favourably with measured results from field load tests.     

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.     

Selection of p–y curves for the design of single laterally loaded piles

Two-dimensional finite element analysis has been used to find load–transfer relationships for translation of an infinitely long pile through undrained soil for a variety of soil-constitutive models. It has been shown that these load–transfer curves can be used as p–y curves in the analysis of single piles undergoing lateral pile head loading in undrained soils with non-linear stress–strain laws. Lateral pile response deduced from 2-D analysis input to the subgrade reaction method has been compared to the behaviour of a single pile analysed using three-dimensional finite element analysis. Good agreement between the two methods for non-linear soils suggests that the 2-D analysis may form a useful design method for calculation of p–y curves. Copyright © 1999 John Wiley & Sons, Ltd.     

An anisotropically elastoplastic solution to excavation responses of a circular opening considering three-dimensional strength

Circular opening is commonly encountered in wellbore drilling of petroleum engineering, boring for cast-in situ pile installation, and tunneling excavation. This paper presents a rigorous solution for the elastoplastic responses of the anisotropic soft soil mass around a circular opening excavated under undrained and drained conditions. Both the anisotropic elastoplastic behavior and the 3D strength of the soft clay are incorporated in the present solutions. The well-established anisotropic critical state elastoplastic model S-CLAY1, which can represent the initial fabric anisotropy and stress-induced anisotropy of soft soil, is further modified by the Spatially Mobilized Plane criterion to consider the 3D strength of geomaterials. Then, the investigated problems, excavation of a circular opening under both short-term (undrained) and long-term (drained) conditions, are formulated as a system of first-order differential equations and are solved as initial value problems. The distributions of stress components and anisotropy parameters around the opening, the stress trajectory of a soil particle at the opening wall, as well as the stress–displacement curve at the opening wall are presented to investigate the elastoplastic responses of the opening. Extensive parameters show that the overconsolidated ratio and coefficient of earth pressure at rest (K₀) have remarkable effects on the elastoplastic responses around a circular opening.

     

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.     

BEM analysis of the interaction factor for vertically loaded dissimilar piles in saturated poroelastic soil

This paper focuses on an analysis by the boundary element method (BEM) of the pile-to-pile interaction for pile groups with dissimilar piles of different pile lengths embedded in saturated poroelastic soil. The behaviour of the poroelastic homogeneous soil is governed by Biot’s consolidation equations. The pile–soil system is decomposed into extended soil and fictitious piles. Considering the compatibility of vertical strain between fictitious piles and soil, the second kind of Fredholm integral equations were obtained to predict the axial force and settlement along pile shafts numerically. For the analysis of the interaction factor, two loading conditions for a two-dissimilar-pile system were proposed: (a) only one pile is loaded and (b) each pile is subjected to a load proportional to the pile length. Furthermore, the two-pile system was extended to pile groups with a rigid cap to capture the optimum design where each pile shares the same loading at the pile heads. The optimum results require shortening the peripheral piles and elongating internal piles, and the consolidation effect needs to be considered due to the adjustment of loading distribution among piles.     

Boundary element analysis of axially loaded piles embedded in a multi-layered soil

In a field, piles are likely installed in a multi-layered soil. Analysis of axially loaded piles in a multi-layered soil is complicated and deserves more attention. A boundary element method is used in this study to analyze an axially loaded single pile in a multi-layered soil using the solution for vertical and horizontal axisymmetric ring loads in a multi-layered elastic medium. Good and reasonable agreement is obtained between the proposed and published solutions for a single pile in a homogenous soil, a finite soil, and a Gibson soil. The proposed solution is also used to evaluate an axially loaded single pile in a multi-layered (8 layers) soil.     

考虑沉桩效应的群桩非线性荷载-沉降解析

考虑沉桩效应对桩周土体力学特性的影响,采用指数函数型荷载传递曲线分别建立了静压桩的桩侧和桩端荷载传递模型。在此基础上,根据群桩加载过程中桩周土体的变形模式,基于荷载传递法描述桩-土界面的非线性行为,采用剪切位移法考虑群桩之间的相互作用,提出了考虑沉桩效应的群桩非线性荷载-沉降混合计算方法。通过开展离心模型试验对该计算方法解答进行了验证,研究了沉桩效应和桩-土界面非线性特征对群桩承载特性的影响。研究结果表明,沉桩效应对桩周土体起到挤密作用,使得桩周土体的强度和刚度增大,从而提高了群桩的承载特性。群桩加载过程中桩-土界面刚度随沉降变形而逐渐减小,使得群桩荷载-沉降曲线呈现出明显的非线性特征。     

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.     

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.     

非均质地基中群桩竖向荷载沉降关系分析

运用剪切位移法计算了桩轴向荷载传递因子。对于桩端采用线性的荷载传递函数,推导了基于弹塑性模型的单桩竖向荷载沉降的解析解。分析过程中考虑了土体强度沿深度线性变化的特性和桩土间的滑移现象,因此更符合大部分土体的实际性状。在此基础上,建立了考虑桩土滑移的桩-桩相互作用系数的计算公式,并将上述方法应用于群桩的分析,获得了群桩的荷载沉降特性。该分析方法克服了目前应用较多的弹性理论方法夸大桩土相互作用的缺点,单桩和群桩的荷载沉降曲线的分析结果和实测数据吻合,证明了该方法的合理性。     

水平受荷长桩弹塑性计算解析解

当考虑桩侧土体非线性本构关系时对水平受荷桩的计算一般需采用数值方法,解析结果相对较少。基于Winkler地基模型和桩侧土体简化的弹塑性本构关系,对均质地基中水平荷载作用下桩头嵌固的长桩进行了解析推导,得到了桩身最大挠度及最大弯矩与荷载关系的统一解析表达式,并采用相同的方法求得高桩情形下桩头挠度的计算式。计算表明,联合荷载作用下桩身泥面处的挠度和转角不等于单个荷载作用时的线性叠加,采用常规的线性叠加法计算将偏于不安全。所求解析式借助计算器即可进行最大挠度和最大弯矩的计算,大大方便了工程的计算应用。     

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.     

The P-y Response of Laterally Loaded Flexible Piles in Residual Soil

This paper describes the main features related to lateral displacements with depth after successive lateral loading–unloading cycles applied to the top of reinforced-concrete flexible bored piles embedded in naturally bonded residual soil. The bored piles under study have a cylindrical shape, with 0.40-m in diameter and 8.0-m in length. Both bored piles types (P1 and P2) include an embedded steel pipe section in their center as longitudinal steel reinforcements: pile type P1 has another 16 steel rods as steel reinforcement to concrete while pile type P2 has no further steel reinforcement. Pile type P1 has three times as much stiffness (EI) and four and a half times the plastic moment (M_y) than pile type P2. A similar load–displacement performance was observed at initial loads as for small displacements of both piles. At this initial loading stage, the response of the reinforced concrete piles is a function of the soil characteristics and of a linear elastic pile deformation. During this stage, piles can even be understood as probes for evaluating soil reactions. For larger horizontal displacements, after the concrete section starts undergoing large deformations, approaching the ultimate bending moment, pile behavior and consequently the load–displacement relation starts to diverge for both piles. For pile P1 the values of relevant lateral displacements are extended to about 2.5-m in depth, while for pile P2 lateral displacements are mostly constrained to about 2.0-m in depth. Measurements of horizontal displacements of pile P1 against depth recorded with a slope indicator show that, after unloading, lateral loads at distinct stages (small and near failure loads), exhibits a much higher elastic phase of the system response. An analytical fitting model of soil reaction is proposed based on the measured displacements from slope indicator. The integration of a continuous model proposed for the soil reaction agrees fairly well with the measured displacements up to moments close to plastic limit. Results of load–displacement show that the stiffer pile (P1) was able to mobilize twice as much lateral load compared to pile P2 for a service limit displacement of about 20 mm. The paper shows results that enable the isolation of the structural variable through real scale pile load tests, thus granting understanding of its importance and enabling its quantitative visualization in examples of piles embedded in residual soil sites.

     

Experimental study on the mechanical behaviour of a heat exchanger pile using physical modelling

This study aims to provide knowledge on the thermo-mechanical behaviour of heat exchanger piles, through a laboratory scale model. The model pile (20 mm in external diameter) was embedded in dry sand. The behaviour of the axially loaded pile under thermal cycles was investigated. After applying the axial load on the pile head, the pile temperature was varied between 5 and 30 °C. Seven tests, corresponding to various axial loads ranging from 0 to 70 % of the pile estimated bearing capacity, were performed. The results on pile head displacement show that heating under low axial load induced heave and cooling induced settlement; the pile temperature-displacement curve was found to be reversible and compatible with the thermal expansion curve of the pile. However, at higher axial loads, irreversible settlement of the pile head was observed after a few thermal cycles. The axial load profile measured by the strain gauges evidenced that the pile head load was mainly transferred to the pile toe. Nevertheless, thermal cycles modified significantly the mobilised skin friction along the pile. The total pressure measured at various locations in the soil mass was also slightly influenced by the thermal cycles.     

Development of p–y curves for undrained response of piles near slopes

The response of laterally loaded piles placed near the crest of clay slopes is analysed. Three-dimensional finite element analyses are presented for piles of different geometries, installed at several distances from slopes of various inclinations. The results of these analyses are used to establish the pattern of lateral load distribution along the pile length in relation to slope inclination and pile to slope distance. Subsequently, p–y curves are developed for the case of undrained lateral loading of piles near the crest of clay slopes, a case for which no such curves exist so far. The proposed p–y curves are implemented into a commercial subgrade reaction computer code and used to perform a series of parametric numerical analyses. The results of these analyses show that the predicted response of piles near slopes with the proposed p–y curves is in good agreement with the response observed in some pile tests reported in the literature.     

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.