Approximate pile-to-pile interaction factors between two dissimilar piles

This paper develops approximations for the settlement interaction factors between two dissimilar piles. Via an extensive parametric study using the computer program GEPAN, approximations are developed for interaction factors for piles having dissimilar diameters but equal lengths, piles having dissimilar lengths, and for piles having dissimilar ground conditions at the pile tips. Correction factors are then given to allow for the effects of piles stiffness and length-to-diameter ratio. The approximations may be employed in analyses for group settlements to allow for the case where not all piles in the group are identical.     

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.     

Numerical Analysis of Pile–Soil–Pile Interaction in Pile Groups with Batter Piles

Battered piles are usually used to counteract lateral forces in a pile group. As there is little spacing between piles, they are affected by one another, and there is interaction between them. In this study, pile–soil–pile interaction in a group of battered piles was numerically simulated using finite element analysis. Double and frictional pile groups under static lateral and axial loadings were analyzed separately. The effects of batter angle, slenderness ratio, spacing between piles, pile–soil stiffness ratio, and soil plasticity on interaction factors were computed and presented in curves.     

Group interaction on vertically loaded piles in saturated poroelastic soil

The pile-to-pile interaction was obtained for vertically loaded piles embedded in homogeneous poroelastic saturated soil. Deduced from Biot’s theory, the fundamental functions of the quasi-static development for the force, displacement and pore pressure were acquired in cylindrical coordinates. The pile–soil system was decomposed into extended soil and fictitious piles, and the compatibility condition was set up between the axial strain of the fictitious piles and the corresponding average strain over the extended soil. This approach results in the governing equations, which consist of the Fredholm integral equations of the second kind and the basic unknowns of the axial forces along the fictitious pile shaft. The axial force and settlement along the pile shaft were calculated based on the axial forces of the fictitious piles. The interaction between the piles was investigated under different consolidation conditions through a two-pile model, and two pile interaction factors were obtained. Stemming from the two-pile analysis, numerical analyses on the settlement of the pile groups were conducted to probe pile interaction with consolidation. The conventional solutions for the single-phase soil-pile problem seem to underestimate the interaction factor if the consolidation effect is taken into account as pile settlement continues. The pile-to-pile interaction can also aggravate the percentage of consolidation settlement (PCS), and as the pile number increases, the value of the PCS will also increase. Several key factors, such as the pile stiffness, pile slenderness ratio and pile spacing, are investigated to better understand the impact of consolidation on pile analysis.     

A simplified nonlinear analysis method for piled raft foundation in layered soils under vertical loading

This paper presents a simplified nonlinear solution for piled raft foundations in layered soils under vertical loading. Based on the elastic–plastic analysis of a single pile in a layered soil, the shielding effect between a receiver pile and the soil is taken into account to modify the conventional interaction factor between two piles. An approximate approach with the concept of the interaction factor is employed to study the nonlinear behavior of pile groups with a rigid cap. Considering the variation of soil properties, the solution to multilayered elastic materials is used to calculate the settlement of the soil. The interactions between pile–soil–raft are taken into account to determine the stiffness matrix of the piled raft. By solving the stiffness matrix equations, the settlement and the load shared by the piles and raft could be obtained. Compared with results of the available published literatures, the proposed solution provides reasonable results.     

A new dynamic interaction factor for the analysis of pile groups subjected to vertical dynamic loads

Τhis paper presents an analytical method for calculating the steady-state impedance factors of pile groups of arbitrary configuration subjected to harmonic vertical loads. The derived solution allows considering the effect of the actual pile geometry on the contribution of pile-soil-pile interaction to the response of the group, via the introduction of a new dynamic interaction factor, defined on the basis of soil resistance instead of pile displacements. The solution is first validated against a published solution for single piles that accounts for the effect of pile geometry on the generated ground vibrations. Accordingly, we show that the derived soil attenuation factor agrees well with existing solutions for pile groups in the high frequency range, but considerable differences are observed in both the stiffness and damping components of the computed impedance when the relative spacing between piles decreases. Numerical results obtained for typical problem parameters suggest that ignoring pile geometry effects while estimating the contribution of pile-soil-pile interaction in the response may lead to inaccurate results, even for relative large pile group spacings.

     

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。     

群桩荷载位移特性研究

将杆系结构有限单元法与荷载传递迭代法相耦合,形成一桩基沉降分析计算的混合法。采用近似解析解中Randolph and Wroth’Model与双曲线模型相结合,模拟桩身与桩周介质边界上剪切滑移的非线性。桩间相互作用在采用弹性理论Mindlin方程解答计算,并考虑了桩间“加筋与遮帘”作用。桩周土介质非均质性特征,采用指数函数模拟。分析了刚性承台下群桩桩数、桩长、桩间距和桩土模量比等群桩工作特性的影响。尤其是桩台基础沉降对群桩相互作用影响机制的研究,对桥梁拼接等对桩基础沉降要求严格的工程有重要的借鉴意义。     

A modulus‐multiplier approach for non‐linear analysis of laterally loaded pile groups

A modulus‐multiplier approach, which applies a reduction factor to the modulus of single pile p–y curves to account for the group effect, is presented for analysing the response of each individual pile in a laterally loaded pile group with any geometric arrangement based on non‐linear pile–soil–pile interaction. The pile–soil–pile interaction is conducted using a 3D non‐linear finite element approach. The interaction effect between piles under various loading directions is investigated in this paper. Group effects can be neglected at a pile spacing of 9 times the pile diameter for piles along the direction of the lateral load and at a pile spacing of 6 times the pile diameter for piles normal to the direction of loading. The modulus multipliers for a pair of piles are developed as a function of pile spacing for departure angle of 0, 90, and 180sup>/sup> with respect to the loading direction. The procedure proposed for computing the response of any individual pile within a pile group is verified using two well‐documented full‐scale pile load tests. Copyright © 2006 John Wiley & Sons, Ltd.     

Non-linear soil–structure interaction in disconnected piled raft foundations

Disconnected piled raft foundations are characterised by no structural connection between the upper raft and the underlying piles, mostly playing the role of settlement-reducers. The resulting raft–pile gap is usually filled with a granular interlayer, through which the loads from the superstructure are transferred to the piles.In this paper, the complex interaction mechanisms involving the foundational components (raft, piles and soil) are numerically investigated by means of 3D finite elements analyses, accounting for soil non-linearity. The main features of the soil–structure interaction mechanisms under purely vertical external loads are explored over a realistic range of raft–soil gaps for different pile configurations, in which the number of piles – i.e. their spacing – is varied. Special attention is also devoted to the structural response of the piles in terms of axial and bending internal stress resultants. In particular, while disconnection beneficially affects the structural pile response, increasing the raft–pile gap tends to reduce the overall settlement/stiffness efficiencies.The numerical results being presented are in substantial agreement with the outcomes from literature small-scale experiments and suggest a number of relevant theoretical inferences.     

Earth pressure evolution of the double-row long-short stabilizing pile system

Double-row stabilizing piles provide larger stabilizing force and lateral stiffness than the single ones. However, the loading shared by the front and rear pile is not the same with each other because of the shadow effects. A double-row long-short stabilizing pile system is verified in this paper. Physical model tests are used to investigate the influence of short rear pile on the earth pressures evolution in the stabilized soil. Numerical models are established and calibrated with the applied displacement–force curve and monitored earth pressure in the physical model test. The influence of the short rear stabilizing pile on the soil–pile interaction is further investigated based on the numerical model. The soil–pile relative displacement, total stabilizing force and bearing proportion of front and rear stabilizing pile are used to evaluate the soil–pile interaction. It is concluded that the total stabilizing force and bearing proportion of front and rear stabilizing pile are not significantly influence by the short rear stabilizing pile when the double-row piles are arranged in a line. When the double-row piles are arranged in a zigzag form, the total resistance provided by the double-row stabilizing piles decreases as the short rear piles are being used.     

An approximate analysis procedure for piled raft foundations

A piled raft foundation comprises both piles and a pile cap that itself transmits load directly to the ground. The aim of such a foundation is to reduce the number of piles compared with a more conventional piled foundation where the bearing effect of the pile cap, or raft, is ignored. This paper describes a ‘hybrid’ approach for the analysis of piled raft foundations, based on a load transfer treatment of individual piles, together with elastic interaction between different piles and with the raft. The numerical analysis is used to evaluate a simple approximate method of estimating the overall response of the foundation from the response of the component parts. The method leads to estimates of the overall foundation stiffness, the proportion of load carried by the pile group and the raft, and an initial assessment of differential settlements. Parametric studies are presented showing the effect of factors such as raft stiffness and pile spacing, length and stiffness, and a worked example is included demonstrating the accuracy of the approximate design approach.     

Cyclic and seismic response of single piles in improved and unimproved soft clays

Presented in this paper are results of two centrifuge tests on single piles installed in unimproved and improved soft clay (a total of 14 piles), with the relative pile–soil stiffness values varying nearly two orders of magnitude, and subjected to cyclic lateral loading and seismic loading. This research was motivated by the need for better understanding of lateral load behavior of piles in soft clays that are improved using cement deep soil mixing (CDSM). Cyclic test results showed that improving the ground around a pile foundation using CDSM is an effective way to improve the lateral load behavior of that foundation. Depending on the extent of ground improvement, elastic lateral stiffness and ultimate resistance of a pile foundation in improved soil increased by 2–8 times and 4–5 times, respectively, from those of a pile in the unimproved soil. While maximum bending moments and shear forces within piles in unimproved soil occurred at larger depths, those in improved soil occurred at much shallower depths and within the improved zone. The seismic tests revealed that, in general, ground improvement around a pile is an effective method to reduce accelerations and dynamic lateral displacements during earthquakes, provided that the ground is improved at least to a size of 13D × 13D × 9D (length × width × depth), where D is the outside diameter of the pile, for the pile–soil systems tested in this study. The smallest ground improvement used in these tests (9D × 9D × 6D), however, proved ineffective in improving the seismic behavior of the piles. The ground improvement around a pile reduces the fundamental period of the pile–soil system, and therefore, the improved system may produce larger pile top accelerations and/or displacements than the unimproved system depending on the frequency content of the earthquake motion.     

水平偏心受荷群桩p乘子计算

水平偏心受荷群桩同时发生水平移动和绕承台中心的转动,使基桩的运动方向各不相同,因此基桩的运动方向成为影响群桩效应的一个关键因素。研究发现：水平偏心受荷的两根桩,前桩运动方向与两桩连线夹角0o≤η≤90o,后桩夹角?90o≤θ≤90o;量化两桩间桩?土?桩相互作用的折减系数与η和θ密切相关,η和θ组合存在一个范围,在该范围内两桩不存在相互作用;当两桩存在相互作用时,相互作用对后桩的影响往往大于对前桩的影响。通过将定量描述水平受荷群桩群桩效应的p乘子概念拓展到水平偏心受荷群桩,综合运用理论分析、试验和数值计算成果,提出了折减系数计算公式,进而给出了广义p乘子经验计算公式。通过试验案例验证了该计算公式的合理性。     

Integral equation method for analysis of piled rafts with dissimilar piles under vertical loading

In a piled raft, the length and arrangement of piles has a significant effect on the stresses and deflections of the raft. The use of piles with different dimensions and properties below a raft is an innovative concept and can optimize the design of a piled raft. In this study, an integral equation method with a fictitious pile model was adopted to analyze the piled raft foundation with dissimilar piles. The Fredholm integral equations of the second kind were obtained for this problem. The loads shared by piles and subsoil, the load transfer, and the settlement of the piled raft were obtained using numerical calculation. The results from the present method were compared with those in the literature. An optimization technique was introduced to design piled rafts with dissimilar piles. The stiffening effect of piles on the surrounding soil is also discussed as compared the conventional interaction factor approach.     

考虑加筋与遮帘效应的层状地基群桩沉降计算

桩群在土中的加筋与遮帘效应是客观存在的,但目前的理论与实践均未能或有效地考虑该效应.基于剪切变形法原理,在计算某一根桩沉降时,考虑了其他各相邻基桩的存在对该桩沉降的折减,即加筋与遮帘效应,得到了桩侧桩-土接触等效剪切弹簧刚度,建立了桩身位移微分方程,分别求得桩顶沉降-桩端沉降、桩顶荷载-桩端压力的递推关系,从而得到了各桩在自身荷载作用下引起自身沉降的柔度系数; 同理,也求得了各邻桩在其桩顶荷载下引起它桩沉降的柔度系数,最终建立了群桩沉降计算的柔度矩阵方程.推导过程中,考虑了地基土的成层性及桩端沉降的相互影响,并提出了基于一定深度内的Mindlin位移解且考虑桩径影响的桩端压力-桩端位移关系新模式.算例结果表明,本文方法与实测值较为接近,且按本文方法求得的群桩中基桩相互作用系数明显小于弹性理论计算结果,且与实测值吻合较好.     

Negative skin friction on pile groups

A numerical procedure is presented for the downdrag analysis of group piles which penetrate a consolidating upper soil layer to socket into a firm bearing stratum of finite stiffness. The settlement of the consolidating upper soil layer under a surcharge load is estimated using Terzaghi's one-dimensional consolidation theory. Parametric solutions are presented to show the influence of various parameters on the performance of the socketed pile groups in terms of the development of the induced downdrag forces and associated pile head settlements. In general, pile–soil–pile interaction has the beneficial effect of reducing the downdrag forces and settlements of the group piles when compared to the corresponding single pile values, provided that the soil settlements are not so large as to cause full slippage at the interface in all the piles. Reasonable agreement is obtained between the theoretical and experimental results for pile groups subjected to negative skin friction.     

Vertically loaded piles in non-homogeneous media

Analytical methods for the axial responses of piles can be classified under three broad categories of (1) simple but approximate analytical solutions, (2) one-dimensional numerical algorithms, (3) full axisymmetric analyses using boundary or finite element approaches. The first two categories rely on the so-called load transfer approach, with interaction between pile and soil determined by independent springs distributed along the pile shaft and at the pile base. The non-linear spring stiffness is related to the elastic–plastic properties of the actual soil partly by empirically based correlations and partly by theoretical arguments based on simplified models of the pile–soil system. This paper presents new closed-form solutions for the axial response of piles in elastic–plastic, non-homogeneous, media. The solutions fall in the first of the three categories above, and have been verified through extensive parametric studies using more rigorous one-dimensional and continuum analyses. The effect of non-homogeneity and partial slip on the load and displacement profiles along the pile shaft is explored, and comparisons are presented with experimental data. © 1997 John Wiley & Sons, Ltd.     

Nonlinear three-dimensional analysis of pile group supported columns considering pile cap flexibility

A numerical method that takes into account the coupling between the rigidities of the piles, the cap, and the column has been developed for analyzing the response of pile group supported columns. Special attention is given to consideration of pile cap flexibility. A load transfer approach using t–z/q–z and p–y curves is used for the analysis of single piles. The finite element technique is used to combine the pile stiffness with the stiffness of the cap and column. The numerical method developed has been verified by comparing the results with other numerical methods for pile groups. Through comparative studies, it has been found that the maximum load on the individual piles in a group is highly influenced by pile cap flexibility. The prediction of the lateral loads and bending moments in the pile cap is much more conservative in the present analysis than in FBPier 3.0 and shows a definitely larger lateral load and bending moment for various cap thicknesses.     

软土地区复合桩基础适用条件的探讨

复合桩基的根本是桩土共同作用,而桩土共同作用的前提则是桩土变形协调,基桩与地基土的支承刚度通常存在数量级上的差异,因此要使桩土的变形协调,必须要采取一定的措施。以桩土共同作用机理为根本对复合桩基的使用条件进行了探讨,指出天然地基承载力满足率小于0.5而采用复合桩基时,桩土共同作用无法形成,最终使整个建筑物的安全度降低;天然地基承载力满足率大于0.6甚至0.7时,复合桩基整体安全度虽容易满足,但整体偏于保守,另外还容易缩小复合桩基适用范围。建议复合桩基使用条件中天然地基承载力满足率大于等于0.5即可。