A simplified analysis method for piled raft foundations subjected to ground movements induced by tunnelling

A simplified method of numerical analysis has been developed to estimate the deformation and load distribution of piled raft foundations subjected to ground movements induced by tunnelling 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, the piles as elastic beams, and the soil is treated as interactive springs. The interactions between structural members, pile–soil–pile, pile–soil–raft and raft–soil–raft interactions, are modelled based on Mindlin's solutions for both vertical and lateral forces. The validity of the proposed method is verified through comparisons with some published solutions for single piles and pile groups subjected to ground movements induced by tunnelling. Thereafter, the solutions from this approach for the analysis of a pile group and a piled raft subjected to ground movements induced by tunnelling are compared with those from three‐dimensional finite difference program. Good agreements between these solutions are demonstrated. The method is then used for a parametric study of single piles, pile groups and piled rafts subjected to ground movements induced by tunnelling. Copyright © 2005 John Wiley & Sons, Ltd.     

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.     

A simplified analysis method for piled raft and pile group foundations with batter piles

A simplified method of numerical analysis has been developed to estimate the deformation and load distribution of piled raft foundations subjected to vertical, lateral, and moment loads, using a hybrid model in which the flexible raft is modelled as thin plates and the piles as elastic beams and the soil is treated as springs. Both the vertical and lateral resistances of the piles as well as the raft base are incorporated into the model. Pile–soil–pile, pile–soil–raft and raft–soil–raft interactions are taken into account based on Mindlin's solutions for both vertical and lateral forces. The validity of the proposed method is verified through comparisons with several existing methods for single piles, pile groups and piled rafts. Workable design charts are given for the estimation of the lateral displacement and the load distribution of piled rafts from the stiffnesses of the raft alone and the pile group alone. Additionally, parametric studies were carried out concerning batter pile foundations. It was found that the use of batter piles can efficiently improve the deformation characteristics of pile foundations subjected to lateral loads. Copyright © 2002 John Wiley & Sons, Ltd.     

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.     

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.     

Three-dimensional finite element analysis for soil slopes stabilisation using piles

This paper presents the analytical methods of slope-stabilising piles using the three-dimensional (3-D) finite element (FE) analysis with the strength reduction method (SRM). This 3-D FE model is employed to overcome the limitations observed in two-dimensional (2-D) FE analysis. The solutions obtained from 3-D FE analyses are verified to be less conservative in this paper. The 3-D analysis is considered to be of particular importance to pile-slope problems. The soil that flows between piles cannot be taken account properly in the 2-D FE analysis. The method adopted in this paper can avoid the assumption of soil movement and the pressure distribution along the piles subjected to soil movement. The numerical analysis employs the Mohr–Coulomb failure criterion with the strength reduction technique for soil and an elastic member for piles. The spacing effect of the pile is considered in the 3-D model, the S/D (S: centre to centre, D: diameter of pile) ratio, equal to 4.0, is found to be equivalent to the single pile stabilisation. The middle portion of the slope is identified as the optimal location to place the piles. The proper length of the pile, which can be used to stabilise the slope, is also examined using 3-D FE analyses. It is concluded that L/H greater or equal 0.70 is recommended (L: pile length, H: slope height). The numerical analyses are conducted based on a coupled analysis, which simultaneously considers both the slope stability and the pile response. The failure mechanisms of the pile-slope system subjected to the pile locations, pile head conditions and pile length are each discussed. The contact pressure, shear force and moment along the piles are presented to illustrate the pile stabilising mechanism herein.     

Response evaluation for horizontally loaded fixed‐head pile groups using 3‐D non‐linear analysis

The response of laterally loaded pile foundations may be significantly important in the design of structures for such loads. A static horizontal pile load test is able to provide a load–deflection curve for a single free‐head pile, which significantly differs from that of a free‐ or fixed‐head pile group, depending on the particular group configuration. The aim of this paper is to evaluate the influence of the interaction between the piles of a group fixed in a rigid pile cap on both the lateral load capacity and the stiffness of the group. For this purpose, a parametric three‐dimensional non‐linear numerical analysis was carried out for different arrangements of pile groups. The response of the pile groups is compared to that of the single pile. The influence of the number of piles, the spacing and the deflection level to the group response is discussed. Furthermore, the contribution of the piles constituting the group to the total group resistance is examined. Finally, a relationship is proposed allowing a reasonable prediction of the response of fixed‐head pile groups at least for similar soil profile conditions. Copyright © 2005 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.     

On the understanding of cyclic interaction mechanisms in an energy pile group

Integrating ground heat exchanger elements into concrete piles is now considered as an efficient energy solution for heating/cooling of buildings. In addition to the static load of buildings, the concrete piles also undergo a cycle of thermal deformation. In the case of single energy pile, calculation methods already exist and permit to perform a proper geotechnical design. In the case of energy pile group, the thermo‐mechanical interactions within the group are more complex. Very few experimental results on the energy pile group are available so that numerical analysis can be an interesting way to provide complementary results about their behavior. This paper deals with a numerical analysis including a comparison between a single energy pile and an energy pile group with different boundary conditions at the pile head. In order to take into account the stress reversal induced by the thermal expansions and contractions, a cyclic elastoplastic constitutive model is introduced at the soil–pile interface. The analysis aims to give some insights about the long‐term cyclic interaction mechanisms in the energy pile group. Based on this qualitative study, some guidance can be brought for the design of energy piles in the case where group effects should be considered. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

A method for the analysis of large vertically loaded pile groups

An iterative method is described for the analysis of vertically loaded pile groups with a large number of vertical piles. The individual pile response is modelled using load-transfer (t–z) curves while pile–soil–pile interaction is determined using Mindlin's solution. The present method not only keeps all the advantages of the so-called ‘hybrid method’, but also makes it possible for practising engineers to solve problems of large non-uniformly arranged pile groups in a time-saving way using a personal computer. Good agreement between the present method of analysis and the direct method is observed. A case history is analysed and the computed response of a large pile group compares favourably with the field measurement. Copyright © 1999 John Wiley & Sons, Ltd.     

On the response prediction of horizontally loaded fixed-head pile groups in sands

The aim of this paper is to investigate the behavior of laterally loaded pile groups in sands with a rigid head and correlate the response of a pile group it to that of a single pile. For this purpose, a computationally intensive study using 3-D nonlinear numerical analysis was carried out for different pile group arrangements in sandy soils. The responses of the pile groups were compared to that of the single pile and the variation of the displacement amplification factor R_a was then quantified. The influence of the number of piles, the spacing, and the deflection level on the group response is discussed. A relationship for predicting the response of a pile group, based on its configuration and the response of a single pile, has been formulated allowing also for soil shear strength which was found to affect the group response. The relationship provides a reasonable prediction for various group configurations in sandy soils.     

Response evaluation of axially loaded fixed‐head pile groups in clayey soils

The aim of this paper is to investigate the interaction between the piles in a group with a rigid head and correlate the response of a group of piles to that of a single pile. For this purpose, a computationally intensive study using 3‐D nonlinear numerical analysis was carried out for different pile group arrangements in clayey soils. The responses of the groups of piles were compared with that of a single pile and the variation of the settlement amplification factor R_a was then quantified. The influence of the number of piles, the spacing, and the settlement level on the group response is discussed. A previously proposed relationship for predicting the response of a pile group, based on its configuration and the response of a single pile, has been modified to extend its applicability for any pile spacing. The modified relationship provides a reasonable prediction for various group configurations in clayey soils. Copyright © 2009 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.     

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.     

Load transfer approach for laterally loaded piles

A two‐parameter model has been proposed previously for predicting the response of laterally loaded single piles in homogenous soil. A disadvantage of the model is that at high Poisson's ratio, unreliable results may be obtained. In this paper, a new load transfer approach is developed to simulate the response of laterally loaded single piles embedded in a homogeneous medium, by introducing a rational stress field. The approach can overcome the inherent disadvantage of the two‐parameter model, although developed in a similar way. Generalized solutions for a single pile and the surrounding soil under various pile‐head and base conditions were established and presented in compact forms. With the solutions, a load transfer factor, correlating the displacements of the pile and the soil, was estimated and expressed as a simple equation. Expressions were developed for the modulus of subgrade reaction for a Winkler model as a unique function of the load transfer factor. Simple expressions were developed for estimating critical pile length, maximum bending moment, and the depth at which the maximum moment occurs. All the newly established solutions and/or expressions, using the load transfer factor, offer satisfactory predictions in comparison with the available, more rigorous numerical approaches. The current solutions are applicable to various boundary conditions, and any pile–soil relative stiffness. Copyright © 2001 John Wiley & Sons, Ltd.     

软土地层高承台桥梁群桩基础横向承载特性研究

高承台群桩基础是高速铁路桥梁基础的一种常用形式,受到风、地震等荷载作用影响,常常需要承受较大的横向荷载。采用室内物理模型试验和三维有限元程序ABAQUS对软土地层中单桩、群桩的横向承载特性进行了研究,软土采用修正剑桥黏土本构模型,试验结果与有限元计算结果吻合较好。群桩研究方案包括了桩数的变化以及桩间距的变化。结果表明,群桩基础的基桩平均横向承载力（总承载力/桩数）较单桩基础显著增加,且水平荷载方向桩间距越大,其横向承载力越大;群桩基础基桩受力存在三维空间效应,不同位置基桩受力大小排序为角桩最大,其次为边桩,最小为中间桩,弯矩极值差异可达20%,群桩基础桩周土影响范围距外围基桩边缘净距离约为16D (D为桩径)。桩与桩相互影响效应对群桩水平承载不利,承台约束效应对水平承载有利。探讨了考虑上述两种效应的群桩效应系数计算方法,通过计算验证了该方法在软土地区高承台群桩基础横向承载力计算中的适用性。     

Analysis of pile-soil interaction under lateral loading using infinite and finite elements

In order to gain a better understanding of pile-soil interaction under lateral loading, this paper presents a numerical analysis which combines the infinite and finite element method. Interest is focused on the group effect on ultimate lateral soil resistance. Firstly, a single isolated pile is analysed and reasonably good agreement is found between existing analytical solutions and results obtained by the present method. A limited parametric study is also presented and some parameters influencing the ultimate lateral soil resistance are identified. The analysis of pile groups is then considered and it is shown that the group effect tends to reduce pile capacity when the spacings between piles are within the practical ranges. The extent of the reduction depends on the arrangement of piles within the group.     

A variational approach for vertical deformation analysis of pile group

A variational approach for the analysis of vertical deformation of pile groups is presented. The method assumes that the deformation of piles can be represented by a finite series. The method applies the principle of minimum potential energy to determine the deformation of piles. Using this method, an analytical solution for pile groups in soil modelled by the theoretical load–transfer curves can be obtained rigorously. Analysis of field tests indicates that the method can predict the performance of pile groups reasonably well.     

Explicit extension of the p–y method to pile groups in sandy soils

The method of “p–y” curves has been extensively used, in conjunction with simplified numerical methods, for the design and response evaluation of single piles. However, a straightforward application of the method to assess the response of pile groups is questionable when the group effect is disregarded. For this reason, the notion of p-multipliers has been therefore introduced to modify the “p–y” curves and account for pile group effect. The values proposed for p-multipliers result from pile group tests and are limited to the commonly applied spacing of 3.0 D and layout less than 3 × 3, restricting the applicability of the method to specific cases. With the aim of extending the applicability of the “p–y” method to pile groups, the authors have already proposed a methodology for estimating the “p _G–y _G” curves of soil resistance around a pile in a group for clayey soils. A complementary research allowing for the estimation of the “p _G–y _G” curves for sandy soils is presented in this paper. The well-known curves of soil resistance around the single pile in sandy soils are appropriately transformed to allow for the interaction effect between the piles in a group. Comparative examples validate the applicability and the effectiveness of the proposed method. In addition, the method can be straightforwardly extended to account for varying soil resistance, according to the particular location of a pile in a group. It can therefore be used in a most accurate manner in estimating the distribution of forces and bending moments along the characteristic piles of a group and therefore to design a pile foundation more accurately.