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.     

An approximate numerical analysis of pile–raft interaction

This paper presents an approximate method of numerical analysis of piled–raft foundations in which the raft is modelled as a thin plate and the piles as interacting springs of appropriate stiffness. Allowance is made for the development of limiting pressures below the raft and of the ultimate axial load capacity of the piles. Comparisons between this analysis and existing solutions verify that, despite the approximations involved, the analysis can provide solutions of adequate accuracy for the settlement and pile load distribution within a piled raft. Comparisons are also made with the results of a series of centrifuge tests and with measurements of the performance of a full-scale piled raft. In both cases, the analysis predicts very well the settlement and proportion of load carried by the piles.     

竖向荷载下刚性板桩筏基础分析方法

根据群桩中桩侧摩阻力分布规律,在桩筏基础中基于弹性理论中的变形协调关系、桩体物理方程和力的平衡关系,推导了竖向荷载作用下桩筏基础的荷载和位移之间的刚度矩阵,从而提出了一种刚性板下桩筏基础的分析方法。刚性板桩筏基础分析中考虑了4种相互作用,分别为桩-土-桩、桩-土-板、板-土-桩和板-土-板相互作用。基础中各桩可具有不同的桩长、桩半径和刚度等特性。应用该方法不需要划分桩-土体单元,分析中的计算矩阵仅与基础中桩数和筏板下土节点数量相关而与其他变量无关,分析过程简洁通用。通过与各种分析方法的比较验证,证明该方法是合理可行的。     

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.     

Finite element simulations of the behavior of piled‐raft foundations using a multiphase model

Finite element simulations of the behavior of a piled raft foundation have been carried out using a multiphase model conceived as an improved homogenization approach. According to this model, the ground reinforced by a group of piles is treated as a homogeneous continuous medium. In this approach, no specific interface elements are necessary to account for the mechanical interaction between the piles and the ground: this interaction is described by means of two scalar parameters, one stiffness parameter and one which can easily be derived from the maximum ground‐pile friction. The implementation of the model into a finite element code provides an efficient tool for the analysis of the influence of the pile number or length on the settlement and bearing capacity of a square piled raft foundation and of the way the total applied load is shared between the raft and the piles. Results are compared with a standard 3D finite element analysis. The comparison highlights the fact that the proposed approach remains to be improved to account for tip resistance. Copyright © 2012 John Wiley & Sons, Ltd.     

多向荷载作用下层状地基刚性桩筏基础分析

提出一种多向荷载作用下层状地基中刚性桩筏基础的计算方法。基于剪切位移法,采用传递矩阵形式分析了竖向荷载下桩顶面-桩顶面相互作用;引入修正桩侧地基模量,采用有限差分法分析了水平荷载下桩顶面-桩顶面相互作用;基于层状弹性半空间理论,分析了多向荷载下桩顶面-土表面、土表面-桩顶面、土表面-土表面的相互作用关系。建立了桩土体系柔度矩阵,得到了多向荷载下层状地基中刚性桩筏基础的受力和变形的关系以及桩的内力和变形沿桩身分布规律。通过与有限元对比,验证了该方法的合理性和修正地基模量的优越性,并对多向荷载作用下的桩筏基础进行了计算分析,计算结果表明,水平力将会引起桩筏基础的倾斜。     

Three-dimensional analysis of bearing behavior of piled raft on soft clay

The piled raft has proved to be an economical foundation type compared to conventional pile foundations. However, there is a reluctance to consider the use of piled rafts on soft clay because of concerns about excessive settlement and insufficient bearing capacity. Despite these reasons, applications of piled rafts on soft clay have been increased recently. Current analysis methods for piled rafts on soft clay, however, are insufficient, especially for calculating the overall bearing capacity of the piled raft. This study describes the three-dimensional behavior of a piled raft on soft clay based on a numerical study using a 3D finite element method. The analysis includes a pile–soil slip interface model. A series of numerical analyses was performed for various pile lengths and pile configurations for a square raft subjected to vertical loading. Relatively stiff soil properties and different loading types were also used for estimating the bearing behavior of the piled raft. Based on the results, the effect of pile–soil slip on the bearing behavior of a piled raft was investigated. Furthermore, the proportion of load sharing of the raft and piles at the ultimate state and the relationship between the settlement and overall factor of safety was evaluated. The results show that the use of a limited number of piles, strategically located, might improve both bearing capacity and the settlement performance of the raft.     

Analysis of piled raft with nodular pile subjected to vertical load using a Winkler model approach

An investigation is made to present analytical solutions provided by a Winkler model approach for analysis of piled rafts with nodular pile subjected to vertical loads in nonhomogeneous soils. The vertical stiffness coefficient along a piled raft with the nodular pile in nonhomogeneous soils is derived from the displacement given by the Mindlin solution for elastic continuum analysis. The vertical stiffness coefficients for the bases of the raft and the nodular part in the nodular pile in a soil are expressed by the Muki solution for the 3‐D elastic analysis. The relationship between settlement and vertical load on the pile base is presented considering the Mindlin solution and the equivalent thickness in the equivalent elastic method. The interaction factor between the shaft of the nodular pile and the soil is expressed taking into account the Mindlin solution and the equivalent elastic modulus. The relationship between settlement and vertical load for a piled raft with the nodular pile in nonhomogeneous soils is obtained by using the recurrence equation of influence factors of the pile for each layer. The percentage of each load carried by both nodular pile and raft subjected to vertical load is represented through the vertical influence factors proposed here. Comparison of the results calculated by the present method for piled rafts with nodular piles in nonhomogeneous soils has shown good agreement with those obtained from the finite element method and a field test. Copyright © 2016 John Wiley & Sons, Ltd.     

Vertical harmonic vibration of piled raft foundations in layered soils

This paper develops a method to analyze the piled raft foundation under vertical harmonic load. This method takes into account the interactions among the piles, soil, and raft. The responses of the piles and raft are formulated as a series of equations in a suitable way and that of layered soils is simulated with the use of the analytical layer‐element method. Then, according to the equilibrium and continuity conditions at the piles–soil–raft interface, solutions for the piled raft systems are obtained and further demonstrated to be correct through comparing with the existing results. Finally, some examples are given to investigate the influence of the raft, pile length‐diameter ratio, and layering on the response of the piled raft foundations. Copyright © 2017 John Wiley & Sons, Ltd.     

Design method of piled-raft foundations under vertical load considering interaction effects

The paper has proposed a design method considering interaction effects for a piled raft foundation. In this method, the raft is considered as a plate supported by a group of piles and soil. The ultimate load capacity of the pile group is taken into account in calculating the settlement when the foundation is subjected to a large vertical external load. In addition, this method supports estimation of the nonlinear behaviour of the piled raft foundation by considering the nonlinear behaviour of the piles.A step-by-step procedure to apply the proposed method to calculate the settlement and distribution of the bending moment of the piled raft foundation is introduced. To verify the reliability of the proposed method, models of a 16-pile raft and a 9-pile raft with different pile lengths embedded in homogeneous silica sand were tested in a centrifuge and comparisons were made between the results of the proposed method, the results of centrifuge tests, and those of Plaxis 3D. Good agreement between centrifuge modelling and the proposed method is demonstrated, thus showing the potential of the proposed method.     

陆上风轮机梁板基础受力特性简化分析

提出一种多向荷载同时作用下的刚性桩筏基础简化计算方法,基于Mindlin解,分析桩顶面-桩顶面、桩顶面-土表面、土表面-土表面的相互作用关系。推导多向荷载下桩土体系柔度矩阵,得到刚性桩筏基础的受力和变形的关系,通过与有限元对比证明了文中方法的正确性,在此基础上对耦合荷载作用下的风机基础的受力和变形特性进行分析。研究表明,耦合荷载作用下风机基础将会产生竖向不均匀沉降,并会引起桩顶轴力的的巨大的差异。     

Piled Raft Design Strategies for High Rise Buildings

Piled rafts have been widely adopted as an effective foundation for designing high-rise buildings because of their efficiency in controlling the total and differential settlements and improving bearing capacity. In many cases the piled rafts settlements are likely to be large, which leads to an increase of the pile length and/or number of piles required to reduce the settlements. However, this increase does not satisfy the design requirements or an economical design. The majority of piled raft foundations has been designed with a uniform pile length and configuration. This paper describes the process of optimizing the design of a piled raft foundation for a high rise building in the Mazandaran province in Iran by considering an economical design methodology in which piles are placed more densely beneath the maximum load positions when the piled raft is subjected to non-uniform loads. By using the ELPLA software in the analysis process, the validity of the software is examined through the results of a report prepared on behalf of Technical Committee TC18 on piled foundations. The study shows that the pile arrangement method can help to considerably reduce the total and differential settlements with similar total pile length as well as the induced bending moments and shear forces of the raft. This study can help practicing engineers to choose pile and raft parameters with the pile arrangement method to produce an economical design.     

Parametric study for optimal design of large piled raft foundations on sand

In designing piled raft foundations, controlling the total and differential settlements as well as the induced bending moments of the raft is crucial. The majority of piled raft foundations have been designed by placing piles uniformly. In such a design method, the settlements of the piled rafts are likely to be large, which leads to an increase of the pile length and/or number of piles required to reduce the settlements. However, this increase does not satisfy the requirement for economical design. On the basis of a parametric study, this paper contributes a framework for considering an economical design methodology in which piles are placed more densely beneath the column positions when the piled raft is subjected to column loads. The analysis uses PLAXIS 3D software, and the validity of the parametric study is examined through the results of centrifuge model tests conducted by the authors. The study shows that the concentrated pile arrangement method can help to considerably reduce the total and differential settlements as well as the induced bending moments of the raft. Moreover, the effects of parameters, such as pile length, pile number, raft thickness and load types, on the piled raft behavior are investigated. This study can help practicing engineers choose pile and raft parameters in combination with the concentrated pile arrangement method to produce an economical design.     

考虑基础刚度影响的风机梁板式桩筏基础模型试验研究

梁板式桩筏基础作为新型风机基础,前景广阔,适当优化结构,可节约成本。采用大型室内模型试验,研究了梁板式桩筏基础在不同筏板刚度情况下的受力变形特性,同时讨论了桩土荷载分担比的关系。研究表明,在工作荷载范围内,适当增大筏板刚度,桩平均轴力增加,外圈桩承担的荷载增大,内圈桩的轴力减小,环梁及肋梁弯矩减小,但继续增加刚度,对桩身轴力、环梁弯矩、肋梁弯矩的影响并不大;随着荷载的增大,土体承担的荷载比逐步增大,趋于稳值。随着梁板式基础刚度增加,基础内外差异沉降减少,但是达到一定刚度后再增加刚度对变形影响较小。梁板式基础刚度的变化会影响基底反力分布的均匀性,且存在一个最优刚度,使基础底部反力分布最为均匀,本次试验中12梁的梁板式基础基底反力比6梁和实体基础更均匀。桩基的分布和梁的分布存在相互影响,改变梁的分布会影响桩顶力,而桩基在梁底下又会使梁的应力产生重新分布。研究成果可为设计桩筏基础提供参考依据。     

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.     

复杂环境中大规模桩筏基础的优化设计方法研究

变刚度优化设计对于复杂环境中的大规模桩筏基础始终是一个重要难题。基于有限元分析提出一种两阶段优化设计方法,该方法首先根据传统均匀布桩方案的桩顶应力分布对群桩进行分区,然后依据每个子区域桩顶应力之间的关系确定基桩数量调整系数,最后通过调整桩间距来改变各子区域的基桩数量,从而实现变刚度优化设计。运用该方法对多层土体中承担非均匀上部结构荷载的大规模桩筏基础进行变刚度优化设计,计算结果表明优化设计后筏板的差异沉降、平均整体弯矩和群桩顶部的差异应力均显著降低。该方法计算简单,应用范围广,且不受复杂土层条件、非均匀上部结构荷载以及桩基础规模大小形状的限制。     

Analysis of piled raft coefficient and load-settlement on sandy soil

A piled raft foundation is a combined foundation, which is developed to utilize the load-carrying capabilities of both raft and piles. To obtain an optimum piled raft design, it is important to properly evaluate and consider the load-sharing behavior between the raft and piles, which changes according to the settlement level of the piled raft. In this study, 27 three-dimensional finite element models were analyzed to investigate the piled raft coefficient with linear and nonlinear load-settlement behaviors. The length of piles was varied between 10, 15, and 20 m. The spacing between pile centers was varied between 3D, 5D, and 7D, and the pile diameter was kept constant. The number of piles and the distance between the exterior piles and the edge of the raft were maintained at 9 and 1 m, respectively. The sand conditions varied between dense, medium, and loose. The results indicated that the piled raft coefficient increases when the load-settlement curve is linear and decreases when the load-settlement curve is nonlinear. The influence of the incremental increase in pile length on the piled raft coefficient is more pronounced in short piles than in longer piles. The raft thickness has a negligible effect on the piled raft coefficient.     

Thermo-hydro-mechanical response of a large piled raft equipped with energy piles: a parametric study

This paper presents the results of a parametric study in which a series of fully coupled, 3-dimensional thermo-hydro-mechanical Finite Element (FE) analyses has been conducted to investigate the effects of the thermal changes imposed by the regular performance of a GSHP system driven by energy piles on a very large piled raft. The FE simulation program has been focused mainly on the evaluation of the following crucial aspects of the energy system design: the assessment of the soil–pile–raft interaction effects during thermal loading conditions; the quantification of the influence of the thermal properties of the soil and of the geometrical layout of the energy piles on the soil–foundation system response, and the evaluation of the influence of the active pile spacing on the thermal performance of the GSHP–energy pile system. The results of the numerical simulations show that the soil–pile–raft interaction effects can be very important. In particular, the presence of a relatively rigid raft in direct contact with the soil is responsible for axial load variations in inactive piles of the same order of those experienced by the thermo-active piles, even when the latter are relatively far and temperature changes in inactive piles are small. As far as the effect of pile spacing is concerned, the numerical simulations show that placing a high number of energy piles in a large piled raft with relatively small pile spacings can lead to a significant reduction of the overall heat exchange from the piles to the soil, thus reducing the thermal efficiency of the system.     

考虑上部结构的桩筏基础非线性共同作用分析

当前虽然已有考虑桩筏非线性的设计,但仍无人在此基础上,考虑上部结构。因此考虑上部结构,进一步认识其与桩筏基础非线性共同作用机理,优化桩筏基础设计,具有重要的现实意义。本文以子结构法凝聚上部结构的荷载及刚度,以平面壳体单元模拟筏板,按有限层法模拟桩土之间的弹性相互作用,用广义剪切位移法模拟桩的非线性工作性状,建立了一种考虑上部结构共同作用的桩筏基础非线性分析方法,并编制了分析程序。通过实例分析,探讨了上部结构与桩筏基础非线性共同作用的机理,研究了合理布桩方式,探讨了以差异沉降为目标的优化设计的可能途径。     

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.