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.     

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.     

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.     

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.     

Vertical response of pile raft foundations subjected to tunneling‐induced ground movements in layered soil

A simplified analysis method has been developed to estimate the vertical movement and load distribution of pile raft foundations subjected to ground movements induced by tunneling based on a two‐stage method. In this method, the Loganathan–Polous analytical solution is used to estimate the free soil movement induced by tunneling in the first stage. In the second stage, composing the soil movement to the pile, the governing equilibrium equations of piles are solved by the finite difference method. The interactions between structural members (such as pile–soil, pile–raft, raft–soil, and pile–pile) are modeled based on the elastic theory method of a layered half‐space. The validity of the proposed method is verified through comparisons with some published solutions for single piles, pile groups, and pile rafts subjected to ground movements induced by tunneling. Good agreements between these solutions are demonstrated. The method is also used for a parametric study to develop a better understanding of the behavior of pile rafts influenced by tunneling operation in layered soil foundations. Copyright © 2011 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 of raft–pile foundation using combined optimization and finite element approach

This paper describes the application of a structural optimization approach combined with the finite element method for the optimal design of a raft–pile foundation system. The analysis takes into account the non-linear behaviour of the soil medium and the piles. For the optimization process, the sensitivity analysis is carried out using the approximate semi-analytical method while the constraint approximation is obtained from the combination of extended Bi-point and Lagrangian polynomial approximation methods. The objective function of the problem is the cost of the foundation. The design variables are the raft thickness, cross-section, length and number of piles. The maximum displacement and differential displacement are selected as the constraints. The proposed method is shown to achieve an optimum design of raft–pile foundation efficiently and accurately. Copyright © 1999 John Wiley & Sons, Ltd.     

Analysis of pile‐raft foundations under complex loads in layered soils

Considering there is hardly any concerted effort to analyze the pile‐raft foundations under complex loads (combined with vertical loads, horizontal loads and moments), an analysis method is proposed in this paper to estimate the responses of pile‐raft foundations which are subjected to vertical loads, horizontal loads and moments in layered soils based on solutions for stresses and displacements in layered elastic half space. Pile to pile, pile to soil surface, soil surface to pile and soil surface to soil surface interactions are key ingredients for calculating the responses of pile‐raft foundations accurately. Those interactions are fully taken into account to estimate the responses of pile‐raft foundations subject to vertical loads, horizontal loads and moments in layered soils. The constraints of the raft on vertical movements, horizontal movements and rotations of the piles as well as the constraints of the raft on vertical movements and horizontal movements of the soils are considered to reflect the coupled effect on the raft. The method is verified through comparisons with the published methods and FEM. Then, the method is adopted to investigate the influence of soil stratigraphy on pile responses. The study shows that it is necessary to consider the soil non‐homogeneity when estimating the responses of pile‐raft foundations in layered soils, especially when estimating the horizontal responses of pile‐raft foundations. The horizontal loads and the moments have a significant impact on vertical responses of piles in pile‐raft foundations, while vertical loads have little influence on horizontal responses of piles in pile‐raft foundations in the cases of small deformations. The proposed method can provide a simple and useful tool for engineering design. Copyright © 2013 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.     

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.     

Proposed nonlinear 3-D analytical method for piled raft foundations

The load distribution and deformation of piled raft foundations subjected to axial and lateral loads were investigated by a numerical analysis and field case studies. Special attention is given to the improved analytical method (YSPR) proposed by considering raft flexibility and soil nonlinearity. A load transfer approach using p–y, t–z and q–z curves is used for the analysis of piles. An analytical method of the soil–structure interaction is developed by taking into account the soil spring coupling effects based on the Filonenko-Borodich model. The proposed method has been verified by comparing the results with other numerical methods and field case studies on piled raft. Through comparative studies, it is found that the proposed method in the present study is in good agreement with general trend observed by field measurements and, thus, represents a significant improvement in the prediction of piled raft load sharing and settlement behavior.     

ANALYSIS OF PILED RAFT SYSTEMS IN LAYERED SOIL

This paper presents a method of analysis for piled raft systems constructed in layered soils. The method presented takes account of the interactions of the raft, piles and soil without the cost of a full three-dimensional rigorous analysis. This is done by the use of finite layer methods for the analysis of the soil and finite element methods for the raft. Examples are provided in the paper for piled rafts constructed on layered soils, and results are presented for bending moments in the raft and loads in the piles.     

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.     

Torsional piles in non-homogeneous media

The torsional response of a pile exhibits features which are a mixture of those for axial and lateral response. At low load levels, the response is dominated by interaction with the upper soil layers and by the pile rigidity itself, similar to laterally loaded piles. However, failure will generally occur by the whole pile twisting, and so the latter part of the response incorporates the integrated effect of all soil penetrated by the pile, as is the case for axial loading.

In view of the above, solutions for the torsional response of pile must endeavour to incorporate accurate modelling of the soil stiffness profile, and also pay appropriate attention to the gradual development of slip (relative twist) between pile and soil. The paper presents analytical and numerical solutions for the torsional response of piles embedded in non-homogeneous soil, where the stiffness profile follows a simple power law with depth. The solutions encompass: (1) vertical non-homogeneity of soil expressed as a power law; (2) non-linear soil response, modelled using a hyperbolic stressstrain law; (3) effect of relative slip between pile and soil for non-homogeneous stiffness and limiting shaft friction; (4) expressions for the critical pile slenderness ratio (or length) beyond which the pile head response becomes independent of the pile length.

The solutions are developed using a load transfer approach, with each soil layer acting independently from neighbouring layers, and are expressed in terms of Bessel functions of non-integer order, and as simple non-dimensionalised charts. The solutions are applied to two well-documented case histories in the latter part of the paper.     

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。     

ANALYSIS OF PILES USED FOR SLOPE STABILIZATION

Piles used for the stabilization of slopes have to be adequately designed to resist the induced lateral loads due to the movement of the unstable slope. In this paper, a numerical method is presented for the analysis of this problem. In this approach, the piles are modelled using beam finite elements. The soil response at the individual piles is modelled using the modulus of subgrade reaction and pile–soil–pile interaction considered using the theory of elasticity. Two case histories, one for single pile and the other for pile group, are analysed which show that the numerical model can predict the general characteristics of the piles reasonably well. The study suggests that the design of the piles based on the computed response from single pile analysis, ignoring group effects, may be unduly conservative.     

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.     

基于DIC技术的桩筏基础工作机理研究

为了深入研究桩筏基础中桩周土体位移场特性及其工作机理,以数字图像相关技术（DIC）的基本原理为基础,编制相应的位移场分析程序,并利用该程序对桩基模型试验中获得的系列图像进行分析,得到了桩周土体位移场渐进性发展变化的全过程,同时对不同桩距桩筏基础的破坏模式作出推断。研究结果表明：利用自行编制的DIC程序分析桩周土体位移场是可行的,并可以得到全场位移。对于不同桩距桩筏基础,小桩距削弱基桩承载力,随着桩距的增大,这种削弱作用减弱。3b（b为方桩边长）桩距桩筏基础中,土体压缩区主要集中在桩端以下土层,基本符合实体深基础的破坏模式;而6b桩距桩筏基础,土体变形区域主要集中在桩身上部1/3L（L为桩长）范围内,明显小于3b桩距桩筏基础的影响深度,基础最终因桩间土体侧向挤出而破坏。     

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.     

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。