Approximate computer analysis of pile groups subjected to loads and ground movements

This paper describes the development of an approximate approach for the analysis and design of piles subjected to axial and lateral loading and also to vertical and horizontal ground movements. The analysis involves a number of simplifications in order to make it feasible to implement. For example, it considers the behaviour of a ‘representative’ pile in a group to characterize the behaviour of all piles in the group, and adopts approximations to derive free-field interaction factors from the conventional interaction factors for direct loading. The analysis has been implemented via a computer program called EMbankment PIle Group (EMPIG) and has the ability to incorporate the following features:

• 1. single piles or pile groups,
• 2. applied vertical, lateral and moment loading on the pile cap,
• 3. the effects of axial and lateral soil movements caused by embankment construction,
• 4. a layered soil profile,
• 5. non-linear axial and lateral response of the piles.

Comparisons between solutions from EMPIG and other independent programs suggest that it is capable of providing results of adequate accuracy for practical design purposes. The analysis has been used to investigate the effects of pile rake on a typical bridge abutment group. The presence of raked piles can have a detrimental effect on group behaviour, especially in the presence of ground movements. Large lateral deflections can be generated and axial forces and moments in the piles are increased. Comparisons are also made with the results of centrifuge model tests on abutment pile groups. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

On the influence of vertical loads on the lateral response of pile foundation

The influence of vertical loads on the lateral response of group piles installed in sandy soil and connected together by a concrete cap is studied through finite elements analyses. The analyses focus on the five piles in the middle row of 3 × 5 pile groups. The vertical load is applied by enforcing a vertical displacement equivalent to 2% of the pile diameter through the pile cap prior to the application of the lateral loads. The results have shown that the lateral resistance of the leading pile (pile 1) does not appear to vary considerably with the vertical load. However, the vertical load leads to 23%, 36%, 64%, and 82% increase in the lateral resistance of piles 2–5, respectively. The increase in the lateral pressures in the sand deposit is the major driving factor to contribute the change in the lateral resistance of piles, depending on the position of the pile in the group. The distribution of lateral loads among piles in the group tends to be more uniform when vertical loads were considered leading to a more economical pile foundation design.     

Three-dimensional finite element study of a single pile response to multidirectional lateral loadings incorporating the simplified state-dependent dilatancy model

Waves and winds can induce lateral loads on piles, which are often multidirectional. The objective of this study is to investigate the response of a single pile subjected to unidirectional and multidirectional lateral loadings using the finite element analysis program ABAQUS. A simplified version of the state-dependent dilatancy model was implemented and embedded into the program to simulate the behavior of the soil around the pile. The results of the analyses indicate that the lateral resistance of the pile along one horizontal direction under multidirectional loading is lower than that under unidirectional loading. The degree of reduction of the resistance increases with the aspect ratio of the displacement path at the pile head. The directions of the force increment vector and the displacement increment vector are generally non-coaxial under multidirectional loading. The soil-pile interaction and soil responses under multidirectional loading are also significantly different than those under unidirectional loading.     

A hypoplastic macroelement formulation for single batter piles in sand

Batter piles are widely used in geotechnical engineering when substantial lateral resistance is needed or to avoid the interference with existing underground constructions. Nevertheless, there is a lack of fast numerical tools for nonlinear soil‐structure interactions problems for this type of foundation. A novel hypoplastic macroelement is proposed, able to reproduce the nonlinear response of a single batter pile in sand under monotonic and cyclic static loadings. The behavior of batter piles (15°, 30°, and 45°) is first numerically investigated using 3D finite element modeling and compared with the behavior of vertical piles. It is shown that their response mainly depends on the pile inclination and the loading direction. Then, starting from the macroelement for single vertical piles in sand by Li et al (Acta Geotechnica, 11(2):373‐390, 2016), an extension is proposed to take into account the pile inclination introducing simple analytical equations in the expression describing the failure surface. 3D finite element numerical models are adopted to validate the macroelement that is proven able to reproduce the nonlinear behavior in terms of global quantities (forces‐displacements) and to significantly reduce the necessary computational time.     

Analysis of kinematic seismic response of tapered piles

In the present work, a two-phase analysis is used to assess the lateral movement of a tapered pile due to kinematic seismic loading resulted from earthquakes. First, the free-field horizontal displacement of the ground due to earthquake is estimated using available theory of wave propagation. Second, these estimated soil movements are imposed on the taper pile in a closed-form solution to compute the pile response. The governing differential equation for an arbitrary pile segment is obtained, which includes the free-field horizontal movement estimated from the first phase. The equation is solved explicitly to obtain the horizontal deflection. Parametric studies show that tapered piles tend to be more flexible than uniform piles of the same volume and length under earthquake loading, which is soundly interesting.     

Three‐dimensional finite element analyses of passive pile behaviour

Piles may be subjected to lateral soil pressures as a result of lateral soil movements from nearby construction‐related activities such as embankment construction or excavation operations. Three‐dimensional finite element analyses have been carried out to investigate the response of a single pile when subjected to lateral soil movements. The pile and the soil were modelled using 20‐node quadrilateral brick elements with reduced integration. For compatibility between the soil–pile interface elements, 27‐node quadrilateral brick elements with reduced integration were used to model the soil around the pile adjacent to the soil–pile interface. A Mohr–Coulomb elastic–plastic constitutive model with large‐strain mode was assumed for the soil. The analyses indicate that the behaviour of the pile was significantly influenced by the pile flexibility, the magnitude of soil movement, the pile head boundary conditions, the shape of the soil movement profile and the thickness of the moving soil mass. Reasonable agreement is found between some existing published solutions and those developed herein. Copyright © 2005 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.     

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 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.     

Vertical stress distributions around batter piles driven in cross‐anisotropic media

This work presents analytical solutions to compute the vertical stresses for a cross‐anisotropic half‐space due to various loading types by batter piles. The loading types are an embedded point load for an end‐bearing pile, uniform skin friction, and linear variation of skin friction for a friction pile. The cross‐anisotropic planes are parallel to the horizontal ground surface. The proposed solutions can be obtained by utilizing Wang and Liao's solutions for a horizontal and vertical point load acting in the interior of a cross‐anisotropic medium. The derived cross‐anisotropic solutions using a limiting approach are in perfect agreement with the isotropic solutions of Ramiah and Chickanagappa with the consideration of pile inclination. Additionally, the present solutions are identical to the cross‐anisotropic solutions by Wang for the batter angle equals to 0. The influential factors in yielded solutions include the type and degree of geomaterial anisotropy, pile inclination, and distinct loading types. An example is illustrated to clarify the effect of aforementioned factors on the vertical stresses. The parametric results reveal that the stresses considering the geomaterial anisotropy and pile batter differ from those of previous isotropic and cross‐anisotropic solutions. Hence, it is imperative to take the pile inclination into account when piles are required to transmit both the axial and lateral loads in the cross‐anisotropic media. Copyright © 2008 John Wiley & Sons, Ltd.     

Uncoupled analysis of stabilizing piles in weathered slopes

This paper describes a simplified numerical approach for analyzing the slope/pile system subjected to lateral soil movements. The lateral one-row pile response above and below the critical surface is computed by using load transfer approach. The response of groups was analyzed by developing interaction factors obtained from a three-dimensional nonlinear finite element study. An uncoupled analysis was performed for stabilizing piles in slope in which the pile response and slope stability are considered separately. The non-linear characteristics of the soil–pile interaction in the stabilizing piles are modeled by hyperbolic load transfer curves. The Bishop's simplified method of slope stability analysis is extended to incorporate the soil-pile interaction and evaluate the safety factor of the reinforced slope. Numerical study is performed to illustrate the major influencing parameters on the pile-slope stability problem. Through comparative studies, it has been found that the factor of safety in slope is much more conservative for an uncoupled analysis than for a coupled analysis based on three-dimensional finite element analysis.     

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.     

Buckling behaviour of single pile and pile bent in the Scotch Road Bridge

The buckling behaviour of the 360 × 152 steel H-piles supporting the integral abutments of the Scotch Road Bridge, located in Trenton, New Jersey, has been studied for the cases of single pile and pile bent. Three-dimensional finite-element models for single pile and pile bent have been developed to study the behaviour of these fully embedded piles under axial and lateral loading. An iterative analysis based on extracting the eigenvalues and eigenvectors (mode shapes) that correspond to the pile(s) critical buckling loads has been adopted. The pile(s) and the surrounding sand were modelled using solid continuum elements in the finite-element model. Material non-linearity is accounted for in both the piles and the soil in the base state of the model. A parametric study has been utilized to determine the effect of the geometric and material properties of the pile and the surrounding sand on the predicted critical buckling loads of the piles. The effects of four parameters have been studied: soil stiffness, pile length, type of connection, and combining vertical and lateral loads. The results from the parametric study showed that the variation of the percentage change in the sand stiffness, pile length, and combining vertical and lateral loads with the critical buckling loads of the 360 × 152 H-piles is nonlinear. Furthermore, the parameters studied are more influential in affecting the critical buckling load of a single pile than a pile bent, with the exception of the ‘type of connection’ parameter.     

高速铁路超长桥桩承载特性试验研究

超长桩广泛已应用于土木工程各个领域,但黄土地区超长桩的承载性状和变形特性尚不十分清楚,需要进一步研究。通过对郑西铁路客运专线某特大桥的4根超长桩现场测试项目的资料分析,得出了超长桩桩身轴力及侧阻力的变化规律,对超长桩的承载特性有了更为清晰的了解。试验结果表明,在桩顶竖向荷载作用下,桩身轴力随荷载的增加发生了局部调整,砂性土层的桩侧摩阻力具有增强效应,黏性土层的桩侧摩阻力具有退化效应;单桩竖向刚度随桩顶荷载的增加而减小,单桩竖向刚度降低40 %～70 %。     

Response of Pile Groups Driven in Sand Subjected to Combined Loads

Although the loads applied on piles are usually a combination of both vertical and lateral loads, very limited experimental research has been done on the response of pile groups subjected to combined loads. Due to pile–soil–pile interaction in pile groups, the response of a pile group may differ substantially from that of a single pile. This difference depends on soil state and pile spacing. This paper presents results of experiments designed to investigate pile interaction effects on the response of pile groups subjected to both axial and lateral loads. The experiments were load tests performed on model pile groups (2 × 2 pile groups) in calibration chamber sand samples. The model piles were driven into the sand samples prepared with different relative densities using a sand pluviator. The combined load tests were performed on the model pile groups subjected to different axial load levels, i.e., 0 (pure lateral loading), 25, 50, and 75% of the ultimate axial load capacity of the pile groups, defined as the load corresponding to a settlement of 10% of the model pile diameter. The combined load test results showed that the bending moment and lateral deflection at the head of the piles increased substantially for tests performed in the presence of axial loads, suggesting that the presence of axial loads on groups of piles driven in sand is detrimental to their lateral capacity.     

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.     

Expanded superposition method for impedance functions of inclined‐pile groups

This paper presents a superposition method expanded for computing impedance functions (IFs) of inclined‐pile groups. Closed‐form solutions for obtaining horizontal, vertical, and rocking IFs, estimated by using pile‐to‐pile interaction factors, are proposed. IFs of solitary inclined piles, crossed IFs, and explicit incorporation of compatibility conditions for pile‐head movements are also appropriately taken into consideration. All of these factors should be known in advance and will be computed and shown for the most relevant cases. The accuracy of the proposed closed‐form solutions is verified for 2 × 2 and 3 × 3 square inclined‐pile groups embedded in an isotropic viscoelastic homogeneous half‐space soil medium, with hysteretic damping. The pile‐to‐pile interaction factors are computed by means of a three‐dimensional time‐harmonic boundary elements–finite elements coupling formulation. The results indicate that the IFs obtained from the proposed method are in good agreement with those obtained from the coupling formulation. Furthermore, crossed vertical‐rocking IFs of solitary piles need to be appropriately considered for obtaining rocking IFs when the number of piles is small. Copyright © 2015 John Wiley & Sons, Ltd.     

桩承式围堤对邻近桥梁桩基的影响分析

桩承式围堤是将上部围堤或堆载荷重通过桩筏基础传递到深层较硬的土层,以减少由于围堤或堆载对邻近桩基产生负摩阻力和侧向推力的一种围堤式构筑物。采用基于Mindlin应力解的桩伐基础简化分析方法、弹性和弹塑性三维数值模拟了嘉兴港海盐港区围堤对杭州湾跨海大桥产生的负摩阻力和侧向推力。通过上述3种方法的分析比较,结果表明,采用的简化分析方法与弹性和弹塑性三维数值模拟结果吻合较好,可作为桩承式围堤结构基础的分析和设计方法。     

水平循环荷载下桩基变形特性的离心模型试验研究

波浪、船舶等长期水平循环荷载作用下,桩基将不可避免地产生附加应力和变形。针对饱和黏土地层,开展离心模型试验研究了船舶系泊水平荷载作用下单桩和群桩的变形特性。发现水平循环加-卸载诱发了桩周土体的塑性变形,进而导致桩身产生了不可恢复的水平位移和弯曲变形。随着循环荷载的增加,单桩和群桩的桩顶最大水平位移和残余水平位移均同时增加,但残余水平位移明显小于最大水平位移。单桩的桩顶残余水平位移与最大位移比值介于0.17～0.22;群桩的桩顶残余水平位移与最大水平位移比值介于0.30～0.84。水平循环加-卸载作用下,桩身残余弯曲应变明显小于最大弯曲应变。单桩的残余弯曲应变与最大弯曲应变比值介于0.13～0.50;群桩的桩身残余弯曲应变与最大弯曲应变比值介于0.23～0.82。群桩前桩的残余和最大弯曲应变明显大于后桩,前桩与后桩的最大弯曲应变、残余应变比值分别高达3.2和3.1。因此,前桩要采取合理的加固和保护措施,以确保桩基长期服役的安全性。