Analysis of rectangular piles subjected to lateral loads in nonhomogeneous soil using a Winkler model approach

An analytical approach using a Winkler model based on two lateral soil displacement components in a three‐dimensional soil is investigated to provide analytical solutions of horizontal response of a rectangular pile subjected to lateral loads in nonhomogeneous soil. The two lateral displacement components of a soil surrounding the rectangular pile are represented by the Fourier series of displacement potential functions in the elastic three‐dimensional analysis. The lateral stiffness coefficient of the rectangular pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient taking into account rocking rotation of a rigid pile shaft. The relationship between horizontal displacement, rotation, moment, and shear force for the rectangular pile subjected to horizontal loads in nonhomogeneous soil is obtainable in the form of the recurrence equation. The formulation of lateral displacement and rotation for a rectangular pile subjected to lateral loads on the pile base in nonhomogeneous soil is proposed by taking into account Mindlin's equation and the equivalent thickness for soil layers in the equivalent elastic method. The difference of lateral behavior between square and circular piles subjected to lateral loads is insignificant. The effect of aspect ratio of the rectangular pile on the lateral behavior is great for the lower stiffness ratio between pile and soil and the larger length–equivalent diameter ratio. The effect of the value of Poisson's ratio of soil on lateral stiffness coefficient is relatively small except Poisson's ratio close to 0.5. The comparison of the results calculated by the current method for a rectangular pile subjected to lateral loads in nonhomogeneous soil has shown good agreement with those obtained from the analytical methods and the finite element method. Copyright © 2015 John Wiley & Sons, Ltd.     

Influence of Relative Pile-Soil Stiffness and Load Eccentricity on Single Pile Response in Sand Under Lateral Cyclic Loading

The environment prevalent in ocean necessitates the piles supporting offshore structures to be designed against lateral cyclic loading initiated by wave action, which induces deterioration in the strength and stiffness of the pile-soil system introducing progressive reduction in the bearing capacity associated with increased settlement of the pile foundation. A thorough and detailed review of literature indicates that significant works have already been carried out in the relevant field of investigation. It is a well established phenomenon that the variation of relative pile-soil stiffness (K _rs ) and load eccentricity (e/D) significantly affect the response of piles subjected to lateral static load. However, the influence of lateral cyclic load on axial response of single pile in sand, more specifically the effect of K _rs and e/D on the cyclic behavior, is yet to be investigated. The present work has aimed to bridge up this gap. To carry out numerical analysis (boundary element method), the conventional elastic approach has been used as a guideline with relevant modifications. The model developed has been validated by comparing with available experimental (laboratory model and field tests) results, which indicate the accuracy of the solutions formulated. Thereafter, the methodology is applied successfully to selected parametric studies for understanding the magnitude and pattern of degradation of axial pile capacity induced due to lateral cyclic loading, as well as the influence of K _rs and e/D on such degradation.     

A three‐dimensional displacement approach for analysis of laterally loaded piles in nonhomogeneous soil

An analytical approach using the three‐dimensional displacement of a soil is investigated to provide analytical solutions of the horizontal response of a circular pile subjected to lateral loads in nonhomogeneous soil. The rocking stiffness coefficient of the pile shaft in homogeneous soil is derived from the analytical solution taking into account the three‐dimensional displacement represented in terms of scalar potentials in the elastic three‐dimensional analysis. The lateral stiffness coefficient of the pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient taking into account the rocking rotation of a rigid pile shaft. The relationship between horizontal displacement, rotation, moment, and shear force of a pile subjected to horizontal loads in nonhomogeneous soil is obtainable in the form of the recurrence equation. The formulation of the lateral displacement and rotation of the pile base subjected to lateral loads in nonhomogeneous soils is presented by taking into account Mindlin's equation and the equivalent thickness for soil layers in the equivalent elastic method. There is little difference between lateral, rocking, and couple stiffness coefficients each obtained from both the two‐dimensional and three‐dimensional methods except for the case of Poisson's ratio near 0.5. The comparison of results calculated by the current method for a pile subjected to lateral loads in homogeneous and nonhomogeneous soils has shown good agreement with those obtained from analytical and numerical methods. Copyright © 2017 John Wiley & Sons, Ltd.     

Analysis of piles subjected to lateral soil movements using a three‐dimensional displacement approach

An analytical approach using the three‐dimensional displacement of a soil is investigated to provide analytical solutions of the horizontal response of a circular pile subjected to lateral soil movements in nonhomogeneous soil. The lateral stiffness coefficient of the pile shaft in nonhomogeneous soil is derived from the rocking stiffness coefficient that is obtained from the analytical solution, taking into account the three‐dimensional displacement represented in terms of scalar potentials in the elastic three‐dimensional analysis. The relationship between horizontal displacement, rotation, moment, and shear force of a pile subjected to lateral soil movements in nonhomogeneous soil is obtainable in the form of the recurrence equation. For the relationship between the lateral pressure and the horizontal displacement, it is assumed that the behavior is linear elastic up to lateral soil yield, and the lateral pressure is constant under the lateral soil yield. The interaction factors between piles subjected to both lateral load and moment are calculated, taking into account the lateral soil movement. The formulation of the lateral displacement and rotation of the pile base subjected to lateral loads in nonhomogeneous soils is presented by taking into account the Mindlin equation and the equivalent thickness for soil layers in the equivalent elastic method. For lateral movement, lateral pressure, bending moment, and interaction factors, there are small differences between results obtained from the 1‐D and the 3‐D displacement methods except a very flexible pile. Copyright © 2015 John Wiley & Sons, Ltd.     

Response of rigid piles during passive dragging

This paper develops a three‐layer model and elastic solutions to capture nonlinear response of rigid, passive piles in sliding soil. Elastic solutions are obtained for an equivalent force per unit length p_s of the soil movement. They are repeated for a series of linearly increasing p_s (with depth) to yield the nonlinear response. The parameters underpinning the model are determined against pertinent numerical solutions and model tests on passive free‐head and capped piles. The solutions are presented in non‐dimensional charts and elaborated through three examples. The study reveals the following:

• On‐pile pressure in rotationally restrained, sliding layer reduces by a factor α, which resembles the p‐multiplier for a laterally loaded, capped pile, but for its increase with vertical loading (embankment surcharge), and stiffness of underlying stiff layer: α = 0.25 and 0.6 for a shallow, translating and rotating piles, respectively; α = 0.33–0.5 and 0.8–1.3 for a slide overlying a stiff layer concerning a uniform and a linearly increasing pressure, respectively; and α = 0.5–0.72 for moving clay under embankment loading.
• Ultimate state is well defined using the ratio of passive earth pressure coefficient over that of active earth pressure. The subgrade modulus for a large soil movement may be scaled from model tests.
• The normalised rotational stiffness is equal to 0.1–0.15 for the capped piles, which increases the pile displacement with depth.

The three‐layer model solutions well predict nonlinear response of capped piles subjected to passive loading, which may be used for pertinent design. Copyright © 2016 John Wiley & Sons, Ltd.     

Development of Analytical Models to Estimate Pile Setup in Cohesive Soils Based on FE Numerical Analyses

This paper presents the numerical simulation of pile installation and the subsequent increase in the pile capacity over time (or setup) after installation that was performed using the finite element software Abaqus. In the first part, pile installation and the following load tests were simulated numerically using the volumetric cavity expansion concept. The anisotropic modified Cam-Clay and Dracker–Prager models were adopted in the FE model to describe the behavior of the clayey and sandy soils, respectively. The proposed FE model proposed was successfully validated through simulating two full-scale instrumented driven pile case studies. In the second part, over 100 different actual properties of individual soil layers distracted from literature were used in the finite element analysis to conduct parametric study and to evaluate the effect of different soil properties on the pile setup behavior. The setup factor A was targeted here to describe the pile setup as a function of time after the end of driving. The selected soil properties in this study to evaluate the setup factor A include: soil plasticity index (PI), undrained shear strength (S _u ), vertical coefficient of consolidation (C _v ), sensitivity ratio (S _r ), and over-consolidation ratio (OCR). The predicted setup factor showed direct proportion with the PI and S _r and inverse relation with S _u , C _v and OCR. These soil properties were selected as independent variables, and nonlinear multivariable regression analysis was performed using Gauss–Newton algorithm to develop appropriate regression models for A. Best models were selected among all based on level of errors of prediction, which were validated with additional nineteen different site information available in the literature. The results indicated that the developed model is able to predict the setup behavior for individual cohesive soil layers, especially for values of setup factor greater than 0.10, which is the most expectable case in nature.     

Analytical solutions for Euler–Bernoulli beam on visco‐elastic foundation subjected to moving load

Analytical solutions for the steady‐state response of an infinite beam resting on a visco‐elastic foundation and subjected to a concentrated load moving with a constant velocity are developed in this paper. The beam responses investigated are deflection, bending moment, shear force and contact pressure. The mechanical resistance of the foundation is modeled using two parameters k_s and t_s — k_s accounts for soil resistance due to compressive strains in the soil and t_s accounts for the resistance due to shear strains. Since this model represents the ground behavior more accurately than the Winkler spring model, the developed solutions produce beam responses that are closer to reality than those obtained using the existing solutions for Winkler model. The dynamic beam responses depend on the damping present in the system and on the velocity of the moving load. Based on the study, dynamic amplification curves are developed for beam deflection. Such amplification curves for deflection, bending moment, shear force and contact pressure can be developed for any beam‐foundation system and can be used in design. Copyright © 2012 John Wiley & Sons, Ltd.     

水平荷载下导管架平台桩基础的非线性有限元分析

导管架平台桩基础的控制荷载主要为风荷载、波浪荷载、地震荷载等水平荷载,为研究水平荷载下导管架平台桩基础的承载特性,采用非线性有限元分析方法对水平荷载下桩-土之间的相互作用进行研究,提出了有效模拟桩基水平承载特性的有限元模型,分析了模型桩的刚度、直径、土质参数中水平土压力系数、剪胀角对桩基承载特性的影响及水平荷载下群桩承载特性,并将有限元计算结果与API规范及模型试验结果进行对比。研究结果表明,非线性有限元分析方法分析水平荷载下桩-土相互作用是可行的,计算结果可为导管架平台的桩基设计提供参考。     

Numerical analysis of the interface shear transfer mechanism of a single pile to tunnelling in weathered residual soil

Three-dimensional (3D) numerical analyses have been carried out to study the behaviour of a single pile to adjacent tunnelling in the lateral direction of the pile. The numerical analyses have included comparisons between the current study, previous elastic solutions and advanced 3D elasto-plastic analyses. In the numerical analyses, the interaction between the tunnel, the pile and the soil next to the pile has been analysed. The study includes the axial force distributions on the pile, the relative shear displacement between the pile and the soil, the shear stresses at the soil next to the pile and the pile settlement. In particular, the shear stress transfer mechanism along the pile related to tunnel advancement has been analysed by using interface elements allowing soil slip. It has been found that existing solutions may not accurately estimate the pile behaviour since several key issues are not included. Due to changes in the relative shear displacement between the pile and the soil next to the pile with tunnel advancement, the shear stresses and axial force distributions along the pile change drastically. Downward shear stress develops at the upper part of the pile, while upward shear stress is mobilised at the lower part of the pile, resulting in a compressive force on the pile. A maximum compressive force of about 0.25–0.52P_a was developed on the pile, solely due to tunnelling, depending on the pile tip locations relative to the tunnel position, where P_a is the service pile loading prior to tunnelling. The majority of the axial force on the pile developed within ±2D in the transverse direction (behind and ahead of piles) relative to the pile position, where D is the tunnel diameter. In addition, mobilisation of shear strength at the pile–soil interface was found to be a key factor governing pile–soil–tunnelling interaction. The reduction of apparent allowable pile capacity due to tunnelling was dependent on the pile location relative to the tunnel position. Some insights into the pile behaviour in tunnelling obtained from the numerical analyses will be reported and discussed.     

A New Computer Program for Pile Capacity Prediction using CPT Data

An interactive computer program “GLAMCPT” is developed for application in soil profiling and prediction of pile load capacity using cone penetration test (CPT) and laboratory soil test results. GLAMCPT calculates pile capacity according to 10 selected methods from European design codes, refereed international publications and recommendations of professional institutions. To demonstrate the capabilities of the program, a database of comprehensive ground investigation and full-scale pile tests in sand, at a Belgian site, is analysed using GLAMCPT. The database comprises 11 static tests and 12 dynamic tests on piles of different construction techniques, including driven pre-cast concrete piles and screwed cast in-situ piles, installed using 5 different procedures. Prior to pile installation, CPTs were carried out at each proposed pile location. Comparison of GLAMCPT predictions with the observed pile capacities reveals that the most accurate of the existing methods yields an average, μ, of predicted to observed pile head capacity [P_uh(p)/P_uh(m)] equal to 0.94. The most consistent method produces a coeffcient of variation (COV) of [P_uh(p)/P_uh(m)] equal to 0.1 and ranking index (RI) of 0.08. Parametric studies have been carried out using GLAMCPT to formulate an improved predictive method, which yielded: μ = 0.99, COV = 0.07 and RI = 0.04.     

Field testing of one-way and two-way cyclic lateral responses of single and jet-grouting reinforced piles in soft clay

Piles supporting transmission towers, offshore structures (such as wind turbines), or infrastructures in seismic areas are frequently subjected to either one-way or two-way cyclic lateral loadings. Relatively little attention, however, has been paid to compare and understand the effects of different loading regimes (one-way or two-way cycling) on lateral responses of piles in soft clay. For this reason, a series of field tests in soft clay are carried out to compare one-way and two-way cyclic responses of single piles and of jet-grouting reinforced piles. The field tests reveal that the single pile subjected to two-way cycling experiences much more rapid degradation in lateral stiffness and capacity, but accumulates much smaller residual pile deflection (δ _p), than the single pile under one-way cycling. This is because the reverse part of the two-way cycling also generates plastic strain, causing additional softening and strength reduction in the soil surrounding the pile. After each cycling, non-zero bending moment (i.e. locked in moment, or M _L) is retained in the single piles, and the M _L increases with the δ _p. The one-way cycling leads to two times larger M _L than the two-way cycling, as it causes greater δ _p. The maximum M _L in the pile after one-way cycling can be up to 40% of the maximum bending moment induced during the previous cyclic loading stage. After application of jet-grouting surrounding the upper part of the single pile, it greatly reduces degradation of lateral pile stiffness, accumulation of δ _p and therefore development of M _L. Compared to the field measurements, the API (API RP 2A-WSD, recommended practice for planning, designing, and constructing fixed offshore platform-working stress design, 21st edn. API, Washington, 2000) code underestimates the lateral stiffness of the pile under one-way cycling, while overestimates that of the pile under two-way cycling, leading to a non-conservative prediction of bending moment in the latter pile.     

Bounding surface model for soil resistance to cyclic lateral pile displacements with arbitrary direction

The development of a two-surface elastic–plastic bounding surface P–Y model for cyclic lateral pile motions is described. The kinematic-hardening model is applicable to the analysis of pile foundations subjected to loading with arbitrary azimuths relative to the pile axis. The model realistically captures the hysteretic energy damping associated with dynamic loading of subsea foundations through physically correct plastic mechanisms and provides results consistent with those observed in physical tests including cyclic loading. Its performance is demonstrated in element states of stress and in pile foundation analyses. The development based on the incremental theory of plasticity results in more robust solutions than may be obtained using alternative elastic, variable moduli and deformation plasticity formulations.     

Load transfer analysis of rock-socketed drilled shafts by coupled soil resistance

The load distribution and deformation of rock-socketed drilled shafts subjected to axial loads are evaluated by a load transfer method. The emphasis is on quantifying the effect of coupled soil resistance in rock-socketed drilled shafts using 2D elasto-plastic finite element analysis. Slippage and shear-load transfer behavior at the pile–soil interface are investigated by using a user-subroutine interface model (FRIC). It is shown that the coupled soil resistance acts as pile-toe settlement as the shaft resistance is increased to its ultimate limit state. Based on the results obtained, the coupling effect is closely related to the ratio of the pile diameter to soil modulus (D/E_s) and the ratio of total shaft resistance against total applied load (R_s/Q). Through comparison with field case studies, the 2D numerical analysis reasonably estimated load transfer of pile and coupling effect, and thus represents a significant improvement in the prediction of load deflections of drilled shafts.     

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.     

Single piles under horizontal loads in sand: determination of <Emphasis Type="Italic">P</Emphasis>–<Emphasis Type="Italic">Y</Emphasis> curves from the prebored pressuremeter test

Lateral load-deflection behaviour of single piles is often analysed in practice on the basis of methods of load-transfer P–Y curves. The paper is aimed at presenting the results of the interpretation of five full-scale horizontal loading tests of single instrumented piles in two sandy soils, in order to define the parameters of P–Y curves, namely the initial lateral reaction modulus and the lateral soil resistance, in correlation with the pressuremeter test parameters. P–Y curve parameters were found varying as a power of lateral pile/soil stiffness, on the basis of which hyperbolic P–Y curves in sand were proposed. The predictive capabilities of the proposed P–Y curves were assessed by predicting the soil/pile response in full-scale tests as well as in centrifuge tests and a very good agreement was found between the computed deflections and bending moments, and the measured ones. Small-sized database of full-scale pile loading tests in sand was built and a comparative study of some commonly used P–Y curve methods was undertaken. Moreover, it was shown that the load-deflection curves of these test piles may be normalised in a practical form for an approximate evaluation of pile deflection in a preliminary stage of pile design. At last, a parametric study undertaken on the basis of the proposed P–Y curves showed the significant influence of the lateral pile/soil stiffness on the non-linear load-deflection response.     

Semi-analytical solutions for vertically and laterally loaded piles in multilayered soil deposits

In geotechnical practice, it is of considerable importance to assess the behavior of vertical–lateral coupled loading piles in multilayered soil deposits. This study deals with a semi-analytical formulation for the performance of a pile suffering from combined vertical and lateral loads. The emphasis is on quantifying the mobilization of the subgrade reaction provided by the layered soil stratums. In the proposed method, subgrade reactions, correlated with both the accumulative axial load transfer and side resistances depending upon the pile–soil interaction, are abstracted as a series of nonlinear springs in both vertical and lateral directions. On account of this, an alternative transfer matrix method is applied to characterize the pile reaction along the depth under the identified boundary conditions atop the pile; meanwhile, the condition of static equilibrium, between two specific pile segments located at the border of soil layers, is also essential. On this basis, validation of the solution is conducted by comparing with observations from experiments and predictions obtained from other existing methods. In addition, the influence of properties in shallow soil layer and the vertical load on the lateral response of the pile is also discussed. The results indicate a reduction in the lateral displacement and the maximum bending moment within the pile with the increase in the shallow soil stiffness, but a growth with the increase in vertical load due to the “P-Δ effect.”     

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.     

冻融条件下模型桩基水平动力试验研究

基于自制的冻土-桩动力相互作用模型试验系统,对-5℃、-3℃及上层融化多年冻土中模型桩基进行了水平向动力试验,主要研究了冻结及上层融化冻土中模型桩基的桩头位移-荷载关系、桩基水平动刚度变化及桩身弯矩分布情况。结果表明：冻土中桩基动力响应特性与土体温度密切相关;正冻土中桩基有较大的侧向刚度,当冻土与桩接触面出现较大间隙时,桩头位移-荷载曲线呈反S形;桩基动力性能随多年冻土温度降低将有所改善;当冻土上部出现融化层时,桩基动响应变化显著,桩头动刚度明显减小,桩基在较小动载下可发生较大侧向位移,同时桩身最大弯矩值较正冻土中偏大,且此弯矩点埋深较大。对于多年冻土区桩基工程,应特别重视夏季上层冻土融化时可能出现的震害。     

Load–Deflection response of transversely isotropic piles under lateral loads

In general, pile materials are assumed to be isotropic during the analysis of the load–deflection response of piles under lateral loads. However, commonly used materials such as reinforced concrete and timber as well as potentially promising new pile materials such as fiber reinforced polymers are typically transversely isotropic materials. Experimental studies have shown that transversely isotropic materials have a high ratio of section longitudinal modulus to the section in‐plane shear modulus (E_zz/G_xz) compared to the value for isotropic materials. The high modulus ratio leads to a more significant shear deformation effect in beam bending. To account for the shear deformation effect, the Timoshenko Beam Theory has been adopted in deriving the solutions for the load–deflection response of transversely isotropic piles under lateral loads instead of the Classical (Euler–Bernoulli) Beam Theory. The load–deflection responses depend on the shear effect coefficient, the lateral soil resistance, the embedment ratio, and the boundary conditions. The deflection of the pile, if the shear deformation effect is considered, is always larger than if it is neglected. Copyright © 2000 John Wiley & Sons, Ltd.     

基于传递矩阵法的层状土中管桩水平动力阻抗分析

在考虑土体分层特性的基础上,分别建立了管桩桩周土体和桩芯土体的水平振动控制方程。通过引入势函数并考虑桩周土和桩芯土径向位移和环向位移的边界条件及其奇偶性,求得了管桩-土动力相互作用的刚度系数和阻尼系数。将土体模拟为连续分布的弹簧-阻尼器,并考虑桩芯土和桩周土的作用,建立了层状土中管桩的水平振动方程。借助初参数法和传递矩阵法求解了管桩的水平振动,得到了管桩桩顶的水平动力阻抗。通过数值分析,得到了土层剪切模量、管桩壁厚、桩周土和桩芯土剪切模量比、土层厚度等对管桩桩顶动力阻抗的影响规律。土层剪切模量、管桩壁厚、桩周土和桩芯土剪切模量比对层状土中管桩水平振动的影响主要在低频处,土层厚度在较宽的频率范围内对管桩水平振动有影响;管桩壁越厚,桩周土的剪切模量越大时,管桩水平动力阻抗的绝对值越大。