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.     

抗滑桩应变特征与内力非线性研究

为探究抗滑桩实际内力与变形间的规律,特别是桩土相互作用下桩体受力、变形、稳定性等特征,通过抗滑桩大型物理模型试验,结合MATLAB拟合推导实现从桩表面应变散点数据到桩身挠度分布的求解。对比同桩长不同加载条件与同加载条件不同桩长两种情况下桩表面应变、桩身弯矩、剪力及挠度,分析抗滑桩的应变特征与内力变化规律。研究表明:单调与循环加载条件下抗滑桩工作阶段划分为三阶段,即未开裂阶段、混凝土开裂-钢筋屈服阶段、钢筋屈服-桩体破坏阶段。未开裂阶段一、二级荷载下由于土的压密性桩体略微回弹,桩表面应变、桩身弯矩、受荷段剪力及挠度出现较小的负值（绝对值约为破坏时的1%）。混凝土开裂-钢筋屈服阶段应变、弯矩、剪力、挠度增速明显加快。钢筋屈服-桩体破坏阶段应变、弯矩、剪力、挠度呈非线性增长,桩体的破坏模式均为弯剪破坏。随着自由端长度的增加,破坏时应变、弯矩增大,而剪力减小,破坏时应变增长约10%,弯矩增长约3%,剪力减少约20%;相对于单调加载,循环加载下最大弯矩值和最大挠度均有增大,最大弯矩增长约2%,最大挠度增长约1%。     

Elastic models for nonlinear response of rigid passive piles

Recent study indicates that the response of rigid passive piles is dominated by elastic pile–soil interaction and may be estimated using theory for lateral piles. The difference lies in that passive piles normally are associated with a large scatter of the ratio of maximum bending moment over maximum shear force and induce a limiting pressure that is ~1/3 that on laterally loaded piles. This disparity prompts this study. This paper proposes pressure‐based pile–soil models and develops their associated solutions to capture response of rigid piles subjected to soil movement. The impact of soil movement was encapsulated into a power‐law distributed loading over a sliding depth, and load transfer model was adopted to mimic the pile–soil interaction. The solutions are presented in explicit expressions and can be readily obtained. They are capable of capturing responses of model piles in a sliding soil owing to the impact of sliding depth and relative strength between sliding and stable layer on limiting force prior to ultimate state. In comparison with available solutions for ultimate state, this study reveals the 1/3 limiting pressure (of the active piles) on passive piles was induced by elastic interaction. The current models employing distributed pressure for moving soil are more pertinent to passive piles (rather than plastic soil flow). An example calculation against instrumented model piles is provided, which demonstrates the accuracy of the current solutions for design slope stabilising piles. Copyright © 2014 John Wiley & Sons, Ltd.     

Load–settlement behavior of rock-socketed drilled shafts using Osterberg-Cell tests

Osterberg-Cell (O-Cell) tests are widely used to predict the load–settlement behavior of large-diameter drilled shafts socketed in rock. The loading direction of O-Cell tests for shaft resistance is opposite to that of conventional downward load tests, meaning that the equivalent top load–settlement curve determined by the summation of the mobilized shaft resistance and end bearing at the same deflection neglects the pile-toe settlement caused by the load transmitted along the pile shaft. The emphasis is on quantifying the effect of coupled shaft resistance, which is closely related to the ratios of pile diameter to soil modulus (D/E_s) and total shaft resistance to total applied load (R_s/Q) in rock-socketed drilled shafts, using the coupled load-transfer method. The proposed analytical method, which takes into account the effect of coupled shaft resistance, was developed using a modified Mindlin’s point load solution. Through comparisons with field case studies, it was found that the proposed method reasonably estimated the load-transfer behavior of piles and coupling effects due to the transfer of shaft shear loading. These results represent a significant improvement in the prediction of load–settlement behaviors of drilled shafts subjected to bi-directional loading from the O-Cell test.     

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.     

Analysis of laterally loaded piles with rectangular cross sections embedded in layered soil

An analysis is developed to determine the response of laterally loaded rectangular piles in layered elastic media. The differential equations governing the displacements of the pile–soil system are derived using variational principles. Closed‐form solutions of pile deflection, the slope of the deflected curve, the bending moment and the shear force profiles can be obtained by this method for the entire pile length. The input parameters needed for the analysis are the pile geometry and the elastic constants of the soil and pile. The new analysis allows insights into the lateral load response of square, rectangular and circular piles and how they compare. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

海洋工程中大直径管桩垂直水平荷载试验研究

通过海洋环境条件下大直径管桩的垂直和水平荷载试验,分析了管桩在垂直和水平荷载作用下的受力特点,得到了管桩的垂直极限承载力、侧摩阻力及端承力、轴向反力系数等结果,以及水平荷载作用下桩顶位移和转角关系、弯矩分布、土抗力、水平地基反力系数的比例系数和最大弯矩点等参数。试验结果表明：垂直荷载作用下,极限承载力可达12000kN,在沉桩过程中部分桩有一定程度的闭塞;大直径管桩能够抵抗水平荷载的作用,弹性长桩的受力性质主要受上部土层的影响。根据试验结果计算的水平地基抗力比例系数m值,对本工程及同类地质条件的桩基设计具有参考价值。     

Piles in fully liquefied soils with lateral spread

The paper provides a new analysis procedure for the assessment of the lateral response of isolated piles/drilled shafts in saturated sands as liquefaction and lateral soil spread develop in response to dynamic loading such as that generated by the earthquake shaking. The presented method accounts for: (1) the development of full liquefaction in the free-field soil that could trigger the lateral spread of the overlying crust layer; (2) the driving force exerted by the crust layer based on the interaction between the pile and the upper non-liquefied soil (crust) layer; and (3) the variation of the excess pore water pressure (i.e. post-liquefaction soil strength) in the near-field soil with the progressive pile deflection under lateral soil spread driving force. A constitutive model for fully liquefied sands under monotonic loading and undrained conditions is developed in order to predict the zone of post-liquefaction zero-strength of liquefied sand before it rebounds with the increasing soil strain in the near-field. The analytical and empirical concepts employed in the Strain Wedge (SW) model allow the modeling of such a sophisticated phenomenon of lateral soil spread that could accompany or follow the occurrence of seismic events without using modifying parameters or shape corrections to account for soil liquefaction.     

Interaction of a cylindrical thin‐walled pile with an inhomogeneous isotropic elastic medium

This paper presents a rigorous analysis for the static interaction of a cylindrical thin‐walled pile with an inhomogeneous isotropic elastic half‐space under vertical, horizontal, and torsional forces individually applied at the top of pile. The inhomogeneity is specified with the exponential variation of shear modulus along depth of the embedding medium, and the Poisson's ratio is assumed to be constant. By means of a set of Green's functions for pile and soil medium and satisfying the compatibility conditions between the 2 interacting media, the formulation is reduced to coupled Fredholm integral equations. Using the adaptive‐gradient elements, capable of capturing the singular stress transfer at both ends of the pile, a numerical procedure is developed and utilized for evaluating the relevant integral equations and studying the inhomogeneity effect on the soil‐pile interaction responses. The analysis results have been validated for different soil‐pile modulus ratios under axial load and for a Poisson's ratio of 0.3 under lateral load. The procedure does not consider the nonlinear behavior of the soil medium or plastic yielding in the pile section, and the impact of the unreliable results for the case of high Poisson's ratio is not examined.     

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.     

Experimental research on horizontal bearing behavior of caisson-pile composite foundationEI北大核心CSCD

In this study, four groups of different types of bridge foundation model are tested to research the horizontal bearing behavior of caisson-pile composite foundation in lab based on the Qiongzhou Strait bridge project. The Q-s curve and horizontal ultimate bearing capacity of these four groups of foundations in sandy soil layer are obtained. Pile bending moment and shear force of pile shaft are analyzed in detail. At the same time, the load sharing ratio of caisson and piles is discussed. The results show that the horizontal ultimate bearing capacities of a single caisson foundation are increased by 1.2 times, 1.6 times and 2 times respectively with adding skirts, steel pipe pile, or steel pipe pile and the skirt. The maximum bending moment point is in the middle of the pile shaft, i.e. at about 0.5 m under the mud surface. The horizontal load is borne mainly by the upper caisson foundation and soil layers above the middle upper part of pile. The maximum shear force is found at the joint of pile top of steel pipe and caisson pile, where the reinforcement measures should be taken in practical engineering. The research achievements could provide a better reference for design or construction of caisson-pile composite foundation.     

带桩沉箱复合基础水平向承载性状模型试验研究

以琼州海峡跨海大桥工程为背景,通过4组不同型式深水桥梁基础模型试验,对新型带桩沉箱复合基础的水平向承载性能进行了初步研究。试验得到了4组模型在砂性土层中的Q-s曲线及水平向极限承载力,并对复合基础在各级水平荷载下的桩身弯矩和剪力进行了详细分析,同时对沉箱-桩荷载分担比展开了讨论。试验结果表明：当增加裙边、钢管桩、或同时增加钢管桩和裙边后能够使单体沉箱基础的水平向极限承载力分别提高1.2倍、1.6倍和2.0倍;桩身最大弯矩点均出现在桩身中部即泥面下约0.5 m处。水平荷载主要由上部沉箱基础及桩身中上部土体承担,钢管桩桩顶与沉箱连接部位出现最大剪力,在实际工程中应在此处采取加固措施。研究成果可为这一新型深水桥梁基础的推广应用提供诸多有益参考。     

主动与被动状态下墙体侧向位移近似计算

极限状态下墙体侧向位移对土压力计算和支挡结构设计影响显著。根据Rankine变形体和Coulomb刚塑体模型,将墙后土体变形分别当作单剪和直剪试验中试样的剪切过程,以达到极限剪切变形（剪应变或单位长度剪切位移）作为进入主被动状态标准,构建了土体变形与墙体位移的几何关系,提出了反映土体变形与强度特性,同时考虑静止时初始应力状态影响的墙体极限侧向位移近似计算模型。分析表明：土体极限剪切变形、滑移区范围、初始应力状态是影响墙体极限位移的核心要素,其中极限剪切变形占据主导作用,是导致不同颗粒组成及密实程度土体进入极限状态所需墙体位移差异显著的主要原因,而主被动区范围不同和因静止土压力系数 1引起的初始剪切变形,则是被动状态墙体位移远大于主动的关键因素;算例中主动与被动状态下墙体位移与墙高之比分别介于0.5‰～13.2‰和?0.4%～?5.2%,且主动状态下细粒土墙体位移大于粗粒土,计算结果与工程经验及相关文献模型试验基本一致。     

Three‐dimensional finite element study of arching behavior in slope/drilled shafts system

Two‐dimensional slope stability analysis for a slope with a row of drilled shafts needs a mechanism to take into account the three‐dimensional effect of the soil arching due to the spaced drilled shafts on slope. To gain a better understanding of the arching mechanisms in a slope with evenly spaced drilled shafts socketed into a stable stratum (or a rock layer), the three‐dimensional finite element modelling technique was used for a comprehensive parametric study, where the nonlinear and plastic nature of the soil and the elastic behavior of the drilled shafts as well as the interface frictions were modelled. Various factors were varied in the parametric study to include (1) the rigidity of the drilled shafts as influenced by its diameter, modulus of elasticity, and total length; (2) shafts spacing and location on the slope; (3) the material properties of rock and the socket length of shaft; and (4) the soil movement and strength parameters. Evidences of soil arching and reduction in the stresses and displacements through the load transfer mechanisms due to the presence of the drilled shafts were elucidated through the finite element method (FEM) simulation results. Design charts based on regression analysis of FEM simulation results were created to obtain a numerical value of the load transfer factor for the arching mechanism provided by the drilled shafts on the slope. Observations of the arching behavior learned from the FEM simulations provide an insight into the behavior of drilled shafts stabilized slope. Copyright © 2009 John Wiley & Sons, Ltd.     

Reliability analysis of piles in spatially varying soils considering multiple failure modes

In most limit state design codes, the serviceability limit checks for drilled shafts still use deterministic approaches. Moreover, different limit states are usually considered separately. This paper develops a probabilistic framework to assess the serviceability performance with the consideration of soil spatial variability in reliability analysis. Specifically, the performance of a drilled shaft is defined in terms of the vertical settlement, lateral deflection, and angular distortion at the top of the shaft, corresponding to three limit states in the reliability analysis. Failure is defined as the event that the displacements exceed the corresponding tolerable displacements. The spatial variability of soil properties is considered using random field modeling. To illustrate the proposed framework, this study assesses the reliability of each limit state and the system reliability of a numerical example of a drilled shaft. The results show the system reliability should be considered for the serviceability performance. The importance measures of the random variables indicate that the external loads, the performance criteria, the model errors of load transfer curves and soil strength parameter are the most important factors in reliability analysis. Moreover, it is shown that the correlation length and coefficient of variation of soil strength can exert significant impacts on the calculated failure probability.     

Limiting equilibrium method for slope/drilled shaft system

The use of drilled shafts to stabilize an unstable slope has been a widely accepted practice. There are two basic design and analysis issues involved: one is to determine the global factor of safety of the drilled shafts stabilized slope and the other one is to determine the design earth thrust on the drilled shafts for structural design of the shafts. In this paper, a limiting equilibrium method of slices based solution for calculating global factor of safety (FS) of a slope with the presence of a row of drilled shafts is developed. The arching mechanisms due to the presence of the drilled shafts on slope were taken into account by a load transfer factor. The method for calculating the net force applied to the drilled shaft from the soil mass was also developed. The interrelationships among the drilled shaft location on the slope, the load transfer factor, and the global FS of the slope/shaft system were derived utilizing the developed numerical closed‐form solution. An illustrative example is presented to elucidate the use of the solution in optimizing the location of the drilled shafts on slope to achieve the desired global factor of safety of the slope/shaft system. Copyright © 2009 John Wiley & Sons, Ltd.     

竖向荷载作用下斜桩荷载传递性状试验研究

通过模型试验研究了竖向荷载作用下砂土中斜桩的荷载传递性状,分析了桩身倾角及长径比对斜桩桩身轴力、弯矩、剪力、桩侧摩阻力及端阻比的影响。试验结果表明：在桩顶竖向荷载作用下,斜桩桩身轴力均小于相应直桩桩身轴力,桩身倾角越大,轴力沿深度衰减得越快,桩长径比越大,轴力沿深度衰减得也越快;斜桩桩身最大弯矩随桩身倾角及长径比的增加而增加,最大弯矩出现的深度与桩身倾角无关,只与长径比相关;不论桩身倾角及长径比的大小,斜桩桩身最大剪力均出现在桩顶截面处,桩身最大剪力随着桩身倾角的增加而增大;桩身倾角越大,斜桩最大摩阻力越大,长径比越大,斜桩最大摩阻力越小,斜桩最大摩阻力出现在桩顶下1/4～1/5桩长处;斜桩端阻比随着桩顶竖向荷载的增加而增大,随着桩身倾角及长径比的增加而减小。     

Analysis of failure of a bridge foundation under rock impact

A bridge pier supported on two drilled shafts collapsed due to the impact by a 130-ton rock in a landslide event. A series of static and dynamic numerical simulations is conducted using a nonlinear finite element analysis program to investigate the bearing behavior and responses of the bridge foundation under rock impact. The rock impact load is evaluated according to the site conditions. The deflection histories at the striking point and the internal forces in the drilled shafts during rock impacts in different directions are analyzed. The bridge pier exhibits significant system effects: the failure of the bridge pier is initiated by the failure of one pier column or one drilled shaft first, followed by the failure of the entire pier. The effects of impact loading direction, striking location, and characteristics of impact load on the behavior of the bridge pier are examined through a parametric study. The capacities of the pier along different loading directions are different due to differences in the group effects of the drilled shafts. The bridge pier is strongest when the impact load is along the 45° direction with respect to the shaft row, and weakest when the impact load is perpendicular to the shaft row.