On predicting displacement-dependent earth pressure for laterally loaded piles

This paper presents the derivation of a depth-dependent soil displacement model for laterally loaded piles for use in the calculation of displacement-dependent earth pressure. A set of fourth-order differential equations are proposed to compute the pile deflection profile along the pile length. The radial displacement of the soil due to pile movement can be evaluated based on the geometric compatibility requirements. The soil displacement pattern is then used in the earth pressure model to provide the pattern of earth pressure distributed around the pile circumference. The experimental data of the pile response, in terms of the p-y curves reported in the literature, are employed for a comparison with calculations from the proposed approach and other analytical models. The advantages of the developed calculation framework have been demonstrated, namely, that it can accurately reproduce the experimental measurements of soil reactions acting on a pile at different depths and that the influence of the pile installation can be taken into account. An illustrative example of cantilever sheet piles is finally provided to show the ability of the proposed method to analyse complicated problems.     

Analysis of laterally loaded short and long piles in multilayered heterogeneous elastic soil

A continuum-based method is developed for the analysis of laterally loaded piles in multilayered, heterogeneous elastic soil. The analysis considers the soil as a layered elastic continuum in which the modulus varies linearly or non-linearly with depth within each layer. Rational soil displacement fields are assumed and differential equations describing the pile and soil displacements are obtained using the principle of minimum potential energy. The differential equations describing the pile and soil displacements are solved using the Ritz method and the finite difference method, respectively, following an iterative numerical scheme. The analysis is used to study different pile geometries embedded in layered soil deposits with heterogeneity in each layer. The pile displacement, rotation, and maximum bending moment obtained from the analysis were found to be in good agreement with those obtained from an equivalent three-dimensional finite element analysis and from other studies available in the literature. The analysis can be used to obtain the pile head displacement, rotation, and maximum bending moment that can then be used in design.     

挤密效应对砂土中水平受荷桩承载特性的影响

砂土中的挤土桩在实际工程中广泛应用,部分挤土桩长期遭受风荷载、波浪荷载等水平循环荷载的作用,而挤土桩对桩周土体的挤密效应会对桩身水平承载力产生较大影响。通过开、闭口桩的室内模型试验,研究分析了砂土初始相对密度、桩径、长径比等因素对挤土桩单调和循环承载特性的影响。结果表明,在不同密实度砂土中,开口桩水平承载力总体上弱于闭口桩。桩径、长径比和土体相对密度都会对开口桩、闭口桩之间承载力的差值造成较大的影响。循环荷载作用下,松砂中不同桩径和埋深的开口桩、闭口桩的水平承载力都随着加载周期的增加而增大,而在中密砂中,随着循环次数的增加,循环加载后承载力增加的幅度较松砂中的减少,甚至出现下降。     

Frequency- and intensity-dependent impedance functions of laterally loaded single piles in cohesionless soil

This paper investigates the frequency-dependent pile-head impedance characteristics of a model soil-pile foundation system under large amplitude loads, inducing soil yielding. Testing was conducted on a scaled single pile embedded in sand under a 1g condition. A laminar shear box mounted on a unidirectional shaking table was used to house the soil-pile foundation system. Quasi-static loads and dynamic loads were applied to obtain the force–displacement relationships and pile-head impedance functions, respectively, through the pile head connected to a loading actuator providing fixity to the pile head in all directions, except horizontal. In the quasi-static case, loads with three different velocities were applied to study the rate-dependent characteristics of the lateral bearing capacity of the pile. The Stereo-PIV system was employed to measure the surface soil displacement around the pile. The lateral bearing capacity changed with the loading velocity, but the soil near the pile showed a consistent failure pattern despite a significant change in velocity. Lateral pile-head dynamic impedance functions were obtained for low-to-high amplitude harmonic loading for a wide range of frequencies. The dynamic stiffness was seen to converge to that of the secant static stiffness with an increase in the amplitude of the dynamic loading for all the excitation frequencies.     

水平荷载作用下单桩的虚拟桩解法及参数

根据MukiSternberg的虚拟桩方法,将水平荷载作用下单桩的问题分解为弹性半空间扩展土和一根虚拟桩的叠加,其中虚拟桩的弹性模量等于桩的弹性模量与土的弹性模量之差。基于水平位移协调条件推导出求解桩土间相互作用所需要的第二类Fredholm积分方程,通过广义胡可定律推导出该积分方程间断点的显式解,从而提高了Fredholm积分方程的数值计算精度并简化了计算程序的编写,根据Mindlin解推导出位移影响函数,简化了位移函数的推导过程。参数分析表明,桩土弹性模量比对单位水平力作用下桩身最大弯矩的位置有明显的影响,随着桩刚度的增加,桩身最大弯矩的位置随之加深。     

被动侧向受荷桩模型试验及颗粒流数值模拟研究

本文采用室内模型试验与颗粒流数值模拟相结合的方法对砂土中被动侧向受荷短桩桩土相互作用性状进行了较系统和深入的研究。在室内模型试验中,研究了短桩在松砂、中密砂、密砂中的挡墙荷载–位移关系,桩顶位移对挡墙位移的响应规律,及桩前、桩后土压力的分布和发展规律。通过开发颗粒流程序模拟室内模型试验在加载条件下桩土相互作用过程中的应力和位移的变化规律,与模型试验的结果进行了对比分析。本文的研究对揭示被动桩与周围土体的作用规律及更深入的了解桩土相互作用机理有参考价值。     

主动侧向受荷桩模型试验与颗粒流数值模拟研究

分别采用室内模型试验与颗粒流数值模拟的方法,对砂土中受水平荷载的桩顶自由短桩桩周土体在加载过程中的应力和位移的发展变化规律以及桩土相互作用性状进行了较系统和深入的研究。在室内模型试验中,研究了短桩在松砂、中密砂、密砂中的位移荷载规律,桩前、桩后土压力的分布和发展规律;并重点通过数字图像无标点量测技术密切关注桩周土体的位移产生和发展变化过程。通过开发颗粒流程序模拟室内模型试验在加载过程中的桩土相互作用过程中应力和位移的发展变化规律,与模型试验的结果进行了对比。给出了砂土中受水平荷载的桩顶自由短桩较完整的变形和破坏模式及极限土压力分布形式。     

Frequency- and intensity-dependent impedance functions of laterally loaded pile groups in cohesionless soil

The frequency-dependent horizontal impedance functions of a model floating 2 × 2 pile group, embedded in cohesionless sand under a 1g condition, were investigated experimentally. The tests were conducted using large amplitude loads inducing soil yielding. The soil-pile system was housed in a laminar shear box fastened to the top of a unidirectional shaking table. Quasi-static and dynamic loads were applied in a lateral direction under the fixed pile-head condition to evaluate the force–displacement relationship and the horizontal impedance functions, respectively. The results of the quasi-static loading exhibited rate-dependent behavior for the lateral load-bearing capacity of the piles. Notably, the analysis of the soil surface near the piles, using a stereo-PIV calibration, demonstrated a consistent failure pattern despite the significant variation in velocity. Furthermore, an important observation was the convergence of the horizontal dynamic impedance functions towards the secant static stiffness as the amplitude of dynamic loading increased.     

基于应变路径法的黏土中水平受荷桩p–y曲线

水平桩的p–y曲线大多是基于试验数据(A P I规范,双曲线),旨在从理论出发推导桩侧土体的p–y曲线。首先,推导了与上限解等价的分步弹性加载理论,并结合刚性圆盘在环状弹性介质中受水平力作用下的弹性力学解以研究桩身水平位移和桩周平均剪应变间的关系;再应用该平均剪应变和土体的双曲线应力应变关系建立联系以得到桩周土体在加载过程中的平均屈服应力即已发挥的土体强度;以此确立二维情况下桩身位移和桩周土反力的关系即p–y骨干曲线。再进一步根据三维的桩侧初始地基模量和桩侧极限承载力,将其推广至三维。该p–y曲线的优点在于可以考虑土体应力应变关系、桩身刚度和长细比对p–y曲线的影响。最后,将本文p–y曲线和传统p–y曲线分别与工程实例以及有限元结果进行对比,并指出传统p–y曲线的不足及恰当的使用范围。     

Centrifuge modelling of the behaviour of pile groups under vertical eccentric load

Annular shaped pile groups are a very common foundation layout for onshore wind turbines and other slender structures. In this study, their performance under vertical loads of moderate to high eccentricity, including moment rotation response and bearing capacity, was investigated by centrifuge testing on small scale physical models embedded in kaolin clay. To identify experimentally the capacity of the examined pile groups under different load paths, the model foundations were loaded monotonically until a clear collapse mechanism was achieved. The testing procedure and the proposed interpretation methodology can be easily adapted to load paths or pile layouts other than those considered in the current study. The experimental data can be adopted as a useful benchmark for mathematical models aimed at predicting the response of pile groups to complex load paths. The results of this testing program can also be used to assess the degree of conservatism of current methods adopted by industry for the design of piled foundations subjected to eccentric loads.     

竖向菏载作用下群桩沉降的一种实用计算方法

群桩沉降是控制桩基设计的一个重要因素,本文采用剪切变形传递法教育处桩身压缩变形,采用等代墩基法计算桩端以下土体整体压缩变形,并以二者相结合计算群桩沉降。     

Responses of single and group piles within MSE walls under static and cyclic lateral loads

To investigate the behavior of piles and the performance of the mechanically stabilized earth (MSE) walls under static and cyclic lateral loading, six reduced-scale model tests of single and group piles within the MSE walls were conducted inside a test box. In the single pile tests, a hollow aluminum tube as a pile was placed at a distance of 2D or 4D (D is pile diameter) behind the wall facing, while in the group pile tests, the piles were only placed at the distance of 2D with a spacing of 3.3D between the piles. The piles were subjected to static lateral loading only and cyclic lateral loading followed by static loading until failure. The test results showed that the lateral load capacity of each pile in the group pile test was approximately 60% that of the single pile, while the wall facing displacements and the geogrid strains in the group pile test were larger than those in the single pile test. The lateral pile capacity, the wall facing displacement, the strain in the geogrid, and the lateral earth pressure behind the wall facing in the static and cyclic loading tests were evaluated at the pile head displacement equal to 20%D.     

On the use of 1g physical models for ground movements and soil-structure interaction problems

The paper focusses on the use of physical modelling in ground movements (induced by underground cavity collapse or mining/tunnelling) and associated soil-structure interaction issues. The paper presents first an overview of using 1g physical models to solve geotechnical problems and soil-structure interactions related to vertical ground movements. Then the 1g physical modelling application is illustrated to study the development of damage in masonry structure due to subsidence and cavity collapse. A large-scale 1g physical model with a 6 m³ container and 15 electric jacks is presented with the use of a three-dimensional (3D) image correlation technique. The influence of structure position on the subsidence trough is analysed in terms of crack density and damage level. The obtained results can improve the methodology and practice for evaluation of damage in masonry structures. Nevertheless, ideal physical model is difficult to achieve. Thus, future improvement of physical models (analogue materials and instrumentation) could provide new opportunities for using 1g physical models in geotechnical and soil-structure applications and research projects.     

In-situ horizontal cyclic loading tests on composite foundation composed of soilbags and piles

The authors have been developing a new composite foundation composed of piles and soilbags. The foundation is characterized by the laying of soilbags between the pile heads and the footing on which a superstructure stands. The expected effect of the foundation is to cut off the fixed connection between the piles and the footing in order to reduce the bending moment of the piles and the response acceleration of the structure. In this study, in-situ horizontal cyclic loading tests were conducted on the proposed composite foundation with two piles to investigate the seismic response characteristics of the foundation at real scale. It was found from the tests that the horizontal force reached its peak due to the uplift of the footing during horizontal loading, and that larger hysteresis damping was obtained than that of spread foundations due to the hysteresis effect in the shear deformation of the soilbags. As for the sectional force of the piles and the vertical stress inside the soilbags, it was found that the axial force and bending moment of the piles concentrated on the pile on the front side in the loading direction, and that the vertical stresses inside the soilbags concentrated just above the pile head on the front side in the loading direction. Although residual horizontal displacement and settlement occurred due to the cyclic load, little damage to the soilbags was observed.     

An integrated approach for fire and explosion consequence modelling

Fire and explosion are accidents which potentially can occur in oil and gas processing facilities. While fire and explosion could occur as a consequence of each other, most published work has assessed fire and explosion separately, ignoring interactions between the two phenomena.The current study proposes a novel approach to model the entire sequences involved in a potential accident using liquid and gas release incidents as two test cases. The integrated scenario is modelled using Computational Fluid Dynamics (CFD) codes FLACS and FDS. An integrated approach is adopted to analyse and represent the effects (injuries/death) of the accident. The proposed approach can be used in designing safety measures to minimize the adverse impacts of such accidents. It can also serve as an important tool to develop safety training to improve emergency preparedness plans.     

横向荷载下群桩相互作用的积分方程解法及参数分析

针对横向受荷桩的相互作用问题,将桩土体系分解为弹性半空间地基土和虚拟桩,基于水平位移协调条件建立两桩相互作用的第二类 Fredholm 积分方程,采用 MATLAB 软件编制程序进行求解。基于 Chen 等提出的横向受荷桩相互作用系数解法,得到了桩顶转角固定条件下水平受荷桩的积分方程解答,与已有算例的对比验证了本文算法的正确性。参数分析表明,固定转角约束条件下两桩的水平位移相互作用系数随着桩间距和荷载方向夹角的增加而减小,随着桩土模量比的增加而增加。基于相互作用系数解法,该方法可应用于转角固定的水平受荷群桩分析。     

An equivalent stiffness approach for modelling the behaviour of compression members according to Eurocode 3

The development of design procedures based on inelastic advanced analysis is a key consideration for future steel design codes. In advanced analysis the effect of imperfections has to be modelled in such a way that the incremental analysis fully captures this effect in the process of moment redistribution. In modelling the influence of imperfections on the behaviour of individual members of real structures, different approaches have been used to globally represent this effect in the overall analysis of structural systems. They are referred to as the initial bow imperfection approach or as the equivalent transverse load approach. When using the abovementioned approaches in analysis of multiple member structural systems, the designer is required to arrange the directions of bow imperfections or equivalent transverse loads in such a way that the imperfection arrangement leads to the least constrained solution, i.e. the lowest ultimate load predicted from all possible sets of member initial imperfection arrangements. Since there is still ongoing research on the development of simple application rules ensuring that the designer obtains a unique solution when choosing a certain set of member initial imperfections, there is at the same time interest in the development of alternative approaches to modelling the influence of member imperfections on the behaviour of structural systems. This paper provides the necessary background information as well as describes the formulation and modelling techniques used in the development of a new approach to modelling the influence of imperfections on the stability behaviour of structural components and systems. This new approach, called hereafter an equivalent stiffness approach, has an advantage over the previously described approaches since an imperfect member is treated as a hypothetically straight element, flexural and axial stiffnesses of which at each load level are predicted in a continuous fashion dependent upon the actual force and deformation states. This type of modelling does not require any explicit modelling of equivalent geometric imperfections or equivalent forces and their directions in advanced analysis; therefore also it does not require any buckling mode assessment. Moreover, the effects of strain hardening and section class may conveniently be included in modelling. Finally, European buckling curves are used to estimate the values of parameters of the developed model that can be immediately used in advanced analysis conducted according to Eurocode 3.     

Numerical modelling of high strength steel beams at elevated temperature

High strength steels are increasingly common in structural engineering applications owing to their favourable strength to weight ratio, excellent sustainability credentials and attractive physical and mechanical properties. However, these grades are under-used in structures owing to a lack of reliable information relating to their structural performance, particularly at elevated temperature. This paper presents a review of high strength steels in structural applications including the key design considerations. Particular focus is given to the lateral torsional buckling response of laterally unrestrained beams. A finite element model is developed to investigate this behaviour at ambient and elevated temperature. A series of beams between 500 and 4500 mm in length are studied in order to develop buckling curves which are comparable with current design provisions. At ambient temperature, it is shown that all of the buckling curves currently included in Eurocode 3 Part 1-1 give unsatisfactory and potentially unsafe predictions. In elevated temperature conditions, the buckling curves presented in Eurocode 3 Part 1–2 depict the behaviour reasonably well but, at relatively high slenderness values, the standard does not always provide a safe prediction. Revised bucking curves are proposed for high strength steel beams for laterally unrestrained beams made from high strength steel.     

An efficient approach for traffic load modelling of long span bridges

Traffic micro-simulation is the newly developed approach for loading calculation of long span bridges. The approach is quite precise, but computationally expensive to consider the full extent of traffic loading scenarios during a bridge lifetime. To address this shortfall, an efficient multi-scale traffic modelling approach is proposed. The proposed approach uses micro- and macro-simulation with different load model varieties (LMVs), or fidelities (levels of detail) of traffic loading in different bridge regions, to achieve optimal computation efficiency while maintaining the precision of loading calculation. Metrics of influence line (IL) characteristics, such as degree of nonlinearity, are proposed to evaluate the appropriateness of the choice of LMV, and standards of the metrics are also investigated to quantify the implementation of LMVs on bridge IL regions in the multi-scale modelling. Finally, two typical ILs are used along with random traffic modelling to study the feasibility of the proposed approach. It is shown that the multi-scale modelling approach proposed here achieves high computational efficiency and accuracy, which is significant for the massive traffic load simulation for lifetime bridge load effect analysis.