Shakedown in layered pavements under moving surface loads

Elastic–plastic deformations in pavements consisting of layers of different frictional materials are investigated. The upper bound, kinematic shakedown theorem is used to obtain estimates of the critical shakedown loads. Fully general three-dimensional deformations are considered. The influence of the loading distribution, interactions between loads, and the effect of varying the thickness, stiffness and strength of the layers are explored. Consequences of this investigation for particular existing designs of flexible pavements are investigated. In particular, it is found that the strength of the subgrade has no effect on the magnitude of the critical shakedown load.     

移动荷载下三维半空间动力安定性下限分析

针对交通移动荷载,基于第一动力安定性理论预测了弹塑性半无限空间动力安定性下限值。通过建立无限元边界的三维动力有限元模型,研究了移动荷载作用下弹塑性半无限空间的动应力分布,构造了稳态动应力下的残余应力场,基于残余应力场的构造提出了动力安定性下限值的预测方法,分析了交通动应力下的安定性下限值以及车辆移动速度对安定性的影响,同时分析了均布荷载和Hertz荷载分布对动力安定性下限值的影响。当荷载移动速度低于Rayleigh波速时,安定性极限值随着速度的增加而增加,而当速度超过Rayleigh波速时,随着速度的增加而减小。研究还发现,当荷载和总重相等时采用圆形均布荷载和Hertz荷载的安定性极限值较为相似。     

Seismic behavior of slopes by lower bound dynamic shakedown theory

Lower bound dynamic shakedown theory is a limit state method. It is employed herein to investigate the safety, which is associated with permanent displacement, of slopes under repeated dynamic loads, mainly earthquakes. An efficient numerical method, previously applied to the static shakedown of pavements, is extended to the dynamic shakedown of slopes in this study. It is shown that dynamic shakedown, unlike other limit state methods, is able to consider the dynamic properties of both the load and subsoil. The effect of the soil strength parameters and dynamic features of the soil and loads are examined thoroughly and some illustrative examples are employed. The short-term and long-term behavior of slopes under seismic loads are studied as well, comparing results of the present study with the well-known displacement method of Newmark.     

RESPONSE OF A LAYERED ELASTIC MEDIUM TO A MOVING STRIP LOAD

Analytical determination of stresses and deformations caused by moving loads is vital to foundation and pavement designs. In current applications, moving loads are often approximated to be vertical impact loads. In this work, however, a live load is modelled as a uniform distribution of normal or shear stresses in actual motion. Then, a layer stiffness approach utilizing linear elasticity is followed in determining the surface and interior deformations due to the live load. By superimposing the two solutions for normal and shear surface stresses, the new approach can be made to provide an approximate solution to the problem of evaluating stresses and deformations caused by a wide wheel load rolling on a layered elastic system. Although elastic solutions in general are inadequate to explain the more significant consequences of pore pressure generation and dissipation in the soil subgrade, these results can certainly be useful to examine the shearing effects of wide rolling wheels on the asphalt layer and immediate settlement of the subgrade. It is found that the dynamic effects of a smoothly rolling wide load are significant at relatively low wheel velocities compared to those of shear waves in the subgrade and base.     

Three‐dimensional shakedown solutions for anisotropic cohesive‐frictional materials under moving surface loads

Previous work on three‐dimensional shakedown analysis of cohesive‐frictional materials under moving surface loads has been entirely for isotropic materials. As a result, the effects of anisotropy, both elastic and plastic, of soil and pavement materials are ignored. This paper will, for the first time, develop three‐dimensional shakedown solutions to allow for the variation of elastic and plastic material properties with direction. Melan's lower‐bound shakedown theorem is used to derive shakedown solutions. In particular, a generalised, anisotropic Mohr–Coulomb yield criterion and cross‐anisotropic elastic stress fields are utilised to develop anisotropic shakedown solutions. It is found that shakedown solutions for anisotropic materials are dominated by Young's modulus ratio for the cases of subsurface failure and by shear modulus ratio for the cases of surface failure. Plastic anisotropy is mainly controlled by material cohesion ratio, the rise of which increases the shakedown limit until a maximum value is reached. The anisotropic shakedown limit varies with frictional coefficient, and the peak value may not occur for the case of normal loading only. Copyright © 2013 John Wiley & Sons, Ltd.     

A two‐mechanism elastoplastic model for shakedown of unbound granular materials and DEM simulations

An elastoplastic model has been developed for the finite elements modelling of repeated load triaxial tests. This model is based on the shakedown theory established by Zarka for metallic structures. To the previous works, which were based on the Drucker–Prager yield surface and the plastic potential of Von Mises, a compression cap has been added to each one. The model straightforwardly determines the purely elastic state or the elastic shakedown state or the plastic shakedown state and calculates the deviatoric and the volumetric plastic strains. The calibration of the elastoplastic model has been carried out with DEM simulations and an unbound granular material for roads under repeated load triaxial tests using finite element method. The calculations underline the capabilities of the model to take into account, with a unique formalism, the accumulation of the deviatoric and volumetric plastic strains along the loading cycles. Copyright © 2011 John Wiley & Sons, Ltd.     

Modelling of rutting of two flexible pavements with the shakedown theory and the finite element method

This paper presents a finite element program, for the modelling of rutting of flexible pavements. In its present version, the program incorporates a permanent deformation model for unbound granular materials based on the concept of the shakedown theory developed by Zarka for metallic structures under cyclic loadings and has been used to estimate the permanent deformations of unbound granular materials (UGM) subjected to traffic loading. The calculation is performed in two steps: the first step consists in modelling the resilient behaviour of the pavement in 3D, using non-linear elastic models, to determine the stress field in the pavement. Then stress paths are derived and used to calculate the permanent deformations and the displacements, using a Drucker–Prager yield surface. An application to the prediction of the permanent deformations of experimental pavements with an unbound granular base, tested on the LCPC pavement testing facility is presented.     

道路安定理论的进展及其应用

30多年来,国际上的道路设计原理及方法逐渐从传统经验法向运用理论框架方面转变。但这些理论框架主要基于土和粒状材料的弹性假设,从而限制了材料塑性性能的发挥。安定分析基于弹塑性理论,可以确定结构在循环或变值荷载作用下的最大承载力,因此,能够被运用于道路承受交通荷载的问题。阐述了安定理论的概念以及两种经典安定定理,回顾了道路安定分析方法的创始及发展过程,包括与试验结果的比较,讨论了残余应力在道路中的分布、两种求解道路安定荷载极限的方法,以及与塑性极限分析的比较,并把一种下限安定分析方法应用于多层柔性路面的设计,最后展望了道路安定理论未来的发展方向。     

敦煌莫高窟北区岩体变异变形及修复对策

敦煌莫高窟北区岩体长期以来在特殊的地形地貌、气象水文、岩土性质、地质构造条件下,受人工开挖、重力、风蚀、雨蚀和洪水冲刷等共同作用,岩体发生风化、卸荷等变异以及崩塌、坍塌和危岩、开裂与裂隙(构造裂隙、卸荷裂隙)等多种变形,严重影响岩体的稳定和洞窟的安全。针对上述变异、变形破坏情况,采用PS材料加粉煤灰浆液灌浆封闭裂隙和岩面喷浆加固相结合的修复方法,有效地防止了岩体变异的进一步扩展和表面风化的加剧,减少了岩体变形和表面风化程度,使石窟得以保护和修复。该方法对黄土及干旱地区石窟保护具有良好的借鉴作用。     

基于下限定理的路面结构安定分析

传统的以弹性理论和经验方法为基础的路面结构设计方法,对路面结构的安全性评价存在着不合理性。安定理论可为复杂荷载作用下的路面结构承载力分析提供理论依据,基于该定理发展了一种应用于路面结构的安定分析方法,并应用于2层路面结构的安定分析,计算给出了荷载作用方式、路面结构形式、材料性质变化对路面安定极限影响的定量分析结果,通过对比表明了安定分析应用于路面结构的可行性。安定极限可为路面结构的分析与设计提供一定的参考价值。     

饱和红层泥岩填料累积变形特性及安定界限研究

最优含水率下红层泥岩作为高速铁路路基填料的适用性已经在西南地区得到了初步验证,但饱和状态下红层泥岩填料的累积变形特性仍不明确。为此,开展了不同围压及动应力下饱和红层泥岩填料的动三轴试验,讨论了围压和动应力对填料累积变形特性的影响。结果表明：不同动应力幅值下,饱和红层泥岩填料的等效模量随振次增加,先迅速减小后趋于稳定。稳定后填料的等效模量具有应力水平相关性,随围压增大而增大,随动应力比增大而呈指数减小。不同动应力幅值下,填料变形可分为塑性稳定型、塑性蠕变型和增量破坏型3种类型。填料应变随振次增加而不再处于稳定阶段的应力状态定为塑性稳定界限应力状态。动应力进一步增加后,填料应变速率发生突增,对应的应力状态为塑性蠕变界限应力状态;塑性稳定与塑性蠕变界限应力状态对应的动应力比均低于静强度,且随围压增加呈指数衰减的规律。基床表层如用红层泥岩作填料,应考虑降雨的影响,并采取排水和改良措施以提高路基稳定性。     

Lateral load distributions on grouped piles from dynamic pile‐to‐pile interaction factors

The load distributions of the grouped piles under lateral loads acting from one side of the pile cap could be approximately modeled using the elasticity equations with the assumptions that the underground structure is rigid enough to sustain the loads, and only small deformations of the soils are yielded. Variations of the soil–pile interactions along the depths are therefore negligible for simplicity. This paper presents the analytical modeling using the dynamic pile‐to‐pile interaction factors for 2 × 2 and 2 × 3 grouped piles. The results were found comparative with the experimental and numerical results of other studies. Similar to others' findings, it was shown that the leading pile could carry more static loads than the trailing pile does. For the piles in the perpendicular direction with the static load, the loads would distribute symmetrically with the centerline whereas the middle pile always sustains the smallest load. For steady‐state loads with operating frequencies up to 30 Hz, the pile load distributions would vary significantly with the frequencies. It is interesting to know that designing the pile foundation needs to be cautioned for steady‐state vibrations as they are a problem of machine foundation. However, for transient loads or any harmonic loads acting upon relatively higher frequencies, the pile loads could be regarded as uniformly distributed. It is hoped that the numerical results of this paper will be helpful in the design practice of pile foundation. Copyright © 2008 John Wiley & Sons, Ltd.     

Kinematic (or hour-glass) mode control for a uniform strain quadrilateral by an assumed strain technique

Finite element and finite difference solid mechanics computer programs have often been observed to overestimate the stiffness of an elastic beam or the collapse load in elasto-plastic problems. There are a number of ways of overcoming these difficulties but many lead to unwanted degrees of freedom in the mesh which continuously degrade the solution if the errors are allowed to accumulate. These unwanted distortions are referred to as spurious or hour-glass modes, and special measures have to be taken if accurate predictions are to be achieved without their appearance. In this paper a new scheme based on assumed strains at the element level is described in the context of a two-dimensional, explicit, finite difference program. The scheme is compared with an earlier solution to this problem and is shown to have some advantages, particularly when irregular meshes and/or large deformations are encountered. Thorough testing indicates that the new formulation passes the patch test and leads to accurate predictions of bending stiffnesses and plastic collapse loads. An underlying consideration of the development was that the new scheme should be applicable to three-dimensional calculations. Although this has not been tested numerically, the extension to three dimensions is discussed.     

铁路路基粗粒土填料临界动应力试验研究

粗粒土填料被广泛应用于铁路基床填料中,直接承受轨道结构传递的列车动循环荷载的长期作用,研究其在列车动荷载作用下的动力行为特征及塑性变形特性可为路基状态评估、沉降控制提供思路。采用GDS动三轴试验系统对铁路基床表层的粗粒土填料动力响应开展研究,通过引入塑性应变率和安定理论,将不同频率、围压、循环动应力比等条件下路基填料的轴向塑性应变的发展规律划分为塑性安定、塑性蠕变和增量塑性破坏3种类型,并确定了塑性安定和塑性蠕变状态的临界动应力水平。研究表明：粗粒土填料的临界循环应力比随着围压的增大而增大,随着荷载频率的增加而减小。通过对试验结果的拟合分析,提出了以围压为变量的临界动应力经验公式,为合理评估列车荷载作用下路基任意深度的动力稳定提供了理论依据。     

Influence of construction technique on the performance of a braced excavation in marine clay

Finite element analyses are used to quantify the effects of construction technique on the performance of braced excavations. It is first shown that the computations can be continued to ‘collapse’ and that the results agree with limit plasticity solutions. A case study involving stratified deposits of marine clay and sand is used to carry out a Class C1 ‘prediction’ of field performance. The influence of construction technique on deformations and strut loads is shown. The results of the computations are in agreement with field observations, assuming a relatively ‘flexible’ construction technique. However, even if much ‘stiffer’ techniques had been used, large field deformations would have been unavoidable under certain circumstances.     

Fundamental results concerning the settlement of a rigid foundation on an elastic medium due to an adjacent surface load

This paper examines the interaction between a rigid circular foundation resting in smooth contact with an isotropic elastic halfspace and a concentrated surface load which acts at a finite distance from the foundation. Owing to the action of the external load the rigid foundation experiences an extra settlement and a tilt. The expressions for the extra settlement and the tilt are evaluated in exact closed form. It is also shown that these deformations due to the external load satisfy Betti's reciprocal theorem. The auxiliary solution required for the application of the reciprocal theorem is derived from the analysis of the problem of a rigid circular foundation resting in smooth contact with an elastic medium and subjected to an eccentric load. The, results developed for the interaction between the rigid circular foundation and the external concentrated load are utilized to generate, among others, solutions for the settlement and tilt induced at a rigid foundation due to its interaction with uniformly or non-uniformly distributed loads with circular and square plan shapes.     

交变载荷作用下边坡的安定性分析

边坡稳定的极限分析方法只适用于比例加载的情况。当其上所受到的全部或部分载荷发生往复变化时,应该采用安定分析来评价边坡的安全性。通常边坡除了受到恒定的重力作用以外,地下水的作用也是一个不能忽视的因素。而由于降雨等原因,地下水位往往会在一定范围内往复变化,使得在稳定的地下水位以上的部分岩土体经常处于干湿循环的状态。根据率形式的Koiter机动安定定理,提出了考虑地下水位往复变化情况的边坡安定上限分析方法。利用抗剪强度参数折减定义的安全系数,定量地计算载荷变化对边坡稳定性的影响。最后通过一个直立边坡的简单算例证明了提出的分析方法的有效性。     

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。     

非均匀载荷和内压作用下石油套管的抗挤能力分析

油井套管往往处于管内外复杂的受力环境下,揭示和分析这些因素对套管抗挤能力的影响就显得非常重要,并可为套管强度设计提供理论依据。根据套管在受到外部非均匀载荷和内压作用下的受力特点和材料力学理论,建立了单位长度的理想圆管的环向应力的计算模型,得到了套管内外壁的环向应力分布规律。计算结果表明：套管发生破坏失效位置在圆周方向与最大水平地应力成90°角的内壁上。依据Von Mises屈服准则由失效点得到了非均匀外挤载荷和内压作用下套管屈曲时抗外挤能力的新公式。实例计算表明：在影响套管的抗挤能力的因素中,外载荷的非均匀系数对套管抗外挤能力影响最大,外载荷的非均匀系数越大,套管抗外挤能力下降得越快;在外载荷非均匀性较小的条件下,提高套管外载荷承载能力可通过增大内压和减小套管径厚比来实现。     

Cyclic shakedown of piles subjected to two‐dimensional lateral loading

Pile foundations are frequently subjected to cyclic lateral loads. Wave and wind loads on offshore structures will be applied in different directions and times during the design life of a structure. Therefore, the magnitude and direction of these loads in conjunction with the dead loads should be considered. This paper investigates a loading scenario where a monotonic lateral load is applied to a pile, followed by two‐way cycling in a direction perpendicular to the initial loading. This configuration is indicative of the complexity of loading that may be considered and is referred to in the paper as ‘T‐shaped’ loading. The energy‐based numerical model employed considers two‐dimensional lateral loading in an elasto‐plastic soil, with coupled behaviour between the two perpendicular directions by local yield surfaces along the length of the pile. The behaviour of the soil–pile system subjected to different loading combinations has been divided into four categories of shakedown previously proposed for cyclic loading of structures and soils. A design chart has been created to illustrate the type of pile behaviour for a given two‐dimensional loading scenario. Copyright © 2009 John Wiley & Sons, Ltd.