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。     

基于统一强度理论的冻结壁弹塑性应力分析

将冻结壁等效为弹性模量、黏聚力呈抛物线分布的功能梯度材料(FGM)厚壁圆筒,基于统一强度理论,考虑中间主应力的影响,推导得到冻结壁的弹性极限荷载、弹塑性应力场及塑性极限荷载的解析解。将所得结果与均质冻结壁进行比较,并分析强度理论参数对各个解析解的影响。研究结果表明:考虑冻结壁的FGM特性,应力分布较均质冻结壁有一定的变化,环向应力由线性分布变为抛物线型分布;环向应力的最大值不再出现在冻结壁的内壁或外壁,而是出现在冻结壁厚度的中部;与均质冻结壁相比,FGM冻结壁的弹性极限荷载较大,但塑性极限荷载却较小;FGM冻结壁的弹性极限荷载、塑性极限荷载、径向应力及环向应力均随强度理论参数的增大而增大。所得结果可为冻结壁的设计提供一定的理论参考。     

岩土材料极限分析上界法的讨论

现行的极限分析上界法,尽管求解结果合理,但理论上却存在一些矛盾：如试验证明,关联流动法则不适用于岩土材料,而现行解法却采用了关联流动法则;传统分析中假设体积不变,但计算中却出现大于实际的体积剪胀变形;按关联流动法则,应力特征线与速度滑移线重合,但在分析中却采用速度方向与应力特征线方向成 角;实际土体破坏时,破坏面上同时存在着剪切力 和正应力 ,但在计算中却反映不出摩擦功。近年在中国日益兴起的广义塑性力学理论为岩土材料的极限分析方法提供了科学的理论基础。作者提出了基于广义塑性力学的极限分析上界法,消除了上述矛盾,并获得了正确的计算结果。通过同经典算法的比较,证明了两种方法的计算结果几乎是一致的,但现行方法计算简便,因而,可作为一种实用的计算方法。论文还对上述两种算法作了系统的分析与比较,指出了它们求解的相同点与不同点。     

地基承载力确定的一种方法

根据三轴和直剪试验的特点并以Mohr强度理论为基础建立了Mohr包线的曲线形式。基于弹性理论导出了条形地基在均布荷载作用下塑性区方程,根据方程可以确定临塑荷载及塑性区的范围。与基于直线型Mohr-Coulomb准则建立起来的塑性区方程相比,该方程能反映土体抗剪强度增长随正应力增加逐渐趋缓的特点。算例分析表明：按两种方法计算得出的临塑荷载相差不大,塑性区连成一片时的荷载也基本一致;两种方法得出的塑性区的形状极为相似;随荷载增加,塑性区向下发展的速度比按传统方法得出的结果稍慢。     

软弱夹层的极限荷载分析

岩土体中的软弱夹层是一种广泛存在的地质体,由于其力学性质较差,容易给工程建设带来安全隐患,对其稳定性的研究逐步引起重视。根据塑性极限平衡分析方法,针对软弱夹层的承载稳定问题,将软弱夹层上下土层当作准刚性层,基于修正Prandtl挤压理论解答对软弱夹层的极限荷载进行了计算。分析过程中认为,准刚性层间的软弱夹层在极限状态下发生塑性挤出破坏,考虑到Prandtl挤压理论的剪应力解答在x方向上的不足,结合不同的边界应力条件,对软弱夹层中的应力分量和夹层表面的极限荷载进行了重新求解。推导的极限荷载实用计算式能综合考虑软弱夹层面的摩擦条件、土层自重及夹层周围的受力状态等因素,并与其他理论计算式的结果进行了对比分析。计算结果分析表明,不考虑土重时,该方法计算的夹层极限荷载随厚度变化规律与Prandtl方法基本一致;考虑土重影响时,该方法计算结果与规范法相似,但在夹层较厚时能更明确地反映宽度对极限荷载的影响。此外,夹层上下边界的摩擦条件对极限荷载的影响程度随夹层宽厚比的不同而变化,对于一定厚度的夹层存在几乎不受摩擦条件影响的临界宽度。其研究结果可为软弱夹层的承载稳定分析提供参考。     

基于混合常应力−光滑应变单元的极限分析方法

极限分析是岩土工程稳定性评价的重要方法之一。传统的有限元极限分析方法,采用低阶三角形单元时需要引入速度间断面并采用特殊网格布局,或者采用高阶三角形单元等措施来克服体积锁定问题和提高数值精度。在光滑有限元法（smoothed finite element method,简称SFEM）的基础上,提出了一种基于新型混合常应力−光滑应变单元的极限分析方法（mixed constant stress-smoothed strain element limit analysis,简称MCSE-LA方法）。在服从关联流动法则和Mohr-Coulomb屈服准则的基础上,MCSE-LA方法最终将数值极限分析转化为以应力和极限荷载乘子为基本未知量的二阶锥规划（second order cone programming,简称SOCP）问题。MCSE-LA方法具有形式简单、优化变量相对较少和无需显式的写出塑性内能耗散函数的优点,并且根据凸锥优化的对偶理论,可以从对偶问题中获得速度场和塑性乘子等信息。此外,还采用基于最大塑性剪应变率的网格自适应加密算法,该算法在塑性区细化网格,显著提高了新数值极限分析方法的计算效率和精度。最后通过边坡稳定分析的结果对比,验证了MCSE-LA方法的计算精度和效率均高于传统的有限元极限分析方法。     

三维塑性极限分析下限法原理及应用

介绍了三维塑性极限分析下限法的基本原理。将计算区域离散为有限个三维空间单元,利用极限分析中的下限定理,借助有限元思想建立数学规划模型,并引入非线性规划的数值方法寻求问题的下限解。以均匀土质边坡的极限荷载作为算例,比较了所得数值解与经典塑性力学理论解,论证了该方法的正确性。     

基于变形加固理论的隧洞与巷道开挖稳定分析

地下工程的开挖稳定和加固分析是岩土工程中的难题之一。变形加固理论是研究荷载超出结构极限承载力的理论,探求的目标是结构在承受荷载超出其极限承载力时维持稳定所需的最优加固力。给定荷载下结构出现不平衡力的区域即为首先破坏的区域;给定荷载下结构总是趋于加固力最小化、自承力最大化的状态。而整体稳定性可采用余能范数进行定量评价。基于三维非线性有限元方法,详细推导了不平衡力和塑性余能范数的表达式。通过典型深部隧洞与巷道开挖及加固的算例,对比分析了加固前后围岩内不平衡力的分布以及塑性余能范数的大小。结果表明,对围岩加固可在一定程度上提高围岩的强度和承载能力。     

斜坡地基刚性桩水平承载力上限分析

为探讨斜坡地基刚性桩水平极限承载力的计算方法，介绍柔性桩的等效刚性桩有效嵌入深度并引入极限水平地基反力分布形式。根据荷载指向坡外及坡内两种情况，提出适用于斜坡地基桩前土体的两种极限破坏模式。然后，基于极限分析上限定理，推导出两种荷载方向下的刚性桩极限承载力，并引入多组现场试验，验证了理论方法的合理性。探讨了边坡坡角、内摩擦角、黏聚力及荷载方向对极限承载力的影响，得出了一些规律性结论，并基于以上分析结果，提出斜坡地基刚性桩水平极限承载力随坡角变化的拟合公式。这些分析为斜坡地基上基桩设计提供了一定的参考，具有理论及工程应用价值。     

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。     

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.     

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.     

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。     

A multiphase approach to the stability analysis of reinforced earth structures accounting for a soil–strip failure condition

A multiphase model, developed in the context of elastoplasticity, is applied to the simulation and design of reinforced earth retaining structures. The main feature of this model is to combine the advantage of a homogenization approach, as regards its computational efficiency, with the ability to account for a specific failure condition at the interface between the soil and the reinforcing strips, which may have a decisive influence on the behavior of the structure. A particular emphasis is put on the stability analysis of this kind of reinforced soil structures, formulated within the framework of the yield design theory. Making use of a generalized rigid block failure mechanism, the stability of a reinforced earth retaining wall is investigated by means of the kinematic approach, leading to upper bound estimates for the stability factor of the structure, which are then favorably compared with the results of an elastoplastic analysis. Special attention is paid to assessing in a quantitative way how a specific soil–strip failure condition affects the stability of the reinforced earth structure as a whole.     

A Similitude Theory for Bucket Foundations Under Monotonic Horizontal Load in Dense Sand

This paper aims at finding force-displacement relationships to be employed in the design of bucket foundations for offshore wind turbine. This is accomplished by combining small-scale tests and element tests within a theoretical framework. A similitude theory, regarding the lateral displacement of bucket foundations under horizontal load, is put forward. A constitutive law of the soil and a load-displacement relationship for the bucket foundation are theoretically obtained. Triaxial tests of sand, and small-scale tests of bucket foundation, are respectively employed to corroborate the theory. Attention is given to the different behaviour shown during the compressive and dilative phases of the soil. Some analogy between triaxial tests and tests of bucket foundation are pointed out. A theoretically derived power law is found capable to represent the dimensionless horizontal load-displacement curves of experimental results. In accordance with the theory, the exponent of the power law slightly varies between tests with considerably different features. The non-dimensional moment-rotation relationship is represented by a power law as well. The approach is considered valid for fatigue design. The study may be an interesting source for further researches on long-term cyclic horizontal loading.     

Shakedown analysis of a slope with cyclic groundwater level

Groundwater levels vary with precipitation and other environmental impacts, rendering wetting and drying cycles in parts of a slope. It may be quite disadvantageous, as groundwater has been implicated as a crucial controlling factor in slope stability. The wetting–drying cycles can be considered as cyclic loads for the slope. In such cases, a shakedown analysis is appropriate for the long‐term safety evaluation. This paper presents an upper bound shakedown analysis method based on strong version of Koiter's theorem to evaluate slope stability. An element integration method is employed to provide limit and shakedown safety factors for the slope. For plane slip surfaces or logarithmic spiral slip surfaces, the validity of the method is verified by two documented examples. Copyright © 2009 John Wiley & Sons, Ltd.     

Zarka shakedown modelling of expansive soils subjected to wetting and drying cycles

Unsaturated expansive soils subjected to wetting and drying cycles result in huge differential settlements of structures built on these materials. The existed models for these materials present large number of parameters that lead to time-consuming procedure to characterise their mechanical behaviour during wetting–drying cycles. In this context, Zarka shakedown theory previously applied to the mechanical loading of granular materials has been used for expansive soils subjected to suction cycles. The parameters of this shakedown-based model were calibrated for two different expansive soils. The comparisons between the experimental results and the calculations for the different tests, demonstrate the capacity of Zarka shakedown theory to simulate the mechanical behaviour of unsaturated expansive soils.     

Derivation of material variability from settlement measurements

In pavement evaluation using non-destructive testing (NDT), a large amount of deflection bowls are analysed in terms of the elastic moduli of the layers. The results are used to evaluate the material variability, which could serve in an overlay design procedure based on the concept of reliability. The model currently used for interpreting deflection bowls is based on the random variable theory which neglects the spatial distribution of the elastic modulus of the material. Since the subgrade and pavement materials have a spatial distribution, the analysis of NDT could lead to an underestimate of the material variability. The random field theory, which is more adequate than the random variable theory, is presented and used to correct the NDT analysis. The pavement is modelled as a multilayer random elastic medium with, for each layer, a constant Poisson's ratio and a random shear modulus characterized by three statistical moments: average value, standard deviation and autocorrelation function. The stochastic integral formulation presented in the previous publications is generalized here for a multilayer system. The multilayer system is analysed with the random field theory and the covariance matrix of the deflection bowl is obtained and used to generate deflection bowls corresponding to the properties of the random field. These bowls are then interpreted with the current procedure and elastic modulus variabilities are computed. It is found that the current procedure for interpreting deflection bowls underestimates the variability of the subgrade, by a factor of 0.4–1.0. It is interesting to note that the average moduli of the Boussinesq layer and of the two layers are not affected by the type of theory used. The variability of the upper layer in the two-layer system is also unaffected for a small variation range.