On the buckling analyses of embedded layers

The published buckling analyses of axially compressed layers embedded in a softer medium, or of multilayers, are based on the notion that the buckling load is P_cr; the so-called critical load which is obtained from a linear eigenvalue problem. The purpose of the present paper is to show that this assumption is generally not justified. For these cases a linearized buckling analysis is not sufficient and buckling of a layer, or of multilayers, has to be determined from a non-linear formulation.     

Buckling failures of reserved thin pillars under the combined action of in-plane and lateral hydrostatic compressive forces

The reasons that pillars with small width-to-height ratios fail remain unclear. This study established a mechanical model for the buckling failure of a thin pillar subjected to compressive forces to investigate the stability of reserved thin pillars (RTPs) on both sides of mining units during barrier pillar recovery. The critical buckling stress of the thin pillar was obtained using the energy variational method, and its relationship to the aspect ratio (length-to-width ratio) was investigated. The buckling instability of RTPs can be determined by comparing the RTP stress obtained from numerical simulations with the buckling stress derived from the mechanical model.     

层状边坡岩体的屈曲和溃屈性态研究

在对层状边坡岩体结构进行稳定性分析的过程中,屈曲和溃屈是两个主要问题。针对边坡岩体结构的赋存特点和分岔特性,以及研究方法仅采用线性理论和已有研究成果只停留在结构屈曲层面上的状况,文章应用初始后屈曲理论和突变理论探讨了岩体结构的屈曲性态和溃屈性态,给出了边坡岩体上部滑动段滑动的条件,得出了边坡岩体的分岔方程和溃屈方程,指出了分岔方程的适用条件和溃屈方程的适用范围,确定了边坡岩体后屈曲状态下溃屈破坏的下限,建立了岩体结构溃屈破坏的判据,并以雅砻江下游的霸王山边坡为例进行研究。结果表明:边坡岩体的赋存状况决定了其势函数的分岔集,从边坡的分岔集可衍生出结构在分岔状态下的分岔载荷和分岔方程;分岔方程表达了边坡岩体结构的屈曲状态,也表达了结构出现屈曲的准则;边坡岩体的赋存状况还决定了岩体结构溃屈破坏时岩体材料屈服的取值范围,而岩体结构溃屈破坏的上限或下限则取决于岩体材料的屈服极限。     

Conical fold terminations in the bannisdale slates of the english lake district

The structure of an area of Silurian rocks in the non-metamorphic Caledonides near Kendal, Cumbria (U.K.) is briefly described. The main folds are periclinal and die away in the southeast of the area. The uniform thickness of sandstone beds around folds shows that they deformed dominantly by buckling and only locally is flattening important. A model is developed to explain the conical attitude of bedding within the periclinal terminations. The model is erected on the basis of buckling alone and is developed to examine the effects of flattening. Inhomogeneity in buckling and flattening over the area is demonstrated using the model and discussed. The pattern of folding is compared to that predicted by earlier, published, experimental work.     

钢井壁失稳原因浅析及预防

钻井法施工的一些开采年限较短、井深和井径较小的竖井中,有时采用钢井壁作为永久支护,但是相对于钢筋混凝土井壁,钢井壁在使用过程中极易发生屈曲变形,甚至导致井简破坏,使用中应引起高度的重视。结合工程实例,对钢井壁失稳时的临界应力、影响因素进行了分析,并提出了相应的预防措施。     

Mechanical behavior of porous solid considering mesoscopic elastic buckling

In this work, the elastic buckling of porous solids was investigated using a lattice spring model (LSM). The capability of the LSM to solve elastic buckling problems was comprehensively verified by comparing well-established numerical and analytical solutions. Following this, the buckling of a porous solid was studied, in which two porous structures were considered, ie, the random porous model and the Voronoi porous model. The results reveal that both the porosity and the shape of the pores influence the elastic buckling bearing capacity of the porous solid. Finally, the mechanical responses of a porous solid with an extra high porosity (0.85) were numerically investigated. Our numerical results demonstrated that the nonlinear elastic response of the porous solid might come from its mesoscale elastic buckling. This work shows the ability and promise of using the LSM as a fundamental numerical tool for the deep investigation of the buckling mechanical behavior of porous solids.     

Buckling behaviour of single pile and pile bent in the Scotch Road Bridge

The buckling behaviour of the 360 × 152 steel H-piles supporting the integral abutments of the Scotch Road Bridge, located in Trenton, New Jersey, has been studied for the cases of single pile and pile bent. Three-dimensional finite-element models for single pile and pile bent have been developed to study the behaviour of these fully embedded piles under axial and lateral loading. An iterative analysis based on extracting the eigenvalues and eigenvectors (mode shapes) that correspond to the pile(s) critical buckling loads has been adopted. The pile(s) and the surrounding sand were modelled using solid continuum elements in the finite-element model. Material non-linearity is accounted for in both the piles and the soil in the base state of the model. A parametric study has been utilized to determine the effect of the geometric and material properties of the pile and the surrounding sand on the predicted critical buckling loads of the piles. The effects of four parameters have been studied: soil stiffness, pile length, type of connection, and combining vertical and lateral loads. The results from the parametric study showed that the variation of the percentage change in the sand stiffness, pile length, and combining vertical and lateral loads with the critical buckling loads of the 360 × 152 H-piles is nonlinear. Furthermore, the parameters studied are more influential in affecting the critical buckling load of a single pile than a pile bent, with the exception of the ‘type of connection’ parameter.     

复杂地基反力模式下高承台嵌岩灌注桩的屈曲稳定分析

为探讨桩侧地基土反力对高承台嵌岩灌注桩桩身屈曲稳定的影响,假定地基反力系数呈更为复杂的幂分布,基于弹性地基梁理论建立桩土体系总势能方程,采用最小势能原理,导出了桩身屈曲临界荷载与稳定计算长度的解析解,并据此获得了地基反力系数分布模式、桩身自重及桩侧摩阻力等对桩身屈曲稳定的影响规律。工程应用分析结果表明,考虑地基反力系数为一般幂分布时,桩身屈曲分析结果更趋合理。     

顺层斜坡溃屈机制与早期识别研究

本文采用物理机制模型、数值模拟和理论计算相结合,分析研究了顺层斜坡滑移-弯曲变形机制,提出了顺层斜坡产生滑移-弯曲变形的地质和力学条件、临溃状态判别与早期识别标志。研究认为:岩层倾角20是滑移-弯曲变形产生的必要地质条件。斜坡前缘岩层弯曲隆起是临溃状态的早期判识标志。岩层倾角、单层厚度、临界坡长和溃屈深度之间相互制约和影响。岩层倾角越大,越易产生溃屈,且溃屈层数和深度越大;斜坡临界坡长与岩层倾角呈负幂函数变化规律;层间黏结作用产生的共弯效应影响弯曲岩层的整体抗弯刚度,从而制约溃屈深度并对斜坡最终溃屈状态起着决定性作用。该成果对于早期防范和识别地质灾害具有重要价值。     

Flaw propagation and buckling in clay-bearing sandstones

Many historically and culturally significant buildings have sandstones that contain swelling clay inclusions in the binding phase. Differential strains that evolve during wetting and drying cycles can generate stresses that are on the order of the strength of the stone, leading to degradation. Most damage observed in the field is surface delamination and buckling of the stone over a flaw, indicating that the damage is occurring during wetting. Classical buckling theory predicts buckling to occur at a particular aspect ratio, or flaw size. The results of this study confirm buckling theory experimentally. Through finite-element simulation and experiment, the study then explores a potential flaw propagation mechanism whereby nonuniform wetting patterns generate stress intensities capable of flaw propagation. As a result, small natural flaws can grow to the critical size necessary for buckling.     

陕西山阳特大型滑坡视向滑移-溃屈破坏力学分析

陕西山阳滑坡为典型的陡倾层状斜向岩质斜坡,其破坏模式不同于常见的顺倾层状岩质斜坡溃屈破坏模式,也不同于斜倾层状山体的视向滑移-剪切破坏模式,更不同于陡倾顺层岩质斜坡的倾倒、倾倒-滑移破坏模式,属于视向滑移-溃屈破坏模式。在实地调查的基础上,从斜坡结构特征、结构面组合特征以及剪出口特征分析了滑坡的破坏模式,进而分析了山阳滑坡的视向滑移-溃屈破坏机制;以梁板理论、层状板裂结构岩体弯曲-溃屈破坏的力学模型为基础,结合斜倾层状岩质滑坡的视向滑动机制研究,建立了基于斜坡自重、地下水静水压力、侧向摩阻力以及斜坡岩体厚度变化作用下的陡倾层状斜向岩质斜坡视向滑移-溃屈破坏力学模型,进行力学分析,推导了溃屈段长度条件方程,并以山阳滑坡为例验证了长度条件方程的正确性。     

The determination of ‘buckling rotation’ and its application to theoretical and experimental models of buckle folds

The quantity ‘buckling rotation’ is defined, for buckle folds, as the total rotation of a fold limb minus the rotation that would occur due to pure shear if no competence contrast existed. Using existing models (theoretical and experimental) of buckle-fold development, the quantity ‘buckling rotation’ has been calculated for successive small increments of strain and plotted against strain or limb dip. The resulting curves are skewed and bell-shaped, indicating an initial sharp increase in buckling rotation early in fold development followed by a gentle, asymptotic decrease. The curve height and position are dependent on the competence contrast and, in multilayer systems, on the ratio of competent to incompetent layer thickness. The initial sharp increase in buckling rotation corresponds to the period of most active layer-parallel shortening during fold development.     

Fold and cleavage development within cambrian metasediments of the vale of ffestiniog,North Wales

New road cuttings have exposed a large part of the Merioneth Series. The rocks are low-grade thinly layered metasediments which have undergone extensive buckling resulting in tectonic ripples, mullions, and crenulations. It is suggested that the periclinal form of these structures may be the result of buckling layered sequences with longitudinal and transverse zones of constraint (heterogeneities). The process is analogous to ‘quilting’ of thin metal sheets and the heterogeneities are perhaps due to layer thickness variation. There are two foliations; which may form a progressive sequence of cleavage development during the evolution of the fold style.     

顺层岩质边坡溃屈变形机制及失稳判定方法

溃屈型破坏是一种常见的顺层岩质边坡破坏模式,溃屈变形发展机制及失稳破坏的定量研究对滑坡工程勘查和防治指导十分重要。本文根据边坡的地质环境和力学作用机制,建立了三维受压板简化模型,其能够考虑岩层自身重力、地震力、静水压力的共同作用和岩体材料塑性变形的影响。基于弹塑性受压板稳定理论,利用能量法推导得到了边坡溃屈变形破坏的临界方程。对于溃屈型边坡的结构失稳和滑动失稳分别提出了相应的稳定性判定方法,并针对不同状态的边坡提出了相应的防治措施建议。以四川省甘孜藏族自治州巴塘县下归哇边坡为例,对所提判定方法的正确性进行了验证。计算结果表明,边坡的临界溃屈长度（a1）为483.8 m,说明下归哇边坡能够发生溃屈变形;现场勘查得知边坡实际溃屈长度（a′）为530.0 m,a′＞a1,可知边坡是稳定的。这与实际情况相吻合,由此证明本文所提出的判定方法可行。     

纵弯叠加褶皱地区应力场研究-以川东北地区为例

川东北地区主体构造为北西向大巴山弧形构造带和北东-北东东向川东弧形褶皱带,发育早期北东向纵弯褶皱和晚期北西向纵弯褶皱,两者构成明显的纵-纵复合叠加,形成典型的限制褶皱、横跨褶皱、斜跨褶皱和移褶等。早、晚两期褶皱和共轭“X”节理均反映出早期应力场为北西-南东向水平挤压,晚期应力场为北东-南西向挤压。     

Layer shortening and fold-shape development in the buckling of single layers

The progressive development of folds by buckling in single isolated viscous layers compressed parallel to the layering and embedded in a less viscous host is examined in several ways; by use of experiments, an analogue model to simulate simultaneous buckling and flattening and by an application of finite-element analysis.The appearance of folds with a characteristic wavelength in an initially flat layer occurs in the experiments for viscosity ratios (μ_layer/μ_host = μ₁/μ₂) of between 11 and 100; progressive fold development after the initial folds have appeared is similar in the experiments and in the finite-element models. Except for the finite-element model for μ₁/μ₂ = 1,000 layer-parallel shortening occurs in the early stages of folding and a stage is reached where little further changes in arc length occur. The amount of layer-parallel shortening increases with decreasing viscosity contrast, and becomes relatively unimportant after the folds have attained limb dips of about 15°–25°.Thickness variations with dip are only significant here for the finite-element model with μ₁/μ₂ = 10, and in experiments for μ₁/μ₂ = 5 where the layer is initially in the form of a moderate-amplitude sine wave. The variations range from a parallel to a near-similar fold geometry, and in general depend on the viscosity contrast, the degree of shortening and the initial wavelength/thickness ratio. They are very similar to the variations predicted by the analogue model of combined buckling and flattening. The difference between the thickness/dip variations in a fold produced by buckling at low viscosity contrast and one produced by flattening a parallel fold is marked at high limb dips and very slight at low limb dips.Many natural folds in isolated rock layers or veins show thickness/dip relationships expected for a flattened parallel fold, and some show relationships expected for buckling at low viscosity contrasts. Studies of the wavelength/thickness ratios in natural folds have suggested that competence contrast is often low. Many folds in isolated rock layers or veins whose geometry may vary between parallel and almost similar, and may be indistinguishable from those of flattened parallel folds, have probably developed by a process of buckling at low viscosity contrasts.     

基桩屈曲的几何非线性有限元分析

将桩身视为空间受力的梁单元,利用更新的拉格朗日坐标体系考虑梁单元的几何非线性;并采用弧长控制法求解有限元非线性方程组,进行基桩屈曲的几何非线性有限元分析。利用Matlab语言编制了相应的计算程序,将某现场木桩压屈试验实测屈曲临界荷载与理论分析比较,吻合良好。大量计算分析表明,桩周土地基系数、基桩埋入比、桩身材料和基桩长细比是影响基桩屈曲荷载大小的重要因素,在设计和施工中都应重视和考虑。     

柴达木盆地成因分析

对柴达木盆地新生代沉降机制存在不同的观点。一个合理的模型必须解释柴达木盆地的两个基本问题： 1）为什么柴达木盆地新生代沉积中心主要位于盆地中部; 2）是什么动力学过程导致盆地发生最大幅度超过15 km的基底沉降。通过对柴达木盆地主要地质特征的分析和对已有盆地模型的评述,本文发展了地壳褶皱模型,认为青藏高原北部上部地壳发生纵弯褶皱是柴达木盆地形成的主要原因。该模型不仅解释了盆地沉积中心的位置,而且揭示了柴达木盆地与周缘其它构造单元的关系。上部地壳发生强烈褶皱与下地壳侧向流动和岩石圈地幔向南俯冲的过程有关。     

Orogen-transverse tectonic window in the Eastern Himalayan fold belt: A superposed buckling model

The Eastern Lesser Himalayan fold-thrust belt is punctuated by a row of orogen-transverse domal tectonic windows. To evaluate their origin, a variety of thrust-stack models have been proposed, assuming that the crustal shortening occurred dominantly by brittle deformations. However, the Rangit Window (RW) in the Darjeeling-Sikkim Himalaya (DSH) shows unequivocal structural imprints of ductile deformations of multiple episodes. Based on new structural maps, coupled with outcrop-scale field observations, we recognize at least four major episodes of folding in the litho-tectonic units of DSH. The last episode has produced regionally orogen-transverse upright folds (F₄), the interference of which with the third-generation (F₃) orogen-parallel folds has shaped the large-scale structural patterns in DSH. We propose a new genetic model for the RW, invoking the mechanics of superposed buckling in the mechanically stratified litho-tectonic systems. We substantiate this superposed buckling model with results obtained from analogue experiments. The model explains contrasting F₃–F₄ interferences in the Lesser Himalayan Sequence (LHS). The lower-order (terrain-scale) folds have undergone superposed buckling in Mode 1, producing large-scale domes and basins, whereas the RW occurs as a relatively higher-order dome nested in the first-order Tista Dome. The Gondwana and the Proterozoic rocks within the RW underwent superposed buckling in Modes 3 and 4, leading to Type 2 fold interferences, as evident from their structural patterns.     

Bifurcations of thick-walled hollow cylinders of geomaterials under axisymmetric compression

This paper derives analytically the condition for the onset of diffuse mode bifurcations in thick-walled hollow cylinders with internal radius a, external radius b and length L under axial compression and confining pressure. The thick-walled cylindrical specimens are made of geomaterial characterized by Rudnicki's constitutive model, and the method of solution for the governing equations is the velocity potential approach employed by Chau. Numerical results show that thick-walled cylinders are stronger than thin-walled cylinders against diffuse mode bifurcations, including both buckling, axisymmetric and non-axisymmetric deformations. In contrast to the conclusion for solid cylinders (Chau), no buckling solution is found for γ = mπa / L smaller than about 0·7 under compression for a fixed and finite value of a / b (i.e. no buckling for long and slender hollow cylinders with small a / L and fixed b / a). When 0·7 < γ < 0·9, buckling is the expected first bifurcation; whereas, when γ > 0·9, bulging or barrelling is anticipated. The exact value of γ that excludes buckling and separates the buckling and barrelling phenomena depends on the current values of the constitutive parameters of the solid. Hollow cylinders with higher degree of anisotropy, disobeying normality flow rule, and subjected to confining pressure are more conducive to bifurcations than cylinders made of materials with isotropy, obeying normality, and subjected to no confining pressure. In addition, diffuse mode bifurcations are found possible in the pre-peak regime of the stress–strain curve. © 1998 John Wiley & Sons, Ltd.