基于非线性破坏准则的边坡稳定性极限分析

上限定理是求解岩土工程问题的有效工具。以上限定理为理论基础,分析边坡的稳定性问题,并考虑了岩土材料破坏准则的非线性特性。在非线性Mohr-Coulomb破坏准则下,采用条分法与极限分析上限法相结合的方法,对边坡稳定性进行分析。通过切线法引入非线性强度参数 、 ,推导了岩土材料在非线性破坏准则下的相关联流动法则,建立功能方程,推导了边坡直线滑裂面、折线滑裂面和光滑曲线滑裂面安全系数F的计算方程。采用数学规划法计算后与工程实际中常用的边坡稳定性分析方法进行对比,并获得安全系数F =1.0时的稳定性系数Ns。与已有的研究成果进行比较分析,结果表明了该方法的正确性及优越性     

非线性破坏准则下的边坡稳定塑性极限分析

利用塑性分析上限定理,考虑岩土介质本身的非线性破坏准则,对各种不同破裂面边坡稳定性分析进行研究。针对破坏边坡破裂面不同,采用外切直线法来分析其上限解,推导出非线性破坏准则下的边坡稳定性系数计算公式,并对较复杂的对数螺旋线破裂面边坡提出初始切线法,较好地求出塑性极限分析上限解。将在非线性破坏准则下按对数螺旋线破裂面推导出的塑性极限分析上限解运用于实际边坡工程,其结果与精确塑性分析结果非常接近,为非线性破坏准则下的边坡稳定塑性极限分析提供了一条新的思路与方法。     

地震效应下非线性抗剪强度参数对裂缝边坡稳定性影响的上限解析

基于非线性Mohr-Coulomb破坏准则,结合极限分析上限法和拟静力分析法,建立功能方程,推导了地震效应下裂缝边坡的安全系数计算方程。采用数学规划方法,计算了不同参数组合条件下的边坡安全系数值,详细分析了非线性条件下一系列参数对边坡稳定性的影响。研究表明,边坡安全系数随非线性参数和地震效应的增大而减小。对比分析可知,在非线性破坏准则下,裂缝深度较大时,裂缝对边坡稳定性影响显著,且边坡越陡影响越大;当裂缝深度超过某个值后,临界破坏面起始端可能不穿过裂缝最底端,而是从裂缝中间某部位穿过。在地震效应作用下,非线性抗剪强度参数对安全系数影响显著。研究成果进一步完善了裂缝边坡稳定性分析内容,所列图表为边坡的设计与施工提供有益参考。     

基于非线性破坏准则的临坡地基承载力上限分析

临坡地基承载能力的确定分析已成为地基设计理论中一个重要研究课题。针对现有地基承载力分析方法大多基于线性Mohr-Coulomb破坏准则。考虑岩土材料破坏的非线性特性,采用非线性破坏准则和多切线法,引入极限分析上限理论,根据临坡条形基础地基破坏模式的非对称性特点,构建出临坡条形基础地基单侧刚性多滑块破坏模型及相应运动允许速度场。在此基础上,利用序列二次规划非线性优化算法,建立临坡条形基础地基极限承载力的确定方法。最后,通过工程实例计算,并与已有研究方法计算结果进行对比分析。结果表明,非线性参数对临坡地基承载力有着重要影响,采用多切线法处理非线性材料强度准则问题理论上更严密,上限解更优,验证了该方法的可行性与合理性。     

非线性破坏准则下边坡稳定性极限分析斜条分法

考虑坡顶均布荷载和地震效应典型情况下,将边坡滑体进行任意斜条块划分,建立了具有倾斜界面的多块体破坏模型。基于极限分析上限法和非线性摩尔-库仑破坏准则,考虑岩体内正应力的不均匀性,引入多点切线法和强度折减法推导得出边坡临界破坏状态下的安全系数Fs通用计算公式。采用序列二次规划法对安全系数Fs的目标函数进行最优化计算,并与既有研究成果进行对比分析,其结果具有较好的一致性,相对误差不超过3.565%,表明了该方法的正确性。同时对比传统单点切线法计算结果,多点切线法较单点切线法获得的边坡安全系数值偏小,表明了多点切线斜条分法偏于保守,是安全的。参数分析表明坡顶均布荷载、地震效应和非线性参数均对边坡安全系数及潜在临界滑裂面有重要影响。多点切线法引入非线性摩尔-库仑破坏准则对边坡进行稳定性极限分析,为相关研究人员提供了一种新的思路与方法。     

变形协调条件下非线性破坏准则的加筋土坡临界高度上限解

针对现有加筋土坡稳定性分析研究大多基于线性Mohr-Coulomb破坏准则的现状,本文考虑了岩土材料破坏的非线性特性,采用非线性破坏准则和外切直线法,引入极限分析上限理论进行研究。根据加筋土坡的工程特性和变形机理,考虑破坏滑动层上筋材与土体变形协调特点及速度变化的连续性,分开计算素土的内力功和筋材能量耗散功率,在此基础上,建立直线破裂面和对数螺线破裂面机构的加筋土坡临界高度确定方法。对极限状态下加筋土坡临界高度的目标函数,采用序列二次规划非线性优化算法,得到上限解。最后,通过工程算例分析,并与已有离心模型试验结果和理论研究方法计算结果进行对比,结果表明本文计算方法考虑间断面滑动层筋材与土体变形协调及速度变化连续性是合理的,得到的上限解更优;非线性参数对加筋土坡稳定性有着重要影响,临界高度随非线性参数m的增大而减小。     

非线性破坏准则与岩土材料地基承载力研究

根据线性Mohr-Coulomb破坏准则,前人运用极限平衡法、滑移线理论或极限分析等方法求解地基承载力问题,但实际上岩土在剪切破坏过程中破坏准则具有非线性。因此,为了研究非线性破坏准则对地基承载力的影响,基于上限定理,通过“切线法”引进变量,根据能量耗散情况,将承载力问题转变为非线性规划问题,运用“序列二次规划算法”求出地基承载力的最优解。数值计算结果表明,当非线性破坏准则转变为线性破坏准则时,非线性参数对地基承载力有重要影响。     

隔堤填筑路堤的稳定性及变形破坏模式分析

隔堤填筑路堤或沿原河堤加宽是高等级公路经常采用的改扩建方式,路堤填筑后对原河堤的稳定性将产生怎样的影响,路堤自身的稳定性及变形破坏具有何特征,是目前沿河公路扩建工程中亟需解决的问题。结合依托工程的现场勘察和室内外试验结果,建立有限元模型,对路堤填筑前后及不同水位渗流条件下原河堤及路堤的稳定性进行了模拟计算和分析。计算结果表明：路堤填筑有利于提高原河堤的稳定性,稳定安全系数可提高约26%;隔堤填筑的路堤受多因素共同作用,容易产生较大的差异沉降,且工后固结时间长、沉降量大,工后沉降达总沉降的35%左右;隔堤填筑的路堤一般仅在远离原河堤一侧边坡发生剪切失稳破坏,渗流对路堤稳定性的影响较小,且不会改变路堤的破坏模式。数值模拟计算可以在工程实施前揭示隔堤填筑路堤的稳定性及变形破坏模式,从而为后一步的工程对策设计提供依据和参考。     

基于Barton-Bandis准则的锚固边坡稳定性分析

结合岩石节理面非线性Barton-Bandis破坏准则,探讨了将Barton-Bandis破坏准则参数转化为线性Mohr-Coulomb破坏准则抗剪强度参数的两种常用方法,通过实例分析了各方法的优劣。推导了加锚单岩石节理面控制的平面滑动岩体边坡抗滑稳定性安全系数计算式,开展了锚固参数分析。研究表明：相对于采用等效线性拟合法或切线等效法获取Mohr-Coulomb抗剪强度参数而言,直接应用Barton-Bandis破坏准则计算节理面控制的岩石边坡稳定性更为直观和简便;随着结构面基本摩擦角、结构面粗糙度系数和结构面壁面有效抗压强度的增大,边坡安全系数逐步提高,且结构面基本摩擦角和粗糙度系数对边坡安全系数的影响程度更为显著;锚索锚固力越大,边坡抗滑稳定性越好,而锚索设置角度越大,边坡抗滑稳定性越低,锚索角度设置不当将明显减小锚固效应的有效性。     

均质边坡稳定性极限曲线法

基于滑移线场理论,按边坡坡面变形量评价其稳定性,提出均质边坡极限曲线法。该法是求有重边坡极限荷载的逆过程,也是强度折减法的对偶过程。以特征线法差分方程组（SCM）和试验方程近似公式（CCM）求得的极限坡面曲线与坡面线相交为变形破坏准则,定义了安全度（DOS）和破坏度（DOF）2个评价指标。该方法不必假设和搜索临界滑动面。经典考题和典型算例的验算表明,随着节点的增加SCM法计算精度增加,边界步长不变时,3次样条插值求得的变形破坏准则判断值不变,说明SCM算法稳定。典型算例的计算数据和图例表明,边坡角变大时边坡稳定性降低,极限坡面曲线与坡面由无交点变为有交点,证明了变形破坏准则的正确性。由2个例题计算结果对比可知,安全系数较大时,SCM法、CCM法计算结果与其具有可比性,相对于原边界条件增加了外荷载;安全系数变小时,SCM法、CCM法偏于保守。34个样本计算正确率为安全系数法67.7%,应力状态法73.5%,CCM法79.4%,SCM法70.6%,表明SCM法和CCM法正确率较高,计算结果可靠,SCM法、CCM法因素敏感性分析结论与安全系数法完全一致。在露天矿边坡稳定性和最终边坡角的分析与计算中,SCM法、CCM法结论与原报告相同,当参数变小时CCM法更有利于实践,具有一定的工程应用价值。     

深部人工冻土黏弹塑损伤耦合本构模型研究及其验证

采用改进的Mohr-Coulomb屈服准则(Zienkiewicz-Pande准则), 建立了能描述人工冻土3个阶段蠕变特性的黏弹塑损伤耦合本构模型. 基于该本构模型建立了模型的柔度矩阵, 将本构模型嵌入到ADINA有限元程序中. 计算表明: 数值模拟得到的人工冻土蠕变特性曲线与实测值吻合良好, 最大误差为4.8%, 说明基于改进的Mohr-Coulomb准则建立的黏弹塑损伤耦合本构模型能够准确的描述人工冻土剪切特性和3个阶段的蠕变特性.获得的本构模型具有参数少、容易确定等优点. 深部人工冻土黏弹塑损伤耦合本构模型的建立, 对于人工冻土结构物长期稳定分析和预测具有重大的理论指导意义.     

A relation between safety factors with respect to strength and height of slopes

Conventional slope stability analysis is usually based on the linear Mohr–Coulomb failure criterion utilizing the notion of safety factors with respect to shear strength, and one of the available slice methods. Failure criteria of most soils are not linear, and it is possible to show that this non-linearity has a very significant effect on calculated safety factors. The present work is based on a non-linear failure criterion, which appears to fit the experimental information better than Mohr–Coulomb. All slice methods utilize various kinematical and static assumptions, which cannot be rationally justified. The present work is based on rigorous variational approach to slope stability analysis, which does not employ any kinematical and static assumptions. Safety factors with respect to shear strength are useful abstractions, but physical significance of results based on them is clear only at failure when they are equal to 1 (at any other value of the safety factor with respect to strength results of the analysis correspond to fictitious material with a modified shear strength function). In the present note, we use the variational analysis in order to establish a simple analytical relation between safety factors with respect to strength and height. These two safety factors provide alternative measures for the stability of a given slope; but the safety factor with respect to height appears to have clearer physical interpretation.     

基于统一强度准则改进式的压力隧洞弹塑性应力分析

基于具有抛物线型强度包络线的统一强度准则,即对双剪双参数统一强度准则进行相应的非线性化处理,考虑了中间主应力影响,分析在渗流作用下压力隧洞弹塑性力学行为。通过分析中间主应力对压力隧洞的塑性区半径影响可知,随着中间主应力的参数的增大,塑性区半径也相应减小。通过考虑和不考虑渗流场影响的实例对比分析表明,考虑渗流场时所得塑性区半径要比不考虑时大,而且随着孔隙水压力的增大,渗流场的影响越显著。隧洞径向应力和切向应力也与中间主应力参数b和渗流场密切相关。通过与直线型统一强度准则对比分析可知,采用两种不同准则时所得结果相差较大。隧洞设计时应根据岩石强度特性合理地选择数b,为强度包络线近似于二次抛物线的围岩隧洞设计提供理论依据     

Upper bound finite element analysis of slope stability using a nonlinear failure criterion

In this study, upper bound finite element (FE) limit analysis is applied to stability problems of slopes using a nonlinear criterion. After formulating the upper bound analysis as the dual form of a second-order cone programming (SOCP) problem, the stress field and corresponding shear strength parameters can be determined iteratively. Thus, the nonlinear failure criterion is represented by the shear strength parameters associated with stress so that the analysis of slope stability using a nonlinear failure criterion can be transformed into the traditional upper bound method with a linear Mohr–Coulomb failure criterion. Comparison with published solutions illustrates the accuracy and feasibility of the proposed method for a simple homogeneous slope stability problem. The proposed approach is also applied to a seismic stability problem for a rockfill dam to study the influence of different failure criterions on the upper bound solutions. The results show that the seismic stability coefficients obtained using two different nonlinear failure criteria are similar but that the convergence differs significantly.     

Stability analysis of rock slopes with a modified Hoek–Brown failure criterion

The original Hoek–Brown (HB) failure criterion was used to analyse the stability of rock slopes. For highly fractured rock, the original HB failure criterion has been modified, but its effect on the stability of rock slopes has not been studied. Within the framework of the kinematical approach of limit analysis, this paper computes the rigorous upper bounds of stability factors of homogeneous rock slopes with the modified HB failure criterion under the plane strain condition, by employing a ‘generalized tangential’ technique. In such technique, instead of using the modified HB failure criterion, a series of linear failure surfaces tangent to the actual non-linear failure surface are utilized to derive the upper bound solutions, incorporating a new parameter n ranging from 0.5 to 0.65. The numerical results are compared with other published solutions for the case of n=0.5. The effects of the n on the stability factors of rock slopes are discussed. Copyright © 2004 John Wiley & Sons, Ltd.     

定向渗流诱导的非均质冻结壁力学特性分析北大核心CSCD

为了合理分析定向渗流诱导的非均质冻结壁的力学特性,将冻结壁最迟交圈的位置视为“危险截面”,通过分段等效的方法结合温度特征点的分布规律,得出该截面的温度曲线表达式;根据冻土力学参数与冻结温度的线性关系,将冻结壁视为随温度函数变化的非均质材料;分别基于M-C准则、D-P准则、广义Tresca准则及双剪强度准则,推导得出定向渗流诱导的非均质冻结壁应力计算公式。基于该公式,结合实际冻结方案的设计参数对冻结壁的力学特性进行计算分析。计算结果表明:冻结壁的承载力随着水流速度的增大而减小,当水流速度为5m·d时,基于M-C、D-P、广义Tresca、双剪强度准则计算得出的弹性极限承载力以及塑性极限承载力分别为2.480、2.462、2.741、3.202以及4.349、4.318、4.561、5.779;当地下水流速增加至10m·d时,对应的弹性极限承载力以及塑性极限承载力降低至2.087、2.085、2.203、2.784以及3.700、3.707、3.908、4.939。冻结壁的径向应力随着相对半径r的增大而增大,而环向应力的分布具有明显的区域差异性;在弹性极限状态下,冻结壁的环向应力的最大值出现在靠近冻结壁中间的位置;在塑性极限状态下,冻结壁的环向应力的最大值出现在冻结壁的分区界线(r=1.685)处。     

重度增加法在某公路边坡稳定性分析中的应用

基于D-P准则,采用关联流动法则,用非线性有限元重度增加法对一非均质不规则公路边坡进行了分析。其原理是保持粘聚力c及内摩擦角φ不变,通过逐步增加土体重度的方法使土体达到临界状态。采用坡顶水平位移随重度增加系数变化的关系曲线上位移陡然增大作为边破的破坏标准。有限元重度增加法事先无须对滑动面的位置和形式做出任何假定,同时考虑了土体的材料非线性和几何非线性,因此利用二维有限元重度法能更好地模拟土坡的破坏,有助于了解土坡的破坏机理。其结果不仅对工程实践具有指导作用,而且对研究土体的破坏机理,探索分析边坡稳定的适用计算方法都有现实意义。用重度增加法得到的安全系数与传统方法的误差在9%左右,因此重度增加法可以用于边坡稳定分析。     

A new rock mass failure criterion for biaxial loading conditions

To simulate brittle rocks, a mixture of glastone, sand and water was used as a model material. Thin galvanized sheets of thickness 0.254 mm were used to create joints in blocks made out of the model material. To investigate the failure modes and strength, both the intact material blocks as well as jointed model material blocks of size 35.6 × 17.8 × 2.5 cm having different joint geometry configurations were subjected to uniaxial and biaxial compressive loadings. A new intact rock failure criterion is proposed at the 3-D level. This criterion is validated for biaxial loading through laboratory experimental results obtained on intact model material blocks. Results obtained from both the intact and jointed model material blocks are used to develop a strongly non-linear new rock mass failure criterion for biaxial loading. In this failure criterion, the fracture tensor component is used to incorporate the directional effect of fracture geometry system on jointed block strength. The failure criterion shows the important role, the intermediate principal stress plays on rock mass strength.     

A new closed-form solution for circular openings modeled by the Unified Strength Theory and radius-dependent Young’s modulus

A new closed-form solution is presented for the stress and displacement distribution surrounding circular openings with finite external radii that are subject to uniform internal and external pressures under plane strain conditions. The specific solution for a deep circular tunnel in an infinite rock mass is also provided. It is assumed that the rock mass is elastic–brittle–plastic and governed by the Unified Strength Theory (UST). In the plastic zone, the radius-dependent Young’s modulus (RDM) model and a non-associated linear flow rule were adopted to establish the radial displacement solution. The new closed-form solution obtained in this paper is a series of results rather than one specific solution; hence, it is suitable for a wide range of rock masses and engineering structures. The traditional solutions, which are based on the Mohr–Coulomb failure criterion and the Generalized Twin Shear Stress yield criterion, can be categorized as special cases of this proposed solution. This new solution agrees reasonably well with the results of a borehole collapse test, a secondary development numerical simulation and an additional closed-form solution using the generalized non-linear Hoek–Brown failure criterion. Parametric studies were conducted to investigate the effects of intermediate principal stress, RDM and dilatancy on the results. It is shown herein that the effects of intermediate principal stress and dilatancy are significant; the RDM model is recommended as the optimum approach for calculating radial displacement and support pressure.