非线性破坏准则的竖直边坡稳定性分析

采用极限分析方法进行边坡稳定性分析通常采用线性MohrColumn破坏准则。但大量实验证明,岩土体的破坏包络线是非线性曲线。基于切线法和积分的思想,推导了基于非线性破坏准则的极限分析上限法求解竖直边坡稳定性和临界高度的计算公式。应用该方法计算了竖直边坡的稳定系数,并与文献中的计算结果进行了比较,结果相差很小。另外,对非线性破坏准则强度参数对竖直开挖边坡稳定性的影响分析结果表明,这些参数对边坡的稳定性分析结果起关键作用。     

Slope stability analysis considering joined influences of nonlinearity and dilation

The soil masses of slopes were assumed to follow a nonlinear failure criterion and a nonassociated flow rule. The stability factors of slopes were calculated using vertical slice method based on limit analysis. The potential sliding mass was divided into a series of vertical slices as well as the traditional slice technique. Equating the external work rate to the internal energy dissipation, the optimum solutions to stability factors were determined by the nonlinear programming algorithm. From the numerical results, it is found that the present solutions agree well with previous results when the nonlinear criterion reduces to the linear criterion, and the nonassociated flow rule reduces to the associated flow rule. The stability factors decrease by 39.7% with nonlinear parameter varying from 1.0 to 3.0. Dilation and nonlinearity have significant effects on the slope stability factors. Foundation item: Project (200550) supported by the Foundation for the Author of National Excellent Doctoral Dissertation of China; Project (200631878557) supported by West Traffic of Science and Technology of China     

Limit analysis for the seismic stability of three-dimensional rock slopes using the generalized Hoek-Brown criterion

The parameters that influence slope stability and their criteria of failure are fairly understood but over-conservative design approaches are often preferred, which can result in excessive overburden removal that may jeopardize profitability in the context of open pit mining. Numerical methods such as finite element and discrete element modelling are instrumental to identify specific zones of stability, but they remain approximate and do not pinpoint the critical factors that influence stability without extensive parametric studies. A large number of degrees of freedom and input parameters may make the outcome of numerical modelling insufficient compared to analytical solutions. Existing analytical approaches have not tackled the stability of slopes using non-linear plasticity criteria and three-dimensional failure mechanisms. This paper bridges this gap by using the yield design theory and the Hoek-Brown criterion. Moreover, the proposed model includes the effect of seismic forces, which are not always taken into account in slope stability analyses. The results are presented in the form of rigorous mathematical expressions and stability charts involving the loading conditions and the rock mass properties emanating from the plasticity criterion.     

Three-dimensional analysis of slopes reinforced with piles

Based on the upper bound of limit analysis, the plane-strain analysis of the slopes reinforced with a row of piles to the 3D case was extended. A 3D rotational failure mechanism was adopted to yield the upper bound of the factor of safety. Parametric studies were carried out to explore the end effects of the slope failures and the effects of the pile location and diameter on the safety of the reinforced slopes. The results demonstrate that the end effects nearly have no effects on the most suitable location of the installed piles but have significant influence on the safety of the slopes. For a slope constrained to a narrow width, the slope becomes more stable owing to the contribution of the end effects. When the slope is reinforced with a row of piles in small space between piles, the effects of group piles are significant for evaluating the safety of slopes. The presented method is more appropriate for assessing the stability of slopes reinforced with piles and can be also utilized in the design of plies stabilizing the unstable slopes.     

Methods applied in Australian industry to evaluate coal mine slope stability

Strata failure is a principal hazard in open cut coal mining as it has the potential to cause multiple fatalities. Prior to the excavation of any slope, a geotechnical assessment should review the likely slope performance, including the risk of slope failure. Controls to manage this risk to an acceptable level should accompany the geotechnical analysis. A survey of 43 practising geotechnical engineers indicated that kinematic and 2D limit equilibrium analyses were the methods most commonly applied to analyse excavated slope stability. While these methods are well established and widely applied in the broad rock engineering disciplines(e.g. civil, hard rock), a recent review of over 60 slope failures suggests these methods have limited suitability for modelling the complex failure mechanisms observed in excavated coal mine slopes. Kinematic techniques do not adequately capture the rock mass component of excavated slope failure and do not provide a geospatial location of potential failure, while 2D limit equilibrium techniques do not adequately capture the 3D mechanisms of excavated slope failures. Methods which do consider the 3D mechanisms of slope failure are summarized for industry consideration and application.     

Upper bound analysis of slope stability with nonlinear failure criterion based on strength reduction technique

Based on the upper bound limit analysis theorem and the shear strength reduction technique, the equation for expressing critical limit-equilibrium state was employed to define the safety factor of a given slope and its corresponding critical failure mechanism by means of the kinematical approach of limit analysis theory. The nonlinear shear strength parameters were treated as variable parameters and a kinematically admissible failure mechanism was considered for calculation schemes. The iterative optimization method was adopted to obtain the safety factors. Case study and comparative analysis show that solutions presented here agree with available predictions when nonlinear criterion reduces to linear criterion, and the validity of present method could be illuminated. From the numerical results, it can also be seen that nonlinear parameter m, slope foot gradient β, height of slope H, slope top gradient α and soil bulk density γ have significant effects on the safety factor of the slope.     

抗滑桩加固边坡稳定性3维极限上限拓展分析

抗滑桩作为常用的边坡加固手段,被广泛应用于工程实践中,其影响下的边坡稳定性分析,具有较高的理论和实践价值。采用极限分析上限法,通过引进参数拓展了边坡3维计算模型,建立了内外功率平衡的边坡安全系数计算框架,并通过优化计算得到一定参数条件下边坡的安全系数上限解和最危险破坏机构形状。在此基础上,分析了抗滑桩加固后边坡破坏模式和稳定性受抗滑桩位置、桩距、坡角、机构限宽等参数的影响规律,并讨论了不同参数条件下破坏面形状的变化规律和边坡稳定性变化的内在机理。结果表明：最安全抗滑桩位置不受机构限宽影响,位于坡面中点与坡顶间的某一位置;当机构限宽较小且抗滑桩位置靠近坡趾时,边坡破坏面通过坡面。抗滑桩位置距离坡趾越远,破坏面越靠近坡面且曲率越大。当桩距较小时,边坡倾向于在抗滑桩位置上方发生次级滑动;边坡整体安全系数随桩距的增大而降低。随着机构限宽的增大,边坡安全系数逐渐降低,并逐渐接近2维破坏机构的安全系数。边坡破坏机构随桩距和机构限宽的增大而增厚。当坡角较小时,边坡破坏面通过坡趾下方。本文方法不仅对边坡破坏机构类型的拓展具有理论意义,而且实现了计算结果的进一步优化。     

Influences of nonassociated flow rules on three-dimensional seismic stability of loaded slopes

The influences of soil dilatancy angle on three-dimensional (3D) seismic stability of locally-loaded slopes in nonassociated flow rule materials were investigated using a new rotational collapse mechanism and quasi-static coefficient concept. Extended Bishop method and Boussinesq theorem were employed to establish the stress distribution along the rupture surfaces that are required to obtain the rate of internal energy dissipation for the nonassociated flow rule materials in rotational collapse mechanisms. Good agreement was observed by comparing the current results with those obtained using the translational or rotational mechanisms and numerical finite difference method. The results indicate that the seismic stability of slopes reduces by decreasing the dilatancy angle for nonassociated flow rule materials. The amount of the mentioned decrease is more significant in the case of mild slopes in frictional soils. A nearly infinite slope under local loading, whether its critical failure surface is 2D or 3D, not only depends on the magnitude of the external load, but also depends on the dilatancy angle of soil and the coefficient of seismic load.     

基于RFPA3D不同加载方法的边坡渐进破坏分析

以锦屏一级左岸边坡为例,建立简化、含软弱结构面的三维地质模型,采用RFPA3D基于离心加载法（Centrifuge）和强度折减法（SRM）模拟边坡渐进破坏过程,通过再现边坡渐进破坏过程,探讨RFPA3D不同加载方法在边坡稳定性分析中的适用性。模拟结果显示:与FLAC、离散元等有限元数值计算方法相比,RFPA3D模拟的边坡渐进破坏过程更加简单直观高效;渐进破坏过程分析表明,在自然工况下左岸煌斑岩脉X、断层F5、F8、F2是控制边坡整体破坏模式的关键因素,在进行边坡开挖时应予以重点关注。稳定性分析表明,采用Centrifuge法计算得到的边坡安全系数为1.75,比采用SRM法计算得到的安全系数1.52高,且Centrifuge法模拟得到的边坡破坏模式与实际工程勘察结果更为一致;因此,分析边坡破坏模式时,推荐采用RFPA-Centrifuge法。     

基于连续-非连续方法的高填方边坡变形稳定性分析

为研究高填方边坡的稳定性,基于连续-非连续耦合分析理论,采用边界墙耦合方法建立了高填方边坡的连续-非连续耦合分析模型,利用强度折减的方法来简化降雨工况,参照实际滑坡工程案例,土体参数应折减15%,进行了降雨影响下的高填方边坡稳定性分析;对细观参数进行折减,求解得到边坡的安全系数为1.60,分析了边坡在极端工况下可能的变形破坏情况。通过该案例探究了连续-非连续耦合方法进行边坡稳定性分析的可行性。结果表明,连续-非连续耦合方法能够快速高效且直观地评估高填方边坡的稳定性。     

基于Hoek-Brown准则确定岩体参数的边坡稳定性分析

以某岩质高边坡为研究对象,通过野外调查分析,根据边坡岩体结构和破坏特征,应用Hoek-Brown经验准则确定岩体抗剪强度参数,采用极限平衡法和FLAC-2D有限差分程序对边坡进行稳定性分析,并依据分析结果制定了加固方案,通过分析验证和现场监测,结果表明边坡加固方案可行.     

Comprehensive analysis of slope stability and determination of stable slopes in the Chador-Malu iron ore mine using numerical and limit equilibrium methods

One of the critical aspects in mine design is slope stability analysis and the determination of stable slopes. In the Chador Malu iron ore mine, one of the most important iron ore mines in central Iran, it was considered vital to perform a comprehensive slope stability analysis. At first, we divided the existing rock hosting pit into six zones and a geotechnical map was prepared. Then,the value of MRMR (Mining Rock Mass Rating) was determined for each zone. Owing to the fact that the Chador-Malu iron ore mine is located in a highly tectonic area and the rock mass completely crushed, the Hock-Brown failure criterion was found suitable to estimate geo-mechanical parameters. After that, the value of cohesion (c) and friction angle (e) were calculated for different geotechnical zones and relative graphs and equations were derived as a function of slope height. The stability analyses using numerical and limit equilibrium methods showed that some instability problems might occur by increasing the slope height.Therefore, stable slopes for each geotechnical zone and prepared sections were calculated and presented as a function of slope height.     

山西乡宁—吉县地区黄土高边坡可靠度研究

在山西乡宁—吉县地区实测了7个具有代表性的自然极限状态黄土高边坡断面,建立边坡地层结构模型; 选取研究区合理的黄土物理力学参数,并分地层年代对10个典型工点的黄土强度参数内聚力和内摩擦角的变异性进行分析; 选取6组典型的强度参数变异系数组合,基于Monte-Carlo法进行可靠度模拟,评价该区边坡稳定性; 采用自然类比法进行边坡设计。结果表明:边坡失效概率随坡高的变化趋势一致,均是中等坡高(49.8 m)的边坡失效概率较大,低坡和高坡的失效概率较低; 当变异系数较小时,边坡失效概率对坡高和坡度的变化敏感,而当变异系数较大时,边坡失效概率对坡高和坡度的变化不敏感; 当坡型一定、强度参数变异系数较小时,边坡的稳定系数基本不变,而当参数变异系数超过某一界限时,稳定系数随变异系数的增大而增大,二者存在非线性相关关系; 研究区黄土边坡处于基本稳定状态,但其失效概率最大达69.3%,平均21.1%,介于20%～30%的比例为33.3%,大于30%的比例为14.3%,可靠度指标介于-0.5～8.5,其中小于2.7的比例为88.1%; 对于坡高约为50 m的黄土高边坡,若取30%作为可接受失效概率,边坡坡度需降至45°以下,如果期望可接受失效概率在10%以内,则坡度不宜超过34°。     

边坡稳定数值计算中失稳判据和岩土强度屈服准则

通过理论分析和典型算例计算,对边坡稳定数值计算中边坡的失稳判据和失稳模式进行了深入的讨论,旨在使数值计算方法更好地服务于工程实际。边坡失稳破坏的力学分析表明,排除人为主观因素的影响,在严格收敛标准下数值计算不收敛、边坡塑性区贯通和特定监测点位移突变这三类常用判据内在的力学表现是一致的,算例1的分析结果进一步证实了该观点。边坡的失稳模式与岩土体的屈服准则密切相关,为使理论计算符合工程实践,应根据岩土体实际抗拉能力对以M-C为典型代表的基于剪切破坏的强度准则进行抗拉修正。以抗拉修正后的M-C强度准则为基础,进一步提出了拉剪复合破坏的强度折减计算流程,算例2的计算结果表明该计算流程是合理的且计算结果的精度要高于现行的计算方法。     

吉贾尔-帕坦喀喇昆仑公路沿线落石和边坡稳定性数值研究

在中巴经济走廊的重要通道喀喇昆仑公路（KKH）沿线，由于构造运动和降雨渗透对破碎岩石和边坡稳定性的不利作用，造成了大量落石和不稳定边坡。利用数值软件DIPS、GeoRock 2D和SLIDE对巴基斯坦北部吉贾尔-帕坦喀喇昆仑公路沿线的落石和边坡稳定性进行了数值研究；以喀喇昆仑公路沿线两个主要的易受落石影响的路段为例，研究落石和边坡的失稳机理。对4组节理进行的赤平投影分析表明：两处边坡断面均易发生平面破坏和楔形破坏。基于极限平衡理论，在静力条件下，边坡断面1的安全系数为0.917，处于不稳定状态，边坡断面2的安全系数为1.131，处于欠稳定状态；但在地震条件下，两处断面边坡的安全系数均小于1，处于不稳定状态。研究结果表明，边坡断面1和断面2的落石回弹高度分别为33 m和29 m。边坡断面1的落石速度在0.5~44 m/s，总动能达到1 135.099 kJ，而边坡断面2的落石具有0.5~40.901 m/s的速度和973.012 kJ的破坏能力。研究表明，KKH沿线的落石和滑坡具有极大的破坏潜力。     

非线性Mohr-Coulomb破坏准则下边坡可靠度上限

传统边坡可靠度分析往往在岩土参数服从线性Mohr-Coulomb（简称线性M-C）破坏准则的假设条件下进行,并且常常采用极限平衡法或有限元法计算安全系数。然而,岩土介质破坏准则具有一定的非线性。为能更加实际地描述岩土破坏机理和得到严格精确的解,基于非线性Mohr-Coulomb（简称非线性M-C）破坏准则,结合极限分析上限法和蒙特卡洛法,进行边坡可靠度上限分析。当非线性参数m=1时,与等效的线性M-C破坏准则进行对比计算,验证了方法的可行性。同时,将初始粘聚力、内摩擦角arctan（c₀/σ_t）和非线性参数作为随机变量且服从截断正态分布,进行了参数变异性和敏感性影响分析。研究表明：非线性M-C破坏准则下,边坡可靠度随初始粘聚力、内摩擦角arctan（c₀/σ_t）和非线性参数变异性的增大而减小;边坡可靠度随初始粘聚力和内摩擦角arctan（c₀/σ_t）的增大而增大,随非线性参数的增大而减小。     

Time-variant reliability analysis of three-dimensional slopes based on Support Vector Machine method

In the reliability analysis of slope, the performance functions derived from the most available stability analysis procedures of slopes are usually implicit and cannot be solved by first-order second-moment approach. A new reliability analysis approach was presented based on three-dimensional Morgenstern-Price method to investigate three-dimensional effect of landslide in stability analyses. To obtain the reliability index, Support Vector Machine (SVM) was applied to approximate the performance function. The time-consuming of this approach is only 0.028% of that using Monte-Carlo method at the same computation accuracy. Also, the influence of time effect of shearing strength parameters of slope soils on the long-term reliability of three-dimensional slopes was investigated by this new approach. It is found that the reliability index of the slope would decrease by 52.54% and the failure probability would increase from 0.000 705% to 1.966%. In the end, the impact of variation coefficients of c and f on reliability index of slopes was taken into discussion and the changing trend was observed.     

碎裂状顺层岩质边坡地震动力响应与破坏模式

川藏铁路沿线存在大量碎裂状顺层岩质边坡,与一般的边坡相比,碎裂状边坡在岩体强风化区域的结构面更多,把岩体切割的更为碎裂,导致整体的动力响应和破坏模式变得复杂。以川藏铁路拉月隧道进口边坡工程为依托,通过实地调研和参考工程地质资料,对结构面的分布规律进行了详细总结,并通过赤平极射投影对边坡的整体稳定性进行了分析。在此基础上利用离散元UDEC对碎裂状顺层岩质边坡的动力特性以及破坏模式展开研究,并探讨了节理参数对位移和加速度响应的敏感性规律。研究结果表明：(1)不同地震荷载作用下,坡面位移规律均呈现先增大再减小的规律,坡面位移响应最大处位于M4处。在输入地震波幅值相同时,Kobe波的坡面位移响应比EL波的剧烈；(2)边坡模型的PGA放大系数呈现明显的高程放大效应,地震波类型会影响PGA的响应规律；(3)FFT频谱分析表明,FFT幅值随着高程的增加呈先增大后减小再增大的规律,且强风化岩体区域的FFT幅值整体小于弱风化岩体区域。在地震波通过强弱风化交界位置的结构面时,会导致局部FFT幅值降低。(4)加载Kobe波时模型的FFT幅值比加载EL波时的大,在不同地震波作用下FFT幅值的最大位置均位于模型的M3测点处。(5)碎裂状边坡的失稳演化过程主要为：坡表震裂→形成落石→强风化岩体下部节理张开→弱风化岩体节理孕育→裂缝发展→强风化岩体区域形成贯通结构面→强风化岩体区域沿结构面下滑失稳破坏→坡脚形成堆积体。(6)节理参数敏感性分析表明,弱风化岩体区域的层理间距对位移的影响最为明显,而强风化节理间距对加速度放大影响最为明显。     

基于强度折减法的抗滑桩加固边坡可靠度分析

抗滑桩是一种常用的边坡加固方法。由于天然土体存在不确定性,导致抗滑桩加固边坡的稳定性也存在不确定性,采用可靠度方法可定量考虑上述不确定性。为更加真实地反映不同抗滑桩加固位置下边坡的滑动面,采用强度折减法来计算边坡的安全系数。基于可靠度理论提出一种抗滑桩加固边坡的稳定性评价方法,采用一阶可靠度与响应面法相结合的方法计算边坡的失效概率。为方便应用,开发了基于FLAC^3D的抗滑桩加固边坡可靠度分析程序。采用钢管混凝土桩加固边坡的算例计算结果表明,抗滑桩的加固位置和桩间距对加固边坡的可靠度有重要影响,在相同的桩间距条件下,边坡可能存在一个最优抗滑桩加固位置。     

基于容重增加法的FLAC3D软件在求解边坡稳定安全系数中的应用

利用容重增加法进行三维边坡的非线性稳定分析,通过FLAC3D软件,基于D—P准则,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。边坡的破坏往往伴随着很大的位移和塑性应变,因此采用坡顶水平位移在重度增加系数达到某一值发生突变作为边坡的破坏标准。不需要事先进行假定,得出的结果与强度折减法计算的结果非常接近。该方法可以很好地模拟土的破坏,对工程实践有一定的指导作用。