Effect of element size on the static finite element analysis of steep slopes

The accuracy of the computed stress distribution near the free surface of vertical slopes was evaluated in this study as a function of the element size, including aspect ratio. To accomplish this objective, a parametric study was carried out comparing stresses computed using the finite element method (FEM) to those obtained from a physical model composed of photoelastic material. The results of the study indicate a reasonable agreement between a gelatin model and the FEM model for shear stresses, and an overall good agreement between the two models for the principal stresses. For stresses along the top of the slope, the height of the element tends to be more important than width or aspect ratio, at least for aspect ratios up to 4. In all cases, the greatest difference between the two models occurs in the vicinity of the slope. Specifically, if H is defined as the slope height, an element height of H/10 appears to be adequate for the study of stresses deep within the slope, such as for typical embankment analyses. However, for cases where tensile stresses in the vicinity of the slope face which are critical, such as for the stability analysis of steep slopes, element heights as small as H/32, or higher‐order elements, are necessary. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite element analysis of progressive failure in long slopes

Progressive failure in long natural clay slopes with an underlying weak shear zone is studied. The clay slope is assumed to be elastic–perfectly plastic, whereas the shear zone may have an elastic–plastic strain softening behaviour. The failure will occur due to the development of large shear deformations in the weak zone. The general behaviour, including the possibility of progressive failure, can be studied by the use of a one-dimensional finite element model. Other interesting matters which can be studied are critical load, critical disturbance and critical length of the slope. Numerical examples show the overall behaviour due to different residual shear strengths of the weak layer, end disturbance or change of pore pressure in the weak layer. Although simple, the proposed finite element model provides a practically applicable tool for the prediction of whether progressive failure will occur and in which manner the local failure will propagate.     

Subsidence on steep slopes due to longwall mining

Summary A two dimensional finite element model is used to simulate the extraction of coal by the longwall method underneath idealized surface slopes. The resulting subsidence, tilt and horizontal displacement values are compared with similar extractions using the same method beneath initially horizontal surfaces. The conclusions of a parametric study using this model, supported by field evidence, indicate that in areas of rugged topography, simple application of the procedures outlined in the National Coal BoardSubsidence Engineer's Handbook (1975) does not give acceptable predictions of the induced ground movements.     

红砂岩高陡岩质边坡稳定性分析及治理

充分利用边坡失稳前自身抗滑能力进行高陡边坡治理，结合工程实例，提出了主动性公路边坡治理的思路。分别利用极限平衡法和有限元数值法，综合考虑了两种方法的优缺点，对红砂岩高陡边坡进行了全面的稳定性分析，并针对性地提出了经济合理的治理方案。     

岩石边坡稳定的块体单元极限分析上限法

将块体单元法与极限分析上限法相结合,提出了岩石边坡稳定的块体单元极限分析上限法。借助于块体单元法离散计算区域,通过块体系统速度场在结构面上满足Mohr-Coulomb屈服条件、关联流动法则、速度边界条件以及块体系统虚功原理,构成求解边坡强度储备安全系数上限解的非线性规划模型,模型的求解采用复合形法。最后研究了一个岩质楔形体边坡算例和小湾水电站进水口边坡实例,通过将块体单元法上限分析计算结果与刚体极限平衡法相比较,验证了该方法的正确性。     

岩质边坡稳定性分析的探讨

通过最大剪应力等值线来确定边坡的滑动面,并与其结构面抗剪强度相比较,给出了确定边坡的稳定系数的方法。     

Improved Bell's method for the stability analysis of slopes

A new procedure based on the approximation to the total normal pressure along the slip surface is developed to compute the factor of safety of slopes for slip surfaces of all shapes. By taking the whole sliding body, instead of an individual slice, as the loaded object, all the equilibrium equations are formulated according to the three‐moment equilibrium conditions rather than the two force equilibrium conditions and one‐moment equilibrium condition. The system of nonlinear equations deduced in this way is well‐scaled and enjoys excellent numerical properties such as the existence of solution with a positive factor of safety, a nearly unlimited scope of convergence and a rapid convergence rate associated with the Newton method. In the case of ?_u =0—the situation where no drainage and no consolidation are involved, furthermore, the system has a unique solution and the factor of safety has an explicit expression. Some typical examples are analyzed to demonstrate the numerical properties of the proposed procedure. Copyright © 2009 John Wiley & Sons, Ltd.     

Fuzzy测度理论在岩质边坡稳定性分析中的应用

目前国内常用的边坡稳定性评价方法主要是传统的极限平衡法,这种方法在分析边坡稳定性时不能够反映边坡真实的情况,因此分析效果不是十分的理想;利用李文秀提出的Fuzzy测度法,通过建立Fuzzy测度模型,可定量地分析岩质边坡的稳定性,并对实际边坡工程有指导性的意义。     

Assessing rockfall susceptibility in steep and overhanging slopes using three-dimensional analysis of failure mechanisms

Rockfalls strongly influence the evolution of steep rocky landscapes and represent a significant hazard in mountainous areas. Defining the most probable future rockfall source areas is of primary importance for both geomorphological investigations and hazard assessment. Thus, a need exists to understand which areas of a steep cliff are more likely to be affected by a rockfall. An important analytical gap exists between regional rockfall susceptibility studies and block-specific geomechanical calculations. Here we present methods for quantifying rockfall susceptibility at the cliff scale, which is suitable for sub-regional hazard assessment (hundreds to thousands of square meters). Our methods use three-dimensional point clouds acquired by terrestrial laser scanning to quantify the fracture patterns and compute failure mechanisms for planar, wedge, and toppling failures on vertical and overhanging rock walls. As a part of this work, we developed a rockfall susceptibility index for each type of failure mechanism according to the interaction between the discontinuities and the local cliff orientation. The susceptibility for slope parallel exfoliation-type failures, which are generally hard to identify, is partly captured by planar and toppling susceptibility indexes. We tested the methods for detecting the most susceptible rockfall source areas on two famously steep landscapes, Yosemite Valley (California, USA) and the Drus in the Mont-Blanc massif (France). Our rockfall susceptibility models show good correspondence with active rockfall sources. The methods offer new tools for investigating rockfall hazard and improving our understanding of rockfall processes.     

岩质高边坡的锚固设计及其稳定性分析

通过分析岩质高边坡的稳定性,采用格构式加固设计,确定了详细的设计方案;采用有限差分方法来模拟加固方案的数值解法,建立了实际的差分模型,经过计算得出加固后的边坡滑动面消失,支护后岩质边坡的稳定性系数满足要求,边坡处于稳定,为以后实际的边坡加固工程设计和计算依据提供借鉴。     

边坡稳定性分析的条块稳定系数法

鉴于传统条分法对边坡安全系数定义和使用的局限性,引入了条块稳定系数的概念。分析了条间力推力线高度的影响因素,假定条间力传递时都具有相同的条间力稳定系数 ,并考虑了条块重力偏心矩的影响。根据条块的力和力矩平衡关系以及条间力假定,建立了求解条块稳定系数的四元方程组。在此基础上,求得条块稳定系数随滑动面的分布状况。根据条块稳定系数随滑动面的分布规律划分了滑体的主滑段、抗滑段和牵引段,大致判断滑坡的滑动模式。根据滑面上抗滑力和下滑力之比的定义,求解边坡整体稳定系数。采用传统条分法和所建立的条块分析法分别以圆弧滑动和折线形滑动的两个实例进行了验算,说明了条块分析法的优越性和可靠性。     

边坡稳定性分析的无条分法

基于滑面应力修正技术并取整个滑体为受力体,实现了对滑体的整体极限平衡分析。同时,利用Green公式将有关域积分转化为边界积分,而无需再对滑体进行条分。该方法数值特性好,亦可方便地将二维的成果向三维推广,从而实现满足全部6个平衡条件的三维严格极限平衡法。本文是二维部分的成果。     

非饱和土边坡稳定分析方法探讨

在对非饱和土边坡进行稳定分析时,应该全面地考虑基质吸力对边坡稳定的贡献。首先,分别探讨了基于Fredlund非饱和土强度表达式和Bishop非饱和土有效应力强度公式将强度折减有限元法推广到非饱和土边坡稳定分析中的具体方法;然后,开发了可以考虑基质吸力两种处理方法的强度折减有限元计算程序;最后,给出了一个非饱和土边坡稳定分析的对比算例,说明了二者的不同特点。     

Limit analysis of the stability of slopes reinforced with anchors

An approach based on the category of upper bound theorem of limit analysis is proposed in this article to consider the reinforcing effect of one row of anchors on slope stabilization. The shear strength reduction technique is used in the determination of the safety factor of the slope. The effect of anchor reinforcement is assumed to be an external axial force applied on the slope, and in the formulas of kinematic limit analysis, the work rate done by the anchor can be calculated. So, the stability analysis can be conducted without any assumptions on the acting position and decomposition of the axial force of anchors. Results were compared with those obtained using both the limit equilibrium method and numerical method. A parametric study was carried out to illustrate the effect of anchor orientation and position on slope stabilization. Copyright © 2011 John Wiley & Sons, Ltd.     

Global method for stability analysis of anchored slopes

Based on the global method, an approach is proposed to consider the effect of anchor reinforcement on slope stability, where equilibrium conditions are formulated in terms of the whole slip body. Anchor pre-tension is assumed to be undertaken by the whole slip body instead of individual slices, causing internal force within slope more realistic. Meanwhile, the optimization model for locating the critical slip surface is of weak nonlinearity and easy to solve using the conventional optimization procedures. The effects of anchoring orientation and position are thoroughly investigated, and interesting results are obtained.     

裂隙黄土边坡三维稳定性极限分析

黄土边坡中竖直裂隙的发育往往会对边坡稳定产生影响。相对于平面应变机制,建立三维破坏机制下边坡稳定性分析方法更能接近实际边坡失稳情况。基于塑性极限分析上限法,考虑预先存在竖直裂隙的三维黄土边坡不同破坏机制（坡面破坏、坡脚破坏和坡底破坏）,建立能量平衡方程及其无量纲临界高度值γH/c表达式,采用随机搜索法得到了临界高度的上限解。分析了约束宽度、边坡坡度、内摩擦角以及裂隙深度对三维竖直裂隙黄土边坡临界高度值的影响。结果表明：对于坡脚破坏机制,临界高度值随着裂隙深度的增加而减小,减小至临界裂隙深度 (δ /H)_min后,裂隙深度的增加不再影响临界高度值;临界裂隙深度随着坡度β 的增大而增大,随着内摩擦角φ 的增大而减小。当约束宽度B/H<0.8时,大多数破坏机制为坡面破坏。当约束宽度B/H=0.8、内摩擦角φ =10° 及约束宽度B/H=0.6、内摩擦角φ =15° 时,边坡的破坏从坡面破坏机制逐渐过渡到坡脚破坏机制。存在竖直裂隙的黄土边坡比完整边坡具有更小的临界高度,约束宽度及内摩擦角会对三维黄土边坡破坏机制产生影响。     

斜坡地下水渗透力计算与稳定性分析

分析了基岩山区斜坡区域地下水的渗流模式,指出斜坡堆积体中地下水的一般特征,根据这个特征建立了条分法中斜坡渗透力的简易计算方法,用于改进传统的剩余推力法和Sarma法。该方法不需要额外补充参数,易于工程勘察人员掌握。提出通过极限状态考察斜坡安全储备的思路,对三峡库区某滑坡在水库蓄水前后的稳定性和安全储备进行了评价,结果表明传统方法计算的稳定性系数过高,当库水位快速下降时滑坡稳定性减弱,地下水渗透力是其中不可忽视的影响因素。     

Dynamic behavior of small-scale model of nailed steep slopes

This paper presents the results of laboratory shaking table tests performed to study the dynamic behavior of reinforced steep slopes. The surface displacements, settlement of the crest and acceleration responses along with strain behavior of the facing wall are examined during the tests. Two 18-cm high steep slopes with slope angles of 60° and 70° are considered. Each slope is reinforced with nine number of hollow aluminum nails placed in three rows. Each nail is glued with three strain gauges to measure the tensile force developed in the nails. Four strain gauges are fixed at the center of the facing wall to measure the development of strains during shaking. The acceleration responses at the base and crest of the model slopes are monitored during the test durations. The numerical simulation of the model tests is performed by a commercial program called FLAC. The numerical results are found to be reasonable close to the corresponding experimental results.     

活树桩固坡对边坡稳定性影响的数值分析

作为一种经济、环保的植物固坡方法,活树桩在发达国家得到了较为广泛的应用.笔者介绍了活树桩固坡方法的应用和施工方法,讨论了其加固机理.采用弹塑性有限元分析活树桩固坡对边坡稳定性的影响,研究了活树桩的入土长度、加固位置、数量、角度及其根系发展等因素对边坡安全系数影响的规律.