状态方程求解中的拉格朗日插值公式应用

用对角矩阵及相似矩阵性质证明了；当状态转移矩阵ｅ￣（Ａｔ）中方阵Ａ的特征根相异时，拉格朗日插值公式与Ｌａｐｌａｃｅ变换法对ｅ￣（ｅｔ）表达具有一致性，并用极限方法对方阵Ａ含二重根时拉格朗日插值公式的应用进行了报导．     

基于塑性力学极限法的赵树岭滑坡稳定性分析

基于塑性力学和极限分析理论,假设坡体处于极限滑动状态时,滑动面各处的岩土体均达到塑性极限状态,各段滑动面以及滑动面斜率改变处的竖直平面,都是速度间断面。在此基础上,通过虚功原理建立内外力功率平衡方程,由此求得基于塑性极限分析法的滑坡稳定性系数表达式。选取三峡库区赵树岭滑坡作为分析实例,根据塑性极限分析法的稳定性系数为1.14,计算结果表明赵树岭滑坡总体稳定,但稳定性富裕度不高。     

一种考虑波动效应的拟动力地震边坡稳定性分析方法

考虑地震波在坡体内的传播特征,基于拟动力法,结合传统静力边坡稳定性分析极限平衡法(瑞典条分法),推导了边坡地震力公式和地震边坡稳定性安全系数公式。在此基础上,借助MATLAB软件开发了最危险滑面搜索和安全系数求解程序,实现了一种考虑波动效应的拟动力地震边坡稳定性分析方法。通过探讨地震动特性对地震边坡稳定性的影响,得到了地震边坡稳定性安全系数随地震动参数的变化规律。对于既定边坡,其安全系数随地震波初始相位呈现周期性波动变化,存在最小安全系数;并且此安全系数随地震系数和地震波波长与边坡坡高比的增大而减小。此外,从波动理论角度揭示了拟动力法与拟静力法的区别与联系,给出了两类方法的适用范围:当地震波波长与边坡坡高比大于10时,两类方法所得结果基本一致,均适用;而当地震波波长与边坡坡高比小于10时,拟静力法所得结果较拟动力法相对保守,仅拟动力法适用。     

Huxley方程的定性分析

运用微分方程定性理论，对Huxley方程进行定性分析，得到了方程在有限奇点的稳定性及极限环不存在性的结论，并借助Maple软件做出相图．     

基于等分圆弧滑面土质边坡的稳定性极限分析方法

基于等分圆弧滑面的简化条件,采用土塑性极限分析理论,建立了土质边坡极限分析模型,并推导得到了土质边坡稳定系数计算公式。该方法考虑了圆弧滑面的内能耗散率作用和边坡土体自重荷载、地震惯性力及孔隙水压力所做的外功率作用,可以解决土质边坡稳定性分析问题,是一种改进的土质边坡稳定性评价极限分析方法。     

基于降雨作用下滑面抗剪强度动态变化的层状边坡稳定性评价

降雨入渗对边坡稳定性具有重要影响。鉴于层状边坡在自然情况中广泛存在，因此，开展在降雨情况下的多层状边坡入渗模型及其稳定性研究具有重要意义。考虑各层土体的渗透性能差异，利用约束函数求得各层土体的有效渗透系数，并基于Ｇｒｅｅｎ－Ａｍｐｔ模型建立层状边坡入渗模型。结合非饱和土强度经验公式，推导了考虑滑面抗剪强度动态变化的层状边坡稳定性方程。最后，对深圳某边坡在不同降雨强度和降雨历时下的稳定性系数进行了计算并对结果进行了分析。结果表明，当湿润锋未达到滑面处时，边坡稳定性系数与降雨历时和降雨强度呈线性关系。考虑边坡入渗能力，提出了降雨入渗临界时间概念。在任意降雨强度下，当降雨历时小于该时间时，边坡均不会失稳。本研究可以用于指导降雨情况下层状边坡的稳定性评价。      

关于在平行断面法资源/储量估算中限制使用梯形体公式的建议

通过理论推导，指出在平行断面法资源／储量估算中，在块段相邻剖面不具有相等对应边的情况下，梯形体公式只是一个近似估算公式，存在着一定的误差。而截面圆锥体公式则是一个精确的通用公式，其使用不受相对面积差大小的限制。因此，在这种情况下，建议放弃使用梯形体公式，而统一使用截面圆锥体公式。     

均质土坡潜在滑面的搜索

均质土坡潜在滑面的确定 ,是对均质土坡进行稳定性计算的必要前提。传统的以瑞典圆弧法为代表的刚体极限平衡方法 ,虽然能够确定出均质土坡的滑面 ,但工作量较大 ,使用不方便。因此 ,在塑性极限分析方法的基础上 ,提出了一种新的搜索滑面的方法     

基于尖点突变理论及非趋势波动分析的滑坡稳定性及变形特征研究

以尖点突变理论及非趋势波动分析为基础，构建滑坡稳定性及变形趋势判断模型。首先利用尖点突变理论对滑坡整体稳定性进行评价，并进一步探讨滑坡的分阶段稳定性特征；再利用非趋势波动分析判断滑坡累计序列和速率序列的整体及分阶段变形趋势，并与稳定性分析结果进行对比。实例表明，两种分析方法的结果具有较好的一致性。在分阶段研究中，等时段和递增时段的分析结果具有明显差异，说明阶段分解方式对结果的影响较大，且以递增时段分析结果的规律性更强。     

某水库山体稳定性研究

某水库导流排砂洞塌方导致右岸山体发生松动,本文在掌握场地岩土工程地质资料的基础上,对右岸岩体节理裂隙分布进行统计,同时采用极限分析能量法和有限元数值模拟方法等对右岸山体的稳定性进行分析研究,并提出相应的加固方案。     

基于内外功率比的非直线坡面型边坡的稳定系数研究

在边坡稳定性上极限分析中, 由于考虑了材料的理想弹塑性本构关系与相关流动法则, 相比极限平衡法更符合岩土材料的特征。在以往的二维边坡极限分析上限法中, 要求坡面形态为规则的直线, 而无论是天然边坡还是人工边坡, 边坡的坡面形态往往并非规则的直线。此外, 以往的边坡极限上限分析中得到的稳定数N_s=c/γH主要针对土坡的临界高度计算, 且未考虑孔压等外力对边坡施加的外功率。不同于传统极限平衡法采用静力学的平衡条件, 本研究针对非直线型坡面边坡稳定性问题, 假定滑动面为对数螺旋线, 基于极限分析上限定理和虚功原理, 提出了一种边坡发生旋转破坏时旋转中心的确定方法, 推导出了非直线型坡面边坡的重力虚功功率和能量平衡方程的解析解, 并提出了基于内、外功率之比的稳定系数K用以评价边坡的稳定性。通过算例比较了不同形态天然边坡的稳定性和人工削坡对边坡稳定性的影响, 并分析了边坡的坡度(β)、土体的内摩擦角(φ)、黏聚力(c)以及孔压系数(r_u)对稳定系数K的影响规律。对于坡度较大的边坡, 通过削坡改变坡面形态提高了边坡的稳定系数K。稳定系数K随黏聚力的增加而非线性增大, 随孔压系数的增加而降低。当黏聚力相对于孔压系数对边坡稳定性影响更大时, 稳定系数K随内摩擦角的增加而增大; 反之, 稳定系数K则随内摩擦角的增加而减小。以上结果符合对边坡稳定性分析的普遍认知, 验证了模型的合理性。另外, 通过将该方法与传统的Bishop法的计算结果进行对比, 发现安全系数F_s=1与稳定系数K=0的临界状态物理意义相同, 稳定系数K随黏聚力非线性增加, 更符合边坡的渐进破坏过程。      

Influence of non-dimensional strength parameters on the seismic stability of cracked slopes

Cracks in rock or soil slopes influence the stability and durability of the slopes. Seismic forces can trigger slope disasters, particularly in the cracked slopes. Considering the nonlinear characteristics of materials, the more generalized nonlinear failure criterion proposed by Baker is adopted. The influence of non-dimensional strength parameters on the stability of cracked slopes under earthquakes is performed using the upper bound limit analysis. The seismic displacement is calculated by adopting the logarithmic spiral failure surface according to the sliding rigid block model. Based on the existing studies, two methods for the stability analysis of cracked slopes under earthquakes are introduced: the pseudo-static method(with the factor of safety(Fs) as an evaluation index), and the displacement-based method(with the seismic displacement as an evaluation index). The pseudo-static method can only determine the instantaneous stability state of the cracked slope, yet the displacement-based methodreflects the stability variation of cracked slopes during earthquakes. The results indicate that the nondimensional strength parameters affect the factor of safety and seismic displacement of slopes significantly. The non-dimensional strength parameter(n) controlling the curvature of strength function shapes on the slope stability is affected by other parameters. Owing to cracks, the effect of non-dimensional strength parameters on seismic displacement becomes more significant.     

西安白鹿塬北缘黄土边坡稳定的可靠度分析

在西安白鹿塬北缘实测了14个黄土自然边坡断面,建立了地质模型,通过采样测试并收集已有的测试资料,获得了各时代黄土地层的物理力学参数,将Morgenstern-Price法稳定性计算公式作为极限状态方程,分别采用Monte-Carlo法和Duncan法进行了边坡稳定的可靠度分析。结果表明:采用Monte-Carlo法和Duncan法得到的14个边坡稳定系数分别为1.11～1.41和1.09～1.33,显示这些边坡处于基本稳定—稳定状态;采用上述两种方法得到的边坡可靠指标分别为0.56～1.79和0.39～1.60,得到的失效概率分别为3.4%～29.0%和5.5%～34.8%,并且共有75%的边坡失效概率大于10%,失效可能性较大。统计结果表明:白鹿塬区边坡的坡高和坡度存在负相关性。低而陡的边坡潜在最危险滑面剪出口较高,失效概率较小;坡高达到50m及以上时,边坡高而缓,剪出口较低,失效概率较大,其中河流下切深,有N2泥岩出露的极高边坡,稳定性最差。Duncan法求解的稳定系数略小于Monte-Carlo法求得的结果,而前者求解的失效概率略大于后者,两种方法计算结果较为接近。由于Duncan法理论简单,计算量小,更宜于在实际工程中应用。     

Theoretical Analysis of Coral Reef Stability in South Sea

In this paper, we utilize the variational limiting equilibrium (LE) procedure to theoretically determine the slope stability of homogeneous coral sand in the South China Sea. By establishing a reasonable functional and calculating its extremum, we can deduce the stability factor of a coral reef identical to that obtained by upper bound analysis. To determine the accuracy of the results obtained using the variational LE procedure, we present some classical examples of homogeneous sand slopes without a hard shell and compare our results with those obtained by the upper bound theorem of plasticity. A series of extensive calculations and comparisons reveal that the results obtained by our proposed analysis method and those obtained using classical methods are slightly different, but the variational results are believable. On the other hand, our method solves some stability factors for reef slopes covered with a hard shell, which indicates that the existence of a hard reef shell may significantly enhance the stability of a reef slope, and that there is strong nonlinear relationship between reef stability and the mechanical characteristics of the reef shell, such as its thickness and strength. Finally, based on the variational results presented in this paper, we present a useful chart that offers a convenient and straightforward way to determine the maximum stability factor of reef slopes. Taking into account the influence of the hard reef shell, we found that, in some limit equilibrium cases, the limit stability factor and critical height of a coral slope could be improved significantly. Therefore, this issue deserves careful attention in engineering practice.     

A new method for the stability analysis of geosynthetic-reinforced slopes

This paper is concerned with the stability analysis of reinforced slopes. A new approach based on the limit equilibrium principle is proposed to evaluate the stability of the reinforced slopes. The effect of reinforcement is modeled as an equivalent restoring force acting the bottom of the slice and added into the general limit equilibrium (GLE) method. The equations of force and moment equilibrium of the slice are derived and corresponding iterative solution methods are provided. The new method can satisfy both the force and the moment equilibrium and be applicable to the critical failure surface of arbitrary form. Furthermore, the results predicted by the proposed method are compared with the calculation examples of other researchers and the centrifuge model test results to validate its correctness and effectiveness.     

平面剪切岩质边坡滑裂面的确定及稳定性分析

由于传统搜索方法对岩质边坡滑裂面的确定无法兼顾效率与精度, 如何迅速准确确定潜在滑裂面仍然是个难题。极限平衡法在岩质边坡稳定性分析中备受认可, 采用岩质边坡平面剪切滑动模型, 以滑裂面的倾角来表征潜在滑裂面的位置; 基于极值法, 推导了极限平衡条件下平面剪切破坏型岩质边坡潜在滑裂面的解析解, 并结合香港秀茂坪路边坡对其准确性进行了验证, 进一步对四川宜宾打营盘山公路多级边坡进行了整体稳定性分析。结果表明: 香港秀茂坪边坡采用本文方法确定的边坡潜在滑裂面倾角与实际滑坡倾角基本一致。实际工程应用中, 采用Slide软件中布谷鸟搜索法和模拟退火法两种搜索方法得到的滑裂面倾角分别为38.0°和37.0°, 本解析法所得倾角为34.8°; 选用Janbu法、Morgenstern-Price法和Sarma法分别计算对应的稳定系数, 结果均为1.04左右, 本文所得稳定系数为1.15, 可见本文方法所得结果基本准确。通过参数敏感性分析发现, 随着黏聚力的增加, 边坡滑裂面倾角越来越小, 稳定系数也随之增加; 而当内摩擦角增大时, 边坡滑裂面倾角和稳定系数也随之增大。      

延安市凤凰山东北麓滑坡危险斜坡的变形特征及稳定性分析

通过对凤凰山东北麓工程地质特征的分析．指出该区存在的不良地质问题有滑坡(滑塌)以及危险斜坡等，并对各滑坡(滑塌)以及危险斜坡的变形破坏特征进行了分析，最后运用斜坡(滑坡)稳定性计算中常用的瑞典法、毕肖普法和剩余推力法对其进行了稳定性验算，为凤凰山东北麓后期的治理设计提供了依据。     

Inversion analysis of the shear strength parameters for a high loess slope in the limit state

It is difficult to obtain reliable shear strength parameters for the stability analysis and evaluation of high loess slopes.Hence,this paper determines slope elements and physical parameter of 79 slopes with heights of[40,120]m based on the measured loess slopes in the Ganquan and Tonghuang subregions of northern Shaanxi Province,China.In the limit state of the loess slope(stability factor Fs is 1.0),a fitting equation for the slope height and width is established.Then,the model is developed by stability analysis software-SLOPE/W,and the comprehensive shear strength parameters corresponding to different slope heights of the high slope in the study area are obtained by inversion using the Morgenstern-Price method.The results show that when the height of the slope increases,the cohesion c increases in the soil,and the internal friction angle j decreases.This change is consistent with the characteristics reflected in the composition and physical properties of the slopes,and the comprehensive strength parametric curves are very similar between the Ganquan subregion and the Tonghuang subregion.A landslide that occurred in Miaodian-zaitou of Jingyang County,Shaanxi Province,is selected to verify this inversion method,and the results show that the calculated shear strength parameters of the inversion are consistent with the measured value of the actual slope.     

Seismic stability analysis of slopes with pre-existing slip surfaces

In analyzing seismic stability of a slope with upper bound limit analysis method, the slip surface is often assumed as a log-spiral or plane slip surface. However, due to the presence of a weak layer and unfavorable geological structural surface or a bedrock interface with overlying soft strata, the preexisting slip surface of the slope may be irregular and composed of a series of planes rather than strictly log-spiral or plane shape. A computational model is developed for analyzing the seismic stability of slopes with pre-existing slip surfaces. This model is based on the upper bound limit analysis method and can consider the effect of anchor bolts. The soil or rock is deemed to follow the Mohr-Coulomb yield criterion. The slope is divided into multiple block elements along the slip surface. According to the displacement compatibility and the associated flow rule, a kinematic velocity field of the slope can be obtained computationally. The proposed model allows not only calculation of the rate of external work owing to the combined effect of self-weight and seismic loading, but also that of the energy dissipation rate caused by the slip surface, interfaces of block elements and anchorage effect of the anchors. Considering a direct relationship between the rate of external work and the energy dissipation rate, the expressions of yield acceleration and permanent displacement of anchored slopes can be derived. Finally, the validity of this proposed model is illustrated by analysis on three typical slopes. The results showed that the proposed model is more easily formulated and does not need to solve complex equations or time consuming iterations compared with previous methods based on the conditions of force equilibrium.