空间三维滑坡敏感性分区工具及其应用

对于滑坡敏感性分区目前有三种方法:定性法、统计法和基于岩土定量模型的确定性方法。定性法基于对滑坡敏感性或灾害评估的人为判断;统计法用一个来源于结合了权重因子的预测函数或指标;而确定性法,或者说是物理定量模型法以质量、能量和动量守恒定律为基础。二维确定性模型广泛用于土木工程设计,而无限边坡模型(一维)也用于滑坡灾害分区的确定性模型。文中提出了一个新的基于GIS(地理信息系统)的滑坡敏感性分区系统,这个系统可用于从复杂地形中确认可能的危险三维(3-D)滑坡体。所有与滑坡相关的空间数据(矢量或栅格数据)都被集成到这个系统中。通过把研究区域划分为边坡单元并假定初始滑动面是椭球的下半部分,并使用Monte Carlo随机搜索法,三维滑坡稳定性分析中的三维最危险滑面是三维安全系数最小的地方。使用近似方法假定有效凝聚力、有效摩擦角和三维安全系数服从正态分布,可以计算出滑坡失稳概率。3DSlopeGIS是一个计算机程序,它内嵌了GIS Developer kit(ArcObjects of ESRI)来实现GIS空间分析功能和有效的数据管理。应用此工具可以解决所有的三维边坡空间数据解问题。通过使用空间分析、数据管理和GIS的可视化功能来处理复杂的边坡数据,三维边坡稳定性问题很容易用一个友好的可视化图形界面来解决。将3DSlopeGIS系统应用到3个滑坡敏感性分区的实例中:第一个是一个城市规划项目,第二个是预测以往滑坡灾害对临近区域可能的影响,第三个则是沿着国家主干道的滑坡分区。基于足够次数的Monte Carlo模拟法,可以确认可能的最危险滑坡体。这在以往的传统边坡稳定性分析中是不可能的。     

Spatial risk analysis of Li-shan landslide in Taiwan

By coupling limit equilibrium analysis and Monte Carlo analysis with a geography information system (GIS), this study implements a method that can evaluate the risk (corresponding to probability of failure in this study) of landslide with consideration of spatial uncertainties. The GIS can adopt the three-dimensional information including surface topography, underground geomaterial distribution and groundwater level to determine slope profiles for analysis. Then the safety of defined slope can be evaluated by limit equilibrium analysis. In this study, the mechanical properties of geomaterial were considered as random variables instead of single values. The slope and groundwater profiles are also randomly adopted. Through a Monte Carlo sampling process, a distribution of safety factor and probability of failure can be determined. This probabilistic risk analysis approach was applied to Li-shan landslide in Central Taiwan.

Due to heavy rains, the sites near the highway 7A (mileage 73 k + 150) and the highway 8 (mileage 82 k) in the Li-shan Township began to subside in mid April 1990. Topography, geology, and groundwater condition of this area were first reviewed. Based on this review, together with field investigations and a series of limit equilibrium back analyses, a general hypothetic model was established to illustrate the failure mechanism of this landslide area. Then the developed probabilistic risk analysis model is applied to spatially evaluate the risk of this landslide area as well as the performance of the remediation treatment.     

二维随机场下边坡稳定性的径向基函数神经网络分析法

岩土参数的随机性会直接影响边坡稳定性评价结果的精度。首先,依据边坡参数的常用分布特征,利用拉丁超立方抽样法生成若干组边坡土性参数和几何参数的随机样本,用有限元强度折减法求解各组样本对应的边坡安全系数。再考虑土性参数的空间变异性,在二维随机场模型下将蒙特卡罗模拟和有限元强度折减法相结合求解各组样本对应的边坡失效概率。然后,利用样本数据及其安全系数和失效概率对径向基函数（RBF）神经网络进行训练和测试,从而建立边坡安全系数和失效概率的预测模型。算例表明,二维随机场模型能相对精确地考虑参数的空间变异性;在此基础上建立的神经网络模型对边坡的安全系数和失效概率具有较高的预测精度,且能极大地节省边坡稳定性分析的时间。     

GIS-Based Probabilistic Mapping of Landslide Hazard Using a Three-Dimensional Deterministic Model

Based on a new Geographic Information Systems (GIS) grid-basedthree-dimensional (3-D) deterministic model and taking the slopeunit as the mapping unit, this study maps landslide hazard usingthe 3-D safety factor index and failure probability. Assuming theinitial slip to be the lower part of an ellipsoid, the 3-D critical slipsurface in the 3-D slope stability analysis is located by minimizingthe 3-D safety factor using the Monte Carlo random simulation.The failure probability of the landslide is calculated using anapproximate method in which the distributions of c, andthe 3-D safety factor are assumed to be in normal distribution.The method has been applied to a case study on three-dimensionallyand probabilistically mapping landslide hazard.     

考虑空间变异性条件下的边坡稳定可靠度高效敏感性分析

在有限数据条件下,可靠度敏感性分析是研究各种不确定性因素对边坡失稳概率影响规律的重要途径。基于直接蒙特卡洛模拟和概率密度加权分析方法提出了一种高效边坡稳定可靠度敏感性分析方法。所提出的方法通过随机场表征岩土体参数的空间变异性,并采用局部平均理论建立岩土体参数的缩维概率密度函数,用于概率密度加权分析中高效、准确地计算不同敏感性分析方案对应的边坡失稳概率。最后,通过一个工程案例--詹姆斯湾堤坝说明了所提出方法的有效性和准确性。结果表明：在敏感性分析过程中,所提出的方法只需要执行一次直接蒙特卡洛模拟,避免了针对不同敏感性分析方案重新产生随机样本和执行边坡稳定分析,节约了大量的计算时间和计算资源,显著提高了基于蒙特卡洛模拟的敏感性分析计算效率;在概率密度加权分析中采用岩土体参数的缩维概率密度函数能够准确地计算边坡失稳概率,避免了有偏估计,使概率密度加权分析方法适用于考虑空间变异性条件下的边坡稳定可靠度敏感性分析问题。     

Slope vulnerability to earthquakes at subregional scale, using probabilistic techniques and geographic information systems

The susceptibility of slopes to failure during earthquakes is calculated, in terms of critical horizontal acceleration, on a subregional scale for the upper part of the Serchio River basin (Tuscany, Italy). According to the working scale (1:10 000) and to the availability and accuracy of the input data, the infinite slope analysis was judged to be the most appropriate method, but particular attention was devoted to the error evaluation due to spatial variability of the geotechnic, geometric, and hydrologic parameters. A geologic, geomorphologic and hydrologic survey of the area was therefore performed, and the geotechnic parameters were collected at local administrations. All the data were stored in a GIS, used as a tool to build the spatial and attribute data base and to prepare the input data layers for the stability analysis. In order to assess the variability of geotechnic parameters, a statistical analysis was performed to assign the best-fitting probability distribution to cohesion, angle of internal friction and unit weight of the soil. As hydrogeologic data were not available for the area, only surface hydrology information could be used; a map of probability of spring occurrences was derived by a bayesian method, the Weight of Evidence Modelling, and was used as groundwater indicator. A Monte Carlo procedure and a first-order second-moment method were applied and compared as error estimators in assessing the slope susceptibility to failure. The differences between the two methods are discussed, and two maps showing, respectively, the critical horizontal acceleration and the probability of failure associated with each slope are presented, together with the curve plotting the reliability index against the probability of failure.     

On the efficient estimation of small failure probability in slopes

The random finite element method (RFEM) combines the random field theory and finite element method in the framework of Monte Carlo simulation. It has been applied to a wide range of geotechnical problems such as slope stability, bearing capacity and the consolidation of soft soils. When the RFEM was first developed, direct Monte Carlo simulation was used. If the probability of failure (p _f ) is small, the direct Monte Carlo simulation requires a large number of simulations. Subset simulation is one of most efficient variance reduction techniques for the simulation of small p _f . It has been recently proposed to use subset simulation instead of direct Monte Carlo simulation in RFEM. It is noted, however, that subset simulation requires calculation of the factor of safety (FS), while direct Monte Carlo requires only the examination of failure or non-failure. The search for the FS in RFEM could be a tedious task. For example, the search for the FS of slope stability by the strength reduction method (SRM) usually requires much more computational time than a failure or non-failure checking. In this paper, the subset simulation is combined with RFEM, but the need for the search of FS is eliminated. The value of yield function in an elastoplastic finite element analysis is used to measure the safety margin instead of the FS. Numerical experiments show that the proposed approach gives the same level of accuracy as the traditional subset simulation based on FS, but the computational time is significantly reduced. Although only examples of slope stability are given, the proposed approach will generally work for other types of geotechnical applications.     

基于FELA的随机场方法在考虑降雨入渗的边坡开挖稳定性分析中的应用

黑山共和国南北高速公路项目部分路段处于复理石地区,降雨集中、空间变异性显著且分层分布的岩土体给道路边坡施工带来了挑战。条分法、常规有限元法等确定性分析方法不能考虑岩土材料的不确定性,给出的具有唯一性、确定性的结果不能反映边坡稳定的不确定性。以该工程某边坡为例,采用有限元极限分析方法（FELA）,考虑岩土材料强度的空间变异性,利用上下限解法得出安全系数的分布区间。由勘察资料得到材料均值、标准差和空间相关长度并重建描述抗剪强度指标的二维随机场,同时考虑开挖岩层的节理分布,分析边坡在分级开挖过程中,各施工步骤的稳定性和破坏模式。与有限元分析结果相比,随机场条件下,部分情况开挖阶段安全系数低于限值,并出现局部破坏和整体破坏两种形式。结合不饱和土理论,模拟暴雨情况下雨水的入渗深度并在饱和区采用降低后的强度参数重新计算。通过蒙特卡洛模拟,得到各工况下安全系数、滑动体体积、挡墙弯矩和锚杆内力的概率密度分布函数。挡墙结构约束土体的变形,使得破坏模式趋向于整体破坏,安全系数分布区间变小。锚杆能带动更多土体进入工作状态,同样约束安全系数分布区间。旱季施工与雨季施工边坡破坏区域不同,同等支护条件下,雨季边坡安全系数分布区间更大,且均值明显降低。      

基于高效随机有限元法的边坡风险评估

提出了基于子集模拟的边坡风险评估的高效随机有限元法（RFEM）,推导了基于子集模拟的边坡失效概率和失效风险的计算公式,并给出了基于高效RFEM的边坡可靠度分析和风险评估流程图。采用一个边坡算例验证了所提方法的有效性。结果表明,基于子集模拟的高效RFEM可以视为是对基于蒙特卡洛模拟的传统RFEM的改进,显著地提高了失效概率和失效风险的计算效率以及失效样本的产生能力,非常适用于分析小失效概率的可靠度问题,极大地增强了RFEM在边坡可靠度分析和风险评估中的实用性。高效RFEM将边坡的整体失效风险分解为对应不同概率水平的边坡失效风险,并量化了它们对整体风险的相对贡献度。在该方法中,边坡可靠度分析和风险评估与确定性边坡有限元分析互不耦合,极大地简化了它们的计算过程。此外,土体不排水抗剪强度的竖向空间变异性对边坡失效风险具有显著的影响。     

Assessment of shallow landslide susceptibility using the transient infiltration flow model and GIS-based probabilistic approach

This study proposes a probabilistic analysis method for modeling rainfall-induced shallow landslide susceptibility by combining a transient infiltration flow model and Monte Carlo simulations. The spatiotemporal change in pore water pressure over time caused by rainfall infiltration is one of the most important factors causing landslides. Therefore, the transient infiltration hydrogeological model was adopted to estimate the pore water pressure within the hill slope and to analyze landslide susceptibility. In addition, because of the inherent uncertainty and variability caused by complex geological conditions and the limited number of available soil samples over a large area, this study utilized probabilistic analysis based on Monte Carlo simulations to account for the variability in the input parameters. The analysis was performed in a geographic information system (GIS) environment because GIS can deal efficiently with a large volume of spatial data. To evaluate its effectiveness, the proposed analysis method was applied to a study area that had experienced a large number of landslides in July 2006. For the susceptibility analysis, a spatial database of input parameters and a landslide inventory map were constructed in a GIS environment. The results of the landslide susceptibility assessment were compared with the landslide inventory, and the proposed approach demonstrated good predictive performance. In addition, the probabilistic method exhibited better performance than the deterministic alternative. Thus, analysis methods that account for uncertainties in input parameters are more appropriate for analysis of an extensive area, for which uncertainties may significantly affect the predictions because of the large area and limited data.     

The evaluation of the probability of rock wedge failure using the point estimate method

In a probabilistic analysis of rock slope stability, the Monte Carlo simulation technique has been widely used to evaluate the probability of slope failure. While the Monte Carlo simulation technique has many advantages, the technique requires complete information of the random variables in stability analysis; however, in practice, it is difficult to obtain complete information from a field investigation. The information on random variables is usually limited due to the restraints of sampling numbers. This is why approximation methods have been proposed for reliability analyses. Approximation methods, such as the first-order second-moment method and the point estimate method, require only the mean and standard deviation of the random variable; therefore, it is easy to utilize when the information is limited. Usually, a single closed form of the formula for the evaluation of the factor of safety is needed for an approximation method. However, the commonly used stability analysis method of wedge failure is complicated and cumbersome and does not provide a simple equation for the evaluation of the factor of safety. Consequently, the approximation method is not appropriate for wedge failure. In order to overcome this limitation, a simple equation, which is obtained from the maximum likelihood estimation method for wedge failure, is utilized to calculate the probability of failure. A simple equation for the direct estimation of the safety factors for wedge failure has been empirically derived from failed and stable cases of slope, using the maximum likelihood estimation method. The developed technique has been applied to a practical example, and the results from the developed technique were compared to the results from the Monte Carlo simulation technique.     

降雨条件下考虑饱和渗透系数变异性的边坡可靠度分析

土体饱和渗透系数表现为天然的变异性,为此基于Green-Ampt模型建立了考虑饱和渗透系数变异性的降雨入渗物理模型,并藉此模型确定了坡体湿润锋深度和含水率分布。然后结合无限长非饱和土边坡稳定模型得到解析形式的反映边坡稳定性的极限状态函数。采用Monte Carlo法对饱和渗透系数进行随机抽样并最终建立降雨条件下考虑饱和渗透系数变异性的边坡概率分析框架。针对一假想边坡,探讨了饱和渗透系数的变异系数、降雨持时和降雨强度对边坡破坏概率以及破坏发生时间概率分布的影响,结果表明：在降雨初期,边坡的破坏概率随饱和渗透系数变异性的增强而逐渐增加,但随着降雨的持续,破坏概率开始随变异性的增强而显著降低;滑坡最可能发生时间的大小并不受饱和渗透系数变异性的影响,而是直接取决于降雨强度;滑坡最可能发生时间所对应的概率却随变异性的增强而逐渐减小。     

Back analysis of slope failure with Markov chain Monte Carlo simulation

Field observed performance of slopes can be used to back calculate input parameters of soil properties and evaluate uncertainty of a slope stability analysis model. In this paper, a new probabilistic method is proposed for back analysis of slope failure. The proposed back analysis method is formulated based on Bayes’ theorem and solved using the Markov chain Monte Carlo simulation method with a Metropolis–Hasting algorithm. The method is very flexible as any type of prior distribution can be used. The method is also computationally efficient when a response surface method is employed to approximate the slope stability model. An illustrative example of back analysis of a hypothetical slope failure is presented. Effects of jumping distribution functions and number of samples on the efficiency of Markov chains are studied. It is found that the covariance matrix of the jumping function can be set to be one half of the covariance of the prior distribution to achieve a reasonable acceptance rate and that 80,000 samples seem to be sufficient to obtain robust posterior statistics for the example. It is also found that the correlation of cohesion and friction angle of soil does not affect the posterior statistics and the remediation design of the slope significantly, while the type of the prior distribution seems to have much influence on the remediation design.     

Probabilistic parameter estimation and predictive uncertainty based on field measurements for unsaturated soil slope

A key issue in assessment of rainfall-induced slope failure is a reliable evaluation of pore water pressure distribution and its variations during rainstorm, which in turn requires accurate estimation of soil hydraulic parameters. In this study, the uncertainties of soil hydraulic parameters and their effects on slope stability prediction are evaluated, within the Bayesian framework, using the field measured temporal pore-water pressure data. The probabilistic back analysis and parameter uncertainty estimation is conducted using the Markov Chain Monte Carlo simulation. A case study of a natural terrain site is presented to illustrate the proposed method. The 95% total uncertainty bounds for the calibration period are relatively narrow, indicating an overall good performance of the infiltration model for the calibration period. The posterior uncertainty bounds of slope safety factors are much narrower than the prior ones, implying that the reduction of uncertainty in soil hydraulic parameters significantly reduces the uncertainty of slope stability.     

An adaptive sampling approach to reduce uncertainty in slope stability analysis

An adaptive sampling approach is proposed, which can sample spatially varying shear strength parameters efficiently to reduce uncertainty in the slope stability analysis. This approach employs a limit equilibrium model and stochastic conditional methodology to determine the likely sampling locations. Karhunen-Loève expansion is used to conduct the conditional Monte Carlo simulation. A first-order analysis is also proposed to ease the computational burden associated with Monte Carlo simulation. These approaches are then tested using borehole data from a field site. Results indicate that the proposed adaptive sampling approach is an effective and efficient sampling scheme for reducing uncertainty in slope stability analysis.     

蒙特卡洛模拟方法在斜坡稳定性评价中的应用

介绍了蒙特卡洛随机模拟的基本原理及在斜坡稳定性评价中的应用，给出了斜坡的破坏概率，模拟的次数与所给误差之间的关系，以岩村滑坡为例进行了计算，结果与实际相吻合。     

中国天山山区降水空间分布模拟及成因分析

为了研究中国天山山区降水空间分布规律及其形成机理,基于研究区DEM及气象站点数据资料,运用偏最小二乘法和GIS技术建立了山区降水估算模型,并分析其降水成因。结果表明:天山山区年降水具有明显的经度和纬度地带性,西段多于东段,北坡(迎风坡)多于南坡(背风坡);研究区降水在海拔4 000 m以下呈线性增加特征,随后显著减少,在5 500 m左右出现第二极大值带;坡度小于50°时降水与坡度呈显著正相关。在地形抬升条件下,随气温下降和相对湿度上升使降水增加,这也是山区降水形成的必要条件。总体来看,偏最小二乘法可以有效解决降水及各因子间多重相关性问题,模型回归效果较显著,在模拟山区降水方面具有一定适用性。     

Modeling 2-D spatial variation in slope reliability analysis using interpolated autocorrelations

This paper deals with slope reliability analysis incorporating two-dimensional spatial variation. Two methods, namely the method of autocorrelated slices and the method of interpolated autocorrelations, are proposed for this purpose. Investigations are carried out based on the limit equilibrium method of slices. First-order-reliability-method (FORM) is coupled with deterministic slope stability analysis using the constrained optimization approach. Systematic search for the probabilistic critical slip surface has been carried out in this study. It is shown that both methods work well in modeling 2-D spatial variation. The results of slope reliability analysis are validated by Monte Carlo simulations. Failure probabilities obtained by FORM agree well with simulation results. It is found that 2-D spatial variation significantly influences the reliability analysis, and that the reliability index is more sensitive to vertical autocorrelation distance than to horizontal autocorrelation distance. Based on this study, failure probability is found significantly overestimated when spatial variation is ignored. Finally, the possible use of the method of interpolated autocorrelations in a probabilistic finite element analysis is suggested.     

公路沿线花岗岩风化区滑坡危险度评价--以日本49号国道合户地区为例

对公路沿线边坡进行稳定性评价及滑坡灾害分析，对于由滑坡、泥石流等引起的公路灾害的防治具有重要指导意义。为了评价处于花岗岩风化区的日本福岛县合户地区49号国道沿线边坡的滑坡危险程度，在调查和分析了该地区的表层破坏模式、并通过简易探测方法摸清了风化土层的厚度分布后，将研究区域划分为边坡单元(Slopeunit)，使用椭球体下半部模拟滑动面的形状，通过随机试算法确定各边坡单元危险滑动面的位置及空间形状；采用一种基于GIS的边坡稳定性三维分析模型计算各边坡单元最小安全系数以及滑坡发生概率，定量评价滑坡灾害危险程度。所有的计算过程及结果显示均在一个基于GIS平台的系统中完成，为如何利用GIS技术更好地为滑坡灾害防治工作服务拓宽了思路。