Stochastic analysis of beams on reinforced earth beds

The present study comprises Monte-Carlo simulation assisted analysis of foundations resting on reinforced earth beds using the concept of beams on an elastic foundation, treating the modulus of subgrade reaction (MSR) as a stationary stochastic field characterised by mean, variance, autocorrelation function (ACF) and the autocorrelation distance (ACD). Realisations of the MSR, generated by solving a stochastic differential equation, are fed to a deterministic distributed parameter model to generate realisations of two dependent stochastic fields, namely deflection and bending moment in the foundation beam, and two random variables, namely the location of occurrence of maximum deflection and the bending moment. Subsequently these realisations are analysed to evolve probability distribution functions, variance and ACF of the dependent stochastic fields and the random variables. It is revealed that the ACF of these fields is independent of the ACF of the MSR. Further, variance of deflection is found to increase as the ACD of the MSR increases, implying requirement of a larger factor of safety when random soils display low frequency (macro level) variations. On the other hand, variance of the bending moment is larger at smaller ACDs of the MSR, indicating that for bending moments a larger factor of safety is required when the random soils display high frequency (micro level) variations.     

Reliability-based design of spread footings on clays reinforced with aggregate piers

ABSTRACT

The economical and safe design of footings supported on aggregate-pier-reinforced clay could benefit from the implementation of a reliability-based approach that incorporates the different sources of uncertainty. Monte Carlo simulations are conducted to quantify the probability distribution of the ultimate bearing capacity for practical design scenarios. A reliability analysis is then conducted to propose design charts that yield the required factor of safety as a function of the major input parameters. The novelty in the proposed methodology is the incorporation of a lower bound shear strength that is based on the remoulded undrained shear strength in the reliability analysis.     

非均质土壤中二维非饱和土壤水分运动的随机分析

以一水平向具有空间变异而垂直向为均质的二维非饱和流动区域中的均匀入渗问题为例,应用Monte Carlo随机模拟方法分析了土壤水分变量的随机统计特性及其一、二阶矩的时空分布规律。在随机分析过程中,将所研究的流动区域土壤水力特性的空间变异性以随空间位置变化的标定参数δ(x)表示,并将标定参数δ(x)视为一维随机空间函数的实现,应用随机生成模型来生成参数δ(x)的随机样本。通过随机模拟分析得到:垂直方向上负压水头方差与平均负压水头近似呈一线性关系;随入渗时间的延长,不同深度处表征负压水头空间变异结构的自相关函数趋于一稳定结构。     

土体冻胀与地基梁相互作用的叠加法研究

根据随机介质的思想,土体冻胀引起的地表隆起近似为正态分布。以上海体育场穿越工程为研究背景,由叠加法基本原理,得出多管冻结冻胀叠加法表达式。将非均布的冻胀荷载简化成多段均布荷载,编制matlab程序求解冻土地基上的弹性地基梁方程,得到冻胀与地基梁（结构）相互作用的位移及接触压力,并用实测数据进行了验证。最后对冻胀与基础梁相互作用的影响因素进行计算分析,得出相互作用的冻胀量随地基梁刚度与外荷载增加而减小、随地基弹性接触系数与自由冻胀量增加而增加。     

Structural stability of gravity dams: a progressive assessment considering uncertainties in shear strength parameters

Structural sliding stability of gravity dams is generally quantified using deterministic factor of safety, FS_det. Large FS_det (e.g. 3 in normal condition), are used in existing guidelines to guard against material and load uncertainties. Some guidelines allow an arbitrary reduction in FS_det (e.g. 2) when the knowledge in strength parameters increases from material test data. Yet, those reduced FS_det are not based on a rational consideration of uncertainties. Propagation of uncertainties could be done using probabilistic analyses, such as Monte-Carlo simulations (MC) which are complex and challenging for practical use. There is thus a need to develop simplified reliability based safety assessment procedures that could rationalise the adjustment of FS_det. This paper presents a progressive analysis methodology using four safety evaluation formats of increasing complexity: (i) deterministic, (ii) semi-probabilistic (partial coefficient), (iii) reliability based Adjustable Factor of Safety (AFS), and (iv) probabilistic. Comprehensive comparisons are made for the sliding safety evaluation of a 80 m gravity dam. Results are presented in terms of sliding factors of safety, allowable water levels, and demand/capacity ratios. It is shown that the AFS formulation, using direct integration, is simple and practical to use in complement to existing dam safety guidelines before undertaking MC simulations.     

Effects of anisotropy in correlation structure on the stability of an undrained clay slope

Slopes are mainly naturally occurred deposits, so slope stability is highly affected by inherent uncertainty. In this paper, the influence of heterogeneity of undrained shear strength on the performance of a clay slope is investigated. A numerical procedure for a probabilistic slope stability analysis based on a Monte Carlo simulation that considers the spatial variability of the soil properties is presented to assess the influence of randomly distributed undrained shear strength and to compute reliability as a function of safety factor. In the proposed method, commercially available finite difference numerical code FLAC 5.0 is merged with random field theory. The results obtained in this study are useful to understand the effect of undrained shear strength variations in slope stability analysis under different slope conditions and material properties. Coefficient of variation and heterogeneity anisotropy of undrained shear strength were proven to have significant effect on the reliability of safety factor calculations. However, it is shown that anisotropy of the heterogeneity has a dual effect on reliability index depending on the level of safety factor adopted.     

Stochastic Modelling of the Impact of Flood Protection Measures Along the River Waal in the Netherlands

River flooding is a problem of international interest. In the past few years many countries suffered from severe floods. A large part of the Netherlands is below sea level and river levels. The Dutch flood defences along the river Rhine are designed for water levels with a probability of exceedance of 1/1250 per year. These water levels are computed with a hydrodynamic model using a deterministic bed level and a deterministic design discharge. Traditionally, the safety against flooding in the Netherlands is obtained by building and reinforcing dikes. Recently, a new policy was proposed to cope with increasing design discharges in the Rhine and Meuse rivers. This policy is known as the Room for the River (RfR) policy, in which a reduction of flood levels is achieved by measures creating space for the river, such as dike replacement, side channels and floodplain lowering. As compared with dike reinforcement, these measures may have a stronger impact on flow and sediment transport fields, probably leading to stronger morphological effects. As a result of the latter the flood conveyance capacity may decrease over time. An a priori judgement of safety against flooding on the basis of an increased conveyance capacity of the river can be quite misleading. Therefore, the determination of design water levels using a fixed-bed hydrodynamic model may not be justified and the use of a mobile-bed approach may be more appropriate. This problem is addressed in this paper, using a case study of the river Waal (one of the Rhine branches in the Netherlands). The morphological response of the river Waal to a flood protection measure (floodplain lowering in combination with summer levee removal) is analysed. The effect of this measure is subject to various sources of uncertainty. Monte Carlo simulations are applied to calculate the impact of uncertainties in the river discharge on the bed levels. The impact of the “uncertain” morphological response on design flood level predictions is analysed for three phenomena, viz. the impact of the spatial morphological variation over years, the impact of the seasonal morphological variation and the impact of the morphological variability around bifurcation points. The impact of seasonal morphological variations turns out to be negligible, but the other two phenomena appear to have each an appreciable impact (order of magnitude 0.05–0.1 m) on the computed design water levels. We have to note however, that other sources of uncertainty (e.g. uncertainty in hydraulic roughness predictor), which may be of influence, are not taken into consideration. In fact, the present investigation is limited to the sensitivity of the design water levels to uncertainties in the predicted bed level.     

Multiobjective optimization-based design of stabilizing piles in earth slopes

Though the technology of using stabilizing piles to prevent landsliding is not new, the design of such piles with a meaningful optimization framework has been rarely reported. In this paper, a multiobjective optimization-based framework for design of stabilizing piles is presented, in which both reinforcement effectiveness and cost efficiency could be explicitly considered. The design parameters considered in the proposed design framework are the pile parameters, including pile diameter, spacing, length, and position, and the design objectives considered are the reinforcement effectiveness and cost efficiency. The design of stabilizing piles is then implemented as a multiobjective optimization problem. In that the desire to maximize the reinforcement effectiveness and that to maximize the cost efficiency are two conflicting objectives, the output of this multiobjective optimization will be a Pareto front that depicts a trade-off between these two design objectives. With the obtained Pareto front, an informed decision regarding the design of stabilizing piles is reached. The effectiveness and significance of the proposed multiobjective optimization-based design framework for stabilizing piles are demonstrated through two illustrative examples: one is the design of stabilizing piles in a one-layer earth slope and the other the design of stabilizing piles in a two-layer earth slope. Further, parametric analyses are conducted to investigate the influences of the pile design parameters on the stability of reinforced slopes.     

基坑体系可靠度的条件概率计算方法

基坑存在多种失效模式,考虑失效模式之间的相关性,双界限法计算体系失效概率存在计算结果区间范围较大的弊端。利用均匀试验和非参数回归方法建立响应面,在响应面的基础上,对Monte Carlo模拟生成的随机参数进行插值,得到各个失效模式指标,结合Pearson相关系数检验两两失效模式之间的相关性,用条件概率方法计算基坑体系失效概率,提出了基于条件概率考虑多失效模式相关的基坑体系可靠度分析方法。在此基础上,通过1个典型算例进行对比分析,计算结果表明,该方法不仅计算简便,而且结果可靠,其结果可为基坑体系可靠度分析理论提供一条新的途径。     

含水层渗透系数空间变异性对地下水数值模拟的影响

地下水数值模拟是目前定量研究地下水水量和水质的重要手段。使用基于随机理论的MonteCarlo方法来进行地下水数值模拟。这种方法能较好地考虑水文地质参数的空间变异性。主要将MonteCarlo方法和确定性模型模拟方法的模拟结果在渗透系数场、水头场、速度场和浓度场等方面进行了比较。结果表明:在模拟三维非均质含水层中的溶质运移问题时,充分考虑了含水层渗透系数空间变异性的MonteCarlo法比确定性方法更为有效,模拟精度提高了很多,且对模拟误差及误差来源有合理的数学解释。     

软土狭长深基坑抗隆起破坏模式试验研究

针对软土地区基坑底土层为饱和软黏土的情况,设计了狭长深基坑的抗隆起离心模型试验,分析不同开挖深度和水位条件下的基坑围护墙弯矩、土压力分布、水平位移以及基坑隆起稳定破坏机制。基于离心模型试验的基本参数和工况,建立了有限元数值模型,分析试验工况基坑的抗隆起稳定性与破坏状态,并进行对比验证。试验结果表明：随着开挖深度和坑外水位的增加,坑底软土层产生向上的隆起变形,当隆起变形较大时,围护墙由于坑内土体侧向约束的减弱,底部产生较大的向坑内的水平位移,同时导致支撑轴力增大,基坑最终表现出围护墙绕某道支撑点向坑内的转动踢脚破坏。数值计算结果表明：随着坑外水位的升高,基坑抗隆起稳定性安全系数逐渐减小,当发生抗隆起稳定破坏时,基坑底产生较大的隆起位移,破坏机制与离心模型试验结果相同。     

Influence of spatially random soil on lateral thrust and failure surface in earth retaining walls

The present study investigates the influence of spatial variability of soil properties on the lateral thrust and failure surface of a 6?m high frictionless rigid earth retaining wall in active condition. The drained friction angle of the soil is modelled as a log-normal anisotropic random field in two dimensions, using the Cholesky decomposition technique. The effect of horizontal and vertical scale of fluctuation is observed on the lateral thrust. The failure surface in the backfill is found to be more or less similar for different combinations of spatial variability in vertical and horizontal directions. Monte-Carlo simulation technique is used to compute the probability of failure and to obtain the worst-case spatial variability configuration.     

基于综合变异系数的地基承载力可靠性分析

采用一次二阶矩法,考虑岩土参量变异系数的试验及历史数据,提出了基于综合变异系数的地基承载力简化可靠性与风险分析方法。利用提出的简化可靠性与风险分析方法,可在传统确定性分析的基础上,采用合理的变异系数,分别得到与地基承载力有关的可靠度、破坏概率和平均期望损失的最可能值及其变化范围,为提出优化的地基基础设计方案和工程决策奠定基础;相对于土重度和黏聚力,地基承载力可靠度对于内摩擦角的变化更加敏感;设计时可以综合考虑所需的安全系数、可靠度和破坏概率,确定合适的基础宽度或基底面积。当地基土的场地勘察统计结果的变异系数权重逐渐增加时,综合变异系数不断减小,其相应的地基承载力的可靠度逐渐增加,而相应的破坏概率逐渐减少。     

石头坪景区边坡几何形态对稳定可靠度的影响分析

兰州金城公园石头坪景区提升改造工程存在大量的自然边坡和人工边坡。因边坡土体物理力学参数存在变异性,采用了蒙特卡洛随机抽样法和极限平衡法按不同坡高及坡度计算分析了边坡稳定可靠性指标及其变化规律,结果表明在景区实际坡高、坡度范围内边坡是稳定可靠的,适宜景区建设,但当坡高、坡度达到实际范围的最大值或超范围时,边坡处于基本稳定或欠稳定状态,建议采取加固措施。     

A practical method for identifying parameters in the seismic design of embankments

The effect of heterogeneity of soils on a seismic design procedure based on residual displacement according to safety factors is examined. Although soils are heterogeneous in nature, at present the seismic designs of embankments implement the assumption that soils are homogeneous. In this study, a seismic reliability analysis using a Monte Carlo simulation and considering the heterogeneity of soil strength was applied to the Newmark sliding block method. The data of the analysis in this study were based on in-situ soil test results of actual airport embankments. This paper indicates a rational and practical approach to modifying the actual heterogeneous soil conditions into homogeneous design parameters for the Newmark sliding block method in homogeneous ground conditions.     

Sensitivity analysis of support safety factor for predicting the effects of contributing parameters on roof falls in underground coal mines

Roof falls accounted for 18.18% of all fatal accidents in Indian coal mines, contributing about 35.29% of all fatal accidents in below-ground operations in 2005. The support safety factor, always preferred in support planning and design of underground coal mines, may be an important predictor for roof falls. In this paper, geotechnical data were collected from 14 roof fall incident places in an underground coal mine, located in the Eastern India, which has bord and pillar method of workings. The mean value of probabilistic support safety factor for the case study mine was found to be 1.24. However, the probability, of the estimated support safety factor of less than or equal to one, was found to be 0.246. Sensitivity analysis was conducted to analyze the effects of the contributing parameters on support safety factor and the likelihood of the roof fall. The multi-variate regression analysis was carried out for the data generated by Monte Carlo method to correlate the contributing factors to support safety factor. It ranked gallery width as the first parameter to control the support safety factor.     

线性分布基床系数弹性地基梁有限单元法改进

弹性地基梁法常用于研究土和结构的相互作用,对于均布荷载和边界条件简单的弹地基梁,采用理论解即可方便地进行计算。侧向荷载作用下桩体、嵌入式挡墙一般根据弹性地基梁理论进行分析,并假定基床系数随深度增加。对于基床系数呈线性分布或呈均匀分布但边界条件复杂的弹性地基梁理论求解困难,通常采用有限差分法或有限单元法近似求解。采用有限单元法计算线性分布基床系数弹性地基梁时,若单元划分数量不够,就存在计算精度不足的问题。采用加权余量法推导了更为精确的2节点5次位移函数和相应的单刚矩阵,得出了线性分布荷载作用下挠度的5次多项式近似解,从而实现只需划分很少的单元数,节点位移及单元内位移的分布即可达到较高的计算精度,极大地提高了计算效率,单元内力的分布可直接由位移函数导出,简化了后处理计算程序。     

滑坡治理工程中钢筋混凝土格构梁设计理论研究

钢筋混凝土格构锚固是滑坡治理的一种有效措施,在三峡工程地质灾害治理中应用广泛。在钢筋混凝土格构梁与预应力锚索复合结构受力分析的基础上,提出了格构锚固的力学模型,将格构梁简化为受集中力作用的弹性地基上的梁,并按无限长梁和有限长梁上受一个集中力和多个集中力作用,分别推导出变形和内力分布表达式,讨论了格构梁工程设计的基本要求,提出了格构梁工程设计的步骤和方法。以三峡工程库区巴东县太矶头滑坡为例,系统介绍了该滑坡治理设计的实施过程。     

基于安全预警分级的基坑安全模糊评价研究

在基坑施工过程中,基坑围护结构设计的稳定安全系数是不可测的,因此,《建筑基坑支护技术规程》（JGJ120－99）和《建筑基坑工程监测技术规范》（GB50497－2009）要求不同安全等级基坑的施工过程中有不同类型的监测项目,并给予相应的安全预警值。由于施工监测项目数据的不同步性,为避免对施工过程安全状态的“突发性”以及应对不同安全状态措施的需要,提出了安全预警分级方法。根据监测项目的实测数据,采用模糊数学方法定义了广义稳定系数评估施工过程的安全状态,并给出了广义稳定系数的安全下限。基于实际工程的监测数据,分析了不同监测项目广义稳定系数的变化过程,指出了安全控制的重点监测内容。     

考虑土体强度的建筑基坑突涌问题分析

基于土体的强度特性，并假设突涌破坏体为方柱体或圆柱体，推导出了考虑土体强度的基坑突涌稳定性计算公式，计算结果表明，对于一般的粘性土， 考虑其强度后的抗力分项系数比不考虑强度的抗力分项系数增加二倍以上，汉口地区许多基坑开挖并没有出现突涌现象，表明土体的抗剪强度对抗力起着不可忽视的作用，因此考虑土体强度的突涌稳定性分析是比较接近工程实际的。