Reliability assessment of excavation systems considering both stability and serviceability performance

Excavation projects related to urban redevelopment and infrastructure improvement are often governed by serviceability-based design, rather than failure prevention criteria. Deformation tolerance specifications are often prescribed based on minimizing potential damage to adjacent structures. A risk-based approach to serviceability performance that systematically incorporates design parameter uncertainty will allow engineers to address soil uncertainty in performance-based design. This paper demonstrates the use of various kinds of reliability methods, such as response surface method (RSM), first-order reliability method (FORM), second-order reliability method (SORM), adaptive importance sampling (AIS), Monte Carlo simulation (MCS) and system reliability, to assess the risk of stability and/or serviceability failure of an entire excavation support system throughout the entire construction process. By considering multiple failure modes (including serviceability criteria) of an excavation, the component and system reliability indices for each excavation step are assessed during the entire excavation process. Sensitivity analyses are conducted for the system reliability calculations, which demonstrate that the adjacent structure damage potential limit state function is the dominant factor for determining excavation system reliability. An example is presented to show how the serviceability performance for braced excavation problems can be assessed based on the system reliability index.     

Probability of serviceability failure in a braced excavation in a spatially random field: Fuzzy finite element approach

A simplified framework is proposed for evaluating the probability of “serviceability failure” in a braced excavation in a spatially random field. Here, the “serviceability failure” is said to occur when the excavation-induced wall or ground movement exceeds specified limiting values. Knowledge of this probability can aid in engineering decision-making to prevent damage to adjacent infrastructures. The proposed framework consists of five elements: (1) finite element method (FEM) for analyzing wall and ground responses in a braced excavation, (2) fuzzy set modeling of parameter uncertainty, (3) spatial averaging technique for handling spatial variability, (4) vertex method for processing fuzzy input through FEM model, and (5) interpretation of fuzzy output. The proposed framework is demonstrated through a well-documented case history. The results show the proposed framework is simple and effective for assessing the probability of serviceability failure in a braced excavation in a spatially random field. To focus on the proposed fuzzy FEM approach, the scope of this paper is limited to one-dimensional modeling of spatial variability with an assumed exponential autocorrelation function.     

考虑参数和模型不确定性的基桩正常使用极限状态可靠度分析

考虑承载力计算模型和荷载不确定性,利用可靠度分析方法和概率统计理论,推导出承载能力极限状态（ULS）和正常使用极限状态（SLS）下可靠度指标的计算公式,给出了两种极限状态下可靠度指标间的线性关系式,研究了桩顶容许沉降 随机性对正常使用极限状态可靠度分析结果的影响。研究结果表明,土体类别和桩型对正常使用极限状态模型因子影响很小;正常使用极限状态下基桩可靠度指标随承载力计算模型和荷载不确定性的增大而减小,但减小幅度逐渐降低,且可靠度指标总变化量不大,工程应用中可忽略承载力计算模型和荷载不确定性在可靠度分析中的影响; 随机性对正常使用极限状态可靠性分析结果的影响很大,随 的增加,正常使用极限状态模型因子和可靠度指标逐渐增大,而模型因子变异性逐渐减小,但桩本身性质并没有任何改变,只是所允许的沉降条件不同。研究结果可为规范修订和工程应用提供参考。     

Probabilistic stability analyses of slopes using the ANN-based response surface

Slope stability analysis is a geotechnical engineering problem characterized by many sources of uncertainty. Some of these sources are connected to the uncertainties of soil properties involved in the analysis. In this paper, a numerical procedure for integrating a commercial finite difference method into a probabilistic analysis of slope stability is presented. Given that the limit state function cannot be expressed in an explicit form, an artificial neural network (ANN)-based response surface is adopted to approximate the limit state function, thereby reducing the number of stability analysis calculations. A trained ANN model is used to calculate the probability of failure through the first- and second-order reliability methods and a Monte Carlo simulation technique. Probabilistic stability assessments for a hypothetical two-layer slope as well as for the Cannon Dam in Missouri, USA are performed to verify the application potential of the proposed method.     

岩土工程可靠度分析的改进响应面法研究

为了提高响应面法的计算效率和精度,对现有的全局响应面法进行了改进。采用径向基函数（RBF）神经网络,代替目前常用的BP网络,迭代过程中在超锥体的范围内构造响应面,逼近隐式的非线性功能函数。数值算例分析表明,与通常的响应面法相比,改进全局响应面法的迭代次数和有限元分析次数均大幅减少,节省机时,有利于提高计算精度。同时,以浅基础和挡土墙为工程背景进行可靠度分析,表明该方法能以较快的收敛速度和较少的有限元分析次数,获得较高精度的可靠度指标,适用于岩土工程的可靠度分析。     

基于改进一次二阶矩法的赵家坡高切坡稳定性分析

为了更客观和科学地评价斜坡的稳定性,采用结构可靠度中的改进一次二阶矩法来分析斜坡的稳定性,同时采用新的、更适于计算机编程的求可靠指标解的迭代方法,对三峡库区赵家坡高切坡第二段稳定性分析标明：（1）潜在滑动面1可靠指标和破坏概率均满足允许风险水平,稳定性程度较高,只需进行表面防护即可;（2）潜在滑动面2可靠指标和破坏概率均不满足允许风险水平,需要进行整体加固并辅以坡面防护;（3）稳定性系数与可靠度分析结果有良好的一致性。     

基于Copula函数的基桩荷载-位移双曲线概率分析

提出了基于Copula函数的基桩荷载-位移双曲线概率分析方法。首先将基桩标准化荷载-位移双曲线模型不确定性转化为双曲线参数不确定性,然后在Copula理论框架下建立了双曲线参数的联合分布函数。最后以钻孔现浇灌注桩试验数据为例证明了所提方法的有效性,并进行了基桩正常使用极限状态可靠度分析。结果表明：Copula函数是构造基桩标准化荷载-位移双曲线参数联合分布函数一种有效的方法,它能够更加准确地实现基桩荷载-位移双曲线的随机模拟,从而得到更为合理的可靠度结果。钻孔现浇灌注桩双曲线模型中两个参数间具有较强的负相关关系,忽略了这种负相关性将会高估基桩的失效概率。此外,常用的Gaussian Copula函数并不是拟合双曲线模型中两个参数间相关结构最优的Copula函数,采用Gaussian Copula函数将会明显低估基桩的失效概率。     

Reliability analysis of piles in spatially varying soils considering multiple failure modes

In most limit state design codes, the serviceability limit checks for drilled shafts still use deterministic approaches. Moreover, different limit states are usually considered separately. This paper develops a probabilistic framework to assess the serviceability performance with the consideration of soil spatial variability in reliability analysis. Specifically, the performance of a drilled shaft is defined in terms of the vertical settlement, lateral deflection, and angular distortion at the top of the shaft, corresponding to three limit states in the reliability analysis. Failure is defined as the event that the displacements exceed the corresponding tolerable displacements. The spatial variability of soil properties is considered using random field modeling. To illustrate the proposed framework, this study assesses the reliability of each limit state and the system reliability of a numerical example of a drilled shaft. The results show the system reliability should be considered for the serviceability performance. The importance measures of the random variables indicate that the external loads, the performance criteria, the model errors of load transfer curves and soil strength parameter are the most important factors in reliability analysis. Moreover, it is shown that the correlation length and coefficient of variation of soil strength can exert significant impacts on the calculated failure probability.     

软土基坑变形失稳形态模拟试验研究

通过不同土性、地下水条件下软土基坑开挖变形失稳的模拟试验, 研究了软土基坑开挖变形发展直至失稳破坏的全过程。通过试验研究, 初步认为软土基坑坑壁在无支护或支护刚度较小的情况下, 其坑壁破坏形态呈抛物线型; 在基坑开挖范围内若存在有砂性土, 且地下水位较高时, 易于发生流砂渗透破坏, 并导致了地表沉陷, 但侧向变形相对较小; 而对于因承压水引起的坑底土体隆起变形, 若不考虑土体的强度特性, 计算结果是偏于安全的。     

一种新的可靠度计算方法及其在工程中的应用

利用神经网络拟合极限状态方程、几何法计算结构可靠度,并推导了基于神经网络的几何法计算公式。最后比较了该法与其他可靠度计算方法的精度以及计算效率,并将该法应用于实际工程当中。     

Reliability Analysis of Excavation Induced Basal Heave

The present study deals with the reliability analysis of basal heave caused by excavation considering uncertainty in the soil properties. The case study considered in the present work has been analyzed deterministically by Hsieh et al. (Can Geotech J 45:788–799, 2008). Taiwan building code is adopted in the method for analyzing the basal heave failure. The random variables (undrained shear strength and total unit weight of clay) are assumed to be normally distributed and uncorrelated. A series of parametric studies have been conducted to calculate the reliability index on the basis of the matrix formulation for the second moment method by Hasofer and Lind (J Eng Mech ASCE 100(1):111–121, 1974) considering different coefficient of variation of undrained shear strength and total unit weight of clay layers. It has been found that for a particular value of coefficient of variation of total unit weight, the reliability index with respect to occurrence of basal heave failure decreases with increase in the coefficient of variation of undrained shear strength. Moreover, the reliability index also decreases when the coefficient of variation of total unit weight increases. It has also been found that the probability of basal heave failure is lower with respect to factor of safety equals to 1.2, as compared to factor of safety equals to 1.0. Sensitivity analysis shows that the undrained shear strength of the bottommost layer and total unit weight of the second layer are the most significant random variables affecting the reliability index. Guidelines are provided for reliability based design where, for ‘target’ reliability index of 2.5 and 3.0, the factor of safety can be chosen such that all the related uncertainties are taken into account, especially with regard to undrained shear strength of the bottommost layer and total unit weight of the second layer. Design guidelines have been provided for this purpose.     

Rock mass excavatability estimation using artificial neural network

One important decision in design of surface mine is the selection of mine equipment and plant. Demand for mechanical excavation is growing in mining industry because of its high productivity and excavation in large scale with lower costs. Several models have been developed over the years to evaluate the ease of excavation and machine performance against rock mass properties. Due to complexity of excavation process and large number of effective parameters, approaches made for this purpose are essentially empirical. There are many uncertainties in results of these models. An attempt is made in this paper to revise the exisiting models. Neural network models for estimation of rock mass excavatability and production rate of VASM-2D excavating machine at Limestone quarry in Retznei, Austria, is presented. Input parameters of this model are Uniaxial compressive strength, tensile strength and discontinuities spacing of rocks. Output is the specific excavation rate per power consumption (bcm/Kwh) as the productivity indicator. Average of deviation between actual data and results estimated by neural network model was only 15% which is in an acceptable range.     

花岗岩隧道脆性破坏的温度效应研究

目前深埋硬岩隧道的岩爆等脆性破坏研究还较少考虑到温度的作用效应。采用精细网格数值模型,提出热-脆性-精细力学计算方法,应用能反映高地应力下硬岩脆性破坏特点的岩体劣化模型,结合能量计算指标,开展了不同温度作用下隧道硬岩脆性破坏的热力耦合分析。以瑞典APSE花岗岩隧洞岩柱为例,进行不同地温下隧道破坏区、能量释放值和应力指标的定量化对比研究。研究结果表明,隧道地温的增加将使岩体产生附加温度应力,进而增大其脆性破坏程度,计算结果与隧道现场的破坏规律基本一致。热-脆性-精细力学计算能合理描述硬岩的损伤和渐进破坏过程,计算结果较好地揭示了花岗岩等硬岩深埋隧道脆性破坏的温度作用效应,对于高应力、高地温下深部工程的稳定性评价具有指导意义。     

Probabilistic forecasting of landslide displacement accounting for epistemic uncertainty: a case study in the Three Gorges Reservoir area,China

Accurate and reliable displacement forecasting plays a key role in landslide early warning. However, due to the epistemic uncertainties associated with landslide systems, errors are unavoidable and sometimes significant in traditional methods of deterministic point forecasting. Transforming traditional point forecasting into probabilistic forecasting is essential for quantifying the associated uncertainties and improving the reliability of landslide displacement forecasting. This paper proposes a hybrid approach based on bootstrap, extreme learning machine (ELM), and artificial neural network (ANN) methods to quantify the associated uncertainties via probabilistic forecasting. The hybrid approach consists of two steps. First, a bootstrap-based ELM is applied to estimate the true regression mean of landslide displacement and the corresponding variance of model uncertainties. Second, an ANN is used to estimate the variance of noise. Reliable prediction intervals (PIs) can be computed by combining the true regression mean, variance of model uncertainty, and variance of noise. The performance of the proposed hybrid approach was validated using monitoring data from the Shuping landslide, Three Gorges Reservoir area, China. The obtained results suggest that the Bootstrap-ELM-ANN approach can be used to perform probabilistic forecasting in the medium term and long term and to quantify the uncertainties associated with landslide displacement forecasting for colluvial landslides with step-like deformation in the Three Gorges Reservoir area.     

基于贝叶斯方法的船坞双排钢板桩围堰整体稳定性可靠度分析

双排钢板桩围堰的整体稳定性具有较大的不确定性,同样安全系数情况下对应的失稳概率可能不同。为了更准确地分析双排钢板桩围堰的整体稳定性,降低稳定性分析中的不确定性,采用贝叶斯方法对船坞双排钢板桩围堰的整体稳定性进行可靠度分析。首先通过统计数据获取土体参数的先验分布,然后基于实测数据采用贝叶斯方法更新参数以得到后验分布,最后根据参数的后验分布采用一次二阶矩计算围堰结构的可靠度。贝叶斯方法从理论的角度解决了已有工程经验和实际案例数据两方面信息有效综合的问题,能在更接近实际情况的前提下进行可靠度分析。     

基于数字钻进技术和量子遗传-径向基函数神经网络的围岩类别超前识别技术研究

围岩类别超前分类是隧道施工过程中必须开展的一项工作,其直接关系到后续的开挖及施工支护方案。为有效地进行隧道围岩类别超前分类,提出了基于数字钻进技术和量子遗传（QGA）-径向基函数（RBF）神经网络的围岩类别超前分类方法。以数字钻进技术为基础,从钻进参数中提取有用信息,构建围岩类别超前分类指标体系。采用量子计算原理对遗传算法进行改进,通过量子位编码和量子旋转门更新种群,以此来确定RBF神经网络的参数,建立了基于QGA-RBF神经网络的围岩类别超前识别系统。最后将该方法应用于青岛胶州湾海底隧道的围岩类别超前识别中,结果表明,该方法具有较高的准确性,其结果为围岩类别超前分类提供了一种新思路。     

Reliability analysis of serviceability performance for an underground cavern using a non-intrusive stochastic method

This paper proposes a non-intrusive stochastic analysis procedure for reliability analysis of the serviceability performance of an underground cavern with an implicit limit state function. This procedure is formulated on the basis of the stochastic response surface method (SRSM) and the deterministic finite element method. First, the SRSM is briefly introduced and implemented through a MATLAB code. Then, the software SIGMA/W is used to perform a deterministic finite element analysis. Next, a link between the MATLAB code and SIGMA/W is developed to automatically pass exchange data between the two platforms. Finally, two examples are presented to illustrate the capacity and validity of the proposed procedure. In the first example, a closed-form limit state function is adopted to validate the SRSM by comparing it with the results obtained from a direct Monte Carlo simulation. In the second example, the serviceability performance of an underground cavern is analyzed to illustrate the capacity of the proposed procedure to handle a reliability problem with an implicit limit state function. The proposed procedure does not require the user to modify the existing deterministic finite element code. The deterministic finite element analysis and the probabilistic analysis are decoupled. This is a major practical advantage because realistic probabilistic analyses are made possible. The SRSM can produce sufficiently accurate reliability results. Furthermore, the method is much more efficient than the direct Monte Carlo simulation. Sensitivity analyses show the effect of the variability of input random variables and the correlation between them on: (1) the probability density functions, (2) the first four order statistical moments, and (3) the probability of failure, which is investigated and discussed.     

Assessment of strut forces for braced excavation in clays from numerical analysis and field measurements

One important consideration in the design of a braced excavation system is to ensure that the structural bracing system is designed both safely and economically. The forces acting on the struts are often determined using empirical methods such as the Apparent Pressure Diagram (APD) method developed by Peck (1969). Most of these empirical methods that were developed from either numerical analysis or field studies have been for excavations with flexible wall types such as sheetpile walls. There have been only limited studies on the excavation performance for stiffer wall systems such as diaphragm walls and bored piles. In this paper, both 2D and 3D finite element analyses were carried out to study the forces acting on the struts for braced excavations in clays, with focus on the performance for the stiffer wall systems. Subsequently, based on this numerical study as well as field measurements from a number of reported case histories, empirical charts have been proposed for determining strut loads for excavations in stiff wall systems.     

基坑土钉支护可靠性分析优化算法

针对基坑工程中岩土参数存在随机性和变异性的特点,基于响应面重构法、遗传算法和禁忌搜索方法研究了土钉墙边坡可靠性分析方法。考虑土钉的加固作用,建立了适用于土钉墙边坡任意形状滑面安全系数计算的改进Morgenstern-Price法。基于响应面原理,将改进Morgenstern-Price法取代传统响应面法中的有限单元法来随机抽样构造响应面函数,建立了一种近似的土钉墙边坡可靠度计算方法。以土体的抗剪强度指标 、 为随机变量,提出了一种能同时确定土钉墙边坡最小可靠度指标 及相应最危险滑面的全局优化计算方法--土钉墙可靠性分析自适应禁忌搜索遗传算法（ATSGA）。结合算例,分别以土钉墙边坡的最小可靠度指标和最小中值安全系数为目标函数,采用ATSGA法搜索其相应的最危险滑动面,结果表明,二者相差较大。     

盾构隧道开挖面稳定的可靠度研究

目前,盾构隧道开挖面稳定性评价方法均是确定性方法。为了考虑土体参数的变异性,提出用可靠方法来评价其稳定程度。采用数值模拟方法,研究了隧道开挖面极限支护压力。基于BP神经网络预测大量给定地层参数工况下的开挖面极限支护压力,对其进行统计,得其概率分布特征。在理论分析的基础上,结合工程实际,探讨了盾构施工土压力的确定原理。建立了隧道开挖面稳定的极限状态方程,对其进行了可靠度分析。该研究除能够科学、合理地评价开挖面的稳定程度外,对于盾构施工过程中合理地设定开挖面支护压力也具有一定的参考作用。