基于子集模拟的边坡可靠度分析方法研究

边坡稳定受到诸多不确定性因素的影响,比如土体性质的空间变异性以及地层情况的不确定性。这些不确定性因素的影响可以通过蒙特卡洛模拟(Monte Carlo Simulation, MCS)进行定量地分析。MCS概念简单并具有广泛的适用性。但是,在小概率失效区域内,MCS计算效率很低,需要庞大的随机样本量来保证一定的计算精度。本文提出了一种实用的边坡可靠度分析方法。通过采用一种高级的MCS方法(Subset Simulation, 子集模拟)来提高小概率区域内的计算效率以及计算精度,并以EXCEL的表单环境为平台,联合使用Visual Basic Application(VBA)编写计算程序。在该程序中,子集模拟、边坡稳定的确定性分析和不确定性分析分别由三个相对独立的计算模块实现。最后,本文以James Bay 土坝为例,简明地说明了所提出方法的有效性,并探索了临界滑动面的不确定性对边坡可靠度分析的影响。     

Incorporating installation effects into the probability analysis of controlled modulus columns

This technical report presents the probabilistic analysis which integrates the Monte Carlo simulation (MCS) with random field theory to model the load–displacement behavior of Controlled Modulus Columns (CMCs) in overconsolidated Poznań clay. Presented study focuses on the practical aspects of statistical analysis of geotechnical data, numerical model development, and results evaluation. Variability and spatial distribution of geotechnical parameters are based directly on field and lab testing. The inherent variability of soil parameters obtained from geotechnical investigation at the site is similar to the values reported in worldwide datasets for clays. The extensive discussion about incorporation of installation effects into numerical modelling is made. It was found that proper incorporation of installation effects is governed by correct estimation of initial stress level and interface shear strength parameters. The Anisotropic Undrained Shear Strength (AUS) model which captures nonlinear behavior and anisotropy of soil (Krabbenhøft et al., 2019) is a good choice to model overconsolidated clay in intact and interface zones. The application of total stress approach, the AUS model, installation effects, and natural (inherent) variability of soil and interface parameters is sufficient to explain differences in CMC load – displacement behavior observed in the field.     

Stability Analysis of Drilled Shafts Reinforced Slope

Drilled shafts have been used as an effective means to stabilize a soil slope with marginal safety factor. A limit equilibrium based slope stability analysis technique is presented in this paper that would allow for the determination of the safety factor of the reinforced slope and the forces acting on the drilled shafts. Specifically, the finite element analysis generated load transfer characteristic curves were incorporated into the traditional method of slice approach to account for the soil arching effects. Mathematical formulation of the proposed analysis method is given in detail, followed by validation of the approach with other analysis methods. Examples of the slopes with or without the drilled shafts are given to illustrate the reasonableness of the solution provided by the proposed approach. The efficiency of using drilled shafts to stabilize a slope is discussed by examing the influence of the shaft location, shaft size and spacing on the calculated safety factor. Finally, a practical case involving the use of the proposed approach is presented.     

Sensitivity analysis of vertically loaded pile reliability

The purpose of this paper is to examine the influence of geotechnical uncertainties on the reliability of vertically loaded pile foundations and the use of this information in decision-making support, especially when gathering the information necessary for reliability analyses. Two case studies of single pile foundations were selected, and each uncertainty source was investigated to identify which are the most important and influential in the evaluation of vertical pile resistance under axial loading. Reliability sensitivity analyses were conducted using FORM (the first-order reliability method) and MCS (Monte Carlo simulations). The characterisation of uncertainties is not an easy task in geotechnical engineering. The aim of the analyses described in this paper is to optimise resources and investments in the investigation of the variables in pile reliability. The physical uncertainties of actions, the inherent variability of soil and model error were assessed by experimental in situ standard penetration tests (SPT) or from information available in the literature. For the cases studied, the sensitivity analysis results show that, in spite of the high variability of the soils involved, model error also plays a very important role in geotechnical pile reliability and was considerably more important than soil variability in both case studies. From a comparison of the two reliability methods (FORM and MCS), it was concluded that FORM is applicable in simple cases and as a first approach because it is an approximate method and sometimes does not have the capability to incorporate every detail of the problem, namely a specific probability density function or more specific limit conditions.     

Reliability-based design in rock engineering: Application of Bayesian regression methods to rock strength data

Reliability-based design(RBD) is being adopted by geotechnical design codes worldwide, and it is therefore necessary that rock engineering practice evolves to embrace RBD. This paper examines the Hoek-Brown(He B) strength criterion within the RBD framework, and presents three distinct analyses using a Bayesian approach. Firstly, a compilation of intact compressive strength test data for six rock types is used to examine uncertainty and variability in the estimated He B parameters m and sc, and corresponding predicted axial strength. The results suggest that within-and between-rock type variabilities are so large that these parameters need to be determined from rock testing campaigns, rather than reference values being used. The second analysis uses an extensive set of compressive and tensile(both direct and indirect) strength data for a granodiorite, together with a new Bayesian regression model, to develop joint probability distributions of m and scsuitable for use in RBD. This analysis also shows how compressive and indirect tensile strength data may be robustly used to fit an He B criterion.The third analysis uses the granodiorite data to investigate the important matter of developing characteristic strength criteria. Using definitions from Eurocode 7, a formal Bayesian interpretation of characteristic strength is proposed and used to analyse strength data to generate a characteristic criterion.These criteria are presented in terms of characteristic parameters mkand s ck, the values of which are shown to depend on the testing regime used to obtain the strength data. The paper confirms that careful use of appropriate Bayesian statistical analysis allows the He B criterion to be brought within the framework of RBD. It also reveals that testing guidelines such as the International Society for Rock Mechanics and Rock Engineering(ISRM) suggested methods will require modification in order to support RBD. Importantly, the need to fully understand the implications of uncertainty in nonlinear strength criteria is identified.     

Shear load transfer for rock-socketed drilled shafts based on borehole roughness and geological strength index (GSI)

The load distribution and deformation of rock-socketed drilled shafts subjected to axial loads were evaluated by a load-transfer approach. The emphasis was on quantifying the shear load-transfer characteristics of rock-socketed drilled shafts based on constant normal stiffness (CNS) direct shear tests performed by varying major factors influencing shaft resistance, including unconfined compressive strength, borehole roughness, initial confining stress, pile diameter, and material properties. Based on the CNS tests and the Hoek–Brown failure criterion, a nonlinear triple curve is proposed for the shear load-transfer function of rock-socketed drilled shafts. It is presented in terms of borehole roughness and the geological strength index (GSI) so that structural discontinuity and surface conditions of the rock mass can be considered. The proposed function was verified by the load test results of ten rock-socketed drilled shafts subjected to axial loads. Seven piles were constructed in completely or moderately weathered rocks of granite-gneiss, and the others were constructed in slightly weathered rocks of clayshale-limestone. Through comparisons with results of load tests, it was found that the shear load-transfer function in the present study is in good agreement with the general trend observed by in situ measurements, and this represents a significant improvement in the prediction of drilled shaft shear behavior.     

考虑地层变异性和土体参数空间变异性的边坡可靠度全概率设计方法

目前边坡稳定设计研究中大多数考虑了土体参数的空间变异性,但忽略了地层变异性的影响。为此,提出了一种同时考虑这两类变异性的边坡可靠度全概率设计方法。在全概率设计框架内,将广义耦合马尔可夫链模型与随机场模型相耦合用于同时表征地层变异性和土体参数空间变异性,给出了所提方法的计算流程。利用澳大利亚珀斯市钻孔资料,以某边坡为例进行可靠度设计,为说明在边坡可靠度设计中同时考虑地层变异性和土体参数空间变异性的重要性,分析了仅考虑土体参数空间变异的情况,进一步分析了同时考虑两类变异性的情况,并对二者进行了比较。结果表明:所提出的边坡可靠度设计方法能够有效地考虑边坡中存在的地层变异性和土体参数空间变异性。当仅考虑土体参数空间变异性时,边坡可靠度设计结果很大程度上取决于所采用地层的分布情况,特别是地层分布中抗剪强度较强土体类型占比高于真实情况时,将导致得到的最优设计方案偏于危险。反之,若地层分布中抗剪强度较弱的土体类型占比高于真实情况,得到的最优设计方案偏于保守。因此,为准确地得到最优设计方案,在边坡可靠度设计中应同时考虑地层变异性和土体参数空间变异性的影响。     

Point bearing stiffness and strength of socketted drilled shafts in Korean rocks

The load distribution and deformation of rock-socketted drilled shafts subjected to axial loads were evaluated via a load-transfer approach to quantify the point bearing load transfer characteristics of rock-socketted drilled shafts based on Hoek-cell triaxial compressive tests and a three-dimensional numerical analysis with varying rock strengths and rock mass conditions. It was found that the ultimate unit point resistance (q_max) was influenced by rock mass discontinuities; moreover, the initial tangent of the point bearing load transfer curve (G_i) was highly dependent on the rock mass modulus and pile diameter. Thus, a point bearing load transfer function for drilled shafts socketted into rock is proposed. Through comparison with the results of field loading tests, it was found that the point load transfer function proposed in the present study is in good agreement with the general trend observed by field loading tests.     

考虑参数空间变异性的失稳边坡参数概率反分析

概率反分析能够有效地考虑岩土体参数不确定性并融合现场监测数据和观测信息等更新岩土体参数统计特征,进而使得边坡稳定性评价更为符合客观工程实际,然而目前参数概率反分析几乎没有考虑参数固有空间变异性的影响。结合多重响应面和子集模拟提出了考虑岩土体参数空间变异性的边坡参数概率反分析方法,并以芝加哥国会街切坡为例,融合边坡失稳和滑动面入滑点与出滑点的大致位置这两个现场观测信息,概率反分析得到边坡不排水抗剪强度参数的后验统计特征。结果表明:本文提出方法可以有效地解决考虑参数空间变异性的低概率水平边坡参数概率反分析问题,具有较高的计算效率。子集模拟中每层随机样本数目对计算结果具有重要的影响,常用的500组样本点难以获得满意的计算结果。此外,土体参数空间变异性对概率反分析计算结果具有重要的影响,考虑参数空间变异性边坡参数由平稳随机场更新为非平稳随机场,与工程实际相符,然而忽略参数空间变异性更新后的参数仍服从平稳分布。     

A New Approach to Estimate Side Resistance of Rock Socketed Drilled Shafts

The uniaxial compressive strength of intact rock is widely used as the sole factor to estimate the side resistance of drilled shafts socketed in rock. However, the side resistance should also depend on in situ rock mass characteristics such as rock type, strength, joint frequency, and weathering conditions. In this study, a new approach is proposed to estimate the side resistance of rock socketed drilled shafts. The approach is based on the GSI rock mass classification, and the Hoek and Brown failure criterion. Inclusion of all these factors into the proposed method explains, to some extent, the differences that are obtained when various empirical methods are used. Comparisons between observed side resistances from field case studies and estimated side resistances with the proposed method show a good correlation. The method appears to be robust since the results are relatively insensitive to estimation from the different rock mass classification and properties and are comparable with predictions from previous empirical correlations.     

Evaluation of interpretation criteria for drilled shafts with tip post-grouting

This paper evaluates the effects of tip post-grouting on various capacity interpretation criteria for drilled shafts under compression loading. A wide array of load test data for drilled shafts constructed using three post-grouting methods, including tube-a-manchette, flat jack, and jet grouting, is utilized for the analysis. The load tests were divided based on the different tip post-grouting methods, then they were further divided based on the soil conditions (undrained or drained). The interpreted capacity and displacement at the interpreted capacity are examined for each interpretation criterion. Furthermore, the interpreted results were compared with current studies on drilled shafts that are not subjected to tip post-grouting techniques to determine the effects of post-grouting methods. Based on these analyses, the normalized load–displacement curves and the relationships between various interpretation criteria for drilled shafts with tip post-grouting are established. The drilled shafts subjected to any post-grouting method produced higher capacity and yield larger displacement with the same amount of normalized capacities for undrained and drained soils compared to drilled shafts not subjected to any post grouting procedures. Among the three grouting methods studied, the jet grouting method can produce a greater capacity than the other methods, especially for drained soil conditions. Finally, specific recommendations to guide the design of drilled shafts with tip post-grouting are provided.     

The systematic use of geotechnical data for characterization of transportation routes

An integrated system approach is presented describing the acquisition, organization and development of route geotechnical data/information for use in planning, analysis and design of complex transportation facilities in geo-technically variable terrain. A unified landform-based approach to geotechnical route characterization is conceptually delineated and formalized. Geotechnical functions required to process data are identified, defined, and integrated into a system within the overall facility design process. Probabilistic techniques used within the characterization approach can objectively consider geotechnical variability and uncertainty including limitations in available geotechnical data/ information. Procedures presented here provide geotechnical tools for project planning, analysis and design of transportation routes.     

Statistical analyses of inherent variability of soil strength and effects on engineering geology design

Clayey soil strata, as all natural deposits, generally show variability in the values of their geotechnical properties. This is due mainly to geological and environmental processes such as deposition and diagenesis, which introduce heterogeneity, anisotropy and variability to soil properties. Other causes of variability, and thus uncertainty, are the representativeness of samples and errors related to testing procedure, measurement and data processing procedures. To improve our knowledge about the inherent variability in the geomechanical properties of clays, this work presents a case study related to the analysis of the strength variability along a log of marine stiff clay deposits, which are apparently quite homogeneous. The analysis was based on pocket penetrometer strength measurement, performed both punctually and across the whole deposit. The adopted testing procedure, which is fast and reliable, provides a really wide dataset of the investigated soil property, with more than 800 data points. These allow for detailed variability analysis, and a reliable estimation of the coefficient of variation as well as research into the best fitting probability density functions, which are key factors for robust design. The presented case study allows discussion of the inherent variability of soil properties, and its influence on the characteristic values of soil strength in geotechnical design.     

Hydromechanical effects of shaft sinking at the Sellafield site

Under the auspices of the DECOVALEX II project, the coupled hydromechanical responses, in the fractured volcanic rocks at Sellafield site, to a pump test and shaft sinking were studied. The aim of this paper is to describe the methodology for determining the hydromechanical effects of the shaft excavation. This methodology is based on the discrete fracture network (DFN) approach for hydraulic analysis and the discrete approach, where the main discontinuities are explicitly represented in the mechanical model. The principal advantage of using the DFN approach is to easily change the scale of the study without important modifications of the network. Hydraulic properties of the different types of discontinuities were evaluated by calibration of the flow rates induced by a long-term pump test in borehole RCF3 drilled on the centreline of one of the proposed shafts. The same fracture network generated to analyse the RCF3 pump test was used to predict the hydromechanical responses of the rock mass to the excavation of a shaft centred on the RCF3 borehole. This methodology offers some additional possibilities such as studies of the excavation damaged zone (EDZ) and its influence on hydraulic conductivity.     

Proposed point bearing load transfer function in jointed rock-socketed drilled shafts

The point bearing behavior of rock-socketed drilled shafts under axial loading is investigated by numerical analysis and a load transfer approach (q–w). A numerical analysis using the distinct element method (DEM) is carried out to investigate the effects of pile diameter and the elastic modulus, discontinuity spacing and the inclination of rock mass on the point bearing behavior. The emphasis is quantifying the point bearing mechanism by taking rock discontinuity into consideration based on field loading tests performed on 39 instrumented piles. A new hyperbolic q–w function is proposed considering the point bearing resistance influence factors, including rock mass discontinuity. Through comparisons with other field data, the proposed q–w function represents a significant improvement in the prediction of the point bearing load transfer characteristics of jointed rock-socketed drilled shafts.     

冻结岩石细观结构及温度场数值模拟研究

冻结岩石是一种内部结构及其复杂的岩土工程材料,热学特性与其细观结构密不可分.随着计算机技术的飞速发展,数字图像处理技术已经越来越多地应用于岩土工程领域.利用数字图像处理技术建立冻结岩石的细观结构模型,精确地描述页岩内部的空间结构及细观介质分布的几何形态.利用几何矢量转换技术,将细观结构模型转换为有限元物理模型,分析了负温条件下非均质冻结岩石冻融循环过程中的温度场分布规律.数值模拟结果表明:岩石的细观结构决定了冻融岩石温度场的分布形态,对岩石冻融损伤破坏过程产生不可忽视的影响.文章所提出的方法可实现考虑冻融岩石细观结构的冻土热、力学特性的定量分析.     

Numerical analysis of a laterally loaded shaft constructed within an MSE wall

Drilled shafts have been widely used to support lateral loads from superstructures. For typical applications, design methods are available to generate lateral load versus displacement curves and to estimate ultimate lateral capacity and displacement of the drilled shaft under a certain lateral load. However, occasionally drilled shafts have to be constructed within the reinforced zones of MSE walls, for instance drilled shafts supporting sound walls, traffic signs, billboards, and other superstructures. Under these circumstances, existing design methods are not applicable because of: (1) the limited horizontal extent of the soil mass; (2) the resistance from reinforcement; and (3) the influence of MSE wall facing. In this regard, a full-scale field study was conducted to investigate the behavior of shafts within the MSE wall, subjected to lateral loads. The test wall was 43 m long and 6 m high and constructed with layers of uniaxial geogrid and selected backfill. Three-dimensional numerical analyses were performed prior to the construction of this test wall (i.e., Class-A prediction) to guide its design and after the field test using the actual material properties (i.e., Class-C prediction). The selected test shaft for the analyses in this study was located at 1.8 m behind the wall facing. The numerical results from the Class-A and Class-C predictions are compared with the field data. The study showed that the Class-A prediction provided useful information for the design of the test wall and development of field test details. The Class-C prediction improved the overall accuracy of the calculations and could serve as a reference for future study.     

基于响应面与重要性抽样的岩土工程可靠度分析方法研究

 由于功能函数非线性强且难以显式表达,岩土工程可靠度分析以往多采用响应面方法解决,但其求解的可靠度指标为几何可靠度。阐明几何可靠度与一般可靠度的实质和两者之间的差异,指出对于功能函数非线性较强的岩土工程问题,采用几何可靠度指标存在较大误差,需进行改进。然后引入V空间重要抽样方法将基本变量随机空间通过Rosenblatt变换和线性正交变换转换至V空间,在响应面方法得到岩土工程的设计验算点及其附近的响应面的基础上,采用重要性抽样方法求解岩土工程可靠度。几个数值算例和工程实例的对比分析表明该方法可行、有效、精度较高,适用于非线性强的岩土工程可靠度求解。     

Application of subset simulation methods to reliability benchmark problems

This paper presents the reliability analysis of three benchmark problems using three variants of Subset Simulation. The original version of Subset Simulation, SubSim/MCMC, employs a Markov chain Monte Carlo (MCMC) method to simulate samples conditional on intermediate failure events; it is a general method that is applicable to all the benchmark problems. SubSim/Splitting is a variant of Subset Simulation applicable to first-passage problems involving deterministic dynamical systems. It makes use of trajectory splitting for generating conditional samples. Another variant, SubSim/Hybrid, uses a combined MCMC/Splitting strategy and so it has the advantages of MCMC and splitting; it is applicable to uncertain and deterministic dynamical systems. Results show that all three Subset Simulation variants are effective in high-dimensional problems and that some computational efficiency can be gained by exploiting and incorporating system characteristics into the simulation procedure.     

考虑岩土参数空间变异性的盾构隧道地表沉降分析

现有随机场理论能够较好地描述单一岩土参数的天然随机性、空间结构性和局部奇异性。当前面临的挑战是如何考虑多个土层、多元及统计相关的岩土参数空间变异性对岩土工程的影响。考虑岩土参数如黏聚力、内摩擦角和压缩模量等具有明显的空间变异性,将随机场理论引入盾构隧道地表沉降可靠指标分析。主要研究工作包括:(1)采用局部均值方法将多个非平稳土层同一岩土参数转化为平稳各向异性随机场变量,并给出随机场的统计特征;(2)简化岩土参数的空间变异性为一般变异性,直接采用响应面方法计算盾构隧道地表沉降可靠指标;(3)提出协同序贯高斯离散算法,在空间网格上实现多元岩土参数随机场的同步离散化,并基于经典Monte-Carlo随机模拟原理和盾构隧道数值计算,直接统计地表沉降的可靠指标;(4)引入子集Monte-Carlo随机模拟加速算法。将以上方法应用于天津~#5、~#6地铁环湖西路站—宾馆西路站区间盾构隧道四线交叠工程,结果表明,采用经典随机理论描述岩土参数的变异性,所得到的盾构隧道地表沉降可靠指标小于基于随机场理论的对应值。该结论为复杂盾构隧道的施工控制与设计优化提供了理论依据。