Robust geotechnical design of shield-driven tunnels

This paper presents a fuzzy set-based robust geotechnical design (RGD) methodology for the design of shield-driven tunnels. Here, uncertain geotechnical parameters required for analysis of tunnel performance (referred to herein as the structure safety and serviceability performance of tunnel cross section) are represented as fuzzy sets. Given fuzzy input parameters, the performance of a shield-driven tunnel will be uncertain, which is expressed in this study as a fuzzy factor of safety, according to the analysis of vertex method. Then, the fuzzy factor of safety for a given design is used to evaluate the failure probability and design robustness, which are, in turn, employed in the proposed RGD framework. Note that a design is considered robust if the performance of the shield-driven tunnel is insensitive to the variation of its uncertain geotechnical parameters. Within the RGD framework, each candidate design in the design space is analyzed for its safety state (in terms of failure probability), design robustness, and cost. The goal of the RGD of a shield-driven tunnel is to bring the safety state to an acceptable level, while maximizing the robustness and cost efficiency simultaneously. To this end, a multi-objective optimization is performed and a Pareto front is obtained, which provides a trade-off that may be used to select the most preferred design. Through an illustrative case, the effectiveness and significance of this new robust design methodology is demonstrated.     

Robust design in geotechnical engineering – an update

This paper presents an update for the robust geotechnical design (RGD) methodology, which seeks an optimal design with respect to design robustness and cost efficiency, while satisfying the safety requirements. In general, the design robustness is achieved if the system response is insensitive to the variation in the uncertain input parameters (called “noise factors”). In other words, a design is considered robust if the system response exhibits little variation, even though there is high variation in the input parameters. Robust design achieves this desirable outcome by carefully adjusting ‘design parameters’ (i.e., the parameters that can be controlled by the designer, such as the geometry and dimensions) without reducing the uncertainty in the noise factors. In this paper, the existing RGD methodology is updated with a gradient-based robustness measure and a simplified procedure for seeking the knee point. The RGD methodology and its simplified version (with new updates) are illustrated with three design examples. The results presented in this paper show that the RGD methodology and its simplified version are effective design tools that considers safety, cost and design robustness simultaneously. The advantages of the simplified RGD approach are discussed.     

Robust design of rock slopes with multiple failure modes: modeling uncertainty of estimated parameter statistics with fuzzy number

The variability of shear characteristics of rock discontinuities is often difficult to ascertain. Thus, even with the reliability-based design (RBD) approach, which allows for consideration of the uncertainty of input parameters, the design of a rock slope system may be either cost-inefficient (overdesign) or unsafe (under-design), depending on whether the variation of input parameters is overestimated or underestimated. The uncertainty about the variation of input parameters is a critical issue in a RBD. This paper presents a feasible approach to addressing this problem using robust design concept. First, the uncertainty of the estimated statistics of input parameters (such as rock properties) is represented by fuzzy sets, which requires only the knowledge of lower and upper bounds of the estimated statistics. Then, the robust design concept is implemented to ensure that the final design is insensitive to, or robust against, the uncertainty of the estimated statistics of input parameters. The design methodology is demonstrated with an application to the design of a rock slope system with multiple failure modes. This design methodology, termed robust geotechnical design (RGD), aims to achieve a certain level of design robustness, in addition to meeting safety and cost requirements. In this paper, the RGD framework is realized through a multi-objective optimization, as it involves three requirements, safety, cost, and robustness. The significance of the design methodology is demonstrated with an example of rock slope design.     

Simplified procedure for reliability-based robust geotechnical design of drilled shafts in clay using spreadsheet

This paper provides a simplified procedure for reliability-based robust geotechnical design (RGD) using spreadsheet. In the RGD methodology, design robustness is achieved by adjusting “design parameters” without reducing the uncertainties in noise factors. This design approach generally involves a multi-objective optimisation, which is computationally challenging. To improve the efficiency of the RGD methodology, the design robustness is evaluated in terms of sensitivity index and the safety requirement is evaluated using mean value first order second moment (MFOSM). To ease the concern that the reliability index obtained with MFOSM may not be sufficiently accurate, a mapping function that relates MFOSM to a more accurate method such as first order reliability method is introduced. To further improve the efficiency of the proposed simplified RGD method, a new simplified procedure along with a more accurate robustness measure is developed that eliminates the need for multi-objective optimisation. With these modifications, the proposed simplified RGD method can efficiently be implemented in a single Excel spreadsheet. The proposed simplified method, which goes beyond any existing reliability-based RGD methods in terms of ease of use and computational efficiency, is illustrated in this paper with an example of robust design of drilled shaft in clay.     

Reliability-based robust design for reinforcement of jointed rock slope

Traditional reliability-based design methodologies often involve selection of design which is of lowest cost and satisfies safety requirements. But, this design is sensitive to variation in statistics of input parameters (noise parameters) and might become unsatisfactory if an underestimation of coefficient of variation of input parameters is made. A relatively new design methodology known as robust geotechnical design (RGD) is applied for the case of reinforcement of rock slope using end-anchored rock bolts. This ensures selection of a cost-effective and safe design for which probability of failure (P_f) of reinforced rock slope is least sensitive to the noise parameters. Reliability-based RGD approach involves evaluation of P_f for each design with different possible noise parameters. Finding P_f for the complex geotechnical structure is computationally expensive, and thus an augmented radial basis function-based response surface is used as a surrogate to the finite element model of rock slope. This response surface, being very efficient, also performs well for a range of values of noise parameters. Later, minimum distance algorithm is applied to obtain a cost-effective and robust design. Finally, a comparison is made in the costs between two robust designs obtained for different target probability of failure for the same rock slope.     

柱下独立基础稳健性设计与分析

岩土工程随机参数统计特征的不确定性,使得岩土工程可靠度设计存在一定风险。岩土工程稳健性设计能够充分考虑随机参数的不确定性结合结构安全性、稳健性和经济性实现最优设计。针对随机参数统计特征的不确定性对柱下独立基础设计的影响,基于可靠度理论和岩土工程稳健性设计方法,考虑岩土参数、混凝土和钢筋材料力学参数统计特征不确定性的影响,以独立基础几何尺寸作为可控设计参数进行设计分析。将独立基础地基承载力、地基变形、基础结构冲切破坏和基础弯曲破坏4种失效模式视为串联系统,进行多失效模式下的结构体系稳健性设计,分析了多失效模式下结构几何参数与结构体系可靠度的关系。结合稳健性和经济性,进行了独立基础多目标优化设计,确定柱下独立基础设计的最优解。     

Calibration of resistance factor for design of pile foundations considering feasibility robustness

The resistance factor for pile foundations in load and resistance factor design (LRFD) is traditionally calibrated considering target reliability index (β_T) and statistics of load and resistance bias factors. However, the resistance bias factor is hard to quantify statistically. Consequently, the design obtained using the calibrated resistance factor can still miss β_T if the variation in resistance bias factor has been underestimated. In this paper, we propose a new resistance factor calibration approach to address this dilemma by considering “feasibility robustness” of design in the calibration process. Herein, the feasibility robustness is defined as a probability that the β_T requirement can still be satisfied even in the presence of uncertainty or variation in the computed bearing capacity. For illustration, LRFD approach for pile foundations commonly used in Shanghai, China is examined. Emphasis is placed on re-calibration of resistance factors at various feasibility robustness levels, with due consideration of the variation in the resistance bias factor. A case study is presented to illustrate the use of the re-calibrated resistance factors. The results show that the feasibility robustness is gained at the expense of cost efficiency; in other words, the two objectives are conflicting. To aid in the design decision-making, an optimal feasibility robustness level and corresponding resistance factors are suggested in the absence of a designer’s preference.     

我国北方新生代玄武岩地下水化学特征及其成因：以河北省张北县为例

为了进一步了解我国北方新生代玄武岩地下水的赋存规律和形成演化机理,以河北省张北县玄武岩地下水为研究对象,在野外采集地下水样、测定水化学和同位素组成的基础上,利用统计分析、离子比例系数、氢氧同位素、反向地球化学模拟等方法,对区内玄武岩地下水的水化学形成机制进行了研究。结果表明：沿地下水径流方向,研究区内玄武岩地下水中多数离子质量浓度呈现增大趋势,补给区的地下水化学类型以HCO3Ca·Mg为主,TDS质量浓度多小于500 mg/L,排泄区地下水中阴离子以Cl-和SO2-4为主,阳离子以Na+为主,TDS质量浓度多大于1 400 mg/L;研究区地下水补给来源为当地大气降水;硅铝酸盐、岩盐、硫酸盐的风化溶解是地下水中离子的主要来源;溶滤作用、阳离子交替吸附作用和农业施肥等人类活动影响是控制地下水化学形成的主要作用。     

Response surface-based robust geotechnical design of supported excavation – spreadsheet-based solution

ABSTRACT

The robust geotechnical design (RGD) approach which involves optimization to obtain a design that is safe, cost-efficient, and robust in the face of uncertainties, can be computationally challenging for complex geotechnical structures. In this study, the RGD approach has become practical by introducing a response surface as a surrogate to finite element- or finite difference-based computer code that is used for analyzing the system, and developing a fast algorithm for the optimization process. For demonstration purposes, a real-world supported excavation project is designed using this modified RGD approach and it is compared with the one designed by a local expert.     

Distribution of the factor of safety,in geotechnical engineering,for independent piecewise linear capacity and demand density functions

In many geotechnical engineering cases, the factor of safety may be defined as the ratio of the capacity, of the geotechnical structure or its support elements, to the pertinent demand. By representing the capacity and the demand as independent piecewise linear random variables, an analytic solution is obtained for the probability density and cumulative distribution functions of the factor of safety. Thus, solutions for the calculation of the mean value, the standard deviation and the minimum and maximum values of the factor of safety, are provided. Application of the developed analytical solutions, to the probabilistic analysis of a published case of rock spalling in a deposition tunnel complex, follows. The methodology allows for the parametric evaluation of the effect of specific design variables to the distribution of the safety factor and to the probability of failure. The closed form solution may be programmed as a computer code that may run easily on a tablet or netbook or even on a smartphone. It proves useful for the probabilistic design of a variety of geotechnical applications, such as foundations, tunneling, mining, underground roof reinforcement, and earth retaining structures, and permits decisions to be taken in terms of risk and reliability.     

Simultaneous Design Characteristics Optimization in an Earth Retaining Structure

The aim of this paper is to present a method for simultaneous optimization of the design characteristics of an earth retaining structure design using quality tools. The design characteristics examined in this paper are safety factor, total displacements and cost. The methodology for the multi-response optimization used is the desirability analysis which gives the appropriate combinations for the design variables. Through standard experimental runs, we process the results for this optimization. The experimental measurements are calculated via finite elements analysis. The designs used are taken from two real-life case studies. This methodology is intended as a guide tool for civil and geotechnical engineers to predict the values of the design variables as long as they can be named and take discrete values. The uniqueness in this study is that approved experimental methodology can simultaneously optimize the design characteristics of an earth retaining structural design, which were until now calculated empirically.     

Spatial estimation of geotechnical parameters for numerical tunneling simulations and TBM performance models

In this paper, we further elaborate on a methodology dedicated to the modeling of geotechnical data to be used as input in numerical simulation and TBM performance codes. The expression “geotechnical data” refers collectively to the spatial variability and uncertainty exhibited by the boundaries and the mechanical or other parameters of each geological formation filling a prescribed 3D domain. Apart from commercial design and visualization software such as AutoCAD Land Desktop^® software and 3D solid modelling and meshing pre-processors, the new tools that are employed in this methodology include relational databases of soil and rock test data, Kriging estimation and simulation methods, and a fast algorithm for forward or backward analysis of TBM logged data. The latter refers to the continuous upgrade of the soil or rock mass geotechnical model during underground construction based on feedback from excavation machines for a continuous reduction of the uncertainty of predictions in unsampled areas. The approach presented here is non-intrusive since it may be used in conjunction with a commercial or any other available numerical tunneling simulation code. The application of these tools is demonstrated in Mas-Blau section of L9 tunnel in Barcelona.     

An intelligent multi-objective EPR technique with multi-step model selection for correlations of soil properties

Current multi-objective evolutionary polynomial regression (EPR) methodology has difficulties on decision-making of optimal EPR model. This paper proposes an intelligent multi-objective optimization-based EPR technique with multi-step automatic model selection procedure. A newly developed multi-objective differential evolution algorithm (MODE) is adopted to improve the optimization performance. The proposed EPR process is composed of two stages: (1) intelligent roughing model selection and (2) model delicacy identification. In the first stage, besides two objectives (model accuracy and model complexity), the model robustness measured by robustness ratio is considered as an additional objective in the multi-objective optimization. In the second stage, a new indicator named selection index is proposed and incorporated to find the optimal model. After intelligent roughing selection and delicacy identification, the optimal EPR model is obtained considering the combined effects of correlation coefficient, size of polynomial terms, number of involved variables, robustness ratio and monotonicity. To show the practicality of the proposed EPR technique, three illustrative cases helpful for geotechnical design are presented: (a) modelling of compressibility, (b) modelling of undrained shear strength and (c) modelling of hydraulic conductivity. For each case, a practical formula with better performance in comparison with various existing empirical equations is finally provided. All results demonstrate that the proposed intelligent MODE-based EPR technique is efficient and effective.

     

再论岩土工程有限元方法的应用问题

岩土工程数值分析方法对于研究复杂的岩土介质与多变的施工措施是一种得力的方法,比传统的解析方法、室内试验方法、模拟试验方法、现场试验方法等具有无可替代的优越性。按岩土工程数值方法的历史发展、作用及发展方向,将其分为4个层次：作为一种高级计算器,直接为某个具体岩土工程的设计服务,对该岩土工程在各种极端设计工况下进行安全性、稳定性的计算分析;作为一种强大的、无与伦比的模拟分析器,对复杂工况条件下复杂岩土工程的各种不利因素的相互作用、相互影响、耦合效应等进行模拟分析;作为一种无成本、可重复的多功能试验机,探索具体岩土工程的稳定机制或某工程措施的加固机制;作为岩土工程数值方法的终极目标,对数值分析方法进行二次开发——研发智能化、快速化、简便化的新型数值分析工具。对这4个层次进行了讨论,并对每个层次进行举例说明。     

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.     

福州轨道交通建设中的岩土工程问题

由于福州盆地工程地质条件的复杂性以及隧道工程的特殊性,在福州轨道交通建设过程中将遇到大量环境岩土工程问题。主要的环境岩土工程问题有:(1)隧道掘进范围内的承压含水层。承压含水层富水性、透水性强,由于开挖深度大,必须考虑下部承压水的影响,避免产生基坑突涌问题。砂砾卵石层直接覆盖于基岩裂隙热水上,受热水构造带高温热水的直接补给以及热传导,地下轨道交通建设对地热场是否存在影响以及地热对轨道交通的影响需要深入研究。(2)软土的大变形与低强度。导致地基失稳与土体结构强度破坏。(3)深大基坑开挖施工引发的可能灾变。基坑开挖易产生滑塌、流泥、突水(涌)、地表沉陷等问题,必须采取有效的支护措施,避免基坑失稳而影响工程安全及周边环境。对这些环境岩土工程问题,应加强勘察新技术的应用,查明建设场地岩土工程地质条件;采用人工地层冻结法、桩基托换技术进行施工;开发和利用适合本地区岩土条件的新技术、新工艺,如新型桩、新的止水、降水措施等基坑支护新技术,以及采用信息化施工新技术。     

路堤边坡稳定可靠度计算中的模型不确定性分析

基于均质路堤边坡Monte Carlo法的稳定可靠度计算,分析了临界滑面搜索策略和稳定分析方法两类模型不确定性对边坡可靠度的影响特性,讨论了边坡失效概率随土工参数变异性的变化规律。研究表明,选用不同的临界滑面搜索策略所得可靠度结果差异不大,参数滑面法（overall slope）的失效概率略大于均值滑面法（global minimum）,但差别对边坡稳定性分析没有实质性影响;土性参数变异水平是影响边坡可靠度的最重要因素,边坡在相同设计参数安全系数下的可靠度指标随参数变异性增大而急剧降低;不同稳定性分析方法对应的安全系数概率密度函数曲线形态基本一致,但失效概率差异明显,因此目标可靠度指标取值应与稳定性分析方法相适应。提出的考虑土工参数变异水平的安全系数取值修正原则,对改进确定性设计的边坡稳定分析技术有积极意义。     

Combined methodology for three-dimensional slope stability analysis coupled with time effect: a case study in Germany

High-steep slopes in open pit mines are much more likely to collapse due to mining operations. Challenges such as data acquisition, precise numerical models and adaptable methodologies have impeded more reliable results of slope stability analysis based on the current methods. Within this context, this paper proposes a combined methodology using light detection and ranging technology to capture high-resolution slope geometry, three-dimensional geological and geotechnical modeling technologies for creating high-quality numerical simulation models and finite-element slope stability analyses combined with a new automatic strength reduction technique to analyze complex geotechnical problems. At the end, the methodology introduces a time series analysis to improve the reliability of the calculated factor of safety. A case study in the deepest open pit mine in Hambach, Germany, was conducted to test and demonstrate the effectiveness and applicability of the proposed methodology.     

浅论岩土工程极限状态设计基本思想

论述了岩土工程极限状态设计的基本思想,包括极限状态的概念、土工参数设计值的确定过程和方法、构造物的重要度和场地地基复杂程度的划分、岩土工程类别、作用载荷组合、分项安全系数和极限状态设计等;给出了土工参数的实测值、导出值、标准值和设计值的确定原则或方法;指出在极限状态设计中,可通过增大设计作用效应或降低设计抗力的方法来进行岩土工程的可靠性设计.     

Heat-exchanger piles for the de-icing of bridges

Of the various types of road structures, bridges are the most exposed to icing; the problem of icing is widely addressed through salting, which reduces the lifespan of the bridge. One promising solution to avoid the use of salt is the seasonal storage of solar heat energy captured directly through the asphalt layer; however, this solution can only be achieved cost effectively if a necessary geostructure is used as a heat exchanger. In this study, such an approach is studied for a bridge crossing a canal, and the geotechnical and energy-related challenges of such a solution are discussed. Bridge piers and abutments are located on piles, which are used as heat exchangers. Depending on local conditions, seasonal storage and natural thermal reload are two possible solutions for the operation of such a system. In particular, the presence of underground water flow is thought to be a significant factor in such a design and is considered here. This study aims to determine the geotechnical and energy design parameters through thermo-hydro-mechanical simulations. A three-dimensional finite-element model analysis is necessary given the distance between bridge piles. Various underground water flow scenarios are studied. The capture of energy and de-icing requirements is based on the few existing structures that use other means of energy exchange with the ground. The results indicate that the use of heat-exchanger piles for de-icing bridges can only be considered at specific sites; however, the efficiency of the solution at those sites is high. Possible foundation and structure stability problems are also considered, such as vertical displacements due to the dual use of the foundation piles.