A generalized surrogate response aided-subset simulation approach for efficient geotechnical reliability-based design

This paper aims to develop an efficient geotechnical reliability-based design (RBD) approach using Monte Carlo simulation (MCS). The proposed approach combines a recently developed MCS-based RBD approach, namely expanded RBD approach, with an advanced MCS method called “Subset Simulation (SS)” to improve the computation efficiency at small probability levels that are often concerned in geotechnical design practice. To facilitate the integration of SS and expanded RBD, a generalized surrogate response f is proposed to define the driving variable, which is a key parameter in SS, for expanded RBD of geotechnical structures (e.g., soil retaining structures and foundations). With the aid of the proposed surrogate response, failure probabilities of all the possible designs in a prescribed design space are calculated from a single run of SS. Equations are derived for integration of the surrogate response-aided SS and expanded RBD, and are illustrated using an embedded sheet pile wall design example and two drilled shaft design examples. Results show that the proposed approach provides reasonable estimates of failure probabilities of different designs using a single run of the surrogate response-aided SS, and significantly improves the computational efficiency at small probabilities levels in comparison with direct MCS-based expanded RBD. The surrogate response-aided SS is able to, simultaneously, approach the failure domains of all the possible designs in the design space by a single run of simulation and to generate more complete design information, which subsequently yields feasible designs with a wide range of combinations of design parameters. This is mainly attributed to the strong correlation between the surrogate response and target response (e.g., factor of safety) of different designs concerned in geotechnical RBD.     

极限平衡条件的拓展与土工结构稳定分析

与土体稳定有关的工程问题诸如挡土结构物上的土压力、地基承载力以及土坡稳定性都与土的极限平衡状态相关 联。将土体一点（单元）的极限平衡条件推广,给出土体沿滑动面的极限平衡条件,证明了该条件的充分必要性。依据该条件,提出了有限元应力分析与极限平衡结合的有限元极限平衡法及土体稳定的安全系数,并明确了安全系数的物理意义,以评价土工结构的稳定性。随后,列举了该方法在土工结构稳定分析中的一些具有代表性的应用,证明了该法是有效的,可以用于分析岩土工程中的稳定问题。     

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.     

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.     

A one-dimensional integral approach to calculating the failure probability of geotechnical engineering structures

This study focuses on the geotechnical engineering structures with implicit or unknown expressions of performance functions. A one-dimensional integral approach (ODIA) consisting of sampling, evaluation of statistical moments for multivariable functions, probability density function fitting, and simple integration of failure probability was developed through system integration. A convergence study of an illustrative example was conducted, and the error analysis revealed that the accuracy of ODIA is equivalent to that of the second-order reliability method. Applications of ODIA to a slope and surrounding rock of an excavation were presented to further confirm the accuracy, efficiency, and practicability of the approach.     

边坡安全系数的多解性讨论

边坡安全系数计算结果直接影响边坡工程设计,而极限平衡法不能给出唯一的安全系数值,研究边坡安全系数的多解性,有助于对边坡稳定性计算结果有一个合理地判断与取舍。先假定滑面正应力的初始分布,然后采用含有3个待定参数的拉格朗日函数对其修正,保证滑体满足所有的力与力矩平衡条件;设定一系列安全系数分别求解平衡方程组,得到对应的待定参数值;最后根据滑面正应力分布的合理性判断边坡安全系数的合理范围。算例表明,圆弧滑面合理安全系数范围在5 %以内,而任意形状滑面安全系数最大取值范围可达15 %。     

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.     

重力式挡土墙抗滑稳定容许安全系数取值标准初探

我国水工挡土墙设计规范中规定稳定性验算采用以安全系数为度量指标,给定的安全系数允许值范围在1.20～1.35之间,低于国外规范的取值。采用可靠度分析方法,建立目标可靠指标与安全系数之间的定量关系。通过分析计算确认安全系数满足对数正态分布。对一个目标可靠指标为3.2的特例获得其安全系数在1.43～1.55之间的结论。根据前期提出的相对安全率指标判据提出了安全系数满足对数正态条件下的计算公式。使用这一判据,论证了将这一特例扩展到不同墙体几何参数和强度指标参数情况时这一可靠指标和安全系数关系的普遍适用性。提出的安全系数取值标定方法和相应成果可供规范修订工作参考。     

Reliability assessment of serviceability performance of braced retaining walls using a neural network approach

In urban environments, one major concern with deep excavations in soft clay is the potentially large ground deformations in and around the excavation. Excessive movements can damage adjacent buildings and utilities. There are many uncertainties associated with the calculation of the ultimate or serviceability performance of a braced excavation system. These include the variabilities of the loadings, geotechnical soil properties, and engineering and geometrical properties of the wall. A risk‐based approach to serviceability performance failure is necessary to incorporate systematically the uncertainties associated with the various design parameters. This paper demonstrates the use of an integrated neural network–reliability method to assess the risk of serviceability failure through the calculation of the reliability index. By first performing a series of parametric studies using the finite element method and then approximating the non‐linear limit state surface (the boundary separating the safe and ‘failure’ domains) through a neural network model, the reliability index can be determined with the aid of a spreadsheet. Two illustrative examples are presented to show how the serviceability performance for braced excavation problems can be assessed using the reliability index. Copyright © 2005 John Wiley & Sons, Ltd.     

既有地铁车站结构安全性评估方法研究

运用有限元程序及有限差分程序研究了新建地下风险工程对既有地铁车站结构的影响。结合既有车站双层风道与西南出入口结构之间的新建3号联络通道施工引起的位移分析,阐述了不同数值方法用于近接工程施工安全性评估的特点,并检算既有结构的承载力,结合既有结构现状调查结果,给出评估结论及推荐施工控制指标：地表沉降不超过7 mm,地表隆起不超过8 mm;车站底板隆起位移控制在7 mm以内,沉降缝两侧结构隆起位移差控制在2 mm以内;轨道的隆起位移不超过5.8 mm,轨道水平不超过±0.6 mm。在上述位移控制指标范围内,得出新建隧道施工后既有地铁结构是安全的。     

重力式挡土墙抗滑稳定分析安全判据和标准

探讨水利、交通等领域挡土墙设计规范中对抗滑稳定安全系数规定的允许值的合理性,认为其相应值与国外相关规定相比偏小。从理论上分析,使用抗力除以土压力的安全系数定义计算土压力相应的强度参数是标准值,而非经分项系数或安全系数折减后的标准值,其允许安全系数宜大于边坡等同类土方构筑物的相应值。认为建立在可靠度理论指导下的分项系数方法可以从根本上摆脱在安全判据方面存在的缺陷。在假定一级建筑物的允许可靠指标为3.7、土的黏聚力和摩擦系数变异系数分别为0.2和0.1的条件下,对一个特定的算例,填土的黏聚力、摩擦系数和基底的摩擦系数分项系数标定值分别为 1.301, 1.209和 1.170,应用提出的相对安全率判据,可以发现上述的分项系数标定值具有普适意义。该成果可以为相关规范的制订提供参考。     

Sinkhole hazards along the eastern Dead Sea shoreline area, Jordan: a geological and geotechnical consideration

For the last four decades, the level of the Dead Sea has been subjected to continual variation which, among other important factors, has led to the occurrence of much subsidence and many sinkholes in the southern Dead Sea area. Sinkhole activities occurred repetitively and were observed in open farms, across roads, near dwellings and near an existing factory, thus causing a serious threat to the locals and farmers of the area and their properties. This paper presents the main results from detailed geological and geotechnical studies of this area. Aerial photo interpretation and borehole drilling aided these studies. Parallel geophysical investigations (vertical electrical sounding and seismic refraction) and hydrological and hydrogeological studies were made by others in the same area to also investigate this phenomenon. It was found that sinkholes are aligned to and follow old water channels and are concentrated parallel to the recent shoreline of the Dead Sea. The development of subsurface cavities is associated mainly with the variation in the level of the Dead Sea over the four past decades, the presence of regional salt intrusion under the surface of salt beds, the fluctuation of the water table and continuous dissolution and the active tectonism of the area. Moreover, this work showed that the area is still under active sinkhole hazards and other parts of the area will be inevitably affected by sinkholes in the future.No practical engineering solution to this problem is feasible. Received: 1 July 1999 / Accepted: 11 October 1999     

多级支挡结构地震主动土压力的极限分析

多级组合支挡结构形式在高边坡防护工程中得到了广泛采用,但现有研究却较少涉及这种支挡结构形式的地震土压力计算问题。应用拟静力法和塑性极限分析上限定理,并且基于强度折减技术,推导了重力式挡墙与两级锚杆挡墙组合支挡结构形式的地震主动土压力及其系数的上限解。该上限解考虑了水平和竖向地震系数、墙背倾角、坡面形式及多级支护方式、土体黏聚力、土体与墙背的黏附力等诸多因素。二级锚杆挡墙实例分析表明：静力条件下主动土压力计算值与现有相关方法的计算结果一致,土的抗剪强度折减系数、上挡墙锚杆轴力等参数,对下挡墙地震主动土压力影响显著。二级组合支挡结构地震主动土压力影响参数敏感性分析表明：水平地震系数以及重力式挡墙墙高和倾角的敏感性较大,上挡墙锚杆的轴力和倾角等参数的敏感性相对较小     

考虑围护摩阻力的地铁车站结构抗浮安全设计

在地下结构抗浮设计中,较少考虑侧壁摩阻力的作用,对于侧摩阻力的的计算方法也不够明确。抗浮安全系数目前尚无统一规定,主要参照类似工程实践经验确定。在宁波轨道交通工程福庆路站抗拔桩静载试验的基础上,以地铁车站结构为研究对象,经过试验分析,对地下车站结构设计中侧壁摩阻力大小进行计算,进而考虑抗浮安全性对车站结构的临界宽度进行计算,可为地铁车站设计提供指导。     

桩基概率极限状态设计中抗力分项系数的研究

根据桩基工作机理，建立了桩基按概率极限状态设计的实用设计表达式，并按照《建筑结构设计统一标准》的规定对设计表达式中分项系数的内涵及规律进行了研究，提出了运用＂等β法＂确定抗力分项系数的方法。通过实例计算验证了此确定方法的可行性和可信性，为桩基由定值设计过渡到概率极限状态设计作了有益的探索。     

On the time-dependent behaviour of glacial sediments: a geotechnical approach

Soft sediments can deform under both changes in stress and changes in strain rate, as well as during sustained loading (e.g. creep). In glacial conditions, soft subglacial sediments can contribute to glacier movements, and when the ice/sediment system is coupled, the rate-sensitivity of the sub-layer can affect the velocity of the glacier. These issues have been the object of studies by several geologists. In parallel, the effects of time and strain rate on the behaviour of soils have been studied for many years by geotechnical engineers, to estimate the long-term performance of ground structures. This paper applies the knowledge acquired in soil mechanics to a geological problem: results on two glacial sediments of different origins, obtained from advanced geotechnical laboratory tests, are presented and analysed in the light of recent advances in soil mechanics. Independently of time effects, the test data show that the pre-failure behaviour is not elastic but that the sediments develop plastic strains before reaching their peak strength, with the stiffness gradually degrading. Results from tests performed with variable strain rates suggest that the time-dependent (viscous) behaviour of the sediments may be governed by their mineralogy, in particular the presence of plastic fines. The viscous behaviour observed in the plastic tills seems to affect the pre-failure behaviour only, for example the yield surface, stiffness, strength, but the criteria of failure, e.g. critical or residual angle of failure are found to be constant and independent of strain rate. The test data also suggest that the viscous behaviour may be related to stress level, being more prevalent at low stresses. These results, obtained under laboratory-controlled conditions, over a large range of strains, pre- and post-peak strength, are a necessary step towards developing constitutive models for subglacial sediments rigorously. It is only after this has been achieved that such models should be implemented in finite element code to analyse ice/sediment systems, with the aim to understand glacier movements better.     

关于滑坡稳定性在滑坡安全系数取值中的作用讨论

在工程界存在着滑坡安全系数取值应考虑滑坡稳定性高低、对稳定系数较低的滑坡应采用较大的安全系数的思想。考虑滑坡稳定性的具体方式有两种:①考虑滑坡的实际稳定状态或变形情况;②考虑设计工况下的稳定系数。考虑滑坡稳定性的理由也有两种:①变形急剧势必危害较大;②滑坡在治理后的安全储备可用"安全储备系数"(即下滑力按安全系数放大后的剩余下滑力与下滑力不作改变时的剩余下滑力之比)来衡量,而"安全储备系数"存在着随稳定系数的减小而减小的规律。文章的研究表明,滑坡变形越急剧滑坡危害越大的规律是不存在的,滑坡"安全储备系数"既不能衡量滑坡在治理后的安全储备,也不随滑坡稳定系数的减小而减小,滑坡安全系数与稳定系数无关,将安全系数取值与稳定系数大小挂钩会导致诸多不合理现象产生。因此,滑坡安全系数取值不应考虑稳定系数大小。     

基于块体单元法的岩石边坡安全系数研究

岩石边坡因其结构面数量众多、块体系统及其滑动方式复杂,给危险块体组合的搜索及其安全系数计算带来很大困难。基于块体单元法,对岩石边坡中的危险块体组合搜索及其安全系数的计算方法进行了研究。首先,在块体元强度折减计算的成果下,根据屈服面贯通理论提出搜索危险块体组合的新方法;然后,对安全系数计算方法进行研究,建议在位移突变判据下采用双线性交叉法计算安全系数;最后,进行了单面、双面和多面滑动以及复杂块体系统的算例分析,并与刚体极限平衡法计算结果进行了对比。结果表明,由于块体单元法考虑了力与力矩的平衡及结构面上应力的非均匀分布,其计算结果更准确。该方法有望广泛应用于复杂岩石边坡稳定分析。     

基于整体稳定性分析法的边坡临界滑动面搜索

临界滑动面搜索是边坡稳定分析中很重要的内容,针对现有方法的不足,提出了一种新的搜索方法。基于边坡稳定性的整体分析法,建立了确定临界滑面的非线性优化模型。该模型将滑面离散点的纵坐标和安全系数都视为独立变量,目标函数取为安全系数本身,约束条件是平衡方程组和滑面凸性。由于目标函数是线性函数,约束条件至多是二次多项式,非线性程度较低,可采用经典优化算法和常见的非线性优化工具求解,比如Matlab。通过实例分析并与传统的滑面搜索方法进行对比表明,所建议的方法在数值稳定性及收敛性方面均具有优势。     

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。