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1.
提出了基于支持向量机（SVM）的边坡可靠度分析新算法。该方法采用均匀设计确定样本点,通过一定数量的确定性计算来训练SVM,拟合边坡的功能函数;采用一阶可靠度方法（FORM）和迭代算法优化SVM模型,获得可靠度指标和验算点信息;在SVM模型基础上进一步通过二阶可靠度方法（SORM）和蒙特卡罗模拟（MCS）计算边坡的失稳概率。以两个典型边坡为例,通过与其他方法比较,证明了该方法的准确性和高效性。结果表明：提出的在标准正态空间（U空间）中取样并构建SVM,在原始空间（X空间）中计算功能函数的算法,有效地解决了具有相关非正态分布变量的可靠度分析问题,并且可很容易扩展到SORM的计算。算例结果证明,该方法的精度高于FORM;而效率优于MCS。分析过程中,边坡安全系数计算和可靠度分析相互独立。因此,该方法既适用于具有显式功能函数的简单问题,也适用于需要软件计算安全系数的实际边坡问题。 相似文献
2.
提出了基于响应面法的边坡稳定二阶可靠度分析的实用算法。选择U空间中的随机变量,通过空间变换和相关矩阵分解,计算试验点的功能函数;通过迭代算法构造响应面、以确保通过最小的计算量获得最优精度,并在此基础上进行FORM/SORM计算。以一岩石边坡的平面滑动问题为例,通过与蒙特卡洛模拟、FORM及随机响应面法的比较,证明了该方法的准确性和高效性。分析了参数的相关性及试验点取值范围对计算结果的影响,讨论了可靠度分析结果中参数敏感性和物理属性问题。该方法可为实际边坡问题的可靠度分析提供参考,并可以用来进行基于可靠度分析的加固设计。 相似文献
3.
A practical approach is proposed in this paper for the reliability assessment of rock tunnel excavations using the moving least squares method (MLSM) and the uniform design. The failure probability is computed by the first-order and the second-order reliability method (FORM/SORM), which is based on the generated MLSM response surface (MLSM-RS) via an iterative algorithm. The proposed approach is first implemented in the analysis of a circular tunnel that consists of three limit state functions to illustrate the efficiency and accuracy of the approach. Then, the method is applied to a non-circular tunnel to demonstrate the feasibility and validity of the method for practical problems, in which numerical procedures are commonly employed to solve the implicit limit state functions. 相似文献
4.
Probabilistic analysis of underground rock excavations using response surface method and SORM 总被引：6，自引：0，他引：6
Probabilistic analysis of underground rock excavations is performed using response surface method and SORM, in which the quadratic polynomial with cross terms is used to approximate the implicit limit state surface at the design point. The response surface is found using an iterative algorithm and the probability of failure is evaluated using the first-order and the second-order reliability method (FORM/SORM). Independent standard normal variables in U-space are chosen as basic random variables and transformed into correlated non-normal variables in the original space of random variables for constructing the response surface. The proposed method is first illustrated for a circular tunnel with analytical solutions considering Mohr–Coulomb (M–C) and Hoek–Brown (H–B) yield criteria separately. The failure probability with respect to the plastic zone criterion and the tunnel convergence criterion are estimated from FORM/SORM and compared to those obtained from Monte Carlo Simulations. The results show that the support pressure has great influence on the failure probability of the two failure modes. For the M–C model, the hypothesis of uncorrelated friction angle and cohesion will generate higher non-performance probability in comparison to the case of negatively correlated shear strength parameters. Reliability analyses involving non-normal distributions are also investigated. Finally, an example of a horseshoe-shaped highway tunnel is presented to illustrate the feasibility and validity of the proposed method for practical applications where numerical procedures are needed to calculate the performance function values. 相似文献
5.
This paper presents a practical procedure for assessing the system reliability of a rock tunnel. Three failure modes, namely, inadequate support capacity, excessive tunnel convergence, and insufficient rockbolt length, are considered and investigated using a deterministic model of ground-support interaction analysis based on the convergence–confinement method (CCM). The failure probability of each failure mode is evaluated from the first-order reliability method (FORM) and the response surface method (RSM) via an iterative procedure. The system failure probability bounds are estimated using the bimodal bounds approach suggested by Ditlevsen (1979), based on the reliability index and design point inferred from the FORM. The proposed approach is illustrated with an example of a circular rock tunnel. The computed system failure probability bounds compare favorably with those generated from Monte Carlo simulations. The results show that the relative importance of different failure modes to the system reliability of the tunnel mainly depends on the timing of support installation relative to the advancing tunnel face. It is also shown that reliability indices based on the second-order reliability method (SORM) can be used to achieve more accurate bounds on the system failure probability for nonlinear limit state surfaces. The system reliability-based design for shotcrete thickness is also demonstrated. 相似文献
6.
Although first-order reliability method is a common procedure for estimating failure probability, the formulas derived for bimodal bounds of system failure probability have not been widely used as expected in present reliability analyses. The reluctance for applying these formulas in practice may be partly due to the impression that the procedures to implement the system reliability theory are tedious. Among the methods for system reliability analysis, the approach suggested in Ditlevsen 1979 is considered here because it is a natural extension of the first-order reliability method commonly used for failure probability estimation corresponding to a single failure mode, and it can often provide reasonably narrow failure probability bounds. To facilitate wider practical application, this paper provides a short program code in the ubiquitous Excel spreadsheet platform for efficiently calculating the bounds for system failure probability. The procedure is illustrated for a semi-gravity retaining wall with two failure modes, a soil slope with two and eight failure modes, and a loaded beam with three failure modes. In addition, simple equations are provided to relate the correlated but unrotated equivalent standard normals of the Low and Tang 2007 FORM procedure with the uncorrelated but rotated equivalent standard normals of the classical FORM procedure. Also demonstrated are the need for investigating different permutations of failure modes in order to get the narrowest bounds for system failure probability, and the use of SORM reliability index for system reliability bounds in a case where the curvature of the limit state surface cannot be neglected. 相似文献
7.
A method based on the linearization of the limit state functions (LSFs) is applied to evaluate the reliability of series geotechnical systems. The approach only needs information provided by first order reliability method (FORM) results: the vector of reliability indices, β, of the LSFs composing the system; and their correlation matrix, R. Two common geotechnical problems—the stability of a slope in layered soil and a circular tunnel in rock—are employed to demonstrate the simplicity, accuracy and efficiency of the suggested procedure, and advantages of the linearization approach with respect to alternative computational tools are discussed. It is also found that, if necessary, the second order reliability method (SORM)—that approximates the true LSF better than FORM—can be employed to compute better estimations of the system’s reliability. 相似文献
8.
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. 相似文献
9.
The first order reliability method (FORM) is efficient, but it has limited accuracy; the second order reliability method (SORM) provides greater accuracy, but with additional computational effort. In this study, a new method which integrates two quasi-Newton approximation algorithms is proposed to efficiently estimate the second order reliability of geotechnical problems with reasonable accuracy. In particular, the Hasofer–Lind–Rackwitz–Fiessler–Broyden–Fletcher–Goldfarb–Shanno (HLRF–BFGS) algorithm is applied to identify the design point on the limit state function (LSF), and consequently to compute the first order reliability index; whereas the Symmetric Rank-one (SR1) algorithm is nested within the HLRF–BFGS algorithm to compute good approximations, yet with a reduced computational effort, of the Hessian matrix required to compute second order reliabilities. Three typical geotechnical problems are employed to demonstrate the ability of the suggested procedure, and advantages of the proposed approach with respect to conventional alternatives are discussed. Results show that the proposed method is able to achieve the accuracy of conventional SORM, but with a reduced computational cost that is equal to the computational cost of HLRF–BFGS-based FORM. 相似文献
10.
A practical and efficient approach of implementing second‐order reliability method (SORM) is presented and illustrated for cases related to foundation engineering involving explicit and implicit limit state functions. The proposed SORM procedure is based on an approximating paraboloid fitted to the limit state surface in the neighborhood of the design point and can be easily carried out in a spreadsheet. Complex mathematical operations are relegated to relatively simple user‐created functions. The failure probability is calculated automatically based on the reliability index and principal curvatures of the limit state surface using established closed‐form SORM formulas. Four common foundation engineering examples are analyzed using the proposed method and discussed: immediate settlement of a flexible rectangular foundation, bearing capacity of a shallow footing, axial capacity of a vertical single pile, and deflection of a pile under lateral load. Comparisons with Monte Carlo simulations are made. In the case of the laterally loaded pile, the friction angle of the soil is represented as a one‐dimensional random field, and pile deflections are computed based on finite element analysis on a stand‐alone computer package. The implicit limit state function is approximated via the response surface method using two quadratic models. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
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. 相似文献
12.
The first-order reliability method (FORM) is used to calculate the reliability index of a circular tunnel subjected to a hydrostatic stress field. The random variables are first assumed to follow the normal distribution. Comparison between analysis using negatively correlated and uncorrelated friction angle and cohesion indicates that the results of reliability analysis are conservative if negative correlation among strength parameters is not modeled. The reliability analysis involving correlated non-normal distributions is also investigated. The probability density functions are obtained from reliability indices and compared to those generated from Monte Carlo simulations. Reliability-based design of tunnel support pressure is also illustrated. 相似文献
13.
Acta Geotechnica - Reliability-based design (RBD) can overcome some limitations and ambiguities in the partial factor design approach found in Eurocode 7 (EC7) and the load and resistance factor... 相似文献
14.
In this paper, a framework based on Bayesian theory and proof pile load test results was used to update resistance factors of axially loaded driven piles. Prior to implementation of the framework, resistance factors were calibrated based on the distribution of the measured-to-predicted pile ultimate bearing capacity using the results of static pile load tests conducted to failure. These resistance factors and the distribution were considered to be “prior.” The prior distribution of the measured-to-predicted ultimate bearing capacity was updated based on Bayesian theory to incorporate additional proof pile load test results. Using the measured-to-predicted load distributions and the updated (or posterior) measured-to-predicted bearing capacity distributions, resistance factors were calibrated (or updated) from the first-order reliability method (FORM) for two different target reliability indices, 2.33 and 3.0. This research attempted to use the results of proof pile load tests, which are generally conducted to verify pile designs, to update resistance factors. The updated resistance factors varied substantially depending on the proof pile load test results. Therefore, the Bayesian implementation can contribute to economical pile designs. 相似文献
15.
In a recent study, the time-dependent increase in axial load resistance of steel H-piles driven into cohesive soils, due to setup, was systematically quantified using measured field data. A method to estimate the setup based on measurable soil properties was subsequently established. These studies highlighted that the uncertainties of the measurements of soil properties and thus the semi-empirical approach to estimate setup are significantly different from those of the methodology used for measuring the pile resistance during retaps at any time after the end of driving. Recognizing that the two sets of uncertainties should be addressed concurrently, this paper presents a procedure for determining the factored resistance of a pile with due consideration to setup in accordance with the load and resistance factor design that targets a specific reliability index. Using the first-order second-moment method, the suggested procedure not only provides a simplified approach to incorporate any form of setup in design, but it also produces comparable results to the computationally intensive first-order reliability method. Incorporating setup in design and construction control is further shown to reduce foundation costs and minimize retap requirements on piles, ultimately reducing the construction costs of pile foundations. 相似文献
16.
《地学前缘(英文版)》2018,9(6):1631-1638
To meet the high demand for reliability based design of slopes, we present in this paper a simplified HLRF(Hasofere Linde Rackwitze Fiessler) iterative algorithm for first-order reliability method(FORM). It is simply formulated in x-space and requires neither transformation of correlated random variables nor optimization tools. The solution can be easily improved by iteratively adjusting the step length. The algorithm is particularly useful to practicing engineers for geotechnical reliability analysis where standalone(deterministic) numerical packages are used. Based on the proposed algorithm and through direct perturbation analysis of random variables, we conducted a case study of earth slope reliability with complete consideration of soil uncertainty and spatial variability. 相似文献
17.
Robust design of rock slopes with multiple failure modes: modeling uncertainty of estimated parameter statistics with fuzzy number 总被引：1，自引：1，他引：0
Changjie Xu Lei Wang Yong Ming Tien Jian-Min Chen C. Hsein Juang 《Environmental Earth Sciences》2014,72(8):2957-2969
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. 相似文献
18.
Probabilistic analyses provide rational means to treat the uncertainties associated with underlying parameters in a systematic
manner. The stability of a 734-m-high jointed rock slope in the west of Norway, the Oppstadhornet rock slope, is investigated
by using a probabilistic method. The first-order reliability method (FORM) is used for probabilistic modeling of the plane
failure problem in the rock slope. The Barton–Bandis (BB) shear strength criterion is used for the limit state equation. The
statistical distributions of the BB criterion parameters, for which comprehensive data were collected and statistically analyzed,
are determined by using distribution fitting algorithms. The sensitivity of the FORM model for the BB criterion is also investigated.
It is found that the model is most sensitive to the mean value of the residual friction angle (ϕ
r) and least sensitive to the mean value of the slope angle (β
f). It is also found that the standard deviation of joint compressive strength (JCS) causes the greatest difference in the
reliability index, which has the least sensitivity to the change in the mean and standard deviation of joint roughness coefficient
(JRC). 相似文献
19.
Efficient Probabilistic Algorithm Illustrated for a Rock Slope 总被引：7，自引：0，他引：7
B. K. Low 《Rock Mechanics and Rock Engineering》2008,41(5):715-734
Summary A new spreadsheet-based algorithm for the first-order reliability method (FORM) is illustrated for a two-dimensional rock
slope of Hong Kong. The new algorithm combines inverse distribution functions and a refined Newton method with the automatic
constrained-optimization search of the design point in the original space of the random variables; it obviates the need for
computations of equivalent normal means and equivalent normal standard deviations. In the rock slope analysis, the versatile
4-parameter beta distribution is used in lieu of a truncated normal distribution. Probabilities of failure inferred from reliability
indices are compared with those from Monte Carlo simulations. The effects of parametric correlations on the required reinforcing
force for a target reliability index value are studied. The intuitive perspective of an expanding equivalent dispersion ellipsoid
in the original space of the basic random variables is also described as it is the basis from which the new approach evolved.
Author’s address: Dr. Bak Kong Low, School of Civil and Environmental Engineering, Nanyang Technological University, Block
N1 #1b-40, 50 Nanyang Avenue, 639798 Singapore 相似文献
20.
Sara Heidarie Golafzani Abolfazl Eslami 《Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards》2020,14(3):216-230
ABSTRACT Since piles are one of the major geotechnical foundation systems, estimation of their axial bearing capacity is of great importance. Employing different design methods, resulting in a wide range of bearing capacity estimations, complicates the selection of an appropriate design scheme and confirms the existence of model error along with the inherent soil variability in bearing capacity prediction. This paper tends to evaluate different predictive methods in Reliability-Based Design (RBD) framework. In this regard, different static analyses, SPT and CPT-based methods are considered to evaluate which approaches collectively and which method individually, have more reliable predictions for compiled data bank. In order to assess reliability indices and resistance factors, two approaches have been considered, i.e. First Order Second Moment method (FOSM) and First Order Reliability Method (FORM). To investigate the reliability indices for different methods in both RBD approaches, various safety factors and loading ratios have been considered. Also, the Load and Resistance Factor Design (LRFD) resistance factors are calibrated for different target reliability indices and loading ratios. Results show that CPT-based methods are more reliable among other methods. Furthermore, the estimated efficiency ratio, i.e. the ratio of resistance factor to resistance bias factor, confirms this agreement. 相似文献