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Load displacement analysis of drilled shafts can be accomplished by utilizing the “t-z” method, which models soil resistance along the length and tip of the drilled shaft as a series of springs. For non-linear soil springs, the governing differential equation that describes the soil-structure interaction may be discretized into a set of algebraic equations based upon finite difference methods. This system of algebraic equations may be solved to determine the load–displacement behavior of the drilled shaft when subjected to compression or pullout. By combining the finite difference method with Monte Carlo simulation techniques, a probabilistic load–displacement analysis can be conducted. The probabilistic analysis is advantageous compared to standard factor of safety design because uncertainties with the shaft–soil interface and tip properties can be independently quantified. This paper presents a reliability analysis of drilled shaft behavior by combining the finite difference technique for analyzing non-linear load–displacement behavior with Monte Carlo simulation method. As a result we develop probabilistic relationships for drilled shaft design for both total stress (undrained) and effective stress (drained) parameters. The results are presented in the form of factor of safety or resistance factors suitable for serviceability design of drilled shafts.  相似文献   

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The 2D random finite element method and the one-dimensional and 2D random limit equilibrium method are used to investigate the influence of spatial variability of soil strength parameters on the probability of failure of simple soil slopes with cohesive undrained shear strength. The combined influence of spatial variability of soil properties and cross-correlation between undrained soil strength and unit weight on the computed probability of failure is explored. The paper identifies conditions where numerical outcomes are similar and where they are not. The limitations of each analysis method are described and implications to analysis and design are identified.

Abbreviations: FEM: finite element method; LEM: limit equilibrium method; RFEM: random finite element method; RLEM: random limit equilibrium method  相似文献   

5.
Drilled shafts are, typically, designed by considering the axial ultimate limit state. In this design methodology, the axial displacement requirements are verified once the design is completed. As an alternative, drilled shafts may be designed by considering the axial service limit state. Service limit state foundation design is more efficient when done using the load and resistance factor design (LRFD) approach. Furthermore, reliability may be rationally incorporated into the design process that utilizes the LRFD method. In this paper, we develop probabilistic approaches for axial service limit state analysis of drilled shafts. The variability of shaft-soil interface properties is modeled by lognormal probability distribution functions. The probability distributions are combined with a closed-form analytical relationship of axial load-displacement curves for drilled shafts. The closed-form analytical relationship is derived based upon the “t–z” approach. This analytical relationship is used with the Monte Carlo simulation method to obtain probabilistic load-displacement curves, which are analyzed to develop methods for determining the probability of drilled shaft failure at the service limit state. The developed method may be utilized to obtain resistance factors that can be applied to LRFD based service limit state design.  相似文献   

6.
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.  相似文献   

7.
约束随机场下的边坡可靠度随机有限元分析方法   总被引:2,自引:1,他引:1  
吴振君  王水林  葛修润 《岩土力学》2009,30(10):3086-3092
目前边坡可靠度中常用的简化分析方法,不考虑边坡土体的空间变异性,每次计算整个边坡都取用相同的强度参数,由离散点试样试验得到的土体参数统计特性只能反映点特性,而边坡的稳定性受滑面上平均抗剪强度特性控制,因此,需要考虑空间范围内的平均特性。描述空间变异性的随机场理论对变异性较高的土体,实际上高估了其空间变异性。把随机场理论和地质统计中的区域化变量理论结合起来,建立约束随机场,并在此基础上进行Monte-Carlo随机有限元分析。计算实例表明,在高变异性条件下约束随机场能有效降低完全随机场的模拟方差,得到更低的破坏概率。对比了随机有限元和简化法的计算结果表明,简化法在土体强度变异性很高时其结果并非偏于保守。另外也指出了可靠度分析中存在的边坡尺度效应和简化法的适用条件。  相似文献   

8.
The influence of vertical spatial variability of sands on the excavation-induced lateral wall deflection and bending moment of excavations supported by cantilever retaining walls is investigated in this paper. Herein, the random finite element method (RFEM) is adopted to explicitly study the effect of one-dimensional spatial variability of internal friction angle of sands on the predicted wall and ground responses. The RFEM analysis consists of three components: (1) finite element method for analyzing lateral wall deflection and bending moment, (2) random field theory implemented with Monte Carlo simulation (MCS), and (3) statistical interpretation of MCS results through confidence intervals. This study reveals the importance of random field modeling in coping with the spatial variability of sands in the problem of supported excavations: (1) neglecting spatial variability of soil property will cause an overestimation of the variation in the predicted wall deflection and bending moment; (2) the estimated probability of failure based on a well-established serviceability limit state may be overestimated or underestimated depending on the chosen limiting lateral wall deflection. This study further investigates the effect of the number of MCS on the confidence intervals of the predicted statistics of the maximum lateral wall deflection and the maximum bending moment. The results also demonstrate that the confidence interval analysis of the predicted statistics of the maximum lateral wall deflection and the maximum bending moment provides a rational tool for interpreting the statistical data from RFEM.  相似文献   

9.
This study aims to extend the multivariate adaptive regression splines(MARS)-Monte Carlo simulation(MCS) method for reliability analysis of slopes in spatially variable soils. This approach is used to explore the influences of the multiscale spatial variability of soil properties on the probability of failure(P_f) of the slopes. In the proposed approach, the relationship between the factor of safety and the soil strength parameters characterized with spatial variability is approximated by the MARS, with the aid of Karhunen-Loeve expansion. MCS is subsequently performed on the established MARS model to evaluate Pf.Finally, a nominally homogeneous cohesive-frictional slope and a heterogeneous cohesive slope, which are both characterized with different spatial variabilities, are utilized to illustrate the proposed approach.Results showed that the proposed approach can estimate the P_f of the slopes efficiently in spatially variable soils with sufficient accuracy. Moreover, the approach is relatively robust to the influence of different statistics of soil properties, thereby making it an effective and practical tool for addressing slope reliability problems concerning time-consuming deterministic stability models with low levels of P_f.Furthermore, disregarding the multiscale spatial variability of soil properties can overestimate or underestimate the P_f. Although the difference is small in general, the multiscale spatial variability of the soil properties must still be considered in the reliability analysis of heterogeneous slopes, especially for those highly related to cost effective and accurate designs.  相似文献   

10.
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.  相似文献   

11.
边坡可靠度分析中通常假定采用平稳或准平稳随机场表征土体参数的空间变异性,然而大量现场试验数据表明,土体参数如不排水抗剪强度沿土体埋深常呈现明显的非平稳分布特征,即其均值和标准差均随埋深发生变化,因此亟需发展土体参数非平稳随机场模型及其模拟方法。针对目前不能有效单独模拟土体参数趋势分量和随机波动分量的不确定性,提出了一种有效的不排水抗剪强度参数非平稳随机场模型,并给出了土体参数二维非平稳随机场模拟方法计算流程,同时将新提出的模型与现有非平稳随机场模型及平稳随机场模型进行了系统比较。最后通过不排水饱和黏土边坡算例验证了提出模型的有效性,并揭示了不排水抗剪强度非平稳分布特征对边坡可靠度的影响规律。结果表明:提出模型能够有效地单独模拟土体参数趋势分量和随机波动分量的不确定性,考虑土体参数均值和标准差随埋深增加而增大的特性,可为表征土体参数非平稳分布特征提供了一条有效的途径。此外,与采用非平稳随机场模拟土体参数空间变异性相比,采用常用的平稳随机场模型会低估边坡失效概率,从而造成偏危险的边坡工程设计方案。  相似文献   

12.
The paper presents a computational procedure for reliability analysis of earth slopes considering spatial variability of soils under the framework of the Limit Equilibrium Method. In the reliability analysis of earth slopes, the effect of spatial variability of soil properties is generally included indirectly by assuming that the probabilistic critical slip surface is the same as that determined without considering spatial variability. In contrast to this indirect approach, in the direct approach, the effect of spatial variability is included in the process of determination of the probabilistic critical surface itself. While the indirect approach requires much less computational effort, the direct approach is definitely more rigorous. In this context this paper attempts to investigate, with the help of numerical examples, how far away are the results obtained from the indirect approach from that obtained from the direct approach. In both the approaches, it is required to use a model of discretization of random fields into finite random variables. A few such models are available in the literature for one-dimensional (1D) as well as two-dimensional (2D) spatial variability. The developed computational scheme is based on the First Order Reliability Method (FORM) coupled with the Spencer Method of Slices valid for limit equilibrium analysis of general slip surfaces. The study includes bringing out the computational advantages and disadvantages of the three commonly used discretization models. The sensitivity of the reliability index to the magnitudes of the scales of fluctuation has also been studied.  相似文献   

13.
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   

14.
This study presents the response of a vertically loaded pile in undrained clay considering spatially distributed undrained shear strength. The probabilistic study is performed considering undrained shear strength as random variable and the analysis is conducted using random field theory. The inherent soil variability is considered as source of variability and the field is modeled as two dimensional non-Gaussian homogeneous random field. Random field is simulated using Cholesky decomposition technique within the finite difference program and Monte Carlo simulation approach is considered for the probabilistic analysis. The influence of variance and spatial correlation of undrained shear strength on the ultimate capacity as summation of ultimate skin friction and end bearing resistance of pile are examined. It is observed that the coefficient of variation and spatial correlation distance are the most important parameters that affect the pile ultimate capacity.  相似文献   

15.
This paper aims at determining the failure probability and the corresponding most predominant failure mode at both ultimate (ULS) and serviceability (SLS) limit states of a circular foundation resting on a (c, φ) soil and subjected to an inclined loading. The failure modes at ULS are the footing sliding and the soil punching while those at SLS are the exceedance of tolerable horizontal and vertical footing displacements. The probabilistic results based on the response surface methodology have shown that at both ULS and SLS, there is a load inclination where neither mode of failure is predominant. This inclination corresponds to the loading configurations situated on the line joining the origin and the maximal point of the interaction diagram. In a second stage, the results of a sensitivity analysis showing the effect of the different statistical parameters of the uncertain variables on the value of the failure probability were presented and discussed.  相似文献   

16.
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.  相似文献   

17.
土质边坡三维可靠度分析   总被引:5,自引:0,他引:5  
梧松  吴玉山 《岩土力学》2003,24(2):284-291
基于空间随机场理论,利用局部平均法研究空间各向异性的土坡的可靠度问题,推导出相应计算公式,并通过计算边坡的最大破坏概率来进行滑坡的空间预测。  相似文献   

18.
The load distribution and deformation of rock-socketed drilled shafts subjected to axial loads are evaluated by a load transfer method. The emphasis is on quantifying the effect of coupled soil resistance in rock-socketed drilled shafts using 2D elasto-plastic finite element analysis. Slippage and shear-load transfer behavior at the pile–soil interface are investigated by using a user-subroutine interface model (FRIC). It is shown that the coupled soil resistance acts as pile-toe settlement as the shaft resistance is increased to its ultimate limit state. Based on the results obtained, the coupling effect is closely related to the ratio of the pile diameter to soil modulus (D/Es) and the ratio of total shaft resistance against total applied load (Rs/Q). Through comparison with field case studies, the 2D numerical analysis reasonably estimated load transfer of pile and coupling effect, and thus represents a significant improvement in the prediction of load deflections of drilled shafts.  相似文献   

19.
Rainfall-induced landslides frequently occur in humid temperate regions worldwide. Research activity in understanding the mechanism of rainfall-induced landslides has recently focused on the probability of slope failure involving non-homogeneous soil profiles. This paper presents probabilistic analyses to assess the stability of unsaturated soil slope under rainfall. The influence of the spatial variability of shear strength parameters on the probability of rainfall-induced slope failure is conducted by means of a series of seepage and stability analyses of an infinite slope based on random fields. A case study of shallow failure located on sandstone slopes in Japan is used to verify the analysis framework. The results confirm that a probabilistic analysis can be efficiently used to qualify various locations of failure surface caused by spatial variability of soil shear strength for a shallow infinite slope failure due to rainfall.  相似文献   

20.
Slopes are mainly naturally occurred deposits, so slope stability is highly affected by inherent uncertainty. In this paper, the influence of heterogeneity of undrained shear strength on the performance of a clay slope is investigated. A numerical procedure for a probabilistic slope stability analysis based on a Monte Carlo simulation that considers the spatial variability of the soil properties is presented to assess the influence of randomly distributed undrained shear strength and to compute reliability as a function of safety factor. In the proposed method, commercially available finite difference numerical code FLAC 5.0 is merged with random field theory. The results obtained in this study are useful to understand the effect of undrained shear strength variations in slope stability analysis under different slope conditions and material properties. Coefficient of variation and heterogeneity anisotropy of undrained shear strength were proven to have significant effect on the reliability of safety factor calculations. However, it is shown that anisotropy of the heterogeneity has a dual effect on reliability index depending on the level of safety factor adopted.  相似文献   

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