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1.
A reliability model is proposed to solve the problem of hybrid uncertainty with both random and interval variables in slope engineering. A hybrid uncertainty model based on the dimension reduction method and Taylor expansion is constructed to approximate the limit state function. Using the polynomial theorem and variable transformation method, the origin and center moments’ interval of the limit state function are calculated. Moment information is applied to the expansion of a three-parameter Weibull distribution, and the cumulative distribution function and probability density function of limit state function are determined. As a result, the failure probability interval of the slope is calculated. The interval uncertainty problem is transformed into an interval certainty problem using Taylor expansion without solving for the statistical moment of limit state function using multiple integrals and iteratively searching for the most probable failure points. The numerical results from two slopes show that the proposed method is effective and feasible.
相似文献2.
考虑参数空间变异性的非饱和土坡可靠度分析 总被引：2，自引：0，他引：2
在考虑多个土体参数空间变异性的基础上,提出了基于拉丁超立方抽样的非饱和土坡稳定可靠度分析的非侵入式随机有限元法。利用Hermite随机多项式展开拟合边坡安全系数与输入参数间的隐式函数关系,采用拉丁超立方抽样技术产生输入参数样本点,通过Karhunen-Loève展开方法离散土体渗透系数、有效黏聚力和内摩擦角随机场,并编写了计算程序NISFEM-KL-LHS。研究了该方法在稳定渗流条件下非饱和土坡可靠度分析中的应用。结果表明：非侵入式随机有限元法为考虑多个土体参数空间变异性的非饱和土坡可靠度问题提供了一种有效的分析工具。土体渗透系数空间变异性和坡面降雨强度对边坡地下水位和最危险滑动面位置均有明显的影响。当降雨强度与饱和渗透系数的比值大于0.01时,边坡失效概率急剧增加。当土体参数变异性或者参数间负相关性较大时,忽略土体参数空间变异性会明显高估边坡失效概率。 相似文献
3.
在岩土工程分析中求解精度控制常常是必需的,在数值流形法中可以通过控制数学覆盖网格的稀疏和覆盖位移的阶数来达到精度的要求。提出了基于等几何分析的数值流形方法,定义了相应的数学覆盖的构造形式,推导了基于二次B样条的9节点数值流形方法分析格式;针对基于Lagrange插值函数的4节点数值流形方法提出了基于T样条思想的数学覆盖网格的局部加密方法。算例计算结果表明,相对于4节点的数值流形方法,基于非均匀有理B样条的9节点数值流形方法具有更高的精度;基于T样条思想的加密网格在保持计算精度的前提下降低了自由度的数量,表明T样条加密是一种自然的局部加密算法。 相似文献
4.
This paper proposes a stochastic response surface method for reliability analysis involving correlated non-normal random variables, in which the Nataf transformation is adopted to effectively transform the correlated non-normal variables into independent standard normal variables. Transformations of random variables that are often used in reliability analyses in terms of standard normal variables are summarized. The closed-form expressions for fourth to sixth order Hermite polynomial chaos expansions involving any number of random variables are formulated. The proposed method will substantially extend the application of stochastic response surface method for reliability problems. An example of reliability analysis of rock slope stability with plane failure is presented to demonstrate the validity and capability of the proposed stochastic response surface method. The results indicate that the proposed stochastic response surface method can evaluate the reliability of rock slope stability involving correlated non-normal variables accurately and efficiently. Its accuracy is shown to be higher than that for the first-order reliability method, and it is much more efficient than direct Monte-Carlo simulation. The results also show that the number of collocation points selected should ensure that the Hermite polynomial matrix has a full rank so that different order SRSMs can produce a robust estimation of probability of failure for a specified performance function. Generally, the accuracy of SRSM increases as the order of SRSM increases. 相似文献
5.
This paper develops a multiple response surfaces approach to approximate the limit state function for slope failure by second‐order polynomial functions, to incorporate the variation of the most probable slip surfaces, and to evaluate the slope failure probability pf. The proposed methodology was illustrated through a cohesive soil slope example. It is shown that the pf values estimated from multiple response surfaces agree well with those pf values that have been obtained by searching a large number of potential slip surfaces in each Monte Carlo simulation (MCS) sample. The variation of number of the most probable slip surfaces is studied at different scale of fluctuation (λ) values. It is found that when full correlation assumed for each of random fields (i.e., spatial variability is ignored), the number of the most probable slip surfaces is equal to the number of random fields (in this study, it is 3). When the spatial variability grows significantly, the number of the most probable slip surfaces or number of multiple response surfaces firstly increases evidently to a higher value and then varies slightly. In addition, the contribution of a specific most probable slip surface varies dramatically at different spatial variability level, and therefore, the variation of the most probable slip surfaces should be accounted for in the reliability analysis. The multiple response surfaces approach developed in this paper provides a limit equilibrium method and MCS‐based means to incorporate such a variation of the most probable slip surfaces in slope reliability analysis. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
6.
For many non-renewable resources, reliable production data are only available from a certain point in time but not from the
beginning of production periods. In order to constrain the unknown historic production of such resources for those ancient
times for which no reliable annual production data are available we present a novel mathematical technique, based on Verhulst’s
logistic function. The method is validated by the United States’ crude oil production for which the complete production cycle,
starting in 1859, is well documented. Assuming that the oil production in the USA between 1859 and 1929 is unknown, our method
yields values for this period of 16.0 gigabarrels (Gb) based on a second-order polynomial fit and 13.5 Gb based on a third-order
polynomial fit of post-1929 production data, respectively. Especially the latter amount compares well with the actual value
of 12.1 Gb, thus illustrating the strength of the method. For global gold (Au) production, our method yields an ancient production
up to the year 1850, when official and reliable production statistics began, of approximately 10,000 metric tons (t) based
on a second-order polynomial fit. For mercury (Hg) a production of 64,000 t was determined for the time up to the year 1900,
when annual production figures started to become available, again using a second-order polynomial fit. While the results obtained
by the application of second-order polynomial functions could be confirmed by higher-order polynomial functions in the cases
of both USA oil as well as global Au production, this was not possible in the case of global Hg production because of a highly
irregular production curve. 相似文献
7.
A number of models have been established to simulate the behaviour of solute transport due to chemical pollution, both in croplands and groundwater systems. An approximate polynomial solution to convection–dispersion equation (CDE) based on boundary layer theory has been verified for the use to describe solute transport in semi-infinite systems such as soil column. However, previous studies have only proposed low order polynomial solutions such as parabolic and cubic polynomials. This paper presents a general polynomial boundary layer solution to CDE. Comparison with exact solution suggests the prediction accuracy of the boundary layer solution varies with the order of polynomial expression and soil transport parameters. The results show that prediction accuracy increases with increasing order up to parabolic or cubic polynomial function and with no distinct relationship between accuracy and order for higher order polynomials (\(n\geqslant 3\)). Comparison of two critical solute transport parameters (i.e., dispersion coefficient and retardation factor), estimated by the boundary layer solution and obtained by CXTFIT curve-fitting, shows a good agreement. The study shows that the general solution can determine the appropriate orders of polynomials for approximate CDE solutions that best describe solute concentration profiles and optimal solute transport parameters. Furthermore, the general polynomial solution to CDE provides a simple approach to solute transport problems, a criterion for choosing the right orders of polynomials for soils with different transport parameters. It is also a potential approach for estimating solute transport parameters of soils in the field. 相似文献
8.
Xiao-hui Tan Meng-fen Shen Xiao-liang Hou Dan Li Na Hu 《Geotechnical and Geological Engineering》2013,31(4):1011-1025
The response surface method (RSM) is a powerful approach for carrying out reliability analysis for complicate engineering with implicit limit state functions. The quality of a response surface mainly depends on the choice of response surface function and the selection of sample points. To investigate the influence of the types of response surface functions and to reduce the computation efforts, two new sampling methods and a hybrid RSM are proposed. In the hybrid RSM, four types of response surface functions and three sampling methods are involved, and each Response surface function can be connected to each sampling method. The four response surface functions are quadratic polynomial without cross terms (PN1), quadratic polynomial with cross terms, radial basic function network (RBFN) and support vector machine (SVM). The three RSMs using the traditional sampling method, the new iterative sampling method and the new experiment design method are RSM1, RSM2 and RSM3, respectively. The accuracy and efficiency of different RSMs are illustrated through three examples. When an iterative method is used for locating sample points, the PN1-based RSM2 is proposed for its accuracy and efficiency. And when an experiment design method is used for locating sample points, the RBFN- or SVM-based RSM3 is suggested because the RBFN or SVM is suitable for global fitting. 相似文献
9.
This paper investigates the performance of normalized response function obtained by normalizing the Cagniard impedance function
by a suitable factor and then rotating the phase by 45‡ to make it purely real for homogeneous half-space and equal to the
square root of the half-space resistivity. Two apparent resistivity functions based on respectively the real and imaginary
parts of this response function are proposed. The apparent resistivity function using the real part contains almost the same
information as that yielded by the Cagniard expression while the one using the imaginary part qualitatively works as an indicator
of the number of interfaces in the earth model. The linear straightforward inversion scheme (SIS), developed by the authors
employing the concept of equal penetration layers, has been used to validate the proposed apparent resistivity functions.
For this purpose, several synthetic and field models have been examined. Five synthetic models are studied to establish the
veracity of the new functions and two well-studied published field data sets are inverted through SIS for comparison. We noticed
that the new function and SIS compliment each other and lead to better understanding of the data information and model resolution. 相似文献
10.
Olga J. Waelder 《Central European Journal of Geosciences》2009,1(2):232-239
Morphometric approaches deal with obtaining quantitative parameters of relief forms. In particular, such parameters can be used for the classification of diverse relief forms. There is a noticeable demand for such approaches in geosciences. For example, the differentiation of valley forms belongs to the research field of geomorphology. A valley form includes important information with respect to the valley genesis. It is assumed that the U-shape probably corresponds to a glacier-induced valley, but the V-shape reflects the fluvial genesis of a valley. A prior generalisation of valley cross-profiles is necessary in order to obtain their morphometric parameters. These parameters contribute to the valley differentiation. The conventional generalisation approaches are based on the approximation of such cross-profiles using a special function. This function can be a catenary curve, a special polynomial or a set of polynomials. An alternative model is the GPL model. In this paper we propose a new generalisation approach, which uses special orthonormal functions. Based on these functions, form coefficients can be obtained for use in cluster analysis, resulting in the shape classification of valley cross profiles. An application of our approach for a real data set is presented. 相似文献
11.
In this paper a new approach is presented, based on evolutionary polynomial regression (EPR), for determination of liquefaction potential of sands. EPR models are developed and validated using a database of 170 liquefaction and non-liquefaction field case histories for sandy soils based on CPT results. Three models are presented to relate liquefaction potential to soil geometric and geotechnical parameters as well as earthquake characteristics. It is shown that the EPR model is able to learn, with a very high accuracy, the complex relationship between liquefaction and its contributing factors in the form of a function. The attained function can then be used to generalize the learning to predict liquefaction potential for new cases not used in the construction of the model. The results of the developed EPR models are compared with a conventional model as well as a number of neural network-based models. It is shown that the proposed EPR model provides more accurate results than the conventional model and the accuracy of the EPR results is better than or at least comparable to that of the neural network-based models proposed in the literature. The advantages of the proposed EPR model over the conventional and neural network-based models are highlighted. 相似文献
12.
紧支径向基函数能使支配方程中的刚度矩阵具有稀疏性,很适合应用于无网格方法中,其缺点是在插值计算时精度不高.点插值方法的插值函数具有Delta函数性质,可以很方便的施加本质边界条件,但在计算插值函数时矩阵易出现奇异.为了提高计算精度并避免点插值法的局限性,首先对紧支径向基函数进行完备性修正,然后用完备性修正的紧支径向基函数代替多项式来形成插值函数,建立了紧支径向基函数点插值方法.由于该方法中的形函数满足Delta函数性质,因此本质边界条件可以像传统的有限元方法一样很容易施加.然后将该方法用于二维弹性静力问题的求解,导出了其相应的离散方程.最后将该方法应用于一个悬臂梁的分析中,初步验证了该方法的有效性与合理性. 相似文献
13.
在材料塑性本构理论中应用热动力学原理一般有两种方法,一是在引入的屈服（包括硬化）、破坏函数和塑性势概念的基础上,从数学上或者根据试验规律,假设（拟合）其函数形式,然后将热力学定律或准热力学公设作为附加约束引入本构模型;二是直接从热动力学出发,通过构造能量函数（热力学势）、耗散函数及较少的限制条件给出全部的塑性本构理论,而得到的本构理论自动满足热动力学原理。长期以来,针对各种不同材料提出的大量屈服破坏函数,许多都是按照第一种方法给出的,却并未见到进行过严格的热动力学限制的验证。研究从塑性本构理论中上述两种研究方式在热力学定律的满足上的一致性出发,将求屈服函数对应的耗散势的问题归结为关于耗散势的偏微分方程求解问题,从理论上演绎出塑性理论中一族率无关线性屈服破坏函数对应的耗散势函数,从而将屈服破坏函数的热动力学验证问题转化为其对应耗散势的正负判断问题,也沟通了塑性理论中屈服破坏函数同热动力学中耗散势在概念上的联系,对于理解屈服破坏函数的热动力学内涵有重要理论意义。特别地,文中给出的求耗散势的方法具有一般性,不仅适合于线性的屈服破坏函数,也适合于非线性的屈服破坏函数。最后,利用热力学第2定律给出了一族线性屈服破坏函数具体的热力学限制条件。 相似文献
14.
纳米矿物是纳米地球科学（Nanogeoscience）的核心研究对象之一.鉴于"纳米矿物"的概念在实际运用时较宽泛,有时与经典定义不符,建议用"纳米结构矿物"代替"纳米矿物",并简析了纳米结构矿物（Nanostructured Minerals）的概念.以管状纳米结构矿物（埃洛石和伊毛缟石）、球状纳米结构矿物（水铝英石）、层间纳米结构矿物（蒙脱石和伊/蒙混层矿物）和多孔纳米结构矿物（硅藻质蛋白石）为例,分析了纳米结构矿物的结构、表面基团的特殊性及其所衍生的特殊界面反应性,讨论了它们对矿物资源利用和油气生成等地球物质循环过程的重要意义. 相似文献
15.
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
16.
A Simplified Failure Criterion for Intact Rocks Based on Rock Type and Uniaxial Compressive Strength 总被引：2，自引：1，他引：1
Jiayi Shen Rafael Jimenez Murat Karakus Chaoshui Xu 《Rock Mechanics and Rock Engineering》2014,47(2):357-369
The uniaxial compressive strength (UCS) of intact rock, which can be estimated using relatively straightforward and cost-effective techniques, is one of the most practical rock properties used in rock engineering. Thus, constitutive laws to represent the strength and behavior of (intact) rock frequently use it, along with additional intrinsic rock properties. Although triaxial tests can be employed to obtain best-fit failure criterion parameters that provide best strength predictions, they are more expensive and require time-consuming procedures; as a consequence, they are often not readily available at early stages of a project. Based on the analysis of an extensive triaxial test database for intact rocks, we propose a simplified empirical failure criterion in which rock strength at failure is expressed in terms of confining stress and UCS, with a new parameter which can be directly estimated from the UCS for a specified rock type in the absence of triaxial test data. Performance of the proposed failure criterion is then tested for validation against experimental data for eight rock types. The results show that strengths of intact rock estimated by the proposed failure criterion are in good agreement with experimental test data, with small discrepancies between estimated and measurements strengths. Therefore, the proposed criterion can be useful for preliminary (triaxial) strength estimation of intact rocks when triaxial tests data are not available. 相似文献
17.
Life-time prediction for rocks under static compressive and tensile loads: a new simulation approach 总被引：2，自引：0，他引：2
The life time or time to failure of rocks under load is governed by microstructural defects, like microcracks, voids etc.
The life time can be predicted either by empirical exponential laws or physical laws based on damage and fracture mechanics.
The proposed numerical model is based on subcritical crack growth using the linear elastic fracture mechanical approach and
is implemented as a numerical cellular automate. The algorithm considers both tensile and shear fracturing. Each cell contains
a microcrack of random length according to a given probability function. Fracture growth is controlled by the Charles equation.
Macroscopic cracks are the results of the coalescence of growing microcracks. Within the numerical approach elasto-plastic
stress redistributions take place. If the stress intensity factors have reached the critical values or the microcrack has
reached the zone dimension, the zone is considered as fractured and residual strength values are assigned. The proposed approach
was applied to rock samples under uniaxial compressive and tensile loads (creep tests). Successful results were obtained in
respect to the predicted life time, damage evolution and the fracture pattern. Conclusions for further improvements and extensions
of this methodology were drawn. 相似文献
18.
19.
Bakhtiar Feizizadeh Majid Shadman Roodposhti Thomas Blaschke Jagannath Aryal 《Arabian Journal of Geosciences》2017,10(5):122
This study compares the predictive performance of GIS-based landslide susceptibility mapping (LSM) using four different kernel functions in support vector machines (SVMs). Nine possible causal criteria were considered based on earlier similar studies for an area in the eastern part of the Khuzestan province of southern Iran. Different models and the resulting landslide susceptibility maps were created using information on known landslide events from a landslide inventory dataset. The models were trained using landslide inventory dataset. A two-step accuracy assessment was implemented to validate the results and to compare the capability of each function. The radial basis function was identified as the most efficient kernel function for LSM with the resulting landslide susceptibility map showing the highest predictive accuracy, followed by the polynomial kernel function. According to the obtained results, it concluded that using SVMs can generally be considered to be an effective method for LSM while it demands careful consideration of kernel function. The results of the present research will also assist other researchers to select the best SVM kernel function to use for LSM. 相似文献
20.
GENERALIZED FLOW LAWS OF POLYPHASE ROCKS: AN OVERVIEW 总被引：1，自引：0，他引：1
Rheological properties of polyphase rocks play an important role in the dynamics of the lithosphere and asthenosphere. However, such fundamental issues have not been well resolved. A theoretical analysis has been made to develop expressions for the flow laws of polyphase rocks in terms of the volume fractions and flow laws of their constituent phases. The flow strengths predicted by the proposed model for common crustal and upper mantle rocks such as granite, diorite, diabase and lherzolite, and for synthetic two-phase composites such as forsterite-enstatite and water ice-ammonia dehydrate aggregates are in good agreement with previously determined experimental values. The proposed theoretical model allows one to calculate, to the first approximation, the flow laws of a large number of polyphase rocks at geologic conditions based on the experimentally determined flow laws of a relatively small number of monomineralic aggregates. 相似文献