Divergence of solutions to perturbation-based advection-dispersion moment equations

Moment equation methods are popular and powerful tools for modeling transport processes in randomly heterogeneous porous media, but the application of these methods to advection-dispersion equations often leads to erroneous oscillations. Perturbative methods, required to close systems of moment equations, become inaccurate for large perturbations; however, little quantitative theory exists for determining when this occurs for advection-dispersion equations. We consider three different methods (asymptotic approximation, Eulerian truncation, and iterative solution) for closing and solving advection-dispersion moment equations describing transport in stratified porous media with random permeability. We obtain approximate analytical expressions for time above which the asymptotic approximation to the mean diverges, in particular quantifying the impact that dispersion has on delaying—but not eliminating—divergence. We demonstrate that Eulerian truncation and iterative solution methods do not eliminate divergent behavior either. Our divergence criteria provide a priori estimates that signal a warning to the practitioner of stochastic advection-dispersion equations to carefully consider whether to apply perturbative approaches.     

基于随机二元指标的边坡稳定性分析

考虑岩土体抗剪强度参数的变异性,综合极限平衡法和可靠性理论构建了安全系数概率密度分布函数模型。结合实际工程特点,以安全系数大于临界值为标准构建有效区,将有效区安全系数均值与对应可靠度相乘,得到以安全系数和可靠度为随机二元指标的有效安全系数。以有效安全系数为定量指标,将边坡宏观特征现象与定量分析相联系,构建意义更为明确的边坡稳定性分析及评价方法。通过工程实例对比了有效安全系数与传统评价指标之间的差异。所得结论可为工程建设提供参考和借鉴。     

宁夏及邻区地震活动能量场时空变化特征

运用随机函数理论,将宁夏及邻区地震活动能量场看作时间和空间的随机函数,用自然正交函数展开方法,系统研究宁夏及邻区主要典型能量场的时间权重系数变化曲线以及典型能量场的空间等值线图。结果发现,目标曲线较大幅度的升、降变化预示了可能发生中强地震的时间段,而等值线图的高值变化（危险区）对应了可能发生中强地震的区域。     

Managing expert-information uncertainties for assessing collapse susceptibility of abandoned underground structures

Assessing the collapse susceptibility of abandoned cavities at a regional scale is associated with large uncertainties that are mainly related to the very nature of the phenomena, but also to the difficulty in collecting exhaustive information at such a scale on often “forgotten” structures. In this context, the expert's role is essential, because he is able to synthesize the information resulting from the inventory and from the commonly imprecise, if not vague, criteria on the basis of his experience and his knowledge of the geological, historical, economic regional context.In this article, we propose mathematical tools for representing and processing this information in order to give flexibility to this step and manage the uncertainty inherent in the expert's information. The first tool, based on the weight of evidence theory, is for managing the uncertainty due to the heterogeneous spatial distribution of the data, whereas the second tool, based on the fuzzy set theory, is for managing the imprecision and incompleteness of available data, which hinder the definition of the class boundaries of the quantitative decision criteria. Based on an appropriate representation of the uncertainty sources (related to the input data and to the expert diagnostic), we then propose a methodology that integrates the uncertainty in the final output of the collapse susceptibility assessment and provides a confidence indicator useful within the decision-making process. The proposed methodology is applied to the Arras territory in the North of France, where abandoned chalk pits (dating back to the Roman ages) and war saps located in the vicinity of the First World War front lines (i.e. covered trenches), raise both difficulties for urban planning.     

偏序向量空间中集值映射的一类扩张定理

经典的Hahn-Banach扩张定理及其推广定理有着非常广泛的应用,但主要都是讨论单值映射的扩张性质。为了进一步讨论多值映射的扩张性质,通过构造的方法,利用了zorn引理及偏序向量空间的完备性,得到了当定义域空间是一个实向量空间,而值域空间是由锥引入序的Dedekind完备的偏序向量空间时集值映射的一类扩张性质,以及当给值域空间引入相应拓扑时连续集值映射的一类扩张性质。其结果进一步推广了Hahn-Banach扩张定理,扩大了其应用范围。     

Quantitative risk assessment of landslide by limit analysis and random fields

Risk may be estimated by multiplying the probability of failure by the consequence. This is acceptable for systems that have a single mode of failure. For systems that have multiple failure modes, such as landslides, the consequences should be assessed individually for each of the failure modes. This paper proposes a new framework of quantitative landslide risk assessment, in which consequences are assessed individually. The framework is generally applicable, and the landslide risk assessments of two typical slopes are presented.     

基于集对分析的膨胀土胀缩性Vague集评价模型

膨胀土胀缩性等级评价是膨胀土地区工程治理中的首要问题。本文探讨了基于集对分析的膨胀土胀缩性等级评价模型,以克服膨胀土胀缩性评价指标的不确定性和复杂性。模型以Vague集描述膨胀土胀缩性等级的确定性和不确定性,并应用集对分析构造Vague集的隶属函数。通过实例应用及与其他方法评价结果的对比分析,表明该模型应用于膨胀土胀缩性等级评价是有效可行的,且具有判断结果准确、易于操作等优点。     

Calibration of the specific barrier model to Iranian plateau earthquakes and development of physically based attenuation relationships for Iran

Earthquake ground-motion relationships for soil and rock sites in Iran have been developed based on the specific barrier model (SBM) used within the context of the stochastic modeling and calibrated against up-to-date Iranian strong-motion data. A total of 171 strong-motion accelerograms recorded at distances of up to 200 km from 24 earthquakes with moment magnitudes ranging from Mw 5.2 to 7.4 are used to determine the region-specific source parameters of this model. Regression analysis was conducted using the “random effects” methodology that considers both earthquake-to-earthquake (inter-event) variability and within-earthquake (intra-event) variability to effectively handle the problem of weighting observations from different earthquakes. The minimization of the error function in each iteration of the “random effects” procedure was performed using the genetic algorithm method. The residuals are examined against available Iranian strong-motion data to confirm that the model predictions are unbiased and that there are no significant residual trends with distance and magnitude. No evidence of self-similarity breakdown is observed between the source radius and its seismic moment. To verify the robustness of the results, tests were performed to confirm that the results are unchanged if the number of observations is changed by removing different randomly selected datasets from the original database. Stochastic simulations, using the derived SBM, are then performed to predict peak ground-motion and response spectra parameters for a wide range of magnitudes and distances. The stochastic SBM predictions agree well with the new empirical regression equations proposed for Iran, Europe and Middle East in the magnitude–distance ranges well represented by the data. It has been shown that the SBM of this study provides unbiased ground-motion estimates over the entire frequency range of most engineering interests (1–10 Hz) for the Iranian earthquakes. Our results are also important for the assessment of hazards in other seismically active environments in the Middle East and Mediterranean regions.     

A risk assessment model for produced water discharge from offshore petroleum platforms-development and validation

Produced water discharge accounts for the greater portion of wastes arising from offshore oil and gas production operations. Development and expansion of Canada’s offshore oil and gas reserves has led to concerns over the potential long-term impacts of produced water discharges to the ocean. To examine this emerging environmental issue at a regional scale, an integrated risk assessment approach was developed in this study based on the princeton ocean model (POM), a random walk (RW) and Monte Carlo simulation. The use of water quality standards arrayed in a Monte Carlo design in the developed approach has served to reflect uncertainties and quantify environmental risks associated with produced water discharge. The model was validated against field data from a platform operating off Canada’s east coast, demonstrating its usefulness in supporting effective management of future produced water discharge.