考虑冻融影响的岩土类材料导热系数计算新方法

从多孔随机混合介质理念出发,提出了考虑相变及未冻水影响的冻融条件下岩土类材料的导热系数计算的新方法,并根据已有的试验数据,利用多孔随机混合介质模型求出了同等条件下的导热系数,研究结果表明：模型的计算结果和试验结果基本一致,其平均偏差为2.3%,最大偏差为5.4%。另外,通过与现有的3种导热系数的取值方法的比较发现：目前广泛使用的指数加权平均法在0℃以上时计算结果较准确,但并不适合计算低温（0℃以下）岩土类材料的导热系数。加权调和平均法和加权算术平均法计算结果误差都很大,且不能反映相变对导热系数的影响。研究成果为低温相变条件下岩土介质温度场的正确求解提供了理论前提。     

基于盲数理论的边坡安全稳定分析研究

岩土工程中的各种信息普遍存在着随机性、模糊性、灰性及未确知性等不确定性,由于实际情况的复杂和试验资料的不足,计算参数往往是多种不确定性的混合体。针对这一特点,利用盲数来表达计算参数的不确定性,将盲信息的数学理论引入到边坡稳定的刚体极限平衡计算方法中,提出了一种安全系数计算的新方法。运用盲数运算法则计算出安全系数在不同的取值区间内的可信度,从而为判断边坡的稳定状态提供了更全面的依据,克服了传统方法描述过于绝对化的问题。实例研究表明,盲数在边坡稳定分析中能更好地考虑参数的不确定性情况,得到的结果更可靠,有较好的实用价值。     

Community‐Derived Standards for LA‐ICP‐MS U‐(Th‐)Pb Geochronology – Uncertainty Propagation,Age Interpretation and Data Reporting

The LA‐ICP‐MS U‐(Th‐)Pb geochronology international community has defined new standards for the determination of U‐(Th‐)Pb ages. A new workflow defines the appropriate propagation of uncertainties for these data, identifying random and systematic components. Only data with uncertainties relating to random error should be used in weighted mean calculations of population ages; uncertainty components for systematic errors are propagated after this stage, preventing their erroneous reduction. Following this improved uncertainty propagation protocol, data can be compared at different uncertainty levels to better resolve age differences. New reference values for commonly used zircon, monazite and titanite reference materials are defined (based on ID‐TIMS) after removing corrections for common lead and the effects of excess ²³⁰Th. These values more accurately reflect the material sampled during the determination of calibration factors by LA‐ICP‐MS analysis. Recommendations are made to graphically represent data only with uncertainty ellipses at 2s and to submit or cite validation data with sample data when submitting data for publication. New data‐reporting standards are defined to help improve the peer‐review process. With these improvements, LA‐ICP‐MS U‐(Th‐)Pb data can be considered more robust, accurate, better documented and quantified, directly contributing to their improved scientific interpretation.     

化学测量中不确定度的计算方法——不确定度连续传递模型计算示例

不确定度连续传递模型的基本步骤为：①对标准曲线的各点进行不确定度评定,给出各点的标准不确定度;②对标准曲线各点的响应值进行多次测定,得出其平均值和标准不确定度;③以这2个标准不确定度为权重进行拟合,得出双误差拟合方程和标准不确定度的计算公式;④计算标准曲线各点与其校准点的差值,并将其转换成标准不确定度;⑤将以上4项按不确定度传播规律计算总不确定度。实际测量时, ①、②、④步用插值法算得。通过一个实例比较了不同拟合方法间结果的差别,说明了运用X、Y的相对误差作为权重的直线拟和,再加上“不确定度连续传递模型”算得的测量不确定度更为合理。     

化学测量中不确定度的计算方法——不确定度连续传递模型计算示例

不确定度连续传递模型的基本步骤为：①对标准曲线的各点进行不确定度评定,给出各点的标准不确定度;②对标准曲线各点的响应值进行多次测定,得出其平均值和标准不确定度;③以这2个标准不确定度为权重进行拟合,得出双误差拟合方程和标准不确定度的计算公式;④计算标准曲线各点与其校准点的差值,并将其转换成标准不确定度;⑤将以上4项按不确定度传播规律计算总不确定度。实际测量时, ①、②、④步用插值法算得。通过一个实例比较了不同拟合方法间结果的差别,说明了运用X、Y的相对误差作为权重的直线拟和,再加上“不确定度连续传递模型”算得的测量不确定度更为合理。     

Variance–Covariance Matrix of the Experimental Variogram: Assessing Variogram Uncertainty

Assessment of the sampling variance of the experimental variogram is an important topic in geostatistics as it gives the uncertainty of the variogram estimates. This assessment, however, is repeatedly overlooked in most applications mainly, perhaps, because a general approach has not been implemented in the most commonly used software packages for variogram analysis. In this paper the authors propose a solution that can be implemented easily in a computer program, and which, subject to certain assumptions, is exact. These assumptions are not very restrictive: second-order stationarity (the process has a finite variance and the variogram has a sill) and, solely for the purpose of evaluating fourth-order moments, a Gaussian distribution for the random function. The approach described here gives the variance–covariance matrix of the experimental variogram, which takes into account not only the correlation among the experiemental values but also the multiple use of data in the variogram computation. Among other applications, standard errors may be attached to the variogram estimates and the variance–covariance matrix may be used for fitting a theoretical model by weighted, or by generalized, least squares. Confidence regions that hold a given confidence level for all the variogram lag estimates simultaneously have been calculated using the Bonferroni method for rectangular intervals, and using the multivariate Gaussian assumption for K-dimensional elliptical intervals (where K is the number of experimental variogram estimates). A general approach for incorporating the uncertainty of the experimental variogram into the uncertainty of the variogram model parameters is also shown. A case study with rainfall data is used to illustrate the proposed approach.     

Uncertainty in spatial average undrained shear strength with a site-specific transformation model

ABSTRACT

Transformation models are used to infer geotechnical properties from indirect measurements. A site-specific transformation model can be calibrated with direct and indirect measurements from a site. When such a model is used, then spatial variability, measurement errors and statistical uncertainty propagate into the uncertainty of the spatial average, which is the variable of interest in most geotechnical analyses. This research shows how all components enter the total uncertainty of a transformation model for undrained shear strength from cone resistance. A method is proposed to estimate the uncertainty in the spatial average undrained shear strength, particularly focusing on the role of averaging of all spatially variable error components. The main finding is that if a considerable share of the measurement and transformation errors is random or spatially variable, the uncertainty estimates can be considerably lower compared to methods proposed earlier, and hence, characteristic values can be considerably higher.     

天津港土性相关距离的计算研究和统计分析

相关距离是随机场理论应用于实际工程可靠度分析的一个重要参数。根据随机场理论,对土性参数相关距离的计算方法进行了研究和改进,提出求解相关距离的波动函数法和加权拟合相关函数法,使相关距离的计算更加简便易行,且精度有所提高。结合大量工程地质勘察资料,对天津港地区典型土层的垂直向相关距离及水平向相关距离进行了计算和统计,获得相关距离的地区性代表值,可作为此地区实际工程的参考。同时,对取样间距及土性指标对相关距离的影响进行了分析,提出了当取样间距变化时相关距离的确定原则,并指出相关距离是反映土的空间固有变异性的基本属性,由不同土性指标求得的相关距离值基本相同。     

A novel random discrete element analysis of rock fragmentation

This paper presents a novel probabilistic approach of random discrete element analysis (RDEA) to investigate the mechanism of rock fragmentation under uniaxial compression. This model combines the advantages of both random field theory and discrete element method in characterizing the spatial variation and uncertainty of microscopic material properties. The numerical results reveal that the stress-strain curves of a group of tests can match well the general trend of the experimental data, with the mean uniaxial compressive strength (UCS) of 10.18 MPa and the mean Young modulus of 1.73 GPa. The coefficient of variation (COV) for the rock samples is much lower than that of the initial random fields of particles because of the averaging effect of microscopic material property in obtaining the bulk values. The rock fragmentation is initiated by the breakage of weak particles within the rock mass, and it develops rapidly as the vertical loading stress approaches the UCS. The final damage zone resides dominantly in the weak region of the rock sample, and the distribution of material property coefficients follows a similar beta distribution as the corresponding initial random field. Rock samples with persistent “pillar-like” structures of strong particles can effectively resist the normal compression, resulting in high rock strengths. The traditional DEM simulation with a set of constant material properties can only represent one extreme realization of random field, which could significantly overestimate the rock strength. The proposed RDEA approach can effectively capture the uncertainty and complex interactions of rock fragmentation in a more realistic and reliable way.     

理论变异函数球状模型的加权线性规划法似合

对理论变异函数球状模型及其套合结构拟合这一问题作了探讨，提出了加权线性规划拟合法。同于该法在目标函数中既可考虑到对不同滞后h下所得实验变异函数值进行加权，又可保证拟合成功，同时还可进行人工干预，因此，方法综合了现有加权多项式拟合法及线性规划拟合法的各自优点，且在计算上较目标规划拟合法更为简单。     

Bearing Capacity of Two-Layered Artificial Ground with Firm Crust and Weak Subgrade Under Circular Pressure

Classical bearing capacity expressions can not afford variant engineering requests, since they were deducted under hypotheses of strip footing on homogeneous soil. An often met case was taken into account that circular footing on two-layered ground, which has firm crust and weak subgrade. Weighted method and layered method were used in capacity deduction, respectively. The former counts layered soils as single layer of weighted structure and material parameters. But it is restricted to conditions with close strength to each layer. The latter is preferred in engineering calculation, which regards the whole bearing capacity as subgrade’s capacity under the influence of the upper layer. Thus the issue is transformed to K. Terzaghi model plus stress reduction and dispersion effects. At last, the expressions gained from both methods and finite element analysis (FEA) were used in an example calculation, respectively. It approves layered calculating method and suggests the corresponding security coefficient based on elastoplastic FEA results.     

地质标准物质不确定度评估方法初探

在分析地质标准物质标准值不确定度来源的基础上,提出了在多个实验室协作研制地质标准物质时,协作单位除提供重现性检测数据外,还应分别提供各项目检测数据的合成不确定度。分析方法或实验室之间的平均值的合成不确定度按不等精度方法处理。标准物质标准值的不确定度由分析方法、检测实验室、样品均匀性和样品稳定性的不确定度合成后乘以扩展不确定度置信水平下的包含因子而得。     

Estimating the Mean Trace Length of Rock Discontinuities

Summary Rock discontinuities appear as traces on exposures such as natural outcrops or tunnel walls. Discontinuity size which has important effects on rock mass behavior is related to trace length.  This paper presents a technique for estimating mean trace length from the observations made on finite, circular sampling windows. The method takes sampling errors into account and it requires, like existing methods using rectangular sampling windows, that the numbers of discontinuities with both ends censored, with one end observed and one end censored, and with both ends observed be known. Knowledge of the lengths of the observed traces and the distribution of trace lengths is not required. A major advantage of the proposed method over the existing methods is that it does not need sampling data about the orientation of discontinuities, i.e. the proposed method is applicable to traces with arbitrary orientation distributions.  To check the validity of the proposed method, theoretical relations between the mean trace length and the mean diameter of circular discontinuities, respectively for lognormal and negative exponential distributions of the diameter of discontinuities, are derived. The proposed method is then applied to analyze data simulated with the FracMan code, and the predicted results are compared to the corresponding theoretical solutions. The results show that the proposed method is satisfactory. Comparisons of the predicted mean trace length with the mean of observed trace lengths show that it is important to consider sampling biases when estimating mean trace length.     

泰斯公式性态分析与误差估计方法

主要目的是分析在原始数据具有随机误差的情况下,利用泰斯公式进行正逆问题计算时,公式本身对误差的传递作用,即对泰斯公式的性态进行分析。研究中采用了函数对数据随机误差传递作用的随机性分析方法。通过较为简单的数学推导,建立了泰斯公式正逆计算问题的原始数据与计算结果所具有随机误差的统计参数之间的近似关系式,并推导出了两类计算问题的条件数。指出在u值较小的情况下,计算_的问题属于"病态"的;在u=0.438点及其附近,计算T的问题为"病态"的;在u值和_的相对误差与T的相对误差的比值很大的情况下,正问题为"病态"的。其它条件下的计算问题属于"良态"的。据此建议利用抽水试验后期资料计算T值,利用前期资料计算_值。另一方面,还提出了在原始数据的误差为已知的情况下,进行误差估计的方法。      

载金炭样品中金分析数据的灰色处理方法

针对金矿山生产中介产品载金炭样品均匀性差、金的分析数据易产生质量争议,并有在不等精度测量条件下难以确定最佳值等问题,文章利用灰色系统理论进行数据处理和分析,通过灰色关联分析确定其权值,从而建立了确定其加权平均值的灰色处理方法。方法经实际样品验证以及与传统的统计方法比较,具有一定的精度,且易于操作和理解,尤其是在不等精度测量的条件下多个单值数据的加权平均值的权值确定等方面,克服了传统统计理论的不足,具有一定的理论优势和实用性,可以解决数据少和分布不明显的测量问题。     

Reliability level III method in design of square pillar resting on weak floor stratum

Summary Current methods of design of pillars resting on weak floor strata involve only a deterministic, conventional safety factor calculation, based on material parameters treated as the mean values taken from observations. In a case where high parameters variability occurs, these methods may lead to fatal design errors resulting in excessive pillar settlement and roof falls. Therefore, to include the influence of parameters quality, the new approach based on reliability level III method was developed. Consideration was given to the identification of the system parameters importance, and to density function for the safety factor treated as a random variable. Design procedure involving floor probability of failure was illustrated by numerical examples.     

Quantifying impacts of forecast uncertainties on predicted storm surges

In this paper, we propose a framework for quantifying risks, including (1) the effects of forecast errors, (2) the ability to resolve critical grid features that are important to accurate site-specific forecasts, and (3) a framework that can move us toward performance-based/cost-based decisions, within an extremely fast execution time. A key element presently lacking in previous studies is the interrelationship between the effects of combined random errors and bias in numerical weather prediction (NWP) models and bias and random errors in surge models. This approach examines the number of degrees of freedom in present forecasts and develops an equation for the quantification of these types of errors within a unified system, given the number of degrees of freedom in the NWP forecasts. It is shown that the methodology can be used to provide information on the forecasts and along with the combined uncertainty due to all of the individual contributions. A potential important benefit from studies using this approach would be the ability to estimate financial and other trade-offs between higher-cost “rapid” evacuation methods and lower-cost “slower” evacuation methods. Analyses here show that uncertainty inherent in these decisions depends strongly on forecast time and geographic location. Methods based on sets of surge maxima do not capture this uncertainty and would be difficult to use for this purpose. In particular, it is shown that surge model bias can play a dominant role in distorting the forecast probabilities.     

A Bayesian framework for updating model parameters while considering spatial variability

The study presents a recent slope failure in India which resulted in the burial of a village and claimed large number of lives. Current methods of probabilistic back analysis incorporate uncertainty in the analysis but do not consider spatial variability. In this study, back analysis is performed using Bayesian analysis in conjunction with random field theory. The probabilistic method is shown to be efficient in back-analysing a slope failure. It also provides confidence in parameter values to be used for post-failure slope design. The back analysis method which does not consider spatial variability overestimates the uncertainty in analysis, which can lead to uneconomical slope remediation design and measures.     

Acquisition and processing of data for isotope-ratio-monitoring mass spectrometry

Methods are described for continuous monitoring of signals required for precise analyses of 13C, 18O, and 15N in gas streams containing varying quantities of CO2 and N2. The quantitative resolution (i.e. maximum performance in the absence of random errors) of these methods is adequate for determination of isotope ratios with an uncertainty of one part in 10(5); the precision actually obtained is often better than one part in 10(4). This report describes data-processing operations including definition of beginning and ending points of chromatographic peaks and quantitation of background levels, allowance for effects of chromatographic separation of isotopically substituted species, integration of signals related to specific masses, correction for effects of mass discrimination, recognition of drifts in mass spectrometer performance, and calculation of isotopic delta values. Characteristics of a system allowing off-line revision of parameters used in data reduction are described and an algorithm for identification of background levels in complex chromatograms is outlined. Effects of imperfect chromatographic resolution are demonstrated and discussed and an approach to deconvolution of signals from coeluting substances described.     

Pathways for adaptive and integrated disaster resilience

The GIS-multicriteria decision analysis (GIS-MCDA) technique is increasingly used for landslide hazard mapping and zonation. It enables the integration of different data layers with different levels of uncertainty. In this study, three different GIS-MCDA methods were applied to landslide susceptibility mapping for the Urmia lake basin in northwest Iran. Nine landslide causal factors were used, whereby parameters were extracted from an associated spatial database. These factors were evaluated, and then, the respective factor weight and class weight were assigned to each of the associated factors. The landslide susceptibility maps were produced based on weighted overly techniques including analytic hierarchy process (AHP), weighted linear combination (WLC) and ordered weighted average (OWA). An existing inventory of known landslides within the case study area was compared with the resulting susceptibility maps. Respectively, Dempster-Shafer Theory was used to carry out uncertainty analysis of GIS-MCDA results. Result of research indicated the AHP performed best in the landslide susceptibility mapping closely followed by the OWA method while the WLC method delivered significantly poorer results. The resulting figures are generally very high for this area, but it could be proved that the choice of method significantly influences the results.