Computer program for presentation of grain-size data by the graphic method

A computer program is described for a Hewlett-Packard desk-top Calculator (Model 9820A)-Plotter (Model 9862A) which plots a histogram, frequency polygon and/or cumulative curve, as well as standard statistical parameters and percentages of gravel, sand, silt, and clay from raw weight data from a sediment grain-size analysis. The program utilizes the graphic method for calculating statistical parameters in contrast to other commonly used computer programs derived for the method of moments. This program is advantageous because (1) it is rapid, (2) it allows direct comparison with grain-size data in the literature which have been computed by the graphic method, (3) either a complete presentation of a distribution can be obtained on one sheet of paper or a series of cumulative curves or frequency polygons can be prepared on a single graph which is ready for publication photocopying, (4) automatic extrapolation of data points from a cumulative curve eliminates inconsistencies arising from manual extrapolation, and (5) the desk-top calculator is more convenient to use, eliminates punching of data cards, and can be operated by someone without a knowledge of computers and programming. Disadvantages of the program are: (1) some authors feel critical percentiles are more accurately read off cumulative curves plotted on a probability ordinate than on an arithmetic ordinate, (2) the cumulative curve is a series of straight-line segments, (3) the frequency polygon is not as accurate a representation of grain-size distribution as a frequency curve and (4) size class intervals for the histogram and frequency polygon are standardized at 0.5φ, even though gravel and mud fractions are analysed at whole φ intervals. For most studies, the advantages of the program outweigh the disadvantages.     

基于不确定度连续传递模型的标准曲线双误差拟合程序

"不确定度连续传递模型"是建立在"约克方程"基础上的双误差标准曲线回归新理论。文章简单介绍了这一理论的基本思路与数学模型以及根据该模型设计出的计算机程序。该程序可进行标准曲线的一次曲线、二次曲线、三次曲线、指数曲线和对数曲线的简单回归、一次曲线的Y-单误差(含相对误差和绝对误差)回归,一次曲线x、y双误差(含相对误差和绝对误差)回归,并可根据回归曲线计算出给定允许最大误差时的检出限。程序功能齐全、界面友好、使用方便,是化学检测实验室必备的工具软件之一。     

高温下岩石损伤本构模型及其验证

为完善高温条件下的岩石损伤本构模型及参数确定方法,基于有效应力理论,引入Weibull分布函数,在微元体强度服从Hoek-brown准则的条件下,考虑残存强度影响,对损伤变量修正,引入损伤修正系数,建立了能够反映高温作用下的岩石损伤特征统计本构模型。考虑岩石损伤过程中的损伤阈值因素,对本构模型采用分段函数的形式。通过试验,获取常规力学参数,依据本构模型参数求解过程,确定本构模型参数值,并拟合模型参数值与温度之间的关系。对模型理论曲线进行验证。结果表明：提出的高温岩石统计损伤本构模型理论曲线与试验曲线具有较好地相似性,更加贴近试验曲线,体现了本构模型的合理性。同时模型理论曲线与岩石三轴试验曲线具有较高的吻合度,说明本构模型能够反映出岩石的全应力− 应变曲线特征,能够体现出模型的适用性。模型为岩石强度的估算和岩石热损伤软化问题提供了参考。     

模拟应变软化岩石三轴试验过程曲线

在经典弹塑性理论框架下,认为岩石材料在应变软化过程中遵守摩尔-库仑强度准则,塑性变形服从非关联流动法则。对两组岩石在三轴试验中呈现的应变软化行为进行了分析,获取了峰值前后强度参数的大小。采用应变软化模拟方法,将应力-应变曲线峰后应变软化阶段简化为一系列应力跌落和塑性流动的脆塑性过程,在给定的强度参数演化规律基础上,得到了岩石的应力-应变曲线、侧向应变-轴向应变曲线、体应变-轴向应变曲线和塑性体应变-轴向塑性应变曲线。模拟得到的应力-应变曲线与试验结果吻合较好,其他曲线与相关试验测试规律基本一致。研究成果对确定岩石强度参数与认识岩石峰后强度演化规律有一定的指导意义。     

边坡可靠度分析的非侵入式随机有限元法

提出基于非侵入式随机有限元法的边坡可靠度分析方法,并编写计算程序NISFEM。采用有限元滑面应力法计算边坡安全系数,将Hermite随机多项式展开与SIGMA/W和SLOPE/W模块有机结合实现边坡可靠度非侵入式随机分析。根据随机多项式展开系数,给出边坡安全系数前4阶统计矩（均值、标准差、偏度和峰度）和Sobol指标解析表达式,并采用Sobol指标进行边坡可靠度参数敏感性分析。最后,以均质土坡可靠度问题为例,证明该方法在边坡可靠度分析中的有效性。结果表明,边坡可靠度分析的非侵入式随机有限元法能够有效地考虑边坡变形对边坡可靠度的影响,计算效率远远高于蒙特卡罗模拟方法（MCS）,是解决复杂边坡可靠度问题一种有效地分析手段;黏聚力和内摩擦角变异性对边坡安全系数前四阶统计矩具有明显的影响,重度变异性对安全系数前4阶统计矩几乎没有影响;抗剪强度参数间负相关性对边坡安全系数均值几乎没有影响,但对安全系数标准差、偏度和峰度均有明显的影响。此外,随着抗剪强度参数间负相关性的增加,边坡安全系数由近似正态分布逐渐变为明显的非正态分布。     

A COMPUTER PROGRAM FOR GRAIN-SIZE DATA1

The computer program presented here seeks to improve estimation of statistical parameters for grain-size data by use of interpolated values. Interpolation is made by fitting a series of overlapping parabolas to the data, and follows the method of Snyder (1961). The values are used in moment formulas to compute standard statistical measures. Skewness and kurtosis are reduced by the interpolation data, and extreme positive values of kurtosis tend to be greatly reduced. The program also picks major modes, the median, and sediment type.     

Log-normal interpolation in grain size analysis

A computer program is described for the display of grain size distributions by log-probability plots. These plots are useful to recognize and interpret log-normal subpopulations. Because log-probability plots of the cumulative curves often show two or more straight line segments we suggest a method of ‘log-normal’interpolation for use in computing statistical parameters. The method combines advantages of graphical methods with those of mathematical moments. Finally, the frequency curve is derived by approximating the log-probability plot of the cumulative curve with spline functions.     

双误差回归模型在ICP-MS测定饮用水中锶的不确定度评定的简化应用

在计算电感耦合等离子体质谱法测定饮用水中锶的浓度(x)时,由于标准系列配制和仪器检测过程中信号(y)漂移产生的不确定度会传递给最终的计算结果。普通的一次或多次线性拟合结果不能真实地反映对于x、y值都含误差的数据拟合情况。文章对标准曲线进行了双误差回归计算,从双误差回归线性方程推导出校准曲线拟合过程产生不确定度的计算公式,建立了方法检出限与曲线拟合参数(x、y、曲线截距和斜率)及其相关不确定度之间的关系式,依据误差连续传递公式及不确定度分量计算公式简化了合成不确定度的表达式。从合成不确定度计算公式中可得出,水样中锶含量的浓度越低,其对应的不确定度越大;标准系列配制过程不细致、仪器灵敏度低,方法检出限越差,与实际测试情况符合。     

土壤水分特征曲线在天然气水合物开采数值模拟中的应用探讨

在使用TOUGH+HYDRATE程序进行水合物开采数值模拟时常用van Genuchten模型计算毛管力,而毛管力大小直接影响水合物开采过程中的产气和产水,因此在数值模拟过程中正确选用模型参数尤为必要。我国某海域天然气水合物储层为未胶结泥质粉砂储层,常规的毛管力测定方法如压汞法、离心法等对该类岩心并不适用,如何测定该类岩心的毛管力并将其应用于van Genuchten模型参数选取具有重要意义。本文探讨了如何应用土壤水分特征曲线测定实验间接获取该类岩心的毛管力数据,为验证该方法的可行性,本文对参考文献[7]中公开的粉砂土壤水分特征曲线测定实验数据进行换算和拟合后得到T+H程序所需的van Genuchten模型参数,结果可为泥质粉砂储层水合物产能研究工作提供参考。     

K0条件下颗粒形状特征对砂土剪切模量的影响

为了研究颗粒形状特征对砂土剪切模量的影响,选取4种形状不同的砂样（福建标准砂和人工石英砂）作为研究对象,通过扫描电镜获取其颗粒微观图像,使用Image Pro Plus软件和自编Matlab程序提取试样颗粒的形状特征。采用改进的半径角和轮廓指数综合描述颗粒偏离圆或椭圆的程度以及棱角变化程度,并基于这两个参数提出颗粒形状因子来综合表征颗粒的形状特征。之后在K0条件下通过弯曲元试验获得不同竖向荷载对应的4个试样的剪切模量,试验结果表明,砂土颗粒的形状因子与砂土的剪切模量具有良好的相关性。最后基于Hertz-Mindlin接触模型,推导出引入形状因子的砂土剪切模量理论计算公式,该计算公式与实测值吻合良好。     

A study of slope stability prediction using neural networks

The determination of the non-linear behaviour of multivariate dynamic systems often presents a challenging and demanding problem. Slope stability estimation is an engineering problem that involves several parameters. The impact of these parameters on the stability of slopes is investigated through the use of computational tools called neural networks. A number of networks of threshold logic unit were tested, with adjustable weights. The computational method for the training process was a back-propagation learning algorithm. In this paper, the input data for slope stability estimation consist of values of geotechnical and geometrical input parameters. As an output, the network estimates the factor of safety (FS) that can be modelled as a function approximation problem, or the stability status (S) that can be modelled either as a function approximation problem or as a classification model. The performance of the network is measured and the results are compared to those obtained by means of standard analytical methods. Furthermore, the relative importance of the parameters is studied using the method of the partitioning of weights and compared to the results obtained through the use of Index Information Theory.     

Statistical relationship between pyrite grain size distribution and pyritic sulfur reduction in Ohio coal

This paper presents a statistical relationship between the pyrite particle size distribution and the potential amount of pyritic sulfur reduction achieved by specific-gravity-based separation. This relationship is obtained from data on 26 Ohio coal samples crushed to 14 × 28 mesh. In this paper a prediction equation is developed that considers the complete statistical distribution of all the pyrite particle sizes in the coal sample.Assuming that pyrite particles occurring in coal have a lognormal distribution, the information about the particle size distribution can be encapsulated in terms of two parameters only, the mean and the standard deviation of the logarithms of the grain diameters. When the pyritic sulfur reductions of the 26 coal samples are related to these two parameters, a very satisfactory regression equation (R² = 0.91) results. This equation shows that information on both these parameters is needed for an accurate prediction of potential sulfur reduction, and that the mean and the standard deviation interact negatively insofar as their influence on pyritic sulfur reduction is concerned.     

城市设计暴雨频率曲线线型的研究

城市排水规划需有一定设计标准的暴雨值,这类设计暴雨的特点是历时短、设计标准不高和统计分布呈反S形。提出了用两端有限对数正态分布和广义指数分布作为频率曲线线型进行计算,可避免用Γ分布适线欠佳的缺点。通过实例,发现采用这两类分布,计算简便,能获得适线较好的结果。     

On an application of cluster analysis for classification of valley cross profiles using special orthonormal functions

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.     

Sensitivity and uncertainty analyses for performance assessment modeling

Sensitivity and uncertainty analyses methods for computer models are being applied in performance assessment modeling in the geologic high-level radioactive-waste repository program. The models used in performance assessment tend to be complex physical/chemical models with large numbers of input variables. There are two basic approaches to sensitivity and uncertainty analyses: deterministic and statistical. The deterministic approach to sensitivity analysis involves numerical calculation or employs the adjoint form of a partial differential equation to compute partial derivatives; the uncertainty analysis is based on Taylor series expansions of the input variables propagated through the model to compute means and variances of the output variable. The statistical approach to sensitivity analysis involves a response surface approximation to the model with the sensitivity coefficients calculated from the response surface parameters; the uncertainty analysis is based on simulation. The methods each have strengths and weaknesses.     

Forecasting the polar motions of the deformable Earth

A mathematical model for the complicated phenomenon of the polar oscillations of the deformable Earth that adequately describes the astrometric data of the International Earth Rotation Service is constructed using celestial mechanics and asymptotic techniques. This model enables us to describe the observed phenomena (free nutation, annual oscillations, and trends) simply and with statistical reliability. The model contains a small number of parameters determined via a least-squares solution using well-known basis functions. Interpolations of the polar trajectory for intervals of 6 and 12 yrs and forecasts for 1–3 yrs are obtained using the theoretical curve. The calculated coordinates demonstrate a higher accuracy than those known earlier.     

Continuous determination of drying-path SWRC of fine-grained soils

Establishing the soil water retention curve, SWRC or the soil water characteristic curve, SWCC, is very useful for determination of unsaturated properties of soils. However, it has been observed that SWRC of a soil is not unique and depends on various factors such as the initial moisture content, density of soil, method of compaction, soil fabric and the path (drying or wetting) adopted for establishing it. In this context, many techniques and instruments have been employed by earlier researchers for determination of the SWRC of soils. However, these techniques entail weighing of the samples during prolonged testing, manually, and hence yield discrete data points. In this situation, AquaSorp® Isotherm Generator (manufactured by Decagon Devices Inc., USA) has been found to be quite useful for continuous determination of the drying-path SWRC of fine-grained soils. This device has been primarily employed for food products, powders and amorphous materials. Hence, demonstration of the utility and limitations of this device for SWRC determination of fine-grained soils becomes essential. With this in mind, extensive studies were conducted on commercially available soils (Kaolinite and Bentonite) by employing this device. In order to understand the influence of specimen specific parameters on the obtained SWRCs, the molding water content and thickness of the specimens were varied and the results have been evaluated critically. Details of the methodology adopted for these investigations, and the findings of the study are presented in this technical note. Based on a critical comparison of the results obtained from this device with those obtained from the dewpoint potentiameter, WP4®, the utility of this device for continuous determination of drying-path SWRC of the soils has also been demonstrated.     

考虑基质吸力的非饱和土邓肯-张统计损伤修正模型

为反映非饱和地基土变形全过程,以某基础工程非饱和土为研究对象,开展固结排水三轴压缩试验。研究发现,非饱和土的偏应力-应变曲线形态近似双曲线,基质吸力对土体力学行为影响十分明显,基质吸力越大,土体偏应力越高。根据非饱和土变形特性及工程特点,选取邓肯-张双曲线模型作为基础模型,引入统计损伤理论,假设非饱和土微元强度服从Weibull概率密度分布,建立邓肯-张统计损伤模型。通过搭建初始切线模量与基质吸力的联系,建立一种新的考虑基质吸力的非饱和土邓肯-张统计损伤模型。给出参数解析方法,得到Weibull分布参数经验表达式,从而修正模型。分析不同基质吸力条件下非饱和土损伤累积规律,采用所建模型和传统邓肯-张模型对比验证非饱和土偏应力-应变试验曲线,证明所建模型的可行性和合理性。研究成果为非饱和土的力学特性研究及辨识模拟提供一定参考。     

Box fractal dimension as a measure of statistical homogeneity of jointed rock masses

A written computer programme to estimate the box fractal dimension (D_B) is verified by estimating D_B of the triadic Koch curve for which the theoretical D is known. The influence of a number of input parameters of the box-counting method on the accuracy of estimated D_B is evaluated using the same Koch curve. The employed size range of the applied box networks was found to be the parameter which has the strongest influence on the accuracy of estimated D_B. This indicated the importance of finding the range of self-similarity or self-affinity for the object considered to select the proper range for the box sizes and, in turn, to obtain accurate estimates of D_B. By calculating D_B for different block sizes sampled from three generated two-dimensional joint patterns, it is shown that D_B can capture the combined effect of joint-size distribution and joint density on the statistical homogeneity of rock masses. The spatial variation of D_B along a 350 m stretch of a tunnel in the shiplock area of the Three Gorges dam site is computed using the joint data mapped on the walls and the roof of the tunnel. This spatial variation of D_B is used, along with the visual geological evaluation of the joint trace maps of the tunnel, in making decisions about statistical homogeneity of the rock mass around the tunnel. The results obtained on statistically homogeneous regions were found to be quite similar to the results obtained from a previous statistical homogeneity investigation which incorporated the effect of number of joint sets and their orientation distributions, but not the spatial variation of D_B. It is recommended that the spatial variation of D_B is used, along with the results of other methods such as contingency table analysis and equal area plots, which incorporate the effect of joint orientation distribution, in addition to the geology of the site, in determining the statistically homogeneous regions of jointed rock masses.     

Evaluation of karstic aquifers contribution to streams by the statistical analysis of recession curves

Karstic aquifers significantly contribute to streams in most of Turkey’s river basins, so studies on karst water resources have great importance for Turkey. Karstic aquifer contributions are generally emerging at several locations near the river bed and are not readily measured by direct hydrometric methods. In this study, the extent of karstic aquifer contributions to a stream will be investigated by the statistical analysis of recession coefficients of recession curves. Six stream gauging stations on different streams in the western Mediterranean region of Turkey are selected. Recession periods of the streams are simulated by exponential and quadratic recession curve models. Recession coefficient series of the stream gauging stations are statistically investigated. The comparison of various statistical parameters shows that the recession coefficient series are fairly related to the karstic aquifer contributions. Especially, the measure of spread parameters, standard deviation and interquartile range of recession coefficient series are related to the extent of the karstic aquifer contributions to streams.