Assessing water quality using water quality index and multivariate analysis

Groundwater is increasingly gaining significance as the main solution to the water supply problems in Ghana, especially in the rural areas. This study was conducted to determine which factors play significant roles in the hydrochemistry of groundwater from the southern Voltaian formation. Conventional graphical and multivariate statistical methods were used. The study reveals three main factors controlling the hydrochemistry. Silicate mineral weathering and reverse cation exchange are the most important processes affecting the hydrochemistry of groundwater at this part of the formation. Interpolation maps created from factor scores suggest that these processes are the most pervasive, recording high scores almost everywhere in the study area. Carbonate mineral weathering is the second most important process in the hydrochemistry. This study finds that carbonate mineral weathering in the area is probably facilitated by carbonic acid rather than sulfuric acid. Chemicals from agricultural activities constitute the third most important process influencing groundwater quality in the area. Eighty samples were used to calculate water quality indices, WQI, which were in turn used to classify groundwater from the study area. Over 98% of the samples fall within the “Excellent” and “Good” categories, suggesting that groundwater from the southern Voltaian formation is generally acceptable for drinking purposes.     

自然水系的计算机处理与分维计算

自然水系的分维值能够反映某一地区一定的地质构造和地壳运动性质,但目前的分维算法大都采用人工完成。本文通过VB编程实现了自然水系的计算机处理与分维计算,并以中国三大水系为例,求得黄河、长江、珠江水系的分维值以及各水系主河道的分维值。该方法快速精确,并能适用于各种线性构造。     

基于孔隙分形维数的土壤大孔隙流水力特征参数研究

根据数字图像制备分析技术得到大孔隙数目、大小和形状等特征数据,用分形理论计算孔隙分形维数,并对两类不同质地土壤的孔隙分形维数进行分析比较,应用基于孔隙分形维数的大孔隙分形模型,建立了土壤水分特征曲线和非饱和导水率的预测模型。结果表明,孔隙分形维数D_v可定量描述不同质地土壤结构,其模型预测精度优于颗粒大小分布估计的分形模型,可用于实际问题的研究。     

矿井涌水量时间序列的长程相关性分析及分维数估算

根据矿井涌水量实测数据,探讨了矿井涌水量时间序列的两个重要特性,即:长程相关性和统计自相似特性。利用小波分析和分形理论在多尺度分析和自相似本质上的一致性,把小波分析和分形理论引入到矿井涌水量时间序列的分析中,得到矿井涌水量时间序列小波变换系数,在此基础上,提出了矿井涌水量时间序列分形维数的小波计算方法,并对巷道涌水量和回采工作面涌水量时间序列的分维值进行了计算,验证了小波分形维数估计法在提取矿井涌水量中所具有的分形特征信息是稳定的和可靠的。     

Water quality parameters along rivers

Water samples have been collected from a part of Surma River along different points and analyzed for various water quality parameters during dry and monsoon periods. Effects of industrial wastes, municipal sewage, and agricultural runoff on river water quality have been investigated. The study was conducted within the Chattak to Sunamganj portion of Surma River, which is significant due to the presence of two major industries-a paper mill and a cement factory. The other significant feature is the conveyors that travel from India to Chattak. This study involves determination of physical, biological and chemical parameters of surface water at different points. The river was found to be highly turbid in the monsoon season. But BOD and fecal coliform concentration was found higher in the dry season. The water was found slightly acidic. The mean values of parameters were Conductivity 84–805μs; DO: dry- 5.52 mg/L, monsoon-5.72 mg/L; BOD: dry-1 mg/L, monsoon-0.878 mg/L; Total Solid: dry-149.4 mg/L, monsoon- 145.7 mg/L. A model study was also conducted and values of different model parameters were estimated.     

基于岩体结构面分布分形维的岩体质量评价

尽管岩体结构面具有空间上的不规则性和结构网络上的复杂性,但由于它又具有自相似的特征,可以运用分形理论来对其进行研究。运用盒计维数法对某矿山巷道围岩体结构面分布的分维数进行计算,验证了岩体结构面分布的分形特征。通过对岩体结构面分布分形维值分布规律的分析发现,分形维数越大、结构面分布越密集,结构面迹线越长,岩体质量越差,表明可将岩体结构面分布的分形维作为岩体质量评价的指标。将计算所得的岩体结构面分布的分维数与按工程岩体分级标准对相应岩体分级所得的岩体质量等级进行对比,提出了一个以岩体结构面分布的分形维作为分级指标的岩体质量评价方案。     

基于岩体结构面统计与分维数的岩体质量评价及其在矿山工程中的应用

以三山岛金矿-510中段和-555中段为例,基于结构面实测数据,利用Matlab对结构面特征进行统计模型,进而实现了岩体裂隙网络Monte-Carlo模拟。然后结合分形理论确定了岩体质量的分维值。研究表明,-510中段和-555中段F3以北的岩体稳定性要好于F3以南的岩体稳定性,从定性和定量的角度对岩体质量进行了分析,为矿山的安全生产提供了一定的依据。     

On the practice of estimating fractal dimension

Coastlines epitomize deterministic fractals and fractal (Hausdorff-Besicovitch) dimensions; a divider [compass] method can be used to calculate fractal dimensions for these features. Noise models are used to develop another notion of fractals, a stochastic one. Spectral and variogram methods are used to estimate fractal dimensions for stochastic fractals. When estimating fractal dimension, the objective of the analysis must be consistent with the method chosen for fractal dimension calculation. Spectal and variogram methods yield fractal dimensions which indicate the similarity of the feature under study to noise (e.g., Brownian noise). A divider measurement method yields a fractal dimension which is a measure of complexity of shape.     

基于岩体不连续面三维分形维岩体质量评价研究

岩体内部不连续面分布具有随机性、不规则性,但又具有统计自相似性。基于三维随机不连续面网络模拟技术,对岩体结构统计均质区内的不连续面进行计算机模拟,并应用分形理论计算岩体不连续面分布的分形维数。岩体不连续面分布分维数具有尺寸效应,随着岩体尺寸增大分维数减小,到一定程度趋于稳定。这一稳定的分维值称之为表征分维数,用此值描述不连续面分布特征。将岩体不连续面分布的表征分维数与按传统岩体分类标准所得岩体质量等级进行对比,提出以岩体不连续面分布表征分维数为指标的岩体质量分类方法。在岩体分类基础上,提出基于表征分维数的岩体等效抗剪强度指标的折减计算。     

利用毛管压力曲线分形分维方法研究流动单元

利用取心井铸体薄片获得的图像资料和毛管压力曲线,通过图像分形几何学方法以分维数的形式定量地表征出了复杂的微观孔隙喉道结构特征,发现能够很好地划分和评价孔隙岩石中油、气、水的渗流差异,可以用于储层微观流动单元表征。文中阐述了岩石微观孔隙喉道结构分形的理论基础、计算方法和应用于表征流动单元的依据。建立了中国西部砾岩低渗透油藏微观孔隙喉道分维数与孔隙度、渗透率之间计算图版,据此在油藏中利用常规测井资料获得的孔隙度、渗透率参数计算微观孔隙喉道分维数,开展全油藏流动单元划分与评价,取得了良好的效果。研究结果表明,利用毛管压力曲线分形分维方法研究储层微观流动单元是一种很有效的途径。     

Statistical self-affinity, fractal dimension, and geologic interpretation

Properties of statistical self-affinity are explored and explained. Semi-variogram analysis can be used for identifying statistical self-affine behavior. This is, however, not the only method available for such an analysis. Some error and interpretation is involved; therefore, estimating the Hurst dimension (and from this the fractal dimension) from the semi-variogram can be misleading. Simulations based on statistical self-affine properties are alternatively used to develop an empirical approach to assessing statistical self-affine behavior. Analyzing simulations using semi-variograms, and comparing these semi-variograms to those from actual data, offers an alternate and perhaps superior approach to the understanding of the statistical self-affine properties of a geologic phenomenon. This empirical approach offers a method of reverse modeling for verifying estimates of Hurst dimension from semi-variograms.     

Geomorphometry and fractal dimension of a riverine badland in Maharashtra

One of the most serious limitations in studying the surface morphometry of a badland landscape is the nonavailability of a very fine resolution data which is essential for such types of studies. Local relief of most of the badlands in India and also from other parts of the world exhibit limited relief amplitude, often within a few meters. The paper reports a case study carried out in a riverine badland formed along the Western Deccan Trap Region. An attempt has been made in the present paper to extract the morphometric variables of the landscape from the DEMs derived from a high resolution field generated data, because the accuracy of the DEM derived values are dependent on the pixel resolution of the DEM from which they are generated. The size of the pixel resolution should be fixed differently for different landscapes depending on the landscape process in the area. The local relief of the area is around 10 m and for such types of landscapes the topographical maps and also the web-available DEMs are of very coarse resolutions which are not suitable for the analysis. Therefore two well defined tributary catchments were chosen from the area under investigation and theodolite surveys were carried out, contours were generated with 10 cm interval, DEMs were derived by using Arc GIS software. SRTM (Shuttle Radar Topography Mission) 90 m resolution data were utilized to generate DEM for the whole basin. Hypsometric and the drainage basin parameters were extracted from these data by using the same software. Fractal dimension of the whole basin and the sample basins were also obtained for the same data. The morphometric data generated were used to understand the geomorphic processes operating in the area.     

Comparison of different models of water quality index in the assessment of surface water quality

The method of water quality index is widely used in evaluation of the surface water quality because of its capability to summarize a number of water quality parameters into one numeric value, along with defined scale of water quality range. The current investigation includes application of modified model for calculating water quality index values, generated using experimental data and literary models. Software was created using modular design. Fourteen physical, chemical and biological parameters representing water quality state along with the assigned weights were elected. Comparison between models generated based on Serbian and American models of water quality index was done. Selected parameters differ mutually in number of parameters used in calculation of index, as well as in values of the weighting factors. In order to enable an efficient water quality analysis and to reconcile the requirements of both Serbian and American model, two software solutions were generated and processed on the example of the water quality of the Danube River in Serbia. Danube water quality was assessed at seventeen measuring locations along the river flow. Index values obtained from the two generated software applications were compared with the results of the official Serbian online calculator. Water quality determined using new generated models shows stricter approach and one class lower water quality compared to the existing Serbian model. Therefore, modular and open-generated simulation software is of great significance for the comparison and testing of different water quality models, not just those two shown in this study.     

Investigation of the effect of aggregate shape and surface roughness on the slake durability index using the fractal dimension approach

Argillaceous rocks cover about one thirds of the earth's surface. The major engineering problems encountered with weak- to medium-strength argillaceous rocks could be slaking, erosion, slope stability, settlement, and reduction in strength. One of the key properties for classifying and determining the behavior of such rocks is the slake durability. The concept of slake durability index (SDI) has been the subject of numerous researches in which a number of factors affecting the numerical value of SDI were investigated. In this regard, this paper approaches the matter by evaluating the effects of overall shape and surface roughness of the testing material on the outcome of slake durability indices.

For the purpose, different types of rocks (marl, clayey limestone, tuff, sandstone, weathered granite) were broken into chunks and were intentionally shaped as angular, subangular, and rounded and tested for slake durability. Before testing the aggregate pieces of each rock type, their surface roughness was determined by using the fractal dimension. Despite the variation of final values of SDI test results (values of I_d), the rounded aggregate groups plot relatively in a narrow range, but a greater scatter was obtained for the angular and subangular aggregate groups. The best results can be obtained when using the well rounded samples having the lowest fractal values. An attempt was made to analytically link the surface roughness with the I_d parameter and an empirical relationship was proposed. A chart for various fractal values of surface roughness to use as a guide for slake durability tests is also proposed. The method proposed herein becomes efficient when well rounded aggregates are not available. In such condition, the approximate fractal value for the surface roughness profile of the testing aggregates could be obtained from the proposed chart and be plugged into the empirical relation to obtain the corrected I_d value. The results presented herein represent the particular rock types used in this study and care should be taken when applying these methods to different type of rocks.     

Prediction of water quality from simple field parameters

Water quality parameters like temperature, pH, total dissolved solids (TDS), total suspended solids (TSS), dissolved oxygen (DO), oil and grease, etc., are calculated from the field while parameters like biological oxygen demand (BOD) and chemical oxygen demand (COD) are interpreted through the laboratory tests. On one hand parameters like temperature, pH, DO, etc., can be accurately measured with the exceeding simplicity, whereas on the other hand calculation of BOD and COD is not only cumbersome but also inaccurate many times. A number of previous researchers have tried to use different empirical methods to predict BOD and COD but these empirical methods have their limitations due to their less versatile application. In this paper, an attempt has been made to calculate BOD and COD from simple field parameters like temperature, pH, DO, TSS, etc., using Artificial Neural Network (ANN) method. Datasets have been obtained from analysis of mine water discharge of one of the mines in Jharia coalfield, Jharkhand, India. 73 data sets were used to establish ANN architecture out of which 58 datasets were used to train the network while 15 datasets for testing the network. The results show encouraging similarity between experimental and predicted values. The RMSE values obtained for the BOD and COD are 0.114 and 0.983 %, respectively.     

矿床储量规模分布的分形模型及其分维的数理分析

矿床储量规模预测在矿产勘查和评价中占有十分重要的位置,而其预测的最主要手段是建立矿床储量规模分布的数学模型.根据矿床储量的统计自相似性,应用概率统计方法建立了矿床储量规模的分形模型.同时,通过模型及其分维值的数理分析,得出不同分维值的地学解释,讨论了分维的线性与非线性最小二乘回归估计法.     

Natural fracture profiles,fractal dimension and joint roughness coefficients

Summary Thirteen natural rock profiles (Barton and Choubey, 1977) are analyzed for their fractal properties. Most of the profiles were found to approximate fractal curves but some also showed features of specific wavelengths and amplitudes superimposed on fractal characteristics. The profiles showed fractal dimensions from 1.1 to 1.5 covering a range of selfsimilar and self-affine curves. The analysis results suggest a negative correlation between fractal dimension,D, and amplitude,A. Joint roughness coefficients (JRC) show a positive correlation with amplitude,A, and a negative correlation with fractal dimension,D. A numerical model of fracture closure is used to investigate the effects of different profile characteristics (D, A and sample size) on the nature of dilation and contact area, using the natural profiles and synthetic fractional Brownian motion profiles. Smooth profiles (low JRC, highD, lowA) display many small contact regions whereas rough fractures (high JRC, lowD, highA) display few large contact areas. The agreement with published experimental data supports the suggested correlations between JRC and the fractal parameters,A andD. It is suggested that observed scale effects in JRC and joint dilation can be explained by small differential strain discontinuities across fractures, which originate at the time of fracture formation.     

Uncertainty in fractal dimension estimated from power spectra and variograms

The reliability of using fractal dimension (D) as a quantitative parameter to describe geological variables is dependent mainly on the accuracy of estimated D values from observed data. Two widely used methods for the estimation of fractal dimensions are based on fitting a fractal model to experimental variograms or power-spectra on a log-log plot. The purpose of this paper is to study the uncertainty in the fractal dimension estimated by these two methods. The results indicate that both spectrum and variogram methods result in biased estimates of the D value. Fractal dimension calculated by these two methods for the same data will be different unless the bias is properly corrected. The spectral method results in overestimated D values. The variogram method has a critical fractal dimension, below which overestimation occurs and above which underestimation occurs. On the bases of 36,000 simulated realizations we propose empirical formulae to correct for biases in the spectral and variogram estimated fractal dimension. Pitfalls in estimating fractal dimension from data contaminated by white noise or data having several fractal components have been identified and illustrated by simulated examples.     

Water quality index of the ground water of bitumen deposit impacted farm settlements using entropy weighted method

Ground water of the farm settlements in the bitumen deposit area of Western Nigeria were tested for pH, conductivity, turbidity, total dissolved solid, sulphate, phosphate, nitrogen nitrate, chloride, alkalinity, total hardness, calcium, magnesium, sodium, potassium and total coliform in the dry season (March) and rainy season (August) of years 2008 and 2009 using atomic absorption spectrometer and standard analytical methods. Conductivity, pH, turbidity, phosphate ions and total coliform values obtained in some of the wells were out of the recommended range for drinking water. Water quality index analysis was carried out using information entropy method. Water quality index of the wells when compared with the permissible limits of international standards, ranked the bore hole as ‘excellent’ in the dry season of year 2009 and just ‘good’ in the rainy season of the same year. Ground water sampling stations were ranked extremely poor at least once out of the four seasons considered. Water quality index ranking also showed that the quality of the wells declined over the years. The correlation coefficient matrix (p < 0.05) of water quality index and the parameters showed significant relationships between water quality index and total coliform (0.99), total dissolved solids and conductivity (0.96), hardness and Ca²⁺ (0.68), hardness and Mg²⁺ (0.75). Water quality index also showed moderate significant relationship with total dissolved solid, conductivity and N–NO₃ ^?. High concentration of total coliform in most of the shallow wells in the environment, due to bitumen deposit, renders them unfit for human consumption unless properly treated.