Application of multiple indicator Kriging for RMR value estimation in areas of new drift excavation during mine site redevelopment

Rock mass rating (RMR) values along additional drifts that are to be constructed during mine site redevelopment (Gagok mine, Korea) were estimated using multiple criteria indicator Kriging with borehole RMR and electrical resistivity tomography data. This study outlines two potential correction methods that supplement indicator Kriging and that can reduce error, allowing more accurate estimation of RMR values. The correction methods used a filtering of indirect data affected by drifts (FIED) method to reduce uncertainties and errors within electrical resistivity tomography data caused by changes in setup and the location of existing drifts. In addition, a correction indicating accurate representation of indirect data (CARI) method was used to resolve distortions in drilling log results. This meant that 73 % of the estimated RMR values were assigned to the correct RMR class, with only 1 % of these values being overestimated. The sensitivity of the FIED method was 4 %, with the linear CARI method having a sensitivity of 56–60 % and the logarithmic CARI method having a sensitivity of 61–65 %.     

Geostatistical integration using 2-D electrical resistivity and 3-D gravity methods for detecting cavities in a karst area

Two-dimensional (2-D) electrical resistivity and three-dimensional (3-D) gravity explorations were undertaken to estimate the 3-D distribution of karst cavities at the area of Yongweol-ri in Korea where ground subsidence has occurred. Although the gravity method is a low-cost way of analyzing a 3-D continuous structure, its vertical resolving power is poor. In contrast, the electrical resistivity method can provide a 2-D and/or 3-D subsurface structure with a much higher lateral and vertical resolution than the gravity method. Accordingly, geostatistical methods and density information were used to enhance the 2-D resistivity structure revealed by the electrical resistivity method into a 3-D structure. The assumptions are, first, that each data set senses the same underlying geological structure in terms of different material properties and, secondly, that two different material properties are correlated locally or globally throughout the entire target area. As a result, the distribution of limestone cavities can be estimated under the assumption that they are mostly filled with groundwater and clayey soils and have abnormally low levels of resistivity and density. The estimated distribution corresponds with the grouting, borehole imaging and monitoring data. In this example, it can be seen that the integration analysis of 2-D electrical resistivity and 3-D gravity methods is a very powerful tool for 3-D subsurface imaging and that the method can provide enhanced imaging capabilities for 3-D cavities.     

Interpretation of variability of rock mass rating by geostatistical analysis: a case study in Western Turkey

Geotechnical interpretation of drillholes for rock mass characterization is commonly based on the engineering judgment. This might result in misrepresentation of the rock mass at unsampled locations. This paper investigates the reproducibility of the spatial variability of rock mass quality (rock mass rating, RMR) using geostatistics. Geotechnical data from an exploratory phase mining project in Western Turkey that covers 2.7 km depth with a total of 14 drillholes composed of 700 samples was used to perform a geostatistical analysis. RMR values of positions, where geotechnical logging was missing, were estimated by applying inverse distance weighting (IDW) and the ordinary kriging (OK) methods. The validation process showed that the OK method is consistently estimating the RMR values better than IDW. The spatial variability of RMR values by geostatistical analysis could provide valuable information in the design and development of underground or surface structures.     

Estimation of regionalized phenomena by geostatistical methods: lake acidity on the Canadian Shield

 This paper describes a geostatistical technique based on conditional simulations to assess confidence intervals of local estimates of lake pH values on the Canadian Shield. This geostatistical approach has been developed to deal with the estimation of phenomena with a spatial autocorrelation structure among observations. It uses the autocorrelation structure to derive minimum-variance unbiased estimates for points that have not been measured, or to estimate average values for new surfaces. A survey for lake water chemistry has been conducted by the Ministère de l'Environnement du Québec between 1986 and 1990, to assess surface water quality and delineate the areas affected by acid precipitation on the southern Canadian Shield in Québec. The spatial structure of lake pH was modeled using two nested spherical variogram models, with ranges of 20 km and 250 km, accounting respectively for 20% and 55% of the spatial variation, plus a random component accounting for 25%. The pH data have been used to construct a number of geostatistical simulations that produce plausible realizations of a given random function model, while 'honoring' the experimental values (i.e., the real data points are among the simulated data), and that correspond to the same underlying variogram model. Post-processing of a large number of these simulations, that are equally likely to occur, enables the estimation of mean pH values, the proportion of affected lakes (lakes with pH≤5.5), and the potential error of these parameters within small regions (100 km×100 km). The method provides a procedure to establish whether acid rain control programs will succeed in reducing acidity in surface waters, allowing one to consider small areas with particular physiographic features rather than large drainage basins with several sources of heterogeneity. This judgment on the reduction of surface water acidity will be possible only if the amount of uncertainty in the estimation of mean pH is properly quantified. Received: 3 March 1997 · Accepted: 16 November 1998     

Geoelectric resistivity sounding of riverside alluvial aquifer in an agricultural area at Buyeo,Geum River watershed,Korea: an application to groundwater contamination study

Twenty profiles of vertical electric soundings (VES) were obtained in a riverside alluvium at the Buyeo area, South Korea, to examine the variations of subsurface geology and associated groundwater chemistry. The combination of the VES data with the borehole data provided useful information on subsurface hydrogeologic conditions. The vestige of an ancient river channel (e.g. oxbow lake) was identified on the resistivity profiles by the lateral continuation of a near-surface perched aquifer parallel to the river. Such a perched aquifer is typically developed in the area with a clay-rich silty surface alluvium which prohibits the infiltration of oxygen. Therefore, groundwater below the oxbow lake shows a very low nitrate concentration and Eh values under the strong anoxic condition. The distribution of water resistivity is correlated with that of measured total dissolved solids concentration in groundwater, while the earth resistivity of the aquifer shows a significant spatial variation. It is interpreted that the earth resistivity of the aquifer is mainly controlled by the soil type rather than by the water chemistry in the study area.     

Estimation and scaling of hydrostratigraphic units: application of unsupervised machine learning and multivariate statistical techniques to hydrogeophysical data

Numerical models provide a way to evaluate groundwater systems, but determining the hydrostratigraphic units (HSUs) used in constructing these models remains subjective, nonunique, and uncertain. A three-step machine-learning approach is proposed in which fusion, estimation, and clustering operations are performed on different data sets to arrive at HSUs at different scales. In step one, data fusion is performed by training a self-organizing map (SOM) with sparse borehole hydrogeologic (lithology, hydraulic conductivity, aqueous field parameters, dissolved constituents) and geophysical (gamma, spontaneous potential, and resistivity) measurements. Estimation is handled by iterative least-squares minimization of the SOM quantization and topographical errors. Application of the Davies-Bouldin criteria to k-means clustering of SOM nodes is used to determine the number and location of discontinuous borehole HSUs with low lateral density (based on borehole spacing at 100 s m) and high vertical density (based on cm-scale logging). In step two, a scaling network is trained using the estimated borehole HSUs, airborne electromagnetic measurements, and numerically inverted resistivity profiles. In step three, independent airborne electromagnetic measurements are applied to the scaling network, and the estimation performed to arrive at a set of continuous HSUs with high lateral density (based on sounding locations at meter (m) spacing) and medium vertical density (based on m-layer modeled structure). Performance metrics are used to evaluate each step of the approach. Efficacy of the proposed approach is demonstrated to map local-to-regional scale HSUs using hydrogeophysical data collected at a heterogeneous surficial aquifer in northwestern Nebraska, USA.     

Geostatistical integration of seismic velocity and resistivity data for probabilistic evaluation of rock quality

This study applied a geostatistical approach to integrate various geophysical results for the probabilistic evaluation of rock quality designation (RQD) in regions between boreholes. Two of the geophysical survey results, electrical resistivity and seismic velocity, were transformed into a probabilistic distribution with the directly observed RQD values at the boreholes using an indicator value method. The initial spatial distribution of RQD, inferred from indicator kriging of observations from the boreholes, was improved by support of the geophysical results based on the integration by a permanence ratio. The integration was good enough to produce results that compensated for the defection of each exploration method. Also, the probabilistic feature of the final product of the RQD distribution made it possible to assess a more quantitative rock quality evaluation and better decision making for safety design.     

基于区域化变量及RMR评价体系的金川III矿区矿岩质量评价

岩体质量的全面评价是自然崩落法矿山可行性研究和初步设计的重要前提和依据。RMR体系是通常采用的综合性评价方法,以钻孔或坑道的局部RMR评价值来表征整个区域的岩体质量具有片面性。因此,以金川III矿区1554水平以上的岩体质量调查数据为样品,首先对其空间结构性及变异性进行了分析,得出调查区RMR参数指标具有区域化变量特征的结论;其次,建立了评价范围内各类工程和岩性区段的三维表面模型,并对该模型用长方体单元进行了离散;然后,借助区域化变量最优无偏估值方法,对各离散单元块的RMR参数指标进行推估,建立了反映全局变化的矿岩质量三维可视化RMR评价模型;最后以RMR评价模型为基础,根据Laubscher崩落图对矿岩初始和持续崩落的水力半径进行了计算。结果表明：III矿区的RMR均值为39.8,矿岩可崩性属较好到很好。预测金川III矿区平均持续崩落水力半径为20.4 m。     

Geostatistical modelling of spatial and depth variability of SPT data for Bangalore

The purpose of this study is to develop a geostatistical model to evaluate the spatial and depth variability of Standard Penetration Test (SPT) data from Bangalore, India. The database consists of 766 boreholes spread over a 220 km² area, with several SPT values (N) in each of them. The geostatistical analysis is done for N corrected (N _corrected) values. The N _corrected value has been corrected for different parameters such as overburden stress, size of the bore hole, type of sampler, hammer energy and length of the connecting rod. The knowledge of the semivariogram of the SPT data is used with kriging theory to estimate the values at points in the subsurface of Bangalore where field measurements are not available. The model is used to compute the variance of estimated data. The model predicts reasonably well the SPT data. The geostatistical model provides valuable results that can be used for seismic hazard analysis, site response and liquefaction studies for the development of microzonation maps. The predicted N values from the developed model can also be used to estimate the subsurface information, allowable bearing pressure of soils and elastic modulus of soils.     

A Combined Three-Dimensional Geological-Geostatistical-Numerical Model of Underground Excavations in Rock

Summary. This paper exploits geological and borehole geotechnical data obtained in the exploratory phase of a tunneling project to investigate in a first place if the kriging interpolation scheme may effectively reproduce the spatial variability of rock mass quality (Rock Mass Rating, RMR) in the vicinity of tunnels. For this purpose a quick solver in Fortran has been developed that performs variography analysis of 3D spatial data, fast kriging estimations of RMR between borehole sampling locations at the centroids of the elements of the numerical model, and model validation. For the purpose of an integrated underground excavation design, a step further is made by incorporating into the 3D mechanical numerical model of the rock mass, the three-dimensional (3D) solid geological model, thus coupling the geology with the ground (geotechnical) model (i.e. each element of the numerical model is assigned a geological material). The mechanical properties of each finite difference cell (or Representative Elementary Volume) of the ground model were then prescribed according to its geological type, the spatial heterogeneity of the rock mass expressed quantitatively with the kriging model, and the upscaling calculations of the mechanical properties of the intact rocks determined in the laboratory, based on the size-effect (strength dependence on size) and Damage Theory. Furthermore, a preliminary numerical simulation of the advance of unsupported tunnels in the model of the heterogeneous rock mass was performed for illustration purposes.     

工程岩体分类方法在小浪底工程中的应用

利用国内外常用的RMR(Rock Mass Ruting)和Q工程岩体分类体系,对小浪底工程中的地下工程进行了岩体的分类研究,并根据分类结果提出了地下工程的支护措施,估计了岩体的抗剪强度和变形模量。工程实践结果表明,分类结果是合适的,依据分类结果制定的支护方案是合适的。运行结果表明工程处于稳定状态。     

Effects of near-surface inhomogeneities on MT responses: An analytical model

An analytical model is suggested to describe the electrostatic field produced by near-surface inhomogeneities responsible for galvanic shift in magnetotelluric (MT) apparent resistivity sounding curves. The near-surface inhomogeneities are modeled in thin-sheet approximation with laterally variable longitudinal conductance and transverse resistance. The model accounts for the TM (transverse magnetic) mode secondary electric field in the conductive layered subsurface below the thin sheet. Equations have been obtained to relate the subsurface geoelectric parameters and the spatial harmonics of the secondary electrostatic field. This secondary field, which is the source of galvanic shift in MT data, turns out to be in-phase with the primary field. The equations derived to simulate galvanic distortions are applicable to long-period MT data acquired by a synchronous array.     

Geophysical assessment of subsurface coastal sediments and their engineering implications

Surface geophysics and a priori information were employed to delineate the subsurface geology at Idi-oro in Abijo, Ibeju Lekki area of Lagos, Nigeria for foundation investigation purpose. Resistivity measurement was conducted using 1-D and 2-D resistivity probing techniques. The resistivity measurements were made with ABEM tetrameter model SAS 1000 system. The 1-D vertical electrical resistivity sounding data were obtained using the Schlumberger electrode array while the 2-D resistivity data were obtained using the dipole–dipole array. The interpreted results revealed three to five subsurface geological layers. This is made up of the top soil with resistivity values that vary from 132.4 to over 2,313.5 Ω?m and thickness values that range from 0.3 to 4.8 m, the fine sand with resistivity values that vary from 221.0 to 3,032.7 Ω?m and thickness values that range from 0.4 to 5.5 m, the medium sand with resistivity values that vary from 202.8 to 1,247.7 Ω?m and thickness values that range from 4.9 to 58.4 m. On the other hand, the clayey sand has the resistivity values that vary from 146.1 to 1,744.0 Ω?m and thickness values that vary from 2.2 to 26.3 m, while the coarse sand has resistivity values that vary from 238.3 to 14,313.9 Ω?m but with no thickness value because the current terminated in this layer. The resistivity data correlate well with borehole logs. On the whole, it is concluded that the investigated area has competent sand layer that can support medium to giant engineering structures with resistivity values that vary from 202 to 14,314 Ω?m and thickness values that vary from 0.8 to 58.4 m.     

Hydrogeophysical imaging of alluvial aquifers: electrostratigraphic units in the quaternary Po alluvial plain (Italy)

The integration of surface geological and geomorphological information with borehole point-data and geophysical (e.g., geoelectrical) images of the subsurface yields spatially consistent representations of alluvial aquifers heterogeneity at different scales, from depositional systems to basin fills. Such an approach requires a conceptual framework to match the stratigraphic units with their evidence from ground-based DC resistivity methods to effectively fill the gaps between sparse borehole data and to obtain valid representations of sedimentary heterogeneities. Such an approach is applied to characterize two sites of the Quaternary aquifers of the central Po Plain (Italy), which represent (1) the middle-upper Pleistocene braided to meandering river depositional systems sitting on Southalpine crust and (2) their down-current counterparts, where they are involved by the latest uplift and deformation due to the tectonic activity of the Apennine frontal thrusts. Electrical resistivity was considered as a proxy of the litho-textural properties of hydrofacies and their major hierarchical association at depth and was interpreted in accordance with the depth-decreasing resolution of ground-based resistivity methods. Thus, it was possible to identify the geophysical signature of hydrostratigraphic units through “Electrostratigraphic Units”, i.e., sedimentary volumes identified by resistivity contrasts that spatially preserve the vertical polarity. Hydrostratigraphy and electrostratigraphy were then joined together through a site-specific relationship between electrical resistivity and hydraulic conductivity, which takes into account the prevailing process of current conduction, the litho-textural properties of hydrofacies and the groundwater electrical conductivity. At the scales of aquifer systems and complexes, this approach permitted to establish the conceptual framework to match hydrostratigraphy, electrostratigraphy, average hydrodynamic properties and distribution of heterogeneities.     

Modelling Short‐Scale Variability and Uncertainty During Mineral Resource Estimation Using a Novel Fuzzy Estimation Technique

For mineral resource assessment, techniques based on fuzzy logic are attractive because they are capable of incorporating uncertainty associated with measured variables and can also quantify the uncertainty of the estimated grade, tonnage etc. The fuzzy grade estimation model is independent of the distribution of data, avoiding assumptions and constraints made during advanced geostatistical simulation, e.g., the turning bands method. Initially, fuzzy modelling classifies the data using all the component variables in the data set. We adopt a novel approach by taking into account the spatial irregularity of mineralisation patterns using the Gustafson–Kessel classification algorithm. The uncertainty at the point of estimation was derived through antecedent memberships in the input space (i.e., spatial coordinates) and transformed onto the output space (i.e., grades) through consequent membership at the point of estimation. Rather than probabilistic confidence intervals, this uncertainty was expressed in terms of fuzzy memberships, which indicated the occurrence of mixtures of different mineralogical phases at the point of estimation. Data from different sources (other than grades) could also be utilised during estimation. Application of the proposed technique on a real data set gave results that were comparable to those obtained from a turning bands simulation.     

Application of multiple-point geostatistics on modelling groundwater flow and transport in a cross-bedded aquifer (Belgium)

Sedimentological processes often result in complex three-dimensional subsurface heterogeneity of hydrogeological parameter values. Variogram-based stochastic approaches are often not able to describe heterogeneity in such complex geological environments. This work shows how multiple-point geostatistics can be applied in a realistic hydrogeological application to determine the impact of complex geological heterogeneity on groundwater flow and transport. The approach is applied to a real aquifer in Belgium that exhibits a complex sedimentary heterogeneity and anisotropy. A training image is constructed based on geological and hydrogeological field data. Multiple-point statistics are borrowed from this training image to simulate hydrofacies occurrence, while intrafacies permeability variability is simulated using conventional variogram-based geostatistical methods. The simulated hydraulic conductivity realizations are used as input to a groundwater flow and transport model to investigate the effect of small-scale sedimentary heterogeneity on contaminant plume migration. Results show that small-scale sedimentary heterogeneity has a significant effect on contaminant transport in the studied aquifer. The uncertainty on the spatial facies distribution and intrafacies hydraulic conductivity distribution results in a significant uncertainty on the calculated concentration distribution. Comparison with standard variogram-based techniques shows that multiple-point geostatistics allow better reproduction of irregularly shaped low-permeability clay drapes that influence solute transport.     

Assessment of groundwater occurrence in Olomoro,Nigeria using borehole logging and electrical resistivity methods

The objective of this study was to assess the subsurface strata and groundwater situation of Olomoro, Nigeria using borehole logging and electrical resistivity techniques. The borehole logging consisting of resistivity and spontaneous potential logs were conducted by using the Johnson Keck logger on a drilled well in the study area. The electrical resistivity survey involving 17 vertical electrical soundings (VES) with a maximum current electrode spacing of 100 to 150 m was conducted using the Schlumberger electrode configuration. Analysis of the well cuttings revealed that the lithology of the subsurface consist of topsoil, clay, very fine sand, medium grain sand, coarse sand and very coarse sand. Results of the downhole logging also revealed that the mean electrical conductivity and the total dissolved solid of the groundwater was obtained as 390 μS/cm and 245 mg/cm³ respectively. These values are within the acceptable limit set by the Standard Organization of Nigeria (SON) for drinking water. The result of the vertical electrical sounding interpreted using the computer iterative modeling revealed the presence of four to five geoelectric layers which showed a close correlation with result from the lithology and downhole logging. Results further showed that the resistivity of the subsurface aquifer ranged between 1584 and 5420 Ωm while the aquifer depths varied between 27.8 and 39.3 m. Groundwater development of the area is suggested using the depth and resistivity maps provided in this study.     

A coupled hydromechanical system defined through rock mass classification schemes

Changes in the hydraulic conductivity field, resulting from the redistribution of stresses in fractured rock masses, are difficult to characterize due to complex nature of the coupled hydromechanical processes. A methodology is developed to predict the distributed hydraulic conductivity field based on the original undisturbed parameters of hydraulic conductivity, Rock Mass Rating (RMR), Rock Quality Designation (RQD), and additionally the induced strains. The most obvious advantage of the methodology is that these required parameters are minimal and are readily available in practice. The incorporation of RMR and RQD, both of which have been applied to design in rock engineering for decades, enables the stress-dependent hydraulic conductivity field to be represented for a whole spectrum of rock masses. Knowledge of the RQD, together with the original hydraulic conductivity, is applied to determine the effective porosity for the fractured media. When RQD approaches zero, the rock mass is highly fractured, and fracture permeability will be relatively high. When RQD approaches 100, the degree of fracturing is minimal, and secondary porosity and secondary permeability will be low. These values bound the possible ranges in hydraulic behaviour of the secondary porosity within the system. RMR may also be applied to determine the scale effect of elastic modulus. As RMR approaches 100, the ‘softening’ effect of fractures is a minimum and results in the smallest strain-induced change in the hydraulic conductivity because the induced strain is uniformly distributed between fractures and matrix. When RMR approaches zero, the laboratory modulus must be reduced significantly in order to represent the rock mass. This results in the largest possible change in the hydraulic conductivity because the induced strain is applied entirely to the fracture system. These values of RMR bound the possible ranges in mechanical behaviour of the system. The mechanical system is coupled with the hydraulic system by two empirical parameters, RQD and RMR. The methodology has been applied to a circular underground excavation and to qualitatively explain the in situ experimental results of the macropermeability test in the drift at Stripa. Copyright © 1999 John Wiley & Sons, Ltd.