Uncertainty quantification of structural and geotechnical parameter by geostatistical simulations applied to a stability analysis case study with limited exploration data

Rock quality designation (RQD) is widely adopted as a fundamental tool in characterizing rock masses since it was devised in 1964. Since the conventional RQD calculation is limited due to its dependence on the selected threshold, previous research introduced generalized RQD to adequately reflect the anisotropy and scale effect of RQD. However, the influence of the joint development inside rock mass on generalized RQD remains unclear. The objective of this work is to investigate characteristics of the generalized RQD in view of different development degrees of discontinuities in rock mass, including spacing (density) and trace length. Three‐dimensional fracture network modelling is employed to simulate the actual rock mass of open‐pit iron mine in China. Virtual scanlines are set to obtain RQD values in different directions. The results primarily show that the generalized RQD should be introduced to calculate the RQD with different thresholds to fully reflect the anisotropy of rock mass. The optimal threshold can be obtained based on an anisotropic coefficient, which is defined by (RQDmax‐RQDmin). It is also indicated that the fracture spacing has a great influence on both the anisotropy of RQD and the selection of the optimal threshold. The optimal threshold of the generalized RQD increases with the increase in the fracture spacing. In addition, the scale effect of RQD in different models is discussed by changing the length of the scanlines. The longer the scanlines we set, the more stable RQD value can be obtained in the model. It is recommended to fit much longer scanline to get realistic RQD in heavily fractured rock mass.

A new uncertainty analysis method based on geostatistical simulation and a case study

A generalised ground model with geotechnical characterisation has been developed for the city of Doha, in Qatar, combining a wide range of ground investigation data and observations during the construction of projects that WS Atkins & Partners Overseas were involved with. The model proposes a geotechnical characterisation and ranges of parameters for the main units found at depths relevant to civil engineering activities. A geotechnical classification system is proposed to differentiate the Simsima Limestone subunits encountered on site, based on rock quality designation (RQD) values and weathering degree. The proposed classification system and the relevant geotechnical parameters have been validated during construction. The construction of all excavations, temporary retaining systems and tunnel excavations that rely on the information presented in this paper has been completed successfully. This confirmed a reasonable agreement between the theory presented in the paper and the practical conditions encountered on site. Best site investigation practices are discussed with highlights on difficulties encountered on site and how they were resolved. RQD and rock mass rating values were found to produce a good representation of the ground conditions while the applicability of the geological strength index classification is believed to be limited.

O objetivo deste trabalho foi avaliar o desempenho da simulação sequencial gaussiana (SSG) e da simulação sequencial indicatriz (SSI) na modelagem da incerteza das predições do K disponível em área de cana-de-açúcar, e comparar as simulações com o método já consagrado de krigagem ordinária (KO). Uma malha amostral com 626 pontos foi instalada em área de 200 ha, no Município de Tabapuã, em São Paulo. As simulações reproduziram a variabilidade dos dados amostrais de K disponível, enquanto a KO superestimou os baixos teores de K e subestimou os altos. O mapa de desvio-padrão obtido a partir da KO mostrou menor variação ao longo da área de estudo, quando comparado aos mapas obtidos a partir das simulações. A SSI obteve acurácia 22% superior à obtida pela SSG, na modelagem da função de distribuição condicional do K. As simulações apresentam maior eficiência que a KO para modelar incerteza na distribuição espacial do K. A SSI apresenta melhor desempenho que a SSG na estimativa dos teores de K disponível, em área de cana-de-açúcar.

A comparison of rock quality designation (RQD) parameters obtained by drill core analysis and the RQD determined using alternative methods is presented using metamorphic rocks such as migmatized gneisses, migmatites, and amphibolites. Methods of borehole–wall imaging using high-resolution acoustic logging, optical televiewer, and simple video inspection as well as the structural analysis of exploration drift walls oriented subparallel to the analysed boreholes are used for alternatively evaluated RQD values. Results show that, in most cases, the RQD index measured directly on a drill core section reaches lower values (about 10%–30%) than the RQD evaluated by alternative methods. Significant differences in determination of the rock mass failure degree using classical and alternative methods may occur, especially in sections with higher frequency of the metamorphic foliation planes created by biotite-rich bands or by dark-coloured melanosome layers. The nature of biotite itself is favourable for the creation of pre-disposed jointing planes, in which the increased drill core disintegration caused by drilling technology or core handling can occur. Results show it is highly appropriate to make these comparisons on a larger scale and thus verify whether the observed differences affect the qualitative classification of the rock mass.

One important part of rock mass investigation is the geomechanical assessment in terms of rock mass classification systems. Rock mass classification is one of themost efficient methods in rock mechanics to provide a basic understanding of rock masscharacterization. Rock mass properties can be determined by a seismic refraction surveyas an indirect geophysical assessment. In this study, the P-wave velocity from seismicrefraction was compared with the Rock Quality Designation (RQD) from the boreholes.The empirical correlation between the RQD and the P-wave velocity was found by usingthe linear regression analysis. The RQD value estimated from the P-wave velocity can beapplied for tropical environment study with geological conditions of volcanic rocks. This study helps to estimate and predict the subsurface rock quality, to reduce investigation costs, and to improve understanding of subsurface rock quality.

The rapid development in the construction of infrastructure on the hilly terrain has led to excavation of large bodies of rock mass to form cut slopes, resulting in the deformation and reduction in the stability of the rock material. As the slopes were cut more than 10 years ago, it is worried that there should be strength deterioration of the rock slope that could affect the stability of the slope. A study should be carried out to evaluate the recent condition of the slope in terms of its stability and safety after a long period of the exposure. A field study was conducted to collect the discontinuity data and laboratory test for the purpose of stability analysis using the existing stability analysis scheme of Rock Mass Rating (RMR) and Slope Mass Rating (SMR). The study was taken place at an exposed cut slope of a highway in Sri Jaya, Pahang. The objective of this study is to determine and evaluate the stability of the rock cut slope. A classification of the discontinuity parameters such as the strength, Rock Quality Designation (RQD), spacing, aperture, infilling, persistence, weathering, and groundwater have been used to determine the rock mass condition. The classification also need laboratory test for the point load strength (PLT) parameter. The RMR classification showed the rock to be very good condition, while the SMR showed the slope to be completely stable to stable. This study provide a good database in assessing the rock slope condition from time to time for the slope authority management.

Collected data in soil heavy metal investigations may contain significant levels of uncertainty, including complex and even unexplainable spatial variations at a small investigation site. Therefore, this study identifies the spatial structure of soil zinc in the northern part of Changhua County in Taiwan to understand the spatial variation and uncertainty of soil zinc. The spatial maps of this heavy metal are simulated by using the geostatistical simulation, and estimated by using ordinary kriging and natural log kriging. The estimation and simulation results indicate that Sequential Gaussian Simulations can reproduce the spatial structure for investigated data. Furthermore, displaying a low spatial variability, the ordinary kriging and natural log kriging estimates can not fit the spatial structure and small‐scale variation for the soil zinc investigated data. The maps of kriging estimates are much smoother than those of simulations. Sequential Gaussian Simulation with multiple realizations has significant advantages at a site with high variation investigated data over ordinary kriging, even natural log kriging techniques. Geographic information systems display these simulation and estimation results.

Matrix method for stability and second-order analysis of Timoshenko beam-column structures with semi-rigid connections

Precisely investigating subsurface conditions is a major concern for both geotechnical and geological engineers. In recent years, growing urbanization and construction of high-rise buildings in Mashhad City, Iran, have increased the demand for 3D models as a basis for subsurface characterization. In this regard, this study deals with the development of a 3D geological engineering model for standard penetration test (SPT) results on Mashhad City sedimentary deposits using sequential indicator simulation (SIS) and sequential Gaussian simulation (SGS) approaches. Reliable estimation of SPT values can be helpful in prediction of other geotechnical properties such as soil strength parameters and bearing capacity. The intense variability of the Mashhad sedimentary basin gives rise to complex and challenging ground conditions for civil engineering work. A better understanding of these deposits is crucial for many current and future civil engineering projects. Since design parameters in the study area are usually determined based on SPT results, 12,440 SPT data collected from 1380 boreholes were employed as the input data. After variability analysis, the SIS procedure was applied to coded data to determine areas with very dense sediments (areas with SPT > 50). Then, data with SPT values < 50 were transformed into normal scores in order for them to be applicable as input data in SGS. Finally, coupled maps showing the results of these two approaches were provided for different depths.

Regional scale inventories of heavy metal concentrations in soil increasingly are being done to evaluate their global patterns of variation. Sometimes these global pattern evaluations reveal information that is not identified by more detailed studies. Geostatistical methods, such as stochastic simulation, have not yet been used routinely for this purpose in spite of their potential. To investigate such a use of geostatistical methods, we analyzed a data set of 14,674 copper and 12,441 cadmium observations in the topsoil of Flanders, Belgium, covering 13,522 km2. Outliers were identified and removed, and the distributions were spatially declustered. Copper was analyzed using sequential Gaussian simulation, whereas for cadmium we used sequential indicator simulation because of the large proportion (43%) of censored data. We complemented maps of the estimated values with maps of the probability of exceeding a critical sanitation threshold for agricultural land use. These sets of maps allowed the identification of regional patterns of increased metal concentrations and provided insight into their potential causes. Mostly areas with known industrial activities (such as lead and zinc smelters) could be delineated, but the effects of shells fired during the First World War were also identified.

Airborne hazardous plumes inadvertently released during nuclear/chemical/biological incidents are mostly of unknown composition and concentration until measurements are taken of post-accident ground concentrations from plume-ground deposition of constituents. Unfortunately, measurements often are days post-incident and rely on hazardous manned air-vehicle measurements. Before this happens, computational plume migration models are the only source of information on the plume characteristics, constituents, concentrations, directions of travel, ground deposition, etc. A mobile ''lighter than air'' (LTA) system is being developed at Oak Ridge National Laboratory that will be part of the first response in emergency conditions. These interactive and remote unmanned air vehicles will carry light-weight detectors and weather instrumentation to measure the conditions during and after plume release. This requires a cooperative computationally organized, GPS-controlled set of LTA's that self-coordinate around the objectives in an emergency situation in restricted time frames. A critical step before an optimum and cost-effective field sampling and monitoring program proceeds is the collection of data that provides statistically significant information, collected in a reliable and expeditious manner. Efficient aerial arrangements of the detectors taking the data (for active airborne release conditions) are necessary for plume identification, computational 3-dimensional reconstruction, and source distribution functions. This report describes the application of stochastic or geostatistical simulations to delineate the plume for guiding subsequent sampling and monitoring designs. A case study is presented of building digital plume images, based on existing ''hard'' experimental data and ''soft'' preliminary transport modeling results of Prairie Grass Trials Site. Markov Bayes Simulation, a coupled Bayesian/geostatistical methodology, quantitatively combines soft information regarding contaminant location with hard experimental results. Soft information is used to build an initial conceptual image of where contamination is likely to be. As experimental data are collected and analyzed, indicator kriging is used to update the initial conceptual image. The sequential Gaussian simulation is then practiced to make a comparison between the two simulations. Simulated annealing is served as a postprocessor to improve the result of Markov Bayes simulation or sequential Gaussian simulation.

ABSTRACTGeostatistical modelling of grades in mineral deposits often requires the simulation of multiple related variables that have sum and fraction constraints. Sum constraints occur when the sum of some variables may not exceed or must equal a given constant. Fraction constraints occur when a variable may not exceed another variable. In this case, the geostatistical simulations should reproduce the histograms, variograms, multivariate relationships and honour the constraints. We present a methodology for the geostatistical simulation of multiple related variables that considers sum and fraction constraints. The methodology is illustrated in a case study. The data were obtained from a bauxite deposit. First, the original variables were re-expressed as ratios. Second, the variables were transformed using the Projection Pursuit Multivariate Transform (PPMT). Then the PPMT transformed variables were simulated independently using sequential Gaussian simulation and back-transformed. The simulations reproduced the histograms, variograms and bivariate relationships and honoured the sum and fraction constraints.

Description of hydrogeologic heterogeneity and evaluation of radionuclide transport at an underground nuclear test

Geostatistical simulation aims at reproducing the variability of the real underlying phenomena. When nonlinear features or large-range connectivity is present, the traditional variogram-based simulation approaches do not provide good reproduction of those features. Connectivity of high and low values is often critical for grades in a mineral deposit. Multiple-point statistics can help to characterize these features. The use of multiple-point statistics in geostatistical simulation was proposed more than 10 years ago, on the basis of the use of training images to extract the statistics. This paper proposes the use of multiple-point statistics extracted from actual data. A method is developed to simulate continuous variables. The indicator kriging probabilities used in sequential indicator simulation are modified by probabilities extracted from multiple-point configurations. The correction is done under the assumption of conditional independence. The practical implementation of the method is illustrated with data from a porphyry copper mine.