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

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

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.

The authors have emphasized the importance of fill sequencing as it relates to slope stability during operations of a lined repository. The neglect of changes in stability during operations has resulted in several large landfill slope stability failures, with one of the most notable and earliest of these the Kettleman Hills hazardous waste landfill slide in 1987. The authors’ approach promotes a two-wedge analysis based on limit equilibrium. Certainly limit-equilibrium techniques are the most common methods used to evaluate slope stability. Few design practitioners use finite-element techniques for performing slope stability, except for very complex situations or forensic analyses. Thus, refinements to approaches promoting limit-equilibrium stability methods are of continued value. Although limit-equilibrium techniques are useful tools for analyzing slope stability, it is important that practitioners recognize inherent limiting assumptions. Fundamentally, limit-equilibrium analyses assume rigid-body mechanics and assume that the factor of safety is uniformly distributed along the presumed failure surface. Except for the case in which residual strengths are used along the entire slip surface and the factor of safety is less than or equal to unity, this modeling limitation does not represent reality, and its use can significantly distort the true understanding of the distribution of the shear stresses along any presumed failure plane. This modeling limitation is likely one of the obscure and half-understood reasons that the historic use of a factor of safety of 1.5 has been required and largely successful for static slope stability analyses. The nonuniform mobilization of shear stresses may result in certain portions of a failure surface reaching, and exceeding, their peak strengths before others. This point was the essential lesson to be taken from the Filz et al. (2001) publication. Previous to Filz et al. (2001), a similar publication by Reddy et al. (1996) made the same point. These are landmark publications that should be studied by any practitioner involved in slope stability analyses, especially those involving geosynthetic lining systems. The Filz et al. (2001) and Reddy et al. (1996) papers indicate that shear stresses in real deformable bodies will initially begin to approach, and eventually may exceed, peak strengths at the outer slope toes of fills and at the base of the back slopes of lined repositories under static filling conditions. The practical recognition of this phenomenon and associated design recommendations relative to evaluating the stability of lined repositories was first widely promoted and published by Stark and Poeppel (1994). Their paper should be recognized as the first for the general design recommendation that postpeak shear strength be used along lined back slopes, while peak strength can be used along the base of lined repositories. An important concept that has been overlooked by the authors is that “a chain is only as strong as its weakest link.” Relative to performing slope stability analyses for multiinterface lining systems, this adage would be translated as “the critical interface will be the one with the lowest peak shear strength.” Fig. 1 of this discussion shows a graph of the peak shear strength envelopes for all eight interfaces considered by the authors in their example. It is clear from this graph that there are two interface strength envelopes that would control the slope stability of any configuration related to their design example: Interfaces II and VI [identical interfaces comprising a geocomposite versus textured high-density polyethylene (HDPE)] have the lowest peak strength at effective normal stresses below approximately 100 kPa, and Interface III [textured HDPE versus the woven side of geosynthetic clay liner (GCL)] has the lowest peak shear strength at effective normal stresses above approximately 100 kPa. Thus, these are the two shear strength envelopes that really should be used in evaluating the slope stability of the example problem. The designer would have to define the zones in which the effective normal stresses are less than 100 kPa and use either the peak or postpeak strength parameters, whichever is deemed appropriate, of Interface II or VI for those zones. For the zones in which the normal stresses are greater than 100 kPa, the designer would use either the peak or postpeak strength parameters, whichever is deemed appropriate, of Interface III. In this particular example, the peak shear strength parameters of Interface VII are so close to those of Interface III that, for the zones in which the designer wished to use postpeak strength parameters, it would be prudent to check the postpeak strength parameters of both those two interfaces and use the one that is the lesser of the two. In this case it would still be Interface III that would control at effective normal stresses greater than 100 kPa. Given the logic described in the preceding paragraph, the need to study the 64 options presented in the authors’ Table 2 is obviated. The most critical interfaces could be chosen based on inspection of the graph of all peak strength envelopes superimposed on one graph, as shown in Fig. 1, and only one analysis for the critical ky would need to be run. Furthermore, using this same logic, the authors’ selections of the critical interfaces in their design example would be judged incorrect on two counts. First, the selection of Interface IV (internal shear strength of GCL) as the critical postpeak interface on the back slope, as indicated in some of the authors’ examples, would not be correct because its peak shear strength is greater than that of either Interface III or VII for all effective normal stresses less than 300 kPa. Thus, Interface IV would not be expected to exceed its peak because either Interface III, or Interface II or VI, would fail first (depending on the effective normal stress) and never allow the GCL to mobilize its full peak internal strength. Second, along the base of the landfill, where the authors have chosen to use peak strength parameters, the critical interface would be different where the normal force was less than 100 kPa (in which case Interface II or VI would govern) compared to where the normal force was greater than 100 kPa (in which case Interface III would govern). The authors’ examples do not indicate the selection of different critical interfaces for different effective normal stresses. Standard industry practice would take this into consideration. In zones where a postpeak shear strength condition is assumed, the authors’ approach for selecting the critical interface is equivalent to selecting the interface with the lowest postpeak shear strength along that interface. If this extreme assumption is to be

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.

Classical methods such as limit equilibrium or limit analysis, dealing with the stability analysis of open cuts and trenches and calculation of critical excavation depth for them, do not fully satisfy the theoretical requirements for stability problems leading to di erent solutions depending on the adopted method. It is now appreciated that geomaterials exhibit considerable heterogeneity, caused by the lithological and inherent variation, which cannot be fully covered by simple methods. This paper highlights the uncertainty embedded in critical excavation depth calculation, arising from spatial variability of shear strength parameters, using Random Finite Di erence Method (RFDM) and Random Limit Equilibrium Method (RLEM). In the present study, the lognormally distributed undrained shear strength is considered spatially correlated throughout the domain. Surface cohesion value and the shear strength density were introduced as the deterministic parameters along with the coecient of variation of undrained shear strength and its scale of uctuation as stochastic parameters; these parameters were studied to see their e ect on uncertainty in critical excavation depth estimation. The results clearly demonstrated the uncertainty in critical excavation depth arising from the inherent variability of shear strength parameters using the RFDM results; however, RLEM did not prove to reflect such uncertainty eciently due to local averaging in prescribed failure surfaces.

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.

The present work quantified the laboratory geotechnical variability by repeatability direct shear test (DS) on alluvial fine-grained soils. The effect of laboratory variability of geotechnical parameters (cohesion c' and friction angle &amp;phiv;&amp;prime;) on slope stability was investigated. A mixture of compacted fine sand (40%) and clayey silt (60%) taken from a quarry fines stockpile was used: these soils are commonly used to backfill exhausted quarries located in the River Paglia alluvial plain (Central Italy). As knew in the literature, the dry density achieved by a given degree of compaction controls the shear strength parameters affecting the performance of compacted soil. Four direct shear tests were conducted following the ASTM D 3080-72 procedure on samples having a dry density of about 16.5 kN/m3, corresponding to 95 % of maximum dry density. Combining four DS tests yielded 256 pairs of shear strength parameters in terms of effective stresses, &amp;phiv;&amp;prime; and c' parameters show normal distribbution with &amp;phiv;&amp;prime;=27.0&amp;plusmn;0.8&amp;deg; and c&amp;prime;=19.22&amp;plusmn;4.08 kPa, for the stress range 100&amp;divide;250 kPa. In most of the 256 combinations, the friction angle decreased as the cohesion increased. It is generally accepted that the strength parameters (c' and &amp;phiv;&amp;prime;) have a negative correlation, although it is appreciated this is not always the case and different cohesion values can be obtained for the same friction angle (i.e., for the same slope of Coulomb failure envelope). The effect of the uncontrolled experimental variability of shear strength parameters on the long-term stability of a single homogeneous slope whose geometry can vary was investigated. Analyzing the factor of safety obtained using all the 256 combinations of shear strength parameters, the probability of having safety factors lower than 1.30 for the different slope heights was calculated. Such analyses demonstrate not only that direct shear testing is reliable, but also that the stability of a slope can be assessed with greater accuracy.

The spatial variability of soil properties is inherent. A series of direct shear tests were carried out on strongly weathered slates samples with weak bedding planes, the result of which indicates the existence of variability of shear strength parameters. Based on the testing results, several numerical simulations of slopes were conducted considering such a variability of shear strength. The results had shown that the weak bedding planes affect the shape of sliding arc as well as the factor of safety of slopes. As the dip angle of bedding planes increases, the shape of the sliding surface changes from circular to a mixed form of circular and planner. When incorporating the spatial variability of weak planes’ shear strength into the stability analysis, the safety factors of slopes would reduce, in which the sliding arc exhibited a sliding band comprising multiple sets of sliding arcs.

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

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.

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.

Effect of spatial variability of shear strength parameters on critical slip surfaces of slopes

Landslides are one of the natural hazards, which have significant negative effects on both humans and the environment. Thus, slope stability analyses and stabilization processes are necessary to obviate or mitigate landslides. In this study, the effect of groundwater level fluctuations and the construction of a building (i.e., a recently built church) on slope stability was investigated on the eastern slope of the Avas Hill, at Miskolc, in Northeast Hungary. Soil movements and groundwater levels were monitored and geological and slope stability models were constructed. Furthermore, the possibility of constructing a retaining system was evaluated to minimize the detrimental effects of both groundwater level fluctuations and the construction of the church. The findings showed that the fluctuation in groundwater levels had a destructive effect on slope stability due to pore-water pressure, which decreased the soil strength of the slope and slope stability. On the other hand, the church added an external load onto the underlying soil leading to an increase in slope instability. Hence, we suggested constructing retaining structures such as gravity retaining walls to increase the soil shear strength and enhance slope stability in the long term.

This report presents the findings of geotechnical testing on two material types retrieved from a surface mine site in Logan County, West Virginia, and investigates geomorphic landform design as an alternative in lieu of typical valley fill design and approximate original contour (AOC) surface mine reclamation design. Laboratory testing was carried out according to ASTM standard test methods. The scope of the testing performed involved grain size distribution analysis, hydrometer analysis, saturated shear strength testing under an insitu consolidation load, Atterberg limits including plastic and liquid limits, compaction at three predetermined compaction energies, and rigid wall permeameter hydraulic conductivity testing. Data was evaluated and analyzed to find to what degree the material particles moved under certain hydraulic gradients and if the particle movement affected the shear strength of the samples. The objectives of the testing were to understand the movement and behavior of small diameter soil particles at a valley fill and use the strength values as input parameters into several modules of GeoStudio(TM) for numerical slope stability modeling.;The numerical modeling involved geomorphic design for a proposed valley fill in southern West Virginia using commercial software following the Geofluv RTM method. A comprehensive seepage and slope stability analysis was then developed using the SEEP/W, SIGMA/W, and SLOPE/W modules of GeoStudio2007(TM) for assessing the groundwater flow characteristics of the blasted, unweathered sandstone fill, an insitu load calculation, and the resultant limit equilibrium analysis of slope stability (static factor of safety). These analyses were performed for both the AOC and geomorphic fill designs.;The cumulative analysis for the geomorphic valley fill alternative design yielded the highest factors of safety. Most cases produced factors of safety over 2.0. The failure locations were sought out to produce the lowest factors of safety for the structure. None of the factors of safety modeled yielded factors of safety under 1.0 for the geomorphic design. The results imply that the geomorphic design can remain very stable when a range of hydrologic conditions and geometries are applied.;Regulations require that reclaimed slope factors of safety must remain above 1.5. The analyses performed showed that the AOC valley fill design could withstand insitu loads and produced slope angles under most hydrologic conditions analyzed. Elevated pore pressures tended to result at the toe of the slope, and decreased the factor of safety. The most critical scenario was a fully saturated toe which yielded a factor of safety of 0.50.;If particle transport can

Estimating reserves and quantifying resources stand as pivotal and intricate endeavours within the realm of coal mining operations. Intricate geological formations compound the challenges in resource estimation, thereby complicating reserve calculations. The uncertainties tied to geological attributes of coal, encompassing parameters like tonnage and coal quality, wield significant sway over resource and reserve computations within coal mines. This research delves into the domain of geological uncertainties, with a specific focus on calorific value, aiming to numerically characterise resources and reserves within an open-pit coal mine situated in Indonesia. To quantify resources, the coal seam geometry underwent simulation via a multipoint geostatistical technique known as single normal equation simulation. A geologically established coal seam served as the training image for generating 20 equiprobable coal models. To simulate CV, 50 realisations were generated for each simulated coal seam, utilising sequential Gaussian simulation. Deviations of the simulated coal seams ranged from -0.07% to 5.48% in comparison to the training image. The CV simulation yielded an average value of 5,920.29 kcal/ kg, accompanied by a standard deviation of 586.54 kcal/kg. However, the average CV spanned from 5,305.26 kcal/kg to 6,526.55 kcal/kg across diverse simulations. For reserve calculation within the context of geological uncertainties, an algorithm rooted in maximum flow graph theory was employed to construct the ultimate pit for the coal mine. Within this final pit, the average stripping ratio was 1.62, coupled with a CV value of 6,019.66 kcal/kg. When juxtaposed with the deterministic model, the findings underscore that the stochastic ultimate pit delineates a more expansive excavation, accompanied by a heightened undiscounted cash flow.