An integrative approach to robust design and probabilistic risk assessment for CO<Subscript>2</Subscript> storage in geological formations

CO₂ storage in geological formations is currently being discussed intensively as a technology with a high potential for mitigating CO₂ emissions. However, any large-scale application requires a thorough analysis of the potential risks. Current numerical simulation models are too expensive for probabilistic risk analysis or stochastic approaches based on a brute-force approach of repeated simulation. Even single deterministic simulations may require parallel high-performance computing. The multiphase flow processes involved are too non-linear for quasi-linear error propagation and other simplified stochastic tools. As an alternative approach, we propose a massive stochastic model reduction based on the probabilistic collocation method. The model response is projected onto a higher-order orthogonal basis of polynomials to approximate dependence on uncertain parameters (porosity, permeability, etc.) and design parameters (injection rate, depth, etc.). This allows for a non-linear propagation of model uncertainty affecting the predicted risk, ensures fast computation, and provides a powerful tool for combining design variables and uncertain variables into one approach based on an integrative response surface. Thus, the design task of finding optimal injection regimes explicitly includes uncertainty, which leads to robust designs with a minimum failure probability. We validate our proposed stochastic approach by Monte Carlo simulation using a common 3D benchmark problem (Class et al., Comput Geosci 13:451–467, 2009). A reasonable compromise between computational efforts and precision was reached already with second-order polynomials. In our case study, the proposed approach yields a significant computational speed-up by a factor of 100 compared with the Monte Carlo evaluation. We demonstrate that, due to the non-linearity of the flow and transport processes during CO₂ injection, including uncertainty in the analysis leads to a systematic and significant shift of the predicted leakage rates toward higher values compared with deterministic simulations, affecting both risk estimates and the design of injection scenarios.     

Seasonal water uptake near trees: a numerical and experimental study

Issues related to the numerical simulation of moisture migration patterns in the unsaturated zone and in the vicinity of mature trees are explored in this paper. The research is based on the use of Richard's equation for unsaturated moisture flow incorporating a sink term. A numerical solution has been achieved via the finite-element method for spatial discretization along with a finite-difference time-marching scheme. An axisymmetric solution is developed to represent water uptake near an established tree. The approach adopted utilizes radial symmetry and assumes a linear distribution of water extraction rates with both depth and radius. The model has been validated by direct comparison with field measurements recorded (by others) for a mature lime tree located on a boulder clay subsoil. Non-linear hydraulic properties have been obtained from independent published data. A good correlation between field data and simulated results has been achieved. The simulation covers a full annual cycle starting from field capacity in winter, extending through a full spring–summer drying period and subsequent autumn recharge. It is believed that this is the first attempt to simulate the behaviour of an established tree over such a time-scale. This relatively straightforward approach is thought to be suitable for development and application to a range of geo-engineering problems (e.g. slope stability, shrinkage/heave prediction, etc).     

A generalized surrogate response aided-subset simulation approach for efficient geotechnical reliability-based design

This paper aims to develop an efficient geotechnical reliability-based design (RBD) approach using Monte Carlo simulation (MCS). The proposed approach combines a recently developed MCS-based RBD approach, namely expanded RBD approach, with an advanced MCS method called “Subset Simulation (SS)” to improve the computation efficiency at small probability levels that are often concerned in geotechnical design practice. To facilitate the integration of SS and expanded RBD, a generalized surrogate response f is proposed to define the driving variable, which is a key parameter in SS, for expanded RBD of geotechnical structures (e.g., soil retaining structures and foundations). With the aid of the proposed surrogate response, failure probabilities of all the possible designs in a prescribed design space are calculated from a single run of SS. Equations are derived for integration of the surrogate response-aided SS and expanded RBD, and are illustrated using an embedded sheet pile wall design example and two drilled shaft design examples. Results show that the proposed approach provides reasonable estimates of failure probabilities of different designs using a single run of the surrogate response-aided SS, and significantly improves the computational efficiency at small probabilities levels in comparison with direct MCS-based expanded RBD. The surrogate response-aided SS is able to, simultaneously, approach the failure domains of all the possible designs in the design space by a single run of simulation and to generate more complete design information, which subsequently yields feasible designs with a wide range of combinations of design parameters. This is mainly attributed to the strong correlation between the surrogate response and target response (e.g., factor of safety) of different designs concerned in geotechnical RBD.     

Evaluation of proposed waste rock dump designs using the SIBERIA erosion model

Computer-based landscape evolution models offer the ability to evaluate landscape stability over the short (annual), medium (decades to hundreds of years) and long-term (thousands of years). Modeling has advantages in that design ideas can be tested, different surface material properties can be evaluated and risk analysis carried out. Landscape evolution models allow landscape surface change through time. These models also offer the advantage that the landscape can be evaluated visually as it develops through time, which is not possible with other types of models. Landscape evolution models can be used for not only soil loss assessment (i.e. tonnes/hectare/year), but also to evaluate the method of soil loss (i.e. rill or interrill erosion). This study examines a range of waste rock dump designs for the Minera Alumbrera Ltd. copper mine, Argentina. An erosion assessment using the SIBERIA erosion model over a 1000-year simulation period demonstrates waste rock dump designs using a conventional stepped design of backsloping benches and caps with angle of repose slopes provide the lowest average erosion rates and depths of incision than do other designs. Caution should be applied in interpreting these results as the SIBERIA erosion model is sensitive to parameter input and in this case was calibrated and run using a generic set of parameters that are not site specific. Nevertheless, the results provide a guide as to the strengths and weaknesses of different rehabilitation designs and demonstrate the insights that modeling studies can provide.     

Numerical investigation of undrained cavity expansion in fine-grained soils

Based on the spherical cavity expansion (SCE) problem, Cudmani and Osinov (Can Geotech J 38:622–638, 2001), Osinov and Cudmani (Int J Numer Anal Method Geomech 25:473–495, 2001) developed a semi-empirical method of interpretation of CPT for coarse-grained soils (sand, gravel) using a hypoplastic constitutive model. Using a material-independent shape factor, the cone penetration resistance was related to the limit pressure required to expand a spherical cavity. The shape factor was observed to be a function of the soil state only, in particular the pressure-dependent relative density. This paper presents an analogous interpretation technique for CPT in fine-grained soils using the shape factor concept, Cavity Expansion approach, and a hypoplastic constitutive model. Relations for the shape factor and the limit pressure have been proposed based on the parameters affecting these quantities. A validation of the proposed interpretation technique with experimental results has also been performed.     

Digital simulation of multivariate two- and three-dimensional stochastic processes with a spectral turning bands method

The space domain version of the turning bands method can simulate multidimensional stochastic processes (random fields) having particular forms of covariance functions. To alleviate this limitation a spectral representation of the turning bands method in the two-dimensional case has shown that the spectral approach allows simulation of isotropic two-dimensional processes having any covariance or spectral density function. The present paper extends the spectral turning bands method (STBM) even further for simulation of much more general classes of multidimensional stochastic processes. Particular extensions include: (i) simulation of three-dimensional processes using STBM, (ii) simulation of anisotropic two- or three-dimensional stochastic processes, (iii) simulation of multivariate stochastic processes, and (iv) simulation of spatial averaged (integrated) processes. The turning bands method transforms the multidimensional simulation problem into a sum of a series of one-dimensional simulations. Explicit and simple expressions relating the cross-spectral density functions of the one-dimensional processes to the cross-spectral density function of the multidimensional process are derived. Using such expressions the one-dimensional processes can be simulated using a simple one-dimensional spectral method. Examples illustrating that the spectral turning bands method preserves the theoretical statistics are presented. The spectral turning bands method is inexpensive in terms of computer time compared to other multidimensional simulation methods. In fact, the cost of the turning bands method grows as the square root or the cubic root of the number of points simulated in the discretized random field, in the two- or three-dimensional case, respectively, whereas the cost of other multidimensional methods grows linearly with the number of simulated points. The spectral turning bands method currently is being used in hydrologic applications. This method is also applicable to other fields where multidimensional simulations are needed, e.g., mining, oil reservoir modeling, geophysics, remote sensing, etc.     

岩体结构随机模型模拟方法

本文论述利用勘探平硐资料研究岩体结构面分布规律及进行岩体结构面随机模型模拟方法。文中首先论述了描述结构面空间分布规律的五个几何参数,即产状、形态、规模、密度和张开度及其相应的概率分布型式;其次简单的介绍了 Monte-Carlo 方法在模拟结构面分布中的应用;最后结合三峡工程实例,论述了利用坝基勘探平硐编录图及现场记录估计结构面产状、迹线长度、中点密度分布参数的方法,并且给出了在参数估计基础上进行 Monte-Carlo模拟的部分结果。本文为岩体结构力学分析提供了一个定量的结构模型。     

An Exploration of the Interplay between the Measurement Uncertainty and the Number of Samples in Contaminated Land Investigations

In the assessment of potentially contaminated land, the number of samples and the uncertainty of the measurements (including that from sampling) are both important factors in the planning and implementation of an investigation. Both parameters also effect the interpretation of the measurements produced, and the process of making decisions based upon those measurements. However, despite their importance, previously there has been no method for assessing if an investigation is fit‐for‐purpose with respect to both of these parameters. The Whole Site Optimised Contaminated Land Investigation (WSOCLI) method has been developed to address this issue, and to allow the optimisation of an investigation with respect to both the number of samples and the measurement uncertainty, using an economic loss function. This function was developed to calculate an ‘expectation of (financial) loss’, incorporating costs of the investigation itself, subsequent land remediation, and potential consequential costs. To allow the evaluation of the WSOCLI method a computer program ‘OCLISIM’ has been developed to produce sample data from simulated contaminated land investigations. One advantage of such an approach is that as the ‘true’ contaminant concentrations are created by the program, these values are known, which is not the case in a real contaminated land investigation. This enables direct comparisons between functions of the ‘true’ concentrations and functions of the simulated measurements. A second advantage of simulation for this purpose is that the WSOCLI method can be tested on many different patterns and intensities of contamination. The WSOCLI method performed particularly well at high sampling densities producing expectations of financial loss that approximated to the true costs, which were also calculated by the program. WSOCLI was shown to produce notable trends in the relationship between the overall cost (i.e., expectation of loss) and both the number of samples and the measurement uncertainty, which are: (a) low measurement uncertainty was optimal when the decision threshold was between the mean background and the mean hot spot concentrations. (b) When the hot spot mean concentration is equal to or near the decision threshold, then mid‐range measurement uncertainties were optimal. (c) When the decision threshold exceeds the mean of the hot spot, mid‐range measurement uncertainties were optimal. The trends indicate that the uncertainty may continue to rise if the difference between hot spot mean and the decision threshold increases further. (d) In any of the above scenarios, the optimal measurement uncertainty was lower if there is a large geochemical variance (i.e., heterogeneity) within the hot spot. (e) The optimal number of samples for each scenario was indicated by the WSOCLI method, and was between 50 and 100 for the scenarios considered generally; although there was significant noise in the predictions, which needs to be addressed in future work to allow such conclusions to be clearer.     

The use of landscape evolution models in mining rehabilitation design

Landscape evolution models can be useful tools for the evaluation of rehabilitation designs for post-mining landscapes. When calibrated for the erodible material, landscape evolution models can predict sediment loss over entire landscapes (i.e. tonnes/hectare/year), method of erosion (i.e. slope wash, gullying) and also where on a hillslope erosion is likely to occur. The models provide the ability to examine simple hillslopes through to complex whole landscapes. These models can also be used for a probabilistic risk assessment of rehabilitation design for high-risk situations such as tailings dams. Importantly, unlike other erosion models they allow the eroded landscape to be visualised. This paper outlines the capabilities of the SIBERIA landscape evolution model for the rehabilitation of mining landscapes and proposes a probabilistic approach for risk assessment and site stability.     

重磁异常解释中的一些复杂因素与对策 ——在海口区域物探成果交流会上的发言提纲

列出了不重视推断解释可靠性问题而导致的严重后果;论述了复杂情况下重、磁异常解释的思路和对策,即如何正确、合理使用方法技术;提出了推断成果可靠性划分方案的建议和新的成果表达方式的建议.     

Gradual Deformation and Iterative Calibration of Sequential Stochastic Simulations

Based on the algorithm for gradual deformation of Gaussian stochastic models, we propose, in this paper, an extension of this method to gradually deforming realizations generated by sequential, not necessarily Gaussian, simulation. As in the Gaussian case, gradual deformation of a sequential simulation preserves spatial variability of the stochastic model and yields in general a regular objective function that can be minimized by an efficient optimization algorithm (e.g., a gradient-based algorithm). Furthermore, we discuss the local gradual deformation and the gradual deformation with respect to the structural parameters (mean, variance, and variogram range, etc.) of realizations generated by sequential simulation. Local gradual deformation may significantly improve calibration speed in the case where observations are scattered in different zones of a field. Gradual deformation with respect to structural parameters is necessary when these parameters cannot be inferred a priori and need to be determined using an inverse procedure. A synthetic example inspired from a real oil field is presented to illustrate different aspects of this approach. Results from this case study demonstrate the efficiency of the gradual deformation approach for constraining facies models generated by sequential indicator simulation. They also show the potential applicability of the proposed approach to complex real cases.     

A Method for Modeling of a Creeping Slope with a Visco-Hypoplastic Material Law

This paper presents the numerical simulation of a creeping slope in Upper Austria, using a visco-hypoplastic material law which describes the mechanical behavior of cohesive soils allowing for viscous effects, i.e. creep and relaxation. The method consists of: (1) determination of the parameters of the material law, based on laboratory tests on soil samples taken from the slope; (2) simulation of the laboratory tests with an element test program in which the used material law was implemented, in order to test whether the model holds for the soils studied; and (3) simulation of slope movements at different sections along the slope, assuming an infinite slope. The simulation results fit well with the field measurements. This demonstrates that despite strongly simplified boundary conditions and limited availability of subsurface data (e.g. density) the visco-hypoplastic law is a promising tool for predicting creep movements.     

复杂表层引起的生物礁解释陷阱分析

生物礁储层是良好的油气储集场所,具有高孔隙度、丰度大、产能高等特点,在油气勘探开发中占有十分重要的地位。常规的生物礁解释主要依据地震时间剖面上的外形隆起,顶底反射,上覆盖层的披覆等特征,但是在实际的生物礁解释中,还存在着很多解释陷阱。这里从常规地震资料处理误差分析的角度出发,首先提出了一种新的适用于起伏地形的波动方程地震叠后正演方法,然后通过对复杂表层条件下的生物礁模型进行地震数值模拟,重点分析了复杂表层条件可能引起的,生物礁的各种解释陷阱,如假隆起、生物礁体分布范围的变化等假象,为生物礁的识剐提供了重要的理论参考。     

Landslide hazard zonation in high risk areas of Rethymno Prefecture,Crete Island,Greece

The central part of Rethymnon Prefecture, Crete Island, suffers from severe landslide phenomena because of its geological and geomorphological settings alternated by the human activities. The main landslide preparatory and triggering causal factors are considered to be the ground conditions (lithology), geomorphological processes (fluvial erosion, etc.), and the man-made actions (excavations, loading etc.). The purpose of this study is to develop a decision support and continuous monitoring system of the area by composing landslide hazard and risk maps. For that reason, several approaches of the weighted linear combination (WLC), a semi-quantitative hazard analysis method, were adopted in a Geographic Information Systems (GIS) environment. The results were validated using a pre-existing landslide database enriched with new landslide locations mapped through image interpretation of a processed IKONOS satellite image. The validation results showed that the WLC method coupled with remote sensing (RS) and GIS techniques can support engineering geological studies concerning landslide vulnerability of hazardous areas.     

Method of predicting tremors on the basis of seismicemission registered in exploitation workings

A method of tremor risk estimation on the basis of seismic emission registered in mining exploitation zones is presented in this paper. A considerable part of the emission registered in these conditions, is generated by mechanical devices used in the mine (miner transporters etc.). Therefore, it is not possible to evaluate the risk of mining rock-bursts properly on the basis of interpretation of emission using known theories and models describing rock mass fracturing. In a new approach presented in this paper, the tremor risk is determined on the basis of time variation of a parameter describing the attenuation of seismic vibrations of the rock medium. The attenuation is assessed from the analysis of seismic emission registered in the frequency range from 30 Hz to 1000 Hz. Information about this parameter is encapsulated in the seismic emission regardless of the means of its generation. The method of estimating the temporal variations of attenuation is based on the analysis of signal envelopes of the microseismic emission. Attenuation trends can be interpreted in a straightforward way. As the stress values keep increasing, the following processes take place in the rock mass: compaction (hardening), dilatancy (softening), and then possibly tremors. At the compaction stage attenuation values are lower, while they increase at the dilatancy stage. This mechanism has been proven in practice. Our results can be used for monitoring tremor risk.     

基于总位移指标的反倾岩质边坡倾倒变形影响因子敏感性分析

为分析反倾边坡倾倒变形影响因子敏感性差异,本文采用数值模拟与灰色关联相结合的方法进行研究。首先将边坡几何特征参数、岩体物理力学参数、岩层力学参数定为反倾边坡第一级倾倒变形影响因子,并从各一级因子中进一步划分出边坡坡度、岩层倾角、岩层柔度等12个次级影响因子;然后对各二级影响因子分别选取11个水平数,并将12个二级影响因子、11级水平数随机组合成11套数值模拟方案,采用UDEC进行各方案数值模拟分析;最后采用灰色关联理论以坡顶倾倒变形水平位移为参考序列对12个二级影响因子进行关联度计算,并进一步分析出了3个一级影响因子敏感性大小。研究结果表明：（1）12个二级影响因子对倾倒变形影响最大的是岩层倾角;（2）三个一级影响因子中几何特征参数对倾倒变形影响最大,岩层层理力学参数对反倾边坡变形影响次之,岩块物理力学参数对反倾边坡变形影响最小。     

Analysis of the effect of trees on block propagation using a DEM model: implications for rockfall modelling

The objective of this research was to use numerical models based on mechanical approaches to improve the integration of the protective role of forests against rockfall into block propagation models. A model based on the discrete element method (DEM) was developed to take into account the complex mechanical processes involved during the impact of a block on a tree. This modelling approach requires the definition of many input parameters and cannot be directly integrated into block propagation models. A global sensitivity analysis identified the leading parameters of the block kinematics after impact (i.e. block energy reduction, trajectory changes, and rotational velocity): the impact velocity, the tree diameter, and the impact point horizontal location (i.e. eccentricity). Comparisons with the previous experimental and numerical studies of block impacts on trees demonstrated the applicability of the DEM model and showed some of the limitations of earlier approaches. Our sensitivity analysis highlights the significant influence of the impact velocity on the reduction of the block’s kinetic energy. Previous approaches usually also focus on parameters such as impact height, impact vertical incidence, and tree species, whose importance is only minor according to the present results. This suggests that the integration of forest effects into block propagation models could be both improved and simplified. The DEM model can also be used as an alternative to classical approaches for the integration of forest effects by directly coupling it with block propagation models. This direct coupling only requires the additional definition of the location and the diameter of each tree. Indeed, the input parameters related to the mechanical properties of the stem and the block/stem interaction in the DEM model can be set to average values because they are not leading parameters. The other input parameters are already defined or calculated in the block propagation model.     

克立格估计的分析解释与协方差函数的代数确定

首先引入利用旋转面作为基函数的函数逼近概念, 在此基础上经过复杂的矩阵推导证明泛克立格法可表示为传统的带权最小二乘多项式拟合与以旋转面作为基函数的函数逼近, 并在一定条件下(随机场高度连续无块金效应) 论证了协方差(即旋转面) 的参数可通过数学分析的方法确定, 给出了以高斯函数为例确定协方差函数的两个准则.      

Improving resolution of gravity data with wavelet analysis and spectral method

Gravity data are the results of gravity force field interaction from all the underground sources. The objects of detection are always submerged in the background field, and thus one of the crucial problems for gravity data interpretation is how to improve the resolution of observed information. The wavelet transform operator has recently been introduced into the domain fields both as a filter and as a powerful source analysis tool. This paper studied the effects of improving resolution of gravity data with wavelet analysis and spectral method, and revealed the geometric characteristics of density heterogeneities described by simple shaped sources. First, the basic theory of the multiscale wavelet analysis and its lifting scheme and spectral method were introduced. With the experimental study on forward simulation of anomalies given by the superposition of six objects and measured data in Songliao plain, Northeast China, the shape, size and depth of the buried objects were estimated in the study. Also, the results were compared with those obtained by conventional techniques, which demonstrated that this method greatly improves the resolution of gravity anomalies. Translated from Progress in Geophysics, 2007, 22(1): 112–120 [译自: 地球物理学进展]     

Finite-difference algorithm with local time-space grid refinement for simulation of waves

This paper presents a new approach to a local time-space grid refinement for a staggered-grid finite-difference simulation of waves. The approach is based on approximation of a wave equation at the interface where two grids are coupled. As no interpolation or projection techniques are used, the finite-difference scheme preserves second order of convergence. We have proved that this approach is low-reflecting, the artificial reflections are about 10^− 4 of an incident wave. We have also shown that if a successive refinement is applied, i.e. temporal and spatial steps are refined at different interfaces, this approach is stable.