An Algorithmic 3D Rock Roughness Measure Using Local Depth Measurement Clusters

Summary. A computational algorithm which uses depth data from a reference plane to a rock fracture surface in calculating a new three-dimensional joint roughness coefficient is presented. Two independent sets of fracture data are investigated. The new coefficient is compared to Barton’s 2D joint roughness coefficient JRC. A measure indicating corrupt data is discussed. The algorithm is also used to show that, in general, rock roughness is only a local variable, not a directional one.     

Characterization and reconstruction of a rock fracture surface by geostatistics

It is well understood that, in studying the mechanical and hydromechanical behaviour of rock joints, their morphology must be taken into account. A geostatistical approach has been developed for characterizing the morphology of fracture surfaces at a decimetre scale. This allows the analysis of the spatial variability of elevations, and their first and second derivatives, with the intention of producing a model that gives a numerical three‐dimensional (3D) representation of the lower and upper surfaces of the fracture. Two samples (I and II) located close together were cored across a natural fracture. The experimental data are the elevations recorded along profiles (using recording steps of 0.5 and 0.02 mm, respectively, for the samples I and II). The goal of this study is to model the surface topography of sample I, so getting estimates for elevations at each node of a square grid whose mesh size will be, for mechanical purposes, no larger than the recording step. Since the fracture surface within the sample core is not strictly horizontal, geostatistical methods are applied to residuals of elevations of sample I. Further, since structural information is necessary at very low scale, theoretical models of variograms of elevations, first and second derivatives are fitted using data of both that sample I and sample II. The geostatistical reconstructions are computed using kriging and conditional simulation methods. In order to validate these reconstructions, variograms and distributions of experimental data are compared with variograms and distributions of the fitted data. Copyright © 2002 John Wiley & Sons, Ltd.     

A New Method for In-situ Non-contact Roughness Measurement of Large Rock Fracture Surfaces

Summary This paper presents a new method for in-situ non-contact measurements of fracture roughness by using a total station (TS). The TS is a non-reflector geodetic instrument usually used for measuring control points in surveying and mapping. By using a special-developed program, the TS can be used as a point-sensor laser scanner to scan a defined area of the fracture surface automatically, in field or in laboratory, at a distance away from the target surface. A large fracture surface can be automatically scanned with a constant interval of the sampling points, both within a defined area or along a cross-section of the exposed rock face. To quantify fracture roughness at different scales and obtain different densities of the scanned points, the point interval can be selected with the minimum interval of 1 mm. A local Cartesian co-ordinate system needs to be established first by the TS in front of the target rock face to define the true North or link the measurements to a known spatial co-ordinate system for both quantitative and spatial analysis of fracture roughness. To validate the method, fracture roughness data recorded with a non-reflector TS was compared with the data captured by a high-accuracy 3D-laser scanner. Results of this study revealed that both primary roughness and waviness of fracture surfaces can be quantified by the TS in the same accuracy level as that of the high accuracy laser scanner. Roughness of a natural fracture surface can be sampled without physical contact in a maximum distance of tens of meters from the rock faces. Received May 24, 2001; accepted July 24, 2002; Published online November 19, 2002     

Algorithmic Simulation of Flow in Rock Fractures

The two sides of a rock fracture are geometrically often very different. The difference or heterogeneity can be captured using aperture. This is also practically very significant because locally low or zero aperture in a rock fracture impedes flow. The aperture measurements of each of five paired rock blocks are discretely digitized (0–9). Each resulting weakly continuous two-dimensional matrix is then traversed by the nflow (new-flow) flow algorithm, once from each entry at one end to the other end. The paths are either incomplete and end surrounded by zeros or are completed at the other (exit) end. The numerical digit distribution is held constant from block to block. Fracture through-flow is defined as the average percentage of complete paths from one end to the other for that block. Fracture roughness is negatively correlated with fracture through-flow (r ~ −0.893). A rough fracture will only allow little flow compared with a smooth fracture with a smoother aperture distribution. Channeling of complete paths toward exit points is discussed for all blocks. Channeling is not related to roughness. A long complete sample path in a very rough fracture is shown. The distribution of numbers of complete paths is also investigated.     

Uncertainties in downscaled relative humidity for a semi-arid region in India

Monthly scenarios of relative humidity (R _H) were obtained for the Malaprabha river basin in India using a statistical downscaling technique. Large-scale atmospheric variables (air temperature and specific humidity at 925 mb, surface air temperature and latent heat flux) were chosen as predictors. The predictor variables are extracted from the (1) National Centers for Environmental Prediction reanalysis dataset for the period 1978–2000, and (2) simulations of the third generation Canadian Coupled Global Climate Model for the period 1978–2100. The objective of this study was to investigate the uncertainties in regional scenarios developed for R _H due to the choice of emission scenarios (A1B, A2, B1 and COMMIT) and the predictors selected. Multi-linear regression with stepwise screening is the downscaling technique used in this study. To study the uncertainty in the regional scenarios of R _H, due to the selected predictors, eight sets of predictors were chosen and a downscaling model was developed for each set. Performance of the downscaling models in the baseline period (1978–2000) was studied using three measures (1) Nash–Sutcliffe error estimate (E _f), (2) mean absolute error (MAE), and (3) product moment correlation (P). Results show that the performances vary between 0.59 and 0.68, 0.42 and 0.50 and 0.77 and 0.82 for E _f, MAE and P. Cumulative distribution functions were prepared from the regional scenarios of R _H developed for combinations of predictors and emission scenarios. Results show a variation of 1 to 6% R _H in the scenarios developed for combination of predictor sets for baseline period. For a future period (2001–2100), a variation of 6 to 15% R _H was observed for the combination of emission scenarios and predictors. The variation was highest for A2 scenario and least for COMMIT and B1 scenario.     

Spatial variability of soil moisture at typical alpine meadow and steppe sites in the Qinghai-Tibetan Plateau permafrost region

Permafrost degradation has the potential to significantly change soil moisture. The objective of this study was to assess the variability of soil moisture in a permafrost region using geostatistical techniques. The experiment was conducted in August 2008 in alpine steppe and meadow located in the Qinghai-Tibetan Plateau permafrost region. Four soil depths (0–10, 10–20, 20–30 and 30–40 cm) were analyzed using frequency domain reflectometry, and sampling made of 80 points in a 10 m × 10 m grid were sampled. Soil moisture was analyzed using classical statistics to appropriately describe central tendency and dispersion, and then using geostatistics to describe spatial variability. Classical statistical method indicated that soil moisture in the permafrost region had a normal distribution pattern. Mean surface soil moisture in alpine meadow was higher than that in alpine steppe. The semivariograms showed that soil moisture variability in alpine cold steppe was larger than that in alpine meadow, which decreased with depths. Nugget values in alpine steppe were low (0.1–4.5), in contrast to alpine cold meadow. Soil moisture in alpine steppe had highly structured spatial variability with more than 93.4% spatial heterogeneity, and the range decreased with depth. Soil moisture content in alpine cold meadow had a moderate spatial dependence with a range of 51.3–169.2 m, increasing with depth.     

Exploring the magnitude–frequency distribution: a cellular automata model for landslides

Landslide magnitude–frequency curves allow for the probabilistic characterization of regional landslide hazard. There is evidence that landslides exhibit self-organized criticality including the tendency to follow a power law over part of the magnitude–frequency distribution. Landslide distributions, however, also typically exhibit poor agreement with the power law at smaller sizes in a flattening of the slope known as rollover. Understanding the basis for this difference is critical if we are to accurately predict landslide hazard, risk or landscape denudation over large areas. One possible argument is that the magnitude–frequency distribution is dominated by physiographic controls whereby landslides tend to a larger size, and larger landslides are landscape limited according to a power law. We explore the physiographic argument using first a simple deterministic model and then a cellular automata model for watersheds in coastal British Columbia. The results compare favorably to actual landslide data: modeled landslides bifurcate at local elevation highs, deposit mass preferentially where the local slopes decrease, find routes in confined valley or channel networks, and, when sufficiently large, overwhelm the local topography. The magnitude–frequency distribution of both the actual landslides and the cellular automata model follow a power law for magnitudes higher than 10,000–20,000 m² and show a flattening of the slope for smaller magnitudes. Based on the results of both models, we argue that magnitude–frequency distributions, including both the rollover and the power law components, are a result of actual physiographic limitations related to slope, slope distance, and the distribution of mass within landslides. The cellular automata model uses simple empirically based rules that can be gathered for regions worldwide.     

Quantitative Parameters for Rock Joint Surface Roughness

Summary The morphologies of two artificial granite joints (sanded and hammered surfaces), one artificial regularly undulated joint and one natural schist joint, were studied. The sanded and hammered granite joints underwent 5 cycles of direct shear under 3 normal stress levels ranging between 0.3–4 MPa. The regularly undulated joint underwent 10 cycles of shear under 6 normal stress levels ranging between 0.5–5 MPa and the natural schist replicas underwent a monotonous shear under 5 normal stress levels ranging between 0.4–2.4 MPa. In order to characterize the morphology of the sheared joints, a laser sensor profilometer was used to perform surface data measurements prior to and after each shear test. Rather than describing the morphology of the joints from the single profiles, our characterization is based on a simultaneous analysis of all the surface profiles. Roughness was viewed as a combination of a primary roughness and a secondary roughness. The surface angularity was quantified by defining its three-dimensional mean angle, θ_s, and the parameter Z2_s. The surface anisotropy and the secondary roughness were respectively quantified by the degree of apparent anisotropy, k _a, and the surface relative roughness coefficient, R _s. The surface sinuosity was quantified by the surface tortuosity coefficient, T _s.  Comparison between the means of the classical linear parameters and those proposed shows that linear parameters underestimate the morphological characteristics of the joint surfaces. As a result, the proposed bi-dimensional and tri-dimensional parameters better describe the evolution of the joints initial roughness during the course of shearing.     

Numerical Modelling of the Heterogeneous Rock Fracture Process Using Various Test Techniques

Summary A series of numerical tests including both rock mechanics and fracture mechanics tests are conducted by the rock and tool (R–T^2D) interaction code coupled with a heterogeneous masterial model to obtain the physical–mechanical properties and fracture toughness, as well as to simulate the crack initiation and propagation, and the fracture progressive process. The simulated results not only predict relatively accurate physical–mechanical parameters and fracture toughness, but also visually reproduce the fracture progressive process compared with the experimental and theoretical results. The detailed stress distribution and redistribution, crack nucleation and initiation, stable and unstable crack propagation, interaction and coalescence, and corresponding load–displacement curves can be proposed as benchmarks for experimental study and theoretical research on crack propagation. It is concluded that the heterogeneous material model is reasonable and the R–T^2D code is stable, repeatable and a valuable numerical tool for research on the rock fracture process.     

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     

A Comparison of Methods for the Stochastic Simulation of Rock Fractures

Methods reported in the literature for rock fracture simulations include approaches based on stochastic geometry, multiple-point statistics and a combination of geostatistics for fracture density and object-based modelling for fracture geometries. The advantages and disadvantages of each of these approaches are discussed with examples. By way of review, the authors begin with the geostatistical indicator simulation method, based on the truncated–Gaussian algorithm; this is followed by multiple-point statistical simulation and then the stochastic geometry approach, which is based on marked point process simulation. A new approach, based on pluriGaussian structural simulation, is then introduced. The new approach incorporates in the simulation the spatial correlation between different sets of fractures, which in general, is very difficult, if not impossible, to accomplish in the three methods reviewed. Each simulation method is summarised together with detailed simulation procedures for each. A published two-dimensional fracture dataset is used as a means of assessing the performance of each simulation method and of demonstrating the concepts discussed in the text.     

Influence of Structural Non-Stationarity of Surface Roughness on Morphological Characterization and Mechanical Deformation of Rock Joints

Summary Structural non-stationarity of surface roughness affects accurate morphological characterization as well as mechanical behaviour of rock joints at the laboratory scale using samples with a size below the stationarity threshold. In this paper, the effect of structural non-stationarity of surface roughness is investigated by studying the scale dependence of surface roughness and mechanical behaviour of rock joints. The results show that the structural non-stationarity mainly affects the accurate characterization of the surface roughness of the fracture samples. It also controls the amount and location of the contact areas during shear tests, which in turn affects the mechanical properties and asperity degradation of the samples. It is concluded that for accurate determination of the morphological and mechanical properties of rock joints at laboratory and field scales, samples with size equal to or larger than the stationarity threshold are required. Author’s address: Nader Fardin, Rock Mechanics Group, Department of Mining Engineering, Faculty of Engineering, University of Tehran, P.O. Box: 11365/4563, Tehran, Iran     

Quantification of recent movement potentials in Schleswig-Holstein (Germany) by GIS-based calculation of correlation coefficients

In order to investigate connections between deep tectonic and halokinetic structures and the development of recent topography, GIS-based calculation of correlation coefficients was carried out between different stratigraphic horizons of the deep Northwest German Basin (NGB) according to the “Geotektonischer Atlas von NW-Deutschland” and surface topography of Schleswig-Holstein. The results show seven areas of high correlation that are traceable from the Base Zechstein up to the recent surface topography. Five areas with high correlation are connected to NNE–SSW trending salt structures within the Glückstadt Trough, i.e. the area of the salt domes Oldensworth, Tellingstedt, Eisendorf and, to the north of Hamburg, the area of the salt domes Elmshorn and Sievershütten. Two areas, however, with NW–SE trending high correlation are located in the northwest (restricted to the Westschleswig Block) and the northeast (south of Fehmarn) outside the Glückstadt Trough. These NW–SE trending correlation areas are not related to known salt structures and/or faults but match the general orientation of faults in the NGB.     

Study of vertical wind profiles in an urban area with complex terrain (Tehran)

In this paper monthly trends of vertical wind profiles within and above an urban area with complex topography (Tehran) have been investigated using data from a Sodar, a 100-m and two 28-m towers and some surface stations. It includes the occurrence, evolution, dissipation time, peak time and maximum height for katabatic–anabatic winds due to topography, return flow and urban circulation. Vertical distributions of wind and the heat and momentum fluxes up to 600 m were also considered.     

A hybrid method for grade estimation using genetic algorithm and neural networks

In the present paper, a new hybrid method is proposed for grade estimation. In this method, the multilayer perceptron (MLP) network is trained using the combination of the Levenberg–Marquardt (LM) method and genetic algorithm (GA). Having a few samples for grade estimation, it is difficult to get a proper result using some function approximation methods like neural networks or geostatistical methods. The neural network training methods are very sensitive to initial weight values when there are a few samples as a training dataset. The main objective of the proposed method is to resolve this problem. Here, our method finds the optimal initial weights by combining GA and LM method. Having the optimal initial values for weights, the local minima are avoided in the training phase and subsequently the neural network sustainability is trained optimally. Furthermore, the hybrid method is applied for grade estimation of Gol-e-Gohar iron ore in south Iran. The proposed method shows significant improvements compared to both conventional MLP and Kriging method. The efficiency of the proposed method gets more highlighted when the training data set is small.     

Application of multivariate spatial analysis in scale-based distribution and source study of PAHs in the topsoil: an example from Tianjin,China

Polycyclic aromatic hydrocarbons (PAHs) in soil originate from various sources under different spatial scales. Coregionalization analysis is more revealing than univariate geostatistical analysis. Scale-dependent spatial features of variables reflect different sources of spatial variability. In this study, 188 topsoil samples in the Tianjin area were collected. The contents of 16 PAHs and soil background properties were determined for all samples. A multivariate geostatistical approach was used for multi-scale spatial analysis for PAH compounds. Results show that coal combustion was the major source for the spatial distribution patterns of PAHs in the topsoil of the studied area. It worked mainly at the short-range scale (5–10 km). Significant spatial variation patterns were identified. In contrast, no significant spatial distribution trends at the nugget (0–5 km) or long-range scales (10–50 km) were seen. Long-range transport and site contamination of PAHs might not be key contributors in forming the distribution pattern of PAHs in the topsoil of Tianjin area.     

Quantification of Natural Fracture Surfaces Using Fractal Geometry

The purpose of this paper is to present an extensive evaluation of the methods to calculate the fractal dimension of natural fracture surfaces. Three methods; variogram analysis (VA), power spectral density (PSD), and roughness-length method (RMS) are applied to 2-D surface data (PSD) and 1-D profiles (VA and RMS) extracted from the surface data of 54 mm diameter crystallized limestone samples. Surface topography of the samples is quantified through a newly designed fully automated device. Before the application, self-affinity of the surface roughness and the applicability of these methods are validated using synthetically generated fractal surfaces. Fractal dimension values of the profiles are obtained as between 1 and 1.5 with a few exceptions. VA and RMS methods yield consistent fractal dimensions while the PSD values are lower than those of the other two methods. In terms of practical applicability, the VA is found more convenient than other two methods because there still exists shortcomings with the PSD and RMS methods due to difficulties in the mathematical analysis of the plots whose slopes are used in the computation of fractal dimension. However, it is observed that the data of limited size fracture surfaces are convenient for fractal analysis and the results are promising for further applications if the fracture surface size is restricted like cores recovered from deep boreholes.     

Geostatistical analysis of spatiotemporal variability of groundwater level fluctuations in Amman–Zarqa basin,Jordan: a case study

The main objective of this study was to assess the spatial and temporal variability of groundwater level fluctuations in the Amman–Zarqa basin, during the period 2001–2005. In the year 2003, as a consequence of war, there was a sudden increase in the population in this basin. Knowing that the basin is already heavily populated and witnesses most of the human and industrial activities in Jordan, this study was prompted to help make wise water resources management decisions to cope with the new situation. Data from 31 fairly distributed wells in the upper aquifer of the basin were subjected to geostatistical treatment. Kriging interpolation techniques have indicated that the groundwater flow directions remained almost constant over the years. The two main directions are SW–NE and E–W. Kriging mapped fluctuations have also showed that drop and rise events are localized in the basin. Forecasting possibilities for management purposes were tackled using autocorrelation analysis. The constructed autocorrelograms indicated, in general, the temporal dependence of seasonal water level fluctuations, and that forecasting can be carried out within a period of 3–21 months. Several suggestions were made to mitigate the drop and rise hazards in the detected sites.     

岩石拉伸剪切破裂试验研究

岩石拉伸剪切破裂是一类特殊应力状态条件下的破裂形式,属于同时受垂直于破裂面的法向拉应力和平行于破裂面的剪应力作用的复合破裂模式。在研制的DSC-800电液伺服测控岩石拉伸剪切试验仪的基础上,进行了大量花岗闪长岩和砂岩的拉伸剪切试验,开展了配套的破裂断口三维激光扫描、扫描电子显微镜（SEM）、岩石物理力学性质试验、颗粒流离散元（PFC）数值模拟等相关试验,利用分形理论研究了岩石拉剪破裂面特征,研究了岩石拉剪-压剪全区破裂准则、剪切速率对岩石拉剪破裂强度的影响,采用颗粒流离散元研究了岩石拉剪破裂过程。研究结论如下:（1）岩石拉剪破裂面的宏观与微观分形维数即粗糙度随着拉应力的增加而增大;（2）岩石的微观断裂形式是拉伸破坏和剪切破坏的结合。当拉应力较小时,岩石的微观断裂形式主要表现为剪切破坏,并且随着拉应力的增加,岩石的拉伸破坏形式表现得更加明显;（3）岩石在拉伸剪切区的破裂拉应力与剪应力成线性负相关关系,在拉伸剪切应力区的岩石破裂线斜率比压缩剪切区大,岩石在拉伸剪切应力条件下比压缩剪切应力条件下容易破裂;（4）在岩石拉伸剪切条件下,剪切速率与剪切强度成非线性反相关关系,随着剪切速率的增加,岩石拉剪破裂面粗糙度增加;（5）建立了岩石拉伸剪切PFC数值试验模型,模拟了岩石拉伸剪切破裂过程中的力链演化以及剪切速率对拉剪破裂面粗糙度的影响,获得了与实验室试验一致的结果。     

Geomorphological analysis of paleo drainage systems and their environmental implications in the desert of Kuwait

 A well-developed drainage network is carved in the hard calcretized and gypcretized gravelly sand of the Pleistocene Dibdibba Formation in northern Kuwait. The present-day aridity suggests that these drainages were developed during pluvial episodes that took place in the post-Pleistocene time and, therefore, are considered as paleo-drainage. Detailed morphometrical analysis of the endoeric drainage systems was performed and the degree of correlation among their different morphometric parameters was investigated. Based on these parameters, the studied drainage basins are statistically grouped into three groups. Such grouping was confirmed by discriminant analysis. The categorical data analysis demonstrated the dependence of these groupings on the surface geology, regional topography, and local geomorphological settings. Infiltration measurements revealed that the drainage bedrocks have a low infiltration rate (<20 cm h^–1), whereas the drainage fill deposits have a relatively high infiltration rate (67–30 cm h^–1). The impact of the drainage system pattern and morphometry on the hydrological conditions is discussed and potential near-surface low salinity to freshwater aquifers is delineated. The role of the studied drainage systems in the occurrence of mobile sand and sand dunes, rainwater harvesting, and land capability are discussed. Received: 8 September 1995 · Accepted: 24 October 1995