Content uploaded by John J. Walsh
Author content
All content in this area was uploaded by John J. Walsh on Aug 17, 2018
Content may be subject to copyright.
A preview of the PDF is not available
Measurement and characterisation of spatial distribution of fractures
Abstract
A variety of line sample (1-D) and map (2-D) datasets of faults and joints has been used to investigate the spatial distributions of fractures and to test techniques of fractal analysis. The natural fracture datasets have been supplemented by synthetic datasets with known characteristics. The fault datasets investigated range in scale from regional to outcrop and the joint datasets are derived from outcrop. 1-D datasets were analysed by the spacing population, interval counting and fracture number interval counting techniques. 2-D datasets were analysed by box-counting and fracture number box-counting techniques. Results indicate that fracture spacing can be characterised in line samples using either the 1-D interval counting technique or, more simply, by measuring the spacing population as the cumulative frequency distribution of spaces between adjacent fractures. Tectonic faults frequently show a power-law spacing population, indicating fractal dimensions of between 0.4 and 1.0 but, except for outcrop data, truncation effects degrade the analysis. Unrefined joint datasets commonly show negative exponential or lognormal spacing-cumulative frequency distributions. However, single orientation joint sets are characterised by a regular spacing and are therefore non-fractal.
... Both fractures and faults often affect the directionality of fluid flow (Gillespie et al., 1993;Bonnet et al., 2001;Agosta et al., 2010;Ceccato et al., 2022), and possibly lead to permeability anisotropies within rock masses (Lorenz et al., 1988(Lorenz et al., , 1989Le Garzic et al., 2011;Holdsworth et al., 2019). To quantify the control exerted by structural heterogeneities on the petrophysical properties of rock volumes, Discrete Fracture Network (DFN) modelling has emerged as a powerful tool to quantify the amounts of fracture porosity and equivalent permeability of geocellular volumes populated by digital fractures (Wilson et al., 2011;Panza et al., 2016). ...
... Taking into account the limit imposed on scaling of open fractures by diagenesis (Forstner and Laubach, 2022;Hooker et al., 2012), fracture and fault networks commonly exhibit variable dimensional and geometrical characteristics at multiple scales of observation (Marchegiani et al., 2006;Hooker et al., 2009;Mercuri et al., 2023). The variability of their dimension is assessed by considering the fracture length (or height) distribution of individual sets, and then computing the scaling laws across several scales (Gillespie et al., 1993;Cowie et al., 1993;Andrews et al., 2019;Bonnet et al., 2001;Bossennec et al., 2021;Forstner and Laubach, 2022). In this work, the dimension of single sets of SB and NSB fractures, and of small and medium faults is tackled in order to derive the input data for DFN modelling (cf. ...
Lower Jurassic to Cretaceous shallow-water carbonate rocks. The carbonates are exposed along the flanks of the
Viggiano Mt., on the eastern side of the High Agri Valley Basin of southern Italy. Furthermore, we employ the
results of field and digital structural analyses to derive the input parameters for subsequent Discrete Fracture
Network modelling (DFN) of geocellular volumes whose dimension and architecture resemble those of the
investigated sites. DFN modelling is carried out for geocellular volumes representing the studied bed packages
(5m-side volumes), outcrops (50m-side volumes), and reservoir-scale carbonate cliffs (500m-side volumes).
Notably, modelling is obtained considering the minimum mechanical aperture value obtained in the field for
porosity computations and theoretical values of fracture hydraulic aperture for permeability computations. This
is because the mechanical aperture values and roughness profiles collected in the field along single fractures are
unreliable due to weathering and localized karst-related dissolution. Our findings reveal that a scale-dependent
geometry characterizes the Cretaceous carbonates over three orders of magnitude. These results support previously
published data, and contrast with those obtained for the Lower Jurassic carbonates, which suffer of some
bias due to the quality of the exposures. After DFN modelling, we show that the amount of computed fracture
porosity is mainly due to the SB and NSB fractures, and that equivalent permeability is greater within faulted
rock volumes. In terms of horizontal permeability, which is the most reliable result after DFN modelling, we
document near isotropic horizontal permeability ellipses at all scales of observations. At individual outcrops, we
note that the permeability ellipses are elongated parallel to the dominant fault sets that denotes how localized
strain affects the directionality of fluid flow. Finally, we summarize the original data in a conceptual model
illustrating the modalities of meteoric fluid infiltration through the vadose zone, and then subsequent horizontal
flow in the phreatic zone present within the fracture carbonates at shallow depths.
... The regularity of fracture spacings was assessed using the coefficient of variation (Cv), derived from the ratio of the standard deviation (SD) to the mean spacing (S) (Cv = SD s ) . The Cv value indicates the distribution of fractures (Kagan & Jackson, 1991;Gillespie et al., 1993Gillespie et al., , 1999Gillespie et al., , 2001Supak et al., 2006). A higher Cv value suggests greater irregularity in the fracture spacing. ...
A multiscale fracturing study was conducted on the Early Jurassic carbonates of the Middle Atlas to unravel the complexities of fracture networks. Satellite imagery analysis identified 112 lineaments predominantly oriented NE–SW, NW–SE, and E–W. At the outcrop scale, a one-dimensional (1D) analysis revealed a dominance of small fractures, with the majority measuring less than 20 cm in length. The fracture size distribution follows a power-law, indicating scale-invariant behavior where smaller fractures are more abundant than larger ones. Furthermore, a positive correlation between bed thickness and fracture spacing was identified, suggesting mechanical and lithological controls on fracture growth. Two-dimensional (2D) analysis revealed a network of widely interconnected fractures, primarily characterized by Y-nodes and X-nodes, which facilitate efficient fluid flow. The fracture intensity varied across different sites, reflecting spatial heterogeneity in fracture occurrence. Four principal fracture sets were identified, related to Atlas tectonic compression. Two later, non-systematic sets intersect the existing sets and are attributed to Neogene and Quaternary tectonic phases. The NW–SE fractures are well-connected, forming a highly complex network dominated by Y-nodes, controlling the groundwater circulation in the Middle Atlas.
"Read the full paper here: https://rdcu.be/eeqVH "
... Variations in fracture properties such as aperture, permeability, porosity, and roughness greatly influence pollutant transport in fractured aquifers. This study is an initial step toward enhancing model predictions for pollutant transport, starting with fracture length variability due to its thorough documentation and available mapping techniques, as detailed by Gillespie et al. (1993) and Weiss (2008). Methods like terrestrial light detection and ranging (LiDAR) surveys, demonstrated by Zeng et al. (2018), Biber et al. (2018), and Espejel et al. (2020), among others, have been used to measure fracture lengths. ...
Pollutant transport in discrete fracture networks (DFNs) exhibits complex dynamics that challenge reliable model predictions, even with detailed fracture data. To address this issue, this study derives an upscaled integral‐differential equation to predict transient anomalous diffusion in two‐dimensional (2D) DFNs. The model includes both transmissive and dead‐end fractures (DEFs), where stagnant water zones in DEFs cause non‐uniform flow and transient sub‐diffusive transport, as shown by both literature and DFN flow and transport simulations using COMSOL. The upscaled model's main parameters are quantitatively linked to fracture properties, especially the probability density function of DEF lengths. Numerical experiments show the model's accuracy in predicting the full‐term evolution of conservative tracers in 2D DFNs with power‐law distributed fracture lengths and two orientation sets. Field applications indicate that while model parameters for transient sub‐diffusion can be predicted from observed DFN distributions, predicting parameters controlling solute displacement in transmissive fractures requires additional field work, such as tracer tests. Parameter sensitivity analysis further correlates late‐time solute transport dynamics with fracture properties, such as fracture density and average length. Potential extensions of the upscaled model are also discussed. This study, therefore, proves that transient anomalous transport in 2D DFNs with DEFs can be at least partially predicted, offering an initial step toward improving model predictions for pollutant transport in real‐world fractured aquifer systems.
... Any fracture surface pattern incorporates different attributes, e.g., linkage, roughness, ruggedness, size distribution/orientation, density each of which may scale independently and be fractal with its own respective, D f . [12] The irregular fracture surface pattern is complex in mesoscope and its surface pattern/morphology is extremely uneven (huge ruggedness) with `rolls and swells. ' The D f provides the quantitative assessment that characterizes the scale-properties of the irregular/complex surface geometry. ...
Culmination of any continuous deformation process is nothing but fracture. Hence, it is possible that the fracture surface would keep the imprint of entire deformation process operated. Experimental quantification of dimple geometry and its fractal dimension (Df) from published fractographs of a maraging steel with different austenite (fcc) fractions have been assessed/correlated with tensile responses. Elongation (e) is found to be directly proportional to dimple size (DIL) and Df while strength properties (yield strength-σys , tensile strength-σuts , hardness-HV) are inversely proportional to DIL and Df. The fracture geometry/patterns on tensile fractographs logically reflect the multiplicity of micro-void nucleating sites at different microstructural conditions due to heat-treatments (H/Ts).
... Their coordinates according to the scanline were recorded and used to quantify the fracture density P10 (Eq. (5); Gillespie et al., 1993). It is to be noted that, the P10 value only takes into account the number of fractures along the scanline and not their spacing. ...
Fractures play a critical role in fluid transport within brittle rocks, particularly in carbonate reservoirs. This study focuses on understanding the relationship between mechanical stratigraphy and natural fractures in the carbonate reservoirs of the Dehram Group in the Zagros region (Fars Arc), Southwest Iran. Using high-resolution borehole images and various well logs, the spatial distribution of fractures in this group are investigated. The study examines mechanical stratigraphy at two scales: large-scale mechanical stratigraphy, characterized by rock strength variations in units thicker than 1 meter, primarily affecting overall fracture intensity; and small-scale mechanical stratigraphy, revealed through borehole images, which significantly influences fracture aperture and continuity. The connectivity of fractures was evaluated using the degree of fracture connectivity (D), with results showing "good" connectivity in terms of increased permeability (D = 2.6) in the Kangan formation and "excellent" connectivity (D = 3.5) in the Dalan formation. Block intensities (R22) were measured at 0.4 in the Kangan and 0.2 in the Dalan, indicating varying degrees of rock fragmentation. Spatial variations in fracture connectivity across different zones are influenced by lithology, strain distribution, and the presence of weakness zones such as faults. These insights are essential for developing predictive models of reservoir performance in naturally fractured carbonate systems.
Fracture trace length distributions are often assumed to follow a power law, which implies that the distribution is scale-independent. The present study tests this assumption by evaluating the goodness-of-fit of three statistical models—the power law, piecewise power law, and lognormal distribution—upon a dataset of 57 trace maps that cover a range of fracture modes, host rock types, network scales, and topologies. The goodness-of-fit was assessed through the unbiased Kolmogorov-Smirnov (KS) test, which accounts for the fitting procedure and the degrees of freedom of each model. The results show that the power law provides a poor fit to trace length distributions, being rejected in 24 trace maps at a significance level of 0.05. In contrast, the piecewise power law and lognormal distribution demonstrated better fits across the fracture networks, with the piecewise power law performing the best overall. The poor fit of the power law can be attributed to mechanical and chemical controls on fracture growth, mainly fracture abutment, as well as stress shadowing and cementation, which affect growth rate at different length scales and result in scale-dependent trace length distributions. The consistent poor fit of the power law across various fracture networks suggests that these controls are prevalent in natural systems. While the power law remains a simple and effective model for trace length distribution, it should be recognized that it overlooks such controls that can influence the mechanical and hydraulic properties of fracture networks. Meanwhile, the fit of the piecewise power-law suggests the existence of a characteristic length where a transition in fracture growth occurs.
Crosshole seismic tomography (CST) could be used to reconstruct the velocity section of media between two holes. One commonly used attribute of fractures reflected in seismic waves is the anisotropy of velocity. Therefore, in this study, the multiple symmetry axes of anisotropic media are utilized to simulate the multiple-set fractures in strata. The anisotropic algebraic reconstruction technique (AART) and anisotropic simultaneous iterative reconstruction technique (ASIRT), extensions of isotropic ART and SIRT, are developed to detect the medium with multiple symmetry axes and strong anisotropy. Full coverage of ray paths in azimuth is needed for these techniques. The performances of these techniques are tested by numerical and physical modeling. Testing results show that the proposed AART and ASIRT methods can successfully detect the multiple-set fractures when the observed data exceeds the estimated parameters. However, in complexly anisotropic and heterogeneous media, the estimation error will significantly increase when using these techniques if the number of estimated parameters is equal to or greater than the number of observed data.
The Viking Graben of the northern North Sea provides an excellent opportunity to study the development of an extensional sedimentary basin. The development of the basin is investigated quantitatively, using a mathematical model which incorporates the rheological, thermal, and flexural isostatic consequences of lithosphere extension by simple-shear on major planar faults in the upper crust, and by distributed pure-shear in the lower crust and mantle. During faulting, the footwall and hangingwall blocks are considered as two interacting flexural cantilevers. Fault displacements during a given interval of time are used as input to the numerical model in order to produce synthetic basin cross-sections and derive post-extension crustal thickness. -from Authors
Describes how seismological progress has led to the contemporary understanding of earthquake origins, and discusses in detail the major contributions to modern theory. There is an initial compilation of quantitative views of earthquake origins and the main part considers the fault-origin model of earthquakes, with detailed examinations of basic concepts (with examples). This is followed by a discussion of physical, rockmechanical and tectonic problems of earthquake occurrence. The final chapter explains how the previous subjects discussed can be brought together to explore the problems of earthquake prediction and control. The text is considered suitable for university students in seismology and solid-earth sciences, and for engineers and construction workers. -from Publisher
This book introduces the fundamental concepts of fractal geometry and chaotic dynamics. These concepts are then related to a variety of geological and geophysical problems, illustrating just what chaos theory and fractals really tell us and how they can be applied to the earth sciences. Petroleum and mineral reserves, earthquakes, mantle convection and magnetic field generation are among the earth's properties that come under scrutiny. This is the first book that covers these topics at an accessible level; the concepts are introduced at the lowest possible level of mathematics and are consistently understandable, so that the reader requires only a background in basic physics and mathematics. Problems are also included for the reader to solve.
