Scaling in fracture systems has become an active field of research in the last 25 years motivated by practical applications in hazardous waste disposal, hy- drocarbon reservoir management, and earthquake haz- ard assessment. Relevant publications are therefore spread widely through the literature. Although it is rec- ognized that some fracture systems are best described by scale-limited laws (lognormal, exponential), it is now recognized that power laws and fractal geometry provide widely applicable descriptive tools for fracture system characterization. A key argument for power law and fractal scaling is the absence of characteristic length scales in the fracture growth process. All power law and fractal characteristics in nature must have upper and lower bounds. This topic has been largely neglected, but recent studies emphasize the importance of layering on all scales in limiting the scaling characteristics of natural fracture systems. The determination of power law expo- nents and fractal dimensions from observations, al- though outwardly simple, is problematic, and uncritical use of analysis techniques has resulted in inaccurate and even meaningless exponents. We review these tech- niques and suggest guidelines for the accurate and ob- jective estimation of exponents and fractal dimensions. Syntheses of length, displacement, aperture power law exponents, and fractal dimensions are found, after crit- ical appraisal of published studies, to show a wide vari- ation, frequently spanning the theoretically possible range. Extrapolations from one dimension to two and from two dimensions to three are found to be nontrivial, and simple laws must be used with caution. Directions for future research include improved techniques for gathering data sets over great scale ranges and more rigorous application of existing analysis methods. More data are needed on joints and veins to illuminate the differences between different fracture modes. The phys- ical causes of power law scaling and variation in expo- nents and fractal dimensions are still poorly understood.

/pdf/scaling-of-fracture-systems-in-geological-media-1uq6op1ap8.pdf

Scaling of fracture systems in geological media

A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

Empirical estimation of rock mass modulus

The theory of flow through fractured rock and homogeneous anisotropic porous media is used to determine when a fractured rock behaves as a continuum. A fractured rock can be said to behave like an equivalent porous medium when (1) there is an insignificant change in the value of the equivalent permeability with a small addition or subtraction to the test volume and (2) an equivalent permeability tensor exists which predicts the correct flux when the direction of a constant gradient is changed. Field studies of fracture geometry are reviewed and a realistic, two-dimensional fracture system model is developed. The shape, size, orientation, and location of fractures in an impermeable matrix are random variables in the model. These variables are randomly distributed according to field data currently available in the literature. The fracture system models are subjected to simulated flow tests. The results of the flow tests are plotted as permeability ‘ellipses.’ The size and shape of these permeability ellipses show that fractured rock does not always behave as a homogeneous, anisotropic porous medium with a symmetric permeability tensor. Fracture systems behave more like porous media when (1) fracture density is increased, (2) apertures are constant rather than distributed, (3) orientations are distributed rather than constant, and (4) larger sample sizes are tested. Preliminary results indicate the use of this new tool, when perfected, will greatly enhance our ability to analyze field data on fractured rock systems. The tool can be used to distinguish between fractured systems which can be treated as porous media and fractured systems which must be treated as a collection of discrete fracture flow paths.

/pdf/porous-media-equivalents-for-networks-of-discontinuous-3bc2n5am14.pdf

Porous media equivalents for networks of discontinuous fractures

Fracture coalescence in rock-type materials under uniaxial and biaxial compression

Applicability of the Decision Aids for Tunneling (DAT) technique is investigated in this study to better understand the efficiency of the decision making process during tunnel construction. For this, a traffic tunnel under construction is adopted and information on the construction procedure, i.e., overall geology, unit cost and construction time for each excavation process, is provided periodically. Various scattergrams in which cost-time simulation results are plotted are obtained according to the simulation methods and final prediction on the construction time/cost is made. It is found that the uncertainty in the cost distribution is greater than the uncertainty in the time distribution foreach cycle simulation and the uncertainties in time and cost for theone time simulations are comparable. Future work will be concentrated on the updating scheme using the face mapping data and various parametric studies will also be performed.

Application of Decision Aids for Tunneling (DAT) to a Drill & Blast Tunnel

Characterisation of Fracture Apertures - Methods And Parameters

Shales have undergone a complex burial diagenesis that involved a severe modification of the pore structure. Reconstituted shales can provide new insights into the nature of the pore structure in natural materials. The effects of diagenesis on the microfabric, pore size distribution, and porosity of Opalinus shale were measured by comparing the behavior of natural and reconstituted specimens. The parent material (Opalinus shale) was reconstituted through multiple grinding operations, sedimentation from a dispersed slurry, and one-dimensional isothermal consolidation. This process produced uniform specimens that were not cemented and had replicable microfabric and engineering properties. The microfabric and mineralogy of the materials were examined using high-resolution scanning/backscattered electron microscopy (SEM/BSEM) and energy-dispersive X-ray spectroscopy (EDS) for specimens with broken and milled surfaces. Mercury intrusion porosimetry (MIP) and N 2 adsorption were used to assess the pore size distributions and specific surface areas of the materials. The microstructure of natural shale was characterized to be highly heterogeneous with significant concentrations of calcareous microfossils, calcite, and quartz particles embedded within the clay matrix. The microfossils were observed to be locally infilled and rimmed by a calcite cement that showed evidence of dissolution. The reconstituted specimens showed a double-structure microfabric that evolved with the level of consolidation stress and converged into a single-structure material (comparable to the natural shale) at a consolidation stress of more than twice the estimated maximum in situ effective stress. The natural shale had a lower specific surface area in comparison to the reconstituted material, which was consolidated at large effective stresses. These differences can be attributed to cementation at a submicron pore scale and highlight chemical diagenesis effects that were not replicated in the reconstituted specimens.

Insights into Diagenesis and Pore Structure of Opalinus Shale Through Comparative Studies of Natural and Reconstituted Materials

Exploration planning is a process of decision making under uncertainty. This paper, Part I of two dealing with the exploration problem, briefly reviews the decision analytical procedure for tunnel exploration, and provides practical techniques to do so. Specifically, this paper presents an approach by which the effect of additional exploration can be assessed before actually committing to exploration, through a process of so-called virtual exploration. This is practically done with an easy-to-use software package developed in Visual Basic for Applications in Microsoft Excel, called the Decision Aids for Tunnel Exploration. Part II will describe the uncertainties that enter into the tunnel exploration decision procedure, and will provide practical techniques to asses the effects of these uncertainties on the exploration decision making.

Decision Analysis Applied to Tunnel Exploration Planning. I: Principles and Case Study

An algorithm for determining the intersections between fractures is presented in this paper. The algorithm is implemented in GEOFRAC, a stochastic fracture pattern-modeling program. Previously, GEOFRAC allowed one to subdivide a fracture network into isolated subnetworks to assess connectivity. A new GEOFRAC feature can be used to analyze length and orientation distributions of the fracture intersections. Connectivity parameters such as the number of intersections per unit volume, C1, and the intersection length per unit volume can be calculated. Intersections and connectivity are important because they govern the fluid flow and stability behavior of rock masses. The program is used to model fracture intersections in the Boston area. The simulations show that for fractures in the Boston area, the mean fracture intersection length ranges from 0.5 to 0.7 m. The results also show that the relative frequency of long intersections (>2.0 m) increases with increasing modeling volume size. In contrast to ...

Herbert H. Einstein

Papers

Application of Decision Aids for Tunneling (DAT) to a Drill & Blast Tunnel

Characterisation of Fracture Apertures - Methods And Parameters

Insights into Diagenesis and Pore Structure of Opalinus Shale Through Comparative Studies of Natural and Reconstituted Materials

Decision Analysis Applied to Tunnel Exploration Planning. I: Principles and Case Study

Modeling Rock Fracture Intersections and Application to the Boston Area