1.1 Problem Statement
Fractures are prevalent in natural and synthetic structural media, even in the best engineered materials. We find fractures in bedrock, in sandstone aquifers and oil reservoirs, in clay layers and even in unconsolidated materials (Figures 1.1 to 1.4).
Fractures are also common in concrete, used either as a structural material or as a liner for storage tanks (Figure 1.5). Clay liners used in landfills, sludge and brine disposal pits or for underground storage tanks can fracture, releasing their liquid contents to the subsurface (Figure 1.6). Even “flexible” materials such as asphalt fracture with time
(Figure 1.7). The fact that fractures are inevitable has led to spending billions of research dollars to construct “safe” long-term (10,000 years or more) storage for high-level nuclear waste (Savage, 1995; IAEA, 1995), both to determine which construction techniques are least likely to result in failure and what are the implications of a failure, in terms of release to the environment and potential contamination of ground water sources or exposure of humans to high levels of radioactivity.
Why do materials fail? In most cases, the material is flawed from its genesis. In crystalline materials, it may be the inclusion of one different atom or molecule in the structure of the growing crystal, or simply the juncture of two crystal planes. In depositional materials, different grain types and sizes may be laid down, resulting in layering which then becomes the initiation plane for the fracture. Most materials fail because of mechanical stresses, for example the weight of the overburden, or heaving
(Atkinson, 1989; Heard et al., 1972). Some mechanical stresses are applied constantly2 until the material fails, others are delivered in a sudden event. Other causes of failure are thermal stresses, drying and wetting cycles and chemical dissolution.
After a material fractures, the two faces of the fracture may be subject
References: Atkinson, B. K., 1989: Fracture Mechanics of Rock, Academic Press, New York, pp. 548 Abdul, A Bai, M., D. Elsworth, J-C. Roegiers, 1993: Multiporosity/multipermeability approach to the simulation of naturally fractured reservoirs, Water Resources Research, 29:6, 1621-1633 Gelhar, L. W., 1986: Stochastic subsurface hydrology: From theory to applications., Water Resources Res., 22(9), 1355-1455. Gierke, J. S., N. J. Hutzler and J. C. Crittenden, Modeling the movement of volatile organic chemicals in columns of unsaturated soil, Water Resources Research, 26:7, 1529-1547 Heard, H. C., I. Y. Borg, N. L. Carter and C. B. Raleigh, 1972: Flow and fracture of rocks, Geophysical Monograph 16, American Geophysical Union, Washington, D Hsieh, P. A., S. P. Neuman, G. K. Stiles and E. S. Simpson, 1985: Field determination of the threedimensional hydraulic conductivity of anisotropic media: 2. Methodology and application to fracture rocks, Water Resources Research, 21:11, 1667-1676 Hsieh, P. A., S. P. Neuman and E. S. Simpson, 1983: Pressure testing of fractured rocks- A methodology employing three-dimensional cross-hole tests, Report NUREG/CR-3213 RW, Dept Hydrology and Water Resources, University of Arizona, Tucson, AZ 85721 IAEA, 1995: The principles of radioactive waste management, International Atomic Energy Agency, Kueper, B. H. and D. B. McWhorter, 1991: The behavior of dense, nonaqueous phase liquids in fractured clay and rock, Ground Water, 29:5, 716-728 Long, J. C. S., 1985: Verification and characterization of continuum behavior of fractured rock at AECL Underground Research Laboratory, Report BMI/OCRD-17, LBL-14975, Batelle Memorial Institute, Hydraulic conductivity and fracture aperture, Water Resources Research, 29:4, 1149-1162 Mercer, J liquids: mass transfer characteristics, Water Resources Research, 26:11, 2783-2796 Mutch, R National Research Council, 1994: Alternatives for ground water cleanup, National Academy Press, Washington, D National Research Council, 1996: Rock Fracture and Fracture Flow: Contemporary Understanding and Applications, Committee on Fracture Characterization and Fluid Flow, National Academy Press, Parker, J. C. and R. J. Lenhard, 1987: A model for hysteretic constitutive relations governing multiphase flow: 1 Parker, J. C. and R. J. Lenhard, 1990: Determining three-phase permeability-saturation-pressure relations from two-phase system measurements, J Parker, B. L., R. W. Gillham and J. A. Cherry, 1994: Diffusive disappearance of immiscible-phase organic liquids in fractured geologic media, Ground Water, 32:5, 805-820 Powers, S. E., C. O. Loureiro, L. M. Abriola and W. J. Weber, Jr., 1991: Theoretical study of the significance of nonequilibrium dissolution of nonaqueous phase liquids in subsurface systems, Water Reitsma, S. and B. H. Kueper, 1994: Laboratory measurement of capillary pressure-saturation relationships in a rock fracture, Water Resources Research, 30:4, 865-878 Savage, D., 1995: The scientific and regulatory basis for the geological disposal of radioactive waste, John Wiley, New York Schuring, J. R., P. C. Chan and T. M. Boland, 1995: Using pneumatic fracturing for in-situ remediation of contaminated sites, Remediation, 5:2, 77-90 Norman R. Warpinski, 1991: Hydraulic fracturing in tight, fissured media, SPE 20154, J. Petroleum Technology, 43:2, 146-209 Warren , J. E. and P. J. Root, 1963: The behavior of naturally fractured reservoirs, Soc. Pet. Eng. J., 3, 245-255 Wilkins, M. D., L. M. Abriola and K. D. Pennell, 1995: An experimental investigation of rate-limited nonaqueous phase liquid volatilization in unsaturated porous media: Steady state mass transfer, Water Resources Research, 31:9, 2159-2172 Zimmerman, R with semianalytical treatment of fracture/matrix flow, Water Resources Research, 29:7, 2127-2137