The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

/pdf/validity-of-cubic-law-for-fluid-flow-in-a-deformable-rock-2ynq4id3hq.pdf

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

This lecture describes the latest findings with respect to the long-term performance of modern municipal solid waste (MSW) landfill barrier systems. Field data relating to the clogging of leachate collection systems and the latest techniques for predicting their performance are examined. It is indicated that the primary leachate collection systems may have service lives that range from less than a decade to more than a century, depending on the design details, waste characteristics and mode of operation. Recent data indicate that landfill liner temperatures can be expected to reach at least 30–40°C for normal landfill operations. With recirculation of leachate the liner temperature increases faster than under normal operating conditions, and may be expected to exceed 40°C. Temperatures (up to 40–60°C) may occur at the base of landfills where there is a significant leachate mound. Temperature is shown to have a significant impact on both contaminant migration and the service life of the liner system. Field...

/pdf/long-term-performance-of-contaminant-barrier-systems-3jua43ep4g.pdf

Long-term performance of contaminant barrier systems

Long-term barrier performance of modified bentonite materials against sodium and calcium permeant solutions

The factors that may affect short-term leakage through composite liners are examined. It is shown that the leakage through composite liners is only a very small fraction of that expected for either...

Short- and long-term leakage through composite liners. The 7th Arthur Casagrande Lecture1 1This lecture was presented at the 14th Pan-American Conference on Soil Mechanics and Geotechnical Engineering, Toronto, Ont., October 2011, and a pre-print appeared in the conference proceedings.

Nathalie Touze-Foltz

Papers

Laboratory investigation of flow rate through composite liners consisting of a geomembrane, a GCL and a soil liner

Performance-based indicators for controlling geosynthetic clay liners in landfill applications

Hydraulic and mechanical behavior of GCLs in contact with leachate as part of a composite liner

Performance of geotextile filters after 18 years' service in drainage trenches

A review of the performance of geosynthetics for environmental protection