In response to Rich Lacey’s article in the February/March 2008 issue of Geosynthetics (“Transmissivity: An ambiguous contradiction,” pp. 26–31), everything he says is correct, but I find the explanation more complicated and confusing than it needs to be for a design practitioner wishing to specify a material.
The essence of this article is the difference between flow rate and transmissivity, and how they are affected by different gradients that may result in laminar vs. turbulent flow. It is not at all incumbent on a designer to run a complete suite of tests at different gradients, and know whether they are on the laminar or turbulent part of the curve, to obtain what they need for a design. Very often a single test is adequate. To avoid confusion, one can use the following simple criteria that are used by design practitioners in this field.
1. If you design and specify using a value for transmissivity, you simply need to require that the laboratory test be run at a gradient equal to or greater than the design condition while subjected to a normal load equal to or greater than that which will occur in the field. This combination of conservative gradient and normal load will always be safe. The higher the gradient is above the design condition, the more conservative the design will be.
2. If you are doing forensic failure analyses to back calculate flow rates, you should consider running the tests as close to the expected field gradient as possible, or over a range of gradients that would bracket the field condition and run sensitivity analyses.
End of story. You need read no further if you want to simply have your life go on, practice safe designs, and have clear specifications for laboratory testing.
Regardless of [the explanation] in this article, you can, and are allowed, to specify something simply called “transmissivity” and not worry about whether it is in the laminar or turbulent flow range, and not worry if it needs a prefix such as “effective.” The lab will do the test at your specified gradient, measure the flow rate under your specified boundary and loading conditions, and will provide you with a calculated transmissivity that is very specific to all of those conditions.
Here are some further thoughts that help round out the picture in case you are interested:
Recognize that, of course, transmissivity is not at all the same as flow rate. In the exact same way, when using Darcy’s law, hydraulic conductivity is not at all the same as flow rate.
In general, engineers design and specify using transmissivity rather than flow rate for geonets or geocomposites, in the same way that they generally design and specify using hydraulic conductivity rather than flow rate for soils. Although less common, flow-rate designs and specifications can be provided if desired.
When flow is slow and/or over smooth material, the flow tends to be laminar. Under laminar flow conditions the value of the transmissivity (or hydraulic conductivity) is independent of gradient. At higher flows over rough materials (such as geonets or coarse gravel) the flow regime tends to change from laminar to turbulent. When this occurs, both transmissivity and hydraulic conductivity will decrease with increasing gradient (because more energy is burned up in turbulent flow).
None of this is new and has been known for decades (probably even more than a century).
It might help to understand the regulatory basis for the use of transmissivity, in lieu of flow capacity. In all federal regulations, including HSWA, RCRA Subtitle C, RCRA Subtitle D, and CERCLA, the minimum design standards for leachate collection and removal layers is specified using a minimum layer thickness and permeability reflecting the original use of granular layers. With the advent of geocomposite drainage layers, the only direct correlation available to designers was to compare the transmissivity of the granular layer to that of the geocomposite. This comparison has been the basis of much debate1 as to the proper means of making it but expressing the flow capacity in terms of transmissivity remains essential in permit applications subjected to regulatory review.
Here are some excellent references if you wish further reading, specifically in the field of geosynthetics:
Geosynthetics International Special Issue on Liquid Collection Systems (2000), Vol. 7, Nos. 4–6.
“Composite drains for side slopes in landfill final covers,” (G.N. Richardson and Aigen Zhao), Designers Forum, Geotechnical Fabrics Report, IFAI, St. Paul, Minn., June/July, 1998.
“Lateral-drainage systems over landfill barrier systems: Flat slopes,” (G.N. Richardson and Aigen Zhao), Designers Forum, Geotechnical Fabrics Report, IFAI, Roseville, Minn., August, 1998.
“Lateral drainage design update— Part 1,” (Richardson, G.N., Giroud, J.P., and Zhao, A.), Designers Forum, Geotechnical Fabrics Report, IFAI, Roseville, Minn., January/February, 2002, pp. 12–17.
“Lateral drainage design update— Part 2,” (Richardson, G.N., Giroud, J.P., and Zhao, A.), Designers Forum, Geotechnical Fabrics Report, IFAI, Roseville, Minn., March, 2002, pp. 18–21.
Tenax Design Manual.
Richard Thiel, Thiel Engineering, Oregon House, Calif.
1 Giroud, J.P., Zhao, A., and Bonaparte, R, 2000, “The Myth of Hydraulic Transmissivity Equivalence Between Geosynthetic and Granular Liquid Collection Layers, “ Geosynthetics International, Special Issue on Liquid Collection Systems, Vol. 7, Nos.4–6, pp. 381–401.