Transmissivity: An ambiguous contradiction

By Richard Lacey, TRI Environmental

Introduction

Specifying the transmissivity of a drainage product seems straightforward. There are only two approaches defined in the governing test method. One is to specify the required transmissivity, while the other is to specify the required in-plane flow rate. Of course, the specification must also include all of the parameters that affect the test results, including the compressive stress and seating period, the hydraulic gradient, and the boundary materials (Lacey 1999).

Even after footnoting all of these details in a specification, there remains another potential source of ambiguity that stems from the technical definition of “transmissivity.” This ambiguity can cause the overestimation of required flow or the acceptance of an underperforming product. The best way to explain the situation is to contrast the two specifications below; one written for flow rate in strict accordance with the standard, and one written for flow rate with ambiguous complications.

Figure 1 shows Product A that meets the flow rate specification. At point “1,” at a gradient of 0.50, the flow rate is 0.21 gpm/ft, which exceeds the required minimum value of 0.20 gpm/ft.

But does Product A also meet the Specification No. 2? Note that the term “transmissivity” has been listed in the Property column in lieu of “flow rate,” which is not unusual. Many specifications will use an abbreviated title of the test method in this column, which logically would be “transmissivity” for this test. But those who are familiar with ASTM D4716 appreciate that these two terms are not interchangeable.

ASTM D4716 “Standard Test Method for Determining the (In-Plane) Flow Rate and Hydraulic Transmissivity of a Geosynthetic Using a Constant Head 1” is both titled and written to distinguish between the two properties. The standard emphasizes the difference between “transmissivity” and “flow rate” with a “Note 6” in section 10 on calculations summarized below:

Note 6—The calculation of the hydraulic transmissivity is applicable only for tests or specific regions of tests conducted under laminar flow conditions. To determine the flow regime, plot the flow rate per unit width vs. the hydraulic gradient for each normal compressive stress. The data points for a given normal compressive stress form a straight line intersecting the origin if the test, or a region of the test, was conducted under laminar flow conditions. The hydraulic transmissivity is equal to the slope of the straight line region on these plots.²

There is also a graphical explanation of the term “transmissivity” provided in the Appendix of ASTM D4716 and reproduced in Figure 2.

If we interpret Specification No. 2 to be a “transmissivity” spec, we might get confused by the units of “gpm/ft,” which implies a flow rate. But it is not unusual for transmissivity specifications to employ these units, since a transmissivity value can easily be calculated from the flow rate and gradient as follows:

Transmissivity, gpm/ft = Flow Rate per Unit Width, gpm/ft ÷ Hydraulic Gradient, i

In an attempt to avoid this confusion, ASTM D4716 dictates a convention of units to be used when reporting transmissivity or flow rate test results. The flow rate results are to be reported in units of m³/s-m or gpm/ft, while the transmissivity values are to be reported in units of m²/s. But this practice has not been universally adopted.

If we then interpret Specification No. 2 to be a transmissivity specification with a minimum transmissivity value of 0.20 gpm/ft, then Product B will meet the requirement as shown in Figure 3. At Point 2, the flow rate is 0.14 gpm/ft and the gradient is 0.50.

Transmissivity, gpm/ft = 0.14, gpm/ft = 0.28 gpm/ft > 0.20 gpm/ft0.50

However, the design engineer actually needs a flow rate of 0.20 gpm/ft at a gradient of 0.50, and Product B will not provide sufficient flow capacity. The use of the term “transmissivity” in the property column, even though the units are consistent with a flow rate value, can be dangerously misleading in this situation. As we have demonstrated, the two specifications in our example are not technically equivalent, and it is very important to differentiate between “flow rate” and “transmissivity.”

In addition to confusing “transmissivity” with “flow rate,” the term “transmissivity” is also often used by laboratories and specifiers for test results that lie outside of the laminar region. In the examples shown above, it would be technically incorrect to report a transmissivity value for Product A above a gradient of approximately 0.10 or for Product B above a gradient of 0.20.

Therefore, a dilemma persists: “How do we clear up the contradictions and ambiguity regarding test results and specifications for transmissivity and/or flow rate?”

One approach might be to define and use additional test parameters. Figure 4 details these for a multiple-gradient test.

The definition of the term “transmissivity” remains the same, but it is enhanced with the adjective “characteristic” to denote the fact that it applies only to the “laminar” region. There are several other quantities defined below that complete the description of the hydraulic behavior. These values could be obtained routinely without running any additional or more complex tests.

• Characteristic Transmissivity, θ_C (m²/s)—The classic hydraulic transmissivity defined in Figure 2 above. The characteristic transmissivity should be based on flow rate data for gradients from 0.02 to 0.10. Once the departure gradient is determined for a given product, set-up and compressive stress, the characteristic transmissivity can be determined with one determination at or below that gradient.
• Effective Transmissivity, θ_Ei (m²/s)—The transmissivity calculated based on a measured flow rate at a gradient that is higher than the departure gradient. The effective transmissivity at a gradient of 0.5 is the flow rate Q 0.5 divided by 0.5
• Departure Gradient, i_D—The hydraulic gradient where the flow rate and gradient relationship departs from a straight line, i.e., the inflection point on the curve.
• Departure Flow Rate, Q_D (L/s-m or gpm/ft)—The flow rate per unit width at the departure gradient.
• Potential Flow Rate, Q_Pi (L/s-m or gpm/ft)—A flow rate on the characteristic transmissivity line. The potential flow rate at a gradient of 0.5 is the characteristic transmissivity times 0.5 and is denoted with Q P 0.5
• In-Plane Flow Rate, Q_i (L/s-m or gpm/ft)—An actual measured flow rate.
• Realized Flow Potential—The ratio of the measured flow rate at a particular gradient divided by the potential flow rate at that gradient, multiplied by 100 and expressed as a two-digit integer. In the example, the RFP at a gradient of 0.5 is Q P .5/ Q 0.5 x 100 = 80.

These quantities and definitions, with the subscript and units conventions, completely describe the hydraulic behavior generated in a typical transmissivity test. Then, even if the units do not follow the intended conventions, the adjective “Effective” could identify the required test result as a “transmissivity” and not a “flow rate.” A “transmissivity” specification could theoretically then be written that is equivalent to the correct specification No. 1 in our example above.

The author realizes that more is not always better, and simple approaches are generally preferred. However, even if this approach seems to make current transmissivity ambiguities more complicated, perhaps the spotlight we are shining on the situation in this forum will promote a better understanding of the transmissivity test and how to prepare and interpret specifications.

Rich Lacey is a senior engineer for TRI Environmental and the leader of the transmissivity task group in ASTM Committee D35.