July 3, 2008

Bouma Calculator

for Estimating Onsite Wastewater System LTAR

David Radcliffe[1] and Larry West[2]

Steady infiltration through an onsite wastewater system (OWS) trench bottom can be used to calculate the design hydraulic loading rate (HLRD) or long term acceptance rate (LTAR) for a soil treatment unit (Siegrist, 2007). In this document, we show how to use an Excel spreadsheet that implements a modified version of the equation developed by Bouma (1975) for steady flux through a trench bottom. Once the flux is known, it can be converted to a LTAR using a safety factor. We show here an example for a sand textural class. Open the Excel spreadsheet file 'Bouma Calculator' (Figure 1).

**Figure 1. Bouma Calculator Excel spreadsheet.**

In the yellow area are shown the user input values that must be provided for the soil of interest. These are the van Genuchten (1980) hydraulic parameters residual water content (Theta-r, cm3/cm3), saturated water content (Theta-s, cm3/cm3), two fitting parameters Alpha (1/cm) and n (unitless), and the saturated hydraulic conductivity (Ks, cm/day). The user has the option of specifying the depth of ponding in the trench (h0, cm), the saturated hydraulic conductivity of the biomat (Kbs, cm/day), and the thickness of the biomat (Zb, cm). The default values for the biomat parameters are shown in Figure 1. The van Genucthen (1980) parameters can be obtained from measurements of the moisture release curve (Theta-r, Theta-s, Alpha, and n) and saturated hydraulic conductivity (Ks) for a soil. Alternatively, one can use the mean values for textural classes shown in the Soil textural classes worksheet (see lower left corner of Figure 1). Click on the 'Soil textural classes' tab and the worksheet in Figure 2 will appear.

**Figure 2 'Soil textural classes' worksheet.**

These parameter values are taken from the Rosetta Lite database in HYDRUS (Šimůnek et al., 2006). To find the flux through a sand textural class, copy the values for the sand class from the Soil textural classes worksheet into the Calculator worksheet (Figure 3). We've also typed in that this is a 'Sand' in cell A4 to remind ourselves, but that's not required for the calculation.

**Figure 3. Copy the parameter values for the sand from the 'Soil textural classes' worksheet into cells B4-F4 in the 'Calculator' worksheet.**

Now the soil tension that results in an equal flow through the biomat and soil beneath the biomat must be found through a trial and error process. In the graph in Figure 3, the flux through the biomat (Qb) is shown as the gray curve and the unsaturated hydraulic conductivity function for the underling soil (K(h)), as the black curve. Both are plotted as a function of the soil tension beneath the biomat on the x-axis. Where the curves cross, flow through the biomat and underlying soil are the same. From the graph it can be seen that the soil tension value where the curves cross is about 40 cm, so enter a trial value for soil tension of 40 in cell A10.

**Figure 4 Based on the graph, enter a trial value of 40 in cell A10 as an estimate of the soil tension where the curves cross (flux through the biomat and soil are equal).**

The difference between Qb and K(h) is show in the 'Residual' cell A13. The residual is positive so you need to increase the trial value slightly. Try a value of 42 (Figure 5). This results in a smaller residual that is negative, so try a value slightly smaller than 42. By this process, you can find that the exact tension that produces a residual of 0.00 is 41.52 cm (Figure 6).

As an alternative to the trial and error approach, you can use the 'Goal Seek' tool in Excel. Put a guess value in cell A10 based on the graph (for example enter 40). Click on 'Tools' on the toolbar and then select 'Goal seek'. In the Goal Seek window, for 'Set cell:' enter A13, for 'To value:' enter zero, and for 'By changing cell:' enter A10. Then click OK. You should see the solution value in A10 of 41.52.

**Figure 5. Put a trial value of 42 in cell A10. This results in a smaller residual that is slightly negative so decrease the trial value slightly.**

Once the residual is zero, the "Flux' shown in cell B15 is an estimate of the steady flux through the trench bottom. For the sand textural class, it is 10.31 cm/day. The flux in gallons per day per square foot (gpd/ft2) is shown in cell B16. To convert this to a LTAR, you must decide on a safety factor. We recommend using a safety factor of 0.50 (cell A19). Using this value, you get an LTAR = 1.26 gpd/ft2 for the sand textural class (cell B21).

This approach is described in more detail in Radcliffe and West (2008a and 2008b).

**Figure 6. By trial and error, you can find that the soil tension that results in a residual of 0.00 is 41.52 cm.**

References

Bouma, J. 1975. Unsaturated flow during soil treatment of septic tank effluent. *J. Environ. Eng. Div. Am. Soc. Civ. Eng.* 101: 967-983.

Radcliffe, D.E., and L.T. West. 2008a. Design hydraulic loading rates for on-site wastewater systems. Vadose Zone Journal. In press.

Radcliffe, D.E., and L.T. West. 2008b. Spreadsheet for converting saturated hydraulic conductivity to long term acceptance rate for on-site wastewater systems. Soil Survey Horizons. Article submitted.

Siegrist, R.L. 2007. Engineering of a soil treatment unit as a unit operation in an onsite wastewater system. In K. Mancl (ed.) Eleventh individual and small community sewage systems conference proceedings. ASABE Publication 701P1107. St Joseph, MI.

Šimůnek, J., M. Th. van Genuchten, M. Šejna. 2006. The HYDRUS software package for simulating two- and three-dimensional movement of water, heat, and multiple solutes in variably-saturated media. Version 1.0, technical manual, PC Progress, Prague.

van Genuchten, M.Th. (1980). A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44:892-898.

2

[1]Crop and Soil Sciences Department, University of Georgia, Athens, GA. .

[2] National Soil Survey Center, USDA-NRCS, Lincoln, NE.