Darcy's law, as defined by Equation 7.1, describes the flow regime in a porous media and is generally accepted for the design of SSF wetlands using soils and gravels as the bed media. A higher level of turbulent flow may occur in beds using very coarse rock, in which case Ergun's equation is more appropriate. Darcy's law is not strictly applicable to subsurface flow wetlands because of physical limitations in the actual system. It assumes laminar flow conditions, but turbulent flow may occur in very coarse gravels when the design utilizes a high hydraulic gradient. Darcy's law also assumes that the flow in the system is constant and uniform, but in reality the flow may vary due to precipitation, evaporation, and seepage, and local short-circuiting of flow may occur due to unequal porosity or poor construction. If small- to moderate-sized gravel is used as the media, if the system is properly constructed to minimize short-circuiting, if the system is designed to depend on a minimal hydraulic gradient, and if the gains and losses of water are recognized, then Darcy's law can provide a reasonable approximation of the hydraulic conditions in a SSF wetland:

H |
Uli |
! |
y |
« / /] A |
ft M |
~ Liner | |||

' - Native Soil |

FIGURE 7.1 Schematic of a subsurface flow constructed wetland. Because v = Q/Wy

FIGURE 7.1 Schematic of a subsurface flow constructed wetland. Because v = Q/Wy then

where v = Darcy's velocity, the apparent flow velocity through the entire cross-

sectional area of the bed (ft/d; m/d). ks = Hydraulic conductivity of a unit area of the wetland perpendicular to the flow direction (ft3/ft2-d; m3/m2-d). s = Hydraulic gradient, or slope, of the water surface in the flow system (ft/ft; m/m).

Q = Average flow through the wetland (ft3/d; m3/d) = [Qin + Qout]/2. W = Width of the SSF wetland cell (ft; m). y = Average depth of water in the wetland (ft; m). Ac = Total cross-sectional area perpendicular to the flow (ft2; m2).

The resistance to flow in the SSF wetland is caused primarily by the gravel media. Over the longer term, the spread of plant roots in the bed and the accumulation of nondegradable residues in the gravel pore spaces will also add resistance. The energy required to overcome this resistance is provided by the head differential between the water surface at the inlet and the outlet of the wetland. Some of this differential can be provided by constructing the wetland with a sloping bottom. The preferred approach is to construct the bottom with sufficient slope to allow complete drainage when needed and to provide outlet structures that allow adjustment of the water level to compensate for the resistance that may increase with time. The aspect ratio (length-to-width) selected for a SSF

TABLE 7.1

Typical Media Characteristics for Subsurface Flow Wetlands

TABLE 7.1

Typical Media Characteristics for Subsurface Flow Wetlands

Media Type |
Effective Size (D10) (mm) |
Porosity (n) (%) |
Hydraulic Conductivity (ks) (ft/d) |

Coarse sand |
2 |
28-32 |
328-3280 |

Gravelly sand |
8 |
30-35 |
1640-16,400 |

Fine gravel |
16 |
35-38 |
3280-32,800 |

Medium gravel |
32 |
36-40 |
32,800-164,000 |

Coarse rock |
128 |
38-45 |
164,000-820,000 |

Note: ft/d x 0.305 |
= m/d. |

wetland also strongly influences the hydraulic regime as the resistance to flow increases as the length increases. Reed et al. (1995) developed a model that can be used to estimate the minimum acceptable width of a SSF wetland channel. It is possible by substitution and rearrangement of terms to develop an equation for determining the acceptable minimum width of the SSF wetland cell that is compatible with the hydraulic gradient selected for design:

where | |

W |
= Width of the SSF wetland cell (ft; m). |

y |
= Average depth of water in the wetland (ft; m). |

Qa |
= Average flow through the wetland (ft3/d; m3/d). |

As |
= Design surface area of the wetland (ft2; m2). |

m |
= Portion of available hydraulic gradient used to provide the necessary |

head, as a decimal. | |

ks |
= Hydraulic conductivity of the media used (ft3/ft2/d; m3/m2/d). |

The m value in Equation 7.2 typically ranges from 5 to 20% of the potential head available. When using Equation 7.2 for design it is recommended that not more than one third of the effective hydraulic conductivity (ks) be used in the calculation and that the m value not exceed 20% to provide a large safety factor against potential clogging and other contingencies not defined at the time of design. Typical characteristics for media (medium gravel is most commonly used in the United States) with the potential for use in SSF wetlands are given in Table 7.1.

For large projects, it is recommended that the hydraulic conductivity (ks) be directly measured with a sample of the media to be used in the field or laboratory prior to final design. A permeameter is the standard laboratory device, but it is not well suited to the coarser gravels and rocks often used in these systems. A

-Perforated plate

-Perforated plate

Outflow

Calibrated container

Outflow

Calibrated container

FIGURE 7.2 Permeameter trough for measuring hydraulic conductivity of subsurface flow media.

permeameter trough that has been used successfully to measure the effective hydraulic conductivity of a range of gravel sizes is shown in Figure 7.2.

The total length of the trough is about 16.4 ft (5 m), with perforated plates located about 1.5 ft (0.5 m) from each end. The space between the perforated plates is filled with the media to be tested. The manometers are used to observe the water level inside the permeameter, and they are spaced about 9 ft (3 m) apart. Jacks or wedges are used to slightly raise the head end of the trough above the datum. Water flow into the trough is adjusted until the gravel media is flooded but without free water on the surface. The discharge (Q) is measured in a calibrated container and timed with a stopwatch. The cross-sectional flow area (Ac) is estimated by noting the depth of the water as it leaves the perforated plate at the end of the trough and multiplying that value by the width of the trough. The hydraulic gradient (s) for each test is (y1 - y2)/x (dimensions are shown on Figure 7.2). It is then possible to calculate the hydraulic conductivity because the other parameters in Equation 7.2 have all been measured. The Reynolds number should also be calculated for each test to ensure that the assumption of laminar flow was valid.

The porosity (n) of the media to be used in the SSF wetland should also be measured prior to final system design. This can be measured in the laboratory using a standard American Society for Testing and Materials (ASTM) procedure. An estimate is possible in the field by using a large container with a known volume. The container is filled with the media to be tested, and construction activity is simulated by some compaction or lifting and dropping the container. The container is then filled to a specified mark with a measured volume of water. The volume of water added defines the volume of voids (Vv). Because the total volume (Vt) is known, it is possible to calculate the porosity (n):

Many existing SSF wetlands were designed with a high aspect ratio (length-to-width ratio of 10:1 or more) to ensure plug flow in the system. Such high aspect ratios are unnecessary and have induced surface flow on these systems because the available hydraulic gradient is inadequate to maintain the intended subsurface flow. Some surface flow will occur on all SSF wetlands in response to major storm events, but the pollutant concentrations are proportionally reduced and treatment efficiency is not usually affected. The system should be initially designed for the average design flow and the impact of peak flows and storm events evaluated.

The previous recommendation that the design hydraulic gradient be limited to not more than 10% of the potential head has the practical effect of limiting the feasible aspect ratio for the system to relatively low values (<3:1 for beds 2 ft deep; 0.75:1 for beds 1 ft deep). SSF systems in Europe with soil instead of gravel have been constructed with up to 8% slopes to provide an adequate hydraulic gradient, and they have still experienced continuous surface flow due to an inadequate safety factor.

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