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The equation for the depth of the stone bed is as follows:
The equation for the depth of the stone bed is as follows:
<math>d= \frac{[Qc\times R + P - q\times T ]}{Vr}</math>
<math>d= \frac{[Q_c\times R + P - q\times T ]}{Vr}</math>
{{Plainlist|1=Where:
{{Plainlist|1=Where:
*''d'' = Stone bed depth (m)
*''d'' = Stone bed depth (m)
*''Q<sub>c</sub>'' = Depth of runoff from contributing drainage area, not including permeable paving surface(m)
*''Q<sub>c</sub>'' = Depth of runoff from contributing drainage area, not including permeable paving surface(m)
*''R'' = A<sub>c</sub>/A<sub>p</sub> = Ratio of contributing drainage area (A<sub>c</sub>) to permeable paving area (A<sub>p</sub>)
*''R'' = A<sub>c</sub>/A<sub>p</sub>; the ratio of contributing drainage area (''A<sub>c</sub>'') to permeable paving area (''A<sub>p</sub>''). Note that the contributing drainage area (''A<sub>c</sub>'') should not contain pervious areas.
*''P'' = Rainfall depth (m)
*''P'' = Rainfall depth (m)
*''q'' = Infiltration rate for native soils (m/day)
*''q'' = Infiltration rate for native soils (m/day)
*''T'' = Time to fill stone bed (typically 2 hr)
*''T'' = Time to fill stone bed (typically 2 hr)
*''Vr'' = Void ratio for stone bed (typically 0.4 for 50 mm dia. stone)}}
*''Vr'' = Void ratio for stone bed (typically 0.35 for 50 mm dia. stone)}}
For designs that include an underdrain, the maximum depth of the stone reservoir below the invert of the underdrain pipe can be calculated as follows:
For designs that include an underdrain, the maximum depth of the stone reservoir below the invert of the underdrain pipe can be calculated as follows:
<math>dr_{max} = \frac{q \times t}{Vr}</math>
<math>dr_{max} = \frac{q \times t}{Vr}</math>
{{Plainlist|1=Where:
{{plainlist|}}
*''dr<sub>max</sub>'' = Maximum stone reservoir depth (m)
*''dr<sub>max'' = Maximum stone reservoir depth (m)
*''q'' = Infiltration rate for native soils (m/hr)
*''q'' = Infiltration rate for native soils (m/hr)
*''Vr'' = Void space ratio for aggregate used (typically 0.35 for 50 mm clear stone)
*''Vr'' = Void space ratio for aggregate used (typically 0.4 for 50 mm clear stone)
*''t'' = Time to drain (design for 48 hour time to drain is recommended)}}
*''t'' = Time to drain (design for 48 hour time to drain is recommended)
The value for native soil infiltration rate (i) used in the above equations should be the design infiltration rate that incorporates a safety correction factor based on the ratio of the mean value at the proposed bottom elevation of the practice to the mean value in the least permeable soil horizon within 1.5 metres of the proposed bottom elevation
The value for native soil infiltration rate (q) used in the above equations should be the design [[infiltration]] rate that incorporates a safety correction factor based on the ratio of the mean value at the proposed bottom elevation of the practice to the mean value in the least permeable soil horizon within 1.5 metres of the proposed bottom elevation.
On highly permeable soils (e.g., infiltration rate of 45 mm/hr or greater), a maximum stone reservoir depth of 2 metres is recommended to prevent soil compaction and loss of permeability from the mass of overlying stone and stored water.
On highly permeable soils (e.g., infiltration rate of 45 mm/hr or greater), a maximum stone reservoir depth of 2 metres is recommended to prevent soil compaction and loss of permeability from the mass of overlying stone and stored water.
If trying to size the area of permeable paving based on the contributing drainage area, the following equation may be used:
If trying to size the area of permeable paving based on the contributing drainage area, the following equation may be used:
<math>A_p= \frac{Q_c\times A_c}{Vr \times dp – P + q\times T}</math>
<math>Ap= \frac{Qc \times Ac}{Vr \times dp – P + q\times T}</math>
[[category:modeling]]
[[category:modeling]]