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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 - i\times T ]}{Vr}</math>
<math>d= \frac{[Qc\times R + P - q\times T ]}{Vr}</math>
where:{{plainlist|}}
where:{{plainlist|}}
*''d'' = Stone bed depth (m)
*''d'' = Stone bed depth (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> = Ratio of contributing drainage area (A<sub>c</sub>) to permeable paving area (A<sub>p</sub>)
*''P'' = Rainfall depth (m)
*''P'' = Rainfall depth (m)
*''i'' = 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 0.4 for 50 mm dia. stone)
Note that the contributing drainage area (Ac) should not contain pervious areas.
Note that the contributing drainage area (Ac) should not contain pervious areas.
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{[i \times t]}{Vr} </math>
<math>dr_{max} = \frac{q \times t}{Vr}</math>
Where:
Where:
{{plainlist|}}
{{plainlist|}}
*''dr<sub>max'' = Maximum stone reservoir depth (m)
*''dr<sub>max'' = Maximum stone reservoir depth (m)
*''i'' = Infiltration rate for native soils (m/hr)
*''q'' = Infiltration rate for native soils (m/hr)
*''Vr'' = Void space ratio for aggregate used (typically 0.4 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)
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>Ap= [Qc \times Ac] / [Vr \times dp – P + i \times T] </math>
<math>Ap= \frac{Qc \times Ac}{Vr \times dp – P + q\times T}</math>
[[category:modeling]]
[[category:modeling]]