Permeable pavements: Sizing

The following calculation is used to size the stone storage bed (reservoir) used as a base course for designs without underdrains. It is assumed that the footprint of the stone bed will be equal to the footprint of the pavement. The following equations are taken from the ICPI Manual

To calculate the total depth of the stone reservoir (all graded layers)

The equation for the depth of the stone bed is as follows:

$d={\frac {[Q_{c}\times R+P-f'\times t]}{V_{R}}}$

Where:

• d = Stone bed depth (m)
• Q_c = Depth of runoff from contributing drainage area, not including permeable paving surface (m)
• R = A_c/A_p; the ratio of contributing drainage area (A_c) to permeable paving area (A_p). Note that the contributing drainage area (A_c) should not contain pervious areas.
• P = Rainfall depth (m)
• f' = Design infiltration rate (m/day)
• t = Time to fill stone bed (typically 2 hr)
• V_R = Void ratio for stone bed (typically 0.4 for 50 mm dia. clear stone)

To calculate the invert of the underdrain from the base of the reservoir

For designs that include an underdrain, the maximum depth of the stone reservoir below the invert of the underdrain pipe (d_{s, max}) can be calculated as follows: $d_{s,max}={\frac {f'\times t}{0.4}}$

Where:

• f' = Design infiltration rate (mm/hr), and
• t = Drainage time (hrs), e.g. 96 hours, check local regulations for drainage time requirements.
• 0.4 = Void ratio of clear stone

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(f') used in the above equations should be the design infiltration rate that incorporates a safety correction factor. 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.

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When sizing the area of permeable paving based on the contributing drainage area, the following equation may be used: Failed to parse (syntax error): {\displaystyle A_p= \frac{Q_c\times A_c}{V_R \times dp – P + q'\times t}}

An underlying bed filled with aggregate or other void-forming fill material that temporarily stores stormwater before infiltrating into the native soil or being conveyed by an underdrain pipe.

The portion of water precipitated onto a catchment area, which then flows as surface discharge from the catchment area past a specified point.

Water from rain, snow melt, or irrigation that flows over the land surface.

The total surface area upstream of a point on a stream that drains toward that point. Not to be confused with watershed. The drainage area may include one or more watersheds.

An alternative practice to traditional impervious pavement, prevents the generation of runoff by allowing precipitation falling on the surface to infiltrate through the surface course into an underlying stone reservoir and, where suitable conditions exist, into the native soil.

The rate at which stormwater percolates into the subsoil measured in inches per hour.

The void ratio (e) of a mixture is the ratio of the volume of void-space to the volume of solids. It is closely related to the concept of porosity (n) where porosity is the ratio of the volume of void-space to the total or bulk volume of the mixture. e = Volume of voids/Volume of solids = n/(1-n)

A perforated pipe used to assist the draining of soils.

The period between the maximum water level and the minimum level (dry weather or antecedent level).