Difference between revisions of "Bioretention: Sizing"

From LID SWM Planning and Design Guide
Jump to navigation Jump to search
Line 179: Line 179:
 
*''A<sub>p</sub>'' is the area of the practice (m<sup>2</sup>),
 
*''A<sub>p</sub>'' is the area of the practice (m<sup>2</sup>),
 
*''f''' is the design infiltration rate of the native soil (mm/h),  
 
*''f''' is the design infiltration rate of the native soil (mm/h),  
*''x'' is the perimeter of the practice (m), and
+
*''x'' is the perimeter of the practice (m),  
 +
* "ln" is the natural logarithm and,
 
*''d<sub>r</sub>'' is the depth of the storage reservoir (m).}}
 
*''d<sub>r</sub>'' is the depth of the storage reservoir (m).}}
  

Revision as of 17:18, 20 May 2020

This article is specific to bioretention, vegetated systems that infiltrate water to the native soil.
If you are designing a planted system which does not infiltrate water, see advice on Planters: Sizing.

The vertical storage zones in a bioretention cell include: ponding, mulch, filter media, choker layer, embedded pipe diameter depth and the storage reservoir.

Many of the dimensions in a bioretention system can be predetermined according to the function of the component. There is greatest flexibility in the ponding depth and the depth of the storage reservoir beneath the optional underdrain pipe. The table below describes some recommended values to use to begin the design process.

Component Recommended depth (with underdrain pipe) Recommended depth (no underdrain pipe) Typical porosity (n)
Surface ponding, maximum (dp, max)
  • 300 mm; filter media Blend A
  • 350 mm; filter media Blend B
See below 1
Mulch 75 ± 25 mm
  • 0.7 for wood based
  • 0.4 for stone
Filter media (dm)
  • 300 mm to support turf grass and accept only roof runoff
  • 600 mm to support shrubs, flowering perennials and deeply rooting decorative grasses and accept both roof and pavement runoff
  • 1000 mm to support trees and accept both roof and pavement runoff
  • 0.4 for sandier Blend A (drainage rate priority)
  • 0.35 for more loamy Blend B (water quality treatment priority)
Choker layer 100 mm 0.4
Perforated pipe and surrounding aggregate 200 mm (i.e. pipe diameter) Not applicable 0.4
Storage reservoir (dr) See below See below 0.4

Before you begin you will need to know the following;

  • Catchment area (i.e. contributing drainage area), Ac (m2)
  • Catchment runoff coefficient, C
  • Catchment impervious area, Ai (m2)
  • Design storm intensity, i (mm/h)
  • Design storm duration, D (h)
  • Infiltration volume target for the design storm event, Vi (m3), based on average annual water budgets for the catchment for pre- and post-development scenarios and equal to the infiltration volume deficit (pre-development minus post-development annual infiltration)
  • Drainage time, t (h), time required to fully drain the active water storage components of the practice (i.e surface ponding and infiltration water storage depths), based on local criteria or long term average inter-event period for the location
  • Field measured infiltration rate of the underlying native soil, f (mm/h), median of field measurements or based on interpolation from median grain-size distribution results
  • Design infiltration rate of the underlying native soil, f' (mm/h), median field measured value, f divided by a safety factor, z
  • Safety factor, z (dimensionless value between 2 and 3) chosen by designer based on consideration of risk factors
  • Proposed surface grade elevation at the practice location (metres above sea level, masl)
  • Elevation of the seasonally high water table or bedrock surface (metres above sea level, masl), below the practice location
  • Effective porosity of the storage reservoir fill material(s), including any void-forming structures (e.g. pipes, chambers, tanks, soil cells, etc.) and surrounding aggregate, nr'
  • Types of plants to be supported by the filter media bed (i.e. grasses vs. mix of grasses, plants and shrubs vs. trees)
  • How runoff will be delivered to the practice (i.e. to surface ponding area, or directly to storage reservoir)

Decide if an underdrain will be included[edit]

  • Step 1: Based on the median measured infiltration rate of the native soil at the proposed location and bottom elevation of the practice, or estimated infiltration rate from median grain-size distribution results, decide if an underdrain will be included in the design. See Design infiltration rate for guidance on field tests, methods and number of test locations and tests (i.e. measurements) to be performed.

If the median field measured or estimated infiltration rate of the underlying native soil (f) is less than 15 mm/h, include an underdrain.

Select a surface ponding depth to begin sizing with[edit]

  • Step 2: Determine a maximum surface ponding depth (dp, max)

For practices without underdrains:

Where:

  • f' = Design infiltration rate (mm/h), and
  • 48 = Maximum permissible drainage time for surface ponded water (h)

Note that conceptually, in designs without underdrains, when filled to their maximum storage capacity, drainage of ponded water is limited by the infiltration rate at the base of the practice.

For practices with underdrains see recommended maximum surface ponding depth for each filter media blend in the table above.

  • Step 3: Select a design surface ponding depth, dp' (m) to begin sizing with:

For practices with soft (i.e. landscaped) edges and bowl-shaped ponding areas calculate the mean surface ponding depth:

Where:

  • dp, max = maximum surface ponding depth (m)


For practices with hard edges and vertical-walled ponding areas (e.g., stormwater planter, soil cell) use the maximum ponding depth:

Determine the infiltration water storage depth of the practice[edit]

  • Step 4: Calculate the infiltration water storage depth of the practice, di which is the depth of water stored by the practice that can drain by infiltration alone.

For practices without an underdrain, components contributing to infiltration water storage include the surface ponding, mulch and filter media depths (i.e. total depth of the practice). The infiltration water storage depth of the practice can be calculated as:

Where:

  • dp' = Design surface ponding depth (m)
  • dm = Depth of mulch (m)
  • nm = Porosity of mulch
  • df = Depth of filter media (m)
  • nf = Porosity of filter media


For practices with the underdrain perforated pipe elevated off the bottom, infiltration water storage is provided by the storage reservoir, dr (i.e. depth below the invert of the underdrain perforated pipe), and only the portion that can reliably drain by infiltration within the specified inter-event drainage time, t. So the infiltration water storage depth of the practice can be calculated as:

Where:

  • f' = Design infiltration rate of underlying native soil (m/h)
  • t = Drainage time (h), time required to fully drain the active storage components of the practice (i.e. surface ponding and infiltration water storage depths), based on local criteria or long term average inter-event period for the location


For practices with the underdrain perforated pipe installed on the bottom and connected to a riser (e.g., standpipe and 90 degree coupling), infiltration water storage is provided by the storage reservoir depth between the inverts of the riser outlet (i.e invert elevation of the 90 degree coupling) and reservoir bottom, and is calculated the same way as above.

To boost drainage performance on fine-textured, low permeability soils, consider designing storage reservoirs even deeper than those calculated using the above approach, that many not fully drain between storm events (i.e. includes inactive water storage), which increases hydraulic head and thereby, infiltration rate at the base of the practice. See Low permeability soils for more information.

Determine the required surface area of the practice[edit]

  • Step 5: Calculate the surface area of the practice (Ap) needed to capture the volume of runoff produced from the catchment by the design storm event.

For practices where flow is delivered to a surface ponding area:

Where:

  • i = Design storm intensity (m/h)
  • D = Design storm duration (h)
  • Ai = Catchment impervious area (m2)
  • dp' = Design surface ponding depth (m)
  • ff, min = minimum acceptable infiltration rate (i.e. saturated hydraulic conductivity) of the filter media (m/h), see Filter media for guidance



For practices where flow is delivered directly to the storage reservoir:

Where:

  • di = Infiltration water storage depth (m), see above for equations for with and without underdrain designs
  • f' = design infiltration rate of the underlying native soil (m/h)
  • D = Design storm duration (h)


  • Step 6: Compare required surface area of the practice to available space.

To decrease Ap, consider increasing ponding depth if feasible and would not create a safety hazard (recommended maximum of 0.45 m), using Darcy 3D drainage equation or tool (see below) to optimize the infiltration water storage depth, assuming both vertical and horizontal drainage, or decreasing the catchment area.

  • Step 7: Calculate catchment impervious area to practice permeable (footprint) area ratio, R, also referred to as I/P ratio:


Adjust dp, di, Ap or Ai to keep R between 5 and 20, and solve the applicable sizing equation from above to determine the required dimensions of the practice.

Determine the required surface area of the storage reservoir[edit]

  • Step 8: Calculate the surface area of the storage reservoir, Ar (m2) needed to capture the infiltration volume target for the design storm event:

{{Plainlist|1= Where:

  • Vi = Infiltration volume target for the design storm event (m3), based on average annual water budgets for pre- and post-development scenarios, and the estimated infiltration volume deficit (pre-development minus post-development infiltration).
  • di = Infiltration water storage depth of the practice (m), see equations above to calculate for with and without underdrain designs.
  • f' = Design infiltration rate of the underlying native soil (m/h)
  • D= Duration of design storm (h)

For practices where inflow is directed to a surface ponding area, if Ar is greater than Ap, use the value for Ar as the required footprint area of the practice, Ap.

  • Step 9: Calculate the required storage reservoir depth, dr (m):

{{Plainlist|1= Where:

  • di' = Design infiltration water storage depth (m)
  • nr' = Effective porosity of the storage reservoir fill material(s).

To minimize the total depth of the practice, dT, and save aggregate, consider installing void-forming structures (e.g. Permavoid, D-Raintank, low profile stormwater chamber, large diameter perforated pipes etc.) embedded in clear stone aggregate in the storage reservoir instead of aggregate alone, which will provide a greater effective porosity (n').

Calculate the total depth of the practice, dT[edit]

  • Step 10: Determine what the planting needs are and assign an appropriate depth of filter media, using the table above.
  • Step 11: Select an underdrain perforated pipe diameter (typically 100 or 200 mm), assign this as an 'embedded' depth equal to the pipe diameter. The perforated pipe depth can be made part of the infiltration water storage of the practice when a riser (standpipe and 90 degree coupling) are used to design the underdrain.
  • Step 12: Sum total depth of bioretention components, and compare to available space (i.e. depth) between the elevations of the proposed surface grade and one (1) metre above the seasonally high water table or top of bedrock in the practice location.
  • Step 13: Adjust component depths to maintain a separation of one (1) metre between the base of the practice and the seasonally high water table or top of bedrock elevation, or a lesser or greater value based on groundwater mounding analysis. See below and Groundwater for more information.

For practices without an underdrain in locations constrained in the vertical dimension, consider decreasing filter media depth (and adjusting supported plant types) and/or catchment impervious area.
For practices with an underdrain in locations constrained in the vertical dimension, consider installing the perforated pipe on the bottom of the storage reservoir and including a riser (saves the depth of aggregate needed to embed the pipe), and/or decreasing filter media depth (and adjusting supported plant types), ponding depth and/or catchment impervious area.

Calculate peak flow rates[edit]

Calculating infiltration practice drainage in 1 dimension[edit]

This spreadsheet compares drainage in a single dimension under zero head conditions, mean head conditions and falling head conditions. It provides a more conservative measurement of the drainage time for the purposes of groundwater mounding (where a shorter drainage time causes a greater impact).

Download drainage time calculator(.xlsx)

Drainage time (3D)[1][edit]

Two practice areas of 9 m2.
x = 12 m (left), x = 20 m (right)

In some situations, it may be desirable to reduce the size of the bioretention required, by accounting for rapid drainage. Typically, this is only worth exploring over sandy textured native subsoils with rapid infiltration.

The drainage time calculator noted above can be used to calculate drainage time assuming three dimensional drainage as well.

  • Begin the drainage time calculation by dividing the area of the practice (Ap) by the perimeter (x)
  • To estimate the time (t) to fully drain the facility

t = [nr' * Ap/f'*x] * ln[(dr + (Ap/x)/Ap/x]

Where:

  • nr' is the effective porosity of the storage reservoir fill material(s),
  • Ap is the area of the practice (m2),
  • f' is the design infiltration rate of the native soil (mm/h),
  • x is the perimeter of the practice (m),
  • "ln" is the natural logarithm and,
  • dr is the depth of the storage reservoir (m).

Note that narrow, linear bioretention features (or bioswales) drain faster than round or blocky footprint geometries.

Groundwater mounding[edit]

When you wish to model the extent of groundwater mounding beneath an infiltration facility use the tool below to determine if there is potential for interaction between groundwater levels and the base of the practice during drainage. This tool uses Hantush's derivation (1967).
Download groundwater mounding calculator(.xlsm)
Note that this is a minor adaptation (metric units and formatting) from the original tool, written and hosted by the USGS.


  1. Woods Ballard, B., S. Wilson, H. Udale-Clarke, S. Illman, T. Scott, R. Ahsley, and R. Kellagher. 2016. The SuDS Manual. 5th ed. CIRIA, London.