Bioretention: Sizing and modeling

Before beginning the sizing calculations most of the following parameters must be known or estimated. The exceptions are the depth (d) and Permeable area (P), as only one of these is required to find the other. Note that some of these parameters are limited:

1. The maximum total depth will be limited by construction practices i.e. not usually > 2 m.
2. The maximum total depth may be limited by the conditions underground e.g. the groundwater or underlying geology/infrastructure.
3. The minimum total depth may be limited by the need to support vegetation i.e. not < 0.6 m.
4. Green roofs, absorbent landscapes and permeable paving often receive very little flow from other surfaces, so that the I/P ratio is close to 1.
5. Infiltration trenches, chambers and bioretention cells have a maximum recommended I/P ratio of 20.

Size a bioretention cell

Apply an appropriate safety correction factor to the measured infiltration rate:

$q'={\frac {q}{SCF}}$

Where:

• q' = Infiltration coefficient in mm/hr (accounting for SCF)
• SCF = Safety correction factor

This article discusses the determination of a suitable infiltration rate to describe the native soils surrounding a proposed infiltration practice.
It does not relate to the hydraulic conductivity or permeability of filter media or planting media used within vegetated BMPs.

The design infiltration rate (f') is used in all sizing calculations for bioretention and bioswales, dry ponds, infiltration trenches and chambers, and exfiltration trenches. It is related to, but not always synonymous with 'permeability', 'field hydraulic conductivity' (K_fc), or 'saturated hydraulic conductivity' (K_sat). Before application a safety correction factor (SCF) is incorporated into the figure, depending upon the source of the raw data, and the risk of failure of the finished practice.

It is highly recommended that testing be conducted on site.

Sources of data

On site testing methods	Off site analysis methods	Unacceptable methods
Borehole Permeameter Double ring infiltrometer Percolation test	Grain size analysis (Hazen method)	Single ring infiltrometer Soil textural classification

Becoming familiar with the different measurement practices

STEP have produced a free online module to provide some basic information on infiltration test methods. Access it HERE

Safety correction

To apply conservatism, the measured or calculated infiltration rate may be divided by a value between 2 and 3 before use in design calculations

Selecting a safety factor

Lower value (closer to 2)	Higher value (closer to 3)
Catchment < 100 m²	Catchment > 100 m²
Permeameter or percolation test on site	Double ring infiltrometer test on site, or grain size analysis used
Loamy or sandy soil texture	Clayey soil texture
No variation in geologic formation, soil texture or soil bulk density within 1.5 metres below the proposed bottom elevation of the practice.	Variation in geologic formation, soil texture or soil bulk density within 1.5 metres below the proposed bottom eleation of the practice observed.
No nearby sensitive receptors	Sensitive receptors in near proximity (e.g. septic systems, building foundations).

Planning for testing

Background Evaluation

Prior to performing testing and developing a detailed site plan, existing site conditions should be inventoried and mapped including, but not limited to:

1. Surficial geology and underlying stratigraphy;
2. Watercourses (perennial and intermittent), waterbodies, wetlands and floodplains;
3. Small headwater drainage features;
4. Topography, slope, and drainage patterns;
5. Existing land cover and land use;
6. Natural heritage conservation areas; and
7. Other man-made features or conditions that may impact design such as existing nearby structures (buildings, infrastructure, etc.).

A sketch plan or preliminary layout plan for the proposed development should be evaluated, including:

1. The preliminary grading plan and areas of cut and fill;
2. The location and water surface elevation of all existing, and location of proposed water supply sources and wells;
3. The location of all existing and proposed on-site wastewater (septic) systems;
4. The location of other features of note such as utility rights-of-way, water and sewer lines, etc.;
5. Existing data from borehole, well and geophysical testing; and
6. Proposed location of development features (buildings, roads, utilities, etc.).

Sampling

Infiltration testing should be carried out at relevant stages down through the profile of a test pit.

The number of test pits or soil borings varies depending on site conditions and the proposed development plan. General guidelines are as follows:

BMP footprint (m²)	Test pit	Borehole
< 50	1	1
50 – 900	1	2
	2	0
> 900	1 every 450 m²	2 every 450 m²
	2 every 450 m²	0
Linear	1 every 450 m²	1 every 50 m

• Tests must be conducted within 10 metres of the infiltration practice footprint area.
• Tests should be performed within 48 hours of a rain event, when the soil is already near, or at field capacity.
• Test locations should be spaced equidistant from one another.
• Make a minimum of seven (7) measurements (i.e. tests) for each test location (i.e., each test pit or borehole).
• An additional round of tests should be conducted at 1.5 metres depth below the proposed bottom elevation of the practice if there is significant variation in geologic formation, soil texture or bulk density compared to conditions at the proposed bottom elevation.
  
• To calculate the median infiltration rate of the native soil at the depth tested, discard the highest and lowest values obtained from each test location and calculate the median from the remaining measurements.

The recommendations above are guidelines Keep in mind that excessive testing and disturbance of the site prior to construction is not recommended.

---

---

Determine if there is a constraint to the depth (d) of the bioretention practice: Depth to GW	or if the land area is limited, determine the I/P ratio::$R={\frac {A_{c}}{A_{p}}}$ Where: R = Ratio of catchment area (Ac) to BMP footprint area (Ap) syn. I/P ratio. Ap = Area of the infiltration practice in m2 Ac = Catchment area in m2
Then
To calculate the require facility area or footprint where the depth is constrained: $A_{p}={\frac {IiD}{V_{R}d+q'D}}$	To calculate the required depth, where the area of the facility is constrained: $d={\frac {D\left[Ri-q'\right]}{V_{R}}}$

Where:

• D = Duration of design storm in hrs
• i = Intensity of design storm in mm/hr
• q' = Infiltration coefficient in mm/hr (accounting for SCF)
• SCF = Safety correction factor
• V_R = Void ratio (porosity), as measured (or default to 0.35 for all aggregates)
• R = Ratio of catchment area (A_c) to BMP footprint area (A_p) syn. I/P ratio.
• A_p = Area of the infiltration practice in m²
• A_c = Catchment area in m²
• d = Depth of infiltration practice in m.

The following equations assume that infiltration occurs primarily through the base of the facility. They may be easily applied for any shape and size of infiltration facility, in which the reservoir storage is mostly in an aggregate.

This spreadsheet tool has been set up to perform either of the above calculations.
Download .xlsx calculation tool

Calculate drawdown time

Three footprint areas of 9 m².
From left to right x = 12 m, x = 14 m, and x = 16 m

The 3 dimensional equations make use of the hydraulic radius (P/x), where x is the perimeter (m) of the facility.
Maximizing the perimeter of the facility directs designers towards longer, linear shapes such as infiltration trenches and bioswales.

To calculate the required depth:

$d=a[e^{\left(-bD\right)}-1]$

Where $a={\frac {A_{p}}{x}}-{\frac {iI}{A_{p}q'}}$ and $b={\frac {xq}{nP}}$

The rearrangement to calculate the required footprint area of the facility for a given depth is not available at this time. Elegant submissions are invited.

To calculate the time (t) to fully drain the facility: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t=\frac{V_{R}A_{p}}{q'P}ln\left [ \frac{\left (d+ \frac{A_{p}}{P} \right )}{\left(\frac{A_{p}{P}\right)}\right]}

The ratio of the impervious catchment (drainage) area to the pervious (footprint) area of the receiving BMP.

A shallow excavated surface depression containing prepared filter media, mulch, and planted with selected vegetation.

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

A parameter that describes the capability of a medium to transmit water.

The engineered soil component of bioretention cell or dry swale designs, typically with a high rate of infiltration and designed to retain contaminants through filtration and adsorption to particles.

Sustainable Technologies Evaluation Program

The land draining to a single reference point (usually a structural BMP); similar to a subwatershed, but on a smaller scale.

Referring to the source of a stream or river.

Best management practice. State of the art methods or techniques used to manage the quantity and improve the quality of wet weather flow. BMPs include: source, conveyance and end-of-pipe controls.

The natural ground material characteristic of or existing by virtue of geographic origin.

The land draining to a single reference point (usually a structural BMP); similar to a subwatershed, but on a smaller scale.

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)

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

A broad category of particulate material used in construction, including sand, gravel, crushed stone, slag, recycled concrete and geosynthetic aggregates, and available in various particulate size gradations.

A broad category of particulate material used in construction, including sand, gravel, crushed stone, slag, recycled concrete and geosynthetic aggregates, and available in various particulate size gradations.

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

The slow movement of water into or through a soil or drainage system.

Penetration of water through the ground surface.

The slow movement of water into or through a soil or drainage system.

Penetration of water through the ground surface.