SoakSIM — Technical Reference

Mathematical Basis & Worked Example

Contents

  1. Overview & Computation Pipeline
  2. Step 1 — Design Rainfall (BOM IFD)
  3. Step 2 — Temporal Patterns (ARR 2019)
  4. Step 3 — Hyetograph Generation
  5. Step 4 — Rainfall Losses (ILSAX Model)
  6. Step 5 — Runoff Routing (Time-Area)
  7. Step 6 — Soakwell Hydraulic Routing (Mass Balance)
  8. Step 7 — Argue (2004) Emptying Time Check
  9. Step 8 — Soil Moderation Factor (U)
  10. Step 9 — ARR Probability-Neutral Pattern Selection
  11. Step 10 — Auto-Design Optimiser
  12. Worked Example
  13. References

1. Overview & Computation Pipeline

SoakSIM sizes soakwell infiltration systems to Australian standards by coupling the ILSAX hydrological model (DRAINS Manual, 2018) with ARR 2019 design inputs and a mass-balance soakwell routing engine consistent with the Stormwater Management Manual for Western Australia (Argue, 2004).

BOM IFD Depths ARR Temporal Patterns Hyetograph ILSAX Losses Time-Area Routing Soakwell Mass Balance Design Check

Each storm duration and AEP combination is simulated for every ARR temporal pattern. The adopted design pattern is selected using the ARR probability-neutral method (Section 9). The critical duration is the one producing the greatest peak soakwell depth.

2. Step 1 — Design Rainfall (BOM IFD)

Design rainfall depths are sourced from the Bureau of Meteorology Intensity-Frequency-Duration (IFD) Design Rainfall Data System (Revised 2016, based on ARR 2019). SoakSIM scrapes the official BOM web interface at:

http://www.bom.gov.au/water/designRainfalls/revised-ifd/

For a given site coordinate (latitude, longitude), the system retrieves a matrix of depth values (mm) across:

The depth $P$ (mm) for a given duration $D$ and AEP is the total rainfall expected to fall in that duration with that annual probability of exceedance.

3. Step 2 — Temporal Patterns (ARR 2019)

ARR 2019 replaces the old single design temporal pattern with an ensemble of 10 temporal patterns per duration. These are expressed as cumulative fraction arrays $\{F_1, F_2, \ldots, F_n\}$ where $F_n = 1.0$.

Patterns are fetched from the ARR Data Hub:

https://data.arr-software.org/

Each pattern represents one historically observed way that rainfall can be distributed across the storm duration. Using all 10 patterns avoids bias toward any single distribution shape.

4. Step 3 — Hyetograph Generation

Each temporal pattern is combined with the BOM design depth to create a time-varying rainfall hyetograph.

Procedure

  1. Compute cumulative rainfall depths: $P_i^{\text{cum}} = F_i \times P_{\text{total}}$
  2. Interpolate onto a regular computational timestep $\Delta t$ (adaptive: 5 min for short storms, up to 60 min for 168-hour storms)
  3. Compute incremental depths per timestep: $p_j = P_j^{\text{cum}} - P_{j-1}^{\text{cum}}$

The result is a depth series $\{p_1, p_2, \ldots, p_N\}$ in mm, where $N = D / \Delta t$.

5. Step 4 — Rainfall Losses (ILSAX Model)

SoakSIM uses the ILSAX hydrological model as described in the DRAINS User Manual (June 2018, Section 8.3.2). Three surface types are modelled independently:

SurfaceLoss MethodDescription
Paved (DCIA)Depression storage onlyDirectly-connected impervious — roofs, sealed driveways. Only a small initial abstraction (typically 1 mm).
SupplementaryDepression storage onlyIndirectly-connected impervious areas that drain to pervious surfaces first.
Grassed (pervious)Horton infiltration + depression storageLawns, gardens. Uses full Horton infiltration capacity curve.

5.1 Depression Storage (Initial Loss)

Depression storage acts as a bucket that must fill before any runoff occurs:

$$p_j^{\text{excess}} = \max\left(0,\; p_j - S_{\text{remaining}}\right)$$

where $S_{\text{remaining}}$ decreases as rainfall fills the depression stores. Typical values: 1 mm (paved), 1 mm (supplementary), 5 mm (grassed).

5.2 Horton Infiltration (Grassed Areas Only)

The Horton equation describes the soil's time-varying infiltration capacity:

$$f(t) = f_c + (f_0 - f_c)\,e^{-k\,t}$$

where:

Soil Type$f_0$ (mm/hr)$f_c$ (mm/hr)
A (Sandy)25025
B (Sandy Loam)20013
C (Clay Loam)1256
D (Heavy Clay)753

The Antecedent Moisture Condition (AMC 1–4) adjusts the starting infiltration rate. Higher AMC = wetter soil = lower starting capacity.

Watson's Non-Iterative Method (DRAINS Eq. 8.7–8.8)

Rather than iterating over the Horton equation, SoakSIM uses Watson's method which splits infiltration into a diminishing component and a constant component:

$$\Delta F_{\text{cap}} = \left(1 - e^{-k\,\Delta t}\right)\left(F_{\text{max}}^{\text{dim}} - F_d\right) + f_c \cdot \Delta t$$

where $F_{\text{max}}^{\text{dim}} = (f_0 - f_c) / k$ is the total diminishing infiltration capacity, and $F_d$ is the accumulated diminishing infiltration so far. The actual infiltration for each timestep is:

$$f_{\text{actual}} = \min\left(p_j,\; \Delta F_{\text{cap}}\right)$$

Excess rainfall (runoff) from the grassed surface for each timestep is:

$$p_j^{\text{excess}} = p_j - f_{\text{actual}}$$

6. Step 5 — Runoff Routing (Time-Area Method)

6.1 Time of Entry (Kinematic Wave Equation)

Each surface type has a travel time computed from the kinematic wave equation (Ragan & Duru, 1972; DRAINS Eq. 8.3):

$$t_e = 6.94 \,\frac{(L \cdot n^*)^{0.6}}{I^{0.4} \cdot S^{0.3}}$$

where:

Total time of entry = $t_e$ + any user-specified additional travel time.

6.2 Time-Area Convolution

A linear time-area histogram represents the proportion of catchment area contributing runoff at each timestep. The runoff hydrograph is generated by convolving excess rainfall with this histogram:

$$Q_n = \frac{A}{360}\sum_{i} h_i \cdot I_{n-i}$$

where:

The three surface discharges (paved, supplementary, grassed) are summed to give the total catchment hydrograph.

7. Step 6 — Soakwell Hydraulic Routing

SoakSIM routes the runoff hydrograph through the soakwell system using a forward-stepping mass balance at each computational timestep, consistent with the principles of the Stormwater Management Manual for WA (Argue, 2004).

Mass Balance Equation

$$S(t+\Delta t) = S(t) + Q_{\text{in}} \cdot \Delta t - Q_{\text{infil}} \cdot \Delta t$$

where $S$ = stored volume (m³), $Q_{\text{in}}$ = inflow rate (m³/s), $Q_{\text{infil}}$ = infiltration rate (m³/s).

7.1 Soakwell Geometry

Concrete soakwells are modelled as hollow cylinders (void ratio = 1.0):

$$V_{\text{storage}} = \frac{\pi}{4}\,d^2\,H$$

where $d$ = internal diameter (m) and $H$ = internal height (m).

Base Infiltration Area

The base slab is not fully open — it has a circular hole whose diameter is 300 mm less than the soakwell diameter:

$$A_{\text{base}} = \frac{\pi}{4}\,(d - 0.3)^2$$

Side-Wall Infiltration Area (Louvres)

Side-wall infiltration occurs through louvre slots cast into the concrete (not the full wall surface). Each louvre is 150 mm wide × 50 mm high, arranged on a 300 mm × 300 mm grid. The open-area ratio of the wall is:

$$\alpha = \frac{150 \times 50}{300 \times 300} = \frac{7500}{90000} \approx 8.33\%$$

The effective side infiltration area is:

$$A_{\text{side}} = \alpha \times \pi\,d\,H = 0.0833 \times \pi\,d\,H$$
Example (1200 × 1200 mm):
Base opening: $\pi/4 \times (1.2 - 0.3)^2 = 0.636$ m²
Full wall area: $\pi \times 1.2 \times 1.2 = 4.524$ m²
Effective louvre area: $4.524 \times 0.0833 = 0.377$ m²
Total infiltration area: $0.636 + 0.377 = 1.013$ m² (vs 5.655 m² if the full wall were open)

7.2 Depth-Dependent Infiltration

Infiltration at each timestep depends on the water depth within the soakwell:

$$Q_{\text{infil}} = k_h \cdot R_f \cdot A_{\text{active}}$$

where:

$$A_{\text{active}} = A_{\text{base}} + A_{\text{side}} \times \frac{h}{H}$$

where $h$ = current water depth. When the soakwell is full, $h = H$, so the entire side wall is active. When nearly empty, only the base and a small side wall portion contribute.

7.3 Spill / Surface Ponding

If stored water exceeds the soakwell capacity ($S > V_{\text{storage}}$), the excess ponds on the surface with a much larger plan area ($\approx 50 \times A_{\text{base}}$). All side walls remain fully submerged, and water drains back into the soakwell as it empties.

7.4 Post-Storm Draining

After the storm ends ($Q_{\text{in}} = 0$), the mass balance continues until $S \approx 0$. The total time from storm end to empty is the numerical drain time.

8. Step 7 — Argue (2004) Emptying Time Formula

The analytical emptying time for a circular soakwell (Argue, 2004; Stormwater Management Manual for WA) is:

$$T = -\frac{4.6\,d}{4\,k_h} \;\log_{10}\!\left(\frac{d/4}{H + d/4}\right)$$

where:

Note: This formula assumes the soakwell is full at the start of draining, drains by infiltration and percolation only (no piped outflow), and that $d \approx H$. SoakSIM's numerical routing (Step 6) is more general — it handles time-varying inflow, partial fill, depth-dependent infiltration, and arbitrary d × H ratios. The Argue formula serves as an analytical cross-check.

9. Step 8 — Soil Moderation Factor (U)

In soakwell sizing, a Soil Moderation Factor ($U$) is applied to field-measured hydraulic conductivity to account for the difference between point-scale test results and actual areal conductivity (Engineers Australia, 2006).

Soil TypeFactor $U$Rationale
Sand0.5Field tests overestimate areal $k_h$ → halve the tested rate
Sandy Clay1.0No correction needed
Medium / Heavy Clay2.0Field tests underestimate areal $k_h$ → double the tested rate

SoakSIM applies this factor as the Soil Moderation Factor input. The user-entered infiltration rate should be the raw field-measured rate; SoakSIM then applies $U$ internally.

Exception: If the design uses a calculated long-term or "lifespan" hydraulic conductivity rather than a raw field test value, $U = 1.0$ may be applied instead.

10. Step 9 — ARR Probability-Neutral Pattern Selection

ARR 2019 provides 10 temporal patterns per duration. To avoid arbitrarily selecting the worst or best case, SoakSIM adopts the probability-neutral approach:

Procedure (per storm duration)

  1. Route all 10 patterns through the soakwell mass balance
  2. Rank by peak soakwell depth (deepest first)
  3. Adopt the Nth highest, where $N$ = the pattern rank parameter (default 4)

This ensures the design is based on a pattern that is neither the most extreme nor the most benign — consistent with ARR guidance that no individual temporal pattern has a defined probability.

The critical duration is then the adopted pattern (across all durations) that produces the greatest peak soakwell depth.

11. Step 10 — Auto-Design Optimiser

When the solver mode is enabled, SoakSIM automatically determines the number and size of soakwells required. The procedure is:

11.1 Initial Estimate (Net-Storage Formula)

For each candidate soakwell size, compute an initial unit count:

$$n = \left\lceil \frac{\forall}{V_{\text{sw}} / U + I_{\text{unit}} \cdot D} \right\rceil$$

where:

11.2 Routing Verification

The formula estimate is then verified by routing:

  1. Route all temporal patterns through $n$ soakwells
  2. Apply ARR probability-neutral selection (Section 10)
  3. If the adopted pattern spills → increment $n$ and repeat
  4. Stop when no adopted pattern spills, or $n$ reaches the maximum (default 50)

11.3 Solver Modes

ModeDescription
Fewest unitsMinimise total soakwell count across all catalogue sizes
Fixed heightOnly consider sizes up to a specified height
Fixed diameterOnly consider sizes up to a specified diameter

12. Worked Example

Problem Statement

Size a soakwell system for a 500 m² (0.05 ha) residential roof in Perth (−31.95°, 115.86°) for the 5% AEP (20-year ARI), 60-minute storm duration. The site has sandy soil with a field-tested hydraulic conductivity of 1.2 m/day (50 mm/hr).

Step A — Design Rainfall

From BOM IFD for Perth at 5% AEP, 60-minute duration:

$$P = 33.5 \;\text{mm}$$

Step B — Temporal Pattern & Hyetograph

ARR provides 10 temporal patterns for the 60-min duration. One example pattern (cumulative fractions at 5-minute intervals) might be:

[0.03, 0.07, 0.12, 0.18, 0.28, 0.52, 0.72, 0.84, 0.92, 0.96, 0.99, 1.00]

The incremental depths (mm per 5-min interval) are these fractions multiplied by 33.5 mm, then differenced:

[1.0, 1.3, 1.7, 2.0, 3.4, 8.0, 6.7, 4.0, 2.7, 1.3, 1.0, 0.3]

Note the characteristic "burst" in the middle of the storm.

Step C — Rainfall Losses

For a fully paved (roof) catchment with depression storage = 1 mm:

Step D — Runoff Volume

Total runoff volume (time-area routing):

$$V = \frac{A \times \text{excess depth}}{1000} = \frac{500 \times 32.5}{1000} = 16.25 \;\text{m}^3$$

The time-area convolution distributes this over the 60-minute storm producing a hydrograph with a peak of approximately 0.0045 m³/s.

Step E — Soakwell Sizing (Argue Formula Cross-Check)

Using the Argue (2004) sizing formula with a 1200 × 1200 mm soakwell ($d = H = 1.2$ m):

Convert $k_h$: $1.2$ m/day $= 1.389 \times 10^{-5}$ m/s

Convert $\tau$: storm time-base $= 60$ min

Soil moderation factor for sand: $U = 0.5$

$$d_{\text{required}} = \sqrt{\frac{\forall}{\frac{\pi}{4}\left(H + 120 \cdot k_h \cdot \tau \cdot U\right)}}$$ $$d_{\text{required}} = \sqrt{\frac{16.25}{\frac{\pi}{4}\left(1.2 + 120 \times 1.389 \times 10^{-5} \times 60 \times 0.5\right)}}$$ $$= \sqrt{\frac{16.25}{0.785 \times (1.2 + 0.05)}} = \sqrt{\frac{16.25}{0.981}} = \sqrt{16.56} = 4.07 \;\text{m}$$

This means a single soakwell of diameter 4.07 m would be needed — far larger than standard products. Hence, multiple standard soakwells are required.

Step F — SoakSIM Numerical Design

SoakSIM's optimiser selects from the catalogue. For 1200 × 1200 mm soakwells:

Initial estimate (net-storage formula):

$$n = \left\lceil \frac{16.25}{1.357/0.5 + 0.226 \times 1.0} \right\rceil = \left\lceil \frac{16.25}{2.714 + 0.226} \right\rceil = \left\lceil \frac{16.25}{2.940} \right\rceil = \lceil 5.53 \rceil = 6$$

SoakSIM then routes all 10 temporal patterns through 6 × 1200 × 1200 soakwells, ranks by peak depth, and adopts the 4th highest. If any adopted pattern spills, it increments to 7, then 8, etc. until no spill occurs.

Step G — Emptying Time Check (Argue Formula)

For a single 1200 × 1200 soakwell, check the emptying time:

$$T = -\frac{4.6 \times 1.2}{4 \times 1.389 \times 10^{-5}} \;\log_{10}\!\left(\frac{1.2/4}{1.2 + 1.2/4}\right)$$ $$T = -\frac{5.52}{5.556 \times 10^{-5}} \times \log_{10}\!\left(\frac{0.3}{1.5}\right) = -99{,}352 \times (-0.699)$$ $$T = 69{,}447 \;\text{s} = 19.3 \;\text{hours}$$
Result: Each soakwell empties in approximately 19.3 hours, which is within the 24-hour drain-time criterion for a 5% AEP design.

Step H — Summary

ParameterValue
Design storm5% AEP, 60-minute duration
Catchment area500 m² (0.05 ha), 100% paved
Design rainfall depth33.5 mm
Runoff volume~16.25 m³
Soakwell size1200 × 1200 mm
Number required (formula)6
Total storage6 × 1.357 = 8.14 m³
Infiltration credit (1 hr)6 × 0.226 = 1.36 m³
Argue drain time~19.3 hours (< 24 hr ✓)
Soil moderation factor0.5 (sand)
Important: The Argue sizing formula assumes average rainfall intensity and a single runoff coefficient. SoakSIM's numerical routing with ILSAX losses and ARR temporal patterns is more rigorous — the final soakwell count may differ from the simple formula estimate because temporal patterns distribute rainfall non-uniformly, creating burst intensities that exceed the average.

13. References

  1. Argue, J.R. (2004). Water Sensitive Urban Design: Basic Procedures for 'Source Control' of Stormwater. Urban Water Resources Centre, University of South Australia.
  2. Ball, J., Babister, M., Nathan, R., Weeks, W., Weinmann, E., Retallick, M. & Testoni, I. (Eds.) (2019). Australian Rainfall and Runoff: A Guide to Flood Estimation. Commonwealth of Australia.
  3. Bureau of Meteorology (2016). Revised Intensity-Frequency-Duration Design Rainfall Data System. Commonwealth of Australia.
  4. Engineers Australia (2006). Australian Runoff Quality. Engineers Australia, Canberra.
  5. O'Loughlin, G. & Stack, B. (2018). DRAINS User Manual — Version 2018.06. Watercom Pty Ltd.
  6. Ragan, R.M. & Duru, J.O. (1972). 'Kinematic wave nomograph for times of concentration'. Journal of the Hydraulics Division, ASCE, 98(HY10), pp. 1765–1771.
  7. Stormwater Management Manual for Western Australia (2004). Department of Water, Government of Western Australia.
  8. Watson, M.D. (1981). 'Non-iterative Horton's equation'. Civil Engineering Transactions, Institution of Engineers Australia, pp. 240–243.

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