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A Study of Underground Stormwater Detention Chambers and
the Creation of the Model for Underground Detention of
Sediment
by
Nicholas David McIntosh
A thesis submitted in conformity with the requirements
A Study of Underground Stormwater Detention Chambers and
the Creation of the Model for Underground Detention of
Sediment
Nicholas David McIntosh
Master of Applied Science
Graduate Department of Civil Engineering
University of Toronto
2015
Abstract
This thesis investigates the hydraulic and runoff treatment capabilities of Underground
Stormwater Detention Chambers (USDC) and compares them to stormwater management ponds,
the industry standard system for runoff detention and treatment. Runoff characteristics were
monitored at a USDC in Markham, Ontario. Characteristics include: total suspended solids,
turbidity, nutrients, metals, bacteria, temperature, and hydrocarbons. The Model for
Underground Detention of Sediment (MUDS) was created to predict the removal of suspended
solids by a USDC. The results indicate that the Markham USDC meets all provincial hydraulic
requirements and most water quality requirements. Also, the Markham USDC provides
equivalent or improved level of service compared to stormwater management ponds for runoff
treatment in most cases. MUDS was proven capable of accurately predicting USDC hydraulics
and suspended solids removal for both event based and continuous based simulations.
III
Acknowledgments
I would first like to thank Dr. Drake for her invaluable advice and guidance throughout the
preparation of this thesis. I would like to thank Jason Spencer (Con Cast Pipe), and Dean Young
and Tim Van Seters (Toronto and Region Conservation Authority) for answering my questions
and providing many helpful suggestions. Thanks and appreciation is also extended to Mark
Hummel and Jacob Kloeze (TRCA) for their field work. Lastly, I would like to thank my wife,
Ali, and parents, David and Brenda, for supporting and encouraging me throughout the years.
IV
Table of Contents
Acknowledgments ........................................................................................................................................ III
Table of Contents ......................................................................................................................................... IV
List of Tables ............................................................................................................................................... VI
List of Figures ............................................................................................................................................. VII
List of Symbols ............................................................................................................................................ IX
2.2.3 Heavy Metals ................................................................................................................................. 16
2.2.4 Temperature ................................................................................................................................... 20
2.2.5 First Flush ...................................................................................................................................... 21
3.1 Field Site ............................................................................................................................................... 30
4.5 Temperature .......................................................................................................................................... 63
6.2 Recommendations for Future Research ................................................................................................ 99
6.2.1 Water Quality ................................................................................................................................. 99
Appendix C: Hydrograph and Depth Figures of Storms used for Validation and Calibration of the SWMM
Model ........................................................................................................................................................ 113
VI
List of Tables
Table 1: TSS Removal Percentage by SWM .............................................................................................. 12 Table 2: Median Total and Soluble Phosphorus, Ammonia and Nitrate/Nitrite Concentrations by Land
Use .............................................................................................................................................................. 15 Table 3: Summary of Nitrogen and Phosphorus Transformations and Removal Mechanisms .................. 15 Table 4: Nutrient Removal Efficiency by SWM Ponds .............................................................................. 16 Table 5: Common Sources of Metal in Urban Runoff (Shaver et al., 2007) .............................................. 17 Table 6: Typical Levels of Metals Found in Stormwater Runoff (µg/L) .................................................... 17 Table 7: Percent Reduction in Metals after Removal of Various Particle Sizes ......................................... 18 Table 8: Percent Removal of Metals by SWM ........................................................................................... 19 Table 9: Metals Provincial Water Quality Requirements ........................................................................... 19 Table 10: Distribution of Event Constituents (EMC) ................................................................................. 28 Table 11: DoubleTrapTM Monitoring Equipment Properties and Purpose .................................................. 34 Table 12: Outflow Equations ...................................................................................................................... 38 Table 13: Particle Tracking Equations (Takamatsu et al., 2010) ................................................................ 40 Table 14: SWMM Subcatchment Properties .............................................................................................. 48 Table 15: SWMM Land Type Roughness and Storage .............................................................................. 48 Table 16: SWMM Conduit Properties ........................................................................................................ 48 Table 17: Sampled Storm Event Hydrologic Parameters ........................................................................... 50 Table 18: Summary of TSS EMC and Turbidity ........................................................................................ 51 Table 19: Summary of TSS and Turbidity Statistical Analysis .................................................................. 51 Table 20: Percent Removal of TSS and Turbidity ...................................................................................... 52 Table 21: Summary of Nutrient EMC ......................................................................................................... 54 Table 22: Summary of Nutrient Statistical Analysis................................................................................... 55 Table 23: Summary of Metals EMC ........................................................................................................... 57 Table 24: Summary of Metals Statistical Analysis ..................................................................................... 59 Table 25: Percent Removal of Metals ......................................................................................................... 61 Table 26: Summary of Bacteria EMC ......................................................................................................... 61 Table 27: Summary of Bacteria Statistical Analysis................................................................................... 62 Table 28: Number of Hydrocarbon Samples below the MDL .................................................................... 65 Table 29: Summary of Hydrocarbon Removal ........................................................................................... 66 Table 30: Hydrocarbon Provincial Water Quality Requirements ............................................................... 67 Table 31: Minimum Acceptable Dissolved Oxygen Concentration in Rivers for the Protection of Aquatic
Life (Canadian Council of Ministers of the Environment, 2015) ............................................................... 69 Table 32: Summary of Calibration and Validation Events ......................................................................... 73 Table 33: MUDS Input Values ................................................................................................................... 74 Table 34: Raw Inflow and Outflow Data Summary ................................................................................... 79 Table 35: TRCA and Average Monitored Storm PSD................................................................................ 82 Table 36: Assessment of Particle Removal Summary ................................................................................ 84 Table 37: Seasonal and Overall TSS Removal Simulation Results ............................................................ 89 Table 38: Summary of Forebay and Residence Time Significance Tests ................................................... 97
VII
List of Figures
Figure 1: StormTrap Cell Top and Bottom - Con Cast Pipe Facilities June 4, 2014 .................................... 2 Figure 2: StormTrap Rebar Cage (Left), Cell Mold (right) - Con Cast Pipe Facilities June 4, 2014 ........... 3 Figure 3: StormTrap Cell in Mold (left) with Manhole Styrofoam (right) - Con Cast Pipe Facilities June 4,
2014 .............................................................................................................................................................. 4 Figure 4: StormTrap after Concrete Pouring (left) Mold Covered by a Tarp (right) - Con Cast Pipe
Facilities June 4, 2014 ................................................................................................................................... 4 Figure 5: Pre vs. Post-Urbanization Hydrographs ........................................................................................ 6 Figure 6: Median Stormwater TSS Concentrations from NSQD ................................................................ 10 Figure 7: Structure With/Without Baffling ................................................................................................. 12 Figure 8: 25/50 M(V) Curve ....................................................................................................................... 22 Figure 9: Particle Sedimentation Paths ....................................................................................................... 26 Figure 10: DoubleTrapTM Location and Service Area ................................................................................ 31 Figure 11: DoubleTrapTM Site and Monitoring Boxes (Left), Construction Zone South of the
DoubleTrapTM (Right) (June 23, 2014) ....................................................................................................... 31 Figure 12: Parkland Surrounding the DoubleTrapTM (June 23, 2014) ........................................................ 32 Figure 13: DoubleTrapTM Monitoring Equipment and Dimensions ........................................................... 33 Figure 14: DoubleTrapTM Dimensions (Side) ............................................................................................. 33 Figure 15: As Built DoubleTrapTM with Individual Cells ........................................................................... 33 Figure 16: Particle Size Distribution (AZO Materials, 2007) ..................................................................... 41 Figure 17: Flocculent Settling Column Test (Viessman & Hammer, 1985) ............................................... 42 Figure 18: Potential Particle Entry Paths .................................................................................................... 43 Figure 19: Flocculent Settling Removal Calculation Example: .................................................................. 43 Figure 20: Model Particle Paths .................................................................................................................. 44 Figure 21: SWMM Model Study Area Map ............................................................................................... 47 Figure 22: Box plots of Suspended Solids and Turbidity ........................................................................... 51 Figure 23: TSS VS Turbidity: Inlet (Right), Hatch 2 and Outlet (Left)...................................................... 53 Figure 24: Box Plots of Nitrogen Species ................................................................................................... 54 Figure 25: Box Plots of Phosphorus Species .............................................................................................. 55 Figure 26: Box Plots of Monitored Metals ................................................................................................. 57 Figure 27: Box Plots of Monitored Bacteria ............................................................................................... 62 Figure 28: YSI Temperature Results .......................................................................................................... 63 Figure 29: Box Plots of Hydrocarbons ....................................................................................................... 66 Figure 30: Depth Profile Results ................................................................................................................. 68 Figure 31: Measured and Modeled Outflow Comparison ........................................................................... 75 Figure 32: Calibration Height and Flow Results ........................................................................................ 76 Figure 33: October 16 Outflow Modeling .................................................................................................. 77 Figure 34: October 16 Depth Modeling ...................................................................................................... 77 Figure 35: October 20 Outflow Modeling .................................................................................................. 77 Figure 36: October 20 Depth Modeling ...................................................................................................... 78 Figure 37: USDC Peak Flow Reduction ..................................................................................................... 79 Figure 38: First Flush Ratio Calibration Example ...................................................................................... 81 Figure 39: TRCA and Average Monitored Storm PSD .............................................................................. 82 Figure 40: Assessment of Particle Removal Results................................................................................... 83 Figure 41: Sensitivity Analysis Results ...................................................................................................... 84 Figure 42: 5 Year Storm Hydrographs ........................................................................................................ 86
VIII
Figure 43: 10 Year Storm Hydrographs ...................................................................................................... 86 Figure 44: Hydrographs for Continuous Simulation ................................................................................... 87 Figure 45: Modeled Depth for Continuous Simulation............................................................................... 88 Figure 46: July to August Simulation Hydrograph ..................................................................................... 90 Figure 47: July to August New Area Hydrographs ..................................................................................... 91 Figure 48: Reduced Catchment Area with TRCA PSD Hydrographs ........................................................ 92
IX
List of Symbols
A Drainage Area (L2) Qr Surface runoff (L3/T)
Af Effective flow area (L2) RTRM Relative thermal resistance to mixing
(-) Ao Orifice area (L2)
B(t) Width at time t (L) RFraction Fraction of particles removed in a
particle wave (-) b First flush coefficient (-)
C Concentration (M/L3) rA Reaction rate (M/L3∙T)
CA Concentration of a pollutant in a
SWM pond (M/L3)
S Surface slope (-)
SA Surface area (L2)
CAo Concentration of a pollutant as it
enters a SWM pond (M/L3)
t time (T)
tf Time for a particle to travel through
the USDC (T) Cd Orifice loss coefficient (-)
Cin Concentration flowing in (M/L3) tlarger Time for the larger particle of two to
reach the bottom of a USDC (T) Cout Concentration flowing out (M/L3)
c Runoff coefficient (-) tsmaller Time for the smaller particle of two to
reach the bottom of a USDC (T) d Orifice diameter (L)
dp Particle diameter (L) V Volume (L3)
F Flow rate (L3/T) Vs Settling velocity of a particle (L/T)
g Gravitational constant (L/T2) Vsc Critical settling velocity (L/T)
Ho Depth of water above midpoint of
orifice (L)
Vsegment Settling velocity of the segment
between two particle sizes (L/T)
Hw Depth of water above the orifice
invert (L)
X Cumulative Volume/Total Volume (-)
x(t) Horizontal position at time t (L)
h Height (L) Y Cumulative mass/Total Mass (-)
hexit Particle exit height (L) Yimean Mean of observed data for the
constituent being evaluated (any units) hini Particle entry height (L)
h(t) Depth of water at time t (L) Yiobs The ith observation for the constituent
being evaluated (any units) hp(t) Depth of a particle at time t (L)
i Rainfall intensity (L/T) Yisim The ith simulated value for the
constituent being evaluated (any units) j Order of a reaction for decay rates (-)
k Decay rate constant (-) y(t) Vertical position at time t (L)
L Pathlength (L) Δh Change in height (L) MFraction Fraction of the total mass of
pollutants attributed to a wave of
particles (-)
Δt Change in time (T)
η Filling ratio of relative depth (-)
μ Dynamic viscosity of a substance
(M/L∙T) n Number of samples taken (-)
nr Manning's roughness coefficient (-) ρs Particle density (M/L3)
P Wetted perimeter (L) ρw Water density (M/L3)
Q Flow rate (L3/T) ρz1 Water density at depth z1 (M/L3)
Qin Flow rate in (L3/T) ρz2 Water density at depth z2 (M/L3)
Qout Flow rate out (L3/T) ρ4 Water density at 4oC (M/L3)
Qp Peak discharge (L3/T) ρ5 Water density at 5oC (M/L3)
1
Chapter 1 Introduction
Underground stormwater detention chambers (USDC) are a novel technology for the
detention and treatment of stormwater runoff; therefore, there is little information available to
accurately predict contaminant removal in the Ontario hydrology and climate. Stormwater
management (SWM) ponds have been the most widely employed management practice in urban
drainage in Ontario for over 40 years (Marsalek et al., 2003). SWM ponds share many similar
features to USDC: both of these stormwater treatment technologies detain runoff with a
permanent pool and an orifice which restricts flow to a set maximum; they both have
sedimentation forebays just after their inlets to capture larger particles which are brought in by
runoff; and both are end-of-pipe systems.
Despite their similarities, there are several key differences between SWM ponds and
USDC which prevent research conducted on SWM ponds from being directly applied to USDC.
1. SWM ponds use a combination of plant species and settling to remove nutrients
and metals from runoff. Also, bacteria present in SWM ponds are deactivated by
sunlight exposure. USDC are dark and unvegetated so pollutant removal
mechanisms are limited to physical processes such as sedimentation.
2. Winter has a significant effect on SWM ponds, such as thermal stratification and a
reduction in dissolved oxygen concentration, its effects on USDC are unknown.
3. The various concrete structures within the USDC change the flow path of the
water significantly, which causes turbulence and may or may not assist in the
removal of contaminants. In SWM ponds the flow hydraulics are assumed to be
very simple and is usually assumed to have a constant speed and direction.
2
4. USDC are not open to the environment so they are not affected by solar radiation.
Therefore, the thermal issues with SWM ponds, such as elevated effluent
temperature and thermal gradients, may be avoided.
All of these factors combine such that the conditions within a USDC are unique and so
must be researched as a separate entity to the SWM pond.
The specific USDC monitored for this project is a StormTrap-DoubleTrapTM unit
produced by Con Cast Pipe. A significant economic advantage of the StormTrap system is the
dynamic behavior in which a system can be designed. Each StormTrap is built from various
types of cells in order to create an individual and tailored design for the site. An example of one
of these cells is shown in Figure 1. The cells are attached in such a way that they direct and store
runoff as required by the engineer.
Figure 1: StormTrap Cell Top and Bottom - Con Cast Pipe Facilities June 4, 2014
Each cell is constructed from a rebar cage that is encased in concrete. Rebar is welded
together on site by hand with the exception of the top/bottom grate, which has a much denser
mesh than the pillars. Clamps are installed in the top of the rebar cage for moving the finished
product. Figure 2 (left) shows a standard rebar cage. The cages are placed inside of a mold with
3
sides that open and close to allow placement of the cage and removal of the finished cell half
(Figure 2 (right)). The molds are coated in a form release agent so that the finished cell can be
removed easily after curing.
Figure 2: StormTrap Rebar Cage (Left), Cell Mold (right) - Con Cast Pipe Facilities June
4, 2014
After the rebar cages are installed, the doors are closed and a high slump concrete is
discharged into the mold. The high slump allows for the concrete to spread easily in and around
the rebar cage and results in a smooth finish for an aesthetic appearance. Manholes can be
installed in the top of a cell by placing a Styrofoam cylinder on top of the rebar cage then
pouring concrete around it. After the concrete has cured, the Styrofoam is removed and a
manhole is placed into the hole that is left. Before and after photos of the concrete pouring
process can be seen in Figure 3 and Figure 4 (left). Following the pouring process, the mold is
covered by a tarp; this tarp holds in steam that is pumped in (Figure 4 (right)). The steam keeps
the concrete moist and regulates the temperature inside the tarp to assist the curing process which
takes 12 hours.
4
Figure 3: StormTrap Cell in Mold (left) with Manhole Styrofoam (right) - Con Cast Pipe
Facilities June 4, 2014
Figure 4: StormTrap after Concrete Pouring (left) Mold Covered by a Tarp (right) - Con
Cast Pipe Facilities June 4, 2014
USDC are an appealing design option for municipalities considering stormwater
management plans because the land on which the system resides can be restored to be used for
alternative purposes, such as parkland, and there is no risk of pedestrians falling in to open water
as with SWM ponds. However, with the strict water quality laws in place for stormwater runoff
treatment, it is risky for engineering consultants to include a newer and less studied technology
in stormwater management designs. A general estimate of cost for a StormTrap is approximately
$250/ m3 for the material and freight, and $50/ m3 for the installation with 500 mm of cover
(Gross, 2015). With more research and design tools available, USDC can be better compared
against other stormwater management technologies and used with greater confidence.
5
The purpose of this research is to gain an understanding of how a USDC acts in an
Ontario climate. Research objectives are to:
1. Identify the stormwater treatment capabilities of underground stormwater
detention chambers using on-site monitoring.
2. Compare the runoff treatment from underground stormwater detention chambers
to stormwater management ponds.
3. Create a model that predicts the removal of contaminants in underground
stormwater detention chambers.
The thesis consists of six chapters, they are structured as follows:
Chapter 1 (Introduction): Introduces thesis topic, outlines objectives, and presents the thesis
structure.
Chapter 2 (Relevant Literature): Presents relative background theory on the removal of
pollutants in SWM ponds and techniques used for modeling this removal.
Chapter 3 (Methodology): Outlines the characteristics of the monitoring site, the equipment
used for monitoring, and how the model was constructed.
Chapter 4 (Water Quality Results): Discusses the results of the site runoff analysis and
compares them to standard SWM pond removal capabilities.
Chapter 5 (Model Results): Discusses the calibration and validation of the SWMM model
hydraulics and hydrology, the assessment of the pollutant removal modeling, and the results of
several simulations.
Chapter 6 (Conclusions and Recommendations): Presents conclusions of the thesis research and
discusses future research directions and recommendations.
Appendix A: Presents the layout of the MUDS Interface as of April 2015.
Appendix B: Provides an explanation of the calculation for removal efficiency by MUDS.
Appendix C: Presents hydrograph and depth figures of storms used for validation and
calibration of the SWMM model.
6
Chapter 2 Relevant Literature
2.1 Urbanization and Stormwater Management
Stormwater management is a key issue in the design of urban infrastructure. Sustained
increases in urbanization have resulted in large-scale replacement of pervious land by impervious
surfaces, which reduces infiltration rates and available surface storage (Natarajan and Davis,
2010). Due to these changes, a larger proportion of urban precipitation becomes runoff. Runoff is
removed from the immediate area through storage and conveyance infrastructure where it is
directed to a nearby water body. Examples of pre- and post-urbanization hydrographs that show
the discharge rate from a watershed can be seen in Figure 5. The pre-urbanization hydrograph
has a significantly smaller peak discharge and the total volume of runoff is far less so there is
less risk of flooding the river or catch basin that is accepting flow from the area.
Figure 5: Pre vs. Post-Urbanization Hydrographs
This phenomenon can be explained simply by using a standard engineering equation for
calculating runoff, the Rational Equation:
7
𝑄𝑝 = 𝑐𝑖𝐴 (1)
where Qp is the peak discharge, c is the runoff coefficient, i is the rainfall intensity, and A is the
drainage area. As an area becomes more impervious, the coefficient c approaches 1, which
results in a larger peak discharge. There are several issues associated with an increased peak
discharge which include: increased flow volumes through rivers; increased flow rates in rivers;
increased duration of high volume and flow rate; and increased frequencies of high runoff events
(Shaver et al., 2007). This results in physical damage to waterways and aquatic habitats by
eroding the soil which supports aquatic plants and shapes the watercourse. A loss of aquatic
plants removes the food source for aquatic organisms and erosion expands the flow channel
increasing flow rates which makes flooding downstream more common (Shaver et al., 2007).
Urban floods occur when the peak discharge exceeds the capacity of the natural and municipal
systems. Depending on the severity of the storm there is potential for significant damage to
property, or even loss of life. For example, a storm which occurred in Toronto in 2013 resulted in
$65 million in damage (National Post, 2014). A stormwater management system will inevitably
fail, but the robustness of the design determines how often it fails and how costly each failure is.
Municipal systems are generally designed for 5-10 year return period events.
Increased runoff volumes are not the only threat to waterways; pollutants which are
prominent in urban areas are transported to receiving water bodies during runoff events.
Pollutants are deposited on impervious surfaces through human activities and atmospheric
deposition; during a runoff event, these pollutants are transported from the surface into the runoff
which then flows into the receiving water body. This process is commonly referred to as non-
point source pollution which is defined as, “having loadings which are discontinuous in time,
frequently not concentrated in a single location, and highly responsive to climate conditions,”
8
(Thomson et al., 1997). The specific types, sources, and environmental issues associated with
stormwater pollutants are explored further in Section 2.2.
The necessity for flow and pollutant control resulting from increased stormwater runoff
has led to the creation of several technologies. These include: coalescing plate separators; dry
Sources of Research Cited by Shaver et al. 2007: aUSEPA, 1983. bSchiff et al., 2001. cPitt et al., 2002. dBarrett et al., 1998. eTiefenthaler et al., 2001
18
Metals can occur in particulate, dissolved, or colloidal forms; however, a great proportion
is bound to particles (Li et al., 2005). For example, in a study by the United States Geological
Survey (2011), 74% of total metal load in Wisconsin storm sewers was in particulate form
(United States Geological Survey, 2011). Particulate-bound pollutants are predominately
attached to smaller particles, and particles less than 25µm in diameter can represent around 90%
of the total surface area (Pettersson, 2002). Particle phases of some metal elements such as
copper and nickel will increase with sample holding time as they tend to precipitate out of their
dissolved form (Li et al., 2008).
Metals which are in their precipitate form can be removed through sedimentation and/or
filtration; the dissolved fraction can be removed through sorption and precipitation processes.
WERF (2005) determined the percent removal of various metals after the removal of several
particle sizes, this is summarized in Table 7.
Table 7: Percent Reduction in Metals after Removal of Various Particle Sizes
Metal Particle Size (µm)
>20 >5 >1 >0.45
Cadmium 20 22 22 22
Copper 26 34 34 37
Lead 41 62 76 82
Iron 52 63 95 97
Zinc 64 70 70 72
Chromium 69 81 82 84
Approximate removal efficiencies of metals in SWM ponds are shown in Table 8. As can
be seen, the physical processes which remove particulates from stormwater runoff also remove
significant portions of metals. However, the most effective method for removing metals from
runoff is removing the various sources from which it originates. The MOECC has several
provincial water quality requirements for metals, those being monitored are listed in Table 9;
these drinking water quality standards.
19
Table 8: Percent Removal of Metals by SWM
Source Total
Arsenic
Total
Cadmium
Total
Chromium
Total
Copper
Total
Iron
Total
Lead
Total
Nickel
Total
Zinc
International
Stormwater
BMP Database,
2011b
23 33 60 40 76 70 53 62
Greater
Vancouver
Sewerage and
Drainage
District, 1999
24
57
73
51
Stormwater
Assessment
Monitoring and
Performance
Program, 2005
10-67
70-87
Wu et al., 1996
52-87
32-80
Table 9: Metals Provincial Water Quality Requirements
Metal Provincial Water Quality Requirement (μg/L) Aluminum *(Interim) 75 Antimony *(Interim) 20
The storms used for assessment all resulted in a predicted removal of 100% of the
particles; therefore, the flow rates and lengths of the storms were not large enough to move
particles from the inlet to the outlet in a single event. While this is problematic for assessing the
accuracy of removal in larger storms, the results do match well with the monitored events after
removing the baseflow from the measured values.
5.2.1 Sensitivity Analysis Sensitivity analysis was conducted on the variables that govern particle removal in
MUDS. The results are shown in Figure 41. The July to August time period was selected for
sensitivity simulations.
Figure 41: Sensitivity Analysis Results
65
70
75
80
85
90
-20% -10% Zero 10% 20%
Par
ticl
e R
em
ova
l Eff
icie
ncy
(%
)
Particle Density USDC Surface Area
85
The original values for particle density, surface area, and length used by MUDS (Table
33) were scaled by -20, -10, 10, and 20% to determine what effect they had on the TSS removal
percent. The length appears to have the largest effect on particle removal. This is intuitive, since
the pathlength of the particle is directly related to how long it has to settle in the USDC. The
surface area has the least effect; it indirectly changes the particle removal by altering the
hydraulics of the USDC.
The three properties all follow linear trends within this ±20% range. The +10% length
value is the only exception. The cause of this discrepancy is most likely due to assumptions
made by MUDS, in particular, the assumption explained in Appendix B – B.4 where the particle
exit height is greater than entry height; this situation may occur several times during the July to
August time period as there are storms which cause a large increase in depth very quickly. If a
large mass of pollutants are present at the very end of the USDC, then they will exit at a height
greater than the entry height which will provide a more conservative removal percentage than
what is actually occurring. Sensitivity analysis of the pathlength was conducted again using the
September – November time period. It was found to follow a linear trend which reinforces the
conclusion that the non-linear trend is a highly situational error based on MUDS’ assumptions.
5.3 Markham USDC MUDS Simulations
5.3.1 Design Storm Simulation In order to determine how well the USDC performs under extreme conditions, two design
storms were simulated with MUDS. Five and ten year storm events with rainfall duration of 2
hours were used; this corresponds to average rainfall intensities of 17.3 mm/hr and 20.2 mm/hr,
respectively (Ministry of Transportation, 2013). The five and ten year events are common design
criteria for quantity control for Ontario municipalities and a 2 hour storm period was selected to
86
test the most extreme conditions for five and ten year storms. For the purposes of this thesis, the
return period of a storm is defined using the average rainfall intensity across a storm event. The
rainfall intensities were assumed to be constant over two hours and were input to the SWMM
model to develop an inflow hydrograph. A first flush ratio of 80/30 was used to predict a highly
concentrated release of pollutants. The designed outlet diameter of 0.12 m was used instead of
the 0.15 m for calibration and validation to evaluate how the USDC acts under designed
conditions. The outflow and inflow hydrographs are shown in Figure 42 and Figure 43.
Figure 42: 5 Year Storm Hydrographs
Figure 43: 10 Year Storm Hydrographs
The peak flow was reduced substantially. The 10 year return period event outflow is well
below the maximum design outflow of 30 L/s, which was the outflow for a 5 year return period
storm. Therefore, the Markham USDC exceeds all hydraulic expectations for reducing peak
0
20
40
60
80
100
120
0 5 10 15 20 25 30
Flo
wra
te (
L/s)
Time (h)
Qout
Qin
0
20
40
60
80
100
120
140
0 5 10 15 20 25 30
Flo
wra
te (
L/s)
Time (h)
Qout
Qin
87
outflow. The model also predicted that 100% of particles would be removed from the runoff
regardless of the extreme conditions. However, the high removal efficiency and peak flow
reduction of the Markham USDC under extreme conditions will undoubtedly be influenced by its
oversizing.
5.3.2 Continuous Simulation (May - Nov) Continuous modeling was conducted to determine how well the USDC removed particles
over several seasons. Rain data gathered at the Milne Dam site during the monitoring period
(May 1st, 2014 – November 30th, 2014) was entered into the SWMM model, and the inflow
hydrograph generated to MUDS. A first flush ratio of 50/50 was used for even distribution of
particles across the entire simulation period. MUDS was designed to be an event-based model, so
the first flush ratio is intended to be used on a per-storm basis, not across an entire year, using a
50/50 first flush releases the particles at a constant rate. The results of the continuous simulation
are shown in Figure 44 and Figure 45.
Figure 44: Hydrographs for Continuous Simulation
88
Figure 45: Modeled Depth for Continuous Simulation
The USDC remained within the hydraulic design parameters (outflow < 30 L/s) for all
storms with the exception of the event that occurred on August 1st, which has an outflow of just
over 200 L/s. Other storms have maximum inflow rates that approach the August 1st storm, but
the outflow does not scale the same way because of the initial conditions of the USDC and the
storm volume. The key difference is the depth in the USDC; the August 1st storm raises the
USDC depth to above the invert depth of the overflow pipes (2.45 m), which causes a severe
increase in the outflow. Using the IDF Curve Lookup tool from the Ministry of Transportation
(2013), the August 1st storm has a 13 year return period, which lies outside the design criteria for
the Markham USDC (5 year return period). Therefore, the Markham USDC is performing to its
design standards for hydraulics.
The overall removal efficiency predicted by MUDS was 81.5%. This matches very
closely with the water quality samples returned from the MOECC labs, which had an average
suspended solids removal of 82%. Therefore, MUDS accurately predicted the removal of
particles in USDC on both an event and continuous basis. In order to more accurately gauge
MUDS' continuous simulation ability, more rain and suspended solids data is required.
89
5.3.3 Seasonal Simulations MUDS was also run to determine how well the USDC removes particles on a seasonal
basis. Three time periods were selected: May-June, July-August, and September-November. The
results of the simulations are presented in Table 37.
Table 37: Seasonal and Overall TSS Removal Simulation Results
Modeled Time Particle Removal
Efficiency (%)
May – June 98.4
July – August 77.8
September -
November 95.1
May - November 81.5
The USDC is able to provide enhanced protection under MOECC standards (80% TSS
removal) except for July-August where it is slightly below the requirement. This makes sense by
examining Figure 45, which shows that this was also the period when the USDC was at the
greatest depth and correspondingly experienced the largest volumes of inflow. Larger volumes
flowing into the USDC lead to longer drainage time and consequently a higher probability that
particles which entered during the storm event or are already present in the USDC will reach the
outlet before settling.
The seasonal rainfall characteristics are an important factor to consider when designing a
USDC. While the Markham USDC achieves an overall removal of 81.5%, the July to August
time period does not meet the enhanced protection standard. If it is required that the USDC
achieve this standard at all times, then an overall removal is irrelavent and the designer should
instead focus on this critical time period where there is a combination of high inflow rates and
large inflow volumes.
Comparing the August 1st storm in Figure 46 to the same storm in Figure 44 shows that
there is a difference of around 70 L/s for the maximum inflow and 90 L/s for the maximum
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outflow. Similar changes can also be observed in the other simulated storms. A change in the
inflow can only be explained by the conditions in the SWMM model, which in turn effects the
outflow. Investigating the runoff values calculated by SWMM revealed that each subcatchment
was releasing more runoff during the continuous simulation. The source of this error could not be
determined. The removal efficiency using the inflow and outflow rates from the May-November
simulation would most likely be lower than what was found using the July-August simulation.
Figure 46: July to August Simulation Hydrograph
5.3.4 Sizing Simulations Finally, MUDS was used to compare how well runoff would have been treated from the
Markham catchment area if the USDC had been sized for the correct catchment area (5.24 ha),
rather than the original area (7.97 ha). The surface area, average width, and length of the USDC
were reduced by the same factor as the contributing area, to roughly 65.7% (5.24/7.97) of the
original value. MUDS was run using these new values to determine if the USDC still meets the
hydraulic and runoff treatment requirements. The July-August time period was used to develop
the inflow hydrograph to determine the performance under the most intense rainfall conditions.
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Figure 47: July to August New Area Hydrographs
The results of the simulation are shown in Figure 47. The changes have a profound effect
on the outflow rates calculated by the USDC. This change most notably occurrs in the August 1st
event where the outflow increases from the original July-August simulation (120 L/s) to just
under 200 L/s. The other storms remain under the hydraulic requirements. The reduction in
length and width drastically reduces the removal efficiency of suspended solids, the new USDC
achieves a removal of 51.2% compared to the original 77.8%.
Another simulation was run with the mixed commercial-residental PSD found by the
Toronto and Region Conservation Authority (2012a). This is shown in Table 35. While the
outflow hydrograph remains the same, the removal efficiency of suspended solids improves from
51.2% to 67.1% with the new PSD. This value is still well below the requirments for enhanced
protection under MOECC standards, indicating that a USDC can not be simply scaled based on
the catchment area. An iterative process is required to determine the appropriate dimensions for
the chamber.
This process was performed using the July-August time period to determine what
dimensions would be needed for the USDC for the reduced catchment area (5.24 ha) and the
TRCA PSD. Surface area, width, and length were all reduced to 80% and 85% of their original
values, resulting in a TSS removal efficiency of 79.1% and 84% respectively. Therefore, a
92
USDC with 85% of the original USDC properties is required for enhanced protection. The
hydraulic results are shown in Figure 48. These would be the required USDC measurements to
achieve enhanced protection during the worst time period of the year. Performing this process
using the May-November inflow hydrographs would likely result in a smaller USDC being
necessary.
Figure 48: Reduced Catchment Area with TRCA PSD Hydrographs
5.4 Summary
The chapter discussed the calibration and validation of the SWMM model hydraulics and
hydrology, the assessment of the pollutant removal modeling, and the results of several
simulations by MUDS. Due to various issues with clogging and the splashpad, only storms from
September onwards were utilized for the modeling process.
The SWMM model was calibrated and validated to ensure adequate simulation of the
hydraulics of the Markham USDC catchment. The NSE equation was used to compare measured
and modeled values. It was found that the SWMM model was more accurate for storms with
larger flow rates, NSE values for smaller flow rate storms were disproportionately affected by
small differences in modeled flow rate. Localized variations in rainfall may be partially
responsible for errors since the Markham USDC and rainfall monitoring site were 3 km apart.
The median modeled outflow and depth were within satisfactory to good prediction range (0.36 –
0.75) as recommended by Moriasi et al. (2007). Analyzing the hydraulic data revealed that the
93
Markham USDC reduced peak flow significantly for all modeled events. The mean and median
peak flow reductions were 66.1 and 77.6% respectively.
Assessment of MUDS’ particle removal model was conducted by comparing the modeled
removal to the mass load efficiency calculated from turbidity and flow data. First flush ratio was
determined on a per storm basis using measured turbidity data and the average PSD across
monitored storm was used. Removal percentages between the measured and modeled results
were consistently within a few percent of each other with one exception. The modeled storms
were not large enough to move particles from the inlet to outlet in a single event; however, the
results show that MUDS is accurate for predicting the removal of contaminants on an event
basis.
Several simulations were performed to determine the treatment and hydraulic capability
of the Markham USDC. A 5 and 10 year storm were input to the SWMM model to develop
inflow hydrographs, a first flush ratio of 80/30 was used to predict a highly concentrated release
of pollutants. Peak flows for both storms were below the maximum design outflow of 30 L/s and
no particles from the storm escaped over the duration of the event. Therefore, the Markham
USDC is performing above its design capacity for hydraulics and removal of TSS.
Continuous modeling was conducted to determine the accuracy of MUDS over an
extended time period and how well the Markham USDC removed particles over several seasons.
Rain data gathered at the Milne Dam site during the monitoring period was input to the SWMM
model. The Markham USDC met the hydraulic requirements except on one occasion where a
12.9 year storm occurred, this is beyond the design capacity of the Markham USDC and so is an
acceptable failure. MUDS predicted a removal efficiency of 81.5% which matches very closely
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with the water quality results (82.1%). Therefore, MUDS is accurate for both event based and
continuous based modeling simulations.
Seasonal simulations were performed to determine whether the time of year has an effect
on USDC performance. The Markham USDC was found to perform worse during the July-
August time period, it was unable to achieve enhanced protection during this simulation. The
poorer performance during this time period was expected as the summer is when more and
higher intensity storms occur.
Finally, sizing simulations were performed on the Markham USDC, it was originally
designed for a 7.97 ha catchment but the contributing area was reduced to 5.24 ha after
installation. MUDS was used to determine the appropriate size by scaling the surface area, width,
and pathlength equally by the ratio of the areas (5.24/7.97). The predicted removal percentage
was 51.2%, the poor performance may have been due to the very find PSD of the Markham site.
Replacing the PSD with one found in the literature resulted in a removal of 67.1%. The surface
area, width, and pathlength were scaled equally to determine the size required for enhanced
protection. The parameters were scaled to 85% of their original values to achieve enhanced
protection; therefore, USDC cannot be scaled by catchment area, they require iterative use of
MUDS to determine appropriate sizing. The conclusions and recommendations from the work on
this thesis are discussed in the following chapter.
95
Chapter 6 Conclusions and Recommendations
6.1 Conclusions
The purpose of this research was to gain an understanding of how a USDC acts in an
Ontario climate. In the following sections, conclusions which address the research objectives will
be discussed. In summary, the research objectives were to:
1. Identify the stormwater treatment capabilities of USDC using on-site monitoring
2. Compare the runoff treatment from USDC to SWM ponds
3. Create a model that predicts the removal of contaminants in USDC
6.1.1 Objective 1 The stormwater treatment capabilities of a newly constructed StormTrap-DoubleTrapTM
were studied using field monitoring equipment installed in Markham, Ontario. This includes
ISCO samplers at the inlet, Hatch 2, and outlet, and YSI monitors at the inlet and outlet.
Monitoring and maintenance was performed by TRCA technicians from May-December 2014.
Samples were captured by the ISCO samplers during storm events; of those, six at the inlet and
eight at Hatch 2 and the outlet were used for water quality analysis. The Markham USDC was
found to provide peak flow reduction and water quality benefits for many monitored pollutants.
1. The USDC achieved an overall 82% removal efficiency of TSS which meets
enhanced protection requirements under MOECC standards (80% removal).
2. The average un-ionized ammonia concentration of 0.25 μg/L was below the MOECC
guideline of 20 μg/L, but total phosphorus far exceeded its guideline (30 μg/L) with
an average concentration of 111 μg/L.
96
3. All monitored metals achieved the provincial water quality requirements for
maximum allowable concentration (MAC) with the exception of aluminum, copper,
and iron.
4. The concentration of E. coli decreased significantly from the inlet to outlet, but the
median E. coli concentration of 212 c/100mL was greater than the MAC for beach
water in Ontario (100 c/100mL).
5. Temperatures were reduced significantly, with an average at the inlet and outlet of
14.5 and 12.5 oC, respectively.
6. Hydrocarbons were also removed very well, with few samples testing above the
MDL. All hydrocarbons met the provincial water quality requirements with the
exception of fluorene, which has a requirement below the lab MDL.
7. Several depth profile measurements taken showed that there was a slight temperature
gradient and a dissolved oxygen gradient between the surface and bottom of the
USDC.
Statistical analysis was performed to ascertain where the majority of removal was
occurring in the USDC for each individual pollutant. Understanding this assists in the design
process by determining whether the key design factor is the forebay or permanent pool. The
results for pollutants which were significantly removed are summarized in Table 38.
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Table 38: Summary of Forebay and Residence Time Significance Tests
Pollutant Paired T-Test Results (p<0.05)
Inlet - Hatch 2 Hatch 2 - Outlet Inlet - Outlet
Total Suspended Solids
Turbidity
Nitrogen; ammonia + ammonium
Nitrogen; nitrate + nitrite
Nitrogen; total
Nitrogen; total Kjeldahl
Phosphorus; phosphate
Phosphorus; total
Aluminum
Antimony
Arsenic
Barium
Boron
Cobalt
Copper
Iron
Lead
Manganese
Nickel
Strontium
Titanium
Vanadium
Zinc
Phenanthrene N/A N/A N/A
Fluoranthene N/A N/A N/A
Pyrene N/A N/A N/A
Napthalene N/A N/A N/A
Fluorene N/A N/A N/A
Escherichia coli
Fecal streptococcus
Pseudomonas aeruginosas
Significant Decrease Significant Increase No Significance
6.1.2 Objective 2 The results of the pollutant removal analysis were MUDS compared against SWM ponds
to determine whether USDC provide an equivalent level of treatment. Values were taken from
various sources in the literature.
1. The removal of TSS by USDC was found to be equivalent to that of SWM ponds.
98
2. Phosphorus removal was either above or equivalent to listed removal rates in SWM
ponds.
3. The removal of metals by USDC are either greater or within the same range of
previously published studies with the exception of arsenic.
4. Effluent concentrations of E. coli were roughly equivalent to SWM ponds.
5. Runoff temperature was significantly reduced between the inlet and outlet whereas
SWM ponds consistently release water at an elevated temperature.
Overall, USDC have exhibited pollutant removal efficiencies at a greater or equivalent
level as SWM ponds.
6.1.3 Objective 3 The Model for Underground Detention of Sediment (MUDS) was developed by Nicholas
McIntosh at the University of Toronto. It has shown to be an accurate model for the prediction of
hydraulics and TSS removal for both event and continuous-based modeling. A sensitivity
analysis was performed on the suspended solids removal and it was found that changes in
particle pathlength have the greatest effect on removal percentage. MUDS was also used to
determine seasonal and particle size distribution effects on USDC performance. The findings of
the modeling process are as follows:
1. The Markham USDC remained beneath the required outflow rate of 30 L/s for 5 and
10 year storms with periods of 2 hours. The removal percentage for these storm
events was 100%.
2. Under continuous simulation from May - November the Markham USDC removed
81.5% of particles. There was one failure event where the outflow exceeded 30 L/s,
but this was during a 13 year return period storm which is outside the design capacity
of the USDC.
99
3. Seasonal simulations revealed that the worst performance by the Markham USDC
(77.8% removal efficiency) took place in the July-August time period.
4. An iterative process was conducted using MUDS to determine the USDC dimensions
for the Markham USDC using the final catchment area and the TRCA mixed
commercial-residential particle size distribution. A USDC with 85% of the original
Markham USDC dimensions would provide enhanced protection. This process also
revealed that USDC could not be linearly scaled based on the catchment area.
6.2 Recommendations for Future Research
Through this study the treatment capability of a USDC has been determined, however
this process has also highlighted several areas in which more research is needed. In the following
sections, recommendations for future research are presented for the categories water quality,
modeling, and USDC design in Ontario.
6.2.1 Water Quality Throughout this study, the gathering and analysis of samples was largely successful.
Only for a few parameters were there issues with gathering data. The analysis of the removal of
hydrocarbons was made impossible by the MDL set by the MOECC laboratories. Some of the
samples at the inlet, and the majority of those at Hatch 2 and the outlet, were below the lab MDL
so statistical analysis could not be performed. While the reduction in hydrocarbon concentration
is a good indication of the USDC treating hydrocarbons well, until more accurate tests are
performed the actual removal efficiency can not be determined. Additional water quality samples
are also required to better identify trends in the removal of pollutants by USDC. A sample size of
only eight events is not large enough to identify small changes in concentration as being
statistically significant.
100
Further research is also required on vertical profiles taken in USDC to determine the
existence and extent of thermal and dissolved oxygen stratification during the summer months.
The summer is when the USDC will be most active, so it is important to determine the
characteristics of the water being released during that time. If there is thermal stratification
during the summer, this may bring into question the thermal benefits provided by USDC. The
strong stratification of dissolved oxygen may also be different in the summer months since the
USDC will be receiving more inflow and so will be more turbulent.
The long term performance of USDC must also be studied. This monitoring program
took place over a single year, in order to ascertain the treatment capability of USDC over it's
lifetime a long term study should be conducted. This would also assist in determining the long
term maintenance requirements for sediment and debris cleanout. Extended monitoring can also
be used to determine whether the accumulation of sediment has an effect on the hydraulics or
treatment process of USDC.
6.2.2 Modeling Additional data is required to confirm the accuracy of MUDS for event and continuous
based simulation. For event-based simulations, larger events that result in particles flowing from
the inlet to the outlet in a single event are required before a non-100% removal will occur. For
continuous based, more data available for conducting simulations will increase the confidence in
prediction accuracy. Extended study of USDC may also reveal that accommodations must be
made for the accumulation of sediment and hydraulic losses.
The TSS removal simulated by MUDS could be expanded to include the removal of
pollutants strongly associated with TSS such as nutrients and metals. This also requires more
101
data, as the relationships between dissolved and particle fractions are complex and dependant on
the individual pollutant.
6.2.3 USDC Design in Ontario Through the course of the monitoring program it has become apparent that orifice plates
are not a practical solution to flow rate management on their own. The orifice plate installed on
the Markham USDC site clogged twice in quick succession due to plastic bags entering the
system with runoff. The clogging disrupted flow through the USDC and caused damage to the
orifice plate, resulting in noticeable leaking and a higher flow rate than designed. Without the
ongoing monitoring program, the clogging would not have been noticed and likely would have
persisted until the next maintenance period.
There are several solutions to preventing orifice clogging in SWM ponds such as a
submerged reverse-slope pipe, a trash rack, and a perforated pipe with wire cloth and stone
jacket (Greater Vancouver Sewerage and Drainage District, 1999). The most practical solution
would be to place a finely meshed grate across the opening from the forebay to the permanent
pool. The mesh would be sized such that any object small enough to pass through would not clog
the orifice plate. This solution would prevent any disruption to flow through the USDC and
miscellaneous garbage and debris would be confined to the forebay but adds another component
to the maintenance of USDC.
102
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Appendix A: Layout of MUDS Interface
The layout below (Appendix Figure A 1) includes sample values in each of the cells
required for MUDS to run and an example of the removal percentage output.
Appendix Figure A 1: Layout of MUDS Interface
t (s) Qin (m3/s) delta t (s) Tank Dimensions h(t) Qout(t) Qout L/s Removal (%)= 82.62389039
0.00 300 SA (m2) = 854 1.38 0 0
300.00 Width (m) = 12
Baseflow Height to Outlet Orifice Invert (m) = 1.38
0 Orifice Diameter (m) = 0.12
Starting Height (m) 1.38
Starting Qout (m3/s) 0
Length (m) 80
Particle Density (Kg/m3) 2650
Particle Size Distribution
d10 (um) 0.8
d20 (um) 1.2
d30 (um) 1.6
d40 (um) 2.2
d50 (um) 3.1
d60 (um) 4.5
d70 (um) 6.6
d80 (um) 10.6
d90 (um) 19.2
First Flush Ratio (Pollutant Mass/Volume)
Percentage of Pollutants 50
Percentage of Flow 50
Overflow Outlets
Number 4
Height to Outlet Orifice Invert 1 (m) = 2.448
Orifice Diameter 1 (m) = 0.525
Height to Outlet Orifice Invert 2 (m) = 2.448
Orifice Diameter 2 (m) = 0.525
Height to Outlet Orifice Invert 3 (m) = 2.448
Orifice Diameter 3 (m) = 0.525
Height to Outlet Orifice Invert 4 (m) = 2.448
Orifice Diameter 4 (m) = 0.525
Water Density (Kg/m3) = 998.21
Water Dynamic Viscosity (Kg/m·s)) = 0.001002
Q Calculation Progress
Treatment Calculation Progress
107
Appendix B: Removal Percentage Calculation
As explained in Section 3.4.3, users are prompted to enter a particle size distribution
before running MUDS. These particle sizes represent thresholds, if a particle size settles to the
bottom of the USDC then a known percentage of TSS has been removed (e.g. if the d50 particle
has settled then 50% of TSS has been removed). MUDS tracks waves of particles as they
progress through the USDC, Appendix Figure B 1 represents how MUDS interprets the tracking
information calculated for each particle wave where hini is the initial height (m), and tf is the time
the particle wave exited the USDC (s). When visualizing the settling paths of these threshold
particle sizes, the settling paths can be interpreted as lines of removal (e.g. the d40 settling path
represents the 60% line of removal). The particles are divided into 10% segments by the lines of
removal.
Appendix Figure B 1: MUDS Settling Path Prediction
The settling velocity of a particle diameter can be determined using the following
equation:
𝑉𝑠 =
ℎ𝑖𝑛𝑖
𝑡𝑓 (B1)
108
The height of the particle at each point in time (hp(t)) can then be determined using this
simple equation of a line:
ℎ𝑝(𝑡) = −𝑉𝑠 ∗ 𝑡 + ℎ𝑖𝑛𝑖 (B2)
Rearranging for time yields equation B3:
𝑡 =
ℎ𝑝(𝑡) − ℎ𝑖𝑛𝑖
−𝑉𝑠=
ℎ𝑖𝑛𝑖 − ℎ𝑝(𝑡)
𝑉𝑠 (B3)
Not all threshold particle sizes reach the bottom of the USDC before reaching the outlet,
when this occurs there is a partial removal of the particles in the segment between the larger
threshold particle size that settled out and the one that did not. An average settling velocity for
the segment must be calculated to determine how much of the segment is removed. One of the
conditions to calculate this partial removal is that the difference between one line of removal
(e.g. 40%) to the time to finish must be equal to the difference between the next line (e.g. 50%)
at the same height. This is represented by the lines labeled a and b in Appendix Figure B 1, and
by the following equations:
𝑎 = 𝑏 (B4)
𝑡𝑓 − 𝑡𝑎 = 𝑡𝑏 − 𝑡𝑓 (B5)
Rearranging yields:
2𝑡𝑓 = 𝑡𝑏 + 𝑡𝑎 (B6)
This equation can be combined with the equation B3:
𝑡𝑎 =ℎ𝑖𝑛𝑖 − ℎ𝑝
𝑉𝑠𝑎 𝑡𝑏 =
ℎ𝑖𝑛𝑖 − ℎ𝑝
𝑉𝑠𝑏
𝑡𝑎 + 𝑡𝑏 =
ℎ𝑖𝑛𝑖 − ℎ𝑝
𝑉𝑠𝑎+
ℎ𝑖𝑛𝑖 − ℎ𝑝
𝑉𝑠𝑏 (B7)
109
𝑡𝑎 + 𝑡𝑏 =𝑉𝑠𝑎(ℎ𝑖𝑛𝑖 − ℎ𝑝) + 𝑉𝑠𝑏(ℎ𝑖𝑛𝑖 − ℎ𝑝)
𝑉𝑠𝑎 ∗ 𝑉𝑠𝑏
Where hp is the height at which a = b. Substituting using equation B6:
2𝑡𝑓 =
(ℎ𝑖𝑛𝑖 − ℎ𝑝)(𝑉𝑎 + 𝑉𝑏)
𝑉𝑠𝑎 ∗ 𝑉𝑠𝑏 (B8)
Finally, the height at which a = b can be calculated by rearranging:
ℎ𝑝 = ℎ𝑖𝑛𝑖 −
2𝑡𝑓 ∗ 𝑉𝑠𝑎 ∗ 𝑉𝑠𝑏
𝑉𝑠𝑎 + 𝑉𝑠𝑏 (B9)
The removal percentage of a segment attributed to the total removal of a wave is the ratio
of the settling velocity of the segment to the critical settling velocity for that wave times the
percentage that segment represents (10%)
𝑅𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =
𝑉𝑠𝑒𝑔𝑚𝑒𝑛𝑡
𝑉𝑠𝑐∗ (𝑑𝑖𝑓𝑓 𝑖𝑛 %) (B10)
The settling velocity of the segment is calculated using equation B11:
𝑉𝑠𝑒𝑔𝑚𝑒𝑛𝑡 =
ℎ𝑖𝑛𝑖 − ℎ𝑝
𝑡𝑓 (B11)
Substituting with equation B9:
𝑉𝑠𝑒𝑔𝑚𝑒𝑛𝑡 =ℎ𝑖𝑛𝑖 − ℎ𝑖𝑛𝑖 +
2𝑡𝑓 ∗ 𝑉𝑎 ∗ 𝑉𝑏
𝑉𝑎 + 𝑉𝑏
𝑡𝑓
𝑉𝑠𝑒𝑔𝑚𝑒𝑛𝑡 =
2𝑉𝑎 ∗ 𝑉𝑏
𝑉𝑎 + 𝑉𝑏 (B12)
Making a final substitution yields the equation for the removal percentage of a segment
attributed to the total removal of a particle wave:
𝑅𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =
2𝑉𝑎 ∗ 𝑉𝑏
(𝑉𝑎 + 𝑉𝑏) ∗ 𝑉𝑠𝑐∗ (𝑑𝑖𝑓𝑓 𝑖𝑛 %) (B13)
The critical settling velocity of the particle wave is calculated using equation B14:
110
𝑉𝑠𝑐 =
ℎ𝑖𝑛𝑖
𝑡𝑓 (B14)
There are special conditions where different removal percentage equations are applied.
These include: (1) removal of particles with settling velocity greater than the critical settling
velocity, this can have any value and is not limited to groupings of 10% (values can be 57%,
44%, etc.); (2) removal of particles left over in a ten percent group after calculating removal of
particles with Vs > Vsc (e.g. for 57% fully removed some fraction of the 3% remaining is
partially removed); (3) the fraction of particles removed with particle diameters smaller than the
d10; (4) when a particle group has a height at the outlet that is greater than the height at which it
entered the USDC, this can occur during high intensity and volume storm events cause the water
surface to rise quickly far above the outlet. The calculations for these situations are explained in
sections B.1 – B.4.
B.1 Particles with Vs > Vsc
MUDS begins by determining the smallest particle size that reached the bottom of the
USDC. Every particle larger than this has been fully removed, for example if a d50 is the smallest
particle size to reach the bottom of the USDC before the wave reaches the outlet then 50% of the
particles have been fully removed. The segment between the smallest to be removed and the next
smallest is divided by the critical settling velocity particle path. Therefore, a portion of the
segment is fully removed and a portion only has partial removal. The percentage of particles
fully removed between the smallest to be removed and the next smallest is calculated by linearly
interpolating between the time it takes the larger particle to reach the bottom, the time for a
particle settling at the critical settling velocity, and the time for the smaller particle to reach the
bottom.
111
𝑅𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =
𝑡𝑓 − 𝑡𝑙𝑎𝑟𝑔𝑒𝑟
𝑡𝑠𝑚𝑎𝑙𝑙𝑒𝑟 − 𝑡𝑙𝑎𝑟𝑔𝑒𝑟∗ (10%) (B15)
Where RFraction is the removal percentage, tf is the time for the particle wave to reach the
outlet (s), tlarger is the time for the larger particle to reach the bottom of the USDC (s), and tsmaller
is the time for the smaller particle (s). The value for tlarger is tracked by MUDS, but tsmaller is
calculated using equation B16.
𝑡𝑠𝑚𝑎𝑙𝑙𝑒𝑟 =
ℎ𝑖𝑛𝑖
𝑉𝑠=
ℎ𝑖𝑛𝑖 ∗ 𝑡𝑓
ℎ𝑖𝑛𝑖 − ℎ𝑒𝑥𝑖𝑡 (B16)
Where hexit is the height at which the particle size exits the USDC. Appendix Figure B 2
shows how MUDS interprets these values.
Appendix Figure B 2: MUDs Interpretation of tlarger and tsmaller
B.2 Partial Removal of Particles after Fully Removed is Determined
The partial removal of the remaining portion of the segment that was not fully removed
in the calculation in Section B.1 is calculated using equation B13, but the value for Vsc is used in
place of Va. To determine what portion of the segment was not fully removed, another linear
interpolation is performed. The final equation for the removal of this segment of the particles is
shown in equation B17.
112
𝑅𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =
2𝑉𝑠𝑐 ∗ 𝑉𝑏
(𝑉𝑠𝑐 + 𝑉𝑏) ∗ 𝑉𝑠𝑐∗
𝑡𝑠𝑚𝑎𝑙𝑙𝑒𝑟 − 𝑡𝑓
𝑡𝑠𝑚𝑎𝑙𝑙𝑒𝑟 − 𝑡𝑙𝑎𝑟𝑔𝑒𝑟∗ (10 %) (B17)
B.3 Removal of Particles between d10 and d0
It is assumed that the diameter of particles for the smallest 10 percent in the particle size
distribution can be linearly interpolated between the d10 and zero. Therefore, the average settling
velocity for those particles is the settling velocity of the d10 divided by two. The formula for the
removal of this section is presented in equation B18.
𝑅𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =
h𝑖𝑛𝑖 − ℎ𝑒𝑥𝑖𝑡
2𝑡𝑓 ∗ 𝑉𝑠𝑐∗ (10 %) (B18)
B.4 Particle Exit Height is Greater than Entry Height
This situation can occur during high intensity and volume storm events that cause the
water level to rise quickly far above the outlet, and results in MUDS interpreting the particle
group as having a negative settling velocity. If a particle size has a negative settling velocity it is
assumed that none of the particles between that particle size and the next largest are removed by
the USDC. While this is not strictly true it is an assumption that gives a more conservative
answer for particle removal.
This circumstance can also effect the removal calculation in Section B.1, a particle size
may settle to the bottom but the next smallest may still exit at a height greater than the entry
height given the right conditions. If this occurs, it is assumed that there is no partial removal of
the 10% section and only the particles with diameters larger than the last to settle are fully
removed. For example, if the d50 is removed but the d40 exits at a height greater than the entry
height then only 50% of that wave is removed.
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Appendix C: Hydrograph and Depth Figures of Storms used for