Source: http://www.mto.gov.on.ca/english/publications/drainage/stormwater/section10.shtml
Timestamp: 2020-06-05 19:37:35
Document Index: 224310486

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Selecting Computational Methods
Where a proposed land development will be discharging stormwater runoff to a receiving drainage system, any potential impacts to the receiving drainage system or the highway drainage system must be examined. Since impacts are assessed through a hydrologic or hydraulic analysis of the highway drainage works, every proposed land development should provide some form of hydrologic or hydraulic analysis. It is recognised that the level of detail required in the hydrologic or hydraulic analysis will vary, depending on the type of land development and the region of the province where it is located. So, before proceeding review the following.
Level of Detail of Analysis
Identifying Catchment Inputs
Selecting Precipitation Data
Performing Culvert Analysis
Performing Bridge Analysis
Assessing Flow in Open Channels
Assessing Channel Erosion
Assessing Flow in Storm Sewers
Assessing Roadway Surface Flooding
Assessing Flow in Stormwater Management Detention Facilities
Assessing the Potential for Scour
Computer Program Characteristics
Level of Detail Analysis
Where a lower level of detail is proposed for the hydrologic or hydraulic analysis, the SWM report should provide rationale on why the lower level of detail is appropriate. As a guide, review the following land development attributes.
The type of land development that is proposed in terms of the amount of impervious areas (i.e. roof tops or paved areas) proposed, the amount of serviced area and the method of servicing (i.e. storm sewers or ditches).
The surrounding land use in terms of the amount of impervious areas proposed (i.e. roof tops or paved areas), the amount of serviced area and the method of servicing (i.e. storm sewers or ditches).
The number of upstream and or downstream riparian owners, including the highway right-of-way.
A more detailed hydrologic or hydraulic analysis may be needed where any of the following may occur (typically, a higher level of detail involves the input of more data):
damage to the property of riparian landowners located upstream or downstream of the highway right-of-way;
the structural integrity of the highway right-of-way is threatened; or
the safety of the travelling public is threatened.
Having considered the level of detail, review the following sections for details on hydrologic or hydraulic analysis that are applicable to land development proposals. MTO recognises that the documentation of computational methodology is within the interests of all the regulatory agencies, not just MTO. However, the hydrologic and hydraulic methods specified within this section are accepted industry practices, and can be applied to the appropriate component of the receiving drainage system.
Flows rates are calculated as part of the hydrologic analysis and are typically determined at key locations along the receiving drainage system for a range of frequencies. The results are generally used as an input to the hydraulic analysis, which involves the calculation of water surface elevations and flow velocities. Table 7 presents the typical range of flow rate frequencies that should calculated at the reference points (i.e. in the receiving drainage system) presented in the table.
Inputs to the flow rate calculation include:
the catchment input parameters that correspond to the calculation reference points (refer to Analysis of Receiving Drainage System - Table 7); and
precipitation data that corresponds to the range of flow rate frequencies that are to be calculated (refer to Analysis of Receiving Drainage System - Table 7).
The methods that can be used for the flow rate calculation as classified in Figure 2 are:
Non-Hydrographic Methods
Method Based on Stream Flow
Methods Based on Precipitation Data
Hydrographic Methods
Figure 2: Flow Rate Calculation
Where a runoff hydrograph has been calculated, it may be necessary to route the flows though the channels or reservoirs to determine the affects of storage and roughness on the shape of the hydrograph. If computer models have been used, possible application errors should also be reviewed.
These methods calculate the peak flow rate based on statistical analysis of the precipitation record or stream flow records. Refer to Selecting Precipitation Data for information on the different types of precipitation data input.
The most common methods used to assess the peak flow rates are those based on modelling of the precipitation-runoff process. Some of these methods are empirical. These methods use statistical representations of the precipitation record, from a rainfall gauging station (e.g. Intensity-Duration-Frequency IDF curve), combined with physical parameters representing the catchment (e.g. area, length, slope, and runoff coefficient), to calculate the peak flow rate at a particular location in a catchment area. These methods can be classified into two types:
Rational Method; and
Regional Frequency Analysis (Modified Index Flood or Northern Ontario Hydrology Method).
Of these methods, the Rational Method is the most suitable method for small land development sites and is therefore, discussed in this section. The Modified Index Flood Method is for watersheds greater than 25 km2 and the Northern Ontario Method is for watersheds between 1 and 100 km2 in area. For information on the use and application of the Modified Index Flood Method and the Northern Ontario Method refer to the "Drainage Management Manual" (MTO 1997), Chapter 8, page 43.
The Rational Method calculates the peak flow rate at a particular location in a catchment due to the runoff contributed from the entire upstream catchment area. The Rational Method is represented by then following equation:
Q = 0.0028 C i A
C = the runoff coefficient (Refer to DMM Design Charts 1.07);
i = the rainfall intensity (mm/hr) (Refer to DMM Design Charts 1.01(a)-(r)); and
A = the area of the contributing catchment (m2).
When applying the Rational Method it is important to demonstrate the applicability of the method. For this purpose, it is important to note the following.
The Rational Method is primarily used as a design tool for the design of minor drainage systems such as storm sewers and ditches. Refer to the section Assessing Flow in Open Channels and Assessing Flow in Storm Sewers for further details.
The Rational Method can provide acceptable estimates of peak flow rates in small non-retentive rural watersheds. It is mostly applied to an urban catchment as a design tool to size storm sewers.
The present practice in the MTO limits its use to:
rural watershed drainage areas less than 100 ha; or
urban watershed drainage areas less than 50 ha.
The catchment area applied to the Rational Method should be that of the entire contributing catchment. The time of concentration is therefore, the time of travel of the flood wave from the furthest point of that catchment to the point of interest (e.g. at a culvert or bridge).
The applicability of the Rational Method for rural watersheds should be reviewed if there is great variability in soil, vegetation or rainfall.
If the Rational Method is not applicable a hydrographic method should be used.
Refer to the DMM, Chapter 8 page 39 for more details and for an example on the application of the Rational Method.
Hydrographic Method
Hydrographic methods calculate the time distribution of flow rate (hydrograph) at any location in a catchment. These methods calculate the response of a catchment to precipitation and snow melt. They apply mathematical representations of the specific physical hydrological processes in a catchment area, such as infiltration, evaporation and detention.
The two basic types of hydrograph methods are based on the two forms of precipitation data that are available:
single event precipitation event; or
continuous precipitation records.
Refer to the information sheet on Selecting Precipitation Data for more details on rainfall data.
Hydrograph simulation methods are required under the following circumstances:
the drainage basin is expected to undergo significant urbanization;
the drainage basin will be subject to stormwater management controls or modifications to the receiving drainage system (i.e. hydrograph routing is required);
the drainage basin contains reservoirs and watercourses;
peak flow rates or volumes of runoff will be calculated from a historical rainfall or precipitation event (e.g. Hurricane Hazel or Timmins storm);
different drainage options are to be tested including regulation (i.e. stormwater management controls, modifications to the receiving drainage system etc.);
if land use, times of concentration, or soils conditions (e.g. CN) vary significantly across the drainage basin; and
the Rational Method or Regional Frequency Analysis Methods are not applicable.
When using hydrographic methods it is essential to provide the specific information on the basis of which the modelling was based. This typically includes the following:
catchment areas, slopes and discretization into subcatchments;
imperviousness ratios, land use types, directly connected areas, depression storage, infiltration parameters, soil parameters (e.g. CN number), and the components of the receiving drainage system; and
the time to peak of the unit hydrograph, recession constants, computational time step, rainfall event(s) including type, duration and discretization time step, and snow accumulation.
For details refer to Identifying Catchment Inputs for details on the parameters presented above.
Single Event Hydrographic Methods
Single event hydrographic modelling simulates the precipitation/runoff process using a short duration precipitation event (i.e. durations ranging from 1hr to a few days). The storm event may be the regulatory storm (Hurricane Hazel, the Timmins Storm or the 100-year storm event) as described in the “Highway Drainage Design Standards” (MTO 2008).
Single Event Methods are used when:
the storm event is a designated design storm (e.g. using a regulatory storm to assess flood line impacts);
stormwater management controls exist or is being proposed;
modifications to the receiving drainage system are proposed;
flow routing in a ditch or storm sewer system may have a major effect on the peak flow; and
impacts to the receiving drainage system must be assessed.
Refer to the DMM, Chapter 8 page 77, for more details.
Single event computer models acceptable to MTO include:
HYMO;
OTTHYMO;
OTTSWMM;
ILLUDAS;
MIDUSS.
Refer to Computer Model Characteristics for more additional information on these models, Identifying Catchment Inputs for information on the input parameters to these models, and Selecting Precipitation Data for details on rainfall data.
Continuous Record Hydrographic Method
Continuous event hydrographic methods calculate the flow rate using the entire long term precipitation record as input. Typical periods of rainfall data ranges from 10 to 40 years. Continuous simulation is expected to generate runoff with a frequency which best approximates reality; however, calibration is required to achieve accuracy.
Continuous simulation can be an expensive, complex and time consuming process. It is used:
when an accurate estimate of peak flow rate return periods is required (e.g. high risk of upstream or downstream impacts, or during legal proceedings);
to simulate low flow or base flow conditions; and
for water quality analysis (i.e. pollutograph routing).
The following are the most common continuous event hydrographic computer models accepted by MTO:
HSP-F;
QUALHYMO;
SWMMIV.
Refer to the DMM Chapter 4, pages 81 and 86 for more detail. Methods not covered in the DMM may be used if it can be demonstrated, through independent recognised references, that these methods are in agreement with the principles outlined in the DMM and are applicable to Ontario conditions.
Routing the Hydrographic through Channels and Reservoirs
Where the hydrologic analysis involves a hydrographic method, the runoff hydrograph should be routed through the channel and reservoir components of the receiving drainage system for the following reasons.
Storage within the channel reach or reservoir may result in the attenuation of the hydrograph peak, changing the time to peak and possibly reducing the peak flow.
Multiple storage facilities located in the same drainage basin will affect the timing of the hydrograph as it travels downstream. This could increase or decrease peak flows in downstream locations. Coordination of stormwater management detention facilities with other drainage structures, on a watershed or subwatershed basis, is a primary consideration.
In catchment areas where natural depressions form part of the receiving drainage system, reservoir routing can be used to determine the possible impacts of any increase in runoff volume to the volume of water stored in the depression areas. For instance, increased runoff volumes could cause a cascading affect, which could result in localised flooding.
Where a suitable drainage outlet does not exist and the stormwater runoff is conveyed via sheet flow, channel or reservoir routing may be used to estimate any impacts caused by increased runoff volumes or peak flows (e.g. localised flooding).
Typically, channel or reservoir routing is completed as part of the hydrologic analysis. Most hydrologic computer models include channel and reservoir routing options that can be applied with minimal input data. Refer to Computer Model Characteristics for more details.
Channel routing typically requires the input of channel cross-section data and roughness coefficients.
Reservoir routing typically requires the input of a storage-discharge relationship for the reservoir. The storage-discharge relationship is a function of the outlet device (i.e. orifice, pipe or weir) and is independent of the inflow rate. The basis for the calculation of the storage-discharge relationship should be provided. Refer to Chapter 8, page 82 for more details. The assessment of parking lot and roof top storage are similar to reservoir in that a stage-storage-discharge relationship should be developed and routing of the hydrograph thought these facilities should be conducted.
Channel routing can also be completed as part of the hydraulic analysis where flow in the channel reach is unsteady (e.g. for very steep or very slopes). Hydraulic channel routing generally requires the use of different computer models. Refer to Computer Model Characteristics for more details.
Separating Major System and Minor System Flow Hydrographs
To assess the major drainage system (i.e. for roadway surface flooding), it is necessary to separate the roadway surface flow into major and minor hydrographs. The minor flow hydrograph is then input into a hydraulic grade line (storm sewers) or backwater analysis (roadside ditches) to determine the total depth of flow and a time history output of velocity. The major flow runoff hydrograph is routed along the roadway surface to determine the total depth of flow and time history of runoff. Refer to Assessing Roadway Surface Flooding for more details.
The actual flow in a storm sewer system (i.e. the minor flow) will depend on the spacing of the catchbasins on the roadway surface and/or the rate at which the catchbasins will capture surface flow from external areas. The flow not captured by the catchbasins will remain on the surface and will become the major flow. To determine an accurate assessment of the storm sewer, the major and minor flow should be separated. For convenience, the minor flow can be assumed to be equal to the surface flow (i.e. stormwater runoff form the roadway surface and/or external areas); however this method can result in a possible over estimation of the hydraulic grade line. Refer to Assessing Flow in Storm Sewers for more details.
Computer Model Characteristics presents the hydrologic computer programs that are capable of separating major and minor flow hydrographs.
Computer application errors can generally be attributed to the following:
incorrectly entered data;
incorrect use of default values intrinsically provided by the program;
incorrect assumptions made in an application;
program misapplication;
incorrect interpretation of modelling results; and
Catchment inputs are parameters that are determined at the reference points in the receiving drainage system as noted in Analysis of Receiving Drainage System - Table 7, and are used as an input to the flow rate calculation.
The total watershed area should include all the land that contributes stormwater runoff to the receiving drainage system. The watershed boundaries should extend far enough upstream and/or downstream to demonstrated that drainage impacts do not occur as a result of the proposed land development.
The watershed area should be discretized into separate drainage catchment areas so that its downstream boundary will be located at a:
reference point, as noted in Analysis of Receiving Drainage System - Table 7 in the receiving drainage system where peak flows are to be calculated; and/or
the upstream section of a culvert, bridge, open channel, storm sewer or stormwater management detention facility that will be analyzed as part of the receiving drainage system analysis; and/or
confluence in the receiving drainage system.
The watershed area should be discretized into separate drainage catchment areas of similar land use, based on the total imperviousness of the catchment.
Catchment Slope (Slope of Watershed)
Slope refers to the representative slope along the longest flow path.
Two methods to determine catchment slope are presented below.
85/10 Method
Sw = 100
SW = watershed slope, %
= difference in elevation, m, between the 85% point and the 10% point obtained from contours, air photos, etc.
hf = sum of heights of rapids and waterfalls between 10% and 85% points, m
L = total length of main channel, including the undefined flow path to head of basin, m
Lf = sum of lengths of rapids and waterfalls, up to 10% of L, m
Equivalent Slope Method
Sn = slope of an individual reach of the channel, m/m
n = number of reaches of approximately equal length
For further details refer to pages 25 to 27 in Chapter 8 of the "Drainage Management Manual" (MTO 1997).
Total Imperviousness Ratio
The total imperviousness ratio defines the amount of paved (i.e. driveways or roadways) and roofed surfaces in a catchment area, as a percentage of area.
It is a key input to most hydrologic computer programs and it can directly affect the peak flow of the runoff hydrograph.
The total imperviousness ratio of a catchment should be determined from appropriate land use mapping such as Official Plans, Secondary Plans, Draft Plans or Site Plans.
General values for generic land uses can be acquired from the planning office of most municipalities.
As a guide, the following table can be used.
Directly Connected Imperviousness Ratio
Directly connected imperviousness ratio defines the amount of paved (i.e. driveways or roadways) and roofed surfaces that are directly connected to the receiving drainage system, as a percentage of area.
If roof leaders are connected to the foundation drains, the directly connected imperviousness ratio will generally be equal to the total imperviousness ratio.
Where roof leaders are not connected to the foundation drains, the directly connected imperviousness ratio will be derived from the paved surfaces only (i.e. driveways or roadways).
Depression Storage Values
Horton Equation - Typical Values
Minimum Infiltration
Rate (mm/hr)
Rate (mm/hr)*
* dry soil conditions, Decay Parameter = 2 hr-1
Green-Ampt Method - Typical Values
IMD3(mm/hr)
Su3 (mm)
Ks2(mm/hr)
A (sand)
0.34 250	 25
B (silt loam)
0.32 200 13
C (sand clay loam)
0.26 125 5
D (clay)
0.21 180 3
For Ontario conditions, the accepted standard is 3.
Can be altered based on a model calibration.
The curve number, CN, is a common input to computer programs and is used to represent the spoil and land use condition of a catchment area.
Three parameters used to define CN are soil type, land use and the antecedent moisture condition.
A variation of CN is the CN*. When using CN *, the initial abstraction Ia applied reflects the actual Ia value for the catchment rather than the assumed value of Ia = 0.2S, where S is the potential abstraction. In such a case the CN values are altered as part of a calibration process. As a result the CN* method should be applied with caution, and it will only be accepted by MTO where the computer model has been calibrated and the CN* values can be verified. Before proceeding with the CN* method, contact an MTO drainage representative for further guidance.
Refer to the page 20 in Chapter 8 of the "Drainage Management Manual" (MTO 1997), for further details. Soil type, land use, antecedent moisture conditions and the corresponding CN are presented in Charts 1.08, 1.09 and 1.10 of Part 4.
Time to Peak (of the unit hydrograph)
The time to peak (of the unit hydrograph)is a key input to most hydrologic computer programs. It is a very sensitive parameter that directly affects the peak flow. For instance, a small time to peak (of the unit hydrograph) will result in a runoff hydrograph with a high peak flow and a short peak time, while a higher value will result in a runoff hydrograph with a lower peak flow and a longer time to peak.
There are three primary methods of calculation. For details refer to page 71 in Chapter 8 of the "Drainage Management Manual" (DMM 1997).
HYMO/OTTHYMO
Rural watershed with watershed slope less than 2%.
tp = 0.0086 A0.422 S -0.46 [L/W] 0.133
Rural watershed with watershed slope greater than 2%.
tp = 0.016 A0.31 S -0.50
Urban watershed.
0.5 tp (using above methods)
tp = time to peak (of the unit hydrograph), hours
S = catchment or watershed slope, m/m
A = drainage area, ha
L/W = length to width, dimensionless
tp = 0.6 tc + 0.5 t
tc = time of concentration, hrs, using MIDUSS method
t = computational time step, hrs
Time to Peak Calculated Using Time of Concentration
tp = 0.67 tc
The recession constant controls the shape of the hydrograph, after the time to peak has passed.
Two approaches can be used.
Rural watershed with watershed slope less than 2%:
K = 0.0095A 0.231 S -0.777 [L/W] 0.124
Rural watershed with watershed slope greater than 2%:;
K = 0.00316A 0.24 S -0.84
For urban watersheds:
K = 0.5K (using above methods)
K = recession constant, hours
Qt = Q0 Kt
log Kt = (log Qt - log Q0)
(tt - t0)
Qt = discharge at time t after the peak, m3/s
Q0 = discharge at the start of recession, m3/s
Kt = recession constant
tt = time after peak
For details refer to page 72 in Chapter 8 of the "Drainage Management Manual" (MTO 1997).
The time of concentration is a measure of the total time that it takes a drop of rain to travel the longest flow path in a catchment area.
When the time of concentration is reached, the entire catchment is contributing to the flow at the catchment confluence point.
Three methods to calculate time of concentration are listed below.
Bransby William Formula
Used if Rational Method runoff coefficient is greater than 0.40.
tc = 0.057 L
Sw0.2 A0.1
Airport Equation
Used if Rational Method runoff coefficient is less than 0.40.
tc = 3.26 (1.1 - C) L0.5
Sw0.33
tc = time of concentration, minutes
L = catchment or watershed length, m
Sw = catchment or watershed slope, %
A = catchment or watershed area, ha
tc = ieff-0.4
k = 6.989 for metric units
L = flow length (m)
S = slope of catchment or watershed, m/m
ieff = effective rainfall (mm/h)
The computational time step is the incremental period of time that a computer program will use when convoluting a rainfall distribution into a rainfall hydrograph.
Typically, the computational time step is set to be equal to 1/5 of the time to peak (of the unit hydrograph). It should be small enough to ensure that the peak of the rainfall distribution is captured in the convolution of the hydrograph rainfall time step. However, some computer models limit the amount of hydrograph co-ordinates that can be stored in memory: so if the time step is too small, the amount of hydrograph co-ordinates derived in the convolution might exceed the memory storage limit, and the hydrograph output could get truncated.
For urban applications, the computational time step should be less than 10 minutes.
The runoff coefficient, C, is used in the Rational method.
Refer to the DMM, Design Chart 1.07 in Part 4.
Flows rates are calculated as part of the hydrologic analysis and are typically determined at key locations along the receiving drainage system for a range of frequencies, as noted in Analysis of Receiving Drainage System - Table 7. Since precipitation data will serve as an input to the flow rate calculation, the frequency of the selected precipitation event must correspond to the flow rate frequency is that is to be calculated. Key characteristics of the precipitation data include type, distribution over time, duration and land use. The precipitation data may be one of the following depending on the type of analysis required and the data available.
Rainfall Intensity from a Representative IDF Curve
Rainfall intensity from a representative IDF curve is applicable when using the Rational Method for calculating the peak flow rate, or for determining the distribution of a synthetic storm event. A representative IDF curve includes one of the following:
MTO district IDF curve (refer to the DMM Part 4, Design Charts 1.01(a) - (r) for this data);
AES IDF curve for a meteorological station closest to the catchment; and
Municipal IDF curve.
Single Representative Storm Event from the Historical Record
A single representative storm obtained from the historical record, usually the regulatory storm, is applicable when using a single event modelling technique for assessing the impact of the regulatory storm (Hurricane Hazel, Timmins Storm or the 100-year event). “Highway Drainage Design Standards” (MTO 2008) specifies the applicable regulatory storm based on the geographic location of the catchment area under investigation.
Synthetic storm events are typically used when a hydrographic flow rate calculation method is necessary. A synthetic storm is produced by distributing the total precipitation volume over the duration of the storm based on a defined mathematical distribution (e.g. Chicago, AES or SCS distributions). Refer to the DMM, Chapter 8 page 10, for more details and to Example 8.1 page 11 for the method of developing a Chicago Storm. Input parameters include the following.
The precipitation volume which should be obtained from a representative Intensity-Duration-Frequency (IDF) curve for the appropriate duration.
The storm duration which has traditionally been chosen to be at least equal to the basin time of concentration. The time of concentration will be longer for basins with significant storage (as in rural catchments), and short for catchments with high imperviousness (as in urban catchments). Where a drainage basin is serviced by a stormwater management detention facility, a long duration storm event should be used. The magnitude of the synthetic storm will vary with the applied storm return period.
The storm event return period, which can vary from 2 to 100 years, and is selected based on the flow rate frequency that is that is to be calculated. Refer to Analysis of Receiving Drainage System - Table 7 for more details.
The rainfall time step, should be small enough to ensure that the peak of the rainfall distribution is captured in the convolution of the hydrograph. However, some computer models limit the amount of hydrograph co-ordinates that can be stored in memory: so if the time step is too small, the amount of hydrograph co-ordinates derived in the convolution might exceed the memory storage limit, and the hydrograph output could get truncated.
Table 9 provides the acceptable synthetic storm events, applicable storm duration and rainfall time step for each of these storm events based on land use. These parameters should always be provided to support the selection of a storm event. For additional information on representative designstorms, refer to DMM, chapter 8 page 10-17.
Table 9: Synthetic Storm Events
Land Use1Applicability
Chicago (Keifer & Chu) Variable (usually 3hr or 4hr) Variable Urban
SCS Type II	 6hr, 12hr or 24hr 15 min Rural
AES (30%) - 1 hr 1 hr 5 min Urban
AES (30%) - 12 hr 12 hr 15 min Rural
AES/Hydrotek 1 hr 5 min
Note: 1 Urban >20% impervious area , Rural<20% impervious area
Continuous Storm Record
A continuous storm record for a representative meteorological station is used when performing continuous hydrological modelling. Typical periods of rainfall data is 10 to 40 years. An alternative to using the entire continuous storm record is the use of a series of individual historical storm events. Each event is analyzed statistically and a frequency analysis of the results is then performed. Refer to the "Drainage Management Manual" (MTO 1997), Chapter 3 Appendix 3A for more details.
Culvert analysis is completed as part of the hydraulic analysis of the receiving drainage system, (culvert components), or to check the capacity of the highway culvert.
Peak flows rates are determined from the hydrologic analysis and are calculated for a range of frequencies as specified in Analysis of Receiving Drainage System - Table 7.
Culvert analysis is used to calculate the headwater level upstream of a culvert based on the flow rate, culvert characteristics and tailwater elevation. Refer to Components of the Receiving Drainage System - Table 6 for culvert characteristics that are required to complete the culvert analysis. Refer to the DMM, Chapter 5, page 17 and Chapter 8 page 134, for details on culvert analysis.
Water Surface Elevations (headwater level)
A culvert will operate in either inlet control or outlet control depending on the magnitude of the flow rate. For each flow rate, the headwater depth is computed for both the inlet and outlet conditions. The headwater level is determined from the condition that governs (i.e. the condition yielding the higher headwater level).
In the case of outlet control, an accurate assessment of tailwater elevation is essential as it has a significant effect on the headwater level. The two main methods of calculating the tailwater elevation are as follows.
The Manning equation which calculates the normal depth downstream of the culvert. This method is valid only if it can be demonstrated that the flow in the downstream channel is steady and uniform.
Backwater analysis which calculates the water level downstream of a culvert, based on the known water level at another point. This method is used if the flow in the channel is steady uniform or gradually varied.
If the calculated tailwater elevation is below the top of the culvert outlet the governing tailwater level will be the greater of the following two levels:
the calculated tailwater elevation; and
(dc+D)/2 (where dc is the critical depth and D is depth of the culvert opening).
Culvert analysis can be conducted either using hand calculation methods or computer models.
Hand calculations: refer to the DMM, Chapter 5, page 17 and Chapter 8 page 134. Culvert analysis nomographs are presented in Part 4 of the DMM, Design Charts 5.39 to 5.49.
Computer models accepted by MTO for backwater analysis (assessing tailwater level) are HEC2/HEC-RAS and WSPRO. Refer to Computer Model Characteristics for more information on these models. The user manuals of these models should be consulted for details on their application. Other models, not mentioned in this document or the DMM, may be used provided it can be demonstrated, through independent recognised references, that these methods are in agreement with the principles outlined in the DMM.
Checking Culvert Capacity
Where the capacity of the highway culvert is being checked, the analysis need only be completed for the design flow frequency.
Assessing Impacts to the Receiving Drainage System
Where headwater levels or flow velocities are being determined for the range of flow rate frequencies specified in Analysis of Receiving Drainage System - Table 7, a separate culvert analysis should be completed for each flow rate. The results can be presented on a culvert performance curve, which plots the headwater level against the flow rate (refer to pg 144 in Chapter 8 of the DMM for more details on performance curves). Where relief flow occurs, weir flow will occur and the performance curve should reflect this condition.
Flow Velocity at the Outlet
Flow velocities should be determined for each of headwater levels determined in the culvert analysis. The exit velocity from a culvert should not result in erosion downstream of the culvert, otherwise, erosion protection should be provided. Refer to the section Assessing the Potential for Erosion for more details.
Bridge analysis is completed as part of the hydraulic analysis of the receiving drainage system, and the bridge components, and to check the capacity of the highway bridge.
Peak flow rates are determined from the hydrologic analysis and are calculated at the upstream section of the bridge for the range of frequencies specified in Analysis of Receiving Drainage System - Table 7. The results will serve as an input to the analysis.
Bridge analysis is used to calculate the headwater level upstream of a bridge based on the flow rate and bridge characteristics. Refer to Components of the Receiving Drainage System - Table 6 for the bridge characteristics that are required to complete the bridge analysis. Refer to the DMM, Chapter 5, page 17 and Chapter 8 page 134, for details on bridge analysis.
The Two basic methods of bridge analysis are:
hand calculations using the equation presented in the discussion below; or
using computer program such as HEC2 or HEC-RAS.
When analysing a bridge structure, the flow through the bridge should be checked for the following cases:
Constricted open channel flow occurs when channel flow is conveyed through a bridge cross-sectional flow area that is less than the stream channel cross-sectional area immediately upstream. The result can be an increase in elevation of the water surface profile upstream of the structure. The head loss at a waterway may be expressed as:
hT = [ KT a2 + a1 {(A2 / A4)2 - (A2 / A1)2}] * [V22/2g]
hT = Total head loss, m
A = Cross-section area perpendicular to flow, m2
a = Velocity head coefficient
V2 = Velocity at entrance, m/s
KT = Total loss coefficient
KT = Kb + Kp + Ke + Ks
Kb = Base coefficient
Kp = Pier coefficient
Ke = Eccentricity coefficient
Ks = Skew coefficient
The number subscripts refer to the section locations. For a subcritical flow analysis, the calculation should start from the downstream end and proceed upstream. Refer to the DMM, Chapter 5 Page 12, for more details.
Pressure flow can occur when the water surface profile is above the maximum soffit elevation on the upstream side of the bridge. A difference in head must exist between the water surface elevations at the upstream and downstream faces of the structure, to force the flow of water, under pressure, through the waterway opening.
Where a bridge soffit is fully submerged, pressure flow, Qp, through waterway openings, may be analyzed using the following equation:
Qp = Cd * A * (2gH)0.5
Qp = flow rate, m3/s
Weir flow occurs if there is relief flow above the top of the roadway. Refer to the DMM, Chapter 3 page 27, for a discussion on relief flow.
Assuming that the roadway performs like a broad-crested weir, using the following equation:
Qw = C * L * H1.5
Qw = Weir discharge, m3/s
L = Length of weir, m
H = Height of upstream water surface above weir crest, m
Refer to the DMM, Chapter 5 page 12 for more details.
Computer models accepted by MTO are HEC2/HEC-RAS and WSPRO. Refer to Computer Model Characteristics for more information on these models. The user manuals of these models should be consulted for details on their application. Other models, not mentioned in this document or the DMM, may be used provided it can be demonstrated, through independent recognised references, that these methods are in agreement with the principles outlined in the DMM.
Checking Bridge Capacity
Where the capacity of the highway bridge is being checked, the analysis need only be completed for the design flow frequency.
Where headwater levels or flow velocities are being determined for the range of flow rate frequencies specified in Analysis of Receiving Drainage System - Table 7, a separate bridge analysis should be completed for each flow rate. The results can be presented on a bridge performance curve, which plots the headwater level against the flow rate (refer to pg 144 in Chapter 8 of the DMM for more details on performance curves). Where relief flow occurs, flow over the roadway will act as a weir flow and the performance curve should reflect this condition.
Flow velocities should be determined for each of headwater levels determined in the bridge analysis. The velocity through a bridge and the exit velocity from a bridge should not result in erosion downstream of the bridge, otherwise, erosion protection should be provided. Refer to the sections Assessing Potential for Scour and Assessment Channel Erosion for more details
Open Channel analysis is completed as part of the hydraulic analysis of the receiving drainage system, for the stream channel and roadside ditch components, or it is used to check the capacity of the highway roadside ditch.
Peak flows rates are determined from the hydrologic analysis and are calculated at the upstream section of the open channel for the range of frequencies specified in Analysis of Receiving Drainage System - Table 7. The results will serve as an input to the analysis. Channel routing may be required as part of the analysis. Refer to Routing the Hydrograph through Channels and Reservoirs for more information on flow routing.
Open channels flow analysis is used to calculate the depth of flow and flow velocities in the steam channel or roadside ditch, when water is flowing under the influence of gravity with a free water surface. Refer to Components of the Receiving Drainage System - Table 6 for stream channel or roadside ditch characteristics required to complete the analysis.
The water surface elevation in an open channel can be determined using the Manning's equation or other similar method, such as the Chazy formula, if the flow is steady and uniform.
The Manning Equation is given by:
Q = (1/n) R2/3 S1/2 A
n = the Manning roughness coefficient
A= the area of the contributing catchment (m2)
R = the hydraulic radius (m2/m)
S = the channel slope (m/m)
However, due to variations in channel cross section, slope and meander pattern, uniform flow condition can not be assumed. In such cases, gradually varied flow condition will govern and backwater analysis would have to be conducted.
Backwater analysis applies the continuity and energy equations in assessing the water surface elevation at each cross-section starting from a point of known water level, which will become the starting water surface elevation.
When assessing drainage impacts, backwater analysis should be conducted for a distance upstream or downstream where there will be no appreciable difference between the pre-development and post-development water surface elevations. Refer to Hydrologic and Hydraulic Analysis of the Receiving Drainage System for further details.
Backwater analysis can be conducted either using hand calculation methods or computer models.
Hand calculations: the most widely used method for conducting backwater analysis for natural and artificial channels is the Standard Step Method. This method is based on the application of the continuity and energy equations. Refer to the "Drainage Management Manual" (MTO 1997), Chapter 8 Page 130, for a worked example on the application of this method.
Where the capacity of the highway roadside ditch is being checked, the analysis need only be completed for the
Where water surface levels or flow velocities are being determined for the range of flow rate frequencies specified in Analysis of Receiving Drainage System - Table 7, a separate analysis should be completed for each flow rate. Water surface levels, storage volume, and flow rates can be presented on stage-storage and stage-discharge curves for both the predevelopment and post-development scenario(s).
Flow velocities should be determined for each of the water levels determined in the analysis. The velocity in a stream channel or roadside ditch should not result in erosion, otherwise, erosion protection should be provided. Refer Assessing Channel Erosion for more details
If changes to a channel slope, shape or meander patterns are being considered, channel stability should be assessed. If a channel becomes unstable, it will attempt to return to an equilibrium state through the processes of aggradation and degradation. The result of these processes will be erosion or sedimentation that can occur at the immediate location of the channel or anywhere within an appreciable distance upstream or downstream. For more details, refer to the "Drainage Management Manual" (MTO 1997), Chapter 9 or to a reference on natural channel design.
An assessment of channel erosion is completed as part of the hydraulic analysis of the receiving drainage system. The purpose of the analysis is to determine if stormwater runoff discharging from the proposed land development will increase flow velocities such that erosion will occur. Erosion will occur if the lining material is inadequate to resist any increase in flow velocity.
The flow velocities calculated as part of the hydraulic analysis for culverts, bridges, open channel, storm sewers, or stormwater management detention facilities , and serve as an input to the channel erosion analysis. Refer to Components of the Receiving Drainage System - Table 6 for erosion protection characteristics that are required to complete the analysis.
The susceptibility of a channel to erosion can be assessed using one of the following methods:
maximum permissible velocity; and
maximum permissible tractive force.
The assessment of scour at a stream crossing is discussed in Assessing the Potential for Scour.
Maximum Permissible Velocity
Maximum permissible velocity is the maximum flow velocity that a channel can withstand without serious deformation of the channel bed or bank. The maximum permissible velocity depends on a number of factors including the bed material, flow depth, velocity, sediment load, channel alignment and vegetation.
When checking the lining of an existing channel the flow velocity should be less than maximum permissible velocity. When designing a channel the hydraulic radius (R) should be less than the hydraulic radius corresponding to the maximum permissible velocity calculated using the Manning equation.
Refer to the "Drainage Management Manual" (MTO 1997), Chapter 5, page 111 for design details and to Design Chart 2.17, for typical maximum permissible velocities for different lining materials.
Maximum Permissible Tractive Force
Tractive force is the shear force exerted by the flow on to the wetted channel surfaces. Tractive stress (N/m2) is the tractive force (N) per unit area (m2). If the tractive force caused by the flow is greater than the resistive forces holding the material, erosion will occur.
The tractive stress varies along the bed and sides of a channel. The following equation can be used to determine the maximum tractive stress along the bed:
= maximum tractive bed stress, N/m2
Kb = tractive force (bed) coefficient
= unit weight of water, 9810 N/m3
S = channel slope, m/m
The maximum tractive stress along the side of a channel can be calculated using the following equation:
= maximum tractive bank stress, N/m2
Kbk = tractive force (bank) coefficient
, R, S as above
Refer to the "Drainage Management Manual" (MTO 1997), Chapter 5 page 112, for more details and to Design Chart 2.25, for permissible unit tractive force values for different soil types.
Storm sewer flow analysis is typically completed to determine if stormwater runoff discharging from the proposed land development will cause the capacity of the storm sewer components to be exceeded, possibly leading to flooding of the roadway surface. The concern for MTO is the potential for surcharging of the highway storm sewer system causing flooding on the highway surface. Consequently, the capacity of the highway storm sewer system should be checked where stormwater runoff discharging from the proposed land development will discharge directly into the highway surface drainage system.
Where a storm sewer component of the receiving drainage system has been designed to convey a major storm (i.e. trunk storm sewer), the storm sewer may have to be analyzed to as part of the receiving drainage system. The purpose of the analysis is to determine if increased water surface elevations or flow velocities will be caused by stormwater runoff discharging from the proposed land development.
The storm sewer analysis must account for the fact that storm sewers are arranged as a network with flow inputs entering at multiple catchbasin or maintenance hole locations. Peak flow rates are determined as part of the hydrologic analysis and are calculated at the locations in the storm sewer system where stormwater runoff from external areas and/or the roadway surface runoff will enter the storm sewer system, for the range of frequencies presented in Analysis of Receiving Drainage System - Table 7. The results will serve as an input to the storm sewer analysis. Where the external flow is conveyed through a stream channel system or reservoir before entering the storm sewer, flow routing may be required as part of the peak flow calculation. Refer to Routing the Hydrograph through Channels and Reservoirs for more information on flow routing.
The actual flow in the storm sewer (i.e. the minor flow) will depend on the spacing of the catchbasins on the roadway surface and/or the rate at which the catchbasins will capture surface flow from external areas. The flow not captured by the catchbasins will remain on the surface and will become the major flow. To determine an accurate assessment of the storm sewer, the major and minor flow should be separated. This will be completed as part of the peak flow calculation.
For convenience, the minor flow can be assumed to be equal to the surface flow (i.e. stormwater runoff form the roadway surface and/or external areas); however this method can result in a possible over estimation of the hydraulic grade line.
Storm sewer flow analysis calculates the depth of flow and flow velocities in the storm sewer. Refer to Components of the Receiving Drainage System - Table 6 for storm sewer characteristics that are required to complete the analysis.
Water Surface Elevation (hydraulic grade line)
To assess the impact of increased flow rates from a proposed land development on storm sewer capacity, the water surface elevation should be checked.
Storm sewers are arranged as a network with flow inputs occurring at multiple locations. In addition, friction and minor losses in the system may account for significant changes in the hydraulic grade line. Therefore, the hydraulic grade line is not necessarily parallel to the pipe slope and a hydraulic grade line analysis is conducted rather than an analysis of the water surface elevation.
In general, a hydraulic grade line analysis for storm sewers may be necessary where:
the capacity of a storm sewer system is not known;
the capacity of a storm sewer system may be limited by a backwater effect at the storm sewer outlet; or
there is a concern that stormwater runoff from the proposed land development will cause the capacity of the storm sewer system to be exceeded, and surcharge it.
Hydraulic grade line analysis applies the continuity and energy equations in assessing the hydraulic grade line at each storm sewer cross-section. It accounts for energy losses as a result of changes in storm sewer slopes, diameters and roughness, as well as, the existence of maintenance holes, catchbasins and junctions. The analysis starts from a point of known water level, and depending on whether the flow is subcritical or supercritical, the analysis proceeds up-stream or down-stream, respectively.
Friction and minor losses in the system may account for significant changes in the hydraulic grade line and should be accounted.
A storm sewer may function as:
an open channel where there is a free water surface condition in the storm sewer; or
a pressure pipe where the storm sewer is functioning in a surcharged condition.
Open Channels (free flowing condition)
Hand calculations: This method is based on the application of the Rational Method and the continuity and energy equations to determine the hydraulic grade line. Refer to the DMM, Chapter 4, Design Example 4.4, page 42, for a worked example on the application of this method. The method assumes that the storm sewer will capture all of the stormwater runoff (i.e. major and minor flows are not separated).
Computer models: The most widely used computer models accepted by MTO are as follows. All of the methods assume that the storm sewer will capture the roadway surface runoff except OTTSWWM, which can separate major and minor flows based on catchbasin capture rates.
MTO Storm Sewer Model;
SWMM/Extran;
ILLUDAS; and
Refer to the section Computer Model Characteristics for more information on these models. The user manuals of these models should be consulted for the details on their application. Other models, not mentioned in this document or the DMM, may be used provided it can be demonstrated, through independent recognised references, that these methods are in agreement with the principles outlined in the DMM.
This method is most commonly completed with the use of SWMM/EXTRAN; however this method assumes that the storm sewer captures all of the surface runoff (major and minor flows are not separated). OTTSWWM/EXTRAN can separate major and minor flows based on catchbasin capture rates.
The capacity of the highway storm sewer should be assessed for the design flow frequency.
Where a storm sewer component of the receiving drainage system conveys flow rates equal to or greater than 25 yr event (i.e. trunk storm sewer), the storm sewer should to be analyzed to as part of the receiving drainage system. In this case, the hydraulic grade line and flow velocities should be determined for the range of flow rate frequencies specified in Analysis of Receiving Drainage System - Table 7.
The exit velocity from a storm sewer should not result in erosion downstream of the storm sewer, otherwise erosion protection should be provided. Refer to the section Assessing Channel Erosion for more details.
Roadway surface flooding analysis is typically completed when stormwater runoff discharging from the proposed land development will cause the capacity of the storm sewer or roadside components to be exceeded. The concern for MTO is the safety of the travelling public: the major system drainage from an external land development and the highway should be assessed to ensure safe driving conditions on the highway for flows up to and including the regulatory event. Part of this assessment should include the identification of the major flow path from the land development site to the highway and from the highway to the receiving drainage system.
Peak flow rates are determined in the hydrologic analysis and are calculated using the frequencies presented in Analysis of Receiving Drainage System - Table 7, which will serve as an input to the analysis.
To assess the major drainage system, it is necessary to separate the roadway surface flow into major and minor hydrographs. The minor flow hydrograph is then input into a hydraulic grade line (storm sewers) or backwater analysis (roadside ditches) to determine the total depth of flow and a time history output of velocity. The major flow is used in the roadway surface analysis to determine the total depth of flow. For convenience, the minor flow can be ignored (i.e. equal to zero) however this method can result in an over estimation of the depth of flow on the roadway surface. Major and minor flow separation can be completed as part of the peak flow calculation.
Refer to Components of the Receiving Drainage System - Table 6 for roadway surface characteristics that are required to complete the analysis.
Hand calculations: assessing the major flow on a roadway surface can be done using the Manning equation.
Computer Programs: In order to use computer programs, these programs should be capable of separating the major and minor flows. OTTSWWM is one program that can perform this function. It does it by separating the flows based on catchbasin capture rates. The major system hydrograph is routed along the highway surface to determine the depth of flow. Refer to the section Computer Model Characteristics for more information on this model. The user manual of this model should be consulted for the details. Other models, not mentioned in this document or the DMM, may be applicable. However, if these models are used it has to be demonstrated, through independent recognised references, that these models are in agreement with the principles outlined in the DMM.
The capacity of the highway major system should be completed for the design flow frequency.
Where a storm sewer component of the receiving drainage system conveys flow rates equal to or greater than 25 yr event (i.e. trunk storm sewer), the major system portion of the storm sewer may have to be analyzed as part of the receiving drainage system. In this case, the depths of flow or flow velocities should be determined for the range of flow rate frequencies specified in Analysis of Receiving Drainage System - Table 7.
The exit velocity from a roadway surface should not result in erosion downstream in the receiving drainage system. Refer to the section Assessing Channel Erosion for more details.
The analysis of stormwater management detention facilities is completed as part of the hydraulic analysis of the receiving drainage system, for the stormwater management control components, or it is used to check the capacity of the highway stormwater management detention facility.
Peak flows rates are determined as part of the hydrologic analysis, and are calculated at the upstream inlet to the stormwater management detention facility for the range of frequencies specified in Analysis of Receiving Drainage System - Table 7. The resulting hydrograph(s) should be routed through the detention facility. Refer to Routing the Hydrograph through Channels and Reservoirs for more information. The analysis of the stormwater management detention facility will require the corresponding stage-storage-discharge relationship as an input.
The water surface elevations in the stormwater management detention facility will be determined from the results of the reservoir routing of the inflow hydrograph. The analysis is completed with the use of a hydrologic computer program. The storage volume and outflow rate can also be determined from the analysis.
Where the capacity of the highway stormwater management detention facility is being checked, the analysis need only be completed for the design flow frequencies.
Where water surface elevations or flow velocities are being determined for the range of flow rate frequencies specified in Analysis of Receiving Drainage System - Table 7, a separate analysis should be completed for each flow rate.
Flow velocities should be determined for the water surface elevations determined in the analysis. The exit velocity from a stormwater management detention facility should not result in downstream erosion, otherwise erosion protection should be provided. Refer to Assessing Channel Erosion for more details.
An assessment of scour is completed as part of the hydraulic analysis of the bridge or culvert. Scour may undermine the foundations of a structure, possibly leading to its failure. Particular attention should be given to the natural stream characteristics. A stream may be unstable due to meandering, degradation or aggradation.
The flow velocities calculated as part of the hydraulic analysis for culverts and bridges serve as an input to the scour analysis. Refer to Components of the Receiving Drainage System - Table 6 for culvert or bridge characteristics that are required to complete the analysis.
Scour in a stream channel is defined as the lowering and/or widening of the streambed due to erosive forces exerted by flowing water. Flowing water in a stream channel exerts force in the direction of flow on the channel boundary surface. If the boundary force due to flow exceeds the resisting force of the boundary material, bed material particles are dislodged, resulting in scour of the streambed. Refer to the "Drainage Management Manual" (MTO 1997), Chapter 5, pages 43-65 and Chapter 9 (Basic Stream Geomorphology for Highway Applications) for more information.
Types of Scour
Natural Scour: The occurrence of scour in the absence of any structural interference is commonly referred to as natural scour. A stream channel goes through progressive bank and bed scour over time due to naturally occurring flows and stream processes, resulting in sediment transport and channel adjustment.
General Scour: The local lowering of a channel bed in the vicinity of a structure waterway opening is called general scour.
Local Scour: Bed degradation that is generally localised around an obstruction, such as piers or groins is called local scour. The depth of local scour is in addition to the depths of natural or general scour in the vicinity.
Factors Affecting Channel Scour
The main purpose of completing a scour analysis is to assess the change in scour vulnerability of a stream channel bed at a water crossing and the adequacy of the existing or proposed scour protection works. When conducting a scour analysis the following are the main factors to be considered:
design flow rate;
stream characteristics, including: width, depth, slope, and meanders;
constriction/obstructions in channel;
water clarity and evidence of scour activity;
design and check flow velocity;
bed material (particle size and cohesiveness);
structure type, configuration and alignment relative to the stream channel; and
scour protection works.
Estimating General / Natural Scour
The methods for predicting scour depth are empirical and based on experience and judgement. These methods are:
the Competent Velocity Method;
the Mean Velocity Method;
the Regime Method; and
the Laursen Method.
These methods are not generalised or universally applicable. Therefore, as a minimum when assessing the scour at the bridge crossing or in a channel these methods should be used to assess the potential for scour. When assessing the applicability of the different methods, the following aspects should be considered:
various methods should be considered and the results compared;
the limitations of each method should be reviewed;
scour depths resulting from any analysis should be compared with soil stratigraphy at that depth; and
selection of the method most suited to a particular site requires experience and judgement, the results from various methods may vary.
Scour may be determined from field measurements such as probing affected areas, surveying the streambed and underwater sounding. Despite extensive research and development, methods for measuring scour in the field are not exact.
Computer Model Characteristics
Hydraulic Computer Model Characteristics
FLOW 1-D
HEC-15
Yes -	 Yes Yes -	 -	 -	 -	 Yes Yes
Gradually Varied
Yes -	 Yes Yes Yes Yes -	 Yes Yes Yes
Rapidly Varied
Yes Yes Yes Yes Yes -	 Yes Yes Yes Yes
-	 -	 -	 -	 -	 Yes Yes -	 -	 -
Yes Yes Yes Yes Yes Yes -	 Yes Yes Yes
Yes -	 -	 Yes Yes -	 Yes Yes -	 -
-	 -	 -	 -	 Yes -	 -	 -	 -	 -
-	 -	 -	 -	 Yes -	 -	 Yes -	 -
Tributary Profile
-	 -	 Yes Yes Yes Yes -	 Yes Yes Yes
-	 -	 Yes Yes Yes -	 -	 Yes -	 -
-	 -	 -	 -	 Yes -	 -	 Yes -	 Yes
-	 -	 Yes -	 Yes -	 -	 Yes -	 Yes
Bridge/Culverts
Hydrologic Computer Model Characteristics
Legend: Y - Yes; L - Low; M - Medium; H - High
OTTHYMO
OTTSWMM
SWMMIV
Watercourse/Channel
Major/Minor System
Ontario Suitability
L L M L L H M M M
M M H M M H M M H