TxDOT PROJECT 0-6070: USE OF THE RATIONAL AND
MODIFIED RATIONAL METHOD FOR HYDRAULIC DESIGN
Presentation by:
Matthew Wingfield P.E., CFM TxDOT San Angelo District
District Hydraulic Engineer
Presentation Outline
1. Background / Objectives
- Why was this research project important to TxDOT?
2. Procedure / Results
- The Rational Method
- The Modified Rational Method
- The proposed Unified Rational Method for Texas
3. Example Problem
4. Summary / Conclusions
Background
• Each year, TxDOT spends billions of dollars on new construction.
• TxDOT is responsible for roadway drainage and conveyance of cross-highway stream flow.
• A component of the design of these drainage systems requires the designer to estimate peak discharge for a selected frequency (probability).
• The Rational and Modified Rational Methods are 2 of several techniques commonly used calculate runoff properties.
Objectives
1. Evaluate the appropriateness of both the rational and modified rational methods,
2. Evaluate the tabulated values of the runoff coefficient (C ), and
3. Construct guidelines for TxDOT designers for selection of appropriate parameter values for Texas watershed conditions (Specifically C and tc).
Procedure
Where, Q = maximum rate of runoff (cfs),
C = Runoff coefficient,
i = avg. rainfall intensity (in/hr), and
A = Drainage area (acres).
CiAQ =
The Rational method
1. Watershed area is limited to 200 acres or less.
2. The frequency of peak discharge is the same as the frequency of the rainfall intensity.
CiAQ =Assumptions of the Rational method…
Procedure Rational Method
Time
Flow
25 year rainfall
25 year peak runoff
Procedure
Source: TxDOT Hydraulic Design Manual
Runoff Coefficient – C
• Account for watershed losses.
• Varies with topo, land use, cover, soil, and moisture content.
• Assignment is somewhat subjective.
Rational Method CiAQ =
Procedure Rational Method
CiAQ =
Analysis of the Runoff Coefficient (C )
1. Researchers compiled a table of C values from engineering literature.
2. Researchers analyzed thousands of storms in Texas from a rainfall-runoff database to determine “back-computed” runoff coefficients.
Results Rational Method
CiAQ =
Analysis of the Runoff Coefficient (C )
1. Determined that tabulated C values are consistent with the “back-computed” C values.
2. The method that the researchers prefer to calculate the C value is based off of a weighted, functionally impervious area approach.
Source: USGS SIR 2004-5041
Intensity – i
• Duration is equal to time of concentration
• Time of Concentration (tc) – when entire watershed contributes to runoff
Procedure Rational Method
CiAQ =
Results Rational Method
1. Very important to the Rational Method as it establishes the duration of the rainfall input required for the system to reach equilibrium.
2. Steeper slopes = Smaller Tc = Greater i and Q.
Analysis of Time of Concentration ( tc )
CiAQ =
Results Rational Method
1. Based on rainfall-runoff data, upper-limit is unidentifiable.
2. 200 acres was a reasonable upper-limit guideline.
3. Some flexibility in upper-limit. Areas as high as 640 acres could use method.
Analysis of the Drainage Area ( A )
CiAQ =
Procedure
• Uses same equation as in the Rational Method,
• Extends rational method produce simple runoff hydrographs.
Modified Rational Method
Modified Rational Method CiAQ =
Results Modified Rational Method
1. Conceptually, the C value for the Rational Method is different than the C value for the Modified rational Method.
2. This method will tend to overestimate total runoff volumes when using tabulated values of the runoff coefficient.
Analysis of the Runoff Coefficient (C )
CiAQ =
Results Modified Rational Method
1. Same watershed area limitations apply as in the Rational Method.
Summary of the Modified Rational Method (MRM)
CiAQ =
2. Performs about as well as other methods in predicting peak runoff and the runoff hydrograph.
Results
3. The MRM can be applied to non-uniform rainfall events.
Summary of the Modified Rational Method (MRM)
4. Volume Overestimation for smaller watersheds
Modified Rational Method CiAQ =
Objectives - Revisited
• Construct guidelines for TxDOT designers for selection of appropriate parameter values for Texas watershed conditions (Specifically C and tc).
• The frequency of peak discharge is the same as the frequency of the rainfall intensity.
Procedure
• Researchers developed an alternative to the conventional Rational Method.
– Eliminates probability adjusted and land-use based runoff coefficients.
– Provides the first tuned version of the rational method for the rainfall frequency and runoff frequency.
Unified Rational Method for Texas
Unified Rational Method for Texas (URAT) AICQ =
Procedure
1. Determine the area of impervious cover within the watershed.
C = 0.85 x IMP + 0.15
Steps for calculating C
Unified Rational Method for Texas (URAT) AICQ =
Where, IMP = Impervious cover as a fraction of watershed area
Procedure
Steps For Determining T
Where, T = Watershed time of equivalence (min),
= Regression coefficients (from tables),
A = Drainage area (acres), and
S = Dimensionless main-channel slope
,β ,α κ
Unified Rational Method for Texas (URAT) AICQ =
Example
• Residential Subdivision
• Tarrant County
• New FM Road
Example Rational Method
CiAQ =
Area
A = 112 acres
Example Rational Method
CiAQ =
Runoff Coefficient Res. Single Family Grass Com. Area Weighted C Value C = 0.36
C = 0.40
C = 0.25
Example Rational Method
CiAQ =
Intensity Time of
Concentration
Tc = 30 min
Sheet Flow = 3.9 min
Shal Conc = 9.5 min
Open Chan = 9.3 min
Open Chan = 6.6 min
Example Rational Method
Intensity Rainfall Depth… Tarrant Co. = 2.3”
hrin
hrxini 6.4
1min60
min303.2
==
CiAQ =
Source: USGS SIR 2004-5041
• Final Calculations…
Example Rational Method
cfsacxhrinxQTarrent 185)112()6.4()36.0( ==
cfsacxhrinxQLubbock 153)112()8.3()36.0( ==
cfsacxhrinxQJackson 226)112()6.5()36.0( ==
CiAQ =
Area
A = 112 acres
Example Unified Rational Method for Texas (URAT)
AICQ =
Runoff Coefficient Determine %
Impervious Area C = 0.40
AICQ =
xIMPC 85.0=15.0+
Impervious Area = 33.2 acres
Example Unified Rational Method for Texas (URAT)
Watershed time of equivalence – T
AICQ = Example Unified Rational Method for Texas (URAT)
County
Tarrant 0.049 0.226 0.814
Lubbock 0.402 0.203 0.737
Jackson 0.033 0.234 0.844
κβ α
min6.6)009.0()112()049.0( 814.0226.0* == −xxTTarrent
min7.33)009.0()112()402.0( 737.0203.0* == −xxTLubbock
25 year variables to Calculate T
min3.5)009.0()112()033.0( 844.0234.0* == −xxTJackson
• If time is less than 10 min, round up to 10 min.
AICQ = Example Unified Rational Method for Texas (URAT)
Source: USGS SIR 2004-5041
Intensity Rainfall Depth… Tarrant = 1.6”/10min
hrin
hrxini 6.9
1min60
min106.1
==
• Final Calculations…
Example
cfsacxhrinxQ Tarrant 430)112()6.9()40.0(* ==
cfsacxhrinxQ Lubbock 159)112()6.3()40.0(* ==
cfsacxhrinxQ Jackson 484)112()8.10()40.0(* ==
AICQ = Unified Rational Method for Texas (URAT)
185cfs
153cfs
226cfs
Rational Method
Summary
1. Runoff coefficient
2. Time of concentration
3. Intensity and area
Comparing the two methods…
Summary
1. The Rational and Modified Rational methods remain appropriate models for small Texas watersheds,
2. Upper limit for the drainage area in the Rational Method appears unidentifiable from analysis, could be extended from 200 to 640 acres.
3. The Modified Rational method can be used to tabulate coefficients and generate runoff hydrographs. Literature C values are on average too large by a factor of 2.
Summary
4. An alternative to the rational method was developed called the Unified Rational Method for Texas.
Conclusions / Questions
Extras
1. Researchers determined the OmegaEM ( ) parameter and mean annual precipitation for each county.
Steps For deriving T
Source: USGS SIR 2009-5087
25 year Regression Equation
Ω
Where, Q = maximum rate of runoff (cfs), P = mean annual precipitation (in),
S = dimensionless main channel slope (ft/ft),
A = Drainage area (acres), and = OmegaEM parameter (from maps). Ω
Unified Rational Method for Texas (URAT) AICQ =
Extras
2. A sequence of drainage areas (from 10 to 10,000 ac) and slopes (from 0.1 to 10) were developed to produce flow values.
Steps For deriving T
Source: USGS SIR 2009-5087
25 year Regression Equation
Where, Q = maximum rate of runoff (cfs), P = mean annual precipitation (in),
S = dimensionless main channel slope (ft/ft),
A = Drainage area (acres), and = OmegaEM parameter (from maps) Ω
Unified Rational Method for Texas (URAT) AICQ =
Extras
3. For each recurrence interval and county, vectors of A and Q were used to compute I or “rainfall intensities of equivalence”.
Steps For deriving T
Where, I = Rainfall intensity of equivalence (in/hr),
Q = flow from previous step (cfs),
C = Runoff coefficient = 0.15, A = Drainage area (acres), and
~
ACQI =
~
~
Unified Rational Method for Texas (URAT) AICQ =
Extras
Steps For deriving T
2 in/hr
T* = 120 min
Unified Rational Method for Texas (URAT) AICQ =
Extras Modified Rational Method
Analysis of the Runoff Coefficient (C )
CiAQ =
Source: Report # 0-6070-1
