TxDOT PROJECT 0-6070: USE OF THE ... - Texas … · TxDOT PROJECT 0-6070: USE OF THE RATIONAL AND...

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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

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 =

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 =

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

CiAQ =

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 =

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.

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

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

Example

• Residential Subdivision

• Tarrant County

• New FM Road

Example Rational Method

CiAQ =

A = 112 acres

CiAQ =

Runoff Coefficient Res. Single Family Grass Com. Area Weighted C Value C = 0.36

C = 0.40

C = 0.25

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

Intensity Rainfall Depth… Tarrant Co. = 2.3”

hrxini 6.4

1min60

min303.2

CiAQ =

• Final Calculations…

cfsacxhrinxQTarrent 185)112()6.4()36.0( ==

cfsacxhrinxQLubbock 153)112()8.3()36.0( ==

cfsacxhrinxQJackson 226)112()6.5()36.0( ==

CiAQ =

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)

Intensity Rainfall Depth… Tarrant = 1.6”/10min

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

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

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.

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

Extras

3. For each recurrence interval and county, vectors of A and Q were used to compute I or “rainfall intensities of equivalence”.

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 =

Extras

2 in/hr

T* = 120 min

Extras Modified Rational Method

CiAQ =

Source: Report # 0-6070-1

TxDOT PROJECT 0-6070: USE OF THE ... - Texas … · TxDOT PROJECT 0-6070: USE OF THE RATIONAL AND...

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