Use of Rational and Modified Rational Method for ... - CTR Library

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2.1.4. Summary and Important Implications for the Rational Method Application of the rational method in practice requires evaluation of the intensity-duration-frequency (IDF) information for the watershed characteristic response time. An underlying implication is that the relative frequency (probability) of runoff is the same as the relative frequency (probability) of the rainfall used in the rational method. The structure of the intensity equation used by TxDOT designers 3 is b i = (T c + d) e , (2.3) where i is the average rainfall rate (L/T ) for the rainfall averaging time, T c , (L/T ), and b, d, and e are parameters used to calibrate Equation 2.3 for a specific locale. The terms of Equation 2.3 are identical to those in the TxDOT Hydraulics Design Manual (page 5–31). The term T c in the Design Manual is referred to as the time of concentration. The event duration or averaging time is in fact a watershed characteristic and not a rainfall characteristic; yet it [T c ] is required to determine an intensity — exactly the double appearance of time Kuichling (1889) alluded to in his extensive treatise on the method. Current application of the method, as per the TxDOT Hydraulic Design Manual 4 , is 1. Determine drainage area, 2. Determine time of concentration, 3. Verify that the rational method assumptions are applicable for the situation (particularly storage and watershed size), 4. Determine e, b, and d values for desired design frequency. Alternatively use Asquith and Roussel (2004) to determine the rainfall depth for the time of concentration and desired design frequency, 5. Compute rainfall intensity, 6. Select runoff coefficients, and 7. Calculate estimated peak discharge. Steps 1, 3, 4, and 7 are straightforward. Steps 2, 5, and 6 are the crucial steps in the method, especially with the following considerations: The determination of the time of concentration is non-trivial. Determination of the time of concentration ultimately selects the rainfall intensity. The selection of runoff coefficients also is non-trivial; in part because of what these coefficients really represent, and in part because of the overall effect on the outcome their numerical value may have. The research analyzed thousands of storms in examining the behavior of rainfall-runoff. The vast majority of the storms processed are storms having comparatively high frequency (less than 2-year 3 The TxDOT Hydraulic Design Manual is available on the internet at the uniform resource locator of http: //onlinemanuals.txdot.gov/txdotmanuals/hyd/index.htm at the time of this writing. 4 http://onlinemanuals.txdot.gov/txdotmanuals/hyd/the_rational_method.htm 8
annual recurrence intervals). Recurrence intervals for most infrastructure design dependent on peak streamflow criteria are larger. Hence, the rainfall intensities processed by the researchers are likely to be comparatively small relative to the needs of a designer. 2.2. The Modified Rational Method The modified rational method (MRM) is a method to parameterize simple runoff hydrographs. The MRM produces a runoff hydrograph (and volume) while the original rational method produces only the peak design discharge. The rational method was originally developed for estimating peak discharge for sizing drainage structures, such as storm drains and culverts. The MRM, which has found widespread use in engineering practices since the 1970s, is typically used to size detention/retention facilities for a specified recurrence interval and allowable outflow rate. The MRM was developed (Poertner, 1974) with the intent of using the rational method for hydraulic structures involving storage on small watersheds. The term “modified rational method analysis” refers to “a procedure for manipulating the basic rational method techniques to reflect the fact that storms with durations greater than the normal time of concentration for a basin will result in a larger volume of runoff even though the peak discharge is reduced” (Poertner, 1974, p. 54). Under this concept, the basic hydrograph is a triangle (Figure 2.1) generated by a rainfall duration D equal to the time of concentration T c , and with a base equal to 2T c . Figure 2.1: The MRM hydrograph when duration of rainfall is equal to T c , from Wanielista and others (1997a). The MRM is based largely on the same assumptions used in the conventional rational method and is a conceptual extension of the rational method for development of runoff hydrographs (Viessman and Lewis, 2003). For the MRM a stormwater runoff hydrograph from a design storm intensity is approximated as either a triangular or trapezoidal hydrograph (depending on the relation between storm duration and time of concentration) with the peak (or plateau) discharge less than or equal to CiA, where C, i, and A have their conventional meaning. 9
Page 2 and 3: NOTICE The United States Government
Page 4 and 5: This page intentionally left blank.
Page 6 and 7: AUTHOR’S DISCLAIMER The contents
Page 8 and 9: Acknowledgements A project of the m
Page 10 and 11: 4.2 Application of the Modified Rat
Page 12 and 13: List of Figures 2.1 The MRM hydrogr
Page 14 and 15: D.5 Modeled and observed peak disch
Page 16 and 17: The modified rational method extend
Page 18 and 19: 2. Technical Aspects of the Rationa
Page 20 and 21: unoff, with a negligible amount of
Page 24 and 25: If the storm duration is equal to t
Page 26 and 27: Figure 2.4: The instantaneous unit
Page 28 and 29: the ratio of peak rate of runoff to
Page 30 and 31: in these cases strictly converts th
Page 32 and 33: 3. A Proposed Unified Rational Meth
Page 34 and 35: with the middle of the C-value rang
Page 36 and 37: 10. The intercepts of β and expone
Page 38 and 39: Limits of the Unified Rational Meth
Page 40 and 41: T ⋆ as a “travel time” is ten
Page 42 and 43: 5. Determine IU ⋆ using T L ⋆ b
Page 44 and 45: Table 3.1: Countywide values of mea
Page 46 and 47: Table 3.1: Countywide values of mea
Page 48 and 49: Table 3.2: Countywide values of sca
Page 56 and 57: Table 3.3: Countywide values of exp
Page 64 and 65: Table 3.4: Countywide values expone
Page 66 and 67: Table 3.4: Countywide values expone
Page 68 and 69: Table 3.5: Comparison of annual pea
Page 70 and 71: LATITUDE, IN DEGRESS 26 30 34 2−y
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PEAK DISCHARGE, IN CFS 0 5 10 15 20
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Figure 4.1: Subdivision X Drainage
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Figure 4.2: Depth-Duration diagram
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coefficient C as in Equation 4.1. W
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(Row 27) and the excess rainfall in
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Figure 4.6: Modified rational metho
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Figure 4.8: Modified rational metho
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this report to estimate T ∗ . Wit
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5. Summary and Conclusions This sec
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coefficients entirely). The method
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Bibliography Akan, A. O. (2002). Mo
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FHWA (1983). Urban Highway Storm Dr
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Roussel, M. C., D. B. Thompson, X.
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A. Literature Review The rational m
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Intensity (in/hr) 0 1 2 3 4 5 0 20
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storms with durations greater than
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The intent is to estimate the disch
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Figure A.3: Modified Rational Formu
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where L is a characteristic length
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Table A.1: Rational method runoff c
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Table A.1: Rational method runoff c
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Figure A.4: Runoff Coefficients for
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B. Basin Development Factor The bas
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3. Storm drains, or storm sewers
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C. The iPar Program and Parsing of
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The values for C can not be decoupl
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Figure C.2: Screenshot of custom-bu
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Figure C.3: Screenshot of output fo
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logSrhs 0.26969 0.04056 6.650 3.44e
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hook operator provides a compact no
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20 MEDIAN TIME-R (LAG TIME), IN HOU
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1 0.9 0.8 0.7 MEDIAN CR 0.6 0.5 0.4
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# print ( DDF .at.F); # print ( IDF
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the .I
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eturn ( get (x, COUNTY_NAMES ))), M
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mycol25
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D. Modified Rational Method The pur
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100.0 Cumulative Distribution (%) 8
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10000 Modeled Q p (cfs) 1000 100 1:
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10000 Modeled Q p (cfs) 1000 100 1:
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where A is the drainage area in squ
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500 Station: 08048550 DryBranch For
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10000 MRM Gamma 1:1 line Modeled Q
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