Repository logo
 

Series expansion of the Modified Einstein Procedure

Simple item page
dc.contributor.authorShah-Fairbank, Seema Chandrakant, author
dc.contributor.authorJulien, Pierre Y., advisor
dc.date.accessioned2024-03-13T20:27:57Z
dc.date.available2024-03-13T20:27:57Z
dc.date.issued2009
dc.description.abstractThis study examines calculating total sediment discharge based on the Modified Einstein Procedure (MEP). A new procedure based on the Series Expansion of the Modified Einstein Procedure (SEMEP) has been developed. This procedure contains four main modifications to MEP. First, SEMEP solves the Einstein integrals quickly and accurately based on a series expansion. Next, instead of dividing the suspended sediment and bed material samples into particle size classes, the total sediment discharge calculation is based on a median grain size in suspension (d50ss). Thirdly, for depth-integrated samples the Rouse number (Ro) is determined directly by calculating the fall velocity (ω) based on dsoss, the shear velocity (u. = -√ghS) and assuming the value of the von Karman constant (κ) is 0.4. For point concentration measurements, the Ro is calculated by fitting the concentration profile to the measured points. Lastly, SEMEP uses the measured unit sediment discharge and Ro to determine the unit bed discharge directly. Thus, SEMEP can determine the unit bed discharge (qb), unit suspended sediment discharge (qs), unit total sediment discharge (qt), ratio of measured to total sediment discharge (qm/qt) and ratio of suspended to total sediment discharge (qs/qt).
dc.description.abstractDepth-integrated concentration measurements, for fourteen streams and rivers in the United States are tested using SEMEP. Based on an evaluation of qm/qt the results indicate that when u*/ω is greater than 5, SEMEP will perform accurately, with a coefficient of determination (R2) of 0.99, concordance correlation coefficient (pc) of 0.98 and Mean Absolute Percent Error (MAPE) of 5%. The high values of R2 and pc, and the low value of MAPE indicate that SEMEP works well. Seven of the fourteen streams and rivers were also tested using the Bureau of Reclamation Automated Modified Einstein Procedure (BORAMEP}, which resulted in a R2 of 0.65, pc of 0.74 and MAPE of 18%. BORAMEP failed to calculated total sediment discharge for over 30% of the samples due to various errors. SEMEP always calculated total sediment discharge and performed better than BORAMEP because the series expansion procedure removed empirical relationships found in the original MEP.
dc.description.abstractThe ratio of suspended sediment to total sediment discharge (qs/qt) as a function of u*/ω and relative submergence (h/ds) is determined using SEMEP. SEMEP supports a classification of the primary modes of sediment transport. It is found that that when u*/ω is less than 0.2, sediment is not transported. When u*/ω is between 0.2 and 0.5, more than 80% of the sediment moves as bed load; when u*/ω is between 0.5 and 2 the sediment transport occurs as mixed load (both as bed and suspended load]; and when u*/a> is greater than 2, more than 80% of the sediment moves as suspended load. Depth-integrated laboratory data corroborates SEMEP results and showed a high degree of variability in qs/qt for mixed loads (0.5<u*/ω<2).
dc.description.abstractFor point velocity and concentration measurements, data from one laboratory and six river measurements are used to test SEMEP. Results indicate that deeper rivers give a better estimate of total sediment discharge compared to shallow rivers. This is because shallower rivers are generally governed by bed load transport. Furthermore, if the ratio of the measured depth to the representative bed particle size (hm/ds) is greater than 1,000, the comparison between SEMEP and measurements of qt are quite accurate with an MAPE less than 25%. These point measurements are also used to explain why a deviation occurs between calculated and measured Ro. The deviation is most pronounced when the value of Ro is greater than 0.5 {u*/ω<5), due to low concentrations and measurement errors. In streams with near uniform concentration profiles, varying the value of Ro from 0.01 to 0.5 (250<u*/ω>5), the total calculated sediment discharge changes by less than 25%.
dc.description.abstractIn summary, the results indicate that SEMEP performs accurately (error less than 25%) when the value of u*/ω is greater than 5 (or Ro less than 0.5). SEMEP calculations are acceptable, but less accurate when u*/ω is between 2 to 5 (1.25>Ro<0.5). Both SEMEP and MEP should not be used when u*/ω is less than 2.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierETDF_Shah-Fairbank_2009_3374620.pdf
dc.identifier.urihttps://hdl.handle.net/10217/237953
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.rights.licensePer the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users.
dc.subjectmeasured load
dc.subjectmodified Einstein procedure
dc.subjectRouse number
dc.subjectsediment transport
dc.subjectseries expansion
dc.subjecttotal load
dc.subjectcivil engineering
dc.subjectenvironmental engineering
dc.titleSeries expansion of the Modified Einstein Procedure
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineCivil and Environmental Engineering
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
ETDF_Shah-Fairbank_2009_3374620.pdf
Size:
9.87 MB
Format:
Adobe Portable Document Format
Download

Collections

2000-2019
Theses and Dissertations