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Finite Depth Seepage Below Flat Apron with End Cutoffs and a Downstream Step

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Finite Depth Seepage Below Flat Apron with End Cutoffs and a Downstream Step University of Central Florida STARS Electronic Theses and Dissertations, 2004-2019 2011 Finite Depth Seepage Below Flat Apron With End Cutoffs And A Downstream Step Arun K. Jain University of Central Florida Part of the Engineering Commons Find similar works at: https://stars.library.ucf.edu/etd University of Central Florida Libraries http://library.ucf.edu This Doctoral Dissertation (Open Access) is brought to you for free and open access by STARS. It has been accepted for inclusion in Electronic Theses and Dissertations, 2004-2019 by an authorized administrator of STARS. For more information, please contact [email protected]. STARS Citation Jain, Arun K., "Finite Depth Seepage Below Flat Apron With End Cutoffs And A Downstream Step" (2011). Electronic Theses and Dissertations, 2004-2019. 1853. https://stars.library.ucf.edu/etd/1853 FINITE DEPTH SEEPAGE BELOW FLAT APRON WITH END CUTOFFS AND A DOWNSTREAM STEP by ARUN K. JAIN B.E. University of Jodhpur, 1990 M.E. J.N.V. University, 1995 A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Civil, Environmental, and Construction Engineering in the College of Engineering and Computer Science at the University of Central Florida Orlando, Florida Summer Term 2011 Major Professor: Lakshmi N. Reddi Arun K. Jain ii ABSTRACT Hydraulic structures with water level differences between upstream and downstream are subjected to seepage in foundation soils. Two sources of weakness are to be guarded against: (1) percolation or seepage may cause under-mining, resulting in the collapse of the whole structure, and (2) the floor of the apron may be forced upwards, owing to the upward pressure of water seeping through pervious soil under the structure. Many earlier failures of hydraulic structures have been reported due to these two reasons. The curves and charts prepared by Khosla, Bose, and Taylor still form the basis for the determination of uplift pressure and exit gradient for weir apron founded on pervious soil of infinite depth. However, in actual practice, the pervious medium may be of finite depth owing to the occurrence of a clay seam or hard strata at shallow depths in the river basin. Also, a general case of weir profile may consist of cutoffs, at the two ends of the weir apron. In addition to the cutoffs, pervious aprons are also provided at the downstream end in the form of (i) inverted filter, and (ii) launching apron. These pervious aprons may have a thickness of 2 to 5. In order to accommodate this thickness, the bed adjacent to the downstream side of downstream cutoff has to be excavated. This gives rise to the formation of step at the downstream end. Closed form theoretical solutions for the case of finite depth seepage below weir aprons with end cutoffs, with a step at the downstream side are obtained in this research. The parameters studied are : (i) finite depth of pervious medium, (ii) two cut offs at the ends, and (iii) a step at the downstream end. iii The resulting implicit equations, containing elliptic integrals of first and third kind, have been used to obtain various seepage characteristics. The results have been compared with existing solutions for some known boundary conditions. Design curves for uplift pressure at key points, exit gradient factor and seepage discharge factor have been presented in terms of non- dimensional floor profile ratios. Publications resulting from the dissertation are: 1. Jain, Arun K. and Reddi, L. N. “Finite depth seepage below flat aprons with equal end cutoffs.” (Submitted to Journal of Hydraulic Engineering, ASCE, and reviewed). 2. Jain, Arun K. and Reddi, L. N. “Seepage below flat apron with end cutoffs founded on pervious medium of finite depth.” (Submitted to Journal of Irrigation & Drainage Engineering, ASCE). 3. Jain, Arun K. and Reddi, L. N. “Closed form theoretical solution for finite depth seepage below flat apron with equal end cutoffs and a downstream step.” (Submitted to Journal of Hydrologic Engineering, ASCE). 4. Jain, Arun K. and Reddi, L. N. “Closed form theoretical solution for finite depth seepage below flat apron with end cutoffs and a downstream step.” (Submitted to Journal of Engineering Mechanics, ASCE). iv I dedicate this dissertation to God Almighty Who has provided me with the strength and motivation to carry on this work My father, Prof. Bal Chandra Punmia Who has been my role model and inspiration to achieve my goals My mother, Kewal Punmia Who has dedicated her life bringing the best in me My wife, Smita Jain Who has encouraged me throughout this work and otherwise and My brother, Ashok K. Jain Who has been taking care of me in all ups and downs of life. v ACKNOWLEDGMENTS I would like to express my deepest appreciation to the Committee Chair Professor Lakshmi Reddi for this guidance, support, and insight throughout the research work. I also thank him for his philosophical guidance and personal attention to re-build my strengths, through the difficult period I went through. Thanks go out to the other committee members, Dr. Manoj Chopra, Dr. Scott Hagen, and Dr. Eduardo Divo for their suggestions and comments. I convey my thanks and appreciation to my family and friends for their understanding, encouragements, and patience. I would like to mention some who have helped me immensely – Rupesh Bhomia, Michel Machado, Mrs. Padma Reddi, Mrs. Kiran Jalota, Justin Vogel, Laxmikant Sharma, Shantanu Shekhar, Mool Singh Gahlot, Juan Cruz and Chandra Prakash Shukla. I would also like to thank Dr. Rose M. Emery, who has been one of the biggest supports during the most difficult times of this study. I thank my son, Aseem Jain for his co-operation and patience. I extend my thanks to Indian Student Association – UCF, and Jain Society of Central Florida, Altamonte Springs and Nurses and doctors at Florida Cancer Institute, Orlando for their everlasting care. Last but not least, I am thankful to all colleagues, staff and faculty in the Civil, Environmental, & Construction Engineering department who made my academic experience at the University of Central Florida a memorable, valuable, and enjoyable one. vi TABLE OF CONTENTS LIST OF FIGURES ....................................................................................................................x LIST OF TABLES ...................................................................................................................xvi CHAPTER 1 INTRODUCTION .................................................................................................1 1.1 General ..............................................................................................................................1 1.2 Early Theories ...................................................................................................................2 1.2.1 The Hydraulic Gradient Theory .................................................................................2 1.2.2 Bligh’s Creep Theory ................................................................................................2 1.2.3 Lane’s Weighted Creep Theory .................................................................................3 1.2.4 Work of Weaver, Harza and Haigh ............................................................................4 1.3 Methods of Analysis ..........................................................................................................5 1.3.1 Finite Difference Method (FDM) ..............................................................................6 1.3.2 Finite Element Method (FEM) ..................................................................................7 1.3.3 Boundary Element Method (BEM) ............................................................................9 1.3.4 Software Packages .................................................................................................. 11 1.3.5 Method of Fragments .............................................................................................. 12 1.3.6 Closed Form Analytical Solutions ........................................................................... 12 1.3.6.1 Khosla’s Analysis .......................................................................................... 14 1.3.6.2 Work by Pavlovsky and other Russian Workers............................................. 14 1.3.6.3 Confined Seepage Research by others ........................................................... 15 1.4 Scope of Present Investigations ...................................................................................... 16 CHAPTER 2 FLAT APRON WITH EQUAL END CUTOFFS ................................................. 18 2.1 Introduction ..................................................................................................................... 18 vii 2.2 Theoretical Analysis ........................................................................................................ 18 2.2.1 First Transformation ................................................................................................ 21 2.2.2 Second Transformation ........................................................................................... 29 2.3 Computations .................................................................................................................. 35 2.4 Design Charts .................................................................................................................. 45 2.5 Comparison with Infinite Depth Case .............................................................................
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