Conformal mapping, Hydraulic structures, Seepage


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. iv 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 nondimensional 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).


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Graduation Date





Reddi, Lakshmi N.


Doctor of Philosophy (Ph.D.)


College of Engineering and Computer Science


Civil, Environmental, and Construction Engineering








Release Date

July 2014

Length of Campus-only Access

3 years

Access Status

Doctoral Dissertation (Open Access)


Dissertations, Academic -- Engineering and Computer Science, Engineering and Computer Science -- Dissertations, Academic

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Engineering Commons