OPTIMAL DESIGN OF BARRAGE ON PERMEABLE FOUNDATION

Abstract

In irrigation engineering barrage is the most exten sively used hydraulic structure for diversion of river flow. A barrage founded on porous medium is designed for surface and sub-surface flow conditions. For given surface flow criteria, the cost of the apron can be minimized with respect to sub-surface flow consideration. The pressure distribution under the floor, which depends on the length and geometry of the floor and depth of sheet piles, governs the quantity of concrete in the floor. A large number of combinationeof total floor length and sheet pile depth are possible for the same value of the safe exit gradient, out of which one will be the optimal. To arrive at the economical design, several trials involving lengthy computations are necessary. To obviate this lengthy procedure, optimisation techniques can be used to arrive at the economical dimensions of barrage structure. The thesis embodies the studies for optimal design of barrage floor founded on porous medium from sub-surface flow consideration. The scope and nature of work undertaken is presented in Chapter-1. This is followed by a literature review in Chapter-2, which embraces shape of scour observed downstream of hydraulic structures, the pertinent theory of seepage for flow under a weir and application of optimisation tech nique to design of barrage floor system. (xiii) For optimal design of barrage floor system, precise knowledge of exit gradient distribution on the downstream side and pressure distribution under the barrage floor, is essential. The safe exit gradient adopted for design pur poses dep.nds upon the grain size distribution of foundation soil. The soil particles at the downstream boundary of flow domain move when the exit gradient approaches the critical value. For ordinary soil met in practice the value of cri tical gradient is about 1.0. However, the recommended safe exit gradient varies from 1/k for barrage founded on boulder stratum to 1/7 when foundation soil is fine silt. Such low values of exit gradient have been recommended due to igno rance about distribution of true exit gradient when the downstream bed is subjected to scour. Solution to the seepage flow under a weir when the downstream bed has been subjected to scour is not available in literature. Chapter-3 deals with flow under a flat bottom weir, resting, on porous medium of infinite depth with segmental circular scour on the downstream. By making use of inversion rule, the flow domain comprising of straight lines and segnvantal circular boundary passing through a point has been converted to a domain consisting of straight lines only. Subsequently Schwarz-Christoffel conformal mapping technique ha.s been used to arrive at the solution. Numerical results are presented for pressure under the apron and exit gradient distribution on the downstream side for various length of the weir and scour. (xiv) In Chapter-^, the problem of seepage flow under a horizontal weir resting on isotropic porous medium of infinite depth with a vertical sheet pile at the toe, and a circular segmental scour commencing from the downstream end of the apron has been analysed, by making use of inver sion rule and Schwarz-Christoffel conformal mapping tech nique. The analysis is exact for semi-circular scour and approximate for segmental circular scour. The distribution of exit gradient on the downstream side has been studied for various depths and lengths of scour. The results for pressure at salient points under the weir have also been given. Chapter-5 deals with flow under a flat bottom weir resting on porous medium of infinite depth with a vertical sheet pile at the toe and aerofoil scour commencing from the downstream end of the apron. An aerofoil is defined uniquely by its area, chord length, maximum ordinate and location of the maximum ordinate. Using these parameters and the Joukowski's equation the corresponding circle'has been found out. The shape of the hydraulic structure in the transformei plane, where the aerofoil becomes a circle does not change appreciably. Using the inverse rule, and Schwarz-Christoffel transformation an approximate solution has been obtained. Numerical results are presented for pressure under the apron and exit gradient distribution on the downstream side for various length of the weir and scour. (xv; The barrage floor generally met in practice com prises of horizontal apron with an inclined step and two vertical sheet piles located at its ends. This configura tion is quite close to a sloping floor with two vertical sheet piles. The solution to flow under a sloping weir with two vertical sheet piles has not been reported so far. In Chapter-6, problem of seepage flow under a slop ing weir with two vertical unequal sheet piles located at the ends of the floor, resting on porous medium of infinite depth, has been analysed by making use of Schwarz-Christo ffel transformation. The analysis quantifies the pressures at the salient points under the sloping floor and the maxi mum exit gradient at the downstream end of the apron. The analysis has been made use of for the optimal design of the sloping weir. Chapter-7 deals with the optimal design of a sloping weir resting on porous me :lium of infinite depth with two unequal vertical sheet piles. Univariate direct search tech nique has been used for arriving at the optimal dimension of the barrage profile. For specified values of head causing seepage, the safe exit gradient, the difference in elevation of upstream and downstream ends of the floor, the depth of upstream floor, the quantity of concrete in upstream flank walls per unit length, the waterway of the barrage, and length of the floor downstream of the gate line, the unique combination of the floor length and depth of upstream and downstream sheet pile for which the (xvi) cost of barrage floor is minimum, is found out. The variation of the optimal cost with the safe exit gradient has been studied. The results show that the value of the specified safe exit gradient greatly influences the optimal cost of the structure. The important conclusions drawn on the basis of investiga.tions reported in the thesis have been given in Chapter-8.