Ways and Means for Disposal of Surplus Water in Storage Reservoirs and other Irrigation and Flood Protective Works

In the paper new way of classifying spillways have been suggested. The various types, merits and demerits or existing spillway devices have been discussed. The considerations governing the choice of a design of a spillway have been mention. A criteria for working out the economics of spillway design has been suggested. An efficient surplus sing device has next been described and compared with other devices. In conclusion it has been suggested that the most efficient and at the same time economical arrangement will be a combination of devices. In conclusion it has been suggested will be a combination of crest gate, volute siphons and high head gates. The appendix gives a list of devices used in dams in various parts of the world.

Modified Proportional V-Notch Weirs

Seven different shaped modified proportional V-notches were designed and pertinent data for their use are given in tables 1 - 4. It is shown that the indication accuracies of these weirs are more than that of the conventional V-notch. For five of the designed weirs the indication accuracies are more than that of the conventional rectangular weir at lower heads of flow. All these proportional weirs, except the parabolic based weir, have added advantages over the V-notch in regard to fixing and finding the crest level. Experiments with five weirs (four symmetrical and one unsymmetrical) having rectangular bases and one (symmetrical) with a parabolic base show very good agreement with the theory and give consistent values for the coefficient of discharge, Cd, varying between 0.588 and 0.605, within the ranges of the experiments.

Seismic response of wrap-faced reinforced soil-retaining wall models using shaking table tests

This paper presents the results of shaking table tests on geotextile-reinforced wrap-faced soil-retaining walls. Construction of model retaining walls in a laminar box mounted on a shaking table, instrumentation, and results from the shaking table tests are discussed in detail. The base motion parameters, surcharge pressure and number of reinforcing layers are varied in different model tests. It is observed from these tests that the response of the wrap-faced soil-retaining walls is significantly affected by the base acceleration levels, frequency of shaking, quantity of reinforcement and magnitude of surcharge pressure on the crest. The effects of these different parameters on acceleration response at different elevations of the retaining wall, horizontal soil pressures and face deformations are also presented. The results obtained from this study are helpful in understanding the relative performance of reinforced soil-retaining walls under different test conditions used in the experiments.

On the design of quadratic weirs

This paper considers the problem of the design of the quadratic weir notch, which finds application in the proportionate method of flow measurement in a by-pass, such that the discharge through it is proportional to the square root of the head measured above a certain datum. The weir notch consists of a bottom in the form of a rectangular weir of width 2W and depth a over which a designed curve is fitted. A theorem concerning the flow through compound weirs called the “slope discharge continuity theorem” is discussed and proved. Using this, the problem is reduced to the determination of an exact solution to Volterra's integral equation in Abel's form. It is shown that in the case of a quadratic weir notch, the discharge is proportional to the square root of the head measured above a datum Image a above the crest of the weir. Further, it is observed that the function defining the shape of the weir is rapidly convergent and its value almost approximates to zero at distances of 3a and above from the crest of the weir. This interesting and significant behaviour of the function incidentally provides a very good approximate solution to a particular Fredholm integral equation of the first kind, transforming the notch into a device called a “proportional-orifice”. A new concept of a “notch-orifice” capable of passing a discharge proportional to the square root of the head (above a particular datum) while acting both as a notch, and as an orifice, is given. A typical experiment with one such notch-orifice, having A = 4 in., and W = 6 in., shows a remarkable agreement with the theory and is found to have a constant coefficient of discharge of 0.61 in the ranges of both notch and orifice.

A generalized mathematical theory and experimental verification of proportional notches

A theory and generalized synthesis procedure is advocated for the design of weir notches and orifice-notches having a base in any given shape, to a depth a, such that the discharge through it is proportional to any singular monotonically-increasing function of the depth of flow measured above a certain datum. The problem is reduced to finding an exact solution of a Volterra integral equation in Abel form. The maximization of the depth of the datum below the crest of the notch is investigated. Proof is given that for a weir notch made out of one continuous curve, and for a flow proportional to the mth power of the head, it is impossible to bring the datum lower than (2m − 1)a below the crest of the notch. A new concept of an orifice-notch, having discontinuity in the curve and a division of flow into two distinct portions, is presented. The division of flow is shown to have a beneficial effect in reducing the datum below (2m − 1)a from the crest of the weir and still maintaining the proportionality of the flow. Experimental proof with one such orifice-notch is found to have a constant coefficient of discharge of 0.625. The importance of this analysis in the design of grit chambers is emphasized.

Electrochemical reduction of Cu(II)-EDTA complex at dropping mercury electrode. An impedance approach

The study of electrochemical reduction of Cu(II)-EDTA system by phase sensitive a.c. impedance method at dropping mercury electrode reveals several interesting features. The complex plane polarograms exhibit loop like shape in contrast to the classical zinc ion reduction where crest like shape is found. Again, the relative placement of peaks of in-phase and quadrature components, and the relative placement of portions before and after the peaks of complex plane polarograms are different from that of zinc ion reduction. The complex plane plots suggest that electrochemical reduction of Cu-EDTA is charge transfer controlled.

Geometrically simple linear weirs using circular quadrants

A detailed theoretical analysis of flow through a quadrant plate weir is made in the light of the generalized theory of proportional weirs, using a numerical optimization procedure. It is shown that the flow through the quadrant plate weir has a linear discharge-head relationship valid for certain ranges of head. It is shown that the weir is associated with a reference plane or datum from which all heads are reckoned.Further, it is shown that the measuring range of the quadrant plate weir can be considerably enhanced by extending the tangents to the quadrants at the terminals of the quadrant plate weir. The importance of this weir (when the datum of the weir lies below its crest) as an outlet weir for grit chambers is highlighted. Experiments show excellent agreement with the theory by giving a constant average coefficient of discharge.

Improved Inverted V-Notch or Chimney Weir

This paper is devoted to the improvement of the measuring range of inverted V-notch (IVN) weir, a practical linear sharp-crested weir, designed earlier by the writers. The range of linearity of IVN can be considerably enhanced (by more than 200%) by the addition of a retangular weir of width 0.265W (W = half crest width) at a depth of 0.735d (d = altitude of IVN), above the crest of the weir, which is equivalent to providing at this depth two vertical straight lines to the IVN, resulting in a chimney-shaped profile; hence, the modified weir is named chimney weir. The design parameters of the weir, that is, the linearity range, base flow depth, and datum constant, which fixes the reference plane of the weir, are estimated by solving the nonlinear programming problem using a numerical optimization procedure. For flows through this weir above a depth of 0.22d, the discharges are proportional to the depth of flow measured above a reference plane situated at 0.08d above the weir crest for all heads in the range 0.22d <= h <= 2.43d, within a maximum percentage deviation of ±1.5 from the theoretical discharge. A significant result of the analysis is that the same linear head-discharge relationship governing the flow through the IVN is also valid for the extended chimney weir. Experiments with three different chimney weirs show excellent agreement with the theory by giving a constant average coefficient of discharge for each weir.

Practical constant-accuracy linear weir

This paper is concerned with the modifications of the Extended Bellmouth Weir (EBM weir) earlier designed by Keshava Murthy. It is shown that by providing inclined sides (equivalent to providing an inward-trapezoidal weir) over a sector of a circle of radius R, separated by a distance 2t, and depth d, the measurable range of EBM can be considerably enhanced (over 375%). Simultaneously, the other parameters of the weir are optimized such that the reference plane of the weir coincides with its crest making it a constant-accuracy linear weir. Discharge through the aforementioned weir is proportional to the depths of flow measured above the crest of the weir for all heads in the range of 0.5R less-than-or-equal-to h less-than-or-equal-to 7.9R, within a maximum deviation of +/-1% from the theoretical discharge. Experiments with two typical weirs show excellent agreement with the theory by giving a constant-average coefficient of discharge of 0.619

On the improvement of chimney weirs

This paper is devoted to the improvement in the range of operation (linearity range) of chimney weir (consisting of a rectangular weir or vertical slot over an inward trapezium), A new and more elegant optimization procedure is developed to analyse the discharge-head relationship in the weir. It is shown that a rectangular weir placed over an inverted V-notch of depth 0.90d gives the maximum operating range, where d is the overall depth of the inward trapezoidal weir (from the crest to the vertex). For all flows in the rectangular portion, the discharge is proportional to the linear power of the head, h, measured above a reference plane located at 0.292d below the weir crest, in the range 0.90d less than or equal to h less than or equal to 7.474: within a maximum error of +/-1.5% from the theoretical discharge. The optimum range of operation of the newly designed weir is 200% greater than that in the chimney weir designed by Keshava Murthy and Giridhar, and is nearly 950% greater than that in the inverted V-notch. Experiments with two weirs having half crest widths of 0.10 and 0.12 m yield a constant average coefficient of discharge of 0.634 and confirm the theory. The application of the weir in the design of rectangular grit chamber outlet is emphasized, in that the datum for the linear discharge-head relationship is below the crest level of the weir.

Seismic Stability and Liquefaction Analysis of Tailings Dam

Proper analysis for safe design of tailings earthen dam is necessary under static loading and more so under earthquake conditions to reduce damages of important geotechnical structure. This paper presents both static and seismic analyses of a typical section of tailings earthen dam constructed by downstream method and located at a site in eastern part India to store non-radioactive nuclear waste material. The entire analysis is performed using geotechnical softwares FLAC(3D) and TALREN 4. Results are obtained for various possible conditions of the reservoir to investigate the stability under both static and seismic loading condition using 1989 Loma Prieta earthquake acceleration-time history. FLAC(3D) analyses indicate the critical maximum displacement at crest of the proposed tailings dam section is 5.5 cm under the static loading but it increases to about 16.24 cm under seismic loading. The slope stability analyses provide the minimum value of factor of safety for seismic loading as 1.5 as compared to 2.31 for static loading. Amplification of base seismic acceleration is also observed. The liquefaction potential analysis in FLAC(3D) indicates considerable loss of shear strength in the tailings portion of the proposed earthen dam section with significantly high values of pore pressure ratio.

Stability of a long unsupported circular tunnel in soils with seismic forces

By using the lower-bound finite element limit analysis, the stability of a long unsupported circular tunnel has been examined with an inclusion of seismic body forces. The numerical results have been presented in terms of a non-dimensional stability number (gamma H/c) which is plotted as a function of horizontal seismic earth pressure coefficient (k (h)) for different combinations of H/D and I center dot; where (1) H is the depth of the crest of the tunnel from ground surface, (2) D is the diameter of the tunnel, (3) k (h) is the earthquake acceleration coefficient and (4) gamma, c and I center dot define unit weight, cohesion and internal friction angle of soil mass, respectively. The stability numbers have been found to decrease continuously with an increase in k (h). With an inclusion of k (h), the plastic zone around the periphery of the tunnel becomes asymmetric. As compared to the results reported in the literature, the present analysis provides a little lower estimate of the stability numbers. The numerical results obtained would be useful for examining the stability of unsupported tunnel under seismic forces.

Seismic response of reduced-scale modular block and rigid faced reinforced walls through shaking table tests

This paper focuses on understanding the seismic response of geosynthetic reinforced retaining walls through shaking table tests on models of modular block and rigid faced reinforced retaining walls. Reduced-scale models of retaining walls reinforced with geogrid layers were constructed in a laminar box mounted on a uniaxial shaking table and subjected to various levels of sinusoidal base shaking. Models were instrumented with ultrasonic displacement sensors, earth pressure sensors and accelerometers. Effects of backfill density, number of reinforcement layers and reinforcement type on the performance of rigid faced and modular block walls were studied through different series of model tests. Performances of the walls were assessed in terms of face deformations, crest settlement and acceleration amplification at different elevations and compared. Modular block walls performed better than the rigid faced walls for the same level of base shaking because of the additional support derived by stacking the blocks with an offset. Type and quantity of reinforcement has significant effect on the seismic performance of both the types of walls. Displacements are more sensitive to relative density of the backfill and decrease with increasing relative density, the effect being more pronounced in case of unreinforced walls compared to the reinforced ones. Acceleration amplifications are not affected by the wall facing and inclusion of reinforcement. (C) 2015 Elsevier Ltd. All rights reserved.