Variations in boundary shear stress in sand bed channels subjected to seepage

Abstract

Field channels are invariably subjected to seepage across the perimeter of their cross sections. Therefore, it is necessary that the effect of seepage be understood clearly, as it may form an important factor to account for in channel design. However, the procedures presently available for the design of stable channels do not take into account the effects of seepage explicitly. It is hoped that a rational methodology will eventually be developed through an extensive investigation of the effect of seepage on the stability of erodible channels in course of time. In this direction, there have been some recent investigations on the seepage effects on channel beds. The present status of work in this area is still far from the desired degree necessary to come up with any general conclusions. The present study was undertaken to enlarge the available database under different flow conditions and to offer alternate methods of analysis to determine qualitatively and quantitatively the relationships describing the effect of seepage on channel beds under controlled conditions in the laboratory. Uniform crushed quartz of 0.80 mm and 0.53 mm sizes was used to form sand beds in the present experimental investigation. The experimental setup has facilities to apply seepage out of the channel (suction) as well as into the channel (injection) perpendicular to the sand bed in a rigid walled flume. The study was made for two conditions of the bed: one, when the bed was below the condition for incipient motion of bed material, and the other, when the bed was transporting sediment. The flow in the open channel with seepage applied perpendicular to the bed is a spatially varied flow. Accordingly, spatially varied flow equations were used to analyse the experimental data collected in the study for the two sand sizes (0.80 mm and 0.53 mm). Also, results are available from a previous study on 0.335 mm sand based on uniform flow analysis. To compare the results of this study with the present investigation, the experimental data were analysed using uniform flow equations also. The effect of seepage was analysed based on the initial condition in the channel and the rate of seepage applied on the bed. A comparison of the average of the ratios of shear stresses with and without seepage, computed from spatially varied flow analysis for the 34 sections along the main channel, and from uniform flow analysis treating the entire channel as a single reach, showed that there is no significant change between the two types of analyses. When the bed was below the condition for incipient motion of bed particles, the difference was within 5 percent of the mean value of the ratio of shear stresses with and without seepage, obtained from the spatially varied flow analysis. The ratios of the bed shear stresses with and without seepage computed from spatially varied flow and uniform flow analyses agreed with each other within 8 percent (of the value computed by spatially varied flow analysis) when the bed was under transporting condition. It was found from the present study that when the bed was below the condition for incipient motion of bed particles, seepage out of the channel (suction) decreases the bed shear stress, whereas seepage into the channel (injection) increases the bed shear stress compared to the bed shear stress for the no seepage condition. The relative change in the bed shear stress due to seepage depends on the initial flow condition in the channel and the rate of seepage applied. The initial flow condition in the channel is expressed as the ratio of the bed shear stress under no seepage condition to the critical shear stress corresponding to the bed material used. The ratio of the bed shear stress with and without seepage ( s / ) is expressed as a function of the ratio of the bed shear stress under no seepage condition to the critical shear stress corresponding to the bed material size ( / c), and the non dimensional seepage velocity expressed as vs / ( g y ), where vs is the applied seepage velocity and y is the average value of the initial depth of flow in the channel. The size of the bed material is thus accounted for implicitly in the critical bed shear stress. The functional relationship was defined based on the experimental data for the sand sizes tested. This gives a quantitative estimate of the change in the bed shear stress due to the applied seepage. The results show that the relative change in bed shear stress decreases as the flow condition approaches the incipient condition for movement of bed particles in suction. In the case of injection, the relative bed shear stress increases at a decreasing rate as the flow condition approaches the incipient condition for movement of bed particles. When the initial flow condition is very close to and below the critical condition for particle movement, the effect of seepage in changing the bed shear stress is found to be insignificant. When the bed was under transporting condition, it is found that suction causes an increase in the bed shear stress when compared to the no seepage condition, as long as the bed material concentration is less than a characteristic value termed as the critical concentration in the present study. In this range, the relative change in bed shear stress due to suction decreases with increase in the concentration, and as the concentration approaches the critical value, the effect of suction decreases and becomes negligible. The boundary shear stress is found to decrease with suction at concentrations higher than the critical concentration. The rate of change in the boundary shear stress due to suction is low at relatively lower values of bed material concentration in this range. The relative change in boundary shear stress with suction is found to be a function of initial flow condition and rate of seepage applied. The initial condition is defined by the inverse ratio of the bed material concentration to critical concentration (Xc / X). The rate of seepage applied is defined by vs / ( g y ), where vs is the seepage velocity perpendicular to the bed and y is the average value of the initial depth of flow in the channel. The ratio of the bed shear stress with and without seepage is expressed as a function of Xc / X and vs / ( g y ). The functional relationship thus developed gives a quantitative estimate of the bed shear stress due to applied rate of suction. The critical concentration is characteristic of the sediment and is found to be predominantly a function of the particle size and therefore of the critical shear stress associated with it. In the present analysis for the three sizes of sand studied, two functional relationships were developed to estimate the critical concentration: one relating to the mean grain size and the other to the critical shear stress. A total of seven Chapters comprise the thesis of the present study. Chapter I gives an introduction to the study. Chapter II presents a review of the literature on earlier studies and outlines the objectives of the present study. Chapter III describes the experimental facility and the procedures of measurements made during the experimental runs. Chapter IV gives the procedures and methodologies used in the analysis of experimental data. Chapter V presents a comprehensive analysis of the experimental data, development of relevant non dimensional parametric relationships and discussion of results. Chapter VI summarises the conclusions drawn from the present study. Chapter VII outlines the scope and suggestions for further study.