The maximum uplift reduction occurred when the distance of filter location downstream the 22 cutoff to the differential head ratio was 1. Introducing a second filter in the downstream side 23 resulted in a further reduction in the exit hydraulic gradient and in the uplift force, which 24 reached 90%. The optimum locations of the two filters occurred when the first filter was 25 placed just downstream the cutoff wall and the second filter was placed nearly at the mid-26 distance between the cutoff and the end toe of the floor. The results showed significant 27 differences between the three-dimensional (3D) and the two-dimensional (2D) analyses. 28 Keywords:Weirs; Regulators; Dams; Control structures; Mathematical modeling; 29 Intermediate filters 30Introduction 31Hydraulic structures are used to control the flow of water in rivers and canals. It is necessary 32 to minimize the uplift pressures and hydraulic gradients beneath such structures to prevent 33 2 flotation, to ensure their structural stability, and to design against soil piping and consequent 34 undermining of the structure. It is common to install cutoff walls beneath the floors of 35 hydraulic strictures to reduce the seepage flow. In addition, intermediate filters are often 36 provided in the floor of the structure as a further measure to reduce the uplift forces and exit 37 hydraulic gradients. The effectiveness of these filters in reducing uplift forces has been 38 analyzed using analytical methods. 39Conformal mapping has been used to produce exact solutions for the problem of 2D seepage 40 beneath a hydraulic structure with a flat floor having two end cutoffs and a filter located at 41 various positions in the floor (Chawla 1975;Kumar et al. 1986). Elganainy (1986) 33% as x/H varied from 1 to 6, respectively. As the ratio W/H increased, the potential for 110 uplift reduction also increased. For W/H=14, the reduction in uplift force varied from 72% to 111 35% as the ratio x/H varied from 1 to 6, respectively. For x/H =1 to 2, only slight or no 112 change was observed in the uplift force. 113The greatest reduction in the uplift force occurred when x/H=1. This is because the uplift 114 pressure is higher just downstream the cutoff than at any other point in the downstream side. 115The filter intercepts some of the streamlines and hence breaks the development of the uplift 116 The exit hydraulic gradient calculated at the center of the canal was smaller than its value at 120 the canal edge because of the water seepage through the banks. The water flows through the 121 banks at a faster rate than below the structure. This is attributed to the existence of sheet pile 122 below the floor that increases the travelling distance of the flowing water. Fig 4 shows again 123 the importance of undertaking a 3D analysis of seepage problems since the exit hydraulic 124 gradient obtained from the 2D analysis is that for the canal center. The 2D analysis also 125 disregards seepage through the canal banks. 126 Results and Discussion of Two Intermediate Filters ...
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