التصميم الامثل للمنشآت الهيدروليكية بطريقة المحاكاة الامثلية

Optimal Design of Hydraulic Structure by Using Simulation-Optimization Method

Abstract

Hydraulic structures such as gravity dams are classified as essential structures which need to high cost to construct it and have the vital role in providing strong and safe water resource. These structures are subjected to seepage problem which is considered to be a dangerous phenomenon that may generate uplift pressure, which may cause the dam to function improperly, in addition to the exit gradient that may cause piping if exceeded a safe value.
This research illustrates the application of a new Genetic Algorithm with Finite Difference Programming (GA-FDP) technique, A MATLAB code was used to perform the GA-FDP optimization model in order to find the optimal design for safe hydraulic structure. The objective was to minimize the construction cost function. The main constraints are those that satisfy a factor of safety against uplift pressure and factor of safety against piping. The proposed GA-FDP model has fulfilled the optimum design task into two stages. Firstly, Finite difference Programming (FDP) analyzed the seepage problem numerically after verification with GeoStudio(2018 R2)SEEP/W to obtain the uplift pressure and exit gradient and to determine other characteristics such as the pressure head, total head, discharge and total cost of the structure. Also, comparing numerical model SEEP/W of calculating uplift force and exit gradient under the dam with benchmark example in soil mechanics which shows a good agreement.
Secondly, the Genetic Algorithm (GA) was applied with finite difference programming to obtain the optimum location and depth for cutoffs needed for the preliminary design of the Dam which satisfied the factors of safety against piping and up lift pressure. In FDP, the seepage problem was analyzed to define the effect of depth ,location, number of cutoffs and isotropic degree on the value of uplift force and exit gradient. The results was observed that the relative head (H/B) had a significant effect on increasing the exit gradient and uplift force. Also, minimum exit gradient was noticed when the cutoff location ratio at the downstream is of (x1/b=1) with a maximum relative depth of (d1/b=0.6), while the minimum uplift pressure was observed when the cutoff location ratio at the upstream is of (x1/B=0) with a minimum relative depth of (d1/B=0.1).
Model result revealed that when a cut-off is at the upstream, the uplift pressure is decreased along the base of floor. Also, the uplift distribution decreases with increasing the depth of cut-off because the cut-off causes an increase in the length of creep, which increases the head loss. Whenever a cut-off is located a drop in the uplift pressure at that location is observed as expected. Also, the uplift pressure starts decreasing when using different lengths of cut-offs compared with the case of no cut-off; this behavior is reversed beyond the point where x = 0.5b.
In the Genetic algorithm-finite difference programming using the constrain of input variables with differential head (H/b)= 0.25,0.5,0.75, floor-length (B)=20m, depth of impervious layer (D=30), and ratio of permeability in x to y (kx/ky = 1,2,4,8). Six various depths ratio (d/B=0.1:0.6), for each depth ratio, various cutoff locations, (b/B=0:1) were used.
It is clear that the results were which obtained from GA-FDP are the optimum solution that’s achieve the two constaints (safety against exit gradient and uplift force) with minimum cost. The optimum locations of cutoff 1(X1/B) varied from (0 to 0.33) B, (0 to 0.24)B, (0 to 0.1)B, and (0 to 0.18)B for Kr equal to(1,2,4, and 8) respectively. The optimum locations of cutoff2 (X2/B) varied from (0.875 to 1) B for various values of Kr. This behaviour is due to prevent increasing the uplift pressure and exit gradient of the structure. The optimum depth of cutoff 1(d1/B) varied from (0 to 0.35)B for Kr equal to (1, 2, 4 ) ,(0 to 0.6)B for Kr equal to 8) and the optimum depth of cutoff2 (d2/B) varied from (0.15 to 0.5) B, (0.1 to 0.6)B, (0.2 to 0.7)B, and (0.3 to 0.7) B for Kr equal to(1,2,4 8) respectively.
It was found that the optimum solution reduced the cost by 81% ,72%, 66%, 53% from the cost of traditional solutions for Kr equal to (1,2,4, and 8) respectively