Optimal design model of gravity dam
There are three elements in optimizing structural design, namely design variables, objective functions and constraints.
design variable
Design variables are quantitative descriptions of design schemes. The section shape of gravity dam is determined by dam height, dam crest width, upstream and downstream breakpoint positions and upstream and downstream dam slopes. For a given project, generally speaking, the dam height is known, the width of dam crest is determined by traffic or structural requirements, and the location of downstream breakpoint is determined by construction and structural requirements. Assume that the upstream dam slope is controlled by x 1, the downstream dam slope is controlled by x2, and the upstream breakpoint is controlled by x3. Therefore, in this paper, the shape of gravity dam section x 1, x2 and x3 are taken as design variables.
The single-width dam section of gravity dam is selected in this optimization design, and the main loads considered are: dead weight, uplift pressure, water pressure and sediment pressure.
objective function
The cost of gravity dam mainly depends on the amount of work on dam coagulation. The unit dam section (the same as the following calculation) is taken as the research object, and the objective function is the cross-sectional area, that is,
(2)
Where: A(x) is the cross-sectional area of the non-overflow gravity dam; H is the height of gravity dam; B0 is the width of dam crest; X 1, x2 and x3 are the control parameters of upstream dam slope, downstream dam slope and upstream breakpoint respectively.
Constraint condition
Geometric constraint
(1) Upstream dam slope. According to the design code for gravity dams, the upstream dam slope range of this optimization is 0 ~ 0.5, that is, 0≤x 1≤0.5(H-x3).
(2) downstream dam slope. According to the design code of gravity dam, the downstream dam slope range of this optimization is 0.5 ~ 0.9, that is, 0.5h ≤ x2 ≤ 0.9h.
(3) The location of the upstream breakpoint. According to the design code of gravity dam, the upstream can be vertical or inclined, so 0 ≤ x3 ≤ h.
Sexual constraint
(1) stress constraints. In the design of gravity dams, generally speaking, it is easy to satisfy that the compressive stress at the toe of the dam is less than the allowable value. Even high dams can be solved by adding concrete marks, and the stress at dam heel should meet the specifications. According to the design code of gravity dam, the normal stress σ after the uplift pressure of dam heel (taking the compressive stress as positive) should be considered, and the normal stress σC at the breakpoint c should meet the following requirements:
(2) Anti-sliding stability constraint. According to the design code of gravity dam, the shear strength formula is used to calculate:
Mathematical model for optimal design of gravity dam section
To sum up, the mathematical model of gravity dam section optimization design is:
solution method
Comparison of this optimization design with other optimization designs.
In order to verify the best design, we will now compare them. The design data are as follows: the known dam height 1 10m in the non-overflow section of gravity dam, the calculated water level of 95m (the elevation of dam foundation surface is 0m), the downstream water level of 5.0m, the dam crest width of 7m and the downstream starting point elevation of100m; ; The bulk density during condensation is 24kN/m3；; ; The volume density of water is10kn/m3; The elevation of sediment is 30m, the floating density is 8kN/m3, and the internal friction angle of silt is 20; The uplift pressure reduction coefficient α at the drainage curtain is 0.3, and the distance from the dam heel is 8m. The shear friction coefficient of dam foundation contact surface is 0.7, which allows the safety factor of anti-sliding stability.
It can be concluded that the optimization results in this paper are good, the stress on dam heel and dam site is small, and the cross-sectional area is also small, which can save 12. 1% of the engineering quantity. By comparison, it shows that the optimal design in this paper is more universal.
label
In a word, the optimization design results show that the obtained optimization design scheme of cross-sectional area saves 12. 1% of the engineering quantity. Therefore, the optimization design method and software described in this paper have good engineering practicability and important reference value for the optimization design of similar projects in the future.
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