Stable anti-floating optimization design method for stilling pool bottom plate

Abstract

The invention provides a stilling pool anti-floating stability optimization design method, which comprises the following steps: preliminarily drawing up the thickness of a bottom plate of a stilling pool according to hydrological data, design given conditions, operation requirements and the like, judging the anti-floating stability of the bottom plate, and when the specification requirements are not met, considering thickening the bottom plate of the stilling pool or arranging an anti-floating anchor rod; according to actual engineering conditions, a nonlinear mathematical model of stilling pool anti-floating anchor optimization design is constructed, the thickness of a stilling pool bottom plate, the distance between anchor rods, the depth of the anchor rods penetrating into rock and the diameter of the anchor rods are selected as design variables, the increased thickness of the stilling pool bottom plate and the increased comprehensive manufacturing cost of the anchor rods are used as objective functions, and the optimal design of the stilling pool anti-floating anchor rods is achieved. A corresponding constraint condition is established by considering an anti-floating stable design specification of the stilling pool, and an objective function approaches to an optimal solution based on an excel planning solving tool. The anti-floating standard requirement is met with the minimum cost, the anti-floating effect is guaranteed, and then the purposes of the minimum work amount and the minimum cost are achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of water conservancy and hydropower engineering applications, and specifically relates to an optimization method for the bottom slab of a stilling basin. Background Technique

[0002] In the anti-floating stability calculation of a stilling basin, the conventional design method is to initially determine the thickness of the stilling basin bottom slab based on the anti-scour performance of the stilling basin. When the downstream water level is relatively high and the uplift force is large, it is often necessary to consider increasing the bottom slab thickness on the basis of the initially determined stilling basin bottom slab thickness or setting anti-floating anchor rods to solve the problem of the anti-floating stability of the bottom slab. The anti-floating anchor rods can provide a certain anchoring force by anchoring into the foundation rock mass to a certain depth. The increment value of the stilling basin bottom slab thickness, the diameter of the anchor rods, the row and spacing of the anchor rods, and the depth of the anchor rods anchoring into the rock mass need to be determined through manual trial calculations. However, due to the existence of four variables, many previous designs did not conduct detailed enough trial calculations, and the four parameters determined were not optimal, thus greatly increasing the construction difficulty of the project and pushing up the project cost. Summary of the Invention

[0003] In view of this, the present invention provides an optimization design method for the anti-floating stability of a stilling basin bottom slab, constructs a mathematical model based on the actual engineering problems, and uses a mathematical programming solution method to determine the optimal solutions for the increment value of the stilling basin bottom slab thickness, the diameter of the anchor rods, the row and spacing of the anchor rods, and the depth of the anchor rods anchoring into the rock mass. The present invention meets the requirements of the anti-floating code with the least cost, ensures the anti-floating effect, and thus realizes the problems of the smallest amount of work and the least cost.

[0004] The specific technical solution is as follows:

[0005] An optimization design method for the anti-floating stability of a stilling basin bottom slab, by adjusting the bottom slab thickness, as well as the spacing, depth, and diameter of the anti-floating anchor rods, with the goal of minimizing the comprehensive cost and the anti-floating stability of the stilling basin meeting the design specifications as the constraint conditions, thereby obtaining the optimal solutions.

[0006] Further, the objective function includes two parts: the cost generated by the increase in the bottom slab thickness, and the cost generated by setting the anti-floating anchor rods.

[0007] Further, the design variables of the objective function are the stilling basin bottom slab thickness x1, the spacing of the anti-floating anchor rods x2, the depth of the anti-floating anchor rods penetrating into the rock x3, and the diameter of the anti-floating anchor rods x4.

[0008] Further, the anti-floating stability of the stilling basin is characterized by the anti-floating stability safety factor of the bottom slab.

[0009] Further, the generalized reduced gradient method is used to solve the optimal solutions.

[0010] Furthermore, according to the hydrological data, the given design conditions and the operation requirements, the thickness of the stilling basin floor is preliminarily determined in combination with the anti-scour requirements of the stilling basin; the anti-floating stability of the floor is calculated based on the preliminarily determined thickness of the stilling basin floor, and when the specification requirements are not met, an optimized design is carried out.

[0011] Beneficial effects

[0012] 1. Compared with the prior art, the present invention constructs a mathematical model based on the actual engineering problems, and makes the objective function approach the optimal solution under the constraint conditions that the stilling basin floor meets the anti-floating stability requirements of the design specifications by using the mathematical programming solution method.

[0013] 2. The present invention avoids the repeated and complicated manual trial calculation process, and greatly improves the efficiency.

[0014] 3. The present invention not only solves the anti-floating technical problems and ensures the anti-floating technical effects, but also realizes cost control, optimizes the thickness of the stilling basin floor and the engineering quantity of the anchor bolts, and saves the engineering cost. Description of the drawings

[0015] Figure 1 、Elevation view of the stilling basin;

[0016] Figure 2 、Flow chart of the method of the present invention;

[0017] Wherein, 1 - stilling basin floor; 2 - anchor bolt; 3 - thickness of the stilling basin floor; 4 - spacing of anchor bolts; 5 - depth of the anchor bolt penetrating into the rock; 6 - diameter of the anchor bolt. Specific embodiments

[0018] According to the hydrological data, the given design conditions and the operation requirements, the present invention preliminarily determines the thickness of the stilling basin floor in combination with the anti-scour requirements of the stilling basin; calculates the anti-floating stability of the floor according to the preliminarily determined thickness of the stilling basin floor, and when the specification requirements are not met, considers thickening the stilling basin floor or setting anti-floating anchor bolts; according to the actual engineering situation, constructs a non-linear mathematical model for the optimized design of the anti-floating anchor bolts of the stilling basin, selects the thickness of the stilling basin floor, the spacing of the anchor bolts, the depth of the anchor bolt penetrating into the rock, and the diameter of the anchor bolt as the design variables, takes the comprehensive cost of the increased thickness of the stilling basin floor and the anchor bolts as the objective function, and establishes corresponding constraint conditions considering the stable design specifications of the anti-floating of the stilling basin, and makes the objective function approach the optimal solution based on the Solver tool of excel.

[0019] The specific steps are as follows:

[0020] The first step: Collect the hydrological data of the dam site area, including the design flood standard and the water level-discharge relationship under various working conditions.

[0021] The second step: According to the hydrological data and the operation requirements, preliminarily determine the thickness of the stilling basin floor according to the anti-scour of the stilling basin.

[0022] Step 3: Calculate the anti-floating stability of the stilling basin floor according to the preliminary design. When the requirements of the specification are not met, consider thickening the stilling basin floor or setting anti-floating anchor rods for design.

[0023] Step 4: Construct a non-linear mathematical model for the optimization design of the anti-floating stability of the stilling basin floor.

[0024] (1) Selection of design variables

[0025] As shown in the attachment Figure 1 Select the thickness x1 of the stilling basin floor, the spacing x2 of the anti-floating anchor rods, the depth x3 of the anti-floating anchor rods into the rock, and the diameter x4 of the anti-floating anchor bars as design variables.

[0026] (2) Establishment of the objective function

[0027] The objective function consists of two parts: one is the cost generated by increasing the thickness of the floor, and the other is the cost generated by setting anti-floating anchor rods.

[0028]

[0029] In the formula:

[0030] A is the area of the stilling basin floor, with the unit of ㎡;

[0031] d is the thickness of the stilling basin floor preliminarily determined according to the anti-scour requirements;

[0032] n is the number of anti-floating anchor rods;

[0033] ρ is the steel density of the anti-floating anchor rods;

[0034] λ is the ratio of the unit price of per cubic meter of concrete to the unit price of per ton of steel fabrication and installation;

[0035] (3) Constraint conditions

[0036] The constraint conditions are anti-floating stability constraints, specifically as follows,

[0037]

[0038] In the formula: P1 is the self-weight of the stilling basin floor, with the unit of KN;

[0039] P2 is the time-averaged pressure on the top surface of the stilling basin floor, with the unit of KN;

[0040] P3 is the effective weight of the foundation when adopting anchoring measures, with the unit of KN;

[0041] Q1 is the pulsating pressure on the top surface of the stilling basin floor, with the unit of KN;

[0042] Q2 is the uplift pressure on the bottom surface of the stilling basin floor, unit: KN;

[0043] K f : Safety factor of anti - floating stability of the floor calculated

[0044] [K]: Minimum safety allowable factor of anti - floating stability of the floor specified in relevant codes

[0045] P1 = γ G x1A,

[0046] P3 = γ' R TA,

[0047]

[0048] In the formula: γ G is the unit weight of reinforced concrete, generally taken as 25 KN / m 3 ;

[0049] γ' R is the buoyant unit weight of rock mass, KN / m 3 ;

[0050] T is the effective depth of the anti - floating anchor rod anchoring foundation, m.

[0051] Step 5: Use the Generalized Reduced Gradient method as the algorithm to solve this optimization problem. The essence of this algorithm is to transform a constrained extreme - value problem into an unconstrained extreme - value problem for solution through implicit elimination of variables. This method is very convenient for solving nonlinear programming problems. Based on the Solver tool in Excel, make the objective function of the stilling basin floor approach the optimal solution under the constraint conditions of meeting stability.

Claims

1. An optimized design method for the anti-floating stability of the stilling basin floor, characterized in that: By adjusting the thickness of the bottom slab, as well as the spacing, depth and diameter of the anti-floating anchor rods, with the goal of minimizing the comprehensive cost and with the anti-floating stability of the stilling basin meeting the design specifications as the constraint condition, an optimal solution is obtained to meet the anti-floating stability requirements.

2. The anti - floating stability optimization design method for the stilling basin floor according to claim 1, characterized in that: The objective function consists of two parts: the cost generated by the increase in the thickness of the bottom slab and the cost generated by setting the anti-floating anchor rods.

3. The anti-floating stability optimization design method for the stilling basin floor according to claim 1 is characterized in that: The design variables of the objective function are the thickness x1 of the stilling basin bottom slab, the spacing x2 of the anti-floating anchor rods, the depth x3 of the anti-floating anchor rods penetrating into the rock, and the diameter x4 of the anti-floating anchor rods.

4. The anti - floating stability optimization design method for the stilling basin floor according to claim 1, characterized in that: The anti-floating stability of the stilling basin is characterized by the anti-floating stability safety factor of the bottom slab.

5. A method for optimizing the anti-floating stability design of a stilling basin floor according to claim 1, characterized in that: The generalized reduced gradient method is used to solve the optimal solution.

6. A method for optimizing the anti - floating stability design of a stilling basin floor according to any one of claims 1 - 5, characterized in that: According to the hydrological data, the given design conditions and the operation requirements, and in combination with the anti-scour requirements of the stilling basin, the thickness of the stilling basin bottom slab is preliminarily determined; the anti-floating stability of the bottom slab is calculated based on the preliminarily determined thickness of the stilling basin bottom slab, and when the requirements of the specifications are not met, an optimized design is carried out.

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