Arch dam abutment block safety evaluation method and device

Abstract

The invention discloses an arch dam abutment block safety evaluation method considering spatial force system decomposition, which comprises the following steps of: calculating an external load borne by an arch dam abutment block by adopting a finite element method, judging the sliding direction of the block, decomposing the external load borne by the block on a block sliding calculation spatial force system, and calculating the sliding force and the anti-sliding force of the block. And calculating a block safety coefficient, and evaluating a block safety state. According to the method, spatial force system decomposition is utilized, the block sliding force and the block anti-sliding force can be accurately decomposed to the block sliding-out direction, the numerical values and the acting directions of the block sliding force and the block anti-sliding force can be more accurately obtained, and the safety of the dam abutment block can be more accurately evaluated. The invention further provides arch dam abutment block safety evaluation equipment.

Description

Technical Field

[0001] The invention belongs to the technical field of arch dam engineering, and in particular relates to a method and equipment for evaluating the safety of an arch dam abutment block. Background Art

[0002] During the design and construction process, arch dams are usually faced with complex structural characteristics of the dam foundation and abutment rock mass, and the development of geological defects, which lead to deformation of the dam foundation and affect the stability of the dam abutment. Among them, the anti-sliding stability of the abutment resistance body is particularly prominent. It is necessary to use a variety of methods such as numerical calculations and model tests to analyze the safety of various possible unfavorable combination blocks, evaluate the dam abutment as a whole, and propose treatment measures, which provide important basis for the design, construction and operation of the project. At the same time, the stress and displacement changes of the arch dam under various working conditions are analyzed to provide suggestions for body optimization design.

[0003] At present, the main research methods for the anti-sliding stability of the dam shoulder resistance body mainly include: using the linear elastic finite element method to study the stress and deformation characteristics of the arch dam and foundation under natural and reinforced conditions, analyzing and evaluating the stress and deformation state of the dam body and foundation, and analyzing and evaluating the influence of major geological defects; using the rigid body limit equilibrium method to analyze the anti-sliding stability of the dam shoulder resistance body, providing a basis for the safety evaluation and reinforcement of potential sliding blocks; using the nonlinear finite element method to study the block stability and geological defect treatment, focusing on the stability of the block, the scope and degree of influence of the main geological defects on the project, proposing the required treatment scope of each major geological defect, and suggesting treatment measures, providing a basis for the formulation of geological defect treatment plans.

[0004] However, the above methods all use the calculation method recommended by the current specifications when evaluating the safety of the dam abutment rock mass. When calculating the sliding force and anti-sliding force of the dam abutment block, the finite element method (including the linear elastic finite element method and the nonlinear finite element method) can relatively accurately obtain the dam abutment load and force, but the direction of the force cannot be strictly calculated according to the direction of the block sliding out. There are corresponding errors when evaluating the safety of the dam abutment block, which may overestimate the size of the anti-sliding force. Therefore, it is necessary to establish a safety evaluation method for the arch dam abutment block that can consider the decomposition of the spatial force system for the finite element calculation method. Summary of the invention

[0005] The present invention aims to provide a method for evaluating the safety of arch dam abutment blocks. The method utilizes spatial force system decomposition to accurately decompose block sliding force and block anti-sliding force into the direction of block sliding out, and can more accurately obtain the numerical size and direction of action of block sliding force and block anti-sliding force, so as to more accurately evaluate the safety of dam abutment blocks.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is: a method for evaluating the safety of an arch dam abutment block, comprising the following steps:

[0007] Step 1), calculating the external load on the arch dam abutment block; the external load on the arch dam abutment block includes the arch end thrust on the arch dam abutment block, the gravity of the arch dam abutment block and the uplift pressure of the arch dam abutment block;

[0008] The calculation of the external load on the abutment block of the arch dam can be obtained by the existing finite element method calculation;

[0009] Step 2), calculating the bottom sliding surface area, side sliding surface area, detachment surface area and coordinates of any three points on each of the bottom sliding surface, side sliding surface and detachment surface of the arch dam abutment block, and obtaining the normal direction of each sliding surface through the coordinates of any three points on each surface;

[0010] The normal direction of the side sliding surface is cross-producted with the normal direction of the bottom sliding surface to obtain the direction of the intersection line of the side sliding surface and the bottom sliding surface, which is the sliding direction of the abutment block of the arch dam;

[0011] The area of ​​each side surface can be obtained by calculating the existing finite element method. The arch dam and foundation are solidly modeled in the existing finite element analysis software, and the coordinate system of each side surface is extracted from the finite element model of the arch dam.

[0012] Step 3), constructing a spatial force system for calculating the sliding of an arch dam abutment block, decomposing the external load on the arch dam abutment block in the spatial force system for calculating the sliding of an arch dam abutment block, and obtaining the components of the external load on the arch dam abutment block in three directions in the spatial force system for calculating the sliding of an arch dam abutment block;

[0013] Step 4), calculating the sliding force of the arch dam abutment block, the sliding force of the arch dam abutment block is the sum of the arch end thrust on the arch dam abutment block and the gravity of the arch dam abutment block in the direction of the intersection of the side sliding surface and the bottom sliding surface,

[0014] Calculate the anti-sliding force of the arch dam abutment block, which is the sum of the friction resistance on the side sliding surface, the friction resistance on the bottom sliding surface, the cohesion resistance on the side sliding surface and the cohesion resistance on the bottom sliding surface;

[0015] Step 5), according to the anti-sliding force of the arch dam abutment block and the sliding force of the arch dam abutment block, the safety factor of the arch dam abutment block is calculated to evaluate the safety status of the arch dam abutment block; the calculation formula of the safety factor K of the arch dam abutment block is: Wherein, F is the anti-sliding force of the arch dam abutment block, and T is the sliding force of the arch dam abutment block.

[0016] According to the embodiments of the present invention, the present invention can be further optimized. The following is the technical solution formed after optimization:

[0017] In one preferred embodiment, the specific steps of calculating the external load on the abutment block of the arch dam by the finite element method in step 1) include:

[0018] Modeling the arch dam and foundation, obtaining the finite element stress of the arch dam abutment, calculating the contact area between the arch dam abutment block and the arch dam abutment, the arch end thrust on the arch dam abutment block is the resultant force obtained by integrating the finite element stress of the arch dam abutment over the contact area;

[0019] Calculating the volume of the arch dam abutment block, and using the volume of the arch dam abutment block to calculate the gravity of the arch dam abutment block;

[0020] The uplift pressure of the arch dam abutment block is the sum of the buoyancy force and the seepage pressure on the arch dam abutment block.

[0021] The arch dam and foundation can be solidly modeled using existing finite element analysis software. The foundation contains various weak structural surfaces. The arch dam is subjected to swept meshing, the foundation is subjected to free meshing, normal constraint boundary conditions are set around the foundation model, loads are applied to the arch dam finite element model, linear elastic finite element calculations are performed, and the finite element stress of the arch dam abutment is obtained.

[0022] The contact area between the arch dam abutment block and the arch dam abutment is calculated in the existing finite element analysis software. The resultant force obtained by integrating the finite element stress of the arch dam abutment on the contact area is the arch end thrust exerted on the arch dam abutment block. The volume of the arch dam abutment block is calculated in the existing finite element analysis software, and the weight of the arch dam abutment block is calculated in combination with the design data.

[0023] In one of the preferred embodiments, in step 2), the bottom sliding surface, side sliding surface and detachment surface of the arch dam abutment block are the weak surfaces of the geological structure of the arch dam abutment.

[0024] In one preferred embodiment, in step 2), the specific steps of obtaining the normal direction of each sliding surface include:

[0025] The coordinates of any three points on the bottom sliding surface are used to obtain two coplanar vectors on the bottom sliding surface. The two coplanar vectors of the bottom sliding surface are cross-producted to obtain the bottom sliding surface normal vector, the normal vector direction points to the outside of the arch dam abutment block, and the normal line direction of the bottom sliding surface is obtained.

[0026] The coordinates of any three points on the sideslip surface are used to obtain two coplanar vectors on the sideslip surface. The two coplanar vectors of the sideslip surface are cross-producted to obtain the normal vector of the sideslip surface. The direction of the normal vector points to the outside of the abutment block of the arch dam, and the normal direction of the sideslip surface is obtained.

[0027] Two coplanar vectors on the deslip surface are obtained by using the coordinates of any three points on the deslip surface, and the normal vector of the deslip surface is obtained by cross-producting the two coplanar vectors of the deslip surface. The direction of the normal vector points to the outside of the arch dam shoulder block, and the normal direction of the deslip surface is obtained.

[0028] In one preferred embodiment, in step 3), in the arch dam abutment block sliding calculation space force system, the specific steps of decomposing the external load on the arch dam abutment block include:

[0029] The external load on the abutment block of the arch dam is moved to the midpoint of the intersection of the side sliding surface and the bottom sliding surface. The external moment on the block is automatically balanced by default, and the following formula is calculated:

[0030]

[0031] The components F of the external load on the abutment block of the arch dam in the three directions of the sliding calculation space force system of the abutment block of the arch dam are obtained. 1 、F 2 、F 3 Among them, F 1 is the component force of the external load on the abutment block of the arch dam in the direction of the normal line of the side sliding surface of the spatial force system in the sliding calculation of the abutment block of the arch dam, F 2 is the component force in the normal direction of the bottom sliding surface of the spatial force system in the sliding calculation of the arch dam abutment block, F 3 is the component force of the external load on the abutment block of the arch dam in the direction of the normal line of the intersection line of the spatial force system in the sliding calculation of the abutment block of the arch dam; (x F ,y F ,z F ) is the vector of the external load on the abutment block of the arch dam in the world coordinate system, (x F1 ,y F1 ,z F1 ) is the unit vector in the normal direction of the side sliding surface of the space force system for calculating the sliding of the arch dam abutment block, (x F2 ,y F2 ,z F2 ) is the unit vector in the normal direction of the bottom sliding surface of the space force system for calculating the sliding of the arch dam abutment block, (x 0 ,y 0 ,z 0 ) is the unit vector in the direction of the normal line of the intersection line of the spatial force system for calculating the sliding of the arch dam abutment blocks.

[0032] In one preferred embodiment, in step 4), the calculation formula for the anti-sliding force of the arch dam abutment block is:

[0033] F=f 1 N 1 +c1 A 1 +f 2 N 2 +c 2 A 2

[0034] Wherein, F is the anti-sliding force of the arch dam abutment block, f 1 is the shear friction coefficient of the sliding surface, f 2 is the shear friction coefficient of the bottom sliding surface, N 1 is the normal force of the side slip surface, that is, the component force of the external load on the abutment block of the arch dam in the normal direction of the side slip surface, N 2 is the normal force of the bottom sliding surface, i.e., the component force of the external load on the abutment block of the arch dam in the normal direction of the bottom sliding surface, c 1 is the shearing cohesion of the sliding surface, c 2 is the shearing cohesion of the bottom sliding surface, A 1 is the side sliding area of ​​the arch dam abutment block, A 2 is the bottom sliding surface area of ​​the arch dam abutment block; then f 1 N 1 is the friction resistance on the sideslip surface, f 2 N 2 is the friction resistance on the bottom sliding surface, c 1 A 1 is the cohesive resistance on the sideslip surface, c 2 A 2 is the cohesive resistance on the bottom sliding surface.

[0035] Based on the same concept, the present invention also provides an arch dam shoulder block safety evaluation device, which includes a memory and one or more processors; one or more programs are stored on the memory, and when the one or more programs are executed by the one or more processors, the one or more processors implement the steps of any one of the above methods.

[0036] Beneficial Effects

[0037] Compared with the prior art, the advantages of the present invention are:

[0038] The present invention provides a method for evaluating the safety of an arch dam abutment block, which constructs a spatial force system and calculates the sliding force and anti-sliding force of the arch dam abutment block in combination with the existing finite element method. The method can accurately decompose the sliding force and anti-sliding force directions of the arch dam abutment block into the sliding direction of the arch dam abutment block by decomposing the spatial force system, and can strictly calculate the numerical magnitude and action direction of the sliding force and anti-sliding force according to the sliding direction, so that the safety evaluation result of the abutment block is more accurate than the existing evaluation result. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 is a flow chart of a method for evaluating the safety of an arch dam abutment block considering the decomposition of a spatial force system according to an embodiment of the present invention;

[0040] Figure 2 is a diagram of an overall finite element model of an arch dam foundation according to an embodiment of the present invention;

[0041] Figure 3 is a schematic diagram of the structure surface of an arch dam foundation according to an embodiment of the present invention;

[0042] Figure 4 are the front view and the back view of the R1 block of the embodiment of the present invention;

[0043] Figure 5 It is a schematic diagram of a space force system for block sliding calculation according to an embodiment of the present invention. DETAILED DESCRIPTION

[0044] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments. It should be noted that the embodiments and features in the embodiments of the present invention can be combined with each other without conflict.

[0045] Example 1

[0046] like Figure 1 As shown, the arch dam shoulder block safety evaluation method considering the spatial force system decomposition provided in Example 1 of the present invention includes the following processes: 1. Calculation of external load of the slider; 2. Determination of the direction of the slider; 3. Spatial force system decomposition 3; 4. Calculation of sliding force and anti-sliding force; 5. Safety evaluation.

[0047] like Figure 2 and Figure 3 As shown, the entity modeling of the arch dam and foundation is completed in the finite element analysis software. The foundation contains various weak structural surfaces. The arch dam is meshed by sweeping, the foundation is meshed by free, and normal constraint boundary conditions are set around the foundation model. Loads are applied to the finite element model of the arch dam, and linear elastic finite element calculations are performed. The arch end thrust on the dam shoulder R1 block is calculated based on the finite element calculation results. The volume of the R1 block is measured in the finite element software, and the gravity is calculated in combination with the design data. The value of the uplift pressure is the sum of the buoyancy and seepage pressure on the block;

[0048] like Figure 4 As shown in the figure, F150, F107, upstream tensile fracture surface and free surface of terrain are used as the side sliding surface, bottom sliding surface, detachment surface and free surface of R1 block respectively. The geometric surface information of R1 block is measured and calculated in finite element software to obtain the normal direction of each sliding surface. The normal direction of side sliding surface F150 and bottom sliding surface F107 are cross-producted to obtain the direction of the intersection line of side sliding surface F150 and bottom sliding surface F107, which is the sliding direction of the block.

[0049] like Figure 5 As shown in the figure, the intersection line direction, the bottom sliding surface normal F107 and the side sliding surface F150 normal together constitute the block sliding calculation space force system. The external loads on the block are all decomposed in this space force system. Each external load is moved to the midpoint of the intersection line between the side sliding surface F150 and the bottom sliding surface F107. The external moment on the block is automatically balanced by default, and the components of the three directions in the space force system are calculated. Taking the three direction unit vectors of the space force system as the basis, the unit normal vector of the side sliding surface F150 can be expressed as (x F150 ,y F150 ,z F150 ), the unit normal vector of the bottom sliding surface F107 can be expressed as (x F107 ,y F107 ,z F107 ), the unit direction vector of the intersection line can be expressed as (x 0 ,y 0 ,z 0 ), calculate formula (1). In formula (1), (x F ,y F ,z F ) is the vector representation of the external load in the world coordinate system. By calculating, F 1 ,F 2 ,F 3 That is, the magnitude of the components of the external load in the three directions of the spatial force system.

[0050]

[0051] As shown in formula (2), the friction resistance F on the sideslip surface F150 and the bottom slip surface F107 is calculated based on the normal force component of the sideslip surface F150 and the bottom slip surface F107 and the design data. F150 With F F107 According to the measured areas of the sideslip surface F150 and the bottom slip surface F107 and the design data, the cohesive resistance F on the sideslip surface F150 and the bottom slip surface F107 is calculated. c150 With F c107 The sum of friction resistance and cohesive resistance is the anti-sliding force F of the block. K , the component force T of the arch end thrust and gravity on the R1 block in the direction of the intersection line G and T Z The sum of the two is the block sliding force T K ;

[0052]

[0053] According to the calculated block anti-sliding force and block sliding force, calculate the R1 block safety factor K R1 , as shown in formula (3), the safety status of the block is evaluated according to the evaluation criteria given in the reference specification.

[0054]

[0055] Example 2

[0056] This embodiment provides a device for evaluating the safety of arch dam shoulder blocks, which includes a memory and one or more processors; one or more programs are stored in the memory, and when the one or more programs are executed by the one or more processors, the one or more processors implement the steps of any one of the above methods.

[0057] The contents explained in the above embodiments should be understood as these embodiments are only used to more clearly illustrate the present invention, and are not used to limit the scope of the present invention. After reading the present invention, various equivalent forms of modifications to the embodiments made by those skilled in the art fall within the scope defined by the claims attached to the present invention.

Claims

1. A method for evaluating the safety of an arch dam abutment block, characterized in that: The following steps are involved: Step 1), calculating the external load on the arch dam abutment block, the external load on the arch dam abutment block including the arch end thrust on the arch dam abutment block, the gravity of the arch dam abutment block and the uplift pressure of the arch dam abutment block; Step 2), calculating the bottom sliding surface area, side sliding surface area, detachment surface area and coordinates of any three points on each of the bottom sliding surface, side sliding surface and detachment surface of the arch dam abutment block, and obtaining the normal direction of each sliding surface through the coordinates of any three points on each surface; The direction of the intersection of the side sliding surface and the bottom sliding surface is obtained by cross-producting the normal direction of the side sliding surface and the normal direction of the bottom sliding surface, which is the sliding direction of the arch dam abutment block. Step 3), constructing a spatial force system for calculating the sliding of an arch dam abutment block, decomposing the external load on the arch dam abutment block in the spatial force system for calculating the sliding of an arch dam abutment block, and obtaining the components of the external load on the arch dam abutment block in three directions in the spatial force system for calculating the sliding of an arch dam abutment block; The space force system for calculating the sliding of the block at the abutment of the arch dam is composed of the direction of the intersection line between the side sliding surface and the bottom sliding surface, the normal direction of the bottom sliding surface and the normal direction of the side sliding surface; Step 4), calculating the sliding force of the arch dam abutment block, the sliding force of the arch dam abutment block is the sum of the arch end thrust on the arch dam abutment block and the gravity of the arch dam abutment block in the direction of the intersection of the side sliding surface and the bottom sliding surface, Calculate the anti-sliding force of the arch dam abutment block, which is the sum of the friction resistance on the side sliding surface, the friction resistance on the bottom sliding surface, the cohesion resistance on the side sliding surface and the cohesion resistance on the bottom sliding surface; Step 5), calculating the safety factor of the arch dam abutment block according to the anti-sliding force of the arch dam abutment block and the sliding force of the arch dam abutment block, and evaluating the safety status of the arch dam abutment block.

2. The arch dam abutment block safety assessment method according to claim 1, characterized in that: Step 1) The specific steps of calculating the external load on the abutment block of the arch dam include: Modeling the arch dam and foundation, calculating the finite element stress of the arch dam abutment, calculating the contact area between the arch dam abutment block and the arch dam abutment, the arch end thrust on the arch dam abutment block is the resultant force obtained by integrating the finite element stress of the arch dam abutment over the contact area; Calculating the volume of the arch dam abutment block, and using the volume of the arch dam abutment block to calculate the gravity of the arch dam abutment block; The uplift pressure of the arch dam abutment block is the sum of the buoyancy force and the seepage pressure on the arch dam abutment block.

3. The arch dam abutment block safety assessment method according to claim 1, characterized in that: In step 2), the bottom sliding surface, side sliding surface and detachment surface of the arch dam abutment block are the weak surfaces of the geological structure of the arch dam abutment.

4. The arch dam abutment block safety assessment method according to claim 1, characterized in that: In step 2), the specific steps of obtaining the normal direction of each sliding surface include: The coordinates of any three points on the bottom sliding surface are used to obtain two coplanar vectors on the bottom sliding surface. The two coplanar vectors of the bottom sliding surface are cross-producted to obtain the bottom sliding surface normal vector, the normal vector direction points to the outside of the arch dam abutment block, and the normal line direction of the bottom sliding surface is obtained. The coordinates of any three points on the sideslip surface are used to obtain two coplanar vectors on the sideslip surface. The two coplanar vectors of the sideslip surface are cross-producted to obtain the normal vector of the sideslip surface. The direction of the normal vector points to the outside of the abutment block of the arch dam, and the normal direction of the sideslip surface is obtained. Two coplanar vectors on the deslip surface are obtained by using the coordinates of any three points on the deslip surface, and the normal vector of the deslip surface is obtained by cross-producting the two coplanar vectors of the deslip surface. The direction of the normal vector points to the outside of the arch dam shoulder block, and the normal direction of the deslip surface is obtained.

5. The arch dam abutment block safety assessment method according to claim 1, characterized in that: In step 3), in the arch dam abutment block sliding calculation space force system, the specific steps of decomposing the external load on the arch dam abutment block include: Move the external load on the abutment block of the arch dam to the midpoint of the intersection of the side sliding surface and the bottom sliding surface, and calculate the following formula: Obtain the components F1, F2, and F3 of the external load borne by the arch dam abutment block in the three directions of the arch dam abutment block sliding calculation space force system; wherein, F1 is the component of the external load borne by the arch dam abutment block in the normal direction of the side sliding surface of the arch dam abutment block sliding calculation space force system, F2 is the component of the external load borne by the arch dam abutment block in the normal direction of the bottom sliding surface of the arch dam abutment block sliding calculation space force system, and F3 is the component of the external load borne by the arch dam abutment block in the normal direction of the intersection line of the arch dam abutment block sliding calculation space force system; (x F ,y F ,z F ) is the vector of the external load on the abutment block of the arch dam in the world coordinate system, is the unit vector in the normal direction of the side sliding surface of the space force system for calculating the sliding of the arch dam abutment block, is the unit vector in the normal direction of the bottom sliding surface of the spatial force system for calculating the sliding of the arch dam abutment blocks, and (x0, y0, z0) is the unit vector in the normal direction of the intersection line of the spatial force system for calculating the sliding of the arch dam abutment blocks.

6. The arch dam abutment block safety assessment method according to claim 1, characterized in that: In step 4), the calculation formula of the anti-sliding force of the arch dam abutment block is: F=f1N1+c1A1+f2N2+c2A2 Wherein, F is the anti-sliding force of the arch dam abutment block, f1 is the anti-shear friction coefficient of the sideslip surface, f2 is the anti-shear friction coefficient of the bottom slip surface, N1 is the normal force of the sideslip surface, i.e., the component of the external load borne by the arch dam abutment block in the normal direction of the sideslip surface, N2 is the normal force of the bottom slip surface, i.e., the component of the external load borne by the arch dam abutment block in the normal direction of the bottom slip surface, c1 is the anti-shear cohesion of the sideslip surface, c2 is the anti-shear cohesion of the bottom slip surface, A1 is the sideslip surface area of ​​the arch dam abutment block, and A2 is the bottom slip surface area of ​​the arch dam abutment block; then f1N1 is the friction resistance on the sideslip surface, f2N2 is the friction resistance on the bottom slip surface, c1A1 is the cohesion resistance on the sideslip surface, and c2A2 is the cohesion resistance on the bottom slip surface.

7. An arch dam abutment block safety assessment device, characterized in that: The device includes a memory and one or more processors; one or more programs are stored in the memory, and when the one or more programs are executed by the one or more processors, the one or more processors implement the steps of any one of the methods of claims 1 to 6.

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