A method and device for evaluating the safety of arch dam abutment blocks

Abstract

The present invention discloses a method for evaluating the safety of arch dam abutment blocks taking into account the decomposition of a spatial force system. The finite element method is used to calculate the external loads on the arch dam abutment blocks, determine the sliding direction of the blocks, decompose the external loads on the blocks on the block sliding calculation spatial force system, calculate the block sliding force and the block anti-sliding force, calculate the block safety factor, and evaluate the block safety status. The present invention utilizes the decomposition of a spatial force system to accurately decompose the block sliding force and the block anti-sliding force into the direction of block sliding, and can more accurately obtain the numerical size and direction of action of the block sliding force and the block anti-sliding force, so as to more accurately evaluate the safety of the dam abutment blocks. The present invention also provides an arch dam abutment block safety evaluation device.

Description

Technical Field

[0001] The present 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] The design and construction of arch dams often face challenges such as complex rock mass structures at the foundation and abutments, as well as the development of geological defects. These can lead to foundation deformation and compromise the stability of the abutments. The anti-sliding stability of the abutment's force-bearing structure is particularly problematic. Numerical calculations, model tests, and other methods are required to analyze the safety of various potential unfavorable block combinations, evaluate the overall abutment, and propose treatment measures, providing a crucial basis for the design, construction, and operation of the project. Furthermore, analyses of stress and displacement changes under various operating conditions are conducted to provide recommendations for optimal design.

[0003] At present, the main research methods for the anti-sliding stability of dam abutment resistance bodies include: using the linear elastic finite element method to study the stress and deformation characteristics of arch dams and foundations 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 dam abutment resistance bodies, providing a basis for the safety evaluation of potential sliding blocks and reinforcement treatment; using the nonlinear finite element method to study the stability of blocks and the treatment of geological defects, focusing on the stability of blocks, the scope and degree of influence of major geological defects on the project, proposing the treatment scope required for each major geological defect, and suggesting treatment measures, providing a basis for the formulation of geological defect treatment plans.

[0004] However, the aforementioned methods all use the calculation method recommended by current specifications when assessing the safety of the dam abutment rock mass. While this method uses the finite element method (including the linear elastic finite element method and the nonlinear finite element method) to calculate the sliding and anti-sliding forces of the abutment blocks, it can relatively accurately obtain the abutment load and forces. However, the direction of the forces cannot be strictly calculated according to the direction of block sliding, resulting in corresponding errors in the assessment of the abutment block safety and potentially overestimating the magnitude of the anti-sliding force. Therefore, it is necessary to develop an arch dam abutment block safety assessment method that can consider the decomposition of spatial force systems, in addition to 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 the block sliding force and block anti-sliding force into the block sliding direction, and can more accurately obtain the numerical size and action direction of the block sliding force and block anti-sliding force, so as to more accurately evaluate the safety of the dam abutment blocks.

[0006] To achieve the above-mentioned 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) Calculate the external loads on the arch dam abutment blocks; the external loads on the arch dam abutment blocks include the arch end thrust on the arch dam abutment blocks, the gravity of the arch dam abutment blocks, and the uplift pressure of the arch dam abutment blocks;

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

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

[0010] A cross product is performed between the normal direction of the sideslip surface and the normal direction of the bottom slip surface to obtain the direction of the intersection line of the sideslip surface and the bottom slip surface, which is the sliding direction of the abutment block of the arch dam;

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

[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 the 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 the arch dam abutment block;

[0013] Step 4) Calculate the sliding force of the arch dam abutment block, which 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] Calculating the anti-sliding force of the arch dam abutment block, where the anti-sliding force is the sum of the friction resistance on the side sliding surface, the friction resistance on the bottom sliding surface, the cohesive resistance on the side sliding surface, and the cohesive resistance on the bottom sliding surface;

[0015] Step 5) Calculate the safety factor of the arch dam abutment block based on the anti-sliding force of the arch dam abutment block and the sliding force of the arch dam abutment block to evaluate the safety status of the arch dam abutment block; the calculation formula of the arch dam abutment block safety factor K 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 arch dam abutment block 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, and calculating the contact area between the arch dam abutment block and the arch dam abutment. The arch end thrust exerted 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 obtaining the weight of the arch dam abutment block by using the volume 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 solid modeled using existing finite element analysis software. The foundation contains various weak structural surfaces. The arch dam is subjected to swept meshing, and 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, and linear elastic finite element calculations are performed to obtain the finite element stress of the arch dam abutment.

[0022] The contact area between the arch dam abutment block and the arch dam abutment is calculated using existing finite element analysis software. The resultant force obtained by integrating the finite element stress of the arch dam abutment over 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 using existing finite element analysis software, and the weight of the arch dam abutment block is obtained by calculation based on design data.

[0023] In one preferred embodiment, 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 direction of the bottom sliding surface is obtained.

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

[0027] The two coplanar vectors on the detachment surface are obtained by the coordinates of any three points on the detachment surface, and the two coplanar vectors of the detachment surface are cross-producted to obtain the detachment surface normal vector, the direction of the normal vector points to the outside of the arch dam abutment block, and the normal direction of the detachment surface is obtained.

[0028] In one preferred embodiment, in step 3), the specific steps of decomposing the external load on the arch dam abutment block in the arch dam abutment block sliding calculation spatial force system 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. The following formula is used to calculate:

[0030]

[0031] 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 direction of the normal to 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 direction of the normal to 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 direction of the normal to 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 sideslip 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 space force system for calculating the sliding of the arch dam abutment block, and (x0, y0, z0) is the unit vector in the normal direction of the intersection line of the space force system for calculating the sliding of the arch dam abutment block.

[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=f1N1+c1A1+f2N2+c2A2

[0034] Among them, F is the anti-slip force of the arch dam abutment block, f1 is the shear friction coefficient of the sideslip surface, f2 is the shear friction coefficient of the bottom slip surface, N1 is the normal force of the sideslip surface, that is, 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, that is, 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 shear cohesion of the sideslip surface, c2 is the 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.

[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 arch dam abutment blocks. This method constructs a spatial force system and combines it with the existing finite element method to calculate the sliding and anti-sliding forces of arch dam abutment blocks. By decomposing the spatial force system, the method accurately decomposes the sliding and anti-sliding forces of the arch dam abutment blocks into the sliding directions of the arch dam abutment blocks. The method can strictly calculate the magnitude and direction of the sliding and anti-sliding forces based on the sliding direction, resulting in a more accurate abutment block safety assessment than existing assessments. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0040] Figure 2 This 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 structural diagram of an arch dam foundation according to an embodiment of the present invention;

[0042] Figure 4 1 is a front view and a back view of the R1 block according to an embodiment of the present invention;

[0043] Figure 5 It is a schematic diagram of the spatial 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, in the absence of conflict, the embodiments and features of the embodiments of the present invention may be combined with each other.

[0045] Example 1

[0046] like Figure 1 As shown, the arch dam abutment 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 slider direction; 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 arch dam and foundation were modeled in finite element analysis software. The foundation included various weak structural surfaces. A swept mesh was applied to the arch dam, and a free mesh was applied to the foundation. Normal constraint boundary conditions were set around the foundation model. Loads were applied to the arch dam finite element model, and linear elastic finite element calculations were performed. The arch end thrust acting on the dam abutment R1 block was calculated based on the finite element calculation results. The volume of the R1 block was measured in the finite element software, and the gravity was calculated based on the design data. The uplift pressure was taken as the sum of the buoyancy and seepage pressure acting on the block.

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

[0049] like Figure 5 As shown in the figure, the intersection line direction, the bottom sliding surface normal F107 and the sideslip surface normal F150 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 sideslip 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 sideslip 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 edge can be expressed as (x0, y0, z0), and the calculation 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 calculation, F1, F2, and F3 are the component forces 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 components of the sideslip surface F150 and the bottom slip surface F107 and the design data. F150 With F F107 , calculate the cohesive resistance F on the sideslip surface F150 and the bottom slip surface F107 based on the measured areas of the sideslip surface F150 and the bottom slip surface F107 and the design data 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] Calculate the R1 block safety factor K based on the calculated block anti-sliding force and block sliding force 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 an arch dam abutment 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.

[0057] The contents described 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 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) Calculate the external loads on the arch dam abutment blocks, where the external loads on the arch dam abutment blocks include the arch end thrust on the arch dam abutment blocks, the gravity of the arch dam abutment blocks, and the uplift pressure of the arch dam abutment blocks; Step 2) calculating the bottom sliding surface area, side sliding surface area, and detachment surface area of ​​the arch dam abutment block and the coordinates of any three points on each of the bottom sliding surface, side sliding surface, and detachment surface, and obtaining the normal direction of each sliding surface through the coordinates of any three points on each surface; Take the cross product of the normal direction of the side sliding surface and the normal direction of the bottom sliding surface to obtain the direction of the intersection of the side sliding surface and 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 the 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 the arch dam abutment block; The space force system for calculating the sliding of the arch dam abutment block is composed of the direction of the intersection line between the sideslip surface and the bottom slip surface, the normal direction of the bottom slip surface and the normal direction of the sideslip surface; Step 4) Calculate the sliding force of the arch dam abutment block, which 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. Calculating the anti-sliding force of the arch dam abutment block, where the anti-sliding force is the sum of the friction resistance on the side sliding surface, the friction resistance on the bottom sliding surface, the cohesive resistance on the side sliding surface, and the cohesive resistance on the bottom sliding surface; Step 5) Calculate the safety factor of the arch dam abutment block based on the anti-sliding force of the arch dam abutment block and the sliding force of the arch dam abutment block, and evaluate 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 arch dam abutment block include: Modeling the arch dam and foundation, calculating the finite element stress of the arch dam abutment, and calculating the contact area between the arch dam abutment block and the arch dam abutment. The arch end thrust exerted 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 obtaining the weight of the arch dam abutment block by using the volume 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 direction of the bottom sliding surface is obtained. The two coplanar vectors on the sideslip surface are obtained by using the coordinates of any three points on the sideslip surface. The normal vector of the sideslip surface is obtained by cross-producting the two coplanar vectors of the sideslip surface. The direction of the normal vector points to the outside of the arch dam abutment block, and the normal direction of the sideslip surface is obtained. The two coplanar vectors on the detachment surface are obtained by the coordinates of any three points on the detachment surface, and the two coplanar vectors of the detachment surface are cross-producted to obtain the detachment surface normal vector, the direction of the normal vector points to the outside of the arch dam abutment block, and the normal direction of the detachment surface is obtained.

5. The arch dam abutment block safety assessment method according to claim 1, characterized in that: In step 3), the specific steps of decomposing the external load on the arch dam abutment block in the arch dam abutment block sliding calculation space force system 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 direction of the normal to 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 direction of the normal to 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 direction of the normal to 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 sideslip 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 space force system for calculating the sliding of the arch dam abutment block, (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 block.

6. The arch dam abutment block safety assessment method according to claim 1, characterized in that: In step 4), the calculation formula for the anti-sliding force of the arch dam abutment block is: F=f1N1+c1A1+f2N2+c2A2 Among them, F is the anti-slip force of the arch dam abutment block, f1 is the shear friction coefficient of the sideslip surface, f2 is the shear friction coefficient of the bottom slip surface, N1 is the normal force of the sideslip surface, that is, 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, that is, 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 shear cohesion of the sideslip surface, c2 is the 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 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 the method according to any one of claims 1 to 6.

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