A method for calculating bending moment of culvert foundation slab nodes based on comprehensive coefficient method

Abstract

The present invention discloses a method for calculating the node bending moment of the foundation floor of a culvert based on a comprehensive coefficient method, which belongs to the technical field of culvert engineering, and includes: constructing a calculation parameter model of the lower structure of the tunnel body based on the difference in stiffness between the foundation floor and the side wall, and calculating the linear stiffness ratio of the foundation floor and the side wall; based on the influence of the linear stiffness ratio of the foundation floor and the side wall on the internal force distribution, according to different working conditions, different culvert types and linear stiffness ratios, a regression analysis is performed on the full-process numerical analysis results of the lower structure of the tunnel body, and a comprehensive coefficient is calculated; based on the comprehensive coefficient, the node bending moment of the foundation floor of the lower structure of the tunnel body is calculated. The present invention will fully consider the linear stiffness ratio of the foundation floor and the side wall to more accurately calculate the node bending moment, which will promote the optimization of culvert design, improve the accuracy and cost-effectiveness of structural design, while reducing unnecessary consumption of materials, and contribute to the sustainable development of road infrastructure.

Description

Technical Field

[0001] The invention relates to the technical field of culvert engineering, and in particular to a method for calculating the bending moment of a culvert foundation bottom plate node based on a comprehensive coefficient method. Background Art

[0002] As a key component of highway and municipal road construction, culverts are increasingly used with the rapid development of the economy and the continuous progress of highway engineering, and their design theories and calculation methods are becoming more mature.

[0003] At present, the design and calculation of culverts mainly adopt two methods: theoretical method and finite element method. The finite element method is favored for its wide applicability and high calculation accuracy, but it also has certain limitations due to the complexity and time-consuming design and calculation process. The theoretical method is widely used for its simple design and calculation process and low cost, especially in the design and calculation of culvert superstructures. Due to the relatively simple structure and clear stress conditions, the theoretical design and calculation methods are quite mature. However, the existing theoretical design and calculation methods for the substructure of culverts, including the foundation slab and side walls, need to be further improved due to their diverse types and complex stress conditions.

[0004] In the prior art, the design method of the culvert substructure mainly relies on the finite element method or the theoretical design method recommended by the specification. For example: Article 9.4.5 of the recommended industry standard of the People's Republic of China JTG / T 3365-02-2020 "Highway Culvert Design Specifications" proposes a design method for an integral foundation slab, and provides calculation formulas for mid-span bending moment and node bending moment. However, these methods do not fully consider the impact of the difference in stiffness between the foundation slab and the side wall on the internal force distribution, resulting in the calculation results of the node bending moment being much higher than the actual value. This situation not only affects the rationality of the structural design, but may also lead to waste of materials. The above problems need to be solved urgently. To this end, the present invention proposes a method for calculating the node bending moment of the culvert foundation slab based on the comprehensive coefficient method. Summary of the invention

[0005] The technical problem to be solved by the present invention is: how to solve the problem that there is currently no reasonable and accurate method to quickly calculate the node bending moment of the integral culvert foundation bottom plate in the prior art and it is economically feasible. A method for calculating the node bending moment of the culvert foundation bottom plate based on the comprehensive coefficient method is provided. This method will fully consider the linear stiffness ratio of the foundation bottom plate and the side wall to more accurately calculate the node bending moment, which will promote the optimization of culvert design, improve the accuracy and cost-effectiveness of structural design, while reducing unnecessary consumption of materials, and contribute to the sustainable development of road infrastructure.

[0006] The present invention solves the above technical problems through the following technical solutions, and the present invention comprises the following steps:

[0007] Step S1: Based on the difference in stiffness between the foundation slab and the side wall, a calculation parameter model of the tunnel lower structure is constructed to calculate the linear stiffness ratio between the foundation slab and the side wall. ;

[0008] Step S2: Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, according to different working conditions, different culvert types and linear stiffness ratios, a regression analysis is performed on the numerical analysis results of the whole process of the tunnel body substructure to obtain the comprehensive coefficient ;

[0009] Step S3: Based on the comprehensive coefficient , calculate the node bending moment of the foundation bottom plate of the tunnel lower structure .

[0010] Furthermore, in the step S1, the calculation parameter model includes the following parameters: the thickness d of the top plate, the thickness t1 of the side wall, the thickness t2 of the foundation bottom plate, the distance H1 from the center point of the top plate to the center point of the foundation bottom plate, the distance L1 between the center points of the two side walls, and the design compressive stress q of the foundation bottom plate.

[0011] Furthermore, the integral culvert includes a top plate, two side walls and a foundation bottom plate. The top plate is made of prefabricated components or cast on site. The top plate and the two side walls are connected by overlapping. The two side walls and the foundation bottom plate are cast as a whole, and the foundation bottom plate extends a predetermined distance to the outside of the two side walls.

[0012] Furthermore, in step S1, the linear stiffness ratio of the base slab to the side wall is calculated as follows:

[0013] ;

[0014] in, is the distance from the center point of the top plate to the center point of the foundation bottom plate, is the distance between the center points of the two side walls, is the thickness of the side wall, The thickness of the base slab.

[0015] Furthermore, in step S2, the comprehensive coefficient The calculation formula is as follows:

[0016] .

[0017] Furthermore, in step S3, the node bending moment of the foundation bottom plate The calculation formula is as follows:

[0018] ;

[0019] in, Design compressive stress for the foundation slab.

[0020] Compared with the prior art, the present invention has the following advantages:

[0021] 1. The present invention proposes a comprehensive coefficient reflecting the influence of the linear stiffness ratio between the foundation slab and the side wall, and provides a more accurate, easy-to-operate and fast method for calculating the bending moment of the node of the integral culvert foundation slab.

[0022] 2. By considering the impact of the difference in stiffness between the foundation slab and the side wall on the internal force distribution, the calculation results can be closer to the actual stress state of the structure, thereby improving the reliability of the design.

[0023] 3. The present invention can accurately calculate the node bending moment value of the foundation slab, thereby allowing differentiated and refined reinforcement design at the mid-span and nodes of the foundation slab, avoiding excessive reinforcement caused by the previous one-size-fits-all and unified reinforcement, reducing unnecessary material usage, and significantly reducing engineering costs. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 A schematic diagram of calculation parameters used in the present invention;

[0025] Figure 2 The bending moment diagram of the numerical simulation analysis result of the integral foundation culvert with a structural size of 6m×4.5m (structure net width×structure net height) and a fill height of 2m in the first embodiment of the present invention;

[0026] Figure 3 The bending moment diagram is a numerical simulation analysis result of an integral foundation culvert with a structural size of 6m×4.5m and a fill height of 10m in the second embodiment of the present invention;

[0027] Figure 4 The bending moment diagram is a numerical simulation analysis result of an integral foundation culvert with a structural size of 6m×4.5m and a fill height of 16m in the third embodiment of the present invention;

[0028] Figure 5 The bending moment diagram is a numerical simulation analysis result of an integral foundation culvert with a structural size of 6m×4.5m and a fill height of 20m in the fourth embodiment of the present invention;

[0029] Figure 6 It is a schematic diagram of the process of the present invention.

[0030] In the figure: 1-top plate; 2-side wall; 3-foundation bottom plate. DETAILED DESCRIPTION

[0031] The following is a detailed description of an embodiment of the present invention. This embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation method and a specific operation process are given, but the protection scope of the present invention is not limited to the following embodiment.

[0032] Embodiment 1

[0033] This embodiment provides a technical solution: a method for calculating the bending moment of the culvert foundation bottom plate node based on the comprehensive coefficient method, such as Figure 1-2 As shown, the following steps are included:

[0034] S1: A calculation parameter model of the tunnel lower structure is constructed based on the difference in stiffness between the foundation bottom plate and the side wall. For the first embodiment of this invention, the integral foundation culvert with a structural size of 6m×4.5m and a fill height of 2m, the detailed calculation parameters are shown in Table 1:

[0035] Table 1 Detailed calculation parameters

[0036]

[0037] Calculate the linear stiffness ratio of the foundation slab to the side wall ;

[0038] The linear stiffness ratio of the foundation slab and the side wall is determined by the following formula:

[0039] ;

[0040] in, is the distance from the center point of the top plate to the center point of the foundation bottom plate, is the distance between the center points of the two side walls, is the thickness of the side wall, The thickness of the base slab.

[0041] S2: Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, a numerical simulation model of the culvert is established. According to different working conditions, different culvert types and linear stiffness ratios, a regression analysis is performed on the numerical analysis results of the whole process of the tunnel body substructure to derive the comprehensive coefficient , determined by the following formula:

[0042] .

[0043] In the present invention, when performing regression analysis, different working conditions include fill height of 0.5~20m, different culvert types include culvert span net width of 2m~6m, culvert net height of 1.5m~5.0m, and the line stiffness ratio is calculated based on specific data, ranging from 0.75~8.396, and then regression analysis is performed on the numerical analysis results of the whole process of the lower structure of the tunnel body.

[0044] S3: Based on comprehensive coefficient , the node bending moment of the foundation bottom plate of the tunnel lower structure calculate.

[0045] Nodal bending moment of foundation slab Determine as follows:

[0046] ;

[0047] in, The design compressive stress for the foundation slab is calculated by applying all upper acting loads according to the inverted beam method.

[0048] For this embodiment 1: the structural dimensions are 6m×4.5m (structure net width×structure net height), the fill height is 2m, and the integral foundation culvert is combined with Figure 2 The calculated value of the present invention is compared with the numerical simulation analysis value (obtained by finite element method simulation analysis) and the standard calculated value (obtained by theoretical method calculation). The results are shown in Table 2. It can be found that the error of the calculated value according to the specification is 49.5% compared with the numerical simulation analysis value, which is a large error. The error of the calculated value according to the present invention is 8.4% compared with the numerical simulation analysis value, which meets the actual engineering accuracy requirements. In addition, the calculated value according to the present invention is closer to the actual stress condition of the structure than the calculated value according to the specification.

[0049] Table 2 Comparison of results of three methods

[0050]

[0051] In the present invention, if Figure 1 As shown, the culvert includes a top plate 1, two side walls 2 and a foundation bottom plate 3. The top plate 1 can be a prefabricated component or cast on site. The prefabricated top plate 1 and the two side walls 2 are connected by overlapping. The two side walls 2 and the foundation bottom plate 3 are cast as a whole. The foundation bottom plate 3 extends a certain distance outside the two side walls 2 to form a stable support structure.

[0052] In the present invention, the node bending moment value of the foundation bottom plate can be calculated more accurately ( ), thereby allowing differentiated and refined reinforcement design at the mid-span and nodes of the foundation slab, avoiding the previous one-size-fits-all approach of uniform reinforcement at the mid-span and nodes that causes excessive reinforcement, reducing unnecessary material usage and significantly reducing engineering costs.

[0053] Embodiment 2

[0054] This embodiment provides a technical solution: a method for calculating the bending moment of the culvert foundation bottom plate node based on the comprehensive coefficient method, such as Figure 1 , Figure 3 As shown, the following steps are included:

[0055] S1: Based on the difference in stiffness between the foundation slab and the side wall, a calculation parameter model of the tunnel lower structure is constructed. For the second embodiment of this invention, the integral foundation culvert with a structural size of 6m×4.5m and a fill height of 10m, the detailed calculation parameters are shown in Table 3:

[0056] Table 3 Detailed calculation parameters

[0057]

[0058] Calculate the linear stiffness ratio of the foundation slab to the side wall ;

[0059] The linear stiffness ratio of the foundation slab and the side wall is determined by the following formula:

[0060] ;

[0061] in, is the distance from the center point of the top plate to the center point of the foundation bottom plate, is the distance between the center points of the two side walls, is the thickness of the side wall, The thickness of the base slab.

[0062] S2: Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, a regression analysis is performed on the numerical analysis results of the entire process of the tunnel substructure according to different working conditions, different culvert types and linear stiffness ratios, and the comprehensive coefficient is derived. , determined by the following formula:

[0063] .

[0064] S3: Based on comprehensive coefficient , the node bending moment of the foundation bottom plate of the tunnel lower structure calculate.

[0065] Nodal bending moment of foundation slab Determine as follows:

[0066] ;

[0067] in, The design compressive stress for the foundation slab is calculated by applying all upper acting loads according to the inverted beam method.

[0068] For the second embodiment: the structural size is 6m×4.5m, the fill height is 10m, the integral foundation culvert is combined with Figure 3 The calculated values ​​of the present invention are compared with the numerical simulation analysis values ​​and the standard calculated values. The results are shown in Table 4. It can be found that the error of the calculated value according to the specification is 74.4% compared with the numerical simulation analysis value, which is nearly doubled and has a large error. The error of the calculated value according to the present invention is 1.5% compared with the numerical simulation analysis value, which meets the actual engineering accuracy requirements, and the calculated value according to the present invention is closer to the actual stress condition of the structure than the calculated value according to the specification.

[0069] Table 4 Comparison of results of three methods

[0070]

[0071] Embodiment 3

[0072] This embodiment provides a technical solution: a method for calculating the bending moment of the culvert foundation bottom plate node based on the comprehensive coefficient method, such as Figure 1 , Figure 4 As shown, the following steps are included:

[0073] S1: Based on the difference in stiffness between the foundation floor and the side wall, a calculation parameter model of the tunnel lower structure is constructed. For Example 3: an integral foundation culvert with a structural size of 6m×4.5m and a fill height of 16m, the detailed calculation parameters are shown in Table 5:

[0074] Table 5 Detailed calculation parameters

[0075]

[0076] Calculate the linear stiffness ratio of the foundation slab to the side wall ;

[0077] The linear stiffness ratio of the foundation slab and the side wall is determined by the following formula:

[0078] ;

[0079] in, is the distance from the center point of the top plate to the center point of the foundation bottom plate, is the distance between the center points of the two side walls, is the thickness of the side wall, The thickness of the base slab.

[0080] S2: Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, a regression analysis is performed on the numerical analysis results of the entire process of the tunnel substructure according to different working conditions, different culvert types and linear stiffness ratios, and the comprehensive coefficient is derived. , determined by the following formula:

[0081] .

[0082] S3: Based on comprehensive coefficient , the node bending moment of the foundation bottom plate of the tunnel lower structure calculate:

[0083] Nodal bending moment of foundation slab Determine as follows:

[0084] ;

[0085] in, The design compressive stress for the foundation slab is calculated by applying all upper acting loads according to the inverted beam method.

[0086] For this embodiment 3: the structural size is 6m×4.5m, the fill height is 16m, the integral foundation culvert is combined with Figure 4 The calculated values ​​of the present invention are compared with the numerical simulation analysis values ​​and the standard calculated values. The results are shown in Table 6. It can be found that the error of the calculated value according to the specification is 98.7% compared with the numerical simulation analysis value, which is twice as large. The error of the calculated value of the present invention is 15.7% compared with the numerical simulation analysis value, which meets the actual engineering accuracy requirements, and the calculated value of the present invention is closer to the actual stress condition of the structure than the calculated value of the specification.

[0087] Table 6 Comparison of results of three methods

[0088]

[0089] Embodiment 4

[0090] This embodiment provides a technical solution: a method for calculating the bending moment of the culvert foundation bottom plate node based on the comprehensive coefficient method, such as Figure 1 , Figure 5 As shown, the following steps are included:

[0091] S1: Based on the difference in stiffness between the foundation slab and the side wall, a calculation parameter model of the tunnel lower structure is constructed. For the fourth embodiment: an integral foundation culvert with a structural size of 6m×4.5m and a fill height of 20m, the detailed calculation parameters are shown in Table 7:

[0092] Table 7 Detailed calculation parameters

[0093]

[0094] Calculate the linear stiffness ratio of the foundation slab to the side wall ;

[0095] The linear stiffness ratio of the foundation slab and the side wall is determined by the following formula:

[0096] ;

[0097] in, is the distance from the center point of the top plate to the center point of the foundation bottom plate, is the distance between the center points of the two side walls, is the thickness of the side wall, The thickness of the base slab.

[0098] S2: Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, a regression analysis is performed on the numerical analysis results of the entire process of the tunnel substructure according to different working conditions, different culvert types and linear stiffness ratios, and the comprehensive coefficient is derived. , determined by the following formula:

[0099] .

[0100] S3: Based on comprehensive coefficient , the node bending moment of the foundation bottom plate of the tunnel lower structure calculate:

[0101] Nodal bending moment of foundation slab Determine as follows:

[0102] ;

[0103] in, The design compressive stress for the foundation slab is calculated by applying all upper acting loads according to the inverted beam method.

[0104] For the fourth embodiment: the integral foundation culvert with a structural size of 6m×4.5m and a fill height of 20m, combined with Figure 5 The calculated values ​​of the present invention are compared with the numerical simulation analysis values ​​and the standard calculated values. The results are shown in Table 8. It can be found that the error between the calculated value according to the specification and the numerical simulation analysis value is 96.3%, which is twice as large. The error between the calculated value according to the present invention and the numerical simulation analysis value is 9.0%, which meets the actual engineering accuracy requirements. In addition, the calculated value according to the present invention is closer to the actual stress condition of the structure than the calculated value according to the specification.

[0105] Table 8 Comparison of results of three methods

[0106]

[0107] Although the embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and are not to be construed as limitations of the present invention. A person skilled in the art may change, modify, replace and vary the above embodiments within the scope of the present invention.

Claims

1. A method for calculating the bending moment of the culvert foundation bottom plate node based on the comprehensive coefficient method, characterized in that: The following steps are involved: Step S1: Based on the difference in stiffness between the foundation slab and the side wall, a calculation parameter model of the tunnel lower structure is constructed to calculate the linear stiffness ratio between the foundation slab and the side wall. ; In step S1, the calculation parameter model includes the following parameters: the thickness d of the top plate, the thickness t1 of the side wall, the thickness t2 of the foundation bottom plate, the distance H1 from the center point of the top plate to the center point of the foundation bottom plate, the distance L1 from the center points of the two side walls, and the design compressive stress q of the foundation bottom plate; In step S1, the linear stiffness ratio of the foundation slab to the side wall is calculated as follows: ; Step S2: Based on the influence of the linear stiffness ratio of the foundation slab and the side wall on the internal force distribution, according to different working conditions, different culvert types and linear stiffness ratios, a regression analysis is performed on the numerical analysis results of the whole process of the tunnel body substructure to obtain the comprehensive coefficient ; In step S2, the comprehensive coefficient The calculation formula is as follows: ; Step S3: Based on the comprehensive coefficient , calculate the node bending moment of the foundation bottom plate of the tunnel lower structure ; In step S3, the node bending moment of the foundation slab ; The calculation formula is as follows: .

2. The method for calculating the bending moment of the culvert foundation bottom plate node based on the comprehensive coefficient method according to claim 1 is characterized in that: The integral culvert includes a top plate, two side walls and a foundation bottom plate. The top plate is made of prefabricated components or cast on site. The top plate and the two side walls are connected by overlapping. The two side walls and the foundation bottom plate are cast as a whole, and the foundation bottom plate extends a predetermined distance to the outside of the two side walls.

Images