A design method for culvert foundation slab based on stiffness difference

Abstract

The present invention discloses a culvert foundation slab design method based on stiffness difference, and belongs to the technical field of culvert engineering. The present invention establishes a calculation formula for the mid-span and node bending resistance of the culvert foundation slab based on the stiffness difference between the foundation slab and the side wall, and provides a convenient and fast integral culvert foundation slab design method; by considering the influence of the stiffness difference between the foundation slab and the side wall on the internal force distribution, the calculation result can be closer to the actual stress state of the structure, and the reliability of the design is improved; based on segmented force and zoned reinforcement, the present invention provides a principle for the division of zoned reinforcement at the mid-span and node of the foundation slab, and through zoned differentiated precise reinforcement, it avoids the past one-size-fits-all approach, and the excessive reinforcement caused by the unified reinforcement of the upper and lower parts at the mid-span node, effectively reducing the project cost.

Description

Technical Field

[0001] The invention relates to the technical field of culvert engineering, and in particular to a culvert foundation bottom plate design method based on stiffness difference. Background Art

[0002] Culverts are an indispensable part of transportation infrastructure and play a vital role in highway and municipal road construction. With the rapid development of the economy and the continuous expansion of highway engineering, the design and calculation methods of culverts are also constantly improving and becoming more mature and complete.

[0003] At present, the existing culvert design and calculation methods mainly use two methods: theoretical method and finite element method. Although the finite element method has significant advantages in calculation accuracy and applicability, its complex design and calculation process also makes this method more cumbersome and time-consuming in actual operation. In contrast, the theoretical method is simpler and relatively low-cost in the design and calculation process, but it is mainly used in the design of the upper structure of the culvert. These structures are relatively simple and the stress conditions are clear, so the theoretical design and calculation methods are relatively mature. However, the design of the lower structure of the culvert, including the foundation slab and side walls, is more complex and changeable, and the existing theoretical design and calculation methods need to be further improved.

[0004] In the existing technology, the design method of the culvert substructure mainly relies on the finite element method or theoretical design method. 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 Code" proposes a practical design method for the integral foundation slab, and gives the calculation formula of the mid-span and node bending moment of the foundation slab, but the calculation result of the node bending moment is quite different from the actual value. "Internal Force Analysis of Integral Foundation of Culvert", Fu Chunhui, "Northern Transportation", 2012.05.051 proposed the calculation formula of the mid-span and node bending moment of the foundation slab, which can be used as a reference in the structural design of the integral foundation slab of the culvert. However, this method does not fully consider the influence of the difference in stiffness between the foundation slab and the side wall on the distribution of internal forces, resulting in a large difference between the mid-span and node bending moments of the foundation slab and the actual value, and the maximum error is nearly doubled. This situation not only affects the rationality and accuracy of the structural design, but also may lead to waste of materials. The above problems need to be solved urgently. To this end, the present invention proposes a design method for the culvert foundation slab based on stiffness difference. Summary of the invention

[0005] The technical problem to be solved by the present invention is how to solve the shortcomings of the existing culvert substructure foundation slab design method, and provide a culvert foundation slab design method based on stiffness difference.

[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: construct a theoretical derivation model of the tunnel lower structure based on the difference in stiffness between the foundation slab and the side wall, and make relevant assumptions;

[0008] Step S2: Based on the displacement method, according to the deformation coordination relationship between the foundation bottom plate and the side wall at the node, the displacement method equation is established with the rotation angle of the foundation bottom plate and the side wall at the node as the equilibrium condition, and the calculation formula of the angular displacement at the node is obtained and simplified;

[0009] Step S3: Based on the displacement method and the simplified calculation formula for the angular displacement at the nodes, the theoretical value of the mid-span bending moment of the foundation bottom plate of the tunnel lower structure and the theoretical value of the node bending moment are calculated;

[0010] Step S4: Based on the segmented force and zoned reinforcement method, the foundation slab is zoned, and the target design bearing capacity of the mid-span zone bending moment and the target design bearing capacity of the node zone bending moment of the foundation slab of the lower structure of the tunnel body are calculated. The required compressive steel bars in each zone are arranged according to the structural reinforcement, and the required tensile steel bars are arranged according to the single-bar bending section reinforcement.

[0011] Furthermore, the 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 the step S1, the relevant assumptions are as follows: assuming that the foundation slab and the two side walls are frame structures, considering the stiffness difference between the foundation slab and the side walls, the bending stiffness of the side wall is EI1, and the bending stiffness of the foundation slab is EI2; assuming that the top plate is the upper support point of the boundary condition of the side wall; assuming that the node between the side wall and the foundation slab is an unfixed hinge; assuming that there are two parallel chain rods in the mid-span of the foundation slab.

[0013] Furthermore, in step S2, the displacement method equation established is as follows:

[0014] ;

[0015] in, is the angular displacement at the node;

[0016] is the stiffness coefficient:

[0017] ;

[0018] exist In the figure, H1 is the distance from the center point of the top plate to the center point of the foundation bottom plate, and L1 is the distance from the center points of the two side walls;

[0019] is the fixed end bending moment of the structural load at the node:

[0020] ;

[0021] exist In the equation, q1 is the lateral earth pressure at the top of the side wall, q2 is the lateral earth pressure at the bottom of the side wall, M is the bending moment transmitted from the top plate to the top of the side wall, and L2 is the distance from the center of the side wall to the outermost side of the foundation bottom plate;

[0022] Then the angular displacement at the node is obtained The calculation formula is as follows:

[0023] .

[0024] Furthermore, in step S2, a first coefficient A, a second coefficient B and a third coefficient C are defined to determine the angular displacement at the node. The calculation formula is simplified, and the first coefficient A, the second coefficient B and the third coefficient C are as follows:

[0025] ;

[0026] ;

[0027] ;

[0028] Simplified angular displacement at the node The calculation formula is as follows:

[0029] .

[0030] Furthermore, in step S3, the theoretical value of the mid-span bending moment of the foundation slab is The calculation formula is as follows:

[0031] ;

[0032] Theoretical value of bending moment at foundation slab node The calculation formula is as follows:

[0033] ;

[0034] in, The linear stiffness ratio of the foundation slab and the side wall is:

[0035] ;

[0036] Among them, t1 is the thickness of the side wall, and t2 is the thickness of the base plate.

[0037] Furthermore, in the step S4, the foundation slab is partitioned based on the segmented force and partitioned reinforcement method, and the calculation formulas for the mid-span and node partition boundary points of the foundation slab are as follows:

[0038] ;

[0039] in, It is the distance from the partition boundary point to the center point of the proximal side wall. The root symmetry principle is that the area from the partition boundary point to the center point of the mid-span of the foundation slab is the node partition of the foundation slab, and the area from the partition boundary point to the outermost area of ​​the foundation slab is the node partition of the foundation slab.

[0040] Furthermore, in step S4, the target design bearing capacity of the mid-span partition bending moment of the foundation slab is The calculation formula is as follows:

[0041] ;

[0042] Target design bearing capacity of the bending moment of the foundation slab node partition The calculation formula is as follows:

[0043] ;

[0044] in, is the importance coefficient of the structure.

[0045] Furthermore, in step S4, according to the calculated target design bearing capacity of the mid-span partition of the foundation slab of the lower structure of the tunnel body and the target design bearing capacity of the node partition, the compressive steel bars required for each partition are reinforced according to the structural reinforcement, and the tensile steel bars required for each partition are reinforced according to the single-bar bending section, that is, the upper steel bars of the mid-span partition of the foundation slab are reinforced according to the single-bar bending section calculation according to the target design bearing capacity, the lower steel bars of the mid-span partition are reinforced according to the structural reinforcement, the upper steel bars of the node partition of the foundation slab are reinforced according to the structural reinforcement, and the lower steel bars of the node partition are reinforced according to the target design bearing capacity.

[0046] Compared with the prior art, the present invention has the following advantages:

[0047] 1. The present invention establishes a calculation formula for the mid-span and node bending resistance of the culvert foundation slab based on the difference in stiffness between the foundation slab and the side wall, and provides a convenient and fast method for designing an integral culvert foundation slab;

[0048] 2. By considering the influence 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, thus improving the reliability of the design;

[0049] 3. Based on segmented force and zoned reinforcement, the present invention provides a principle for the division of reinforcement at the mid-span and node of the foundation slab. Through differentiated and precise reinforcement in different zones, it avoids the excessive reinforcement caused by the one-size-fits-all approach in the past and the unified reinforcement of the upper and lower parts at the mid-span node, thereby effectively reducing the project cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 is a schematic flow chart of a culvert foundation bottom plate design method based on stiffness difference in an embodiment of the present invention;

[0051] Figure 2 is a schematic diagram of calculation parameters used in an embodiment of the present invention;

[0052] Figure 3 Theoretical derivation model of the culvert foundation slab design method based on stiffness difference in the embodiment of the present invention;

[0053] Figure 4 It is a 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 10m in the first embodiment of the present invention;

[0054] Figure 5 It is a 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 20m in the second embodiment of the present invention.

[0055] In the figure: 1-top plate; 2-side wall; 3-foundation bottom plate. DETAILED DESCRIPTION

[0056] 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.

[0057] Embodiment 1

[0058] like Figure 1 As shown, this embodiment provides a technical solution: a culvert foundation bottom plate design method based on stiffness difference, comprising the following steps:

[0059] Step S1: construct a theoretical derivation model of the tunnel lower structure based on the difference in stiffness between the foundation slab and the side wall, and make relevant assumptions;

[0060] Step S2: Based on the displacement method, according to the deformation coordination relationship between the foundation bottom plate and the side wall at the node, the displacement method equation is established with the rotation angle of the foundation bottom plate and the side wall at the node as the equilibrium condition, and the calculation formula of the angular displacement at the node is obtained and simplified;

[0061] Step S3: Based on the displacement method and the simplified calculation formula for the angular displacement at the nodes, the theoretical value of the mid-span bending moment of the foundation bottom plate of the tunnel lower structure and the theoretical value of the node bending moment are calculated;

[0062] Step S4: Based on the segmented force and zoned reinforcement method, the foundation slab is zoned, and the target design bearing capacity of the mid-span zone bending moment and the target design bearing capacity of the node zone bending moment of the foundation slab of the lower structure of the tunnel body are calculated. The required compressive steel bars in each zone are arranged according to the structural reinforcement, and the required tensile steel bars are arranged according to the single-bar bending section reinforcement.

[0063] In this embodiment, the culvert includes a top plate 1, two side walls 2 and a foundation bottom plate 3. The top plate 1 is obtained by prefabricated components or cast on site. The 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 to the outside of the two side walls 2 by a predetermined distance. Figure 2 shown.

[0064] In this embodiment, in step S1, the following assumptions are made: the foundation slab and the two side walls are assumed to be frame structures. Considering the difference in stiffness between the foundation slab and the side walls, the bending stiffness of the side walls is EI1 and the bending stiffness of the foundation slab is EI2. The top slab is assumed to be the upper support point of the boundary condition of the side wall. The node between the side wall and the foundation slab is assumed to be an unfixed hinge. The foundation slab is assumed to have two parallel chain rods in the middle of its span, such as Figure 3 shown.

[0065] In this embodiment, the calculation parameters involved include: the thickness of the top plate d, the thickness of the side wall t1, the thickness of the foundation bottom plate t2, 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 point of the two side walls, the distance L2 from the center of the side wall to the outermost side of the foundation bottom plate, the lateral earth pressure q1 at the top of the side wall, the lateral earth pressure q2 at the bottom of the side wall, the design compressive stress q of the foundation bottom plate, and the bending moment M transmitted from the top plate to the top of the side wall. Figure 2 The detailed calculation parameters are shown in Table 1.

[0066] Table 1 Detailed calculation parameters

[0067]

[0068] In this embodiment, in step S2, the displacement method equation established is as follows:

[0069] ;

[0070] in, is the angular displacement at the node; is the stiffness coefficient:

[0071] ;

[0072] is the fixed end bending moment of the structural load at the node:

[0073] ;

[0074] Then the angular displacement at the node is obtained The calculation formula is as follows:

[0075] .

[0076] In this embodiment, in step S2, a first coefficient A, a second coefficient B and a third coefficient C are defined to determine the angular displacement at the node. The calculation formula is simplified, and the first coefficient A, the second coefficient B and the third coefficient C are as follows:

[0077] ;

[0078] ;

[0079] ;

[0080] Simplified angular displacement at the node The calculation formula is as follows:

[0081] .

[0082] In this embodiment, in step S3, the theoretical value of the mid-span bending moment of the foundation slab is The calculation formula is as follows:

[0083] ;

[0084] Theoretical value of bending moment at foundation slab node The calculation formula is as follows:

[0085] ;

[0086] in, The linear stiffness ratio of the foundation slab and the side wall is:

[0087] .

[0088] In this embodiment, in step S4, the foundation slab is partitioned based on the segmented force and partitioned reinforcement method. The calculation formulas for the mid-span and node partition boundary points of the foundation slab are as follows:

[0089] ;

[0090] in, It is the distance from the partition boundary point to the center point of the near side wall. According to the principle of symmetry, the area from the partition boundary point to the center point of the mid-span of the foundation slab is the mid-span partition of the foundation slab, and the area from the partition boundary point to the outermost area of ​​the foundation slab is the node partition of the foundation slab.

[0091] In this embodiment, in step S4, the target design bearing capacity of the mid-span partition bending moment of the foundation slab is The calculation formula is as follows:

[0092] ;

[0093] Target design bearing capacity of the bending moment of the foundation slab node partition The calculation formula is as follows:

[0094] ;

[0095] in, is the importance coefficient of the structure, which is taken as 1.0.

[0096] In this embodiment, according to the calculated target design bearing capacity of the mid-span partition of the foundation slab and the target design bearing capacity of the node partition of the lower structure of the tunnel body, the required compressive steel bars in each partition are reinforced according to the structural reinforcement, and the required tensile steel bars in each partition are reinforced according to the single-bar bending section. That is, the upper steel bars in the mid-span partition of the foundation slab are reinforced according to the single-bar bending section calculation according to the target design bearing capacity, the lower steel bars in the mid-span partition are reinforced according to the structural reinforcement, the upper steel bars in the node partition of the foundation slab are reinforced according to the structural reinforcement, and the lower steel bars in the node partition are reinforced according to the target design bearing capacity.

[0097] For this embodiment 1: the structural dimensions are 6m×4.5m (structure net width×structure net height), the integral foundation culvert with a fill height of 10m, combined with Figure 4 , compared with the theoretical value of mid-span bending moment It can be found that the error between the calculated value in the specification and the numerical simulation analysis value is 2.6%, and the error between the calculated value in the present invention and the numerical simulation analysis value is 9.9%. 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 double, and the error is relatively large. The error of the calculated value according to the present invention is 11.8% compared with the numerical simulation analysis value. The calculation results of the present invention meet the actual engineering accuracy requirements, and the node bending moment calculation results of the present invention are closer to the actual stress condition of the structure than the calculated values ​​according to the specification.

[0098] Table 2 Comparison of results of three methods

[0099]

[0100] Based on segmented force and zoned reinforcement, the present invention provides the reinforcement demarcation principle of the mid-span and node zones of the foundation slab and the bending resistance calculation formula of the mid-span and node zones of the slab. Through differentiated and precise reinforcement of zones, it avoids the excessive reinforcement caused by the one-size-fits-all approach of mid-span and node zones in the past, and the unified reinforcement of the upper and lower parts of the mid-span node zones, thereby effectively reducing the project cost.

[0101] Embodiment 2

[0102] like Figure 1 As shown, this embodiment provides a technical solution: a culvert foundation bottom plate design method based on stiffness difference, comprising the following steps:

[0103] Step S1: construct a theoretical derivation model of the tunnel lower structure based on the difference in stiffness between the foundation slab and the side wall, and make relevant assumptions;

[0104] Step S2: Based on the displacement method, according to the deformation coordination relationship between the foundation bottom plate and the side wall at the node, the displacement method equation is established with the rotation angle of the foundation bottom plate and the side wall at the node as the equilibrium condition, and the calculation formula of the angular displacement at the node is obtained and simplified;

[0105] Step S3: Based on the displacement method and the simplified calculation formula for the angular displacement at the nodes, the theoretical value of the mid-span bending moment of the foundation bottom plate of the tunnel lower structure and the theoretical value of the node bending moment are calculated;

[0106] Step S4: Based on the segmented force and zoned reinforcement method, the foundation slab is zoned, and the target design bearing capacity of the mid-span zone bending moment and the target design bearing capacity of the node zone bending moment of the foundation slab of the lower structure of the tunnel body are calculated. The required compressive steel bars in each zone are arranged according to the structural reinforcement, and the required tensile steel bars are arranged according to the single-bar bending section reinforcement.

[0107] In this embodiment, the culvert includes a top plate 1, two side walls 2 and a foundation bottom plate 3. The top plate 1 is obtained by prefabricated components or cast on site. The 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 to the outside of the two side walls 2 by a predetermined distance. Figure 2 shown.

[0108] In this embodiment, in step S1, the following assumptions are made: the foundation slab and the two side walls are assumed to be frame structures. Considering the difference in stiffness between the foundation slab and the side walls, the bending stiffness of the side walls is EI1 and the bending stiffness of the foundation slab is EI2. The top slab is assumed to be the upper support point of the boundary condition of the side wall. The node between the side wall and the foundation slab is assumed to be an unfixed hinge. The foundation slab is assumed to have two parallel chain rods in the middle of its span, such as Figure 3 shown.

[0109] In this embodiment, the calculation parameters involved include: the thickness of the top plate d, the thickness of the side wall t1, the thickness of the foundation bottom plate t2, 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 point of the two side walls, the distance L2 from the center of the side wall to the outermost side of the foundation bottom plate, the lateral earth pressure q1 at the top of the side wall, the lateral earth pressure q2 at the bottom of the side wall, the design compressive stress q of the foundation bottom plate, and the bending moment M transmitted from the top plate to the top of the side wall. Figure 2 The detailed calculation parameters are shown in Table 3.

[0110] Table 3 Detailed calculation parameters

[0111]

[0112] In this embodiment, in step S2, the displacement method equation established is as follows:

[0113] ;

[0114] in, is the angular displacement at the node; is the stiffness coefficient:

[0115] ;

[0116] is the fixed end bending moment of the structural load at the node:

[0117] ;

[0118] Then the angular displacement at the node is obtained The calculation formula is as follows:

[0119] .

[0120] In this embodiment, in step S2, a first coefficient A, a second coefficient B and a third coefficient C are defined to determine the angular displacement at the node. The calculation formula is simplified, and the first coefficient A, the second coefficient B and the third coefficient C are as follows:

[0121] ;

[0122] ;

[0123] ;

[0124] Simplified angular displacement at the node The calculation formula is as follows:

[0125] .

[0126] In this embodiment, in step S3, the theoretical value of the mid-span bending moment of the foundation slab is The calculation formula is as follows:

[0127] ;

[0128] Theoretical value of bending moment at foundation slab node The calculation formula is as follows:

[0129] ;

[0130] in, The linear stiffness ratio of the foundation slab and the side wall is:

[0131] .

[0132] In this embodiment, in step S4, the foundation slab is partitioned based on the segmented force and partitioned reinforcement method. The calculation formulas for the mid-span and node partition boundary points of the foundation slab are as follows:

[0133] ;

[0134] in, It is the distance from the partition boundary point to the center point of the near side wall. According to the principle of symmetry, the area from the partition boundary point to the center point of the mid-span of the foundation slab is the mid-span partition of the foundation slab, and the area from the partition boundary point to the outermost area of ​​the foundation slab is the node partition of the foundation slab.

[0135] In this embodiment, in step S4, the target design bearing capacity of the mid-span partition bending moment of the foundation slab is The calculation formula is as follows:

[0136] ;

[0137] Target design bearing capacity of the bending moment of the foundation slab node partition The calculation formula is as follows:

[0138] ;

[0139] in, is the importance coefficient of the structure, which is taken as 1.0.

[0140] In this embodiment, according to the calculated target design bearing capacity of the mid-span partition of the foundation slab and the target design bearing capacity of the node partition of the lower structure of the tunnel body, the required compressive steel bars in each partition are reinforced according to the structural reinforcement, and the required tensile steel bars in each partition are reinforced according to the single-bar bending section. That is, the upper steel bars in the mid-span partition of the foundation slab are reinforced according to the single-bar bending section calculation according to the target design bearing capacity, the lower steel bars in the mid-span partition are reinforced according to the structural reinforcement, the upper steel bars in the node partition of the foundation slab are reinforced according to the structural reinforcement, and the lower steel bars in the node partition are reinforced according to the target design bearing capacity.

[0141] For the second 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 4. It can be found that the error between the calculated value in the specification and the numerical simulation analysis value is 5.4%, and the error between the calculated value in the present invention and the numerical simulation analysis value is -3.5%. It can be found that the error between the calculated value in the specification and the numerical simulation analysis value is 96.3%, which is twice as large. The error between the calculated value of the present invention and the numerical simulation analysis value is 7.9%. The calculation results of the present invention meet the actual engineering accuracy requirements, and the calculation results of the mid-span bending moment and the node bending moment of the present invention are closer to the actual stress condition of the structure than the calculated values ​​in the specification.

[0142] Table 4 Comparison of results of three methods

[0143]

[0144] 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 culvert foundation slab design method based on stiffness difference, characterized in that: The following steps are involved: Step S1: Based on the difference in stiffness between the foundation slab and the side walls, a theoretical derivation model of the tunnel lower structure is constructed, and relevant assumptions are made; in the step S1, the relevant assumptions are as follows: the foundation slab and the two side walls are assumed to be frame structures, and considering the difference in stiffness between the foundation slab and the side walls, the bending stiffness of the side walls is EI1, and the bending stiffness of the foundation slab is EI2; the top plate is assumed to be the upper support point of the boundary conditions of the side wall; the node between the side wall and the foundation slab is assumed to be an unfixed hinge; and the mid-span of the foundation slab is assumed to be two parallel chain rods; Step S2: Based on the displacement method, according to the deformation coordination relationship between the foundation bottom plate and the side wall at the node, the displacement method equation is established with the rotation angle of the foundation bottom plate and the side wall at the node as the equilibrium condition, and the calculation formula of the angular displacement at the node is obtained and simplified; Step S3: Based on the displacement method and the simplified calculation formula for the angular displacement at the nodes, the theoretical value of the mid-span bending moment of the foundation bottom plate of the tunnel lower structure and the theoretical value of the node bending moment are calculated; In step S3, the theoretical value of the mid-span bending moment of the foundation slab is The calculation formula is as follows: ； Theoretical value of bending moment at foundation slab node The calculation formula is as follows: ； in, A , B , C is the relevant parameter when the calculation formula of the angular displacement at the node is simplified, L1 is the distance between the center points of the two side walls, The linear stiffness ratio of the foundation slab and the side wall is: ； Among them, t1 is the thickness of the side wall, and t2 is the thickness of the foundation plate; Step S4: Based on the segmented force and zoned reinforcement method, the foundation slab is zoned, and the target design bearing capacity of the mid-span zone bending moment and the target design bearing capacity of the node zone bending moment of the foundation slab of the lower structure of the tunnel body are calculated. The required compressive steel bars in each zone are arranged according to the structural reinforcement, and the required tensile steel bars are arranged according to the single-bar bending section reinforcement.

2. A culvert foundation slab design method based on stiffness difference according to claim 1, characterized in that: The 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. The foundation bottom plate extends a predetermined distance to the outside of the two side walls.

3. The method for designing culvert foundation slab based on stiffness difference according to claim 2, characterized in that: In step S2, the displacement method equation established is as follows: ； in, is the angular displacement at the node; is the stiffness coefficient: ； exist In the figure, H1 is the distance from the center point of the top plate to the center point of the foundation bottom plate, and L1 is the distance from the center points of the two side walls; is the fixed end bending moment of the structural load at the node: ； exist In the equation, q1 is the lateral earth pressure at the top of the side wall, q2 is the lateral earth pressure at the bottom of the side wall, M is the bending moment transmitted from the top plate to the top of the side wall, L2 is the distance from the center of the side wall to the outermost side of the foundation bottom plate, and q is the design compressive stress of the foundation bottom plate; Then the angular displacement at the node is obtained The calculation formula is as follows: 。 4. The method for designing culvert foundation slab based on stiffness difference according to claim 3 is characterized in that: In step S2, a first coefficient is defined A , the second coefficient B and the third coefficient C , for the angular displacement at the node The calculation formula is simplified, the first coefficient A , the second coefficient B and the third coefficient C They are as follows: ； ； ； Simplified angular displacement at the node The calculation formula is as follows: 。 5. The method for designing culvert foundation slab based on stiffness difference according to claim 4, characterized in that: In step S4, the foundation slab is partitioned based on the segmented force and partitioned reinforcement method. The calculation formulas for the mid-span and node partition boundary points of the foundation slab are as follows: ； in, It is the distance from the partition boundary point to the center point of the proximal side wall. The root symmetry principle is that the area from the partition boundary point to the center point of the mid-span of the foundation slab is the node partition of the foundation slab, and the area from the partition boundary point to the outermost area of ​​the foundation slab is the node partition of the foundation slab.

6. A culvert foundation slab design method based on stiffness difference according to claim 5, characterized in that: In step S4, the target design bearing capacity of the mid-span partition bending moment of the foundation slab is The calculation formula is as follows: ； Target design bearing capacity of the bending moment of the foundation slab node partition The calculation formula is as follows: ； in, is the importance coefficient of the structure.

7. The method for designing culvert foundation slab based on stiffness difference according to claim 6, characterized in that: In step S4, according to the calculated target design bearing capacity of the mid-span partition of the foundation slab and the target design bearing capacity of the node partition of the lower structure of the tunnel body, the compressive steel bars required for each partition are reinforced according to the structural reinforcement, and the tensile steel bars required for each partition are reinforced according to the single-bar bending section, that is, the upper steel bars of the mid-span partition of the foundation slab are reinforced according to the single-bar bending section calculation according to the target design bearing capacity, the lower steel bars of the mid-span partition are reinforced according to the structural reinforcement, the upper steel bars of the node partition of the foundation slab are reinforced according to the structural reinforcement, and the lower steel bars of the node partition are reinforced according to the target design bearing capacity.

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