A sloping pier foundation structure and design method

Abstract

The application relates to a slope pier foundation structure and a design method, the slope pier foundation structure comprising a rock foundation, the rock foundation being externally provided with a compensation foundation, the rock foundation and the compensation foundation being provided with an enlarged foundation, the compensation foundation comprising a plurality of pile foundations and a bearing platform, and the bearing platform being installed on the plurality of pile foundations. The compensation foundation is arranged on the slope, the enlarged foundation is arranged on the compensation foundation and the rock foundation, the compensation foundation and the rock foundation jointly provide support for the enlarged foundation, the depth of the foundation pit is avoided from being excavated, the amount of mountain excavation and the amount of slope protection engineering are reduced, and the technical problem that when the pier foundation is located on a slope terrain and the geological condition is high-bearing-capacity bedrock geology, the pier foundation adopts the enlarged foundation, in order to make the foundation bearing capacity of the whole range of the bottom surface of the enlarged foundation meet the design requirement, the depth of the foundation pit excavation needs to be greatly increased, thereby causing the amount of mountain excavation and the amount of slope protection engineering to greatly increase is solved.

Description

Technical Field

[0001] This application relates to the field of bridge engineering technology, specifically to a sloping bridge pier foundation structure and design method. Background Technology

[0002] Currently, in addition to bearing the dead load generated by the bridge structure's own weight and the live load generated by trains or cars, the main pier foundations of long-span bridges also need to withstand additional loads generated by environmental factors such as temperature and wind. The external loads borne by the main pier foundations often reach tens of thousands or even hundreds of thousands of tons, making the foundation scale extremely large. For the construction of long-span bridges in mountainous areas, the pier foundations are often located on sloping terrain. When the surface cover layer at the pier location is thin and the geological conditions are bedrock with high bearing capacity, it is more economical and reasonable to use spread foundations for the pier foundations than to use pile foundations.

[0003] In related technologies, enlarged foundations often require the entire foundation bottom surface to be placed on a bedrock support surface with high bearing capacity. For a support surface at a specific elevation on a sloping terrain, the area near the inner side of the slope has a higher bearing capacity due to the greater burial depth of the strata, while the area near the outer side of the slope often has a lower bearing capacity due to the shallower burial depth of the strata. In order to ensure that the bearing capacity of the foundation throughout the entire area of ​​the enlarged foundation bottom surface meets the design requirements, the excavation depth of the foundation pit needs to be significantly increased, which leads to a significant increase in the amount of mountain excavation and slope protection engineering. This not only increases the project investment but also causes greater damage to the mountain environment, and the construction risks of the foundation pit and slope also increase accordingly.

[0004] Therefore, it is necessary to design a new sloping bridge pier foundation structure to overcome the above problems. Summary of the Invention

[0005] This application provides a slope bridge pier foundation structure and design method, which can solve the technical problem in related technologies where, when the bridge pier foundation is located on a slope and the geological conditions are bedrock with high bearing capacity, the bridge pier foundation adopts an enlarged foundation. In order to ensure that the bearing capacity of the foundation throughout the entire bottom surface of the enlarged foundation meets the design requirements, the excavation depth of the foundation pit needs to be greatly increased, which leads to a significant increase in the amount of mountain excavation and slope protection engineering.

[0006] In a first aspect, embodiments of this application provide a sloping bridge pier foundation structure, which includes a rock foundation, a compensating foundation provided outside the rock foundation, an enlarged foundation provided on the rock foundation and the compensating foundation, the compensating foundation including multiple pile foundations and a pile cap, the pile cap being installed on the multiple pile foundations.

[0007] Secondly, embodiments of this application provide a design method for a sloping bridge pier foundation structure. The design method employs the aforementioned sloping bridge pier foundation structure and includes the following steps:

[0008] Based on the maximum stress σ on the top surface of the rock foundation under the main working conditions max-m and minimum stress σ min-m The range of values ​​is used to determine the top surface area of ​​the rock foundation;

[0009] Based on the maximum stress σ of the foundation support surface under the main force and additional force conditions max-a and minimum stress σ min-a The range of values ​​is used to determine the area of ​​the foundation support surface and calculate the top surface area of ​​the compensated foundation, where the sum of the top surface area of ​​the rock foundation and the top surface area of ​​the compensated foundation is equal to the area of ​​the foundation support surface.

[0010] Based on the top surface area of ​​the compensated foundation and the maximum stress σ on the foundation support surface under the main force and additional load conditions. max-a The total load on the pile top is determined by the self-weight of the pile cap, and the pile diameter, number of piles and pile length are determined based on the total load of the pile foundation and in combination with geological conditions.

[0011] In conjunction with the second aspect, in one embodiment, the maximum stress σ on the top surface of the rock foundation under the main working conditions is... max-m and minimum stress σ min-m The range of values ​​for is used to determine the top surface area of ​​the rock foundation, including:

[0012] According to σ max-m ≤[σ] and σ min-m ≥0 determines the top surface area of ​​the rock foundation, where [σ] is the allowable bearing capacity of the rock foundation, and the maximum stress σ on the top surface of the rock foundation under the main working condition is... max-m The calculation formula is:

[0013]

[0014] The minimum stress σ on the top surface of the rock foundation under the main working condition. min-m The calculation formula is:

[0015]

[0016] In the formula σ max-m σ represents the maximum stress on the top surface of the rock foundation under the main working conditions. min-m The minimum stress on the top surface of the rock foundation under the main working conditions, N m M represents the vertical force at the centroid of the top surface of the bridge pier foundation relative to the rock foundation under the main working conditions. xm M is the longitudinal bending moment at the centroid of the top surface of the pier foundation relative to the rock foundation under the main working conditions. ym A is the transverse bending moment at the centroid of the top surface of the pier foundation relative to the rock foundation under the main working conditions. b I is the area of ​​the top surface of the rock foundation. xbFor the moment of inertia of the top surface of the rock foundation along the bridge direction, I yb Let x be the transverse moment of inertia of the top surface of the rock foundation. b y is the distance from the stress calculation point to the transverse centroidal axis of the top surface of the rock foundation. b It is the distance from the stress calculation point to the centroidal axis along the bridge direction from the top surface of the rock foundation.

[0017] In conjunction with the second aspect, in one embodiment, the maximum stress σ of the foundation support surface under the main force plus additional force condition is... max-a and minimum stress σ min-a The range of values ​​is used to determine the area of ​​the foundation support surface and calculate the top surface area of ​​the compensated foundation, including:

[0018] According to σ max-a ≤[σ] and Determine the area of ​​the foundation support surface, where [σ] is the allowable bearing capacity of the rock foundation, [e] is the allowable eccentricity of the vertical force on the pier foundation relative to the centroid of the foundation support surface, W is the section modulus of the edge of the foundation support surface with lower stress, A is the area of ​​the foundation support surface, and N... a The vertical force at the centroid of the bridge pier foundation relative to the foundation support surface under the main force plus additional force condition is σ, which represents the maximum stress σ on the foundation support surface under the main force plus additional force condition. max-a The calculation formula is as follows:

[0019]

[0020] The minimum stress σ on the foundation support surface under the main force and additional stress conditions. min-a The calculation formula is as follows:

[0021]

[0022] In the formula σ max-a σ represents the maximum stress on the foundation support surface under the condition of main force plus additional force. min-a The minimum stress on the foundation support surface under the condition of main force plus additional force, N a M represents the vertical force at the centroid of the bridge pier foundation relative to the ground support surface under the condition of main force plus additional force. xa M is the longitudinal bending moment of the bridge pier foundation at the centroid of the ground support surface under the main load and additional load conditions. ya Let A be the transverse bending moment of the bridge pier foundation at the centroid of the ground bearing surface under the condition of main force plus additional force, and let I be the area of ​​the ground bearing surface. x I is the longitudinal moment of inertia of the foundation support surface. y Let x be the transverse moment of inertia of the foundation support surface, x be the distance from the stress calculation point to the transverse centroidal axis of the foundation support surface, and y be the distance from the stress calculation point to the longitudinal centroidal axis of the foundation support surface.

[0023] According to A c =AA b The area of ​​the top surface of the compensated foundation is calculated, where A c To compensate for the top surface area of ​​the foundation, let A be the area of ​​the foundation support surface. b It represents the area of ​​the top surface of the rock foundation.

[0024] In conjunction with the second aspect, in one embodiment, the method of calculating the maximum stress σ on the foundation support surface under the main force plus additional force conditions is based on the top surface area of ​​the compensated foundation. max-a The total load on the pile top is determined by the self-weight of the pile cap, including:

[0025] The top surface area of ​​the foundation will be compensated, and the maximum stress σ on the foundation support surface under the main force and additional force conditions will be calculated. max-a The total load at the pile top is obtained by substituting the self-weight of the pile cap into the formula for calculating the total load at the pile top, where the formula for calculating the total load at the pile top is as follows:

[0026] N z =A c *σ max-a +G c ,

[0027] In the formula N z For the total load at the pile top, A c To compensate for the top surface area of ​​the foundation, G c For the weight of the foundation.

[0028] In conjunction with the second aspect, in one embodiment, the design method further includes the following steps: determining whether the anti-sliding stability coefficient K of the enlarged foundation meets the requirements based on the top surface area of ​​the compensating foundation and the top surface area of ​​the rock foundation, wherein the compensating foundation and the enlarged foundation are cast separately, and the calculation formula for the anti-sliding stability coefficient K of the enlarged foundation is:

[0029]

[0030] In the formula, K is the anti-sliding stability coefficient of the spread foundation, K≥1.3, N is the vertical pressure of the spread foundation base, H is the horizontal thrust of the spread foundation base, and A c To compensate for the top surface area of ​​the foundation, A b Let A be the area of ​​the top surface of the rock foundation, and let A be the area of ​​the foundation support surface. c To increase the friction coefficient between the bottom surface of the foundation and the top surface of the compensating foundation, μ b To increase the coefficient of friction between the bottom surface of the foundation and the top surface of the rock foundation.

[0031] In conjunction with the second aspect, in one embodiment, the design method further includes the following steps: determining whether the total area of ​​the multiple pile foundations meets the requirements based on the top surface area of ​​the compensating foundation and the area of ​​the foundation support surface, wherein the total area A of the multiple pile foundations... z The calculation formula is:

[0032]

[0033] In the formula, A z Let N be the total area of ​​the multiple pile foundations, N be the vertical pressure on the enlarged foundation base, and A be the total area of ​​the pile foundations. c To compensate for the top surface area of ​​the foundation, let A be the area of ​​the foundation support surface, μ c To increase the friction coefficient between the bottom surface of the foundation and the top surface of the compensating foundation, [τ] is the allowable shear stress of the pile foundation section.

[0034] In conjunction with the second aspect, in one embodiment, the design method further includes the following steps: determining whether the anti-sliding stability coefficient K of the enlarged foundation meets the requirements based on the top surface area of ​​the rock foundation and the area of ​​the foundation support surface, wherein the enlarged foundation and the compensating foundation are integrally cast, and the calculation formula for the anti-sliding stability system K of the enlarged foundation is:

[0035]

[0036] In the formula, K is the anti-sliding stability coefficient of the spread foundation, K≥1.3, N is the vertical pressure of the spread foundation base, H is the horizontal thrust of the spread foundation base, and A b Let A be the area of ​​the top surface of the rock foundation, and let A be the area of ​​the foundation support surface. b To increase the coefficient of friction between the bottom surface of the foundation and the top surface of the rock foundation, A z Let τ be the total area of ​​the multiple piles, and [τ] be the allowable shear stress of the pile section.

[0037] In conjunction with the second aspect, in one embodiment, the design method further includes the following steps: determining whether the thickness of the pile cap meets the requirements based on the pile diameter and the center-to-center distance between adjacent piles, wherein the formula for calculating the thickness T of the pile cap is:

[0038]

[0039] In the formula, T is the thickness of the pile cap, S is the center distance between adjacent piles, and d is the diameter of the pile.

[0040] In conjunction with the second aspect, in one embodiment, the ratio of the center-to-center distance S of the adjacent pile foundations to the diameter d of the pile foundations is greater than or equal to 2.

[0041] The beneficial effects of the technical solutions provided in this application include:

[0042] By setting up a compensating foundation on the outside of the slope, and then setting up an enlarged foundation on the compensating foundation and the rock foundation, the combination of the compensating foundation and the rock foundation provides support for the enlarged foundation. Under the condition of ensuring the structural safety of the bridge foundation, the deep excavation of the foundation pit is avoided, and the amount of mountain excavation and slope protection engineering is reduced. This solves the technical problem in related technologies where, when the bridge pier foundation is located on a slope and the geological conditions are bedrock with high bearing capacity, the use of an enlarged foundation for the bridge pier foundation requires a significant increase in the depth of the foundation pit in order to meet the design requirements for the bearing capacity of the foundation throughout the bottom area of ​​the enlarged foundation, which leads to a significant increase in the amount of mountain excavation and slope protection engineering. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 A side view of a sloping bridge pier foundation structure provided in an embodiment of this application;

[0045] Figure 2 A top view of the rock foundation and the compensated foundation provided in the embodiments of this application;

[0046] Figure 3 for Figure 2 Sectional view of AA;

[0047] Figure 4 A structural schematic diagram of the compensating foundation and the enlarged foundation provided in the embodiments of this application;

[0048] Figure 5 A bottom view of the compensated foundation and enlarged foundation provided for an embodiment of this application.

[0049] In the diagram: 1. Rock foundation; 2. Compensating foundation; 21. Pile foundation; 22. Pile cap; 3. Spread foundation; 4. Bridge pier. Detailed Implementation

[0050] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0051] This application provides a slope bridge pier foundation structure and design method, which can solve the technical problem that when the bridge pier foundation is located on a slope and the geological conditions are bedrock with high bearing capacity, the bridge pier foundation adopts an enlarged foundation. In order to make the bearing capacity of the foundation in the entire range of the bottom surface of the enlarged foundation meet the design requirements, the excavation depth of the foundation pit needs to be greatly increased, which leads to a large increase in the amount of mountain excavation and slope protection engineering.

[0052] See Figure 1 , Figure 4 and Figure 5 As shown in the figure, this application provides a slope bridge pier foundation structure, which includes a rock foundation 1, a compensation foundation 2 outside the rock foundation 1, an enlarged foundation 3 on the rock foundation 1 and the compensation foundation 2, the compensation foundation 2 including multiple pile foundations 21 and a pile cap 22, the pile cap 22 being installed on the multiple pile foundations 21.

[0053] In this embodiment, multiple piles 21 are inserted into the bedrock. These piles 21 are arranged at the same elevation as the terrain in an area with low bearing capacity on the outer side of the slope. The pile cap 22, combined with the planar arrangement of the multiple piles 21, can be L-shaped. The multiple piles 21 are located at the bottom of the pile cap 22, which surrounds the outer side of the rock foundation 1. A bridge pier 4 is cast on the enlarged foundation 3. The enlarged foundation 3 and the compensating foundation 2 can be cast separately or integrally. The multiple piles 21 are located at the far... On the side away from the slope, multiple piles 21 and the pile cap 22 are integrally cast and formed. The top surface of the compensation foundation 2 and the top surface of the rock foundation 1 can be set to be flush. The top surface of the compensation foundation 2 and the top surface of the rock foundation 1 form a complete foundation support surface. The enlarged foundation 3 is set on the foundation support surface. The compensation foundation 2 and the rock foundation 1 together provide support for the enlarged foundation 3. Under the condition of meeting the stress safety of the bridge foundation, the deep excavation of the foundation pit is avoided, and the amount of mountain excavation and slope protection engineering is reduced.

[0054] This embodiment sets up the compensation foundation 2 on the outside of the slope, and sets up the enlarged foundation 3 on the compensation foundation 2 and the rock foundation 1. The compensation foundation 2 and the rock foundation 1 together provide support for the enlarged foundation 3. Under the condition of ensuring the structural safety of the bridge foundation, it avoids deep excavation of the foundation pit, reduces the amount of mountain excavation and slope protection engineering, and solves the technical problem in related technologies where the bridge pier foundation is located on a slope and the geological conditions are bedrock with high bearing capacity. When the bridge pier foundation adopts an enlarged foundation, the excavation depth of the foundation pit needs to be greatly increased in order to meet the design requirements of the bearing capacity of the foundation throughout the bottom area of ​​the enlarged foundation, which leads to a large increase in the amount of mountain excavation and slope protection engineering.

[0055] See Figure 1-3As shown in the figure, this application provides a design method for a sloping bridge pier foundation structure. The design method adopts the above-mentioned sloping bridge pier foundation structure and includes the following steps:

[0056] S1: Based on the maximum stress σ on the top surface of rock foundation 1 under the main working condition. max-m and minimum stress σ min-m The range of values ​​is used to determine the top surface area of ​​rock foundation 1.

[0057] S2: Based on the maximum stress σ of the foundation support surface under the main force plus additional force condition. max-a and minimum stress σ min-a The range of values ​​is used to determine the area of ​​the foundation support surface and calculate the top surface area of ​​the compensated foundation 2, where the sum of the top surface area of ​​the rock foundation 1 and the top surface area of ​​the compensated foundation 2 is equal to the area of ​​the foundation support surface.

[0058] S3: Based on the top surface area of ​​the compensated foundation 2 and the maximum stress σ of the foundation support surface under the main force plus additional force condition. max-a The total load on the pile top is determined by the self-weight of the pile cap 22, and the pile diameter, number of piles and pile length of the pile foundation 21 are determined based on the total load of the pile foundation 21 and in combination with the geological conditions.

[0059] In this embodiment, based on the maximum stress σ on the top surface of the rock foundation 1 under the main working condition... max-m and minimum stress σ min-m The range of values ​​is used to determine the top surface area of ​​rock foundation 1, based on the maximum stress σ on the foundation support surface under the main force and additional load conditions. max-a and minimum stress σ min-a The range of values ​​is used to determine the area of ​​the foundation support surface. Using the top surface area of ​​rock foundation 1 and the area of ​​the foundation support surface, the top surface area of ​​the compensated foundation 2 can be calculated. Then, based on the top surface area of ​​the compensated foundation 2 and the maximum stress σ of the foundation support surface under the main force plus additional load conditions... max-a The total load at the pile top is determined by the self-weight of the pile cap 22, and the formula for calculating the total load at the pile top is as follows:

[0060] N z =A c *σ max-a +G c ,

[0061] In the formula N z For the total load at the pile top, A c To compensate for the top surface area of ​​foundation 2, G c Based on the self-weight of the pier cap 22, and considering the total load at the top of the piles and geological conditions, the pile diameter, number of piles, and pile length of the pile foundation 21 can be determined according to the conventional design methods for bridge foundations.

[0062] Furthermore, in some embodiments, the maximum stress σ on the top surface of the rock foundation 1 under the main working condition is... max-m and minimum stress σ min-m The range of values ​​for is used to determine the top surface area of ​​rock foundation 1, including:

[0063] According to σ max-m ≤[σ] and σ min-m ≥0 determines the top surface area of ​​rock foundation 1, where [σ] is the allowable bearing capacity of rock foundation 1, and the maximum stress σ on the top surface of rock foundation 1 under the main working condition is given by σ. max-m The calculation formula is:

[0064]

[0065] The minimum stress σ on the top surface of the rock foundation 1 under the main working condition. min-m The calculation formula is:

[0066]

[0067] In the formula σ max-m σ represents the maximum stress on the top surface of rock foundation 1 under the main working condition. min-m The minimum stress on the top surface of rock foundation 1 under the main working condition is N. m M represents the vertical force at the centroid of the top surface of the bridge pier foundation relative to the rock foundation 1 under the main working conditions. xm M is the longitudinal bending moment of the pier foundation at the centroid of the top surface of the rock foundation 1 under the main working condition. ym A is the transverse bending moment at the centroid of the top surface of the pier foundation relative to the rock foundation 1 under the main working condition. b I is the area of ​​the top surface of the rock foundation 1. xb Let I be the moment of inertia of the top surface of the rock foundation 1 along the bridge direction. yb Let x be the transverse moment of inertia of the top surface of rock foundation 1. b y is the distance from the stress calculation point to the transverse centroidal axis of the top surface of the rock foundation. b It is the distance from the stress calculation point to the centroidal axis along the bridge direction from the top surface of the rock foundation.

[0068] In this embodiment, the maximum stress σ on the top surface of the rock foundation 1 under the main working condition is... max-m The calculation formula and the minimum stress σ on the top surface of the rock foundation 1 under the main working condition. min-m Substituting the calculation formula into σ max-m ≤[σ] and σ min-mIf the area is ≥0, the top surface area of ​​rock foundation 1 can be determined. Based on the top surface area of ​​rock foundation 1 and the distribution of rock strata from geological survey, the design elevation of the top surface of rock foundation 1 is determined. This ensures that the top surface of rock foundation 1 meets the bearing capacity requirements while the area of ​​the top surface of rock foundation 1 is greater than or equal to the design area. Under the main working conditions, the vertical force N at the centroid of the top surface of the bridge pier foundation relative to rock foundation 1 is... m The longitudinal bending moment M at the centroid of the top surface of the bridge pier foundation relative to the rock foundation 1 under the main working conditions. xm The transverse bending moment M at the centroid of the top surface of the bridge pier foundation relative to the rock foundation 1 under the main working conditions. ym The longitudinal moment of inertia I of the top surface of the rock foundation 1 can be obtained through calculation and analysis of the bridge superstructure. xb The transverse moment of inertia I of the top surface of the rock foundation 1 yb The distance x from the stress calculation point to the centroidal axis of the transverse bridge of the top surface of the rock foundation. b And the distance y from the stress calculation point to the centroidal axis along the bridge direction from the top surface of the rock foundation. b It can be obtained through geometric calculation. The reference rectangular coordinate system takes the centroid of the top surface of the rock foundation 1 as the origin, the x-axis along the bridge direction and the y-axis along the bridge direction. The area of ​​the top surface of the rock foundation 1 is determined according to the main working conditions. This can avoid excessive uneven settlement deformation of the foundation support surface under long-term daily operation load due to the compensation of the vertical stiffness difference between the foundation 2 and the rock foundation 1, which would lead to cracking of the foundation structure.

[0069] In the specific design of the top surface area of ​​rock foundation 1, an initial value can be set for the top surface area of ​​rock foundation 1, and the initial top surface area A of rock foundation 1 can be obtained through geometric calculation. b The initial top surface moment of inertia along the bridge direction of the rock foundation 1 xb The initial transverse moment of inertia I of the top surface of the rock foundation 1 yb The initial distance x from the stress calculation point to the transverse centroidal axis of the top surface of the rock foundation. b The initial distance y from the stress calculation point to the centroidal axis of the top surface of the rock foundation along the bridge direction. b Substituting each parameter into the maximum stress σ on the top surface of the rock foundation 1 under the main working condition, max-m and minimum stress σ min-m The calculation formula is used to obtain σ. max-m and σ min-n Then check σ max-m and σ min-m Does σ satisfy? max-m ≤[σ] and σ min-m If the initial top surface area of ​​the rock foundation 1 is too small, the top surface area of ​​the rock foundation 1 should be appropriately increased and recalculated until σ ≥ 0. max-m and σ min-m Satisfying σ max-m≤[σ] and σ min-m ≥0, and keep the basic safety margin within 10%.

[0070] Furthermore, in some embodiments, the maximum stress σ of the foundation support surface under the main force plus additional force condition is... max-a and minimum stress σ min-a The range of values ​​is used to determine the area of ​​the foundation support surface and calculate the top surface area of ​​the compensated foundation 2, including:

[0071] Step 1: Based on σ max-a ≤[σ] and Determine the area of ​​the foundation support surface, where [σ] is the allowable bearing capacity of the rock foundation 1, [e] is the allowable eccentricity of the vertical force on the pier foundation relative to the centroid of the foundation support surface, W is the section modulus of the edge of the foundation support surface with lower stress, A is the area of ​​the foundation support surface, and N... a The vertical force at the centroid of the bridge pier foundation relative to the foundation support surface under the main force plus additional force condition is σ, which represents the maximum stress σ on the foundation support surface under the main force plus additional force condition. max-a The calculation formula is as follows:

[0072]

[0073] The minimum stress σ on the foundation support surface under the main force and additional stress conditions. min-a The calculation formula is as follows:

[0074]

[0075] In the formula σ max-a σ represents the maximum stress on the foundation support surface under the condition of main force plus additional force. min-a The minimum stress on the foundation support surface under the condition of main force plus additional force, N a M represents the vertical force at the centroid of the bridge pier foundation relative to the ground support surface under the condition of main force plus additional force. xa M is the longitudinal bending moment of the bridge pier foundation at the centroid of the ground support surface under the main load and additional load conditions. ya Let A be the transverse bending moment of the bridge pier foundation at the centroid of the ground bearing surface under the condition of main force plus additional force, and let I be the area of ​​the ground bearing surface. x I is the longitudinal moment of inertia of the foundation support surface. y Let x be the transverse moment of inertia of the foundation support surface, x be the distance from the stress calculation point to the transverse centroidal axis of the foundation support surface, and y be the distance from the stress calculation point to the longitudinal centroidal axis of the foundation support surface.

[0076] Step 2: According to A c =AA b The area of ​​the top surface of the compensated foundation 2 is calculated, where A cTo compensate for the top surface area of ​​foundation 2, let A be the area of ​​the foundation support surface. b Let be the area of ​​the top surface of rock foundation 1.

[0077] In this embodiment, the maximum stress σ on the foundation support surface under the main force plus additional force condition is... max-a The calculation formula and the minimum stress σ of the foundation support surface under the main force plus additional force condition. min-a Substituting the calculation formula into σ max-a ≤[σ] and The area of ​​the foundation support surface can then be determined. The top surface of the rock foundation 1 and the top surface of the compensated foundation 2 together constitute the foundation support surface. The area of ​​the foundation support surface is equal to the required planar dimensions of the enlarged foundation 3. The vertical force N at the centroid of the pier foundation relative to the foundation support surface under the main force plus additional force conditions is... a Under the condition of main force plus additional force, the longitudinal bending moment M at the centroid of the pier foundation relative to the foundation support surface. xa The transverse bending moment M at the centroid of the bridge pier foundation relative to the ground support surface under the main load and additional load conditions. ya The longitudinal moment of inertia I of the foundation support surface can be obtained through bridge structural calculation and analysis. x The transverse moment of inertia I of the foundation support surface y The distance x from the stress calculation point to the centroidal axis of the foundation support surface in the transverse direction and the distance y from the stress calculation point to the centroidal axis of the foundation support surface in the longitudinal direction can be obtained through geometric calculation. The reference rectangular coordinate system takes the centroid of the foundation support surface as the origin, the longitudinal direction as the x-axis, and the transverse direction as the y-axis. The area of ​​the foundation support surface and the top surface area of ​​the compensation foundation 2 are determined according to the main load conditions and additional force conditions. This can ensure the stability of the foundation support surface and the stress safety of the foundation structure under extreme load conditions such as storms, giant waves, cold waves, and high temperatures.

[0078] In the specific design process of the foundation support surface area, an initial value can be set for the foundation support surface first, and the initial area A and the initial longitudinal moment of inertia I of the foundation support surface can be obtained through geometric calculations. x The initial transverse moment of inertia I of the foundation support surface y The initial distance x from the stress calculation point to the transverse centroidal axis of the foundation support surface, and the initial distance y from the stress calculation point to the longitudinal centroidal axis of the foundation support surface are used to substitute these parameters into the maximum stress σ of the foundation support surface under the main force plus additional force condition. max-a and minimum stress σ min-a The calculation formula is used to obtain σ. max-a and σ min-a Then check σ max-a and σ min-a Does σ satisfy? max-a ≤[σ] and If the initial area of ​​the foundation support surface is too small, the area of ​​the foundation support surface should be appropriately increased and recalculated until σ max-a and σ min-a Satisfying σ max-a ≤[σ] and And keep the basic safety margin below 10%.

[0079] Furthermore, in some embodiments, the method of calculating the top surface area of ​​the compensated foundation 2 and the maximum stress σ of the foundation support surface under the main force plus additional force conditions is further described. max-a The total load on the pile top is determined by the self-weight of pile cap 22, including:

[0080] The top surface area of ​​the compensated foundation 2 and the maximum stress σ of the foundation support surface under the main force and additional force conditions will be calculated. max-a The total load at the pile top is obtained by substituting the self-weight of the pile cap 22 into the calculation formula for the total load at the pile top, wherein the calculation formula for the total load at the pile top is as follows:

[0081] N z =A c *σ max-a +G c ,

[0082] In the formula N z For the total load at the pile top, A c To compensate for the top surface area of ​​foundation 2, G c For the weight of the foundation 22.

[0083] In this embodiment, the sum of the top surface load of the compensating foundation 2 and the self-weight of the pile cap 22 equals the total load at the pile top. The top surface area A of the compensating foundation 2 is... c The maximum stress σ on the foundation support surface under main force plus additional force conditions max-a And the self-weight G of the pier 22 c Substituting the values ​​into the formula for calculating the total load at the pile top, we can obtain the total load N at the pile top. z Based on the total load of the pile foundation and combined with the geological conditions, the pile diameter, number of piles and pile length of pile foundation 21 can be determined according to the conventional design method of bridge foundation.

[0084] Furthermore, in some embodiments, the design method further includes the following steps: determining whether the anti-sliding stability coefficient K of the enlarged foundation 3 meets the requirements based on the top surface area of ​​the compensated foundation 2 and the top surface area of ​​the rock foundation 1, wherein the compensated foundation 2 and the enlarged foundation 3 are cast separately, and the calculation formula for the anti-sliding stability coefficient K of the enlarged foundation 3 is:

[0085]

[0086] In the formula, K is the anti-sliding stability coefficient of the enlarged foundation 3, K≥1.3, N is the vertical pressure of the enlarged foundation base, H is the horizontal thrust of the enlarged foundation base, and A c To compensate for the top surface area of ​​foundation 2, A b Let A be the area of ​​the top surface of rock foundation 1, and let A be the area of ​​the foundation support surface. c To increase the friction coefficient between the bottom surface of the foundation and the top surface of the compensating foundation, μ b To increase the coefficient of friction between the bottom surface of the foundation and the top surface of the rock foundation.

[0087] In this embodiment, the top surface area A of the compensating foundation 2 will be... c The top surface area A of the rock foundation 1 b Substituting into the calculation formula of the anti-sliding stability system K of the enlarged foundation 3, where the vertical pressure N and horizontal thrust H of the enlarged foundation base can be obtained through bridge structure calculation and analysis, and the friction coefficient μ between the bottom surface of the enlarged foundation and the top surface of the compensating foundation... c And increase the friction coefficient μ between the bottom surface of the foundation and the top surface of the rock foundation. b The anti-sliding stability coefficient K of the enlarged foundation 3 can be obtained by consulting design specifications or on-site tests. If the anti-sliding stability coefficient K of the enlarged foundation 3 is greater than or equal to 1.3, then there is no need to adjust the structural dimensions of the enlarged foundation 3. If the anti-sliding stability coefficient K of the enlarged foundation 3 is less than 1.3, then the thickness of the enlarged foundation 3 should be adjusted to increase the self-weight of the enlarged foundation, thereby increasing the vertical pressure N of the base of the enlarged foundation until the anti-sliding stability coefficient K of the enlarged foundation 3 is greater than or equal to 1.3.

[0088] Furthermore, in some embodiments, the design method further includes the following step: determining whether the total area of ​​the multiple pile foundations 21 meets the requirements based on the top surface area of ​​the compensating foundation 2 and the area of ​​the foundation support surface, wherein the total area A of the multiple pile foundations 21 z The calculation formula is:

[0089]

[0090] In the formula, A z Let N be the total area of ​​multiple pile foundations 21, N be the vertical pressure at the base of the enlarged foundation, and A be the total area of ​​the pile foundations 21. c To compensate for the top surface area of ​​foundation 2, let A be the area of ​​the foundation support surface, μ c To increase the friction coefficient between the bottom surface of the foundation and the top surface of the compensating foundation, [τ] is the allowable shear stress of the pile foundation section.

[0091] In this embodiment, the top surface area A of the compensating foundation 2 will be... c Substitute the area A of the foundation support surface into the total area A of the multiple pile foundations 21. zThe calculation formula is as follows: the vertical pressure N of the enlarged foundation base can be obtained through bridge structure calculation and analysis, and the friction coefficient μ between the bottom surface of the enlarged foundation and the top surface of the compensating foundation is... c The allowable shear stress [τ] of the pile foundation section can be obtained by consulting design specifications or field tests. This can be determined by referring to the design specifications based on the concrete strength grade used for pile foundation 21. The total area A of multiple pile foundations 21 is... z The total area A of multiple pile foundations 21 can be calculated using the pile diameter and number of piles. z If the requirements are met, there is no need to adjust the pile diameter and number of piles. If the total area of ​​multiple pile foundations 21 does not meet the requirements, the pile diameter and number of piles need to be adjusted until the total area of ​​multiple pile foundations 21 meets the requirements.

[0092] Furthermore, in some embodiments, the design method further includes the following steps: determining whether the anti-sliding stability coefficient K of the enlarged foundation 3 meets the requirements based on the top surface area of ​​the rock foundation 1 and the area of ​​the foundation support surface, wherein the enlarged foundation 3 and the compensation foundation 2 are integrally cast, and the calculation formula for the anti-sliding stability system K of the enlarged foundation 3 is:

[0093]

[0094] In the formula, K is the anti-sliding stability coefficient of the enlarged foundation 3, K≥1.3, N is the vertical pressure of the enlarged foundation base, H is the horizontal thrust of the enlarged foundation base, and A b Let A be the area of ​​the top surface of rock foundation 1, and let A be the area of ​​the foundation support surface. b To increase the coefficient of friction between the bottom surface of the foundation and the top surface of the rock foundation, A z Let τ be the total area of ​​the multiple piles 21, and let [τ] be the allowable shear stress of the pile section.

[0095] In this embodiment, the top surface area A of the rock foundation 1 is... b Substituting the area A of the foundation support surface into the calculation formula of the anti-sliding stability system K of the enlarged foundation 3, where the vertical pressure N and horizontal thrust H of the enlarged foundation base can be obtained through bridge structure calculation and analysis, and the friction coefficient μ between the bottom surface of the enlarged foundation and the top surface of the rock foundation. b The allowable shear stress [τ] of the pile foundation section can be obtained by consulting design specifications or field tests. This can be determined by referring to the design specifications based on the concrete strength grade used for pile foundation 21. The total area A of multiple pile foundations 21 is... zThe anti-sliding stability coefficient K of the enlarged foundation 3 can be calculated from the pile diameter and the number of piles. If the anti-sliding stability coefficient K of the enlarged foundation 3 is greater than or equal to 1.3, then there is no need to adjust the structural dimensions of the enlarged foundation 3. If the anti-sliding stability coefficient K of the enlarged foundation 3 is less than 1.3, then the thickness of the enlarged foundation 3 should be adjusted to increase the self-weight of the enlarged foundation, so as to increase the vertical pressure N of the base of the enlarged foundation until the anti-sliding stability coefficient K of the enlarged foundation 3 is greater than or equal to 1.3.

[0096] Further, see Figure 1 As shown, in some embodiments, the design method further includes the following steps: determining whether the thickness of the pile cap 22 meets the requirements based on the pile diameter and the center-to-center distance between adjacent piles, wherein the formula for calculating the thickness T of the pile cap 22 is:

[0097]

[0098] In the formula, T is the thickness of the pile cap 22, S is the center distance between adjacent piles, and d is the diameter of the pile.

[0099] In this embodiment, the center distance S between adjacent pile foundations and the pile diameter d are substituted into the calculation formula for the thickness T of the pile cap 22. If the thickness T of the pile cap 22 meets the requirements, there is no need to adjust the thickness T of the pile cap 22. If the thickness T of the pile cap 22 does not meet the requirements, the thickness T of the pile cap 22 needs to be adjusted until the thickness T of the pile cap 22 meets the requirements.

[0100] Further, see Figure 1 As shown, in some embodiments, the ratio of the center distance S between adjacent pile foundations to the diameter d of the pile foundation is greater than or equal to 2.

[0101] In the description of this application, it should be noted that the terms "upper," "lower," etc., indicating the orientation or positional relationship are based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this application. Unless otherwise expressly specified and limited, the terms "installed," "connected," and "linked" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication between two elements. For those skilled in the art, the specific meaning of the above terms in this application can be understood according to the specific circumstances.

[0102] It should be noted that in this application, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0103] The above description is merely a specific embodiment of this application, enabling those skilled in the art to understand or implement this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A design method for a sloping bridge pier foundation structure, the sloping bridge pier foundation structure comprising a rock foundation, a compensating foundation provided outside the rock foundation, an enlarged foundation provided on the rock foundation and the compensating foundation, the compensating foundation comprising multiple pile foundations and a pile cap, the pile cap being installed on the multiple pile foundations, characterized in that, The design method includes the following steps: Based on the maximum stress on the top surface of the rock foundation under the main working conditions and minimum stress The range of values ​​for is used to determine the top surface area of ​​the rock foundation. according to and Determine the area of ​​the top surface of the rock foundation, where The allowable bearing capacity of the rock foundation, wherein the maximum stress on the top surface of the rock foundation under the main working condition is defined as... The calculation formula is: ， The minimum stress on the top surface of the rock foundation under the main working conditions. The calculation formula is: ， In the formula This represents the maximum stress on the top surface of the rock foundation under the main working conditions. This represents the minimum stress on the top surface of the rock foundation under the main working conditions. This refers to the vertical force at the centroid of the top surface of the bridge pier foundation relative to the rock foundation under the main working conditions. The bending moment along the bridge direction at the centroid of the top surface of the pier foundation relative to the rock foundation under the main working conditions. The transverse bending moment of the bridge pier foundation at the centroid of the top surface relative to the rock foundation under the main working conditions. The area of ​​the top surface of the rock foundation. The moment of inertia of the top surface of the rock foundation along the bridge direction. The moment of inertia of the top surface of the rock foundation in the transverse direction. Let be the distance from the stress calculation point to the transverse centroidal axis of the top surface of the rock foundation. This is the distance from the stress calculation point to the centroidal axis along the bridge direction from the top surface of the rock foundation; Based on the maximum stress on the foundation support surface under the main force and additional stress conditions and minimum stress The range of values ​​is used to determine the area of ​​the foundation support surface and calculate the top surface area of ​​the compensated foundation. The sum of the top surface area of ​​the rock foundation and the top surface area of ​​the compensated foundation equals the area of ​​the foundation support surface. according to and Determine the area of ​​the foundation support surface, where The allowable bearing capacity of the rock foundation. Let W be the allowable eccentricity of the vertical force acting on the bridge pier foundation relative to the centroid of the foundation support surface, W be the section modulus of the edge of the foundation support surface with lower stress, and A be the area of ​​the foundation support surface. The vertical force at the centroid of the bridge pier foundation relative to the foundation support surface under the main force plus additional force condition, and the maximum stress on the foundation support surface under the main force plus additional force condition. The calculation formula is as follows: ， The minimum stress on the foundation support surface under the main force and additional force conditions. The calculation formula is as follows: ， In the formula The maximum stress on the foundation support surface under the condition of main force plus additional force. The minimum stress on the foundation support surface under the condition of main force plus additional force. The vertical force at the centroid of the bridge pier foundation relative to the ground support surface under the condition of main force plus additional force. The longitudinal bending moment of the bridge pier foundation at the centroid of the ground support surface under the condition of main force plus additional force. The transverse bending moment of the bridge pier foundation at the centroid of the ground support surface under the condition of main force plus additional force. This represents the area of ​​the foundation support surface. The moment of inertia along the bridge direction of the foundation support surface. The transverse moment of inertia of the foundation support surface. The distance from the stress calculation point to the transverse centroidal axis of the foundation support surface is denoted as . The distance from the stress calculation point to the centroidal axis along the bridge direction from the foundation support surface is denoted as . according to The area of ​​the top surface of the compensated foundation was calculated, where To compensate for the top surface area of ​​the foundation, let A be the area of ​​the foundation support surface. The area of ​​the top surface of the rock foundation; Based on the top surface area of ​​the compensated foundation and the maximum stress on the foundation support surface under the main force and additional force conditions. The total load on the pile top is determined by the self-weight of the pile cap, and the pile diameter, number of piles and pile length are determined based on the total load of the pile foundation and in combination with geological conditions.

2. The design method as described in claim 1, characterized in that, The above is based on the top surface area of ​​the compensated foundation and the maximum stress on the foundation support surface under the main force and additional load conditions. The total load on the pile top is determined by the self-weight of the pile cap, including: The compensation will cover the top surface area of ​​the foundation and the maximum stress on the foundation support surface under the main force and additional load conditions. The total load at the pile top is obtained by substituting the self-weight of the pile cap into the formula for calculating the total load at the pile top, where the formula for calculating the total load at the pile top is as follows: ， In the formula This represents the total load at the pile top. To compensate for the top surface area of ​​the foundation, For the weight of the foundation.

3. The design method as described in claim 1, characterized in that, The design method further includes the following steps: determining whether the anti-sliding stability coefficient K of the enlarged foundation meets the requirements based on the top surface area of ​​the compensated foundation and the top surface area of ​​the rock foundation, wherein the compensated foundation and the enlarged foundation are cast separately, and the calculation formula for the anti-sliding stability coefficient K of the enlarged foundation is: , In the formula, K is the anti-sliding stability coefficient of the enlarged foundation. N represents the vertical pressure of the enlarged foundation base, and H represents the horizontal thrust of the enlarged foundation base. To compensate for the top surface area of ​​the foundation, Let A be the area of ​​the top surface of the rock foundation, and let A be the area of ​​the foundation support surface. To increase the friction coefficient between the bottom surface of the foundation and the top surface of the compensating foundation, To increase the coefficient of friction between the bottom surface of the foundation and the top surface of the rock foundation.

4. The design method as described in claim 1, characterized in that, The design method further includes the following steps: determining whether the total area of ​​the multiple pile foundations meets the requirements based on the top surface area of ​​the compensating foundation and the area of ​​the foundation support surface, wherein the total area of ​​the multiple pile foundations... The calculation formula is: ， In the formula, Where is the total area of ​​the multiple pile foundations, and N is the vertical pressure on the enlarged foundation base. To compensate for the top surface area of ​​the foundation, let A be the area of ​​the foundation support surface. To increase the friction coefficient between the bottom surface of the foundation and the top surface of the compensating foundation, This represents the allowable shear stress of the pile foundation section.

5. The design method as described in claim 1, characterized in that, The design method further includes the following steps: determining whether the anti-sliding stability coefficient K of the enlarged foundation meets the requirements based on the top surface area of ​​the rock foundation and the area of ​​the foundation support surface, wherein the enlarged foundation and the compensation foundation are integrally cast, and the calculation formula for the anti-sliding stability system K of the enlarged foundation is: , In the formula, K is the anti-sliding stability coefficient of the enlarged foundation. N represents the vertical pressure of the enlarged foundation base, and H represents the horizontal thrust of the enlarged foundation base. Let A be the area of ​​the top surface of the rock foundation, and let A be the area of ​​the foundation support surface. To increase the coefficient of friction between the bottom surface of the foundation and the top surface of the rock foundation, The total area of ​​the multiple pile foundations. This represents the allowable shear stress of the pile foundation section.

6. The design method as described in claim 1, characterized in that, The design method further includes the following steps: determining whether the thickness of the pile cap meets the requirements based on the pile diameter and the center distance between adjacent piles, wherein the formula for calculating the thickness T of the pile cap is: ， In the formula, T is the thickness of the pile cap, S is the center distance between adjacent piles, and d is the diameter of the pile.

7. The design method as described in claim 6, characterized in that, The ratio of the center distance S between adjacent pile foundations to the diameter d of the pile foundation is greater than or equal to 2.

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