Bridge pier deformation calculation method under debris flow impact effect

Abstract

The invention relates to the technical field of piers, in particular to a pier deformation calculation method under the impact action of debris flow. The method comprises the steps that the pier forms an elastic deformation area under the impact effect of debris flow; calculating the transverse displacement of the elastic deformation area by using a deflection curve equation; the shearing deflection of the elastic deformation area is calculated according to the virtual work principle for the sheared section; the sum of the transverse displacement generated in the elastic deformation area and the shearing deflection is the pier top displacement of the pier generated in the elastic deformation area. According to the method for calculating the deformation of the bridge pier under the impact action of the debris flow, the pier top displacement of the bridge pier generated in the elastic deformation area is calculated through superposition of the transverse displacement and the shear deflection of the elastic deformation area. According to the method, the influence of bending deformation and shearing deformation of the bridge pier on the overall deformation of the bridge pier is comprehensively considered, so that the calculation result is more accurate, and more accurate technical support and scientific basis are provided for debris flow impact resistance of a bridge structure.

Description

Technical Field

[0001] The invention relates to the technical field of bridge piers, and in particular to a method for calculating the deformation of bridge piers under the impact of debris flow. Background Art

[0002] Debris flows in mountainous areas of my country are widespread and large in scale, and it is difficult for many bridges to cross the debris flow gullies one by one. As the main supporting structure of bridge engineering, bridge piers are crucial to the safety performance of bridge structures. Once damaged, the consequences are disastrous. Therefore, it is very necessary to explore the deformation and failure mechanism of bridge piers under the impact of debris flows and study the deformation analysis of bridge piers, which can provide technical support and scientific basis for bridge structures to resist the impact of debris flows.

[0003] When a bridge pier is impacted by a debris flow, it will produce impact, abrasion, scouring and other effects. The debris flow will cut off the bridge pier, destroy the bridge deck, damage the bridge foundation by cutting, bury the bridge by accumulation, damage the bridge protection project by erosion, and the impact force will be too large to cause the bridge pier to be damaged. At present, the response of bridge piers under the impact of debris flow mainly focuses on the response law of bridge piers. Most of the studies have analyzed the bridge piers through numerical simulation software, and no detailed research has been conducted on the deformation and damage mechanism of bridge piers and the relevant deformation calculation formulas and methods.

[0004] As a reinforced concrete composite structure, the displacement of a bridge pier is not a simple deformation calculation, but a superposition of multiple displacement modes. Accurately judging the deformation modes of the bridge pier is the key to calculating the displacement of the bridge pier. The deformation of the bridge pier can be divided into bending deformation and shear deformation. At present, there are few studies on the shear deformation of the bridge pier when it is hit laterally, and it is basically focused on the shear deformation of simply supported beams. The main concrete structure design specifications at home and abroad only give the calculation method of bending deformation deflection when introducing the calculation of deflection, and there is no calculation method for shear deformation, such as: Concrete Structure Design Code GB50010-2010 (2015 Edition), European Concrete Structure Design Code Eurocode 2 (STRUCTURES-PARTCEDO, 2004).

[0005] At present, most scholars focus on the bending deformation of bridge piers, ignoring the influence of shear deformation on the overall deformation. Therefore, it is urgent to provide a method for calculating the deformation of bridge piers under the impact of debris flow, which takes into account both bending and shear deformation, so as to provide more accurate technical support and scientific basis for bridge structures to resist debris flow impact. Summary of the invention

[0006] The purpose of the present invention is to provide a method for calculating the deformation of bridge piers under the impact of debris flow, so as to solve the technical problem that the current research on the deformation of bridge piers in the prior art focuses on the bending deformation of the bridge piers, while ignoring the influence of shear deformation on the overall deformation.

[0007] In order to achieve the above object, the present invention adopts the following technical solutions: A method for calculating the deformation of bridge piers under the impact of debris flow, comprising: The bridge piers form elastic deformation areas under the impact of debris flow; calculating the lateral displacement of the elastic deformation region using a deflection curve equation; Calculating the shear deflection of the elastic deformation area by using the virtual work principle for the shear section; Calculate the displacement of the pier top caused by the elastic deformation area:

[0008] in, is the displacement of the top of the pier caused by the elastic deformation area; is the lateral displacement of the elastic deformation area; is the shear deflection of the elastic deformation area.

[0009] Furthermore, it also includes: When the bottom of the pier is impacted and the longitudinal tensile reinforcement yields to form a plastic hinge, the pier body is divided into a plastic hinge area and the elastic deformation area from the bottom to the top; Obtaining the plastic hinge top yield displacement generated in the plastic hinge region by integrating the cross-sectional yield curvature of the plastic hinge region in the length direction of the plastic hinge region; Calculate the total displacement of the pier top:

[0010] in, is the total displacement of the pier top; is the yield displacement of the plastic hinge top generated in the plastic hinge area.

[0011] Furthermore, the steps of dividing the pier body of the bridge pier into a plastic hinge area and the elastic deformation area from the bottom to the top in sequence include: Calculate the length of the plastic hinge region:

[0012] in, is the length of the plastic hinge region; is the yield strength of the steel bar; is the diameter of the steel bar; Circular cross-section diameter; Calculate the length of the elastic deformation area:

[0013] in, is the length of the elastic deformation zone; H is the height of the pier.

[0014] Furthermore, in the case where the debris flow does not contain large rocks, the lateral displacement of the elastic deformation area The calculation formula is:

[0015] in, is the length of the elastic deformation area; is the overall impact pressure of debris flow; For debris flow depth; is the bending stiffness of the pier; is the height of the pier; is the angle between the bearing surface of the bridge pier and the direction of the debris flow; It is a heavy debris flow; is the velocity of debris flow; g is the acceleration of gravity; θ is the angle between the force-bearing surface of the building and the direction of the debris flow; is the building shape factor; In the case of debris flow with large rocks impacting, the lateral displacement of the elastic deformation area The calculation formula is:

[0016] in, is the length of the elastic deformation area; is the impact pressure of the stone; is the height of the rock impact point from the ground; is the bending stiffness of the pier; is the impact velocity of the large rock; The weight of the stone; is the height of the pier; It is the angle between the large stone and the bearing surface of the bridge pier; is the acceleration due to gravity; The shear deflection of the elastic deformation area The calculation formula is:

[0017] in, is the shear force of the section at the deflection calculation location under unit force is the integral of the length along the pier height direction is the shear force non-uniformity coefficient Shear force of bridge pier under actual load is the shear stiffness of the pier; The yield displacement of the top of the plastic hinge generated in the plastic hinge area The calculation formula is:

[0018] Among them, is the section yield curvature function, and the section curvature is linearly distributed along the pier height. ; is the yield curvature of the cross section, ; is the effective height of the section; The compressive stress of concrete reaches When the concrete compressive strain is calculated When the value is less than 0.002, it is taken as 0.002; is the design value of steel bar tensile strength; is the elastic modulus of the steel bar; is the cross-section reinforcement ratio; is the design value of concrete strength; Combined with the above formula, when the debris flow does not contain large rocks and the bridge pier has no plastic hinge, the displacement of the pier top is The calculation formula is:

[0019] in, is the bending stiffness of the pier in the elastic stage , is the shear stiffness of the pier in the elastic stage; When the debris flow does not contain large rocks, the total displacement of the pier top is The calculation formula is:

[0020] In the case of debris flow and large rocks impact, when the bridge pier has no plastic hinge, the displacement of the pier top is The calculation formula is:

[0021] in, is the bending stiffness of the pier in the elastic stage , is the shear stiffness of the pier in the elastic stage; When a large rock in a debris flow hits a bridge pier, the total displacement of the bridge pier top is The calculation formula is: .

[0022] Furthermore, after the step of dividing the pier body of the bridge pier into the plastic hinge area and the elastic deformation area from the bottom to the top, the method further includes: Determining whether cracks occur in the plastic hinge region; If no cracks occur in the plastic hinge region, the lateral displacement The calculation formula for the bending stiffness of the bridge pier is is the bending stiffness of the pier in the elastic stage , shear deflection The shear stiffness of the bridge pier in the calculation formula is the shear stiffness of the pier in the elastic stage ; If cracks occur in the plastic hinge region, the crack type of the plastic hinge region is determined, and the crack type includes bending cracks and shear cracks; When a bending crack occurs in the plastic hinge region, the lateral displacement The calculation formula for the bending stiffness of the bridge pier is is the effective bending stiffness of the crack section; When shear cracks occur in the plastic hinge region, the shear deflection The shear stiffness of the bridge pier in the calculation formula is the effective shear stiffness of the crack section.

[0023] Furthermore, the step of determining the crack type in the plastic hinge region includes: Calculation of shear forces corresponding to flexural cracking and the shear force corresponding to shear cracking , and obtain the actual shear force in the impact ; Compare , as well as The size of the three; like , then only bending cracks will occur in the plastic hinge region; like , then only shear cracks will occur in the plastic hinge region; like , then there are both bending cracks and shear cracks in the plastic hinge region.

[0024] Furthermore, the shear force corresponding to flexural cracking is The calculation formula is:

[0025] Shear force corresponding to shear cracking The calculation formula is:

[0026] in; is the bending moment at bending cracking; is the tensile strength of concrete; is the moment of inertia of the pier section; is the distance from the centroid of the section to the tension edge; is the shear force during bending cracking; is the actual bending moment when the bridge pier is impacted by debris flow; is the actual shear force in impact; is the shear force during shear cracking; is the effective height of the section; is the area of ​​the tensile longitudinal reinforcement; is the characteristic value of compressive strength of concrete cylinder; is the section width.

[0027] Furthermore, the calculation method of the effective bending stiffness of the crack section is: Calculate the average crack spacing:

[0028] in, is the average crack spacing; is the load form influence coefficient, which is 1.1 for axial tension members and 1.0 for bending and eccentric load members; The distance from the outer edge of the outermost longitudinal tensile reinforcement to the bottom edge of the tensile zone is 20mm when it is less than 20mm and 65mm when it is greater than 65mm. is the equivalent diameter of the longitudinal reinforcement in the tension zone, , For the tension zone The number of longitudinal reinforcements, For the tension zone The nominal diameter of the steel bar, is the relative bonding characteristic coefficient of the longitudinal tensile reinforcement, which is 0.7 for plain round reinforcement and 1.0 for ribbed reinforcement; It is the longitudinal tensile reinforcement ratio calculated based on the effective tensile concrete cross-sectional area, which is equal to the ratio of the area of ​​the longitudinal tensile reinforcement to the effective tensile concrete cross-sectional area; According to the geometric relationship, the average crack spacing is obtained and effective height of section The formula relationship is:

[0029] In the formula, is the cross-sectional curvature is the compression of the concrete under pressure, is the elongation of the tensile reinforcement at the crack location, ; is the average strain of the reinforcement between the crack sections, is the average strain at the edge of the concrete in the compression zone between the crack sections, is the bending moment value calculated according to the quasi-permanent combination of loads is the ratio of the average strain between cracks to the steel bar strain in the crack section, Design value of concrete tensile strength is the reinforcement stress in the crack section, is the cross-sectional area of ​​the tensile reinforcement is the elastic modulus of the steel bar To determine the comprehensive influence coefficient of the moment of resistance of the average strain of the tensile edge concrete is the elastic modulus of concrete is the equivalent diameter of the longitudinal reinforcement in the tension zone is the longitudinal tensile reinforcement ratio calculated based on the effective tensile concrete cross-sectional area; Calculate the effective bending stiffness of the cracked section:

[0030] in, is the effective bending stiffness of the crack section.

[0031] Furthermore, the calculation method of the effective shear stiffness of the crack section is: According to the truss model, the actual shear force Under the action of

[0032]

[0033] Calculate the effective shear stiffness of the cracked section:

[0034] In the formula, is the effective shear stiffness of the crack section; is the compression of the truss concrete; is the deformation of the shear stirrups at the crack location; is the average strain at the edge of the concrete in the compression zone between the inclined crack sections, is the average strain of the stirrups between the crack sections, is the stirrup spacing; is the area of ​​stirrups; is the cross-section internal force arm; is the stirrup ratio; is the inclination angle of the concrete diagonal strut in the truss model, which can be taken as 45° for calculation.

[0035] Furthermore, when only bending cracks occur in the plastic hinge region, the total displacement of the pier top is ; When only shear cracks occur in the plastic hinge region, the total displacement of the pier top is ; When there are both bending cracks and shear cracks in the plastic hinge region, the total displacement of the pier top is ; Combined with the above formula, when the debris flow does not contain large rocks, The calculation formula is:

[0036] in, is the ratio of elastic modulus of steel bar to concrete, ; is the tensile reinforcement ratio; In the case of debris flows that do not contain large rocks, The calculation formula is:

[0037] In the case of debris flows that do not contain large rocks, The calculation formula is:

[0038] In the case of large rocks impacting debris flow, The calculation formula is:

[0039] In the case of large rocks impacting debris flow, The calculation formula is:

[0040] In the case of large rocks impacting debris flow, The calculation formula is: .

[0041] Beneficial effects of the present invention: The present invention provides a method for calculating the deformation of bridge piers under the impact of debris flow, comprising: The bridge piers form elastic deformation areas under the impact of debris flow; The lateral displacement of the elastic deformation area is calculated using the deflection curve equation; For the shear section, the shear deflection of the elastic deformation area is calculated using the principle of virtual work; Calculate the displacement of the pier top caused by the elastic deformation area:

[0042] in, is the displacement of the top of the pier caused by the elastic deformation area; is the lateral displacement of the elastic deformation area; is the shear deflection of the elastic deformation area.

[0043] The method for calculating the deformation of bridge piers under the impact of debris flow provided by the present invention uses the deflection curve equation to calculate the lateral displacement of the elastic deformation area, uses the virtual work principle to calculate the shear deflection of the elastic deformation area, and calculates the pier top displacement of the bridge pier generated by the elastic deformation area through the superposition of the lateral displacement and shear deflection of the elastic deformation area. Since the method comprehensively considers the influence of the bending deformation and shear deformation of the bridge pier on the overall deformation of the bridge pier, its calculation result is more accurate, thereby providing more accurate technical support and scientific basis for the bridge structure to resist the impact of debris flow. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] In order to more clearly illustrate the specific implementation methods of the present invention or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0045] Figure 1 A schematic diagram of a bridge pier model in a method for calculating bridge pier deformation under debris flow impact provided in Embodiment 1 of the present invention; Figure 2 A schematic diagram of the deformation of a pier model under impact in the method for calculating the deformation of a pier under the impact of a debris flow provided in the first embodiment of the present invention; Figure 3 A calculation model for curved cracks in a method for calculating bridge pier deformation under debris flow impact provided in the first embodiment of the present invention; Figure 4 A calculation model for shear cracks in the method for calculating the deformation of bridge piers under the impact of debris flow provided in the first embodiment of the present invention; Figure 5 A schematic diagram of the structure of a debris flow impact simulation device for calculating the deformation of a bridge pier under the impact of a debris flow provided in the first embodiment of the present invention; Figure 6 A schematic diagram of a pier model in a method for calculating pier deformation under debris flow impact provided in the second embodiment of the present invention.

[0046] icon: 1-Material box; 2-Test water tank; 3-Flow rate measuring instrument; 4-Video recorder; 5-High-speed camera; 6-Waste pool; 7-Bridge pier model. DETAILED DESCRIPTION

[0047] The technical solution of the present invention will be clearly and completely described below in conjunction with the embodiments. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0048] Embodiment 1 This application mainly studies the bending and shear deformation of bridge piers during normal use (no cracks or partial cracks that do not affect the normal use of bridge piers). The influence of second-order effects, pile foundations at the bottom of bridge piers and pile-soil effects are not considered. The proposed formula does not include the deformation response of longitudinal reinforcement and stirrups after yielding. The calculation formula of this application is mainly based on the conventional calculation section in the Code for Design of Concrete Structures (GB 50010-2010). Different sections can be converted using the code.

[0049] In order to reflect the universality of the research, this application takes the most common single-pier bridge pier as the research object, and studies the damage mechanism and deformation of the pier body when debris flow blocks impact. Figure 1 and Figure 2 When a bridge pier is impacted by a debris flow, it mainly generates lateral impact force. The lower part of the bridge pier is connected to the foundation, and the upper part bears vertical load. Based on the above constraints, the calculation model of the bridge pier is simplified to a cantilever beam structure with a fixed lower end and a vertical pressure on the upper part.

[0050] Based on the above calculation model, a first embodiment of the present invention provides a method for calculating the deformation of a bridge pier under the impact of a debris flow, the method comprising the following steps: The bridge piers form elastic deformation areas under the impact of debris flow; The lateral displacement of the elastic deformation area is calculated using the deflection curve equation; For the shear section, the shear deflection of the elastic deformation area is calculated using the principle of virtual work; Calculate the displacement of the pier top caused by the elastic deformation area: (1) in, is the displacement of the top of the pier caused by the elastic deformation area; is the lateral displacement of the elastic deformation area; is the shear deflection of the elastic deformation area.

[0051] The method for calculating the deformation of bridge piers under the impact of debris flow provided by the present invention uses the deflection curve equation to calculate the lateral displacement of the elastic deformation area, uses the virtual work principle to calculate the shear deflection of the elastic deformation area, and calculates the pier top displacement of the bridge pier generated by the elastic deformation area through the superposition of the lateral displacement and shear deflection of the elastic deformation area. Since the method comprehensively considers the influence of the bending deformation and shear deformation of the bridge pier on the overall deformation of the bridge pier, the calculation formula for the displacement of the bridge pier in the whole process under the impact of debris flow is established by the superposition method, and the calculation result is more accurate, thereby providing more accurate technical support and scientific basis for the bridge structure to resist the impact of debris flow.

[0052] Furthermore, when the bottom of the pier is impacted and the longitudinal tensile reinforcement yields to form a plastic hinge, the pier body is divided into a plastic hinge area and the elastic deformation area from the bottom to the top; The yield displacement of the top of the plastic hinge generated in the plastic hinge region is obtained by integrating the yield curvature of the cross section of the plastic hinge region in the length direction of the plastic hinge region. Calculate the total displacement of the pier top: (2) in, is the total displacement of the pier top; is the yield displacement at the top of the plastic hinge generated in the plastic hinge area.

[0053] It should be noted that the different impact forces of debris flows will cause different deformations of bridge piers, specifically: If the impact force of the debris flow is small, the bridge pier is in the elastic stage as a whole. At this time, the pier body is in the elastic deformation area as a whole. Therefore, the total displacement of the pier top is the displacement of the pier top generated in the elastic deformation area. ; As the impact of the debris flow continues to increase, the pier enters the elastoplastic stage. At this time, due to the influence of the constraint at the bottom of the pier, stress concentration will occur at the bottom of the pier, and plastic hinges will appear first. However, the upper part of the pier is still in the elastic stage because the force it receives is small or unstressed. Therefore, the bottom of the pier is the plastic hinge area, and the upper part of the pier is the elastic deformation area. The total displacement of the pier top is The displacement of the bridge pier top caused by the elastic deformation area The yield displacement of the top of the plastic hinge generated by the plastic hinge area The superposition of When the impact of the debris flow is too great, the bridge pier enters the plastic failure stage. At this time, cracks appear in the concrete section of the plastic hinge area, and the total displacement of the pier top is The displacement of the bridge pier top generated by the elastic deformation area The yield displacement of the top of the plastic hinge generated by the plastic hinge area of superposition.

[0054] In summary, when the pier is in the elastic stage, the deformation of the pier is calculated using formula (1); when the pier is in the elastoplastic stage and the plastic failure stage, the deformation of the pier is calculated using formula (2).

[0055] Furthermore, the steps divide the pier body of the bridge pier into a plastic hinge area and an elastic deformation area from the bottom to the top, including: Calculate the length of the plastic hinge region: (3) in, is the length of the plastic hinge region; is the yield strength of the steel bar, which is a known value; is the diameter of the steel bar, which is a known value; The diameter of the circular section is a known value; Calculate the length of the elastically deformed region: (4) in, is the length of the elastic deformation zone; H is the height of the pier, which is a known value.

[0056] In the above formula, the length of the plastic hinge region is Calculated according to "Code for Seismic Design of Highway Bridges" (TGT 2231-01-2020).

[0057] It should be noted that the calculation method provided in this application can be applied to both debris flow fluid and debris flow large rock impact. The calculation methods of the two cases are similar, and the only difference is the lateral displacement of the elastic deformation area. The calculation formula is different. The calculation method provided in the first embodiment of the present application takes the case where the debris flow does not contain large rocks as an example.

[0058] Furthermore, the step of calculating the lateral displacement of the elastic deformation region using a deflection curve equation includes: The maximum displacement of the pier is at the top of the pier. Using the boundary condition at the bottom of the pier (at x=0, the deflection and rotation are both zero) combined with the deflection curve equation, the lateral displacement of the elastic deformation area is obtained. The calculation formula is: (5) in, is the overall impact pressure of debris flow (kPa), taken from the Code for Design of Debris Flow Prevention and Control Projects (DZ / T0239-2004), ; For debris flow depth; is the bending stiffness of the pier; is the height of the pier; is the angle between the bearing surface of the bridge pier and the direction of the debris flow (°); is the debris flow weight (kN / m3); is the debris flow velocity (m / s); g is the gravitational acceleration ( =9.8 );θ is the angle between the bearing surface of the building and the direction of the debris flow impact (°); is the building shape factor, a circular building , rectangular building , square building ; The above parameters are all known values.

[0059] It should be noted that in formula (5), is the length of the elastic deformation area; when the pier does not form a plastic hinge, the pier body is in the elastic deformation area as a whole. is zero, is equal to the pier height H of the pier; when the pier forms a plastic hinge, .

[0060] Furthermore, the step of calculating the shear deflection of the elastic deformation region using the virtual work principle for the shear section includes: When a bridge pier is hit laterally by a debris flow, not all sections of the pier are subject to shear force. Therefore, the deformation of the pier body under shear force is directly applied to the shear section using the principle of virtual work. to seek; Shear deflection in the elastic deformation area The calculation formula is: (6) in, is the shear force of the section at the deflection calculation location under unit force is the integral of the length along the pier height direction is the shear force non-uniformity coefficient Shear force of bridge pier under actual load is the shear stiffness of the pier; the above parameters are all known values.

[0061] In the above formula, the yield displacement of the top of the plastic hinge generated in the plastic hinge area is The calculation formula is: (7) in, is the section yield curvature function, and the section curvature is linearly distributed along the pier height. ; is the yield curvature of the cross section, ; is the effective height of the section; The compressive stress of concrete reaches When the concrete compressive strain is calculated When the value is less than 0.002, it is taken as 0.002; is the design value of steel bar tensile strength; is the elastic modulus of the steel bar; is the cross-section reinforcement ratio; is the design value of concrete strength; the above parameters are all known values.

[0062] Substituting formulas (5) and (6) into formula (1), when the pier does not form a plastic hinge (that is, the pier is in the elastic stage), the displacement of the pier top is The calculation formula is: (8) in, is the bending stiffness of the pier in the elastic stage; 1 is the shear stiffness of the pier in the elastic stage; the above parameters are the initial parameters of the pier and are known values.

[0063] Substituting formulas (5), (6), and (7) into formula (2), when the bottom of the pier is impacted and the longitudinal tensile reinforcement yields to form a plastic hinge (that is, the pier is in the elastic-plastic stage and the plastic failure stage), the total displacement of the pier top is The calculation formula is: (9) On the basis of the above steps, when the bottom of the pier is impacted and the longitudinal tensile reinforcement yields to form a plastic hinge, the calculation method of the pier in the elastic-plastic stage and the plastic failure stage is further studied. The difference between the calculation methods of the pier in the elastic-plastic stage and the plastic failure stage is mainly: the bending stiffness of the pier and shear stiffness of bridge piers The value of is different.

[0064] Furthermore, after the step of dividing the pier body of the bridge pier into the plastic hinge area and the elastic deformation area from the bottom to the top, the method further includes: Determine whether cracks occur in the plastic hinge area; If no cracks occur in the plastic hinge region (at this time, the pier is in the elastic-plastic stage), the lateral displacement In the calculation formula is the bending stiffness of the pier in the elastic stage , shear deflection In the calculation formula is the shear stiffness of the pier in the elastic stage ; If cracks occur in the plastic hinge area (at this time, the bridge pier is in the plastic failure stage), the crack type in the plastic hinge area is determined, and the crack types include bending cracks and shear cracks; When a bending crack occurs in the plastic hinge region, the lateral displacement In the calculation formula is the effective bending stiffness of the crack section; When shear cracks occur in the plastic hinge region, the shear deflection In the calculation formula is the effective shear stiffness of the crack section.

[0065] Furthermore, the step of determining the crack type in the plastic hinge region includes: Calculation of shear forces corresponding to flexural cracking and the shear force corresponding to shear cracking , and obtain the actual shear force in the impact ; Among them, the shear force corresponding to bending cracking is The calculation formula is: (10) Shear force corresponding to shear cracking The calculation formula is: (11) in; is the bending moment at the time of bending cracking, calculated by elastic beam theory, ; is the tensile strength of concrete; is the moment of inertia of the pier section; is the distance from the centroid of the section to the tension edge; is the shear force during bending cracking; is the actual bending moment when the bridge pier is impacted by debris flow; is the actual shear force in impact; is the shear force during shear cracking; is the effective height of the section; is the area of ​​the tensile longitudinal reinforcement; is the characteristic value of compressive strength of concrete cylinder; is the section width; the above parameters are known values; Compare , as well as The size of the three; like , then only bending cracks will occur in the plastic hinge region; like , then only shear cracks will occur in the plastic hinge region; like , then there are both bending cracks and shear cracks in the plastic hinge region.

[0066] As described above, in this embodiment, when the impact force of the debris flow is too large and cracks appear in the concrete cross section of the plastic hinge area, the calculated values ​​of formulas (10) and (11) are first compared with the actual shear force V in the impact to clarify different failure mechanisms, and then targeted calculations are performed on different failure mechanisms to obtain more accurate calculation results.

[0067] After the bending crack appears, the bending stiffness of the plastic hinge area will change due to the influence of the bending crack. is no longer applicable, and the effective bending stiffness of the crack section is introduced. The calculation model is shown in Figure 3 The strain of the compressed concrete and the tensile steel bars is unevenly distributed along the height of the pier, the neutral axis is wavy, and the curvature distribution is also uneven. To simplify the calculation, the strain, neutral axis position and curvature on the cross section are all averaged, the average crack spacing is taken as a calculation unit, and the crack length to the neutral axis position is taken, and the average value is used. Figure 3 Medium triangle With triangle Similarity relationship, calculate the effective height of the section , and then calculate the effective bending stiffness of the crack section .

[0068] Based on the above calculation principle, the calculation method of the effective bending stiffness of the crack section is: Calculate the average crack spacing : (12) in, is the average crack spacing; is the load form influence coefficient, which is 1.1 for axial tension members and 1.0 for bending and eccentric load members; The distance from the outer edge of the outermost longitudinal tensile reinforcement to the bottom edge of the tensile zone is 20mm when it is less than 20mm and 65mm when it is greater than 65mm. is the equivalent diameter of the longitudinal reinforcement in the tension zone, , For the tension zone The number of longitudinal reinforcements, For the tension zone The nominal diameter of the steel bar, is the relative bonding characteristic coefficient of the longitudinal tensile reinforcement, which is 0.7 for plain round reinforcement and 1.0 for ribbed reinforcement; is the longitudinal tensile reinforcement ratio calculated based on the effective tensile concrete cross-sectional area, which is equal to the ratio of the area of ​​the longitudinal tensile reinforcement to the effective tensile concrete cross-sectional area; the above calculation parameters are all known values; According to the geometric relationship, the average crack spacing is obtained and The formula relationship is: (13) In the formula, is the cross-sectional curvature is the compression of the concrete under pressure, is the elongation of the tensile reinforcement at the crack location, ; is the average strain of the reinforcement between the crack sections, is the average strain at the edge of the concrete in the compression zone between the crack sections, is the bending moment value calculated according to the quasi-permanent combination of loads is the ratio of the average strain between cracks to the steel bar strain in the crack section, Design value of concrete tensile strength is the reinforcement stress in the crack section, is the cross-sectional area of ​​the tensile reinforcement is the elastic modulus of the steel bar To determine the comprehensive influence coefficient of the moment of resistance of the average strain of the tensile edge concrete is the elastic modulus of concrete is the equivalent diameter of the longitudinal reinforcement in the tension zone is the longitudinal tensile reinforcement ratio calculated based on the effective tensile concrete cross-sectional area; the above parameters are known values; Combining formulas (12) and (13), the effective bending stiffness of the crack section is calculated: (14) in, is the effective bending stiffness of the crack section.

[0069] After the shear crack appears, the shear stiffness of the bridge pier in the elastic stage is affected by the shear crack. No longer applicable, the effective shear stiffness of the cracked section is introduced The shear deformation is calculated using the truss model, which can better simulate the stress state of the component under the shear force and can calculate the shear bearing capacity and shear stiffness. Figure 4, assuming that there is no aggregate bite force between shear cracks, there is no tension in the concrete between the oblique cracks and the oblique cracks are parallel to each other, and the concrete oblique compression rod remains linear elastic; the left side of the truss model is equivalent to the tensile longitudinal reinforcement, the right side is equivalent to the compressive zone concrete, the oblique compression web member is equivalent to the compressive concrete between the shear cracks, and the transverse tension web member represents the shear stirrups.

[0070] Based on the above calculation principle, the calculation method of the effective shear stiffness of the crack section is: According to the truss model, the actual shear force Under the action of

[0071] (15) Combined with formula (15), the effective shear stiffness of the crack section is calculated: (16) In the formula, is the effective shear stiffness of the crack section; is the compression of the truss concrete; is the deformation of the shear stirrups at the crack location; is the average strain at the edge of the concrete in the compression zone between the inclined crack sections, is the average strain of the stirrups between the crack sections, is the stirrup spacing; is the area of ​​stirrups; is the cross-section internal force arm; is the stirrup ratio; is the inclination angle of the concrete diagonal strut in the truss model, which can be taken as 45° during calculation; the above parameters are known values.

[0072] For the sake of distinction, in this embodiment, when only bending cracks occur in the plastic hinge region, the total displacement of the pier top is ; When only shear cracks occur in the plastic hinge region, the total displacement of the pier top is ; When there are both bending cracks and shear cracks in the plastic hinge region, the total displacement of the pier top is ; When only bending cracks occur in the plastic hinge region, the bending stiffness of the pier is is the effective bending stiffness of the crack section , the shear stiffness of the pier is the shear stiffness of the pier in the elastic stage ; Substitute formula (14) into formula (9) , get the total displacement of the pier top The calculation formula is: (17) in, is the ratio of elastic modulus of steel bar to concrete, ; is the tensile reinforcement ratio.

[0073] When only shear cracks occur in the plastic hinge region, the flexural stiffness of the pier is is the bending stiffness of the pier in the elastic stage , the shear stiffness of the pier is the effective shear stiffness of the crack section ; Replace formula (16) with formula (9) , get the total displacement of the pier top The calculation formula is: (18) Combining formulas (9), (14), and (16), the total displacement of the pier top is obtained: The calculation formula is: (19) In order to verify the correctness of the method for calculating the deformation of bridge piers under the impact of debris flow provided in this application, a physical model test is conducted on the method. In the physical model test, the pier body damage mechanism and the correlation between the deformation law of the bridge pier and the impact force of the debris flow are studied by changing factors such as the mass of the block and the impact height. At the same time, the calculation method for the displacement of the top of the bridge pier under the impact of debris flow proposed by the method is verified.

[0074] Reference Figure 5 The debris flow impact simulation device provided in this embodiment includes a material box 1, a test water tank 2, a flow rate measuring instrument 3, a video recorder 4, a high-speed camera 5, a waste pool 6, a bridge pier model 7 and a displacement meter, wherein: The test water tank 2 is tilted relative to the horizontal plane. It consists of a bottom steel plate and side glass plates. The dimensions of the water tank are 6.5m long, 0.35m wide, and 0.37m high. The transparent glass plates on the sides are convenient for observing the test phenomena. The flow rate measuring instrument 3 is used to measure the flow rate of the fluid in the test water tank 2; The material box 1 and the waste pool 6 are respectively arranged at the upper end and the lower end of the test water tank 2; Video recorder 4 is used to record the experimental process; Two high-speed cameras 5 are set up, located on the impact side and behind the bridge pier, to capture the impact shape of the debris flow and the deformation process of the bridge pier; The bridge pier model 7 is placed in the test water tank 2; The displacement meter is used to measure the deformation of the pier model 7. During the test, ensure that the displacement direction of the end of the displacement meter is consistent with that of the pier model 7 and remain horizontal. It is used to measure the displacement of the top of the pier when the debris flow impacts the pier.

[0075] Based on the above device, the physical model test provided in this embodiment includes the following steps: Step 1, making a test pier model 7; Step 2: releasing the debris flow to impact the bridge pier model 7, and recording the actual pier top displacement data of the bridge pier model 7; Step 3: Compare the actual pier top displacement data with the pier top displacement data obtained by this calculation method to verify the accuracy of this method.

[0076] Wherein, step 1, making a test pier model 7, comprises: The test prototype is a single-column pier on National Highway 317 from Wenchuan to Maerkang. The pier parameters are as follows: pier diameter 1.8m, pier height 10m, pier concrete strength grade C30, concrete cover thickness 40mm, longitudinal reinforcement 30 32, stirrups 14@200; The bridge pier model 7 is made according to the size of the test water tank, and the size relationship between the prototype and the bridge pier model 7 is 40:1; The similarity criterion is derived by dimensional analysis, and its general function expression is: ,in: for stress; is the deflection; For impact load; is the bending moment; For strain; is the height of the pier; is the elastic modulus of the material, is the moment of inertia of the cross section; then the prototype and the model satisfy the following relationship: , =40, =1600, =64000, =1 =40, =1, =2560000; According to the similar simulation calculation results, the size of the pier model 7 is determined to be 4.5 cm in diameter and 25 cm in height. The bridge deck cap is made on the upper part and the size is scaled according to the actual size.

[0077] Since this test is to explore the deformation law of the bridge pier, no model steel bars are configured inside the pier when making the pier. =1:1, using C30 grade fine stone concrete of actual bridge pier as the main material of bridge pier model 7. The reinforcement ratio of the prototype bridge pier is 0.948%, and galvanized steel wire is configured according to the reinforcement ratio. The longitudinal steel bars are replaced by 8 fine steel wires with a diameter of 0.78mm (calculated according to the cross-sectional reinforcement ratio for the cross-sectional area of ​​the steel bars), and the stirrups are tied with 0.5mm fine steel wires with a spacing of 1cm. The coarse aggregate of C30 grade fine stone concrete is selected from stones with a particle size of 5-10mm, and the fine aggregate is medium-coarse sand with a particle size of 0.2-0.5mm. The cement uses ordinary silicate cement of P.O42.5 grade. The mass ratio of each material is cement: stone: sand: water = 4.61:12.51:5.12:1.75.

[0078] Among them, step 2, releasing the debris flow to make the debris flow impact the bridge pier model 7, and recording the actual pier top displacement data of the bridge pier model 7, includes: Debris flows are divided into three groups according to density, one of which is clear water flow; After the pier model 7 is manufactured, the slope of the debris flow channel is controlled to remain unchanged at 15° based on the actual situation of the test site, and the debris flow is released from the same height.

[0079] In order to realize the inclusion of blocks in the debris flow in the real debris flow disaster, the debris flow raw material ratio design is based on the Jiangjiagou debris flow. The Jiangjiagou debris flow is located in an area where the Xiaojiang fault earthquake is extremely frequent. The mountain composed of Proterozoic metamorphic slate, shale, and mud shale is already very broken. Although the Jiangjiagou debris flow is not a rainstorm-type debris flow, when the rainfall is less than 20mm, the hillside soil layer is soaked. As long as another 20mm of rain falls, a debris flow can be generated, so it is called a "rain-flood-type debris flow". Due to the lithology, the clay component in the debris flow is very high, often reaching more than 10%, so the mud slurry of the debris flow is very viscous, which can suspend and hold up huge soil and stones, and its density is 1.8×10³~2.3×10³kg / m³. In order to prevent the crushed stone particle size from being too large relative to the pier diameter after the bridge pier model 7 is reduced in the scale test, the crushed stone is screened by artificial screening to retain the crushed stone with a particle size less than 10 mm. Table 1 is a debris flow material configuration table.

[0080] Table 1

[0081] Wherein, step 3, comparing the actual pier top displacement data with the pier top displacement data obtained by the calculation method, comprises: The speed of the debris flow when impacting the bridge pier is calculated by a high-speed camera 5, and then the speed of the debris flow is substituted into the calculation formula of the debris flow impact force to obtain the actual debris flow impact force; This method is used to determine the actual stage of the bridge pier and select a suitable calculation formula to calculate the displacement of the pier top; The pier top displacement data measured in the test and the pier top displacement values ​​obtained by this calculation method are listed in Table 2 to check the similarity between the theoretical calculation results of the pier top displacement under different stages of impact and the actual measurement results of the test; Table 2 is a comparison of the pier top displacement under debris flow test conditions and the calculation results.

[0082] Table 2

[0083] It can be seen from Table 2 that the calculated displacement results of the pier top after each stage of impact are very close to the measured values. The maximum difference between the calculated displacement of the pier top in the dragon head impact stage and the measured value is -12.1%, and the maximum difference between the calculated displacement of the pier top in the stable fluid impact stage and the measured value is -12.2%. The similarity between the theoretical calculation results of the pier top displacement under different stages of impact and the actual measurement results of the test is more than 85%. The results show that the calculation method of the pier top displacement proposed in this application has good applicability and high accuracy.

[0084] Embodiment 2 The calculation method provided in the second embodiment takes the impact of a large rock in a debris flow as an example. The difference from the first embodiment is only in the lateral displacement of the elastic deformation area. The calculation formula is different, and the rest of the calculation methods are the same, which will not be described here.

[0085] Reference Figure 6 In this embodiment, the lateral displacement of the elastic deformation area is The calculation formula is: (20) in, is the impact pressure of the rock, taken from the Code for Design of Debris Flow Prevention and Control Projects (DZ / T0239-2004). ; is the height of the rock impact point from the ground; is the bending stiffness of the pier; is the impact velocity of the large rock; The weight of the stone; is the height of the pier; It is the angle between the large stone and the bearing surface of the bridge pier; is the acceleration due to gravity.

[0086] In this embodiment, when the pier does not form a plastic hinge, the displacement of the pier top is The calculation formula is: (twenty one) in, is the bending stiffness of the pier in the elastic stage, is the shear stiffness of the pier in the elastic stage; When a plastic hinge is formed at the bottom of the pier, the total displacement of the pier top The calculation formula is: (twenty two) In this embodiment, when only bending cracks occur in the plastic hinge region, the total displacement of the pier top is ; When only shear cracks occur in the plastic hinge region, the total displacement of the pier top is ; When there are both bending cracks and shear cracks in the plastic hinge region, the total displacement of the pier top is ; The calculation formula is: (twenty three) The calculation formula is: (twenty four) The calculation formula is: (25) The experimental simulation device and method of the calculation method provided in this embodiment are similar to those in the first embodiment and are not repeated here.

[0087] Embodiment 3 Based on the above formula, the present embodiment 3 provides a specific process of a method for calculating the deformation of bridge piers under the impact of debris flow, as follows: Determine whether a plastic hinge is formed at the bottom of the pier; If no plastic hinge is formed at the bottom of the pier, it means that the pier is in the elastic stage. At this time, the pier body is in the elastic deformation area as a whole, and the displacement of the pier top is the superposition of the lateral displacement and shear deflection in the elastic deformation area. If a plastic hinge is formed at the bottom of the pier, the pier body is divided into a plastic hinge area and an elastic deformation area from bottom to top. At this time, the total displacement of the pier top is the superposition of the lateral displacement of the elastic deformation area, the shear deflection of the elastic deformation area and the yield displacement of the plastic hinge top.

[0088] Furthermore, after the step of dividing the pier body of the bridge pier into a plastic hinge area and an elastic deformation area from the bottom to the top, the step further includes: Determine whether cracks occur in the plastic hinge area; If there is no crack in the plastic hinge area, it means that the pier is in the elastic-plastic stage. At this time, the flexural stiffness of the pier in the calculation formula is is the bending stiffness of the pier in the elastic stage , the shear stiffness of the pier is the shear stiffness of the pier in the elastic stage ; If cracks occur in the plastic hinge area, it means that the pier is in the plastic failure stage, and the crack type in the plastic hinge area should be determined; When only bending cracks occur in the plastic hinge area, the bending stiffness of the pier in the calculation formula is is the effective bending stiffness of the crack section , the shear stiffness of the pier is the shear stiffness of the pier in the elastic stage ; When only shear cracks occur in the plastic hinge area, the flexural stiffness of the pier in the calculation formula is is the bending stiffness of the pier in the elastic stage , the shear stiffness of the pier is the effective shear stiffness of the crack section ; When both bending cracks and shear cracks exist in the plastic hinge region, the bending stiffness of the pier in the calculation formula is is the effective bending stiffness of the crack section , the shear stiffness of the pier is the effective shear stiffness of the crack section .

[0089] Embodiment 4 Based on the formula in the calculation method provided in the first embodiment, the fourth embodiment provides a specific flow of a method for calculating the deformation of a bridge pier under the impact of a debris flow without large rocks, as follows: Determine whether a plastic hinge is formed at the bottom of the pier; If no plastic hinge is formed at the bottom of the pier, the pier deformation is calculated using formula (8); If a plastic hinge is formed at the bottom of the pier, the pier body is divided into a plastic hinge area and an elastic deformation area from the bottom to the top; Determine whether cracks occur in the plastic hinge area; If no cracks occur in the plastic hinge region, the pier deformation is calculated using formula (9), where: is the bending stiffness of the pier in the elastic stage , is the shear stiffness of the pier in the elastic stage ; If cracks occur in the plastic hinge area, continue to determine the type of cracks in the plastic hinge area; When only bending cracks occur in the plastic hinge region, the pier deformation is calculated using formula (17); When only shear cracks occur in the plastic hinge region, the pier deformation is calculated using formula (18); When both bending cracks and shear cracks exist in the plastic hinge region, formula (19) is used to calculate the pier deformation.

[0090] Embodiment 5 Based on the formula in the calculation method provided in the second embodiment, the fifth embodiment provides a specific process of a method for calculating the deformation of a bridge pier under the impact of a large rock in a debris flow, as follows: Determine whether a plastic hinge is formed at the bottom of the pier; If no plastic hinge is formed at the bottom of the pier, the pier deformation is calculated using formula (21); If a plastic hinge is formed at the bottom of the pier, the pier body is divided into a plastic hinge area and an elastic deformation area from the bottom to the top; Determine whether cracks occur in the plastic hinge area; If no cracks occur in the plastic hinge region, the pier deformation is calculated using formula (22), where: is the bending stiffness of the pier in the elastic stage , is the shear stiffness of the pier in the elastic stage ; If cracks occur in the plastic hinge area, continue to determine the type of cracks in the plastic hinge area; When only bending cracks occur in the plastic hinge region, the pier deformation is calculated using formula (23); When only shear cracks occur in the plastic hinge region, the pier deformation is calculated using formula (24); When both bending cracks and shear cracks exist in the plastic hinge region, formula (25) is used to calculate the pier deformation.

[0091] In summary, in the calculation method of pier deformation under debris flow impact provided by the present invention, when no plastic hinge is formed at the bottom of the pier, the pier body of the pier is in the elastic deformation area as a whole. At this time, the displacement of the pier top is the superposition of the lateral displacement and shear deflection of the elastic deformation area; when a plastic hinge is formed at the bottom of the pier, the pier body of the pier is divided into a plastic hinge area and an elastic deformation area from bottom to top. At this time, the total displacement of the pier top is the superposition of the lateral displacement of the elastic deformation area, the shear deflection of the elastic deformation area, and the yield displacement of the top of the plastic hinge. Further, when a plastic hinge is formed at the bottom of the pier, it is also necessary to determine whether cracks are formed in the plastic hinge area and the type of cracks formed. Different calculation formulas are used for different crack types (the difference is that the values ​​of the flexural stiffness of the pier and the shear stiffness of the pier are different). The calculation method provided in this embodiment comprehensively considers the influence of bending deformation and shear deformation on the overall deformation of the pier, and can provide more accurate technical support and scientific basis for bridge structures to resist debris flow impact.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for calculating the deformation of bridge piers under the impact of debris flow, characterized in that: include: The bridge piers form elastic deformation areas under the impact of debris flow; calculating the lateral displacement of the elastic deformation region using a deflection curve equation; Calculating the shear deflection of the elastic deformation area by using the virtual work principle for the shear section; Calculate the displacement of the pier top caused by the elastic deformation area: in, is the displacement of the top of the pier caused by the elastic deformation area; is the lateral displacement of the elastic deformation area; is the shear deflection of the elastic deformation area.

2. The method for calculating the deformation of bridge piers under the impact of debris flow according to claim 1 is characterized in that: Also includes: When the bottom of the pier is impacted and the longitudinal tensile reinforcement yields to form a plastic hinge, the pier body is divided into a plastic hinge area and the elastic deformation area from the bottom to the top; Obtaining the plastic hinge top yield displacement generated in the plastic hinge region by integrating the cross-sectional yield curvature of the plastic hinge region in the length direction of the plastic hinge region; Calculate the total displacement of the pier top: in, is the total displacement of the pier top; is the yield displacement of the plastic hinge top generated in the plastic hinge area.

3. The method for calculating the deformation of bridge piers under the impact of debris flow according to claim 2 is characterized in that: The steps divide the pier body of the bridge into a plastic hinge area and the elastic deformation area from the bottom to the top, and include: Calculate the length of the plastic hinge region: in, is the length of the plastic hinge region; is the yield strength of the steel bar; is the diameter of the steel bar; Circular cross-section diameter; Calculate the length of the elastic deformation area: in, is the length of the elastic deformation zone; H is the height of the pier.

4. The method for calculating the deformation of bridge piers under the impact of debris flow according to claim 3 is characterized in that: When the debris flow does not contain large rocks, the lateral displacement of the elastic deformation area The calculation formula is: in, is the length of the elastic deformation area; is the overall impact pressure of debris flow; For debris flow depth; is the bending stiffness of the pier; is the height of the pier; is the angle between the bearing surface of the bridge pier and the direction of the debris flow; It is a heavy debris flow; is the velocity of debris flow; g is the acceleration of gravity; θ is the angle between the force-bearing surface of the building and the direction of the debris flow; is the building shape factor; In the case of debris flow with large rocks impacting, the lateral displacement of the elastic deformation area The calculation formula is: in, is the length of the elastic deformation area; is the impact pressure of the stone; is the height of the rock impact point from the ground; is the bending stiffness of the pier; is the impact velocity of the large rock; The weight of the stone; is the height of the pier; It is the angle between the large stone and the bearing surface of the bridge pier; is the acceleration due to gravity; The shear deflection of the elastic deformation area The calculation formula is: in, is the shear force of the section at the deflection calculation location under unit force is the integral of the length along the pier height direction is the shear force non-uniformity coefficient Shear force under actual load on bridge pier is the shear stiffness of the pier; The yield displacement of the top of the plastic hinge generated in the plastic hinge area The calculation formula is: in, is the section yield curvature function, and the section curvature is linearly distributed along the pier height. ; is the yield curvature of the cross section, ; is the effective height of the section; The compressive stress of concrete reaches When the concrete compressive strain is calculated When the value is less than 0.002, it is taken as 0.002; is the design value of steel bar tensile strength; is the elastic modulus of the steel bar; is the cross-section reinforcement ratio; is the design value of concrete strength; Combined with the above formula, when the debris flow does not contain large rocks and the bridge pier has no plastic hinge, the displacement of the pier top is The calculation formula is: in, is the bending stiffness of the pier in the elastic stage , is the shear stiffness of the pier in the elastic stage; When the debris flow does not contain large rocks, the total displacement of the pier top is The calculation formula is: In the case of debris flow and large rocks impact, when the bridge pier has no plastic hinge, the displacement of the pier top is The calculation formula is: in, is the bending stiffness of the pier in the elastic stage , is the shear stiffness of the pier in the elastic stage; When a large rock in a debris flow hits a bridge pier, the total displacement of the bridge pier top is The calculation formula is: 。 5. The method for calculating the deformation of bridge piers under the impact of debris flow according to claim 4 is characterized in that: After the pier body of the bridge pier is divided into the plastic hinge area and the elastic deformation area from the bottom to the top in the above steps, the following steps are also included: Determining whether cracks occur in the plastic hinge region; If no cracks occur in the plastic hinge region, the lateral displacement The calculation formula for the bending stiffness of the bridge pier is is the bending stiffness of the pier in the elastic stage , shear deflection The shear stiffness of the bridge pier in the calculation formula is the shear stiffness of the pier in the elastic stage ; If cracks occur in the plastic hinge region, the crack type of the plastic hinge region is determined, and the crack type includes bending cracks and shear cracks; When a bending crack occurs in the plastic hinge region, the lateral displacement The calculation formula for the bending stiffness of the bridge pier is is the effective bending stiffness of the crack section; When shear cracks occur in the plastic hinge region, the shear deflection The shear stiffness of the bridge pier in the calculation formula is the effective shear stiffness of the crack section.

6. The method for calculating the deformation of bridge piers under the impact of debris flow according to claim 5 is characterized in that: The step of determining the crack type of the plastic hinge region includes: Calculation of shear forces corresponding to flexural cracking and the shear force corresponding to shear cracking , and obtain the actual shear force in the impact ; Compare , as well as The size of the three; like , then only bending cracks will occur in the plastic hinge region; like , then only shear cracks will occur in the plastic hinge region; like , then there are both bending cracks and shear cracks in the plastic hinge region.

7. The method for calculating the deformation of bridge piers under the impact of debris flow according to claim 6 is characterized in that: Shear force corresponding to flexural cracking The calculation formula is: Shear force corresponding to shear cracking The calculation formula is: in; is the bending moment at the time of bending cracking, calculated by elastic beam theory, ; is the tensile strength of concrete; is the moment of inertia of the pier section; is the distance from the centroid of the section to the tension edge; is the shear force during bending cracking; is the actual bending moment when the bridge pier is impacted by debris flow; is the actual shear force in impact; is the shear force during shear cracking; is the effective height of the section; is the area of ​​the tensile longitudinal reinforcement; is the characteristic value of compressive strength of concrete cylinder; is the section width.

8. The method for calculating the deformation of bridge piers under the impact of debris flow according to claim 5 is characterized in that: The calculation method of the effective bending stiffness of the crack section is: Calculate the average crack spacing: in, is the average crack spacing; is the load form influence coefficient, which is 1.1 for axial tension members and 1.0 for bending and eccentric load members; The distance from the outer edge of the outermost longitudinal tensile reinforcement to the bottom edge of the tensile zone is 20mm when it is less than 20mm and 65mm when it is greater than 65mm. is the equivalent diameter of the longitudinal reinforcement in the tension zone, , For the tension zone The number of longitudinal reinforcements, For the tension zone The nominal diameter of the steel bar, is the relative bonding characteristic coefficient of the longitudinal tensile reinforcement, which is 0.7 for plain round reinforcement and 1.0 for ribbed reinforcement; It is the longitudinal tensile reinforcement ratio calculated based on the effective tensile concrete cross-sectional area, which is equal to the ratio of the area of ​​the longitudinal tensile reinforcement to the effective tensile concrete cross-sectional area; According to the geometric relationship, the average crack spacing is obtained and effective height of section The formula relationship is: In the formula, is the cross-sectional curvature is the compression of the concrete under pressure, is the elongation of the tensile reinforcement at the crack location, ; is the average strain of the reinforcement between the crack sections, is the average strain at the edge of the concrete in the compression zone between the crack sections, is the bending moment value calculated according to the quasi-permanent combination of loads is the ratio of the average strain between cracks to the steel bar strain in the crack section, Design value of concrete tensile strength is the reinforcement stress in the crack section, is the cross-sectional area of ​​the tensile reinforcement is the elastic modulus of the steel bar To determine the comprehensive influence coefficient of the moment of resistance of the average strain of the tensile edge concrete is the elastic modulus of concrete is the equivalent diameter of the longitudinal reinforcement in the tension zone is the longitudinal tensile reinforcement ratio calculated based on the effective tensile concrete cross-sectional area; Calculate the effective bending stiffness of the cracked section: in, is the effective bending stiffness of the crack section.

9. The method for calculating the deformation of bridge piers under the impact of debris flow according to claim 8, characterized in that: The calculation method of the effective shear stiffness of the crack section is: According to the truss model, the actual shear force Under the action of Calculate the effective shear stiffness of the cracked section: In the formula, is the effective shear stiffness of the crack section; is the compression of the truss concrete; is the deformation of the shear stirrups at the crack location; is the average strain at the edge of the concrete in the compression zone between the inclined crack sections, is the average strain of the stirrups between the crack sections, is the stirrup spacing; is the area of ​​stirrups; is the cross-section internal force arm; is the stirrup ratio; is the inclination angle of the concrete diagonal strut in the truss model, which can be taken as 45° for calculation.

10. The method for calculating the deformation of bridge piers under the impact of debris flow according to claim 9, characterized in that: When only bending cracks occur in the plastic hinge region, the total displacement of the pier top is ; When only shear cracks occur in the plastic hinge region, the total displacement of the pier top is ; When there are both bending cracks and shear cracks in the plastic hinge region, the total displacement of the pier top is ; Combined with the above formula, when the debris flow does not contain large rocks, The calculation formula is: in, is the ratio of elastic modulus of steel bar to concrete, ; is the tensile reinforcement ratio; In the case of debris flows that do not contain large rocks, The calculation formula is: In the case of debris flows that do not contain large rocks, The calculation formula is: In the case of large rocks impacting debris flow, The calculation formula is: In the case of large rocks impacting debris flow, The calculation formula is: In the case of large rocks impacting debris flow, The calculation formula is: 。

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