A seismic design method and system for anti-falling beam restraint cables of a cross-fault beam bridge

Abstract

This invention discloses a seismic design method and system for anti-falling beam restraint cables in fault-crossing beam bridges, relating to the field of bridge seismic isolation and reduction design. It discloses two stiffness calculation formulas applicable to anti-falling beam restraint cables in fault-crossing beam bridges and proposes a seismic design method for these cables. The method proposed in this invention limits the relative displacement between the pier and the beam within allowable limits, preventing beam fall or support failure in fault-crossing beam bridges. The design results of this invention exhibit good seismic performance, meeting the displacement requirements for anti-falling beams under the dual effects of seismic dynamics and permanent displacement caused by fault rupture, thus improving bridge safety under strong earthquakes and making it suitable for engineering applications.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of anti-seismic design method and system of anti-falling beam limiting cable of cross-fault beam bridge, belong to bridge seismic mitigation design field. BACKGROUND

[0002] Generally, when carrying out bridge anti-seismic design, bridge across active fault will be avoided.However, due to the need of economic development and national strategy, there are a certain number of cross-fault bridges.Compared with conventional bridges, the dynamic response of cross-fault bridge under the action of earthquake is more complex, the earthquake damage is more serious, and the disaster prevention and mitigation is more difficult.When carrying out anti-seismic design, only the dynamic action of ground motion needs to be considered for conventional bridges, while the double action of ground motion dynamic action and permanent displacement generated by fault rupture needs to be considered for cross-fault bridge anti-seismic design.

[0003] Earthquake disasters in previous times show that under the action of permanent displacement generated by fault rupture, the earthquake damage of cross-fault bridge often shows falling beam caused by large displacement of pier beam, which needs to be reduced by reasonable limiting anti-seismic design.A solution to this problem is to design the stiffness of limiting cable so that the relative displacement of pier beam is limited within the expected range.However, due to the complexity of cross-fault bridge under the action of earthquake, there is currently no design method for limiting cable of cross-fault bridge, which leads to no basis for cross-fault bridge seismic mitigation design.

[0004] Therefore, in order to solve the above problems, the present application provides a stiffness calculation formula and anti-seismic design method and system of anti-falling beam limiting cable of cross-fault beam bridge, which can conveniently, efficiently and accurately calculate the required design stiffness of limiting cable. SUMMARY

[0005] The purpose of the present application is to solve the problem of no cable stiffness calculation method for the design of anti-falling beam limiting cable of cross-fault beam bridge.The present application provides a stiffness calculation formula and anti-seismic design method and system of anti-falling beam limiting cable of cross-fault beam bridge, which is mainly used to calculate the design stiffness of limiting cable according to the equivalent pier stiffness, equivalent support stiffness, allowable pier beam displacement, seismic response requirement and permanent ground displacement of cross-fault beam bridge.Under this stiffness, the relative displacement of pier beam of cross-fault beam under the action of earthquake can be limited within the allowable pier beam displacement.

[0006] The technical scheme adopted by the present application is as follows:

[0007] S1, determine the stiffness calculation method of anti-falling beam limiting cable of cross-fault beam bridge, which is calculated according to formula one or formula two;

[0008] Formula one is:

[0009]

[0010] Among them, K r For the design stiffness of the anti-falling beam limit cable of the cross-fault beam bridge, K peff For the equivalent pier stiffness, K beff For the equivalent support stiffness, Δ a To allow for pier-beam displacement, Δ eq0 For the initial seismic response requirements, The mathematical formula for a 1-layer, 4-neuron, 4-input-variable artificial neural network is given, where i represents the i-th neuron of the artificial neural network, j represents the j-th input variable, and variable x1 is the yield stiffness K of the bridge pier. py Variable x2 represents the permanent ground displacement Δ of trans-fault ground motion. rup Variable x3 represents the allowable pier-beam displacement Δ a Variable x4 represents the initial seismic response demand Δ eq0 w 1i,j w represents the weight coefficient of the j-th input variable at the i-th neuron. 2i Let b be the weight coefficient of the i-th neural population. 1i Let b1 be the bias of the i-th neural population, and b2 be the overall bias coefficient of the artificial neural network. For Formula 1, the values ​​of all weight coefficients and bias coefficients are shown in the table below:

[0011]

[0012] Formula 2 is:

[0013]

[0014] All variables are interpreted the same way as in Formula 1. For Formula 2, the values ​​of all weights and paranoia coefficients are shown in the table below:

[0015]

[0016] Both Formula 1 and Formula 2 above contain This formula is derived directly from the characteristics of bridges spanning faults and the design experience of experts, and can also be considered as the calculation formula for the design stiffness of conventional bridge limit cables.

[0017] S2, Calculate the equivalent pier stiffness μ represents the displacement ductility of the pier, which is equal to the ratio of the maximum deformation to the yield deformation of the pier. The yield stiffness K of the pier is also mentioned. py It is the default value.

[0018] S3, Calculate the equivalent support stiffness K b,eff For bearings such as plate rubber bearings and lead-core rubber bearings, whose mechanical properties can be represented by a bilinear model, the equivalent bearing stiffness... Kb1 and K b2 are the pre-yield stiffness and post-yield stiffness of the bilinear model, respectively, Δ b1 is the yield displacement.

[0019] S4, calculate the allowable pier-girder displacement Δ a = min{γΔ bt , aΔ support}; wherein the allowable pier-girder displacement Δ a is the minimum value of the allowable bearing displacement γΔ bt and the product of a and the supported length of the main girder Δ support , γ is the allowable shear strain of the bearing, γΔ bt is the thickness of the bearing rubber layer; a is a safety factor, which is 0.8, or other values less than 1 according to the specific design safety degree.

[0020] S5, the initial seismic response demand Δ eq0 can be obtained by finite element calculation of the cross-fault bridge, but this method needs finite element modeling and is not easy to obtain directly. The initial seismic response demand Δ eq0 can also be calculated by a simplified calculation method, Δ eq0 = Δ eq0,d + Δ eq0,s , wherein Δ eq0,d is the initial seismic response demand dynamic component under the action of seismic motion, and Δ eq0,s is the initial seismic response demand quasi-static component under the action of permanent displacement.

[0021] For the above simplified calculation method, the initial seismic response demand dynamic component Δ eq0,d is calculated by the linear response spectrum analysis method, and the initial seismic response demand quasi-static component Δ eq0,s can be calculated by the following formula:

[0022] For the cross-fault side:

[0023] For the non-cross-fault side:

[0024] wherein K beff,N is the equivalent stiffness of the bearing on the non-cross-fault side, K beff,F is the equivalent stiffness of the bearing on the cross-fault side, and the permanent ground displacement Δ rup of the cross-fault seismic motion is a design preset value.

[0025] S5, after the above parameters are determined, these parameters are brought into formula one or formula two, so that the design stiffness K r of the anti-falling beam limiting cable of the cross-fault girder bridge can be calculated. Formula one and formula two contain All the weights and bias coefficients in the term are obtained by mathematical expansion of a high-precision artificial neural network model trained by 34337 groups of design parameters.

[0026] Another aspect of the present application also provides an anti-seismic design system for the anti-falling beam limiting cable of a cross-fault beam bridge, which can realize the anti-seismic design method described above, and comprises:

[0027] A rigidity calculation method determination module is configured to determine a calculation method for the rigidity of the anti-falling beam limiting cable of the cross-fault beam bridge, which is calculated according to Formula I or Formula II.

[0028] An equivalent pier rigidity calculation module is configured to calculate the equivalent pier rigidity

[0029] An equivalent support rigidity calculation module is configured to calculate the equivalent support rigidity K b,eff .

[0030] A permissible pier-beam displacement calculation module is configured to calculate the permissible pier-beam displacement Δ a .

[0031] An initial seismic response demand calculation module is configured to calculate the initial seismic response demand Δ eq0 according to the formula Δ eq0,d = Δ eq0,s . eq0 .

[0032] A design rigidity calculation module for the anti-falling beam limiting cable of the cross-fault beam bridge is configured to calculate the design rigidity K r of the anti-falling beam limiting cable of the cross-fault beam bridge by substituting the parameters into Formula I or Formula II.

[0033] Advantages:

[0034] (1) The present application provides a calculation formula for quickly and accurately calculating the design rigidity of the anti-falling beam limiting cable of the cross-fault beam bridge, which solves the problem of inaccurate calculation using the conventional design formula for the limiting cable of the bridge. The design rigidity of the limiting cable calculated using the formula provided by the present application can effectively control the relative displacement of the pier and beam of the cross-fault beam bridge under the dual action of the seismic dynamic force and the permanent displacement caused by the fault rupture, meet the displacement requirement for the anti-falling beam of the bridge, and is conducive to improving the safety of the cross-fault bridge under strong earthquakes.

[0035] (2) The present application provides an anti-seismic design method for the anti-falling beam limiting cable of the cross-fault beam bridge, which is convenient for designers to operate, overcomes the problems of difficult operation and long time consumption of the traditional iterative design method, and ensures the accuracy of the design to reach 94%.

[0036] (3) The stiffness calculation formula and the anti-seismic design method of the anti-falling beam limiting inhaul cable of the cross-fault beam bridge provided by the application can not only prevent the cross-fault beam bridge from falling, but also prevent the support from being damaged by limiting the displacement of the support, thereby greatly reducing the collapse and damage risk of the cross-fault bridge under the action of the earthquake. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 is a flow chart of the anti-seismic design method of the anti-falling beam limiting inhaul cable of the cross-fault beam bridge provided by the application;

[0038] Figure 2 is a schematic diagram of the cross-fault beam bridge of the embodiment of the application;

[0039] Figure 3 is an effect comparison diagram of the embodiment of the application.

[0040] In the figure: 11-cross-fault side limiting inhaul cable; 12-non-cross-fault side limiting inhaul cable; 2-pier; 31-cross-fault side support; 32-non-cross-fault side support; 41-cross-fault side main beam; 42-non-cross-fault side main beam; 5-fault. DETAILED DESCRIPTION

[0041] In order to make the purpose, technical scheme and advantages of the application clearer and more apparent, the application will be further described in detail below in combination with the drawings and embodiments.

[0042] The application provides an anti-seismic design method of an anti-falling beam limiting inhaul cable of a cross-fault beam bridge, as shown in the figure, comprising the following steps: Figure 1

[0043] S1, determining the initial design parameters of the piers and supports of the cross-fault beam bridge, including: pier displacement ductility μ, pier yield stiffness K py , main beam support length Δ support , allowable shear strain of support γ, anti-falling beam safety factor, pre-yield stiffness K b1 and post-yield stiffness K b2 of the double-reduction model, yield displacement Δ b1 of the support, thickness Δ bt of the rubber layer of the support, permanent ground displacement Δ rup of the cross-fault ground motion. The recommended value of the anti-falling beam safety factor is 0.8, and other values less than 1 can also be taken according to the design needs.

[0044] S2, calculating the allowable pier beam displacement Δ a = min{γΔ bt , 0.8Δ support}. Calculating the equivalent pier stiffness K Calculating the equivalent support stiffness K ​Where the equivalent support stiffness of the bridge across the fault side and the non-fault side may be different, and needs to be calculated respectively, denoted as K beff,F and K beff,N .

[0045] S3, calculate the initial seismic response demand Δ eq0 = Δ eq0,d + Δ eq0,s , wherein the initial seismic response demand dynamic component Δ eq0,d is obtained by simplifying the bridge into a two-degree-of-freedom system through linear response spectrum analysis method.

[0046] The initial seismic response demand pseudo-static component Δ eq0,s can be calculated by the following formula:

[0047] For the fault side:

[0048] For the non-fault side:

[0049] By comparing Δ eq0 and Δ a , it is determined whether the anti-falling beam limiting cable design is needed, if Δ eq0 > Δ a , the limiting cable design is needed, if Δ eq0 < Δ a , the limiting cable design is not needed.

[0050] S4, the above parameter values are substituted into formula one or formula two to directly calculate the limiting cable design stiffness required for the fault side and the non-fault side of the fault bridge, denoted as K r,F and K r,N .

[0051] The following is a specific embodiment:

[0052] Taking a span bridge as an example, as shown in Figure 2 , the fault bridge includes fault side limiting cable 11, non-fault side limiting cable 12, pier 2, fault side support 31, non-fault side support 32, fault side main beam 41, non-fault side main beam 42 and fault 5. The design method includes the following steps:

[0053] S1, determine the initial design parameters of the fault bridge pier and support, the pier displacement ductility μ = 1, the pier yield stiffness K py = 23.67 kN / mm, the main beam support length Δ support = 500 mm, the support allowable shear strain γ = 2, the anti-falling beam safety factor is 0.8, the pre-yield stiffness K b1 = 15.4 kN / mm and the post-yield stiffness Kb2 = 2.4 kN / mm, yield displacement of bearing Δ b1 = 143 mm, thickness of bearing rubber layer Δ bt = 6.4 mm, permanent ground displacement of cross-fault ground motion Δ rup = 544 mm.

[0054] S2, calculate allowable pier-beam displacement Δ a = min{2 x 143, 0.8 x 500} = 286 mm. Calculate equivalent pier stiffness K Calculate equivalent bearing stiffness K In this embodiment, the equivalent bearing stiffness of the cross-fault side and the non-cross-fault side of the bridge is the same, K beff,F = K beff,N = 5.8 kN / mm.

[0055] S3, calculate initial seismic response demand Δ eq0 = Δ eq0,d + Δ eq0,s , wherein the dynamic component of the initial seismic response demand Δ eq0,d By simplifying the bridge into a two-degree-of-freedom system, the linear response spectrum analysis method is used to obtain,

[0056] The quasi-static component of the initial seismic response demand Δ eq0,s can be calculated by the following formula:

[0057] For the cross-fault side:

[0058] For the non-cross-fault side: Therefore, for the cross-fault side: It is indicated that the anti-falling beam limiting cable design needs to be carried out; for the non-cross-fault side: No special design is needed.

[0059] S4, substitute the above parameter values into formula one, K r,F = 26.8 kN / mm; substitute the above parameter values into formula two, K r,F = 27.5 kN / mm; substitute some of the above parameters into the traditional formula The effective value of the limiting cable verified by the iteration method and the finite element is K r,F = 26.4 kN / mm.

[0060] Figure 3After comparing the limit cable designed by formula 1, formula 2, traditional formula and iterative method, the dynamic finite element analysis results of the specific embodiment bridge show that the stiffness of the limit cable calculated by formula 1 and formula 2 is close to the iterative method, the relative displacement of the pier and beam can be limited within the allowable displacement, the traditional formula underestimates the stiffness of the limit cable of the fault-crossing beam bridge, the relative displacement of the pier and beam exceeds the allowable displacement, and the bridge is seriously damaged.

[0061] Through the embodiment, it is shown that the design method of the application can calculate the correct stiffness of the anti-falling beam limit cable, the relative displacement of the pier and beam of the fault-crossing beam bridge is limited within the allowable displacement. The design result of the method has good seismic performance, meets the displacement requirement of the anti-falling beam under the double action of the dynamic action of the earthquake and the permanent displacement generated by the fault rupture, is beneficial to improving the safety of the bridge under strong earthquakes, and can be used in engineering.

[0062] Those skilled in the art can easily understand that the above description is only the preferred embodiment of the application, and is not used to limit the application, and any modification, equivalent replacement and improvement made within the spirit and principle of the application should be included in the protection scope of the application.

Claims

1. An anti-seismic design method of a fall-prevention cable of a cross-fault beam bridge, characterized in that, It comprises the following steps: S1, determining the stiffness calculation method of the anti-falling beam limiting cable of the cross-fault beam bridge, which is calculated according to formula one or formula two; the formula one is: ； wherein, is the design stiffness of the anti-falling beam limiting cable for the cross-fault beam bridge, is the equivalent pier stiffness, is the equivalent support stiffness, is the allowable pier-beam displacement, is the initial seismic response demand, is the mathematical formula of the 1-layer 4-neuron 4-input variable artificial neural network, wherein i represents the neuron of the i-th artificial neural network, j represents the j-th input variable, variable x1 is the yield stiffness of the pier , variable x2 is the permanent ground displacement of the cross-fault ground motion , variable x3 is the allowable pier-beam displacement , and variable x4 is the initial seismic response demand , represents the weight coefficient of the j-th input variable at the i-th neuron, is the weight coefficient of the i-th neuron population, is the bias of the i-th neuron population, and b2 is the population bias coefficient of the artificial neural network; the formula two is: ； Wherein, the meaning of each variable is same as formula one; S2, calculate the equivalent pier stiffness ; wherein, μ is the displacement ductility of the pier, μ is equal to the ratio of the maximum deformation and yield deformation of the pier, the pier yield stiffness is a preset value; S3, calculate the equivalent bearing stiffness ; equivalent bearing stiffness , and respectively are the pre-yield stiffness and post-yield stiffness of the double-reduction model, is the yield displacement; S4, calculate the allowable pier girder displacement ; wherein, the allowable pier girder displacement is the allowable bearing displacement and a is the minimum value of the product of the length of the main girder supported , is the allowable shear strain of the bearing, is the thickness of the bearing rubber layer; a is the safety factor, a < 1; S5, calculate the initial seismic response demand according to formula , wherein is the dynamic component of the initial seismic response demand under the action of seismic motion, is the quasi-static component of the initial seismic response demand under the action of permanent displacement; S6, after the above parameters are determined, these parameters are brought into formula one or formula two to calculate the design stiffness of the anti-falling beam limiting cable of the cross-fault girder bridge ; The values of the weight coefficient and the bias coefficient in the formula one of the step S1 are determined according to the following table: ； The values of the weight coefficient and the bias coefficient in the formula two are determined according to the following table: 。 2. The seismic design method of the anti-falling beam limiting inhaul cable for a cross-fault beam bridge according to claim 1, characterized in that, In the step S3, the support applicable to the double-fold model is a support whose mechanical properties can be represented by a double-fold line model.

3. The seismic design method of the anti-falling beam limiting inhaul cable for a cross-fault beam bridge according to claim 2, characterized in that, The support comprises a plate-type rubber support or a lead-core rubber support.

4. The seismic design method for the anti-falling beam limiting inhaul cable of a cross-fault beam bridge according to claim 1, characterized in that, In the step S4, the safety factor a is 0.

8.

5. The seismic design method of the anti-falling beam limiting inhaul cable for a cross-fault beam bridge according to claim 1, characterized in that, The initial seismic response demand dynamic component in the step S5 is obtained by a simplified calculation method ; in the simplified calculation method, the initial seismic response demand dynamic component is calculated by a linear response spectrum analysis method; the initial seismic response demand quasi-static component is calculated by the following formula: for the fault-crossing side: ; for the non-fault-crossing side: ; wherein is the equivalent stiffness of the support on the non-fault-crossing side, is the equivalent stiffness of the support on the fault-crossing side, the permanent ground displacement of the fault-crossing ground motion is a design preset value.

6. An anti-seismic design system of a fall-prevention cable for a cross-fault beam bridge, capable of realizing the anti-seismic design method of any one of claims 1-5, characterized in that, It comprises: The rigidity calculation method determination module is configured to determine a calculation method of the anti-falling beam limiting inhaul cable rigidity of the fault-crossing beam bridge, and the calculation is performed according to Formula One or Formula Two. The equivalent pier rigidity calculation module is configured to calculate the equivalent pier rigidity an equivalent support stiffness calculation module for calculating an equivalent support stiffness ; a pier-beam displacement allowance calculation module for calculating a pier-beam displacement allowance ; an initial seismic response demand calculation module for calculating an initial seismic response demand according to a formula ;​ The design stiffness calculation module of the anti-falling beam limiting inhaul cable of the fault-crossing beam bridge is used to substitute the parameters into formula one or formula two to calculate the design stiffness of the anti-falling beam limiting inhaul cable of the fault-crossing beam bridge .

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