Sluice structure anti-seismic safety prediction method based on finite element internal force method

Abstract

The invention discloses a water gate structure anti-seismic safety prediction method based on a finite element internal force method, which comprises the following steps: firstly, establishing a three-dimensional finite element model of a water gate chamber structure, carrying out dynamic analysis on the water gate chamber structure by adopting a vibration mode decomposition response spectrum method based on ADINA finite element analysis software, and superposing a dynamic calculation result and a static calculation result; based on a stress calculation result after dynamic and static superposition, performing internal force conversion by adopting a finite element internal force method to obtain bending moments, shearing forces and axial forces at different components; and finally, comparing and analyzing the obtained bending moment, shearing force and axial force at different components with the bending moment, shearing force and axial force in a bearing capacity limit state, and predicting the anti-seismic safety of the lock chamber structure. According to the method, the limitation of a finite element numerical simulation technology in anti-seismic safety review of the water gate structure can be made up, internal force results of different parts under the action of an earthquake are more visually provided for designers, and corresponding bases and references can be provided for the designers to carry out anti-seismic safety design.

Description

Technical Field

[0001] The invention relates to seismic safety prediction of a sluice structure, and in particular to a seismic safety prediction method for a sluice structure based on a finite element internal force method. Background Art

[0002] The sluice project is mainly composed of the sluice chamber, anti-seepage and drainage, energy dissipation and anti-scouring, two-bank connection and management and maintenance facilities, among which the sluice chamber is the main part of the sluice for water retention and discharge. Earthquakes have a great impact on the safety of sluices, so it is particularly important to conduct seismic safety review of sluice structures.

[0003] Finite element numerical simulation technology has been widely used in the seismic analysis of sluices. It should be pointed out that the results of finite element numerical simulation are mainly used to analyze buildings with results such as displacement and stress, while the "Design Code for Hydraulic Concrete Structures" (SL191-2008) uses structural internal forces to verify the bearing capacity when determining whether the structure meets the safety requirements. The finite element numerical simulation method for seismic analysis of sluices cannot clearly and intuitively give the distribution and change rules of the structural internal forces, which is not conducive to the designers to verify the seismic safety of the sluice structure according to the design specifications. Summary of the invention

[0004] Purpose of the invention: The purpose of the present invention is to provide a method for predicting the seismic safety of a sluice structure based on the finite element internal force method, so as to solve the problems existing in the above-mentioned existing methods.

[0005] Technical solution: Some embodiments of the present disclosure propose a method for predicting the seismic safety of a sluice structure based on a finite element internal force method, the prediction method comprising:

[0006] (1) Establish a three-dimensional finite element model of the sluice chamber based on the structural dimensions of the sluice chamber;

[0007] (2) The potential fluid unit is used to simulate the dynamic water pressure of the water body in front of the gate, and the natural vibration characteristics of the gate structure are analyzed to obtain the natural vibration frequencies and vibration modes of each order of the gate structure;

[0008] (3) Based on the ADINA finite element analysis software, appropriate earthquake motion parameters were selected to perform modal decomposition response spectrum method dynamic calculation on the sluice chamber structure, and the displacement, acceleration and stress distribution of different areas of the sluice chamber structure under earthquake action were obtained;

[0009] (4) The inertial force at each node under the earthquake is obtained based on the obtained acceleration at each node, and the inertial force at each node is used as a point load;

[0010] (5) Based on the ADINA finite element analysis software, the preset material parameters, boundary conditions, and different static loads and point loads are input to perform finite element calculations on the sluice chamber structure, and the displacements and stresses of different areas of the chamber structure under the combined action of different static loads and point loads are obtained;

[0011] (6) Based on the displacements and stresses in different areas of the lock chamber structure, the finite element internal force method is used to transform the internal forces and obtain the bending moment, shear force and axial force at different components;

[0012] (7) Compare the bending moment, shear force and axial force obtained at different construction locations with the bending moment, shear force and axial force at the ultimate bearing capacity state to predict the seismic safety of the gate chamber structure.

[0013] Optionally, the specific process of analyzing the self-vibration characteristics of the sluice structure is: using potential fluid units to simulate the dynamic water pressure of the water body in front of the sluice, and its control equation is as follows:

[0014]

[0015] In the formula, P represents the dynamic water pressure. At the same time, a fluid-solid coupling boundary is set between the water body and the structure to simulate the energy transfer between the water body and the structure, as follows:

[0016]

[0017] Where n is the external normal direction of the fluid domain on the fluid-solid coupling surface; ρ is the density of the water body; is the absolute acceleration along the normal direction of the fluid-structure interaction surface.

[0018] Optionally, determine the basic earthquake intensity, peak ground acceleration and characteristic period T in the area g ; Determine the damping ratio η of the sluice chamber structure and the representative value β of the maximum value of the response spectrum max According to the calculation results in step (2), based on the modal decomposition response spectrum method, the seismic effects of each modal order are combined according to the square sum root to obtain the displacement and stress of different areas of the lock chamber structure under the earthquake. The specific calculation steps are as follows:

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025] Where β is the amplification factor; T is the natural vibration period of the structure; T g is the characteristic period; β max is the representative value of the maximum value of the response spectrum; {δ0} i is the vibration mode vector of the i-th vibration mode; η i is the i-th order revitalization participation coefficient; is the maximum absolute acceleration of the i-th vibration mode; {U max} i is the maximum relative displacement of the ith vibration mode; {σ max} i is the maximum stress of the i-th vibration mode; β i is the amplification factor of the i-th vibration mode; k is the seismic coefficient; g is the gravitational acceleration; {σ0} i is the stress corresponding to the i-th vibration mode; ω i ,ω j are the i-th and j-th order vibration mode circular frequencies respectively; S E is the earthquake effect; S i , S j are the seismic effects of the i-th and j-th vibration modes respectively; m is the number of vibration modes used in the calculation; ρ ij is the vibration mode correlation coefficient between the i-th and j-th vibration modes; ζ i , j are the damping ratios of the i-th and j-th vibration modes respectively; γ ω is the circular frequency ratio, γ ω =ω j / ω i ;ω i ,ω j are the i-th and j-th order vibration mode circular frequencies respectively.

[0026] Optionally, the inertial force F at node i under earthquake action i for:

[0027] F i =m i a i (9)

[0028] m i =ρ i V i (10)

[0029]

[0030] In the formula, m i is the mass of the i-th node; a i is the horizontal acceleration at the i-th node, which is divided into the acceleration along the river and the acceleration along the water flow; V iis the volume occupied by the i-th node; n is the number of units sharing i nodes; V j is the unit volume that shares the i-th node.

[0031] Optionally, the specific process of performing finite element calculation is:

[0032] Import the established three-dimensional finite element model of the sluice chamber into the finite element analysis software; input the preset material parameters, boundary conditions, different static loads and point loads in the finite element analysis software to perform dynamic and static superposition calculations on the sluice chamber structure; among them, the material parameters mainly include the concrete density, elastic modulus and Poisson's ratio in different areas, the boundary conditions are three constraints imposed on the bottom of the gate bottom plate, and the different static loads include deadweight load, water load, sediment load, uplift pressure, soil pressure, wave pressure, wind load, highway bridge load and hoist load;

[0033] In addition, the elastic modulus of concrete adopts the equivalent elastic modulus. In the linear elastic stage, the steel bar and concrete are deformed in coordination, and the specific effective principles are as follows:

[0034]

[0035] In the formula, E d E is the equivalent elastic modulus of reinforced concrete material; c is the elastic modulus of plain concrete; E s is the elastic modulus of the steel bar; A s is the cross-sectional area of ​​the steel bar; A is the cross-sectional area of ​​the concrete.

[0036] Optionally, the specific process of internal force transformation using the finite element internal force method is as follows:

[0037] Any structure can be divided into two substructures I and II with a cross section p, and the equation is satisfied after applying corresponding constraint boundary conditions

[0038] [K]{δ}={F} (13)

[0039] Where [K] is the overall stiffness matrix of the structure, {δ} is the structural displacement vector, and {F} is the load vector on the structure;

[0040] Select any cross section on these two substructures and apply a set of equal and opposite constrained internal forces to them, then we can get the deformation equation of equation [K]{δ}={F}:

[0041]

[0042] Where c and i are the nodes on section p and non-section p respectively; k ii k is the nodal force generated at node i when the node i undergoes unit displacement and the displacements of other nodes are 0;ic is the nodal force generated at node c when the node i undergoes unit displacement and the displacements of other nodes are 0; k ci is the nodal force generated at node i when node c undergoes unit displacement and the displacements of other nodes are 0; k cc F is the nodal force generated at node c when the node c undergoes unit displacement and the displacements of other nodes are 0; i With F c are the node load vectors on non-p and p sections respectively; {f c} I 、{f c} II They represent the constraint internal forces between the two substructures I and II on the p surface. According to the force balance equation, {f c} I +{f c} II =0 I ;

[0043] Substituting the node displacement obtained from formula (13) into formula (14) yields:

[0044] {f c} I =-{f c} II ={F c} I -[k ci ] I {δ i} I -[k cc ] I {δ c} I (15)

[0045] In formula (15), the internal force f of section p is c It can be solved cyclically based on the unit nodes containing p sections in the I or II substructure;

[0046] The steps of solving the internal forces of the structure using the force method in structural mechanics are as follows:

[0047] δ ij X+Δ p =0 (16)

[0048] In the formula, represents the structural flexibility matrix; Represents the unknown force array, Represents a free term array. Optionally, the specific process of the moment, shear and axial force bearing capacity of the gate chamber structure under the ultimate bearing capacity state is as follows:

[0049]

[0050] KN≤f c bx+f′ y A′ s -σ s A s (18)

[0051]

[0052]

[0053]

[0054] Where: M is the design value of the bending moment; K is the bearing capacity safety factor; f y is the design value of tensile steel bar strength; f′y is the design value of compressive steel bar strength; f c is the design value of concrete axial compressive strength; b is the calculated width of concrete compression zone; x is the calculated height of concrete compression zone; h0 is the effective height of the section; A s , A′ s is the cross-sectional area of ​​the longitudinal tensile and compressive reinforcement; a′ s is the distance from the combined force point of the compressive reinforcement to the compressed edge; N is the design value of the axial pressure; e is the distance from the axial pressure action point to the combined force point of the longitudinal reinforcement on the tensile side or the side with less compression; e0 is the eccentricity of the axial pressure to the center of gravity of the section; η is the eccentricity increase coefficient of the axial pressure considering the influence of the second-order effect of the eccentrically compressed member; σ s is the stress of the longitudinal reinforcement on the tensile side or the side with less compression; a s is the distance from the longitudinal reinforcement resultant point on the tensile side or the side with less compression to the edge of the section; V is the design value of the section shear force; V c V is the shear bearing capacity of concrete; sv is the shear bearing capacity of stirrups; V sb A is the shear bearing capacity of the bent steel bar; sv A is the total cross-sectional area of ​​each limb of the stirrups configured in the same section; sb is the cross-sectional area of ​​the bent steel bar in the same bending plane; α s is the angle between the bent steel bar on the inclined section and the longitudinal axis of the member; s is the spacing of stirrups along the length of the member; f yv f is the design value of stirrup tensile strength; t It is the design value of concrete axial tensile strength.

[0055] Optionally, if the bending moment, shear force and axial force at different parts of the gate chamber structure under the earthquake action calculated by the finite element internal force method are less than the bending moment, shear force and axial force bearing capacity at different parts of the gate chamber structure under the ultimate bearing capacity state, the seismic safety requirements are met; otherwise, the seismic safety requirements are not met.

[0056] Beneficial effects:

[0057] According to the structural characteristics of the water gate chamber, the embodiment of the present disclosure establishes a three-dimensional finite element model of the water gate chamber structure, and based on the ADINA finite element analysis software, adopts the vibration mode decomposition response spectrum method to perform dynamic analysis on the water gate chamber structure, and superimposes the dynamic calculation results with the static calculation results; based on the stress calculation results after dynamic and static superposition, the finite element internal force method is used to transform the internal force, and the bending moment, shear force and axial force at different components are obtained; finally, the bending moment, shear force and axial force at different components are compared and analyzed with the bending moment, shear force and axial force under the ultimate bearing capacity state, and the seismic safety of the gate chamber structure is predicted. It can make up for the limitations of finite element numerical simulation technology in the seismic safety review of water gate structures, provide designers with more intuitive internal force results of different parts under earthquake action, and provide designers with corresponding basis and reference for seismic safety design. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is the finite element model of the shallow hole gate chamber structure;

[0059] Figure 2 It is the first principal stress cloud diagram of the shallow hole gate frame column structure under normal water storage level condition (Pa);

[0060] Figure 3 It is the third principal stress cloud diagram of the shallow hole gate frame column structure under normal water storage level condition (Pa);

[0061] Figure 4 This is the structural characteristic cross-section of the bent column under normal water storage level conditions;

[0062] Figure 5 is the bending moment diagram at section a of the bent column under normal water level condition based on the finite element internal force method (kN·m);

[0063] Figure 6 It is the shear force diagram at section a of bent column under normal water level condition based on finite element internal force method (kN);

[0064] Figure 7 It is the axial force diagram (kN) of the bent column section b under normal water level condition based on the finite element internal force method;

[0065] Figure 8 It is a simplified calculation diagram of the bent column structure in the downstream direction;

[0066] Fig. 9 is the bending moment diagram at section a of the bent column under normal water level condition based on the structural mechanics method (kN·m);

[0067] Fig.10 is the shear force diagram (kN) at section a of the bent column under normal water level conditions based on the structural mechanics method;

[0068] Fig.11 It is the axial force diagram (kN) of the bent column section b under normal water level condition based on the structural mechanics method;

[0069] Fig.12 is the comparison of bending moment diagrams at section a of bent column under normal water level condition calculated by different methods (kN·m);

[0070] Fig.13 It is the comparison of shear force diagrams at section a of bent column under normal water level condition calculated by different methods (kN);

[0071] Fig.14 It is the comparison of the b-axis force diagram of the bent column section under normal water level condition calculated by different methods (kN);

[0072] Fig.15 It is the water body grid before and after the shallow hole gate chamber structure gate;

[0073] Fig.16 It is the first-order vibration mode of the shallow hole gate;

[0074] Fig.17 It is the second-order vibration mode of the shallow hole gate;

[0075] Fig.18 is the acceleration cloud diagram of the chamber structure of the shallow hole gate under earthquake action (m / s 2 );

[0076] Fig.19 It is the acceleration cloud diagram of the chamber structure of the shallow hole gate in the downstream direction under the earthquake action (m / s 2 );

[0077] Fig. 20 is the first principal stress cloud diagram of the shallow hole gate chamber structure under static and dynamic superposition (Pa);

[0078] Fig.21 It is the third principal stress cloud diagram of the chamber structure of the shallow hole gate under static and dynamic superposition (Pa);

[0079] Fig. 22 It is the bending moment diagram (kN·m) at section b under static and dynamic superposition based on the finite element internal force method;

[0080] Fig.23 It is the shear force diagram (kN) at section b under static and dynamic superposition based on the finite element internal force method;

[0081] Fig.24 It is the axial force diagram (kN) at section b under static and dynamic superposition based on the finite element internal force method. DETAILED DESCRIPTION

[0082] The present invention is further described below in conjunction with the accompanying drawings and specific examples.

[0083] A shallow hole gate of a certain hub project has 22 holes, each with a net width of 4.2m and a height of 8.2m. The top surface elevation of the gate bottom plate is 22.49m. The gate piers are made of C25 reinforced concrete, two holes in one unit, the gate piers are split, the side piers are 0.7m thick, and the middle piers are 1.0m thick. A flat vertical steel gate is used, the main gate slot is located upstream, and maintenance gate slots are set at the upstream and downstream ends respectively. The maintenance bridge and the highway bridge are located on the upstream and downstream sides of the pier top respectively. This calculation mainly conducts static and dynamic calculation and analysis on the structure of the one-unit gate chamber in the middle hole of the shallow hole gate. According to the structural characteristics of the gate chamber, a three-dimensional finite element model including the gate bottom plate, gate piers and the frame columns of the hoisting and closing machine room is established. The specific model is attached to the instruction manual. Figure 1 shown.

[0084] The water depth before and after the lock chamber structure under normal water level conditions is shown in Table 1.

[0085] Table 1 Lock chamber structure water depth before and after the lock

[0086]

[0087] Based on the ADINA finite element analysis software, the finite element static calculation of the sluice chamber structure is carried out. First, the established three-dimensional finite element model of the sluice chamber structure is imported into the ADINA finite element analysis software; secondly, the preset material parameters, boundary conditions and different loads are input into the ADINA finite element analysis software; then, based on the ADINA finite element analysis software, the static calculation of the sluice chamber structure is carried out. Among them, the material parameters mainly include the concrete density, elastic modulus and Poisson's ratio in different areas, and the boundary conditions are three constraints imposed on the bottom of the gate bottom plate.

[0088] In addition, in order to reflect the role of steel bars, the elastic modulus of concrete adopts an equivalent elastic modulus. In the linear elastic stage, steel bars and concrete are deformed in a coordinated manner. The specific equivalent principles are as follows:

[0089]

[0090] In the formula, E d is the equivalent elastic modulus of reinforced concrete material, GPa; E c is the elastic modulus of plain concrete, GPa; E s is the elastic modulus of the steel bar, GPa; A s is the cross-sectional area of ​​the steel bar, m 2 ; A is the concrete cross-sectional area, m 2 .

[0091] The material parameters used in the calculation are shown in Table 2 below, where the material parameters given in the table are all equivalent material parameters. At the same time, according to the "Water Gate Design Code" (SL265-2016), the calculation mainly considers self-weight load, water load, sediment load, uplift pressure, earth pressure, wave pressure, wind load, highway bridge load, hoist load and earthquake load.

[0092] Table 2 Concrete material parameters of each chamber structure

[0093]

[0094] Taking the upper frame column as an example, the correctness of the finite element internal force method in the analysis of the sluice structure is verified. The reinforced concrete frame column is located on the top of the gate pier. The pier top elevation is 32.74m, the frame column top elevation is 41.24m, the middle crossbeam top elevation of the frame column is 38.74m, the column spacing vertically in the water flow direction is 5.2m, and the column spacing along the water flow direction is 2.9m. The frame column is a single-span frame along the water flow direction. The cross-sectional dimensions of the upper frame beam along the water flow are 0.60m×0.60m, the cross-sectional dimensions of the middle crossbeam are 0.60m×0.50m, and the cross-sectional dimensions of the frame column are 0.60m×0.60m. The main force-bearing steel bars are Ф grade, and the elastic modulus of Ф grade steel bars is E s =2.0×10 5 N / mm2, compressive strength and tensile strength are f y =f′ y =300MPa. The cross-sectional dimensions of the bent column are 0.60m×0.60m, the steel bars are 4Ф25 on both the tension and compression sides, and the design value of the steel bar protective layer thickness is 45mm.

[0095] The cloud diagram of the stress calculation results of the shallow hole gate frame column structure under normal water level operation conditions is attached in the specification. Figure 2 and 3 As can be seen from the figure, under normal water storage conditions, the maximum tensile stress value of the shallow hole gate column structure is 0.22Mpa, and the maximum tensile stress area appears at the mid-span position of the bottom surface of the upper beam at the top of the middle column; the maximum compressive stress value is 0.82Mpa, which appears slightly above the bottom of the downstream column of the middle column. According to the stress characteristics of the column structure, considering the cross-sectional reinforcement position and combining the stress calculation results, a certain number of characteristic sections are selected, see the attached manual for details. Figure 4 .

[0096] Based on the stress calculation results, combined with the finite element internal force method, the bending moment diagram, shear force diagram and axial force diagram of the bent column under normal water level conditions are obtained. See the attached manual for details. Figure 5 , Attachment Figure 6 and attached Figure 7 The steps of internal force transformation using the finite element internal force method are as follows:

[0097] Any structure can be divided into two substructures I and II by a cross section P, and the equations are satisfied after applying corresponding constraint boundary conditions.

[0098] [K]{δ}={F} (13)

[0099] Where [K] is the overall stiffness matrix of the structure, {δ} is the structural displacement vector, and {F} is the load vector on the structure.

[0100] Select any cross section on these two substructures and apply a set of equal and opposite constrained internal forces to them, then we can get the deformation equation of equation [K]{δ}={F}:

[0101]

[0102] Where c and i are the nodes on section p and non-section p respectively; k ii k is the nodal force generated at node i when the node i undergoes unit displacement and the displacements of other nodes are 0; ic is the nodal force generated at node c when the node i undergoes unit displacement and the displacements of other nodes are 0; k ci is the nodal force generated at node i when node c undergoes unit displacement and the displacements of other nodes are 0; k cc F is the nodal force generated at node c when the node c undergoes unit displacement and the displacements of other nodes are 0; i With F c are the node load vectors on non-p and p sections respectively; {f c} I 、{f c} II They represent the constraint internal forces between the two substructures I and II on the p surface. According to the force balance equation, {f c} I +{f c} II =0 I .

[0103] Substituting the node displacement obtained from equation (13) into equation (14) yields:

[0104] {f c} I =-{f c} II ={F c} I -[k ci ] I {δ i} I -[k cc ]I{δ c} I(15)

[0105] Since the displacement is described by piecewise interpolation function in finite element, the internal force f of section p in equation (15) is c It can be solved by looping over the unit nodes containing the p-section in the I or II substructure.

[0106] In conjunction with the instruction manual Figure 5 , Attachment Figure 6 and attached Figure 7 , it can be seen that the maximum bending moment of the upper beam is 26.04kN·m, located at the mid-span position, at which time the lower surface of the beam is under tension; the bending moment of the corresponding cross-section position of the frame columns at both ends of the beam is 20.76kN·m, at which time the upper surface of the beam is under tension. The maximum and minimum values ​​of the shear force of the upper beam are both 75.71kN, located at the connection between the upper beam and the frame column, which is due to the symmetry of the frame column structure. Since the frame column bears the upper load and the deadweight of the structure, the axial force increases from top to bottom, and the compression at the bottom of the frame column reaches the maximum value, which is 322.5kN, which conforms to the general force law of the frame column.

[0107] The gate column frame is integrally cast in the direction of water flow, and a single column is cast perpendicular to the water flow. There is no connection between the column frames. Therefore, the structural mechanics method is used to verify the calculation of the integral frame structure model in the direction of water flow. In order to more clearly compare the results of the frame column structure in the structural mechanics method and the finite element internal force method, the upper structure of the frame column is simplified here and applied to the upper surface of the upper beam of the frame column in the form of load. The load mainly includes the load borne by the upper beam of the frame column structure q1, the self-weight of the upper beam q2, the self-weight of the middle beam q3, and the self-weight of the frame column q4. The specific calculation model is shown in the attached manual. Figure 8 .

[0108] The steps of solving the internal forces of the structure using the force method in structural mechanics are as follows:

[0109] δ ij X+Δ p =0 (16)

[0110] In the formula, represents the structural flexibility matrix; Represents the unknown force array, Represents an array of free terms.

[0111] Instructions attached Fig. 9 , Attachment Fig.10 and attached Fig.11The bending moment diagram, shear force diagram, and axial force diagram of the bent column structure under the limit state of normal use calculated by the structural mechanics method are given. It can be seen from the figure that the maximum bending moment of the bent column is 61.58kN·m, located at the intersection of the bent column and the upper beam. The shear force here is also the maximum value of the structure, the maximum shear force is 136.82kN, and the maximum axial force is located at the bottom of the bent column, which is 323.28kN, which conforms to the general force law of the frame structure.

[0112] Instructions attached Fig.12 , Attachment Fig.13 and attached Fig.14 A comparison diagram of the internal forces of the characteristic cross-section of the bent column structure calculated by the structural mechanics method and the finite element internal force method is given. It can be seen that for the upper beam of the bent column, the maximum values ​​of the positive and negative bending moments calculated by the structural mechanics method are greater than the results calculated by the finite element internal force method. The shear forces calculated by the two methods have the same law, but there are still certain differences in the maximum values ​​calculated; for the bent column, the axial force laws and values ​​calculated by the two methods are similar, with only a slight difference at the position of the middle beam of the bent column.

[0113] When analyzing the reasons for the difference in the internal force distribution of the bent column structure under the two methods, it can be seen that when the bent column structure is calculated using the structural mechanics method, the column and beam are simplified as rods because a two-dimensional plane calculation is used. At this time, the upper beam and the bent column are in point contact. The maximum negative bending moment is located at the contact position between the upper beam and the bent column. From this point to the two ends of the beam, there is a cantilever structure. The contact point between the bent column and the upper beam is the fixed constraint point of the cantilever. In the calculation diagram, the length of the cantilever beam is the distance between the center axis of the beam and the column, ignoring the cross-sectional size of the bent column structure. Therefore, when bearing the upper load, a large bending moment and shear force are generated. When the finite element internal force method is used for calculation and analysis, it is a three-dimensional space calculation. The internal force here is converted from the node internal force on the cross section. At this time, the influence of the cross section of the bent column is considered, and the bending moment and shear force are smaller than those calculated by the structural mechanics method. In actual engineering, the bent column and the upper beam are in surface contact, so the calculation results of the finite element internal force method are more in line with the actual stress conditions of the structure. At the same time, the beam and column are in contact with each other with variable cross-sections, and structural mechanics simplifies this, ignoring the effect of the increased contact area between the upper beam and the column, which leads to an increase in the mid-span bending moment, which is inconsistent with the actual situation. A comprehensive comparison shows that when calculating the internal force of the bent-column structure, the finite element internal force method is more accurate.

[0114] The structural self-vibration characteristic analysis method is used to consider the influence of the water body in front of the gate on the gate chamber structure, and the self-vibration analysis of the shallow hole gate chamber structure is carried out. The potential fluid unit is used to simulate the dynamic water pressure of the water body in front of the gate. The specific water unit is shown in the attached manual. Fig.15 . Its control equation is as follows:

[0115]

[0116] In the formula, P represents the dynamic water pressure. At the same time, a fluid-solid coupling boundary is set between the water body and the structure to simulate the energy transfer between the water body and the structure, as follows:

[0117]

[0118] Where n is the external normal direction of the fluid domain on the fluid-solid coupling surface; ρ is the density of the water body; is the absolute acceleration along the normal direction of the fluid-structure interaction surface.

[0119] Table 3 Periodic table of natural vibration frequency of shallow hole gate chamber structure

[0120]

[0121] Table 3 gives the calculation results of the natural frequency of the shallow hole gate chamber structure, as shown in the table. It can be seen from the table that the fundamental frequency of the natural frequency of the shallow hole gate chamber structure under normal water storage conditions is 2.764Hz. The present invention gives the first two vibration modes of the shallow hole gate side hole gate chamber structure, as shown in the attached manual. Fig.16 and attached Fig.17 shown.

[0122] According to the China Earthquake Motion Parameter Zoning Map (GB18306-2015), the basic earthquake intensity of the area where the hub project is located belongs to the VII degree zone, the corresponding peak acceleration of the earthquake is 0.1g, and the characteristic period of the earthquake response spectrum is T g is 0.35s, the site category is Class II, and the earthquake fortification intensity is 8 degrees; according to the "Seismic Design Standard for Hydraulic Structures" (GB 51247-2018), the damping ratio of the sluice structure is 7%, and the representative value of the maximum value of the response spectrum is β max Take 2.25. Finally, in the ADINA finite element analysis software, the earthquake effects of each vibration mode are combined according to the square sum and square root to obtain the displacement, acceleration and stress of different areas of the lock chamber structure under the earthquake. Among them, the calculation results of the cross-river acceleration and the downstream acceleration are shown in the attached manual. Fig.18 and attached Fig.19 The specific calculation steps are as follows:

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] Where β is the amplification factor; T is the natural vibration period of the structure; T g is the characteristic period; β max is the representative value of the maximum value of the response spectrum; {δ0} i is the vibration mode vector of the i-th vibration mode; η i is the i-th order revitalization participation coefficient; is the maximum absolute acceleration of the i-th vibration mode; {U max} i is the maximum relative displacement of the ith vibration mode; {σ max} i is the maximum stress of the i-th vibration mode; β i is the amplification factor of the i-th vibration mode; k is the seismic coefficient; g is the gravitational acceleration; {σ0} i is the stress corresponding to the i-th vibration mode; ω i ,ω j are the i-th and j-th order vibration mode circular frequencies respectively; S E is the earthquake effect; S i , S j are the seismic effects of the i-th and j-th vibration modes respectively; m is the number of vibration modes used in the calculation; ρ ij is the vibration mode correlation coefficient between the i-th and j-th vibration modes; ζ i , j are the damping ratios of the i-th and j-th vibration modes respectively; γ ω is the circular frequency ratio, γ ω =ω j / ω i ;ω i ,ω j are the i-th and j-th order vibration mode circular frequencies respectively.

[0130] According to the acceleration at each node calculated by the vibration mode decomposition response spectrum method, the inertial force at each node under the earthquake is derived. The inertial force F at node i under the earthquake i for:

[0131] F i =m i a i (9)

[0132] m i =ρ i V i (10)

[0133]

[0134] In the formula, m i is the mass of the i-th node; a iV is the horizontal acceleration at the ith node, which is divided into the acceleration in the cross-river direction and the acceleration in the downstream direction. The value can be positive or negative. When superimposing the dynamic and static accelerations, the positive and negative conditions in the cross-river direction and the downstream direction should be considered respectively. i is the volume occupied by the i-th node; n is the number of units sharing i nodes; V j is the unit volume that shares the i-th node.

[0135] The inertia force at the above point i is applied as a point load to the static calculation of the normal water level, and the calculation result is the dynamic and static superposition calculation result. Fig. 20 and attached Fig.21 The first principal stress and third principal stress cloud diagrams of the shallow hole gate chamber structure under static and dynamic superposition are given respectively. It can be seen from the figure that under the influence of earthquake action, large tensile stress is generated at the junction of the frame column and the gate pier and at the connection between the upstream side pier and the gate bottom plate. In order to check whether the structure is safe, the bearing capacity of its cross section should be calculated separately. Taking the frame column as an example, based on the finite element internal force method, the distribution law of bending moment, shear force and axial force at the characteristic section position is obtained, as shown in the attached manual. Fig.23 , Attachment Fig.24 shown.

[0136] As can be seen from the figure, the internal force distribution of the bent column tends to decrease with the increase of the component height, and changes at the middle beam position. This is because the cross-section change at this location has a certain impact on the internal force. The maximum bending moment and axial force of the bent column occur at the junction of the bent column and the gate pier, where the maximum bending moment and axial force are 189.66kN·m and 280.63kN respectively, and the maximum shear force is 33.04kN, located at the connection between the middle beam and the bent column.

[0137] The calculation formulas for the bending moment, shear force and axial force bearing capacity of the gate chamber structure under the ultimate bearing capacity state are as follows:

[0138]

[0139] Where: M is the design value of the bending moment; K is the bearing capacity safety factor; f y is the design value of tensile reinforcement strength; f′ y is the design value of compressive reinforcement strength; f c is the design value of concrete axial compressive strength; b is the calculated width of concrete compression zone; x is the calculated height of concrete compression zone; h0 is the effective height of the section; A s , A′ s is the cross-sectional area of ​​the longitudinal tensile and compressive reinforcement; a′ s It is the distance from the resultant force point of the compressive reinforcement to the compressive edge.

[0140] KN≤f c bx+f′ y A′ s-σ s A s (18)

[0141]

[0142]

[0143] Where: N is the design value of axial pressure; e is the distance between the axial pressure action point and the resultant force point of the longitudinal reinforcement on the tensile side or the side with less compression; e0 is the eccentricity of the axial pressure to the center of gravity of the section; η is the eccentricity increase coefficient of the axial pressure considering the influence of the second-order effect of the eccentrically compressed member; σ s is the stress of the longitudinal reinforcement on the tensile side or the side with less compression; a s It is the distance from the resultant force point of the longitudinal reinforcement on the tensile side or the side with less compression to the edge of the section; x is the calculated height of the concrete compression zone.

[0144]

[0145] Where: V is the design value of cross-section shear force; V c V is the shear bearing capacity of concrete; sv is the shear bearing capacity of stirrups; V sb A is the shear bearing capacity of the bent steel bar; sv A is the total cross-sectional area of ​​each limb of the stirrups configured in the same section; sb is the cross-sectional area of ​​the bent steel bar in the same bending plane; α S is the angle between the bent steel bar on the inclined section and the longitudinal axis of the member; s is the spacing of stirrups along the length of the member; f yv f is the design value of stirrup tensile strength; t It is the design value of concrete axial tensile strength.

[0146] The bending moment, shear force and axial force at different parts of the lock chamber structure under the earthquake action calculated by the finite element internal force method are compared with the bending moment, shear force and axial force bearing capacity at different parts of the lock chamber structure under the ultimate bearing capacity state. If the bending moment, shear force and axial force at different parts of the lock chamber structure under the earthquake action calculated by the finite element internal force method are less than the bending moment, shear force and axial force bearing capacity at different parts of the lock chamber structure under the ultimate bearing capacity state, the seismic safety requirements are met, otherwise the seismic safety requirements are not met.

[0147] Table 4. Verification table of the ultimate limit state of bending bearing capacity of bent column structure under earthquake action

[0148]

[0149] Table 5 Compressive bearing capacity limit state calculation table of bent column structure under earthquake action

[0150]

[0151] Table 6 The ultimate limit state calculation table of shear bearing capacity of bent column structure under earthquake action

[0152]

[0153] Tables 4, 5 and 6 respectively verify the bearing capacity of typical cross-sections of bent columns under the ultimate state of seismic bearing capacity, and it is found that the bending, shear and compressive bearing capacities of bent columns meet the requirements of the specifications.

[0154] The above descriptions are only some preferred embodiments of the present disclosure and an explanation of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by a specific combination of the above-mentioned technical features, but should also cover other technical solutions formed by any combination of the above-mentioned technical features or their equivalent features without departing from the above-mentioned inventive concept. For example, the above-mentioned features are replaced with the technical features with similar functions disclosed in the embodiments of the present disclosure (but not limited to) and the technical solutions formed.

Claims

1. A method for predicting seismic safety of sluice structures based on finite element internal force method, characterized in that: include: (1) Establish a three-dimensional finite element model of the sluice chamber based on the structural dimensions of the sluice chamber; (2) The potential fluid unit is used to simulate the dynamic water pressure of the water body in front of the gate, and the natural vibration characteristics of the gate structure are analyzed to obtain the natural vibration frequencies and vibration modes of each order of the gate structure; (3) Based on the ADINA finite element analysis software, appropriate earthquake motion parameters were selected to perform modal decomposition response spectrum method dynamic calculation on the sluice chamber structure, and the displacement, acceleration and stress distribution of different areas of the chamber structure under earthquake action were obtained; (4) The inertial force at each node under the earthquake is obtained based on the obtained acceleration at each node, and the inertial force at each node is used as a point load; (5) Based on the ADINA finite element analysis software, the preset material parameters, boundary conditions, and different static loads and point loads are input to perform finite element calculations on the sluice chamber structure, and the displacements and stresses of different areas of the chamber structure under the combined action of different static loads and point loads are obtained; (6) Based on the displacements and stresses in different areas of the lock chamber structure, the finite element internal force method is used to transform the internal forces and obtain the bending moment, shear force and axial force at different components; (7) Compare the bending moment, shear force and axial force obtained at different construction locations with the bending moment, shear force and axial force at the ultimate bearing capacity state to predict the seismic safety of the gate chamber structure.

2. The method for predicting seismic safety of a sluice structure based on the finite element internal force method according to claim 1 is characterized in that: The specific process of analyzing the self-vibration characteristics of the sluice structure in step (2) is as follows: using a potential fluid unit to simulate the dynamic water pressure of the water body in front of the sluice, and its control equation is as follows: In the formula, P represents the dynamic water pressure. At the same time, a fluid-solid coupling boundary is set between the water body and the structure to simulate the energy transfer between the water body and the structure, as follows: Where n is the external normal direction of the fluid domain on the fluid-solid coupling surface; ρ is the density of the water body; is the absolute acceleration along the normal direction of the fluid-structure interaction surface.

3. The method for predicting seismic safety of a sluice structure based on the finite element internal force method according to claim 1 is characterized in that: The specific process of performing modal decomposition response spectrum method dynamic calculation on the sluice chamber structure in step (3) is as follows: Determine the basic earthquake intensity, peak acceleration and characteristic period T of the region g ; Determine the damping ratio of the sluice chamber structure and the representative value of the maximum value of the response spectrum β max According to the calculation results in step (2), based on the modal decomposition response spectrum method, the seismic effects of each modal order are combined according to the square sum and square root to obtain the displacement, acceleration and stress of different areas of the lock chamber structure under the earthquake. The specific calculation steps are as follows: Where β is the amplification factor; T is the natural vibration period of the structure; T g is the characteristic period; β max is the representative value of the maximum value of the response spectrum; {δ0} i is the vibration mode vector of the i-th vibration mode; η i is the i-th order revitalization participation coefficient; is the maximum absolute acceleration of the i-th vibration mode; {U max } i is the maximum relative displacement of the i-th order vibration mode; {σ max } i is the maximum stress of the i-th vibration mode; β i is the amplification factor of the i-th vibration mode; k is the seismic coefficient; g is the gravitational acceleration; {σ0} i is the stress corresponding to the i-th vibration mode; ω i ,ω j are the i-th and j-th order vibration mode circular frequencies respectively; S E is the earthquake effect; S i , S j are the seismic effects of the i-th and j-th vibration modes respectively; m is the number of vibration modes used in the calculation; ρ ij is the vibration mode correlation coefficient between the i-th and j-th vibration modes; ζ i , j are the damping ratios of the i-th and j-th vibration modes respectively; γ ω is the circular frequency ratio, γ ω =ω j / ω i ;ω i ,ω j are the i-th and j-th order vibration mode circular frequencies respectively.

4. The method for predicting seismic safety of a sluice structure based on the finite element internal force method according to claim 1 is characterized in that: In step (4), the inertial force F at node i under earthquake action is i for: F i =m i a i (9) m i =ρ i V i (10) In the formula, m i is the mass of the ith node; a i is the horizontal acceleration at the i-th node, which is divided into the acceleration along the river and the acceleration along the water flow; V i is the volume occupied by the i-th node; n is the number of units sharing i nodes; V j is the unit volume that shares the i-th node.

5. The method for predicting seismic safety of a sluice structure based on the finite element internal force method according to claim 1 is characterized in that: The specific process of performing finite element calculation in step (5) is as follows: Import the established three-dimensional finite element model of the sluice chamber into the finite element analysis software; Input the preset material parameters, boundary conditions, different static loads and point loads into the finite element analysis software to perform dynamic and static superposition calculations on the sluice chamber structure; Among them, the material parameters mainly include the density, elastic modulus and Poisson's ratio of concrete in different areas. The boundary conditions are three constraints imposed on the bottom of the gate slab. The different static loads include deadweight load, water load, sediment load, uplift pressure, earth pressure, wave pressure, wind load, highway bridge load and hoist load. In addition, the elastic modulus of concrete adopts the equivalent elastic modulus. In the linear elastic stage, the steel bar and concrete are deformed in coordination, and the specific effective principles are as follows: In the formula, E d E is the equivalent elastic modulus of reinforced concrete material; c is the elastic modulus of plain concrete; E s is the elastic modulus of the steel bar; A s is the cross-sectional area of ​​the steel bar; A is the cross-sectional area of ​​the concrete.

6. The method for predicting seismic safety of a sluice structure based on the finite element internal force method according to claim 1 is characterized in that: In step (6), the specific process of using the finite element internal force method to transform the internal force is as follows: Any structure can be divided into two substructures I and II with a cross section p, and the equation is satisfied after applying corresponding constraint boundary conditions [K]{δ}={F} (13) Where [K] is the overall stiffness matrix of the structure, {δ} is the structural displacement vector, and {F} is the load vector on the structure; Select any cross section on these two substructures and apply a set of equal and opposite constrained internal forces to them, then we can get the deformation equation of equation [K]{δ}={F}: Where c and i are the nodes on section p and non-section p respectively; k ii k is the nodal force generated at node i when the node i undergoes unit displacement and the displacements of other nodes are 0; ic is the nodal force generated at node c when the node i undergoes unit displacement and the displacements of other nodes are 0; k ci is the nodal force generated at node i when node c undergoes unit displacement and the displacements of other nodes are 0; k cc The nodal force generated at node c when the node c undergoes unit displacement and the displacements of other nodes are 0; F i With F c are the node load vectors on non-p and p sections respectively; {f c } I 、{f c } II They represent the constraint internal forces between the two substructures I and II on the p surface. According to the force balance equation, {f c } I +{f c } II =0 I ; Substituting the node displacement obtained from formula (13) into formula (14) yields: {f} c } I =-{f c } II ={F c } I -[k ci ] I {d} i } I -[k cc ] I {d} c } I (15) In formula (15), the internal force f of section p is c It can be solved cyclically based on the unit nodes containing p sections in the I or II substructure; The steps of solving the internal forces of the structure using the force method in structural mechanics are as follows: d ij X+D p =0(16) In the formula, represents the structural flexibility matrix; Represents the unknown force array, Represents an array of free terms.

7. The method for predicting seismic safety of a sluice structure based on the finite element internal force method according to claim 1 is characterized in that: In step (7), the specific process of the bearing capacity of the gate chamber structure under the ultimate bearing capacity state, including the bending moment, shear force and axial force, is as follows: KN≤f c bx+f′ y A′ s -σ s A s (18) Where: M is the design value of the bending moment; K is the bearing capacity safety factor; f y is the design value of tensile reinforcement strength; f′ y is the design value of compressive reinforcement strength; f c is the design value of concrete axial compressive strength; b is the calculated width of concrete compression zone; x is the calculated height of concrete compression zone; h0 is the effective height of the section; A s , A' s is the cross-sectional area of ​​longitudinal tensile and compressive reinforcement; a' s is the distance from the combined force point of the compressive reinforcement to the compressed edge; N is the design value of the axial pressure; e is the distance from the axial pressure action point to the combined force point of the longitudinal reinforcement on the tensile side or the side with less compression; e0 is the eccentricity of the axial pressure to the center of gravity of the section; η is the eccentricity increase coefficient of the axial pressure considering the influence of the second-order effect of the eccentrically compressed member; σ s is the stress of the longitudinal reinforcement on the tensile side or the side with less compression; a s is the distance from the longitudinal reinforcement resultant point on the tensile side or the side with less compression to the edge of the section; V is the design value of the section shear force; V c is the shear bearing capacity of concrete; V sv is the shear bearing capacity of stirrups; V sb A is the shear bearing capacity of the bent steel bar; sv A is the total cross-sectional area of ​​each limb of the stirrups configured in the same section; sb is the cross-sectional area of ​​the bent steel bar in the same bending plane; α S is the angle between the bent steel bar on the inclined section and the longitudinal axis of the member; s is the spacing of stirrups along the length of the member; f yv f is the design value of stirrup tensile strength; t It is the design value of concrete axial tensile strength.

8. The method for predicting seismic safety of a sluice structure based on the finite element internal force method according to claim 1 is characterized in that: If the bending moment, shear force and axial force at different parts of the gate chamber structure under the earthquake action calculated by the finite element internal force method in the step (7) are less than the bending moment, shear force and axial force bearing capacity at different parts of the gate chamber structure under the ultimate bearing capacity state, then the seismic safety requirements are met; otherwise, the seismic safety requirements are not met.

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