A method for constructing a mathematical model of vehicle-reinforced concrete bridge pier impact force

Abstract

A method for constructing a mathematical model of vehicle-reinforced concrete bridge pier impact force comprises: (1) carrying out a drop hammer impact test on a compressed reinforced concrete pier column to obtain a time history test curve of the strain rate of the pier column under the action of the drop hammer impact; (2) establishing a finite element model of the drop hammer impact on the reinforced concrete pier column taking into account the strain rate effect; (3) correcting the strain rate threshold in the mathematical model of the concrete strain rate effect; (4) calculating the impact kinetic energy, strain rate and impact force under different impact speeds and impact masses; (5) defining a mathematical expression between the impact kinetic energy, strain rate and impact force, determining the constant coefficient in the mathematical expression through regression analysis, and establishing a mathematical model of vehicle-reinforced concrete bridge pier impact force. The present invention constructs a mathematical model of vehicle-reinforced concrete bridge pier impact force taking into account the impact kinetic energy and strain rate, which truly reflects the impact force response of the concrete bridge pier under vehicle collision and can provide a reference for the anti-collision design of cross-line bridge pier columns.

Description

Technical Field

[0001] The invention relates to a method for constructing a mathematical model of vehicle-reinforced concrete bridge pier impact force, and belongs to the technical field of collision dynamics research. Background Art

[0002] In recent years, with the rapid development of my country's economy, the demand for transportation has increased, and the large-scale construction of cross-line structures such as road overpasses has become an important way to alleviate ground traffic pressure. However, due to factors such as vehicle overloading, imperfect road administration, and driving errors, accidents involving vehicles hitting bridge piers have occurred repeatedly. According to incomplete statistics, from 2015 to 2021 alone, there were an average of more than 100 vehicle collision accidents with bridge piers in Beijing each year. About 53% of the bridge piers in the city have been hit by vehicles, of which nearly 20% have been damaged, causing huge economic losses and social impacts. Impact force is an important parameter in the anti-collision design of bridge piers. Reasonable evaluation and calculation of impact force is an important prerequisite for the safe design of bridge piers.

[0003] Vehicle-reinforced concrete bridge pier collision is a very complex dynamic problem. It is a nonlinear dynamic response process under the action of huge impact load in a very short time. At present, there is no unified calculation formula in the engineering community for the specific calculation of vehicle impact load. my country's "Highway Bridge and Culvert Design Code" stipulates that the design impact force of a vehicle hitting a bridge pier in the direction of the lane is 1000kN, and the design impact force in the direction perpendicular to the lane is 500kN, and the action position is 1.2m above the road surface. Although the code has made quantitative provisions for the design impact force, it does not consider the influence of vehicle impact speed and impact mass on the impact force. In this regard, many scholars have proposed to use the impact kinetic energy as an indicator to explore the influence of impact speed and impact mass on the impact force. For example, the Journal of East China Jiaotong University published "Analysis of Vehicle-Bridge Pier Collision Response Based on HJC Model"; However, under different impact speed and mass combinations, even if the impact kinetic energy is the same, the actual impact force may be significantly different. This is because there is an obvious strain rate effect in the process of vehicle impacting bridge piers, and the current research on vehicle-reinforced concrete bridge pier collision ignores the influence of strain rate effect on impact force. Therefore, it is particularly important to construct a mathematical model that can truly reflect the impact force between vehicles and reinforced concrete bridge piers. Summary of the invention

[0004] The purpose of the present invention is to solve the problem that the existing mathematical model of vehicle-reinforced concrete bridge pier impact force ignores the influence of strain rate on impact force, and to propose a method for constructing a mathematical model of vehicle-reinforced concrete bridge pier impact force.

[0005] The technical solution implemented by the present invention is as follows: a method for constructing a mathematical model of vehicle-reinforced concrete bridge pier impact force, comprising the following steps:

[0006] S1. Carry out drop-hammer impact test on reinforced concrete pier columns under compression and obtain the strain rate time history test curve of the pier columns under drop-hammer impact.

[0007] S2. Combined with the mathematical model of concrete and steel strain rate effect, a finite element model of reinforced concrete pier column drop hammer impact is established.

[0008] S3. Calculate the time history curve of the drop weight strain rate of the compressed reinforced concrete pier column, and modify the strain rate threshold in the mathematical model of concrete strain rate effect by comparing with the test curve.

[0009] S4. Based on the modified mathematical model of concrete strain rate effect, LS-DYNA software was used to construct a finite element model of vehicle-reinforced concrete pier collision, and the impact kinetic energy, strain rate and impact force under different impact speeds and impact masses were calculated.

[0010] S5. Define the mathematical expressions between impact kinetic energy, strain rate and impact force. Combine the calculated impact kinetic energy, strain rate and corresponding impact force under different impact conditions, determine the constant coefficients in the mathematical expressions through regression analysis, and establish a mathematical model of vehicle-reinforced concrete bridge pier impact force.

[0011] The mathematical model combining concrete and steel bar strain rate effects includes concrete strain rate effect and steel bar strain rate effect;

[0012] The mathematical expression of concrete strain rate effect is as follows:

[0013]

[0014] In the formula, f cd and f cs are the dynamic and static compressive strength of concrete respectively; is the strain rate; is the concrete strain rate threshold, with an initial value of 30s -1 .

[0015] The mathematical expression of the steel bar strain rate effect is as follows:

[0016]

[0017] In the formula, σ d and σ s are the stresses of the steel bars under dynamic and static forces, respectively.

[0018] The strain rate threshold steps in the modified concrete strain rate effect mathematical model are as follows:

[0019] (1) Calculation of strain rate threshold correction coefficient

[0020] in represents the calculated strain rate peak value, Indicates the test strain rate peak value: When α≥0, the modified strain rate threshold is If α<0, the modified strain rate threshold is

[0021] (2) Based on the modified concrete strain rate threshold, the impact finite element model is used to recalculate the strain rate time history curve of reinforced concrete pier columns under drop hammer impact;

[0022] (3) Calculation of strain rate peak difference coefficient

[0023] If |β|≤0.05, it indicates that the modified concrete strain rate threshold meets the requirement. Otherwise, recalculate α and repeat step (1) until the requirement is met.

[0024] The steps of calculating the impact kinetic energy, strain rate and impact force under different impact speeds and impact masses are as follows:

[0025] (1) Applying the modified concrete strain rate effect model, combined with the steel and concrete unit types, damage model and steel strain rate effect model, a reinforced concrete pier model considering the strain rate effect is established;

[0026] (2) Shell elements are used to simulate the front, wheels and cabin of the car; solid elements are used to simulate the engine and the mass block in the cabin; a vehicle finite element model is established by defining the surface-to-surface contact between the various components of the vehicle model, in which the impact speed of the vehicle is controlled by changing the horizontal speed of the vehicle and the wheel speed, and the impact mass is controlled by changing the density of the mass block in the cabin;

[0027] (3) The contact parts between the front of the vehicle, the carriage and the pier model, as well as the contact parts between the wheels and the ground are all set to surface contact; the upper structure of the pier column is simplified to an axial load applied to the top of the pier, and the boundary condition of the pier bottom foundation is set to a rigid constraint of consolidation, and a finite element model of vehicle-reinforced concrete pier contact is established;

[0028] (4) According to the possible vehicle impact mass and impact speed in an actual collision accident, different working condition combinations under the action of different impact speeds v and impact masses m are proposed to obtain the corresponding impact kinetic energy E = mv 2 / 2;

[0029] (5) Based on the strain rate cloud map within the vehicle impact height range, extract the maximum value as the strain rate during the collision process

[0030] (6) According to the impact force time history curve under the impact condition, the corresponding peak impact force is extracted as the impact force P of the reinforced concrete pier.

[0031] The steps for establishing the mathematical model of vehicle-reinforced concrete bridge pier impact force are as follows:

[0032] (1) Define the mathematical expressions between impact kinetic energy, strain rate and impact force:

[0033]

[0034] Where E is the impact kinetic energy, is the strain rate, is the impact force, a, b, c, d, e, f are constant coefficients;

[0035] (2) for the impact kinetic energy, strain rate and corresponding impact force under different impact conditions obtained in step S4, a least squares method nonlinear numerical regression analysis is performed to obtain the values ​​of constant coefficients such as a, b, c, d, e and f in the impact force calculation formula;

[0036] (3) Through the error parameters SSE, RMSE and R 2 To judge the fitting effect of the mathematical model of vehicle-reinforced concrete bridge pier impact force, where:

[0037]

[0038]

[0039]

[0040] Where P i is the original value calculated in step S4; is the predicted value based on the mathematical model; w i is the weight value; is the average value of the original data. The RMSE and SSE values ​​are required to be less than 0.1. 2 Greater than 0.9.

[0041] The beneficial effect of the present invention lies in that, on the basis of taking into account the contribution of the impact kinetic energy to the vehicle-reinforced concrete pier impact force, the present invention further incorporates the influence of the pier strain rate effect on the impact force, and constructs a vehicle-reinforced concrete pier impact force mathematical model that takes into account the impact kinetic energy and strain rate, thereby truly reflecting the impact force response of the concrete pier under the vehicle collision, and providing a reference for the anti-collision design of the cross-line bridge pier column. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 A flow chart for constructing a mathematical model of vehicle-reinforced concrete bridge pier impact force according to the present invention;

[0043] Figure 2aIt is the test curve of the drop weight impact strain rate time history curve;

[0044] Figure 2b It is the calculation curve of the drop weight impact strain rate time history curve;

[0045] Figure 3 It is a vehicle-reinforced concrete bridge pier collision model;

[0046] Figure 4 It is a comparison diagram between the mathematical model of the present invention and the numerical simulation. DETAILED DESCRIPTION

[0047] The present invention is further described below in conjunction with the accompanying drawings and specific implementation methods.

[0048] like Figure 1 As shown, in this embodiment, a method for constructing a mathematical model of a vehicle-reinforced concrete bridge pier impact force includes the following steps:

[0049] S1: The reinforced concrete pier is 4000 mm long, with a cross-sectional size of 300 mm × 300 mm. The material is C30 concrete, and the corresponding uniaxial compressive strength is 34.9 MPa.

[0050] The longitudinal reinforcement of the specimen is 4 HRB400 steel bars with a diameter of 25mm, the stirrups are HRB400 steel bars with a diameter of 12mm and a spacing of 150mm, and the thickness of the concrete cover is 35mm.

[0051] According to the reinforcement structure diagram of the specimen pier, the steel bars are tied, the grouting sleeve is inserted into the steel bars and fixed, the formwork is supported and poured, and after pouring, it is cured at room temperature for 14 days to form. Before the test, the impact contact surface of the prefabricated reinforced concrete pier is roughened and coated with an interface agent, and two longitudinal strain gauges are symmetrically arranged at the bottom of the section corresponding to the drop hammer impact point. The test uses a fixed drop hammer weight and changes the drop hammer impact height to change the drop hammer impact speed. The axial load of 19.49kN is applied to the reinforced concrete pier through the hydraulic jack compression spring. The strain time history curve of the pier is recorded using the longitudinal strain gauge at the bottom of the section at the drop hammer impact point. The strain rate time history test curve is obtained by calculating the strain change slope in each time step in the strain time history curve.

[0052] S2: Use ANSYS / LS-DYNA to establish the finite element models of the drop hammer, concrete and steel bars. Then define the contact of each part to ensure that the meshes of each part will not penetrate each other. The impact between the concrete and the drop hammer is set to surface contact. Use node constraints to replace the support constraints in the actual test. Do not consider the elastic deformation of the support end constraints. By loading the nodes at the sliding end of the reinforced concrete pier to simulate the axial load, the initial velocity of the drop hammer impact is proposed, and the influence of the gravity field on the calculation results is considered. Finally, define the calculation hourglass to avoid zero energy in the model.

[0053] Each part is divided into hexahedral meshes, and the entire finite element model contains 2645 nodes and 2399 solid units. The concrete material uses the K&C material damage model, and the corresponding state equation parameter values ​​are shown in Table 1; the damage behavior of the steel bar material uses the MPK kinematic strengthening damage model; the strain rate threshold in the concrete strain rate effect model is 30s -1 .

[0054] Table 1. K&C state equation parameters

[0055] λ η <![CDATA[ε v ]]> P / MPa K / MPa 0.00002 0.98 0.02896 240 6568

[0056] In the table, λ is the equivalent plastic strain; η is the damage parameter; ε v is the volume strain; P is the hydrostatic pressure; K is the unloading bulk modulus.

[0057] S3: The strain rate time history curves of the test and numerical simulation are shown in Figure 2a and Figure 2b As shown in Table 2, by comparing the strain rate peak values ​​in the strain rate time history calculation curve and the test curve, the optimal value search is carried out by combining the dichotomy method. The strain rate threshold correction in the mathematical model of concrete strain rate effect is shown in Table 2.

[0058] Table 2 Strain rate threshold correction calculation table

[0059] Calculation times <![CDATA[Test value / s -1 > <![CDATA[Calculated value / s -1 > Coefficient of variation β Whether the requirements are met Correction factor <![CDATA[Correction threshold / s -1 > 1 54.32 40.68 0.25 no 1.13 33.9 2 54.32 45.97 0.15 no 1.08 36.6 3 54.32 49.65 0.09 no 1.05 38.4 4 54.32 52.13 0.04 yes / /

[0060] Therefore, the strain rate threshold correction coefficient is taken as 1.05, and the corrected strain rate threshold is taken as 38.4s -1 .

[0061] S4: A reinforced concrete pier with a diameter of 0.8 m and a concrete strength of C30, which is commonly used in cross-line bridge piers, was selected for collision numerical simulation. The diameters of the longitudinal reinforcement and stirrups were 13 mm and 11 mm respectively, and both were made of HRB400 steel bars.

[0062] The finite element model of the bridge pier considers the bond slip between the steel bar and the concrete material for separate modeling (steel bar and concrete are modeled separately). The established vehicle finite element model is imported to control the collision contact parameters between the two. The front of the vehicle, the carriage and the bridge pier adopt surface-to-surface contact, and the friction coefficient is 0.2. The established overall collision model is as follows: Figure 3 shown.

[0063] The vehicle speed in my country's road traffic is generally above 20km / h and below 120km / h, so 20km / h is set as the lower limit of the simulated impact speed, and on this basis, 20km / h is gradually increased to the upper limit of the impact speed of 120km / h, for a total of 6 groups. 8t is set as the lower limit of the impact mass, and 9t is gradually increased to the upper limit of the impact mass of 53t, for a total of 6 groups. A total of 36 calculation conditions are used for vehicle-reinforced concrete bridge pier collision calculations, as shown in Table 3.

[0064] Table 3 Calculation conditions of vehicle-reinforced concrete bridge pier collision

[0065] Condition No. 1 2 3 4 5 6 Impact mass (t) 8 8 8 8 8 8 Impact speed (km / h) 20 40 60 80 100 120 Condition No. 7 8 9 10 11 12 Impact mass (t) 17 17 17 17 17 17 Impact speed (km / h) 20 40 60 80 100 120 Condition No. 13 14 15 16 17 18 Impact mass (t) 26 26 26 26 26 26 Impact speed (km / h) 20 40 60 80 100 120 Condition No. 19 20 21 22 23 24 Impact mass (t) 35 35 35 35 35 35 Impact speed (km / h) 20 40 60 80 100 120 Condition No. 25 26 27 28 29 30 Impact mass (t) 44 44 44 44 44 44 Impact speed (km / h) 20 40 60 80 100 120 Condition No. 31 32 33 34 35 36 Impact mass (t) 53 53 53 53 53 53 Impact speed (km / h) 20 40 60 80 100 120

[0066] Using the established vehicle-reinforced concrete bridge pier collision finite element model, the impact kinetic energy, strain rate and impact force are calculated as shown in Table 4.

[0067] Table 4 List of impact kinetic energy, strain rate and impact force

[0068]

[0069]

[0070] S5: Numerical regression analysis is used to perform nonlinear curve fitting on the data in Table 4, and the mathematical model of impact force is obtained as follows:

[0071]

[0072] Comparison of mathematical model and numerical simulation impact force calculation results Figure 4 shown.

[0073] Among them, SSE = 0.00007538, RMSE = 0.0864, ​​R 2 =0.92, which meets the requirements, indicating that the fitting effect of the impact force mathematical model is relatively ideal.

Claims

1. A method for constructing a mathematical model of vehicle-reinforced concrete bridge pier impact force, characterized in that: The method comprises the following steps: S1. Carry out a drop hammer impact test on a reinforced concrete pier column under compression, and obtain a time history test curve of the strain rate of the pier column under the drop hammer impact; S2. Combine the mathematical models of concrete and steel strain rate effects to establish a finite element model of reinforced concrete pier column drop hammer impact; S3. Calculate the time history curve of the drop weight strain rate of the compressed reinforced concrete pier column, and modify the strain rate threshold in the mathematical model of concrete strain rate effect by comparing with the test curve; S4. Based on the modified concrete strain rate effect mathematical model, a finite element model of vehicle and reinforced concrete bridge pier contact is established to calculate the impact kinetic energy, strain rate and impact force under different impact speeds and impact masses; S5. Define mathematical expressions between impact kinetic energy, strain rate and impact force, combine the calculated impact kinetic energy, strain rate and corresponding impact force under different impact conditions, determine the constant coefficients in the mathematical expressions through regression analysis, and establish a mathematical model of vehicle-reinforced concrete bridge pier impact force; The steps for establishing the mathematical model of vehicle-reinforced concrete bridge pier impact force are as follows: (1) Define the mathematical expressions between impact kinetic energy, strain rate and impact force: Where E is the impact kinetic energy, is the strain rate, is the impact force, a, b, c, d, e, f are constant coefficients; (2) for the impact kinetic energy, strain rate and corresponding impact force under different impact conditions obtained in step S4, a least squares method nonlinear numerical regression analysis is performed to obtain the values ​​of constant coefficients such as a, b, c, d, e and f in the impact force calculation formula; (3) Through the error parameters SSE, RMSE and R 2 To judge the fitting effect of the mathematical model of vehicle-reinforced concrete bridge pier impact force, where: Where P i is the original value calculated in step S4; is the predicted value based on the mathematical model; w i is the weight value; is the average value of the original data. The RMSE and SSE values ​​are required to be less than 0.

1. 2 Greater than 0.

9.

2. The method for constructing a mathematical model of vehicle-reinforced concrete bridge pier impact force according to claim 1, characterized in that: The mathematical model combining concrete and steel bar strain rate effects includes concrete strain rate effect and steel bar strain rate effect; The mathematical expression of concrete strain rate effect is as follows: In the formula, f cd and f cs are the dynamic and static compressive strength of concrete respectively; is the strain rate; is the concrete strain rate threshold, with an initial value of 30s -1 ; The mathematical expression of the steel bar strain rate effect is as follows: In the formula, σ d and σ s are the stresses of the steel bars under dynamic and static forces, respectively.

3. The method for constructing a mathematical model of vehicle-reinforced concrete bridge pier impact force according to claim 1, characterized in that: The strain rate threshold steps in the modified concrete strain rate effect mathematical model are as follows: (1) Calculation of strain rate threshold correction coefficient in represents the calculated strain rate peak value, Indicates the test strain rate peak value: When α≥0, the modified strain rate threshold is If α<0, the modified strain rate threshold is (2) Based on the modified concrete strain rate threshold, the impact finite element model is used to recalculate the strain rate time history curve of reinforced concrete pier columns under drop hammer impact; (3) Calculation of strain rate peak difference coefficient If |β|≤0.05, it indicates that the modified concrete strain rate threshold meets the requirement. Otherwise, recalculate α and repeat step (1) until the requirement is met.

4. The method for constructing a mathematical model of vehicle-reinforced concrete bridge pier impact force according to claim 1, characterized in that: The steps of calculating the impact kinetic energy, strain rate and impact force under different impact speeds and impact masses are as follows: (1) The modified concrete strain rate effect model is applied, combined with the steel and concrete unit types, damage model and steel strain rate effect model, to construct a reinforced concrete pier model considering the strain rate effect. On this basis, a finite element model of vehicle-reinforced concrete pier contact is established. (2) According to the possible vehicle impact mass and impact speed in an actual collision accident, different working condition combinations under the action of different impact speeds v and impact masses m are proposed to obtain the corresponding impact kinetic energy E = mv 2 / 2; (3) Based on the strain rate cloud map within the vehicle impact height range, the maximum value is extracted as the strain rate during the collision process. (4) According to the impact force time history curve under the impact condition, the corresponding peak impact force and the average of the impact force platform value are extracted as the impact force P of the reinforced concrete pier.

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