A method for assessing damage to concrete bridge piers after vehicle impact

Abstract

A method for assessing damage to concrete bridge piers after vehicle impact, comprising: (1) calculating the impact kinetic energy under different impact speed and impact mass combinations; E , strain rate #imgabs0# and section damage factor d k ; (2) Establishing cross-sectional damage factor d k and impact kinetic energy E , the mathematical model between strain rate #imgabs1#; (3) obtain the strain rate #imgabs2#-impact kinetic energy E Damage state evaluation threshold expression; (4) Establish strain rate #imgabs3#-impact kinetic energy E The damage status assessment cloud map determines the damage status of concrete piers. This method not only considers the contribution of vehicle impact kinetic energy to concrete pier damage, but also takes into account the influence of strain rate effects on concrete pier impact damage. This method establishes a method for assessing the degree of damage to concrete piers after vehicle impact. This method truly reflects the degree of damage to concrete piers after vehicle impact, providing a reference for the crash-resistant design of concrete piers and the rapid and accurate assessment of pier structures after vehicle impact.

Description

Technical Field

[0001] The invention relates to a method for assessing damage to a concrete bridge pier after a vehicle impact, and belongs to the technical field of bridge engineering protection. Background Art

[0002] Current research indicates that the extent of damage to concrete bridge piers after a vehicle impact is closely related to the kinetic energy of the impact, which is a combination of the vehicle's impact velocity and impact mass. Consequently, domestic and international researchers have proposed different damage assessment methods for concrete piers after vehicle impact, using vehicle impact force, pier deformation, residual bearing capacity, and dynamic shear force as damage assessment indicators, respectively, based on impact velocity and impact mass. However, the actual damage state of concrete piers after impact demonstrates that even with equal impact kinetic energy, the actual extent of damage can vary significantly. This is due to the significant strain rate effect on concrete piers during a vehicle impact, and current damage assessment methods ignore the impact of this strain rate effect on pier damage. Therefore, there is an important practical need to establish a method for assessing the extent of damage to concrete piers after vehicle impact, by further accounting for the material strain rate effect, in addition to the impact kinetic energy. Summary of the Invention

[0003] The purpose of this invention is to propose a method for assessing the damage of concrete piers after vehicle impact, in view of the fact that the existing different concrete pier vehicle impact damage assessment methods ignore the influence of strain rate effect on pier damage, resulting in inaccurate assessment.

[0004] The technical solution for implementing the present invention is as follows: a method for assessing damage to a concrete bridge pier after a vehicle impact, comprising the following steps:

[0005] S1, carry out drop hammer impact test on concrete pier column and obtain the strain rate time history test curve of pier column.

[0006] S2, based on LS-DYNA software, combined with the mathematical model of concrete and steel strain rate effect, established a finite element model of concrete pier column drop hammer impact.

[0007] S3, using the established impact finite element model, calculate the time history curve of the drop hammer strain rate of the concrete pier column, and modify the strain rate threshold in the mathematical model of the concrete strain rate effect by comparing it with the experimental curve.

[0008] S4, based on the modified concrete strain rate effect mathematical model, establish the vehicle and concrete bridge pier contact finite element model, calculate the impact kinetic energy E, strain rate under different impact speed and impact mass combination conditions and cross-sectional damage factor d k .

[0009] S5, establish the cross-sectional damage factor d by numerical regression k and impact kinetic energy E, strain rate Mathematical models between them.

[0010] S6, according to the damage state limit of the pier, calculate the section damage factor thresholds p and q to obtain the strain rate -The impact kinetic energy E damage state judgment threshold expression.

[0011] S7, establish strain rate - Impact kinetic energy E damage state assessment cloud map, based on the actual impact kinetic energy E and strain rate The damage condition of concrete bridge piers is determined by location in the damage status assessment cloud map.

[0012] The mathematical model of concrete and steel bar strain rate effect includes concrete strain rate effect and steel bar strain rate effect;

[0013] The mathematical expression of concrete strain rate effect is as follows:

[0014]

[0015] Where, 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 ;

[0016] The mathematical expression of the steel bar strain rate effect is as follows:

[0017]

[0018] Where, σ d and σ s are the stresses of steel bars under dynamic and static forces, respectively.

[0019] The strain rate threshold steps in the mathematical model for modifying the concrete strain rate effect are as follows:

[0020] (1) Calculation of strain rate threshold correction coefficient

[0021] in represents the calculated strain rate peak, 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

[0022] (2) Based on the revised concrete strain rate threshold, the impact finite element model is applied to recalculate the strain rate time history curve of the concrete pier column under the drop hammer impact;

[0023] (3) Calculation of strain rate peak difference coefficient

[0024] 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.

[0025] The cross-sectional damage factor d k Calculate as follows:

[0026]

[0027] Where n is the number of cross-sectional elements, d is the element damage factor, when d = 0, it means the element is in an undamaged state, and when d = 1, it means the element is in a completely damaged state.

[0028] The cross-sectional damage factor d k and impact kinetic energy E, strain rate The mathematical model expression is as follows:

[0029]

[0030] Where a, b, and c are constant coefficients, and their values ​​are determined through numerical regression analysis.

[0031] The strain rate -The steps for determining the expression of the impact kinetic energy E-damage state judgment threshold are as follows:

[0032] (1) Calculate the cross-sectional damage factor threshold p when the bottom of a concrete bridge pier exhibits a small amount of deformation but no cracking after a vehicle impact;

[0033] (2) Calculate the cross-sectional damage factor threshold q when the impact area and the pier bottom are slightly deformed after a vehicle impact on a concrete bridge pier, and some concrete cracks and spalls;

[0034] (3) When the cross-sectional damage factor d k When p and q are respectively, substitute the cross-sectional damage factor d k and impact kinetic energy E, strain rate The mathematical model between them gives the strain rate -The expression of the damage state judgment threshold of impact kinetic energy E is as follows:

[0035]

[0036] The strain rate -The steps for establishing the impact kinetic energy E damage status assessment cloud map are as follows:

[0037] (1) With the impact kinetic energy E as the horizontal axis, the strain rate is the vertical axis, according to the strain rate - The damage state judgment threshold expression of impact kinetic energy E, and the cross-sectional damage factor d k is the damage state judgment threshold curve corresponding to p and q;

[0038] (2) d k = p, the damage state judgment threshold curve and the interval enclosed by the horizontal and vertical axes are defined as the mild damage interval, and the cross-sectional damage factor d k The interval enclosed by the two corresponding damage state judgment threshold curves when p and q are defined as the moderate damage interval; the remaining intervals are defined as the severe damage interval, and the strain rate is obtained. - Impact kinetic energy E damage status assessment cloud map.

[0039] The beneficial effect of the present invention is that, compared with the existing method for assessing the damage of concrete piers after a vehicle impact, the present invention, on the basis of considering the contribution of the kinetic energy of the vehicle impact to the damage of the concrete pier, further takes into account the influence of the strain rate effect on the damage of the concrete pier after a vehicle impact, and establishes a method for assessing the degree of damage to the concrete pier after a vehicle impact, thereby truly reflecting the degree of damage to the concrete pier after a vehicle impact, and providing a reference for the anti-collision design of the concrete pier and the rapid and accurate assessment of the pier structure after a vehicle impact. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 is a flow chart of the method of the present invention;

[0041] Figure 2 is the damage status judgment threshold curve;

[0042] Figure 3 It is the damage assessment status cloud map. DETAILED DESCRIPTION

[0043] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0044] like Figure 1 As shown, a method for assessing damage to a concrete bridge pier after a vehicle impact comprises the following steps:

[0045] S1: A concrete pier was prepared for a drop-hammer impact test. The pier was 4000 mm long, with a cross-section of 300 mm x 300 mm. The concrete was made of C30 concrete, resulting in a uniaxial compressive strength of 34.9 MPa. The longitudinal reinforcement consisted of four HRB400 steel bars with a diameter of 25 mm, and the stirrups were HRB400 steel bars with a diameter of 12 mm and a spacing of 150 mm. The concrete cover thickness was 35 mm. The reinforcement was tied according to the reinforcement diagram for the pier. The grouting sleeves were inserted into the steel bars and secured. The formwork was then supported and poured. After pouring, the concrete was cured at room temperature for 14 days to form the pier. Before testing, the impact contact surface of the concrete pier was roughened and coated with an interface agent. Two longitudinal strain gauges were symmetrically placed at the bottom of the cross-section corresponding to the drop-hammer impact point. The test used a fixed drop hammer with an impact mass of 270 kg, an impact height of 2 m, and an impact velocity of 6.27 m / s. An axial load of 19.49 kN was applied to the concrete pier column through a hydraulic jack compression spring. The strain time history curve of the pier column was recorded using a longitudinal strain gauge at the bottom of the cross section at the drop hammer impact point. The strain rate time history test curve was obtained by calculating the slope of the strain change in each time step in the strain time history curve.

[0046] In S2, finite element models of the drop weight, concrete pier, and reinforcement were established using ANSYS / LS-DYNA. The contact between the concrete pier and the drop weight was set to surface-to-surface. Lagrange constraints were used to define the contact between the reinforcement and concrete, taking into account the bond-slip effect between the reinforcement and concrete. Node constraints, one hinged at one end and fixed at the other, replaced the support constraints used in actual tests. Elastic deformation of the support-end constraints was not considered. Axial load effects were simulated by applying horizontal loading to the nodes at the sliding end of the concrete pier. All parts of the finite element model were meshed using a hexahedral mesh, totaling 2645 nodes and 2399 elements. The K&C material damage model was applied to the concrete material in the model, and the corresponding equation of state parameters are shown in Table 1.

[0047] Table 1 K&C state equation parameters

[0048] λ η <![CDATA[ε v ]]> P / MPa K / MPa 0.00002 0.98 0.02896 240 6568

[0049] The damage behavior of steel bar material adopts MPK dynamic reinforcement damage model; the strain rate threshold in concrete strain rate effect model is 30s. -1 .

[0050] In the table, λ is the equivalent plastic strain, η is the damage parameter, and ε v is the volume strain, P is the hydrostatic pressure, and K is the unloading bulk modulus.

[0051] S3: Experimental and numerically simulated strain rate time history curves. The strain rate peaks in the calculated strain rate time history curves and the experimental curves are compared. The optimal value search is carried out using the dichotomy method. The strain rate threshold correction in the mathematical model of concrete strain rate effect is shown in Table 2.

[0052] Table 2 Strain rate threshold correction calculation

[0053] 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 / /

[0054] Therefore, the strain rate threshold correction coefficient is taken as 1.05, and the corrected strain rate threshold is taken as 38.4s -1 .

[0055] S4: Concrete piers with a diameter of 0.8m and a concrete strength of C30, commonly used in cross-line bridge piers, were used for collision numerical simulation. The longitudinal reinforcement and stirrups were 13mm and 11mm in diameter, respectively, and HRB400 steel was used. The pier finite element model was modeled separately, taking into account the bond-slip between the steel and concrete materials. The established vehicle finite element model was imported, and the collision contact parameters were controlled. Surface-to-surface contact was assumed between the vehicle head, carriage, and pier, with a friction coefficient of 0.2. A vehicle-concrete pier contact finite element model was established.

[0056] Vehicle speeds on Chinese roads generally range from 20 km / h to 120 km / h. Therefore, 20 km / h was set as the lower limit for the simulated impact velocity. From this limit, the velocity range was gradually increased by 20 km / h to the upper limit of 120 km / h, for a total of six groups. The lower limit for the impact mass was 8 tons, and the upper limit was gradually increased by 9 tons to 53 tons, for a total of six groups. A total of 36 calculation conditions were used for the vehicle-concrete bridge pier collision simulation, as shown in Table 3.

[0057] Table 3 Calculation conditions for vehicle-concrete bridge pier collision

[0058] Working condition number 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 Working condition number 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 Working condition number 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 Working condition number 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 Working condition number 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 Working condition number 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

[0059] The impact kinetic energy, strain rate and damage factor d are calculated using the established vehicle-concrete bridge pier contact finite element model. k As shown in Table 4.

[0060] Table 4 Impact kinetic energy, strain rate and damage factor d k

[0061]

[0062]

[0063] S5: Use numerical regression analysis to perform nonlinear curve fitting on the data in Table 4 to obtain the damage factor d kThe calculation formula between impact kinetic energy and strain rate is as follows:

[0064]

[0065] S6: Using the vehicle-concrete bridge pier contact finite element model established in step S4, the cross-sectional damage factor threshold value p = 0.3 is obtained when the bottom of the concrete bridge pier is slightly deformed but not cracked after the vehicle impact, and the cross-sectional damage factor threshold value q = 0.7 is obtained when the impact area and the bottom of the concrete bridge pier are slightly deformed after the vehicle impact, and some concrete cracks and peels off. Substitute p = 0.3 and q = 0.7 into the calculation formula in step S5 respectively to obtain the strain rate -The expression of the damage state judgment threshold of impact kinetic energy E is as follows:

[0066]

[0067] S7: With the impact kinetic energy E as the horizontal axis, the strain rate is the vertical axis, according to the strain rate established in step S6 - The damage state judgment threshold expression of impact kinetic energy E, and the cross-sectional damage factor d k The corresponding damage state judgment threshold curves when are 0.3 and 0.7 are as follows: Figure 2 shown.

[0068] The damage state judgment threshold curve (d k =0.3) and the interval surrounded by the horizontal and vertical coordinates is defined as the mild damage interval, the interval surrounded by the two damage state judgment threshold curves is defined as the moderate damage interval, and the remaining intervals are defined as the severe damage interval. The strain rate is obtained. - Impact kinetic energy E damage status assessment cloud map, such as Figure 3 shown.

Claims

1. A method for assessing damage to concrete bridge piers after vehicle impact, characterized in that: The method comprises: (1) Calculate the impact kinetic energy E and strain rate under different impact velocity and impact mass combinations and cross-sectional damage factor d k ; (2) Establish the cross-sectional damage factor d through numerical regression k and impact kinetic energy E, strain rate Mathematical models between; (3) According to the damage state limit of the pier, calculate the section damage factor thresholds p and q to obtain the strain rate -The impact kinetic energy E damage state judgment threshold expression; (4) Establishing strain rate - Impact kinetic energy E damage state assessment cloud map, based on the actual impact kinetic energy E and strain rate Determine the damage status of concrete piers by location in the damage status assessment cloud map; The cross-sectional damage factor d k and impact kinetic energy E, strain rate The mathematical model expression is as follows: Where a, b, and c are constant coefficients, and their values ​​are determined by numerical regression analysis; The strain rate -The steps for determining the expression of the impact kinetic energy E-damage state judgment threshold are as follows: (1) Calculate the cross-sectional damage factor threshold p when the bottom of a concrete pier exhibits a small amount of deformation but no cracking after a vehicle impact; (2) Calculate the cross-sectional damage factor threshold q when the impact area and the pier bottom are slightly deformed after a vehicle impact on a concrete bridge pier, and some concrete cracks and spalls; (3) When the cross-sectional damage factor d k When p and q are respectively, substitute the cross-sectional damage factor d k and impact kinetic energy E, strain rate The mathematical model between them gives the strain rate -The expression of the damage state judgment threshold of impact kinetic energy E is as follows: The strain rate -The steps for establishing the impact kinetic energy E damage status assessment cloud map are as follows: (1) With the impact kinetic energy E as the horizontal axis, the strain rate is the vertical axis, according to the strain rate - The damage state judgment threshold expression of impact kinetic energy E, and the cross-sectional damage factor d k is the damage state judgment threshold curve corresponding to p and q; (2) d k = p, the damage state judgment threshold curve and the interval enclosed by the horizontal and vertical axes are defined as the mild damage interval, and the cross-sectional damage factor d k The interval enclosed by the two corresponding damage state judgment threshold curves when p and q are defined as the moderate damage interval; the remaining intervals are defined as the severe damage interval, and the strain rate is obtained. - Impact kinetic energy E damage status assessment cloud map.

2. The method for assessing damage to concrete bridge piers after vehicle impact according to claim 1, characterized in that: The cross-sectional damage factor d k Calculate as follows: Where n is the number of cross-sectional elements, d is the element damage factor, when d = 0, it means the element is in an undamaged state, and when d = 1, it means the element is in a completely damaged state.

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