Keywords

1 Introduction

In recent decades, with the continuous development of highway bridges in China, the traffic mileage of expressway is also increasing. Plate rubber bearing is widely used because of its simple structure, simple processing, manufacturing and installation, simple maintenance and low cost. According to the survey, the terrain of Shanxi Province is complex and the temperature difference between day and night is large. Under the influence of coal transportation, the traffic volume increases suddenly. This makes the bridges in this area overloaded seriously, resulting in the stiffness problems of 95% of the bridge bearings, and the durability of the bearings will be affected.

Chen Yanjiang et al. [1] studied the influence of recycled rubber on the durability of plate rubber bearing from the perspective of material, and came to the conclusion that the amount of recycled rubber added into the branch seat rubber can be determined by detecting the mechanical index of compression shear modulus before and after bearing aging, so as to judge the early failure of bearing; Xu Yue et al. [2] studied the influence of plate rubber bearing stiffness on the stress and deformation of bridge structure through T-beam finite element analysis. It is concluded that the loss of bearing stiffness has little influence on internal force, but has great influence on structural deformation; Huang Yueping [3], studied the influence of uneven rubber layer thickness on the durability of plate rubber bearing, and concluded that uneven rubber layer thickness will lead to the improvement of its mechanical properties, and the processing and testing process should be strictly controlled during the production and inspection of rubber bearing.

The above studies are from the perspective of materials and bridge structure stress. However, in the actual bridge operation, under the influence of environmental factors such as load and climate, the bearing stiffness will be reduced, which will have a great impact on the bearing durability and bridge durability. This paper mainly studies the stiffness damage of bearing, taking a 2 × 40 m T-beam bridge as an example, the damage of the bearing is simulated, and then by changing the bearing stiffness, the stress, stress and offset are analyzed to obtain the impact of the reduction of bearing stiffness on the bearing.

2 Bearing Damage Simulation

There are two very important mechanical indexes of the bearing: compressive elastic modulus and shear elastic modulus, so the design of the bearing is inseparable from these two data. According to the above analysis, the damage of plate rubber bearing can be simplified as the change of shape coefficient and shear modulus of rubber bearing [4].

Support damage simulation can generally be carried out from the following two aspects: a. change the plane size of the support; b. Change the rubber shear modulus in the bearing. In the finite element software, the elastic connection is generally used to simulate the restraint effect of the bearing. Since the degrees of freedom in six directions

SDx, SDy, SDz, SRx, SRy, SRz, in the elastic connection are determined according to the plane size and shear stiffness g of the rubber bearing, the damage degree of the bearing can be effectively simulated by adjusting the corresponding restraint stiffness [5,6,7,8,9,10,11,12,13].

The stiffness calculation formula of plate rubber bearing is:

Stiffness in x-axis direction of element local coordinate system: SDx = EA/L;

Stiffness of element local coordinate system in Y, Z axis direction: SDy = SDz = GA/L; Rotational stiffness in x-axis direction of element local coordinate system: SRx = GIp/L; Rotational stiffness of element local coordinate system in Y-axis direction: SRy = EIy/L; Rotational stiffness of element local coordinate system in Y-axis direction: SRz = EIz/L.

3 Model Building

The supporting bridge is a river crossing bridge. The main beam adopts C50 concrete, and its superstructure is fabricated prestressed concrete T-beam. The bearing is teflon plate rubber bearing, its differential settlement is Δ = 5 mm and the specification of the side fulcrum bearing is GJZF4400 × 400 × 85 mm, and the specification of the middle fulcrum support is GJZ F4550 × 550 × 130 mm. The bridge is located in the environment with large temperature difference between day and night. Rigid connection between main beam and pier; In order to comprehensively analyze the bearing stress, under the basic load combination, simulate the displacement and stress of the bearing under the combined overall temperature rise of 30 °C and overall temperature drop of 30 °C and concrete shrinkage and creep. The bridge model and model bearing reaction are shown in Figs. 1 and 2.

Fig. 1.
figure 1

Depends on the 2 × 40 m finite element model of the bridge

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Fig. 2.
figure 2

Reaction value of rear support of bidirectional movable support of the model

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4 Bearing Durability Analysis

4.1 Stress and Deformation Analysis

In order to better analyze the impact of stiffness reduction of two-way movable bearing, this paper takes longitudinal bearing, transverse bearing and two-way movable bearing for comparison, and takes a point for each type of bearing for analysis. In the environment with large temperature difference, the thermal expansion and cold contraction of concrete beam and the shrinkage and creep of concrete have a great impact on the bearing. Therefore, considering the shrinkage and creep of 10 years and the temperature difference of 30°, the stress and offset of the bearing are analyzed. The stress and offset of various bearings under different working conditions are shown in the Tables 1, 2and3 below.

Table 1. Forces and offsets of longitudinal movable supports under different working conditions
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Table 2. Forces and offsets of lateral movable supports under different working conditions
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Table 3. Forces and offsets of bidirectional movable supports under different working conditions
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It can be seen from the above table that the longitudinal displacement of the longitudinal movable bearing is large, and the temperature has a great impact on the longitudinal stress and displacement of the bearing. When the temperature rises by 30 °C, the longitudinal displacement of the bearing changes by 13.4 mm; When the temperature drops by 30 °C, the longitudinal displacement of the support changes by 16.58 mm.

The vertical displacement of the lateral movable bearing is large, but the temperature has a great influence on the lateral displacement. When the temperature rises to 30 °C, the lateral displacement of the bearing changes by 1.61 mm; When the temperature drops by 30 °C, the lateral displacement of the support changes by 1.64 mm.

The support reaction force of two-way movable bearing is small, the vertical displacement is small, and the longitudinal and transverse displacement is large. Temperature change has great influence on longitudinal and transverse displacement. The variation amplitude of longitudinal displacement is similar to that of longitudinal movable support, and the variation amplitude of transverse displacement is similar to that of transverse movable support.

According to the specification, for the support GJZF4400 × 400 × 85 mm, the limit value of two-way movable bearing along the bridge direction is 90 mm, the limit value of transverse bridge direction is 40 mm, the limit value of one-way movable bearing along the bridge direction is 90 mm, and the limit value of transverse bridge direction is 3 mm; For the support GJZF4550 × 550 × 130 mm, the limit value of unidirectional movable bearing along the bridge is 130 mm, and the limit value of transverse bridge is 3 mm. According to the results of the above analysis, the maximum longitudinal displacement of the support is 18% of the longitudinal limit and the maximum transverse displacement of the support is 55% of the transverse limit. Although the displacement meets the requirements of the specification, the lateral offset of the support is obviously larger than the longitudinal offset.

According to the above analysis results, the bearing reaction value is less than the maximum bearing capacity of the bearing, and there is nearly 30% surplus, which meets the requirements of the specification. However, with the passage of time, the bearing disease will reduce the rubber stiffness of the bearing, and the surplus in the design may be offset in the operation process, making the bearing reaction greater than the design value, resulting in the failure of the bearing.

4.2 Bearing Stiffness Damage Analysis

The above analysis of the force and deflection of the support under three different conditions shows that the force of the support has a certain margin in the design. However, during the operation of the bridge, the stiffness of the support will continue to weaken, causing the surplus to be gradually offset, which will have a great impact on the durability of the support. Next, for the support of the bridge, under three different conditions, the force and displacement of the support are analyzed under the conditions of constant stiffness of the support and reduction of 20%, 40%, and 60%. Because the force and deformation changes of the two-way movable support under different working conditions are relatively large, this article takes the two-way movable support as an example to analyze the influence of the change of the stiffness of the support on the force and deformation of the support. The 10-year shrinkage and creep of the concrete, the combined temperature rise of 30 °C, and the combined temperature drop of 30 °C support offset and force are shown in Figs. 3, 4 and 5.

Fig. 3.
figure 3

10-year shrinkage and creep of concrete

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Fig. 4.
figure 4

Temperature rising 30 °C

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It can be seen in Fig. 3 that under the condition of shrinkage and creep of the concrete 10, the value of the support in the F(x) and F(y) directions is very small, which can be ignored and unchanged, and the support is in these three directions. The force changes are very small. However, the offset changes in the three directions of the support are different. The offset in the D(z) direction is very obvious, from −1.2065 mm to −3.0557 mm; the support is in the D(x) direction. Before the stiffness of the seat is reduced to 40%, the offset changes more gently, but when the stiffness is reduced to 60%, the offset of the support is larger.

Fig. 5.
figure 5

Temperature cooling 30 °C

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Fig. 6.
figure 6

Comparison of three working conditions

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It can be seen from Fig. 5 and Fig. 6 that under the temperature difference of 30 °C, the stress change of the bearing is roughly the same as that under the shrinkage and creep of concrete, with little change; The variation range of bearing offset in D(x) and D(y) directions is very small, but the increase range of vertical displacement is very obvious, from −1.2055 mm to −3.0548 mm.

In conclusion, the reduction of bearing stiffness weakens the bearing durability. Under the three different conditions given above, the increase of stiffness damage of bidirectional movable bearing reduces the stress in x and y directions and increases the stress in z direction, but the increase range is small; The influence on the longitudinal and transverse deformation of the bearing is very small and can be ignored, but it has a great influence on the vertical displacement of the bearing. The vertical deformation change of support under three working conditions is shown in the figure below.

It can be clearly seen from Fig. 6 that under the condition of 10-year shrinkage and creep, the stiffness of the two-way movable bearing is reduced to 60%, which is 1.8492 mm higher than the vertical extrusion deformation without reduction, with an increase of about 60.52%; Under the condition of combined temperature rise of 30 °C, the vertical extrusion deformation of the support increases by 1.8491 mm, with an increase of about 60.49%; When the combined cooling temperature is 30 °C, the vertical extrusion deformation of the support increases by 1.8493 mm, with an increase of about 60.54%. Therefore, with the passage of time, the stiffness of the support is continuously reduced and the vertical displacement of the support is continuously increased, which is not conducive to the durability of the support, and the increase of the extrusion deformation of the support is more likely to cause bulging cracks.

5 Conclusion

  1. (1)

    Concrete shrinkage and creep have little effect on the displacement of the support, but the change in temperature will greatly increase the longitudinal and lateral displacement of the support, and the longitudinal displacement will reach about 4–5 times of the original. The offset range is 60 times as much as before. Although the displacement of the support varies greatly, it still meets the standard support offset limit. The maximum longitudinal displacement of the support is 18% of the longitudinal limit, and the maximum lateral displacement of the support is 55% of the transverse limit.

  2. (2)

    The stiffness damage of the support has little influence on the longitudinal and lateral displacement and force, but it has a greater influence on the vertical compression deformation of the support.

  3. (3)

    When the rigidity of the plate rubber bearing is reduced to 40% of the previous one, the vertical compression deformation of the bearing is increased by 61%, which is likely to cause the bearing to produce bulging cracks, which will increase the rigidity of the bearing over time Reduction is not conducive to the durability of the support.