Seismic performance analysis of long-span continuous rigid frame bridge with Engineered Cementitious Composite at expansion joints

In this paper, OpenSees software is used to establish a numerical simulation analysis model of a long-span continuous rigid frame bridge with Engineered Cementitious Composite (ECC) expansion joint reinforcement scheme. The seismic response characteristics and laws of structures with ordinary concrete and ECC concrete at expansion joints are compared and analyzed, and their seismic performance is evaluated. The results show that the use of ECC material at the beam end position can effectively reduce the peak response of the structure under earthquake action and reduce the number of collisions. ECC material has a strong energy dissipation capacity and can reduce the collision damage of the beam section near the bridge expansion joint under earthquake action.


Introduction
Long-span continuous rigid frame bridges built in mountainous areas and poor geological areas are often threatened by earthquake disasters.Under the action of the earthquake, a large displacement is easy to occur at the end of a long-span continuous rigid frame bridge, and a beam-end collision occurs.Scholars at home and abroad have established a large number of collision models to study the seismic response of the expansion joint area of long-span continuous rigid frame bridges.
Jankowski R [1,2] considered that the Kelvin collision model can simulate the bridge collision reaction more ideally.Fan [3,4] established a collision model of continuous beams, considering the nonlinearity of bridge bearings and the plasticity of bridge piers, and carried out collision analysis by applying longitudinal time-history loads.The analysis results show that the large difference in the period of adjacent bridge spans will lead to greater collision response between adjacent bridges.When the period ratio of adjacent bridge spans is greater than 0.7, the structural seismic response caused by collision is not obvious.Based on the theory of straight rod coaxial, it is concluded that the initial stiffness of the collision element should be 0.5 times the axial stiffness of the shorter main beam.Wang Junwen and Zhang Yunbo [5] used ANSYS modeling analysis to study the influence of seismic action considering the traveling wave effect on the collision effect at the expansion joint of a continuous beam.Shi [6] used the Hertz-damp model to simulate the change of stiffness and energy dissipation in the process of bridge collision.The results show that when the height difference between the two main piers is large, the difference in the collision gap will have a greater impact on the collision response of the low pier under the action of an earthquake.The difference in collision stiffness has a significant effect on the collision response of high and low piers.
At present, ECC materials are mostly used to build bridge deck connecting plates at expansion joints, eliminating traditional expansion joint devices and realizing seamless bridges.However, the current research pays more attention to the fatigue performance of the bridge deck under the impact load of the vehicle and the deformation of the bridge deck under the action of temperature.There are few studies on the use of ECC materials at the beam end to reduce the collision force under earthquake.Therefore, it is of great significance to use ECC concrete materials at the beam end to reduce the damage to the beam section at the expansion joint and improve the seismic performance of the bridge.
In this paper, the OpenSees program is used to simulate and analyze the long-span continuous rigid frame bridge with the ECC expansion joint enhancement scheme, and the results are compared and analyzed.Based on the fiber element theory, the nonlinear beam-column element of the end beam section of the long-span and long-span rigid frame continuous beam bridge is established.The seismic response characteristics and laws of the structure using traditional concrete and ECC concrete at the expansion joint are compared and analyzed.The application of ECC concrete in the seismic design of long-span continuous rigid frame bridges is evaluated, and the prospect of new materials in the seismic design of bridge structures is discussed.

Finite element model
OpenSees builds models by establishing sub-objects such as nodes, elements, sections, materials, constraints, and loads, and performs finite element analysis.Each sub-object has multiple commands to meet different needs.The required model is established by using different OpenSees commands for research work [7].

Simulation of collision unit
The expansion joint of the bridge is set at the end of the bridge, which is used to connect the beam body with the abutment or beam body to ensure the smooth running of the vehicle.Under the action of earthquake, the collision between beams or between beams and abutments is easy to occur.This problem is the focus of this paper.The collision is a nonlinear problem, and it is difficult to carry out numerical simulations [8].At present, three methods are commonly used to simulate the collision effect: the coefficient recovery method, the Lagrange multiplier method, and the contact element method.The contact element method is the most commonly used method to simulate the collision effect of the beam end, so the contact element method is selected in this paper.In this paper, the simplified Hertz-damp model introduced by Muthukumar [9], which can be better applied to finite element simulation, can consider the stiffness change and energy dissipation of the spring during the collision process.

Cross-section material
The concrete material model in the pier section uses Concrete02, and the steel bar uses Steel02.The pier material uses C40 concrete, the steel bar uses HRB400, and the thickness of the concrete protective layer is 7cm.The fiber section of the pier is shown in figure 2. Blue is the protective layer of concrete, yellow is the confined concrete, and red is the steel bar.
The ordinary concrete model of the 1.2m beam section at the end of the main beam adopts Concrete02, the steel bar uses Steel02, the ECC concrete uses ECC01, and the steel bar uses Steel02.The main beam uses C50 concrete, the steel bar uses HRB400, and the thickness of the concrete protective layer is 10 cm.The fiber section of the main beam is shown in figure 3. Blue and yellow are protective layer concrete, purple is confined concrete, and red is steel bar.

Structural model
According to a large number of earthquake damage studies, for most bridges, the main girder is generally in an elastic state under earthquake action, so the main girder is simulated by an elastic beam element.Among them, the 1.2m beam section at both ends of the main bridge needs to add fiber elements to see the damage to the beam end structure under the action of the earthquake.The fiber section is shown in Section 2.3, and the collision element is described in Section 2.2.
Through the destruction of the bridge caused by a large number of earthquakes, it is found that the destruction of the pier will lead to damage or even damage to the bridge, so it is necessary to simulate the pier in the seismic response analysis of the bridge structure.To correctly simulate the dynamic behavior of bridge piers, the displacement-based beam-column element is used to simulate the pier components, in which the fiber section adopts the pier section in section 2.4.

Natural vibration characteristics
The OpenSees visualization model is obtained by using OSLite software to test the model structure.At the same time, the bridge model built by OpenSees is simply checked by using Midas Civil.The comparison model of the OpenSees model and Midas Civil is shown in figure 4.
By using OpenSees software and Midas Civil software for eigenvalue analysis, the period and frequency of each mode of vibration are compared.The comparison of the first twelve periods and frequencies is shown in table 1.Through table 1, it can be found that the period and frequency of the two models are similar, which proves that OpenSees modeling is correct.

Input of seismic wave
The Imperial Valley-01 was selected as the seismic wave, and the peak acceleration (PGA) of the seismic wave was 0.6g. Figure 5 is the displacement time history curve corresponding to the seismic wave Imperial Valley-01.In the case of longitudinal input of seismic waves, the collision analysis is carried out on the end beam section of a continuous rigid frame bridge with ordinary concrete and ECC concrete.

Time-history curve analysis
Figure 6 is the time history curve of the collision force at the expansion joint under the action of the seismic wave Imperial Valley-01.From figure 7, it can be seen that when the 1.2m beam section at the beam end adopts ordinary concrete, the peak value of the collision force is 63160kN, when the 1.2m beam section at the beam end adopts ECC concrete, the peak value of the collision force is 37980kN, and the peak value of the collision force of the 1.2m beam section at the beam end adopts ECC concrete is 46.5 % lower than that of ordinary concrete.At the same time, the use of ECC concrete can effectively reduce the number of collisions at the beam end. Figure 7 is the displacement curve of the beam end under the action of the seismic wave Imperial Valley-01.From Figure 7, it can be seen that the peak displacement of the beam end is 0.086 m when ordinary concrete is used at the beam end, and the peak displacement of the beam end is 0.056 m when the ECC concrete is used at the beam end.The peak displacement of ECC concrete is 35.6 % lower than that of ordinary concrete.From the displacement peak position, it can be seen that when ECC concrete is used, the displacement peak lags behind that of ordinary concrete.Except for the peak displacement of about 5s, the displacement of other periods is much smaller than that of ordinary concrete, which shows that ECC concrete has a buffering effect.Figure 8 is the axial force time history curve of the beam end beam section under the action of seismic wave Imperial Valley-01.It can be seen from figure 8 that under the action of seismic waves, the peak axial force of the beam end is 21350 kN when ordinary concrete is used at the beam end.When ECC concrete is used, the peak axial force of the beam end is 12700 kN, and the peak axial force decreases by 40.5 %.

Beam end fiber section analysis
Under the action of seismic wave Imperial Valley-01, the fiber section analysis of the model with ordinary concrete and ECC concrete at the beam end is carried out respectively.Unit 1 is the beam section at the beam end, and unit 2 is the beam section with ordinary concrete after the beam section at the beam end.The stress-strain curves of element 1 and element 2 bending moment-curvature, section roof reinforcement, and core and edge concrete under the two schemes of ordinary concrete and ECC concrete are analyzed respectively.9 that under the action of seismic wave Imperial Valley-01, the hysteretic region of the bending moment-curvature curve of the model with ECC concrete in unit 1 is larger and fuller than that of ordinary concrete.The enclosed area of the curve increases obviously and the shape expands.The hysteresis region of the bending moment-curvature curve of the model with ECC concrete in unit 2 is smaller than that of ordinary concrete, the curve surrounding area is reduced and the shape shrinks.It can be seen that by using ECC concrete, the energy dissipation capacity is stronger, and the seismic performance of the bridge is enhanced.

Steel stress-strain curve.
From figure 10 (a), it can be seen that under the action of the seismic wave Imperial Valley-01, the beam end adopts the ordinary concrete model unit 1.The steel bar is in the elastic section, the maximum tensile strain is 3.87 × 10-5, the maximum compressive strain is 8.44 × 10-5, the maximum tensile stress is 7.7MPa, and the maximum compressive stress is 17.1MPa.It can be seen from figure 10 (b) that under the action of seismic wave Imperial Valley-01, the beam end adopts ECC concrete model unit 1 steel bar in the elastic section, the maximum tensile strain is 1.4 × 10-6, the maximum compressive strain is 1.9 × 10-4, the maximum tensile stress is 0.037 MPa, and the maximum compressive stress is 38.1 MPa.It can be seen from figure 10(c) that under the action of seismic wave Imperial Valley-01 when ordinary concrete is used at the beam end, the steel bar of unit 2 is in the elastic section, the maximum tensile strain is 3.87 × 10-5, the maximum compressive strain is 8.44 × 10-5, the maximum tensile stress is 7.7MPa, and the maximum compressive stress is 17.1MPa.When the beam end adopts ECC concrete, the steel bar of unit 2 is in the elastic section, the maximum tensile strain is 1.4 × 10-6, the maximum compressive strain is 1.9 × 10-4, the maximum tensile stress is 0.086 MPa, and the maximum compressive stress is 9.9 MPa.
Compared with ordinary concrete, ECC concrete is used at the beam end, the steel bar is not pulled and the compressive stress is large.After using ECC concrete, the compressive stress of element 2 is reduced by 42 % compared with that of ordinary concrete.It can be seen that the use of ECC concrete can reduce the collision damage of the beam section near the bridge expansion joint under earthquake action.

Stress-strain curve of edge concrete.
It can be seen from figure 11 (a) that under the action of seismic wave Imperial Valley-01 when ordinary concrete is used at the beam end, the edge concrete of unit 1 is in the elastic section, the maximum tensile strain is 3.87 × 10-5, the maximum compressive strain is 8.53 × 10-5, the maximum tensile stress is 1.35 MPa, and the maximum compressive stress is 2.9 MPa.The beam end adopts ECC concrete, and the edge concrete of Unit 1 is in the elastic section.The maximum tensile strain is 2.1 × 10-7, the maximum compressive strain is 1.9 × 10-4, the maximum tensile stress is 0.003 MPa, and the maximum compressive stress is 2.4 MPa.
It can be seen from figure 11 (b) that under the action of seismic wave Imperial Valley-01 when ordinary concrete is used in the 1.2m beam section at the beam end, the edge concrete of element 2 is in the elastic section, the maximum tensile strain is 3.83 × 10-5, the maximum compressive strain is 8.54 × 10-5, the maximum tensile stress is 1.34 MPa, and the maximum compressive stress is 2.9 MPa.When the beam end adopts ECC concrete, the edge concrete of element 2 is in the elastic section, the maximum tensile strain is 4.6 × 10-7, the maximum compressive strain is 4.9 × 10-5, the maximum tensile stress is 0.034 MPa, and the maximum compressive stress is 1.7 MPa.
Compared with ordinary concrete, ECC concrete is used at the beam end, the edge concrete is not pulled, the compressive stress is small, and the compressive strain is large.After using ECC concrete, the compressive stress of element 2 is reduced by 30 % compared with element 1.It can be seen that the use of ECC concrete at the beam end can reduce the collision damage of the beam section near the expansion joint of the bridge under an earthquake.

Figure 1 .
Figure 1.Facade diagram of continuous rigid frame bridge (cm)

Figure 2 .
Figure 2. Fiber section of pier.Figure 3. Fiber section of the main girder.

Figure 3 .
Figure 2. Fiber section of pier.Figure 3. Fiber section of the main girder.

Figure 4 .
Comparison of two models.

Figure 7 .
Figure 7. Time history curve of beam end displacement.Figure8is the axial force time history curve of the beam end beam section under the action of seismic wave Imperial Valley-01.It can be seen from figure8that under the action of seismic waves, the peak axial force of the beam end is 21350 kN when ordinary concrete is used at the beam end.When ECC concrete is used, the peak axial force of the beam end is 12700 kN, and the peak axial force decreases by 40.5 %.

Figure 8 .
Figure 8.Time history curve of beam end axial force.
(a) Unit 1 of ordinary concrete is used.(b) Unit 1 of ECC concrete is used.(c) Unit 2 of ordinary concrete and ECC concrete is used..

Figure 10 .
Stress-strain curve of steel bar in concrete section roof.

Figure 11 .
Stress-strain curve of edge concrete.

Table 1 .
Comparison of the first 12 cycles of the structure.