Seismic Response Analysis of Continuous Beam Bridges with Engineered Cementitious Composite (ECC) in Plastic Hinge Region

This study investigates the seismic performance of potential plastic hinge regions in small and medium-sized bridges using Engineered Cementitious Composite (ECC) concrete. A 4×40m continuous beam bridge is used as an example, with time-history analysis conducted using the OpenSees finite element software, and the type of concrete material in the cross-section of the bridge pier’s plastic hinge region is varied to analyze the structural natural vibration characteristics and seismic responses of the bridge structure under earthquake action. The time-history analysis of seismic motion shows that after replacing the bridge pier’s plastic hinge region with ECC, the stiffness of the bridge pier significantly decreases, and the natural vibration period of the bridge increases. Under the action of longitudinal earthquakes, the energy dissipation capacity and seismic performance of the bridge pier increase with the increase in ECC content in the plastic hinge region at the bottom of the bridge pier. Furthermore, under earthquake action, the concrete at the edge of the cross-section using ordinary concrete throughout cracks under tension, while the tensile stress in the cross-sections using different proportions of ECC concrete remains the same and does not crack under tension, remaining elastic under compression, which also reflects the good seismic performance of ECC concrete.


Introduction
In recent years, due to regional economic development needs, some mountainous areas have also begun to vigorously develop transportation infrastructure construction, building a large number of bridge structures.However, these areas have large terrain fluctuations and are often in high-intensity areas, with frequent earthquake disasters, so there are high requirements for the span and seismic performance of bridges.Through a large amount of earthquake disaster research, it has been found that under the action of earthquake forces, the upper structure is less damaged, and it is mainly the damage of the bridge pier components that leads to the collapse of the bridge.Therefore, seismic research on bridges mainly targets the lower structure, and the seismic design of bridge piers has a very important impact on the overall seismic performance of the bridge.
At present, two methods are mainly used to improve the seismic performance of bridge piers.One is to optimize the bridge design scheme to ensure the good construction of important components and reduce the damage caused by earthquakes to the bridge piers.The second is to use new and excellent performance civil engineering materials to improve the seismic performance of bridge piers [1].Due to the geographical conditions of mountainous areas, if only relying on optimizing bridge structure design and protecting important components, it may not meet the requirements of earthquake intensity, and it will increase a lot of construction costs.Therefore, the need to study new seismic materials has become a research focus.Some scholars have researched Engineered Cementitious Composite (ECC), which is a material that improves the tensile performance of concrete by adding fiber materials to the cement base.By combining ECC materials with reinforced concrete structures, the seismic performance of bridges is improved [2].Compared with ordinary concrete, ECC materials add a certain amount of fiber, remove coarse aggregate, and have a relatively low elastic modulus than ordinary concrete, and its deformation ability is stronger, and the ductility performance has a large improvement [3][4][5][6][7].The ultimate tensile strain of ECC material is much larger than that of ordinary concrete, and ECC concrete will not produce large cracks when it is under tension, but evenly distributed small cracks, reflecting its good ability to control crack width [8].
Victor C. Li and others [3] at the University of Michigan first proposed adding fiber to the concrete matrix to obtain fiber-reinforced cement-based composites (ECC) with good ductility, toughness, and uniform and fine crack cracking.The tensile stress of ECC material gradually transfers from concrete to the fiber in ECC material, so that ECC material appears tensile strain hardening effect.As ECC continues to stretch and deform, the fibers in it continue to slip, so ECC material has good energy dissipation performance.Xu and others [9] proposed to use ECC concrete to replace ordinary concrete only in the potential plastic hinge area of the bridge pier, obtained ECC/RC composite columns, and gave the results of repeated cyclic load tests of 9 scaled pier column specimens.The results show that compared with RC columns, the ECC/RC group has better ductility, energy dissipation capacity, and slow stiffness degradation.The increase in axial load is detrimental to the ductility performance of the ECC/RC composite column, but it can significantly increase the bearing capacity while maintaining the integrity of the structure.Due to the large volume of concrete used in the potential plastic hinge area of the bridge pier and the high cost of ECC materials, Zhang [10] suggested using ECC to wrap ordinary concrete in the potential plastic hinge area of the bridge pier, proposed the design concept of PP-ECC sleeve, and designed and manufactured 4 scaled bridge piers with different ECC wrapping thicknesses for single-sided cyclic loading tests.The results show that compared with the RC column with all ECC materials in the plastic hinge area, the use of ECC material in the precast wrapped ECC column with different thicknesses is reduced by 44%, but its bearing capacity, ductility, and energy dissipation capacity have not decreased.Gul Mian Asfahan Ali [11] studied the repeated load test of the special anti-bending frame structure using ECC material in the beam-column joint.The test results show that the structure with ECC has significantly improved in ductility, bearing capacity, and energy dissipation.Because ECC has strong shear resistance and ductility performance after adding ECC, ECC can solve the shear stress requirements of components without using any stirrups.
Although scholars have conducted a lot of research on ECC materials, most of the tests and numerical analyses are based on components, and the mechanical properties of ECC materials are studied based on this, and there is a lack of research at the bridge structure level.And because of the high cost of ECC materials, how to reduce costs as much as possible while ensuring the excellent seismic performance of ECC materials, and provide solutions for practical engineering applications, is the main problem that needs to be solved at present.Therefore, this article uses the professional seismic analysis software OpenSees to establish a finite element model (FEM) to establish a numerical model of the potential plastic hinge region of the bridge structure, and conduct seismic response analysis of the potential plastic hinge region of the bridge pier using different cross-section ECC concrete, further studying the impact of ECC material wrapping thickness on the seismic performance of the cross-section, providing a reference for practical engineering applications.

Ordinary Concrete Constitutive Model
The ordinary concrete constitutive model used in this article is the Concrete02 Material model in OpenSees.The model uses the Scott-Kent-Park model, which can simulate the tensile strengthening phenomenon of concrete, considers the constraint of stirrups on the core concrete in the reinforced concrete section, and corrects the peak compressive stress, compressive strain, and slope of the tensile softening section of concrete.After correction, the constitutive model of concrete has low calculation cost, good convergence performance, and accurate calculation results.

ECC Concrete Constitutive Model
The ECC model in OpenSees uses the Engineered Cementitious Composites Material (ECC01) constitutive model, which is a constitutive model proposed by Han et al. [12] in 2003 for ECC materials.To analyze the performance of ECC materials under earthquake loads, in addition to considering material damage, the energy dissipation capacity of ECC materials must also be considered.Based on this, Tong-Seok Han and others [12] proposed the material function definition of ECC materials under reciprocating loads.Therefore, the ECC constitutive model used in this paper is the constitutive model proposed by Tong-Seok Han for cyclic loading.

Steel constitutive model
OpenSees provides a variety of selectable steel material constitutive model commands.This article uses the Steel02 Material command.This OpenSees command uses the Menegotto-Pinto model.This steel material constitutive model can well simulate the strengthening of steel during tension, and can linearly handle the softening stage of steel under tension.This model can also reflect the Bauschinger effect of steel well, and has high calculation efficiency and accuracy.

FEM and analysis
3.1.Parameters 3.1.1Material properties.In this paper, the bridge piers use C40 concrete, and the steel bars use HRB400.The parameter values of ECC unconstrained and constrained concrete materials (see in table 1) refer to the experimental and simulation data of Li et al. [13].At the same time, in order to study the impact of ECC materials enhancing RC bridge piers on the mechanical properties and seismic performance of the structure, four groups of ECC concrete with different contents are proposed in the plastic hinge zone, and a group of full-section concrete is proposed for numerical analysis.

Analysis of vibration characteristic
This paper uses OpenSees to perform dynamic characteristic analysis and extracts the natural frequency and mode of the bridge structure.This article gives the frequency and period of the first 6 modes under different plastic hinge enhancement schemes in table 2.
When the potential plastic hinge area at the bottom of the bridge pier is wrapped with ECC material, the periods of the four ECC-enhanced bridge pier potential plastic hinge area schemes all significantly increase, and they are shown as Scheme 5 > Scheme 4 > Scheme 3 > Scheme 2 > Scheme 1.The first to sixth order periods significantly increase after the potential plastic hinge area at the bottom of the bridge pier is wrapped with ECC material, and they increase with the growth of the ECC material content wrapped at the bottom of the potential plastic hinge area, ranging from a 6.3% increase to a 27% increase.Since the potential plastic hinge area at the bottom of the bridge pier is wrapped with ECC material, the elastic modulus of the ECC material is small, which leads to a decrease in the stiffness of the bridge pier, thereby increasing the natural vibration period of the bridge.

Response results and analysis of bridge seismic
The seismic fortification intensity of this project is 7 degrees, and the site category is Class II.According to the " Specifications for Seismic Design of Highway Bridges" (JTG-T 2231-01-2020) [15], the design basic earthquake acceleration is 0.10g, the design characteristic period is 0.35s, the seismic importance coefficient Ci: 1.0 (E2 action), 0.34 (E1 action), site coefficient Cs: 1.0, damping coefficient Cd: 1.0, and the structural damping ratio is 0.05.The E2 response spectrum curve is obtained based on the basic seismic motion parameters of the structure.According to the E2 response spectrum curve, three earthquake waves are selected, and the amplitude of the seismic motion acceleration is taken as 0.3g.The earthquake wave parameters are shown in table 3.

Analysis of displacement
This section analyzes the displacement time history of the top section of the pier, and the pier selects Pier 1 as the analysis object.The displacement in the bridge direction at the top of the bridge pier under the action of the three earthquake waves and the time to reach the maximum displacement are shown in table 4， and the displacement curve of the pier top under the action of one seismic wave is shown in figure 2.
From table 4, it can be seen that under the action of Earthquake Wave 1, the maximum displacement of the top of the bridge pier decreases with the increase in the ECC content of the bottom section, with a maximum decrease of 13%; under the action of Earthquake Wave 2, the maximum displacement of the top of the bridge pier does not change much with the increase in the ECC content of the bottom section, around 70mm; under the action of Earthquake Wave 3, the maximum displacement of the top of the bridge pier increases with the increase in the ECC content of the bottom section, with a maximum increase of 14%.This shows that the impact of different earthquake waves on the displacement of the bridge pier is different, and it does not change with the change in the ECC content of the bottom plastic hinge area of the bridge pier.Combining the displacement time history curves of the top of the pier obtained from different bottom plastic hinge schemes under the action of earthquake waves (see in Figure 2), it can be seen from the time when the displacement of the top of the pier reaches the maximum that different bottom plastic hinge area enhancement schemes have little impact on the displacement of the top of the bridge pier, and there will be no lag effect.

4.2.Analysis of internal force
According to the three earthquake waves mentioned above, the maximum bending moment and shear force at the bottom of the bridge pier of the bridge model under the action of longitudinal earthquakes are extracted for comparison and analysis.The result is shown in table 5 and table 6.
From Figure 3 and Figure 4, it can be seen that under the action of different earthquake waves, the shear force of the bottom section of the bridge pier decreases continuously with the increase of ECC concrete content in the bottom plastic hinge area, but the overall decrease is not large, and the shear force under different bridge pier plastic hinge enhancement schemes is between 5120kN~5260kN.It can also be seen that under the action of three earthquake waves, different plastic hinge ECC enhancement schemes all increase the maximum bending moment of the bottom section of the bridge pier.The bending moment of the bottom section of the bridge pier increases continuously with the increase of ECC concrete content in the bottom plastic hinge area, and the full-section ECC concrete increases the bending moment of the full-section ordinary concrete section by 17%~39%.

4.3.Analysis of longitudinal bridge pier plastic pesponse
By using the Borrego earthquake wave to perform time-history analysis on different plastic hinge area ECC enhancement schemes, the moment-curvature curve of the fiber section at the bottom of the bridge pier is obtained as shown in figure 5.It can be seen that under the enhancement scheme of the bottom plastic hinge area of the bridge pier, the moment-curvature curve hysteresis area of the full-section ECC concrete section is large and the shape is relatively full, and it increases with the increase of ECC content in the bottom plastic hinge area.The area of the curve enclosure significantly increases, and the shape expands at the same time.It can be seen that as the ECC content in the bottom plastic hinge area increases, the energy dissipation capacity of the bottom section of the bridge pier is stronger, and the seismic performance of the bridge pier is enhanced.From the above stress-strain figure 6 and figure 7 of the rebar of the fiber section at the bottom of the bridge pier under the enhancement scheme of the bridge pier plastic hinge area, and table 7, it can be concluded that under the action of Earthquake Wave 1, the rebar is always in an elastic state, and the tensile stress decreases continuously with the increase of ECC content in the bottom plastic hinge area of the bridge pier, with area of the bridge pier, with the maximum decrease of 56% when the bottom section of the bridge pier adopts the ECC enhancement scheme.The compressive stress increases continuously with the increase of ECC content in the bottom plastic hinge area of the bridge pier, and the full-section ECC concrete increases by 69% compared to the full-section ordinary concrete section.From figure 8, it can be concluded that under the action of an earthquake, the concrete no longer maintains linear elasticity.The edge concrete of the full-section ordinary concrete section cracks under the action of the earthquake.The edge concrete tensile stress of the four enhancement schemes of the bottom plastic hinge area of the bridge pier is the same at 2.9MPa, but it does not crack under tension and is in an elastic state under compression.The compressive stress of the edge concrete of the fiber section at the bottom of the bridge pier increases continuously with the increase of ECC content in the bottom plastic hinge area of the bridge pier, but all are less than the compressive stress of ordinary concrete.The full-section ECC concrete increases by 50% compared to the 0.3ECC concrete edge concrete.The tensile strain of the edge concrete of the fiber section at the bottom of the bridge pier decreases continuously with the increase of ECC content in the bottom plastic hinge area of the bridge pier.The ECC concrete reduces the tensile strain of the edge concrete of the fiber section at the bottom of the bridge pier by 43% compared to the 0.3ECC concrete section.The compressive strain of the edge concrete of the fiber section at the bottom of the bridge pier increases continuously with the increase of ECC content in the bottom plastic hinge area of the bridge pier, and the full-section ECC concrete increases by 50% compared to the 0.3ECC concrete section.
From figure 9, it can be concluded that under the action of an earthquake, ECC concrete no longer maintains linear elasticity when under tension, but it does not crack under tension and is in an elastic state under compression.The tensile stress of ECC concrete of the four enhancement schemes of the bottom plastic hinge area of the bridge pier is the same at 2.9MPa.The compressive stress of the edge concrete of the fiber section at the bottom of the bridge pier increases continuously with the increase of ECC content in the bottom plastic hinge area of the bridge pier.The ECC concrete increases by 55.6% compared to the 0.3ECC concrete edge concrete.The tensile strain of ECC concrete in the fiber section at the bottom of the bridge pier decreases continuously with the increase of ECC content in the bottom plastic hinge area of the bridge pier.The ECC concrete reduces the tensile strain of ECC concrete in the fiber section at the bottom of the bridge pier by 43% compared to the 0.3ECC concrete section.The compressive strain of ECC concrete in the fiber section at the bottom of the bridge pier increases continuously with the increase of ECC content in the bottom plastic hinge area of the bridge pier, and the full-section ECC concrete increases by 55.6% compared to the 0.3ECC concrete section.

Figure 1 .
Figure 1.Enhanced plastic hinge zone enhancement scheme

Figure 2 .
Figure 2. Displacement curve of pier top under the action of Borrego.

Figure 5 .
Figure 5.Comparison of bending moment-curvature of pier bottom section.

Figure 6 .
Figure 6.Stress-strain curve of fiber section steel bar at the bottom of ordinary concrete pier.

Figure 7 .
Figure 7.The stress-strain curve of the fiber section edge concrete at the bottom of the pier.

Figure 8 .
Figure 8.The stress-strain curve of the fiber section ECC concrete at the bottom of the pier.

Table 1 .
[14] Element and Section Parameters.In this paper, the main beam is simulated by the Elastic Beam Column in OpenSees.Zero-length elements are used to simulate the bearings, and a bilinear restoring force model is used to simulate the relative slip between the plate rubber bearing and the bottom of the beam or the top of the pier.A fiber plastic hinge model is used to perform acceleration time-history analysis on double-column piers.Referring to the experimental results of Liang et al.[14]on seismic research using ECC materials in the potential plastic hinge area of bridge piers, displacement-based beam-column elements are used to simulate the bridge pier components in the plastic hinge area.

Table 2 .
Comparison of Frequency and Period under different schemes.

Table 4 .
The peak displacement of pier top and its reaching time under three seismic waves.

Table 5 .
The internal force of pier section and its reaching time under the action of three seismic waves.

Table 6 .
The internal force of pier section and its reaching time under the action of three seismic waves (continued).: In the table, V represents shear force, M represents bending moment, and t represents time. Note

Table 7 .
Stress-strain of fiber section steel bar at pier bottom.