Impact Analysis of Section Seismic Capacity in Potential Plastic Hinge Zone of Engineered Cementitious Composite Based on OpenSees

In this paper, OpenSees is used to analyze the moment-curvature (M-φ) curves of the bottom cross section of 4×40m continuous girder piers under the same reinforcing conditions, which are completely made of C40 concrete, partially made of Engineered Cementitious Composite material concrete(ECC) outsourced concrete, and completely made of ECC concrete, and then evaluate its seismic performance. Meanwhile, the yield curvature and ultimate curvature changes of the abutment section under different axial compression ratios are investigated. The results show that the yield curvature and ultimate curvature of ECC are larger than those of ordinary concrete, and the deformation capacity of ECC is stronger under the same axial force. The results also show that the yield moment and yield curvature of the section gradually increase with the increase of axial compression ratio, and the curvature ductility of the section deteriorates.


Introduction
Recently, with the continuous development of modern technology and the transportation industry, bridges are not only used to cross rivers and seas but also to cross mountainous areas and poor geological regions.Most of these areas are high-intensity areas with frequent seismic disasters, so there is high demand for the span and seismic performance of bridges.A large number of seismic disaster research found that under the action of seismic force, the superstructure damage is less, At present, scholars have carried out a lot of research on ECC material, but most of the scholars are on the components of the test, based on the test on the mechanical properties of ECC material, the lack of bridge structural level of the study, failed to the application of ECC material and the bridge structure of the mechanical characteristics of the study and the good combination.To effectively use ECC material, based on the existing research, this study establishes a simulation model of the potential plastic hinge region of the bridge structure with the help of Opensees professional seismic simulation software, conducts an analysis of the influence of the cross-section seismic capacity of the potential plastic hinge region of the ECC concrete, and further researches the seismic performance of the ECC-steel reinforced concrete composite structure, to provide references for the application of the ECC material in the actual project.

Material constitutive relationship
In this paper, OpenSees is used to analyze the seismic analysis of bridges.It is necessary to define the constitutive relationship models of concrete, steel bars, and ECC concrete materials, and use the MomentCurvature.tclfile on the OpenSees official website to perform bending moment-curvature analysis.In OpenSees, the two materials of multi-axial force and uniaxial force are widely used.In this paper, the finite element model is established by selecting the uniaxial force material.

Constitutive model of ordinary concrete
Concrete02 Material model in OpenSees is selected as the constitutive model of ordinary concrete.The model can simulate the tensile strengthening phenomenon of concrete, the calculation cost is not high, and the convergence performance is good.It can well reflect the improvement of the ultimate compressive strength and ultimate compressive strain of the core concrete caused by the confinement of stirrups.
The Scott-Kent-Park model is adopted in the concrete02 Material model.The model considers the constraint effect of stirrups on the core concrete in the reinforced concrete section and corrects the slope of the peak compressive stress, compressive strain, and tensile softening section of the concrete.After the correction, the calculation cost of the constitutive model of concrete is low, the convergence performance is good, and the calculation results are more accurate.The constitutive equation of the Scott-Kent-Park model is equation (1). where '' 0.5 3 0.29 3 0.002 145 1000 4 h -the width of the core concrete.
The calculation of the ultimate compressive strain of concrete is shown in equation ( 4).When the compressive strain of concrete is greater than 0.004, the concrete protective layer will be damaged, affecting the mechanical properties of concrete [12] and the constitutive relationship of concrete is shown in figure 1. 0.004 0.9 300

Constitutive model of ECC concrete
Engineered Cementitious Composites Material (ECC01) constitutive model is used in the ECC model in OpenSees.This constitutive model was proposed by Han et al. [13] in 2003, which is suitable for the numerical calculation of ECC.The stress-strain curve of ECC is shown in figure 2 where E is the elastic modulus of ECC concrete.
The ECC compression skeleton line is shown in figure 4, and its constitutive model is as follows equation (4).When the strain  is greater than 0 and less than cp  , ECC is in the elastic working stage.After that, with the gradual increase of compressive strain, and finally to the ultimate compressive strain cp  , the compressive stress also reaches the ultimate compressive stress cp  ; then, the ECC material gradually softens to reach the failure strain cu  , and the compressive stress becomes zero.
The above is the constitutive equation of ECC material considering material damage under uniaxial tensile and compressive loads.In addition, the energy dissipation capacity of ECC material must also be considered.On this basis, Tong-Seok Han et al.proposed the definition of material function of ECC material under reciprocating load, which is very effective to simulate the seismic response of building structures under earthquake action.The tensile constitutive curve of ECC material under reciprocating load is shown in figure 5, and its constitutive function is shown in equation (7).
Where t  ≥ 1 is a constant, which is determined by the cyclic unloading test.When the ECC material is in Where cprl  is the minimum compressive strain in the process of stress load loading, * cul  is determined by equation (12).
where cul


is the minimum compressive strain during partial unloading under pressure load, t b is a material constant that needs to be determined by experiments.

Stress-strain relationship of steel bar
In this paper, the Steel02 Material command is used, and the OpenSees command uses the Menegotto-Pinto model.The use of this steel material constitutive model can well simulate the strengthening of steel bars during tension, and can linearly deal with the tensile softening stage of steel bars [14].The constitutive relationship of the steel bar is shown in figure 6 and the equation ( 13).This constitutive model of steel material has high computational efficiency and high accuracy in Figure 6.
The constitutive model of the steel material can also well reflect the Bauschinger effect of the steel bar [15].  where In the equations ( 14) and ( 15), the meaning of ( 0  , 0  ) and ( r  , r  ) is shown in figure 7. Their values will be updated to new values after the strain response changes.The R in Equation ( 13) will control the shape of the transition curve, and R can be used to reflect the Bauschinger effect.B is the strain hardening rate, namely B=E1/E0.The calculation of R is shown in equation (16).
After the strain reversal, ξ will also be updated to a new value at the same time.R0 is the initial value of R, a1 and a2 are constants, which can be determined by experiments.Philip and other scholars believe that the isotropic hardening problem of steel bars can be solved by using the stress translation of the linear yield asymptotic line of steel bars according to the maximum plastic strain of steel bars, as shown in equation (17).
where εy -yield strain of steel bar; εmax -the maximum absolute value of strain a3 and a4determined by experiments; σy-yield stress of steel bar.

Project background
In this paper, a 4 × 40 prestressed small box girder in the Inner Mongolia Autonomous Region is taken as the project background.The height of the precast beam is 2.2m and the width of the bridge deck is 12m.The pier is a double-column rectangular solid pier.The height of the pier is 16m, 19m and 24m.The section of pier is a rectangular section with a length and width of 1.5m.The pier support adopts GYZ450 × 99 plate rubber bearing, and the transition pier adopts GYZF4350 × 87 four fluorine slide plate rubber bearing.The main beam adopts C40 concrete, the pier cap beam adopts C40 concrete, and the longitudinal reinforcement and stirrup adopt HRB400.The elevation diagram of the continuous bridge and the side view of the pier cap beam, as shown in figure 8 and figure 9.

Model parameters
The cross-section of the pier is reinforced concrete hollow section, using C40 concrete, the longitudinal reinforcement of the pier is HRB400 steel bar, the stirrup is HRB400 stirrup, the stirrup spacing is 136 mm, the volume stirrup ratio is 1.5%, and the thickness of the protective layer is 40 mm.The cross-section of the pier is shown in figure 10.In this paper, the pier uses C40 concrete.The material parameters of ordinary unconstrained and constrained concrete are shown in table 1.The material parameters of ECC unconstrained and constrained concrete refer to the experimental and simulation data of Li et al. [16].The material parameters are shown in table 2, and the material parameters of the steel bar are shown in table 3. Transition parameter cR1 of the Bauschinger effect curve 0.925 Transition parameter cR2 of the Bauschinger effect curve 0.15

Moment-curvature ductility analysis method of pier section
OpenSees divides the cross-section into several grids of specified size by itself.Each grid on the cross-section is a different fiber.The fibers are steel bars and concrete fibers respectively.The concrete fibers are divided into unconstrained and constrained concrete fibers, and the corresponding constitutive models of the fibers are given respectively.Finally, the MomentCurvature.tclfile in the OpenSees official website is used to calculate the bending moment-curvature curve of the section by numerical integration [17].
The bending moment-curvature curve of the pier section is obtained by OpenSees analysis and the curvature ductility coefficient / y       .After determining the reinforcement ratio and volume stirrup ratio of the pier section, the curvature ductility of the section is mainly related to the axial compression ratio η and the material of the pier section.Then compare and analyze the relationship between these two factors and curvature ductility.

ECC enhancement scheme for plastic hinge zone
Referring to the test results of Liang Xingwen et al. [18] who used ECC materials for seismic research in the potential plastic hinge area of the pier, it is considered that the top and bottom of the pier of the continuous rigid frame bridge are both potential plastic hinge areas.The influence of ECC material-reinforced RC pier on the mechanical properties and seismic performance of the structure was studied.The full-section ordinary concrete, outsourcing 30%, 50%, 70% ECC concrete, and full-section ECC concrete were used.The ordinary concrete scheme was compared with four different pier potential plastic hinge zone ECC concrete enhancement schemes.A total of five cross-section schemes are compared.The scheme design is shown in figure 11.(e) Scheme 5: Full-section ECC concrete.Figure 11.Ordinary concrete and ECC enhancement scheme for plastic hinge zone.

Influence of pier section material
To study the influence of ECC material reinforced RC pier on the mechanical properties and seismic performance of the structure, the bending moment-curvature analysis of different pier sections with 3.4 section ECC reinforced plastic hinge zone scheme is carried out by using OpenSees.The initial axial force is 6356 kN at the bottom of the pier under the dead load in the analysis of the Midas Civil main bridge model.Figure 13 is the comparison of the analysis results curve, and table 4 is the calculated value of OpenSees.The axial force-bending moment analysis of the pier section of different ECC-reinforced plastic hinge zone schemes in Section 3.4 is carried out by using OpenSees.Figure 12 shows the comparison of the analysis results.From figure 13, it can be seen that the ultimate curvature of the ECC-reinforced RC section is higher than that of the ordinary concrete section.Because the ultimate compressive strain of full-section ECC concrete is 0.03, and the ultimate compressive strain of full-section concrete is 0.004, the deformation capacity of the ECC reinforced pier is stronger under the same axial force.With the increase of ECC content, the ultimate curvature increases continuously, up to 65.3%.The ultimate bending moment of ECC concrete decreases with the increase in ECC concrete content, but the decrease is not large.The ultimate bending moment of full-section 100% ECC concrete is 7% lower than that of 30% ECC concrete.The yield curvature of ECC concrete is greater than that of ordinary concrete.The yield curvature of ordinary concrete is 0.0125, the yield curvature of 30% ECC concrete is 0.0248, and the yield curvature of 30% ECC concrete is 97.8% higher than that of ordinary concrete.For ECC concrete, the yield curvature increases with the increase of ECC concrete content, and the yield curvature of full-section ECC concrete is 7.7% higher than that of 30% ECC concrete.The flexural capacity of ECC is also significantly higher than that of ordinary concrete.With the increase of ECC concrete content, the yield bending moment increases gradually.The yield bending moment of full-section ECC concrete is 9101kN•m, while that of full-section ordinary concrete is 4348kN•m.The yield bending moment of full-section ECC concrete is about 109.3% higher than that of full-section ordinary concrete.From the axial force-bending moment curves of the sections in Figure 13, it can be seen that under different ECC-reinforced plastic hinge zone schemes, different sections basically reach the maximum bending moment value when the axial force N = 40000kN, and the maximum bending moment value increases with the increase of the ECC content of the section.When the axial force N = 40000kN, the ordinary concrete section M = 14729.5kN•m,the 0.3ECC concrete section M = 16345.5kN•m,the ECC concrete section M = 17187.9kN•m,the maximum bending moment of the 0.3ECC concrete section is 11.0% higher than that of the ordinary concrete section, and the maximum bending moment of the ECC concrete section is 16.7% higher than that of the ordinary concrete section.
In summary, the plastic hinge area of the pier is enhanced by ECC concrete material, which can improve the bearing capacity and deformation capacity of the section.

Influence of axial compression ratio
In concrete members, the axial compression ratio has a great influence on the bearing capacity and ductility of the section.To study the relationship between the bending moment-curvature of the section and the axial compression ratio, a total of ten cases of axial compression ratio η = 0.05, 0.1,0.15,0.2,0.25,0.3,0.35,0.4,0.45 and 0.5 were taken respectively.The bending moment-curvature analysis of the section of 30% ECC concrete was carried out by using OpenSees, and the curvature ductility coefficient of the section was calculated, as shown in figures 14 and 15.By comparing and analyzing the relationship between bending moment-curvature, curvature ductility coefficient and axial compression ratio of Figure 5 and Figure 6, the following findings can be obtained in table 5 and table 6: (1)When the axial compression ratio is 0.5, the yield bending moment is 12834.20kN•m,which is 303.6% higher than that when the axial compression ratio is 0.05.When the strength of concrete is the same, its tensile strength is also the same.When the bending moment of the component reaches the cracking load of the component, the pressure is applied on the section to offset the tensile stress generated by the bending of the component.Therefore, the bending moment must be increased to make the component crack.Therefore, with the increase of axial compression ratio, the cracking load is also increasing.The axial pressure inhibits the generation and development of cracks, and the yield bending moment of the section is improved.
(2) It can be seen from Figure 13 that the ultimate curvature decreases gradually with the increase of the axial compression ratio.When η = 0.05, the ultimate curvature of the section reaches the maximum value of 0.5262.When the axial compression ratio gradually increases, the axial force of the section gradually increases, so the height of the neutral axis of the section decreases.When the axial compression ratio reaches a certain value, the height of the neutral axis is reduced to 0. The section is in the full section compression state, and the ultimate curvature of the section reaches the minimum.Therefore, the larger the axial compression ratio, the smaller the ultimate curvature of the section, resulting in the deterioration of the deformation capacity of the structure.At the same time, the increase in axial compression ratio will also lead to a change in the failure mode of the component.
(3) It can be seen from Figure 14 that the ultimate bending moment increases with the increase of the axial compression ratio.When the axial compression ratio η = 0.05, the ultimate bending moment of the section is 1515.7kN•m.When the axial compression ratio η = 0.5, the ultimate bending moment is 8051.34kN•m,which is increased by 431.2%.With the increase of the axial compression ratio, the neutral axis of the section decreases continuously, and the tensile stress generated by the bending moment of the section is offset.At this time, although the action point of the resultant force becomes smaller from the bottom surface, the resultant force of the section increases with the increase of pressure, so the ultimate bending moment of the section will increase with the increase of axial compression ratio.
(4) It can be seen from Figure 14 that with the increase of axial compression ratio, the curvature ductility coefficient of the section decreases gradually in the form of a concave curve.With the increase of axial compression ratio, the ultimate curvature of the section will decrease greatly, but the yield curvature of the section is less affected by the axial compression ratio, so the curvature ductility coefficient of the section will decrease with the increase of axial compression ratio, but the decrease tends to be gentle.
In summary, with the increase of the axial compression ratio of the section, the curvature ductility of the section becomes worse, and if the axial compression ratio is too large, the component will change from bending failure to shear failure.

Conclusion
This chapter mainly analyzes the cross-section of the pier bottom section of the 4 × 40m continuous beam bridge.The OpenSees and concrete constitutive model, ECC material constitutive model, and steel constitutive model are introduced, and the bending moment-curvature ductility analysis theory is introduced.For the actual bridge pier section, OpenSees is used to analyze the P-M-φ curve of several ECC-reinforced plastic hinge zone schemes, such as C40 concrete, partial ECC concrete, and ECC concrete under the same reinforcement condition.Meanwhile, the yield curvature and ultimate curvature of the pier section under different axial compression ratios are studied.The following conclusions can be drawn: (1) The ultimate curvature of ECC is greater than that of ordinary concrete.Under the same axial force, the deformation ability of ECC is stronger.With the increase of ECC content, the ultimate curvature increases continuously, and the maximum increase is 65.3%.The ultimate bending moment of ECC concrete decreases with the increase of ECC concrete content.
(2) The yield curvature of ECC concrete is greater than that of ordinary concrete.Compared with the yield curvature of ordinary concrete, the yield curvature of 30% ECC concrete increases by 97.8%.For ECC concrete, the yield curvature increases with the increase of ECC concrete content, and the yield curvature of full-section ECC concrete is 7.7% higher than that of 30% ECC concrete.The flexural capacity of ECC is also significantly higher than that of ordinary concrete.With the increase of ECC concrete content, the yield bending moment gradually increases, and the yield bending moment of full-section ECC concrete is about 109.3% higher than that of ordinary concrete.
(3) With the increase of axial compression ratio, the yield bending moment and yield curvature of the section gradually increase.When the axial compression ratio is η = 0.5, the yield bending moment is 303.6% higher than that when the axial compression ratio is η = 0.05.
(4) With the increase of the axial compression ratio of the section, the curvature ductility of the section will also become worse, and if the axial compression ratio is too large, the component will change from bending failure to shear failure.
The parameters in the Menegotto-Pinto constitutive model are shown in figure7.

Figure 7 .
Figure 7. Monotone envelope parameters of steel bar.

Figure 12 .
Figure 12.Comparison of bending moment-curvature analysis under different ECC enhancement schemes.

Figure 14 .
Figure 14.Relationship between bending moment-curvature and axial compression ratio of ECC30% concrete section.

Figure 15 .
Figure 15.Relationship between curvature ductility and axial compression ratio of ECC30% concrete section. .

Table 2 .
Parameters of ECC concrete.

Table 3 .
Parameters of longitudinal reinforcement.

Table 4 .
Moment-curvature analysis calculation values under different ECC enhancement schemes.

Table 5 .
Bending moment curvature and curvature ductility coefficient of ECC30% concrete section under different axial compression ratios.

Table 6 .
Bending moment curvature and curvature ductility coefficient of ECC30% concrete section under different axial compression ratios.