Research on the flexural capacity of corroded recycled aggregate concrete beams by finite elements method

In this paper, based on the experimental fitting method of recycled concrete beams with corroded rebar, finite element analysis by changing the values of factors affecting the flexural capacity was conducted. The results showed that the flexural capacity of recycled concrete beams increased with the increase of section width and height.


Introduction
The corrosion of steel bars in concrete is a key task in analyzing the degradation of existing structural performance [1].In recent years, research on steel bar corrosion in concrete has mainly focused on the mechanism of steel bar corrosion, the speed and degree of steel bar corrosion, as well as the protection and mechanical properties of steel bars after corrosion [2][3].In recent years, there have been certain achievements in the research on the performance of recycled concrete structures both domestically and internationally [4][5][6].However, there is still relatively little research on the degradation of the performance of recycled concrete structures, especially the mechanical properties of recycled concrete structures after steel corrosion, and more in-depth research is needed.
There are many complex influencing factors when applying the finite element method to the analysis of reinforced concrete structures, among which the most important is the nonlinearity of the structure, including material nonlinearity and geometric nonlinearity [7].Compared with ordinary concrete, recycled concrete aggregates have old mortar on the surface, so their nonlinear characteristics are different and require further research.
In this paper, the finite element analysis software is applied to conduct nonlinear numerical analysis of beams, and the reliability which for degradation of flexural obtained from preliminary experimental simulations in literature is verified [8].

Verification of the reliability of Eq(1) when the corrosion level less than 15%
The experimental data has compared in literature [8].The results show that Eq (1) is reliable when the level is less than 15%.

Material constitutive relationship
The different parameters of recycled concrete are shown in Table 2.The constitutive relationship of recycled concrete under uniaxial compression adopts the formula fitted by Xiao Jianzhuang [9], as shown in Eq (2).
The constitutive relationship of corroded steel bars adopts a double line ideal elastic-plastic model.This model assumes that the steel bars are linear elastic before yielding, and once yielding, they enter an ideal plastic state.The strain increases but the stress no longer increases, and the relationship is a straight line, as shown in figure .The effect of steel bar corrosion on yield strength and elastic modulus was studied using the results of artificial climate environment, as shown in table 3.

Establishment of finite element model
When using Ansys analysis, there are mainly two types: separated and integral [10].The separated model is a method that treats steel bars and concrete as different elements.The advantage of this method is that it can consider the bonding and sliding effects between steel bars and concrete, and the results are more practical.The disadvantage is that the arrangement of steel bars is complex, and the calculation is not easy to converge.A separate model established are shown in figure.2.

Verification of the reliability of Eq(1) when the corrosion level more than 15%
The reliability of Eq (1) has been verified when the longitudinal rebar corrosion level is less than 15%.
To verify the reliability of Eq (1) when the longitudinal rebar corrosion level is more than 15%.The results is shown in figure .3.

Figure 3. Comparison results
From figure 3, after increasing the corrosion level of longitudinal rebar, the values still conforms well to the finite element simulation value.Therefore, Eq (1) is reliable when the corrosion level is more than 15%.
The results of simulation calculation using finite element software are shown in table 4, the influence of section width on the flexural capacity of recycled concrete beams is much smaller than that of section height.

Conclusions
The following conclusions are presented through finite element analysis: (1) The fitting equation is reliable consistent with the experimental values.
(2) The flexural capacity of recycled concrete beams increases with the increase of width and height, but the influence of width on the flexural capacity of recycled concrete beams is smaller than that of height.

Figure 1 .
Figure 1.Ideal elastic-plastic model of steel bars.

Figure 2 .
Figure 2. Concrete and steel element model.

Table 1 .
Verification of the applicability of Eq.(1) when corrosion level less than 15%

Table 2 .
Parameter expression of recycled concrete

Table 3
Nominal yield strength and elastic modulus of corroded steel bars

Table 4 .
Simulation results