This paper presents an effective method of parameter ascertainment for the skeleton curve of corroded compressionbending members to establish its restoring force model. An assumption which considers the skeleton curve of damaged and undamaged members has similar shape is introduced into the fitting process of parameters. Meanwhile, twodimensional plane section assumption is used to simplify the mathematical model and reduce the computational cost. Several sets of experimental data were compared with the prediction by the method developed in this paper, for its verification. The case studies show that the experimental trends can be captured very well.
Reinforced concrete (RC) structures exposed to the aggressive environmental conditions may cause different types of structural damage. For example, wind, waves, corrosive environment, and extreme temperatures all can impact the existing structures. During the entire service life of the RC structure, the continuous penetration of harmful ions induces cracking and spalling of the concrete cover [
In this paper, our particular attention is the corroded compressionbending members of RC structures subjected to the seismic hazard. Numerous corrosion experiments have shown that the deterioration of concrete durability not only reduces the load carrying capacity, but also causes a shift of the failure mechanism from the ductile to the brittle type in a number of cases [
Restoring force model contains hysteresis rules and skeleton curve; this paper only discusses the skeleton curve of restoring force model. For shear reinforced concrete structure, the structure of column between the layers is a typical hydraulic member. As shown in Figure
The forcerestoring model of reinforcement concrete members with flexure and compression.
In this paper, the parameter determination of skeleton curve of noncorroded compressionbending members still is used as which of corroded reinforced concrete elements what proposed in the literature [
Symmetrically reinforced rectangular cross section.
According to those experimental researches [
The forcerestoring model of corroded reinforcement concrete members with flexure and compression.
The yield of corroded members can be still defined as reinforcement yielding or the ultimate compression strain of concrete. One of the most crucial factors affecting the service life of reinforced concrete (RC) structures attacked by aggressive ions is reinforcement corrosion. Corrosion of reinforcing steel produces corrosion products with higher volume than the original steel resulting in cracking of the concrete surrounding the bars. Corrosion leads to a reduction in the crosssectional area of the reinforcing steel (or mass loss) and a loss of bond between the reinforcing steel and the concrete. These will be resulting in cross section deformation of reinforced concrete bending components no longer accord with flat section assumption under the action of repeated loading. But if the assumption of plane section is not correct, the whole analysis process will be very difficult. In this paper, based on the analysis of the reference literature [
It can be seen that the difference between (
Layer yield shear force
To the actual structure, the shear span ratio of compressionbending member is larger (more than 4); we only consider bending deformation in calculating the yield story drift
A very limited number of research programs have been conducted for corroded reinforced concrete flexural members in the laboratory. In this paper, we assume that the limit shear force
In the present work, the destruction of the damaged reinforced concrete bending member still defined as limit shear force is 85% [
The collapsing displacement
After geometric conversion,
According to (
In this study, the physical and mechanical performance indexes of the corroded reinforcements are the cross section area
The current evaluation of rebar corrosion degree mostly uses mass loss ratio or area loss ratio; in this work, we adopted the researcher Y.L.Hui's [
The relationship of area loss and mass loss.
Mass loss ratio  The relationship of mass loss ratio 

Less than 10% 

10%∼20% 

20%∼30% 

30%∼40% 

The yield strength
Lee et al. [
Compared with the undamaged members, the damaged concrete bending members involved in the concrete mechanical properties change have two parameters: the axial compressive strength and elastic modulus of concrete. Considerable research work has been carried out on the effect of corrosion on the mechanical properties of concrete; there have been several studies [
The following selected test instances were to be calculated to validate the effectiveness of the proposed parameters which determine the skeleton curve of the forcerestoring model of corroded reinforced concrete members with flexure and compression.
This example comes from the literature [
Details of test specimen (unit: mm).
An external current method [
Mass loss rate and the yield strength of corrosion steel bar.
Number of specimens  ZZ1  Z2  Z3  Z4  Z5  Z6  Z7 

Mass loss rate  0%  20%  18%  18%  23%  6%  25% 
Yield strength/MPa  415.6  413.7  415.4  413.3  404.0  408.2  395.8 
All the columns were tested under combined constant axial load and reversed cyclic lateral force in a testing frame, as shown in Figure
Loading device.
Lateral displacement history.
In this paper, the test yield shear force of the specimens, the yield displacement, ultimate shear, limit displacement, the collapsing shear force and its corresponding displacement, and so on six parameters were calculated, by the proposed approach of the skeleton curve parameter determination of corroded compressionbending members restoring force model. The numerical and experimental results are shown in Tables
The comparison between theoretical value and experimental value.
Number of specimens  Axial compression ratio  Corrosion rate (%)  Experimental value ( 
Calculation value ( 
Ratio  Experimental value ( 
Calculation value ( 
Ratio 

ZZ1  0.27  0  41.78  47.70  1.14  9.32  10.37  1.11 
Z2  0.27  20  38.51  37.24  0.97  7.08  9.81  1.39 
Z3  0.27  18  37.11  38.06  1.03  7.85  9.87  1.26 
Z4  0.27  18  36.31  38.06  1.05  6.79  9.87  1.45 
Z5  0.27  23  31.34  33.72  1.08  8.03  9.52  1.19 
Z6  0.27  6  41.15  44.91  1.09  9.36  10.27  1.09 
Z7  0.27  25  36.89  32.96  0.89  9.03  9.44  1.05 
Note: ratio = calculation value/experimental value, the ratio in the following table are calculated according to this definition.
The comparison between theoretical value and experimental value.
Number of specimens  Axial compression ratio  Corrosion rate (%)  Experimental value ( 
Calculation value ( 
Ratio  Experimental value ( 
Calculation value ( 
Ratio 

ZZ1  0.27  0  50.15  52.65  1.05  22.54  21.07  0.94 
Z2  0.27  20  45.79  41.10  0.90  13.20  19.86  1.50 
Z3  0.27  18  43.54  42.01  0.96  14.32  19.98  1.40 
Z4  0.27  18  42.27  42.01  0.99  13.22  19.98  1.51 
Z5  0.27  23  37.01  37.23  1.01  15.20  19.23  1.27 
Z6  0.27  6  49.65  49.57  1.00  22.37  20.84  0.93 
Z7  0.27  25  44.37  36.38  0.82  15.62  19.07  1.22 
The comparison between theoretical value and experimental value.
Number of specimens  Axial compression ratio  Corrosion rate (%)  Experimental value ( 
Calculation value ( 
Ratio  Experimental value ( 
Calculation value ( 
Ratio 

ZZ1  0.27  0  42.63  44.75  1.05  41.54  26.66  0.64 
Z2  0.27  20  38.92  34.94  0.90  28.02  24.73  0.88 
Z3  0.27  18  37.01  35.71  0.97  24.10  24.92  1.03 
Z4  0.27  18  35.93  35.71  0.99  23.61  24.92  1.06 
Z5  0.27  23  34.42  31.64  0.92  19.12  23.79  1.24 
Z6  0.27  6  42.20  42.13  1.00  39.51  26.22  0.66 
Z7  0.27  25  37.71  30.93  0.82  19.24  23.56  1.22 
The yield shear force
As shown in Table
The limit shear force
It can be seen from Table
The collapsing shearing force
The calculated results of the test collapsing shearing force and its corresponding displacement are listed in Table
This case was presented by N. D. Tao group [
Experimental simulation is relatively close to actual engineering. In order to simulate the corrosion in actual engineering, first, the specimens were exposed outdoors for 2 years and 6 months, second, the specimens were immersed in a water tank containing 3%∼5% NaCl solution, an external current method was utilized to induce corrosion (Figure
In order to study the effect of axial compression ratio on the seismic performance of corroded members, three axial compression ratios (
Reinforcement corrosion rate between 4.06%∼8.96%.
The failure mode of the members is bending failure.
Corrosion test device diagram.
Six parameters were calculated by the method described in this paper. The comparison between the calculation results and the test results is shown in Tables
The comparison between theoretical value and experimental value.
Number of specimens  Axial compression ratio  Corrosion rate (%)  Experimental value ( 
Calculation value ( 
Ratio  Experimental value ( 
Calculation value ( 
Ratio 

XZ7  0.2  4.06  44.32  48.58  1.09  23.23  25.73  1.11 
XZ8  0.2  5.87  42.45  47.70  1.12  16.85  25.64  1.52 
XZ9  0.2  6.56  41.66  47.36  1.14  21.71  25.60  1.18 
XZ5  0.4  4.23  51.30  53.13  1.04  20.40  16.02  0.79 
XZ10  0.4  5.87  55.73  52.39  0.94  20.70  15.97  0.77 
XZ1  0.4  7.64  49.50  51.60  1.04  19.75  15.92  0.81 
It can be seen from Table
The comparison between theoretical value and experimental value.
Number of specimens  Axial compression ratio  Corrosion rate (%)  Experimental value ( 
Calculation value ( 
Ratio  Experimental value ( 
Calculation value ( 
Ratio 

XZ7  0.2  4.06  38.43  42.66  1.11  13.42  9.68  0.72 
XZ8  0.2  5.87  36.08  41.89  1.16  10.12  9.64  0.95 
XZ9  0.2  6.56  35.94  41.59  1.16  9.91  9.63  0.97 
XZ5  0.4  4.23  44.45  51.15  1.15  12.04  11.36  0.94 
XZ10  0.4  5.87  46.31  50.44  1.09  10.77  14.16  1.31 
XZ1  0.4  7.64  42.05  49.68  1.18  10.84  13.62  1.25 
From Tables
The comparison between theoretical value and experimental value.
Number of specimens  Axial compression ratio  Corrosion rate (%)  Experimental value ( 
Calculation value ( 
Ratio  Experimental value ( 
Calculation value ( 
Ratio 

XZ7  0.2  4.06  37.67  41.29  1.04  55.39  32.44  0.59 
XZ8  0.2  5.87  36.09  40.54  1.12  47.18  32.25  0.68 
XZ9  0.2  6.56  37.62  40.26  1.07  42.02  32.20  0.77 
XZ5  0.4  4.23  43.61  45.16  1.05  36.36  20.18  0.56 
XZ10  0.4  5.87  47.37  44.54  0.94  29.59  20.10  0.68 
XZ1  0.4  7.64  42.07  43.86  1.04  32.52  20.01  0.62 
Collapsing shear force
The parameter determination method of skeleton curve for corroded specimen was proposed in this paper according to the skeleton curves of undamaged member. The model was verified through test example, and conclusions can be made as follows:
The restoring force model of corroded reinforced concrete bending members and skeleton curve in shape compared with uncorroded members are the similar. It can be considered that their parameters reduced in different damage degrees between the corroded and uncorroded members.
For the yield shear force, the limit shear force, and the collapsing shear force of the proposed model, calculation results have good agreement with the test results, while it was different for the yield displacement, the limit displacement, and the collapsing displacement. And the possible causes of are discussed in this paper.
Due to the lack of experiment research on the restoring force model for the damaged structure, something should be done to further improve the established model to make the theory model more close to actual situation.
The authors declare that they have no conflicts of interest.
This work was financially supported by the National Natural Science Foundation of China (51208155 and 51308166) and Weihai Science and Technology Development Plan Project (2013DXGJ08 and 2015DXGJMS011). And this project was also supported by Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (HIT.NSRIF.2015119).