Advances in Civil Engineering

Volume 2018, Article ID 7208031, 12 pages

https://doi.org/10.1155/2018/7208031

## Seismic Performance of a Corroded Reinforce Concrete Frame Structure Using Pushover Method

^{1}School of Civil Engineering, Zhengzhou University, Zhengzhou 450001, China^{2}Liuzhou Administration of Power Supply of Guangxi Grid Company, China Southern Power Grid, Liuzhou 545005, China

Correspondence should be addressed to Guifeng Zhao; nc.ude.uzz@oahzfg

Received 7 January 2018; Revised 17 March 2018; Accepted 1 April 2018; Published 2 May 2018

Academic Editor: Song Han

Copyright © 2018 Meng Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

SAP2000 software was used to build the finite element model of a six-storey-three-span reinforced concrete (RC) frame structure. The numerical simulation of the seismic performance of the RC frame structure incorporating different levels of rebar corrosion was conducted using pushover analysis method. The degradation characteristics of the seismic performance of the corroded structure under severe earthquake were also analyzed. The results show that the seismic performance of the RC frame decreased significantly due to corrosion of the longitudinal rebars. And the interstory drift ratios increase dramatically with the increasing of the corrosion rate. At the same time, the formation and development of plastic hinges (beam hinges or column hinges) will accelerate, which leads to a more aggravated deformation of the structure under rare earthquake action, resulting in a negative effect to the seismic bearing capacity of the structure.

#### 1. Introduction

The building seismic fortification requirements are gradually improving around the world, and the buildings in strict accordance with design and construction code also showed good seismic performance during earthquakes. But in recent years, the houses collapses, highway cracks [1], and casualties caused by earthquakes are still high, such as the Wenchuan earthquake, the India-Pakistan earthquake [2], and the Chilean earthquake [3]. The postdisaster survey data show that collapsed or severely damaged houses are mainly multistorey masonry buildings or concrete frame structures with relatively poor seismic performance [4].

Currently, multistory masonry houses have been gradually restricted to be built and used in large and medium-sized cities, while the reinforced concrete frame buildings are still widely used in schools, office buildings, residential buildings, street shops, and other buildings due to their flexible plan layout and strong adaptability. With the increase of service years, under the induction of external corrosion factors, the material of reinforced concrete frame structure will deteriorate [5–8], resulting in the durability damage (such as surface cracks [9], carbonization, spalling, and steel corrosion [10]). Among which, the corrosion of steel bar is regarded as the prime factor that affecting the durability of concrete structures [11–13]. Corrosion leads to the degradation of geometric parameters and mechanical properties of the rebar and, to some extent, weaken the static bearing capacity of a concrete structure and increase its brittleness. Meanwhile, the seismic performance will be inevitably impaired [14–17]. Therefore, it is of important theoretical significance and engineering guiding value to study the degradation law of seismic performance of corroded reinforced concrete frame structures. At the same time, it can also provide reference about the seismic performance evaluation and maintenance reinforcement for the old reinforced concrete frame structures in the seismic area.

In this paper, the finite element model of a six-storey-three-span corroded reinforced concrete (RC) frame structure was built using SAP2000 software [18, 19]. The numerical simulation of the seismic performance of the corroded RC frame structure was conducted using pushover analysis method [20] because pushover analysis method is the most widely used and convenient method for the seismic performance analysis of the middle-low level RC frame structure. Pushover method is based on the structural static elastic-plastic analysis theory, by increasing the lateral load on the inertial force center of each floor of the structure to obtain the relationship between internal forces and deformation response in this process. Finally, using the seismic demand spectrum and capacity spectrum (ATC-40 response spectrum or Chinese code response spectrum) to estimate the performance point index of the structure, one can easily evaluate the seismic performance of the structure [21]. The main advantage of the pushover analysis method is that the elastic-plastic response of the structure can be considered and the calculation results are stable. This paper also analyzed the degradation law of the seismic performance indicators of the corroded RC frame structure under severe earthquake. The results were expected to provide a reference for seismic safety analysis, reliability assessment, maintenance reinforcement, and reconstruction of corroded RC frame structures.

#### 2. Mechanical Properties of Corroded Reinforced Concrete Materials

##### 2.1. Degradation of the Mechanical Properties of Concrete Cover

A large number of experiments and theoretical analyses have shown that the concrete cover of a RC frame structure will be cracked and peeled off due to the role of rust expansion force after the steel corrosion. In addition, it weakens the bond strength between the rebar and concrete, hence reducing the service life of the structure [22, 23]. Considering that the core concrete binding force of an ordinary reinforced cement concrete member is mainly from the protective layer, the cracking and peeling of the concrete cover will reduce its restraint on the core concrete and further weaken the load and deformation capacity of the member. Therefore, the degradation of mechanical properties of the protective concrete cover should not be ignored during structural analysis. Due to the strong random characteristics of the deterioration of the cover concrete, it is difficult to use analytic methods to determine the degree and location of deterioration. In order to simplify the calculation, (1) is used here to calculate the strength of the cover concrete [24, 25].where is the peak value of the compressive strength of the concrete cover after the steel bar corrosion; is the correlation coefficient between the rebar surface shape and its diameter, and it is usually suggested to be 0.1; is the generalized cracking strain of concrete; is the original width of the member; is the cross-sectional width of the corrosion member; is the number of longitudinal rebars; is the total width of the corrosion crack; is rust oxidation products and the volume ratio coefficient before rust, and it can be taken value 2.0; is the width of the corrosion crack; is the depth of steel bar corrosion; is the corrosion loss rate of the rebar section; and is the radius of the steel rebar before corrosion, and it can be taken as the weighted average value when the reinforcement diameters are different.

##### 2.2. Degradation of the Corrosion Steel Bar Mechanical Properties

Usually, because the distribution of rust factors (such as cracks, chloride ions, and sulfate ions [26]) has significant random characteristics, the corrosion status of reinforcement in RC members often appears as pitting corrosion. Numerical analysis usually adopts the method of equivalent uniform corrosion to deal with the degradation of mechanical properties of pit corroded steel bars, so as to improve the accuracy of numerical simulation or theoretical analysis [27]. It is assumed that the cross section of the rebar is in a uniform corrosion state, but its mechanical properties are degradated according to the pit corrosion equation. In order to consider the effect of pitting corrosion on the mechanical properties of corroded rebar, the nominal yield stress and elastic modulus of the corroded rebar are calculated by (2) [28], and the ultimate stress and strain [29] can be calculated by (3).where () is the nominal yield strength of the steel bar before (after) corrosion; () is the nominal modulus of elasticity of the steel bar before (after) corrosion; () is the nominal ultimate strength of the steel bar before (after) corrosion; () is the nominal ultimate strain of the steel bar before (after) corrosion; and stands for the mass loss rate of the corroded steel. The relationship between and can be seen in (4) [28].

#### 3. Pushover Analysis Results of the Noncorroded RC Frame Structure

##### 3.1. Engineering Background and Calculation Parameters

For the purposes of comparison, a model of noncorroded RC frame building was presented here. The building model has six stories with typical story height 3.6 m, and the overall plan area is 24 × 12 m. All beams are 300 × 550 mm. The columns in 1–3 storeys are 500 × 500 mm, while the columns in 4–6 storeys are 400 × 400 mm, rectangular. Figure 1 shows the typical structural layout. It can be seen that the building model is a typical biaxially symmetric structure. Therefore, to simplify the following computation, only the plane frame in axis ③-③ (Figure 1(b)) is selected to perform pushover analysis.