Shock and Vibration

Volume 2016 (2016), Article ID 4792786, 17 pages

http://dx.doi.org/10.1155/2016/4792786

## Effect of Temperature Variation on Modal Frequency of Reinforced Concrete Slab and Beam in Cold Regions

College of Transportation, Jilin University, Changchun 130025, China

Received 3 January 2016; Revised 17 May 2016; Accepted 1 June 2016

Academic Editor: Mickaël Lallart

Copyright © 2016 Hanbing Liu 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

Changes of modal frequencies induced by temperature variation can be more obvious than those caused by structural damage, which will lead to the false damage identification results. Therefore, quantifying the temperature effect on modal frequencies is a critical step to eliminate its interference in damage detection. Due to the nonuniform and time-dependent characteristics of temperature distribution, it is insufficient to obtain the reliable relationships between temperatures and modal frequencies using temperatures in air or at surface. In this paper, correlations between measured temperatures (air temperature, surface temperature, mean temperature, etc.) and modal frequencies for the slab and beam are comparatively analyzed. And the quantitative models are constructed considering nonuniform temperature distribution. Firstly, the reinforced concrete slab and beam were constructed and placed outside the laboratory to be monitored. Secondly, the correlation coefficients between modal frequencies and three kinds of temperatures are calculated, respectively. Thirdly, simple linear regression models between mean temperature and modal frequencies are established for the slab and beam. Finally, five temperature variables are selected to construct the multiple linear regression models. Prediction results reveal that the proposed multiple linear regression models possess favorable accuracy to quantify the temperature effect on modal frequencies considering nonuniform temperature distribution.

#### 1. Introduction

In order to guarantee the safety operation of structures, structural health monitoring (SHM) systems have been widely implemented on the existing and newly built bridges in the past few decades [1–3]. Vibration-based Damage Identification (VBDI), as one of extremely important parts of SHM system, has been developed to monitor bridge performance and identify structural damage [4–6]. However, a practical difficulty exists because modal parameters vary with the changing environmental conditions. In order to avoid the false damage identification results, the changes of modal parameters caused by environmental variation must be understood, quantified, and discriminated from those caused by structural damage [7–10].

Numerous investigations have indicated that temperature is the most important environmental factor affecting structural vibration properties [11, 12]. And its effect can be more significant than that caused by structural damage [13]. Corresponding researches have also demonstrated that mode shapes are not sensitive to temperature variation, and the change of modal damping may be masked by measurement noise [14–16]. Therefore, the temperature effect on modal frequencies has attracted much more attention. Researchers from Los Alamos National Laboratory monitored the Alamosa Canyon Bridge in New Mexico during 24 hours. They found that the first three modal frequencies varied about 4.7%, 6.6%, and 5.0%, when the temperature of bridge deck changed by about 22°C [17, 18]. It was more significant than the changes of modal frequencies caused by artificial cut in I-40 Bridge [19]. Peeters and De Roeck [20] reported that the first four modal frequencies of Z24 Bridge in Switzerland varied by 14%–18% during monitoring period of 10 months. There was a bilinear relationship between measured frequencies and temperatures above and below 0°C because of the asphalt layer freezing at cold temperature. Later progressive damage tests indicated that modal frequencies decreased by less than 10% till final destructive damage [21]. As indicated by these researches, structural damage cannot be accurately identified if temperature effect is not quantified and eliminated.

During the past 20 years, considerable efforts have been devoted to investigating temperature effect on modal frequencies of RC bridges. Askegaard and Mossing [22] continuously monitored a three-span RC bridge for three years, and seasonal change of modal frequencies reached 10%. Desjardins et al. [23] studied the modal frequencies and average girder temperature of Confederation Bridge during monitoring period of 6 months. The variation of temperature from −20°C to 25°C led to the reduction in modal frequencies by 4%. Liu and DeWolf [24] found that the modal frequencies changed about 6% during one full year. And a linear regression analysis demonstrated that the modal frequencies were decreased by 0.8%, 0.7%, and 0.3% as temperature increases by one degree Celsius. Mosavi et al. [25] monitored the vibration responses and temperature of a two-span steel-concrete composite bridge during 24 h period. Frequencies in all modes changed 1-2% from night to noon and did not change significantly from night to morning. In summary, it has been widely observed that temperature significantly affects the modal frequencies of RC bridges with a negative correlation [26, 27].

Some researchers have been investigating the correlation and evaluating the degree of temperature influence on modal frequencies based on field test data [28]. However, vibration test in practical engineering is easily affected by external factors (service load, wind, temperature, boundary condition, damage, measurement noise, etc.) [29]. It is difficult to separate the effect of temperature on modal frequencies from others, which results in the unconvinced correlations between measured modal frequencies and temperature. Therefore, the controlled laboratory experiments are necessary and imperative to provide accurate and reliable results regarding the temperature effect on modal frequencies. Xia et al. [15] conducted an experiment on a two-span continuous concrete slab out of laboratory for nearly two years. It was found that the negative correlation between modal frequencies and air temperature could be observed for the first four modes. Comparative study with cantilever beams made of steel and aluminum indicated that the modal frequencies variations of RC slab were much larger than those of metallic beams [13]. For these laboratory experiments and field testes, air temperature and surface temperature are measured to discover the correlations with modal frequencies. However, the temperature distribution in RC bridge is nonuniform and time-dependent. The relationships between modal frequencies and temperature at surface (or in air) are incomplete and unreliable.

Considering that the relationships between modal frequencies and temperature cannot be sufficiently captured using air temperature or surface temperature, Xia et al. [30] investigated the variation of modal frequencies versus nonuniform temperature distribution for a RC slab. It was clearly shown that modal frequencies decreased with the increasing of temperature. In addition, a better linear correlation between modal frequencies and structural temperatures was observed than air temperature and surface temperature. However, the tests are only carried out from 8:00 am to 10:00 pm on 11 February 2009. During test period, air temperatures only fluctuated from 17°C to 27°C. It is insufficient to investigate the correlation and quantify temperature influence on modal frequencies, especially in cold regions. Moreover, temperature along width direction is assumed to be uniformly distributed, and nonuniform temperature distribution is only considered along vertical direction in Xia et al.’s research. In practice, the temperature distribution of an entire bridge is generally nonuniform throughout the cross section. Therefore, studying the correlation and quantifying temperature effect using nonuniform temperature distributions along both width and height directions are necessary for engineering application of damage identification methods.

This paper aims to investigate the correlations between modal frequencies and temperatures for RC slab and beam in cold regions and quantify the temperature effect. The RC slab and beam were constructed and placed outside the laboratory to periodically measure the modal frequencies and temperatures (air temperature, surface temperature, mean temperature, etc.). Correlations between modal frequencies and three kinds of temperatures are contrastively analyzed. In addition, simple linear regression models (SLRM) between modal frequencies and mean temperature are established. And the temperature effect on modal frequencies is evaluated based on thermal mechanics theory and thermal properties of concrete. In order to improve the accuracy of quantification, multiple linear regression models (MLRM) are developed to formulate the relationship between modal frequencies and nonuniform temperature distribution. A better prediction performance indicates that MLRM can be used to accurately quantify temperature effect on modal frequencies for structural health monitoring and damage identification.

#### 2. Description of Experiment

##### 2.1. RC Slab and Beam

The RC slab and beam constructed for monitoring temperatures and modal frequencies are shown in Figure 1. The slab is 600 mm wide and 150 mm high, and beam is 300 mm wide and 400 mm high. The lengths of them are both 4000 mm, and calculated span lengths are 3700 mm. RC slab and beam are simply supported on concrete piers by plate rubber supports. A 150 mm overhang is present at each end of the slab and beam. In order to avoid the localized damage at support positions, the metal plates with 5 mm thickness are embedded into slab and beam over supports. In addition, the concrete blocks with the length of 400 mm and the same cross section dimensions as the RC slab and beam are constructed and placed on the side of slab and beam. They are used to measure the mass variations, which can reflect the effect of air humidity on the mass of RC slab and beam. The RC slab, beam, and corresponding concrete blocks were produced on 8 June 2015. Design strength of concrete is 40 MPa, and the mixture proportions are listed in Table 1. Common Portland cement of grade 42.5 (normal type) containing 20% active admixture is used as cementitious material. Natural river sand (medium sand) with fineness modulus 2.7 is adopted as fine aggregate. And crushed gravels with a nominal maximum size of 31.5 mm are used as coarse aggregate. Three concrete cube specimens (150 mm × 150 mm × 150 mm) were poured at the same time with slab and beam. The compressive strengths of cube specimens are measured by crushing the specimens cured for 28 days under the standard curing condition of 20 ± 3°C and 95% relative humidity [31]. Mean value of tested compressive strengths is 48.5 MPa, which is larger than the designed one. The high quality of materials, favorable curing condition, and large extra coefficient of cement could account for the larger tested compressive strength of cube specimens. In order to reduce the influence of inadequate curing on experimental tests, RC slab and beam were covered in plastics after pouring concrete and cured on the ground outside the laboratory for more than 90 days. They were hoisted and placed at supports on 12 September 2015 for installing the measurement equipment and preparing to start the tests.