Journal of Sensors

Volume 2019, Article ID 1359853, 13 pages

https://doi.org/10.1155/2019/1359853

## Damage Quantification in Concrete under Fatigue Loading Using Acoustic Emission

^{1}School of Civil Engineering, Central South University, 68 South Shaoshan Road, Changsha 410075, China^{2}National Engineering Laboratory for High Speed Railway Construction, 68 South Shaoshan Road, Changsha 410075, China^{3}Engineering Technology Research Center for Prefabricated Construction Industrialization of Hunan Province, Central South University, 68 South Shaoshan Road, Changsha 410075, China

Correspondence should be addressed to Zhiwu Yu; nc.ude.usc@uywhz

Received 24 May 2019; Accepted 17 July 2019; Published 3 November 2019

Academic Editor: Jerome Rossignol

Copyright © 2019 Zhi Shan 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

Acoustic emission (AE) is an effective nondestructive evaluation method for assessing damage in materials; however, few works in the literature have focused on one quantification method of damage in concrete under fatigue loading by using AE for characterizing the entire three main deterioration behaviors simultaneously. These deterioration behaviors include Young’s modulus degradation, fatigue total strain, and residual strain development. In this work, an AE quantification method of fatigue damage in concrete was developed, by combining AE and a fiber bundle-based statistical damage model (fiber bundle-irreversible chain model). By establishing a relationship between normalized AE counts and the damage variable based on the fiber bundle-irreversible chain model, the method was proposed. Additionally, this method was verified against the experimental results. It is able to capture the mechanisms of damage accumulation and characterize the three deterioration behaviors simultaneously.

#### 1. Introduction

Acoustic emission (AE), as a nondestructive evaluation and diagnostic technique, has been developed for more than three decades [1–6]. By considering the highly sensitively detecting results of active microscopic events (e.g. microcrack initiation and propagation) in materials provided by AE, it is widely adapted for materials research [1–9]. In detail, by applying AE sensors on certain materials, the propagated elastic waves produced by the abovementioned events are detected; further, the location and state of the damage/crack are determined [7–9].

The understanding of deterioration behaviors for concrete under fatigue loads is essential for the assessment and analysis of relevant structures. Specifically, those deterioration behaviors consist of Young’s modulus degradation, fatigue total strain, and residual strain development, which further cause an abrupt failure of the structures. For example, the repeated train loading on high-speed railway concrete structures typically results in the safety problems by the influence of such deterioration. Recently, there are significant advancements in AE techniques on the continuous monitoring for materials under fatigue loading [10–12]. For example, Kahirdeh et al. [11] proposed a parametric approach to estimating acoustic information entropy and relative entropy of aluminum alloys by examining the acoustic signal. In addition, the researchers also observed the relationship between the evolutions of those variables and the fatigue damage concerning the hardness change, respectively.

However, few works in the literature have focused on one quantification method of damage in concrete under fatigue loading by using AE for characterizing the entire three deterioration behaviors simultaneously. Specifically, most contributions only considered the experimental investigations on the empirical relationship between a single deterioration behavior and a certain AE parameter [13–19]. For instance, Wang et al. [15] conducted the comparison on the fatigue properties among plain concrete, rubberized concrete, and polypropylene fiber-reinforced rubberized concrete by applying AE, and the results showed a linear correlation between the AE counts and the residual strain for plain and rubberized concrete, respectively. Additionally, based on a AE rate process theory, Ohtsu and Watanabe [17], Suzuki and Ohtsu [18], and Dai and Labuz [19] defined a probability density function of AE events, which was dependent on the stress level for investigating the evolution of (where and denotes the stress and strength, respectively) on concrete. Furthermore, Ohtsu and Watanabe [17] and Suzuki and Ohtsu [18] observed the relationship between a key parameter and a damage variable for concrete. In detail, the key parameter was obtained by fitting the evolution of with a hyperbolic function, and the damage variable was introduced by considering the stiffness degradation.

For nearly one hundred years, a class of simple statistical damage models, namely, fiber bundle models (FBMs), have received growing attention in both the physics and engineering communities [20–24], due to their deceptively simple appearance coupled with an outstanding richness of mechanical behaviors. The classical FBMs were developed to characterize the progressive elastic deformation damage relating to Young’s modulus degradation, which is represented by the continuously breaking of fibers. However, it is unable to characterize the development of irreversible/residual strains in materials. The development of irreversible/residual strain is a significant property for describing the fatigue behaviors in the sense of material behavior. Therefore, in order to characterize such property, the irreversible deformation element was introduced into the classical FBMs [24–30]. Specifically, the irreversible deformation element is able to simulate the development of irreversible strains represented by the progressive fracture of elements. These models [24–30] were developed to characterize both the progressive elastic deformation damage resulted from the micro mode-I crack process and the irreversible/residual deformation damage produced by serials of types of cracks. The types of cracks are generally distinguished as follows: the irreversible opening of mode-I crack due to locking mechanisms of crack faces [31], the irreversible sliding-like of mode-II crack (not mode-II microcracks) due to toughness of crack faces [32, 33], the irreversible-frictional sliding over crack surface [34, 35], the irreversible cracking of fracture process zone [27, 36], the irreversible mode-II microcracks [37, 38], and other cracking mechanisms [39, 40]. It is verified that the irreversible deformation element is able to effectively model the development of the irreversible/residual strains in the materials [24–30]. Precisely, the fibers and irreversible deformation elements with random thresholds are introduced in FBMs for modelling the events of microcracking in the materials, which were detected by AE sensors.

Furthermore, the fiber bundle-irreversible chain model (BCM, the expression “plastic chain” [41] is corrected by “irreversible (deformation) chain” in this work based on the literature [27, 31–40]) was developed based on the FBMs for describing the abovementioned deterioration behaviors of quasibrittle materials under fatigue loading during the lifetime. This model was verified to be able to capture the major microscopic mechanisms of the deterioration behaviors against the experimental results [41]. Recently, Sa’nchez-Molina et al. [42] proposed a stochastic model for modelling the soft tissue failure under monotonic loading by combining the FBM and AE. The relationship between fiber failure number and AE counts and the relationship between damage variable and AE cumulative energy were both examined. Although this method only considered the relationship between AE parameters and stress response of the material under monotonic loading, it provides us a new approach to studying the deterioration behaviors under fatigue loading by using AE.

In this work, a method of quantification of damage in concrete under fatigue loading is proposed based on AE and BCM. This method is aimed at characterizing the three deterioration behaviors simultaneously. The outline of the work is as follows: after a brief introduction of the BCM relating to the damage accumulation, the quantification method of fatigue damage in concrete is developed, and subsequently, this method is verified by comparing the predictions with experimental results.

Note that this work only focuses on the damage and AE responses of the concrete materials (i.e., the representative volume elements (RVEs)) due to the sophisticated behaviors under fatigue loading, although a number of works have been contributed by researchers concerning that of reinforced concrete structures. Considering that the materials’ behaviors are essential for further analysis of the mechanical behaviors of structures, a great number of studies have been already conducted in the literature [14, 15, 17, 19, 28, 29, 31, 42, 43]. In addition, the damages of concrete structures subjected to mode-I, mode-II, and mixing mode loading were classified by using AE [3]. However, the feasibility of such method is probably limited for concrete material due to the differences between the damage behaviors of structures and materials caused by different scales. In the perspective of material, concrete mainly consists of three constituents: the cement matrix (a microdefect-filled material), the aggregates, and the interface between the matrix and aggregates (transition halo, the weakest zone in concrete, which is highly oriented because of wall effects). Therefore, it causes concrete containing full of flaws and preexisting cracks from nanoscale to mesoscale and results in the complex damage behaviors in the material; e.g., when the concrete material is subjected to uniaxial tension, there are different modes of cracks generated during the loading. The further work concerning the damage and AE responses of reinforced concrete structures will be conducted by the authors’ research team.

#### 2. Fiber Bundle-Irreversible Chain Model with Damage Accumulation

The BCM with the damage accumulation was developed based on the statistical methods, namely, FBMs. This model is aimed at characterizing the deterioration behaviors of quasibrittle material under fatigue loading [41]. The main methodology of the theoretical method is briefly introduced.

The BCM [41] was composed of a bundle of parallel linearly elastic fibers with the same Young’s modulus and a chain of linked perfectly irreversible deformation elements with the same Young’s modulus . Each irreversible deformation element was presumed to obtain the same irreversible strain after reaching its threshold, driven by the effective stress [30, 41]. After each fiber breaking event, the load of the failed fiber was assumed to be equally redistributed over the intact ones in the bundle in an equal-load sharing pattern without consideration of their distance from the failure point [20–30]. Under fatigue loading, the fibers progressively fail due to breaking and the irreversible deformation elements gradually fracture due to the abovementioned cracks [27, 31–40]. Specifically, two mechanisms (elastic and irreversible deformation damage accumulation) are considered as follows [41]: (i)Fiber () fails instantaneously at time when the strain reaches its breaking threshold (ii)Irreversible deformation element () fractures instantaneously at time when the strain (corresponding to the effective stress ) reaches its fracturing threshold

The system BCM experiences an accumulation process of both types of damages during the lifetime; hence, the system, rather than the individual fiber or irreversible deformation element, is endowed with a memory of the load history. Consequently, this methodology introduces a scaling method for characterizing the deterioration behaviors of concrete in time space [41].

By using the statistical theory [20–30], the accumulated elastic and irreversible deformation damage and up to time can be calculated by integrating the time over the entire failures of fibers and fractures of irreversible deformation elements, respectively [41]: where denotes the time and and and and denote the probability densities and the cumulative distributions of the breaking thresholds and the fracture thresholds in time space, corresponding to the breaking thresholds and the fracturing thresholds in total strain space, respectively [41]. Furthermore, for describing the nonlinear behavior of concrete which coupled both the accumulated elastic and irreversible deformation damages, the total damage variable up to time can be obtained by integrating over the entire history of both fiber failures and irreversible deformation element fractures [41], such that where denotes the probability density coupling with fiber failures and irreversible deformation element fractures and denotes the cumulative distribution of thresholds coupling with fiber failures and irreversible deformation element fractures in time space (i.e., thresholds ), relative to the thresholds in total strain space (i.e., threshold ).

Therefore, the constitutive relationship of the BCM under a constant maximum loading was obtained such that [41]

To characterize the evolution of the total damage variable conveniently, the parameters and were introduced [41] by using an analytical method based on the fatigue failure surface concept [44, 45] as follows: where and denote the total damage variable after the time of first loading cycle and at the time to fatigue failure, respectively, which are affected by or the stress level ( denotes the strength); they are calibrated by the analytical method based on the fatigue failure surface concept [44, 45], and is in the interval , varied with different stress levels ; denotes the normalized total damage variable; it is a parameter by normalizing from to and defined by the equation , in the interval .

#### 3. Acoustic Emission Quantification of Fatigue Damage

##### 3.1. Relationship between AE Parameter and Fatigue Damage

In AE, several parameters are usually evolved including amplitude, duration, energy, threshold, frequency, rise time, and counts. Among these parameters, the amplitude, energy, and counts were typically applied to investigate the damage of materials. Figure 1 illustrates that all the counts (), accumulated energy (Ae), energy rate, and amplitude experience a three-stage process during the lifetime of typical concrete under fatigue loading. By observing the relationship between the AE parameters and fatigue damage, the following are found: (1)By using a certain modification method, AE counts are able to characterize the evolution of damage in materials under fatigue. The count is defined as the number of times the AE signal amplitude exceeds a given threshold during experiments. The reasons are concluded as follows: initially, the application of AE counts on material characterization is verified. Although several researchers regarded the AE counts as an unreliable indicator of damage, it is considered the most direct response to the microstructural variation in materials [46]. A number of works on studying the relationship between fatigue behaviors and AE responses of materials have been conducted by using AE counts [15, 17, 42, 46–55]. Based on AE counts, the literature [56, 57] defined a new AE parameter, average frequency (AF), for fracture mode classification. Moreover, Figure 1(a) and other literatures [15, 47, 48] show the evolution trend of AE counts and the typical fatigue strain development are similar to each other. In addition, it is presumed that the AE counts are in certain correlation with the number of failure/fracture events in the BCM. Although it is found that a large variation of AE counts could be resulted by changing a threshold by only a small proportion, in this work, after using a certain modification method (e.g., normalization) on AE counts, the resulted parameter relative to AE counts is undergoing a stable evolution process.