# Correlation between Coda Wave and Stresses in Uni-Axial Compression Concrete
## 1 Introduction  
Stress is a key index to reflect the condition and safety of concrete structures. However, the measurement of actual stress in existing structures has been difficult to achieve, causing issues in civil engineering [1]. In practice, stresses are mainly converted by measured strains in the structures and the accuracy of the estimated stress depends on the selected constitutive relation. At the same time, because we are unable to fully grasp the stress or strain histories of a given structure, the strains are usually incrementally measured during the test period, resulting in a stress increment but not actual stress [2; 3].  
Non-destructive testing (NDT) is the main method used to test and evaluate structural performances [4; 5]. According to the acoustics (emitted by the internal crack or generated by a transducer) received from the structure, the internal damage of the structure can be monitored [5]. Among NDT technologies, acoustic wave velocity in concrete has been widely used in the determination of concrete elastic modulus, strength measurement, and damage detection [6; 7; 8; 9]. However, due to the characteristics of multicomponent and inhomogeneous concrete materials, the traditional acoustic measurement technology faces great challenges in the application of concrete stress measurement [10].  
Coda wave is an indirect wave formed by multiple scattering in the medium. The main sources of coda wave are diffraction and scattering caused by the inhomogeneity of the medium, and its sensitivity to change in the medium's properties is higher than that of a direct wave. The coda wave interference (CWI) technique takes advantage of the characteristics of the coda wave to detect tiny changes in medium by comparing the waveform before and after the disturbance [11]. [PERSON] put forward thecoda wave analysis method in 1969 [12]. In 2002, [PERSON] et al. used CWI to estimate the nonlinearity of the seismic wave velocity and found that CWI exhibited extreme sensitivity to variations in the medium [13]. After that, the researchers further improved the effectiveness of CWI on the measurement for velocity variation in concrete caused by temperature [14], micro damage [15; 16; 17], and a uniform stress field [18]. In 2014, [PERSON] conducted an experimental study to demonstrate the effectiveness of CWI in concrete stress measurement [19].  
[PERSON] and [PERSON] pointed out that the development of NDT should depend on a better understanding of the performance of materials and forward modeling. Moreover, it should put forward a practical method to obtain high accuracy and realistic feasibility results from NDT [4]. Therefore, the correlation between the stress and the coda wave velocity of concrete should be discussed for the better application of CWI technology in concrete stress detection. Microcracks in concrete close or expand under stresses, leading to changes in the medium's characteristics. The tiny changes in the concrete acoustic-elasticity properties can be amplified by CWI, and its accuracy can reach up to \(2\times 10^{-5}\)[6]. It is feasible to estimate stress using CWI according to the correlation between the coda wave velocity and microcracks [20].  
This paper discussed the mechanism of detecting the stress of concrete using the CWI technique. A correlation model of sound velocity and stress in concrete based on the acoustic elasticity theory was proposed. An experimental study was conducted to measure the changes of wave velocity in the concrete under stress according to the CWI technique. Overall, this paper provided a new approach for stress estimation in concrete structures.