## 1 Introduction  
The elastic modulus of concrete is an important factor for the trustworthy design, construction, and maintenance of structures, and can predict the deformation in an actual stress state [1; 2]. The static elastic modulus (_Ec_) of concrete uses the secant elastic modulus of the stress-strain curve as obtained by ASTM C469. However, a large number of specimens is required to obtain a reliable representative value, and it is difficult to provide a sufficient assessment, owing to constraints on time and the difficulty of testing [3; 4]. One alternative method comprises obtaining a dynamic elastic modulus (_Ed_), while resonance frequency test and ultrasonic pulse velocity method can be applied according to ASTM C215 and ASTM C597, respectively [5; 6]. Among ultrasonic test methods, a pressure wave (P-wave) measurement provides easy and convenient testing, but the distribution of the data is large, owing to uneven distributions of aggregates, moisture, and voids in the test piece. In addition, although a large correlation between _Ec_ and compressive strength (_fc_) has been reported as a result of using a shear wave (S-wave), which has a larger energy than a P-wave, it is difficult to measure and obtain consistent data (especially at low ages), owing to the influences of voids and moisture in the concrete [7; 8; 9; 10]. The resonance frequency test is known for consistently predicting the Ed with less fluctuation in the collected data, as it is simple to measure and grasps the overall dynamic characteristics of the specimen. The resonance frequency test assumes that the concrete has a homogeneous elastic modulus, density, Poisson's ratio, etc., and uses a method to calculate a theoretical elastic modulus for an initial stress range [6, 11]. In the ASTM, the relationship between the dynamic modulus for the longitudinal (LT) and transverse (TR) modes was proposed using physical parameters such as the dimensions, mass, and first resonance frequency (\(f1\)) [6]. [PERSON] et al. applied f1 and the second resonance frequency (\(f2\)) of the LT mode in the Rayleigh Ritz theory, proposing a general equation for the Ed and dynamic Poisson's ratio [11]. The _Eds_ measured by these non-destructive examination (NDE) methods were larger than the value of _Ec_, and several empirical equations for predicting _Ec_ through a certain reduction in the _Ed_ ratio have been proposed [12, 13, 14]. However, the _Ed_ measured according to the NDE method has a large deviation and degree [10]. In addition, the _Ed_ measured with the resonance frequency test has been assumed to be the initial chord elastic modulus (_Ei_), owing to the deformation of an initial very small stress in the stress-strain curve. Nevertheless, concrete is a nonhomogeneous, inelastic material, and thus the value of _Ed_ as measured with the theoretical equation such as ASTM's is different from the actual Ei value [10]. In previous studies, the _Ei_ was defined as a slope in the range of 10-50 \(\upmu\) in the stress-strain curve, and was compared to _Ed_ and _Ec_. The modulus of elasticity was _Ed_ \(>\)_Ei_ (10 \(\upmu\)-50 \(\upmu\)) \(>\)_Ec_, and it was determined that there was a difference of 11.62% between the _Ec_ and _Ei_. [15]. However, if the range of _Ei_ is set to (10-50 \(\upmu\)) as in the previous studies, the correlation with _Ec_ may be small, as the measured value in the initial part of the stress-strain curve is unstable, and has high variation [9, 16]. Therefore, if the correct _Ei_ value is extracted, the correlation of _Ei_-_Ec_ is expected to be greater than that of _Ed_-_Ec_. To overcome the limitations of the fracture test and predict _Ec_ more accurately, a non-destructive method for accurately predicting _Ei_ is required.