Advances in Materials Science and Engineering

Volume 2017 (2017), Article ID 1651753, 13 pages

https://doi.org/10.1155/2017/1651753

## Evaluating the Dynamic Elastic Modulus of Concrete Using Shear-Wave Velocity Measurements

^{1}R&D Center, JNTINC Co. Ltd., 9 Hyundaikia-ro, 830 Beon-gil, Bibong-Myeon, Hwaseong, Gyeonggi-do 18284, Republic of Korea^{2}Department of Architectural Engineering, Dong-A University, 37 Nakdong-Daero, 550 Beon-gil, Saha-gu, Busan 49315, Republic of Korea^{3}Department of Safety Engineering, Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon 22012, Republic of Korea^{4}Department of Civil Engineering, Chungnam National University, 99 Daehak-ro, Yuseong-gu, Daejeon 34134, Republic of Korea

Correspondence should be addressed to Seong-Hoon Kee; rk.ca.uad@eekhs

Received 4 January 2017; Revised 27 April 2017; Accepted 2 May 2017; Published 24 July 2017

Academic Editor: Giorgio Pia

Copyright © 2017 Byung Jae Lee 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

The objectives of this study are to investigate the relationship between static and dynamic elastic moduli determined using shear-wave velocity measurements and to demonstrate the practical potential of the shear-wave velocity method for in situ dynamic modulus evaluation. Three hundred 150 by 300 mm concrete cylinders were prepared from three different mixtures with target compressive strengths of 30, 35, and 40 MPa. Static and dynamic tests were performed at 4, 7, 14, and 28 days to evaluate the compressive strength and the static and dynamic moduli of the cylinders. The results obtained from the shear-wave velocity measurements were compared with dynamic moduli obtained from standard test methods (P-wave velocity measurements according to ASTM C597/C597M-16 and fundamental longitudinal and transverse resonance tests according to ASTM C215-14). The shear-wave velocity measured from cylinders showed excellent repeatability with a coefficient of variation (COV) less than 1%, which is as good as that of the standard test methods. The relationship between the dynamic elastic modulus based on shear-wave velocity and the chord elastic modulus according to ASTM C469/C469M was established. Furthermore, the best-fit line for the shear-wave velocity was also demonstrated to be effective for estimating compressive strength using an empirical relationship between compressive strength and static elastic modulus.

#### 1. Introduction

In the design of structures, the elastic modulus of concrete () is a fundamental parameter in estimating the deformation of a structural element under service conditions. In practice, has been estimated from compressive strength based on the design code rather than on direct measurement. This practice could underestimate and demand higher compressive strength to achieve a desired than is actually required in structural design [1]. Furthermore, has been demonstrated to be an effective parameter for condition assessment of concrete in existing structures [2, 3]. Destructive tests such as core extraction have been used widely to acquire accurate information on elastic properties of concrete. However, they are labor-intensive and time-consuming and cannot be applied ubiquitously over the entire area of the structure.

There are several nondestructive evaluation (NDE) methods to estimate elastic properties of concrete including ultrasonic pulse velocity measurements according to ASTM C597/C597M-16 [4] and resonance frequency tests according to ASTM C215-14 [5]. The elastic modulus determined by NDE methods is typically called the dynamic elastic modulus, which is generally greater than static elastic modulus measured in accordance with ASTM C469/C469M-14 [6]. Dynamic modulus has been assumed to be initial tangent modulus at zero stress determined in the standard test because only negligible stress is applied during ultrasonic pulse velocity (UPV) measurements and resonance frequency tests [7]. Philleo [8] also explained that the difference between dynamic and static moduli is based on the fact that the nonhomogeneous characteristics of concrete affect the two moduli in different ways. Moreover, the difference between the two moduli decreases as concrete strength increases: the dynamic elastic modulus is generally 20, 30, and 40% higher than the static elastic modulus for high-, medium-, and low-strength concrete, respectively [2]. Lydon and Balendran [9] proposed an empirical relationship as follows:The British testing standard BS8100 Part 2 [10] provides another empirical equation as follows: It is noteworthy that this equation does not apply to concrete containing more than 500 kg of cement per cubic meter of concrete or to lightweight aggregate concrete [7]. A more general relationship was proposed by Popovics [11] for both lightweight and normal density concrete, taking into account the effect of concrete density as follows: where is the density of the hardened concrete in a unit of kg/m^{3}.

The two standard NDE methods for evaluation of dynamic elastic modulus have advantages and limitations. The P-wave velocity method is convenient to use and has clear advantages over the resonance method in that the testing is not confined to regularly shaped laboratory specimens and results are not sensitive to inelastic effect [8]. P-waves move particles parallel to the direction of propagation and can propagate through media with enough lateral stiffness: they thus can propagate in solid, liquid, and gas media. Consequently, P-wave velocity in porous materials is affected by the properties of three difference phases in the media. Dynamic elastic modulus determined by P-wave velocity measurements has been known to possess the characteristics of concrete, heterogeneous, and porous material, such as type of aggregate, water content, air voids, and porosity compared with the static elastic modulus. In addition, P-wave velocity values depend on confinement conditions in solid media: the P-wave velocities in unbounded solid media (), thin plates (), and thin rods () are called constrained, partially constrained, and unconstrained compressive wave velocities, respectively, and are expressed as the following equations [12]:Figure 1 shows the variations of P-waves with Poisson’s ratio for elastic homogeneous and isotropic media. Given Poisson’s ratio, P-wave velocity is in a range between unconstrained and constrained velocities [13]. P-wave velocity increases with increasing the degree of confinement, and the confinement effect increases as Poisson’s ratio increases. In the field practice, however, it is sometimes not easy to evaluate accurate dynamic elastic moduli from P-wave velocity measurements because of difficulties in estimating the confinement effect in the field and the absence of theoretical or practical formula relating P-wave velocity and dynamic elastic modulus that takes into account the confinement effect. In this sense, some of previous researchers argue that the P-wave velocity method is nonreliable and not recommended for estimating the dynamic elastic modulus of concrete [1, 7, 14]. In contrast, resonance frequency testing has been used widely to evaluate the dynamic elastic modulus of concrete, which is less sensitive than P-wave velocity. However, resonant frequency testing necessarily needs regularly shaped concrete specimens; thus, in situ application of this method is labor-intensive and time-consuming and is inappropriate for general application over the entire area of a structure.