**1. Introduction**

During the design, construction, and maintenance of concrete structures, static elastic modulus (*Ec*) and compressive strength (*fc*) are critical properties for analyzing structural stability parameters such as member force, stress, deflection, and displacement [1,2]. In addition, these properties are indicators of concrete deterioration. Therefore, *Ec* and *fc* have been used to evaluate the conditions of structures such as pavements and bridge decks. The specimen cores of existing concrete structures are typically extracted and tested to determine *Ec* and *fc,* according to the recommended ASTM C469/C469M-14 guidelines. *Ec* is typically predicted from *fc*; however, this yields a relatively large error [3]. The standard testing methods for determining *Ec* and *fc* cannot be used to evaluate the entire area, owing to the need for test permissions and several specimens. Furthermore, the values of *Ec* and

*fc* vary at di fferent locations in the concrete structure, and these di fferences may increase with aging. Therefore, it is necessary to determine *Ec* and *fc* using a nondestructive evaluation (NDE) method that can be applied at several locations in a structure without damaging the structure.

The elastic modulus measured using the NDE method is generally called the dynamic elastic modulus (*Ed*). Ultrasonic pulse velocity (UPV) measurements based on the ASTM C597/ASTM C597M-16 guidelines and resonance frequency tests conducted in accordance with the ASTM C215-14 specifications are used to determine *Ed* [4,5]. As for ASTM C215, Subramaniam et al. have improved the standard equation using the second resonance frequency as well as the first. Although it has the advantage of finding the dynamic Poisson ratio, its accuracy is insignificant [6]. The *Ed* determined with the NDE method is generally higher than the *Ec* obtained by following the ASTM C469/C469M-14 recommendations [7]. The *Ed* determined with the P-wave measurement was the largest, and the *Ed* determined with the resonant frequency test was located in the middle compared to *Ec* [8,9]. The *Ed* value with the S-wave measurement was more correlated with *Ec* and *fc* than the *Ed* using the P-wave measurement and resonant frequency [10]. However, the S-wave is di fficult to measure, and the dispersion of the measured values may be large at a low age. Additionally, it is more di fficult to predict the properties of early aged and low-strength concrete (which include moisture and voids) and high-strength concrete. It has been known that the static modulus (secant modulus of elasticity) determined by the destructive test according to ASTM C469 and the dynamic modulus determined by non-destructive tests such as ASTM C597 and ASTM C215 have a nonlinear proportional relationship, and the static modulus is 10–20% less than the dynamic modulus [11]. Since the dynamic modulus is determined by the slope at a very low stress range, it is less statistically stable than the elastic modulus, but it has the advantage of being simple to test without the damaging of the specimen [12]. Therefore, it is essential to develop a method that can be used to more accurately predict *Ec* from *Ed* because it is di fficult to measure all the specimens with the destructive test.

Various equations have been proposed for predicting *Ec* based on *Ed*. For example, Lydon and Balendran, BS 8110 Part 2, and Popovics proposed empirical equations for predicting *Ec* from *Ed,* using the NDE method [11–13]. Among previously proposed equations, the BS 8110 Part 2 equation yields similar values to the *Ed* value measured using the UPV through P-waves, and the Popovics equation provides results that are similar to *Ed* obtained through resonance frequency tests using longitudinal and transverse modes [10]. In addition, the Lydon and Balendran results are lower than those obtained using other equations [9]. Most of the previous studies attempted to relate Ec values with Ed values using statistical regression analysis such as linear or nonlinear regression [8]. However, these equations may lead to a significant error in predicting *Ec* if the Ed value obtained from another test method is used. As described above, because the deviation and the degree of change in the *Ed* value di ffers significantly for each NDE method, it is di fficult to apply these equations for the accurate prediction of *Ec*.

Additionally, correlation equations have been proposed by CEB-FIP, the ACI 318 Committee, and the ACI 363 Committee as methods for predicting *fc* using *Ed* [14–16]. However, when predicting *fc* using *Ed*, the prediction error may increase in a step-by-step relational expression because the procedures for predicting *Ec* in *Ed* and *fc* in *Ec* are employed. Therefore, it is necessary to apply a method that can solve the problems of the existing prediction of linear regression and predict *Ec* and fc more accurately by utilizing various *Ed* that can be obtained through experiments. Recently, Chavhan and Vyawahare [17] proposed a study to predict fc from *Ed* with P-wave velocity tests but did not obtain a good relationship, even with only 22 specimens. Thus, for the relationship between *Ec* or fc and *Ed,* the classical or regression equations could not give an accurate estimation for *Ec* from *Ed* because the *Ed* value di ffers according to the test method [18]. Additionally, there exists considerable nonlinearity between *Ec* or *fc* and *Ed* [19].

In this regard, the machine learning (ML) technology has been applied and improved in many areas of concrete, but it has been used to predict *Ec* and *fc* limitedly with various components [20], to establish a correlation between *Ec* and fc [21], and to estimate fc from ultrasonic velocity and

rebound hardness [22]. Furthermore, the estimation of *Ec* or fc from *Ed* has been little studied due to the difficulties in testing enough specimens. Thus, these studies have focused on obtaining more accurate predictions of concrete strength and conditions using (ML) algorithms such as support vector machine (SVM), ensemble, and artificial neural networks (ANNs) [21–24].

In most studies, ML methods contributed to predicting fc with higher accuracy than conventional linear regression methods. In addition, it was used to predict the characteristics of concrete using various variables as follows. Erdal et al. used an ANN and ensemble for comparing the accuracy of strength prediction for high-performance concrete, and the method of applying the ensemble was found to be slightly better [25]. Yuvaraj et al. confirmed the applicability of several variables to the SVM model by predicting the fracture characteristics of concrete beams according to the ratio of concrete mixtures from the SVM model [26]. Yan and Shi used four theoretical equations, linear regression, and ANN and SVM models to confirm the accuracy of *Ec* prediction with *fc*, and the ANN and SVM methods were found to be the best methods [27]. Cihan employed SVM, ANN, and ensemble to predict the compressive strength and slump value of concrete, and reported that ANN and ensemble were better than SVM [28]. Young et al. employed SVM, ANN, and linear regression (LR) to estimate 28-day intensity from 10,000 data with varying mixing ratios and reported that ANN and SVM were more accurate than LR [29]. Among the many ML methods, the SVM, ANN, ensemble, and LR methods contributed to the prediction of concrete quality using various variables. However, previous studies only considered cases such as the prediction of strength and the modulus of elasticity using different combinations of materials, ultrasonic pulse velocity, and *fc*. Very few studies have attempted to predict *Ec* and *fc* using two or more *Eds* and ML.

In this study, various combinations were used to overcome the differences in the characteristics of the eigen-data of *Eds* through the ML methods and to confirm the possibility of predicting actual *Ec* and *fc* values more accurately than conventional linear equations. Various *Ed* values were obtained with UPV measurements and resonance frequency tests. Additionally, by determining the S-wave velocity (*Vs*), according to the recommended guidelines of ASTM C215-14 and ASTM C597M-16 and by determining *Ed* using *Vs*, the differences with respect to existing *Ed* values were verified and then utilized to improve the accuracy of the prediction. Four ML methods—SVM, ANN, ensemble, and LR—were trained on four *Ed* datasets, and a five-fold validation was performed to prevent the overfitting of the prediction results. Subsequently, the predicted and measured values for *Ec, fc*, and Ed were compared using the mean squared error (MSE) and mean absolute percentage error (MAPE). Thus, this study aimed to confirm how much accuracy can be improved compared to that obtained with the classical and regression equation by predicting *Ec* and *fc* directly from the Ed value, which is a representative property value in the non-destructive testing method, associated with ML. An attempt was made to predict exactly how much and how the *Ec* and *fc* values will be affected not only by the four ML methods that can predict Ed but also by a combination thereof.

### **2. Materials and Methods**

### *2.1. Materials and Preparation of Specimens*

The concrete specimens were composed of Type I Portland cement, river sand, crushed granite with a size of up to 25 mm, and supplementary cementitious materials (SCMs), i.e., fly ash and slag cement. The concrete of this study replaces about 50% of the cement with fly ash (FA) and Granulated Blast Furnace Slag (GBFS), and is composed of a mixture that causes the development of the initial strength to be slow at a low age but the long-term strength to be high. It is mainly used in mass concrete that generates less heat of hydration and requires long-term strength. Two water/binder (W/B) ratios of 0.45 and 0.35 were used, which were expected to achieve 28-day target compressive strength values of 20 MPa and 40 MPa, respectively. Two concrete mixture groups—Mix 1 and Mix 2—were prepared; the proportions of these mixture groups are presented in Table 1. Two hundred and ninety-five concrete specimens were cast using 150 mm × 300 mm plastic molds, in accordance

with the ASTM C31/C31M-12 specifications [30]. The specimens were removed from the molds after 24 h and then cured in water. *Ed, Ec*, and *fc* tests were performed at the different curing ages of 4, 7, 14, and 28 d. The 28-day average compressive strengths for Mixes 1 and 2 were 19.19 MPa and 43.94 MPa, respectively.


**Table 1.** Proportions of the concrete mixture groups 1.

1 SCMs: Supplementary cementitious materials, W: water, C: cement, S: sand, G: crushed cobblestone, FA: fly ash, SC: slag cement, AE: air-entraining agent, and SP: superplasticizer.

### *2.2. Static Tests for Elastic Modulus and Compressive Strength*

As a pretest preparation procedure, both ends of each specimen were polished and kept perpendicular to the measurement by removing protrusions on the specimen surface. The *Ec* and *fc* values of each specimen were determined using a universal testing machine (UTM, Instron, Norwood MA, USA) with a capacity of 1000 kN, according to the ASTM C469/C469M-14 and ASTM C39/C39M-14a specifications (Figure 1) [7,31]. The UTM was operated at a loading speed of approximately 0.28 MPa/s.

**Figure 1.** Experimental setup for determining static elastic modulus and compressive strength of concrete specimens.

### *2.3. P- and S-Wave Measurements for Calculating Dynamic Elastic Modulus*

The P-wave velocity (*Vp*) was determined according to the ASTM C597M-16/C597M-16 recommendations, using a pair of P-wave transducers (MK 954, MKC Korea, Seoul, Korea) connected to a pulser-receiver (Ultracon 170, MKC Korea, Seoul, Korea) [4]. Figure 2a depicts the method of determining *Vp* using a receiving transducer. A longitudinal pulse of 52 kHz was transmitted through the specimens' interior, and the *Vp* values of the concrete specimens were determined. The measured signal was digitized to a sampling frequency of 10 MHz using an oscilloscope (NI-PXIe 6366, National Instruments, Austin, TX, USA). The *Ed* based on *Vp* is expressed as Equation (1):

$$Ed.Vp = \frac{(1+\nu)(1-2\nu)}{(1-\nu)}\rho V\_p^2 \tag{1}$$

where *Ed.Vp* is the *Ed* of the specimen for the experimentally measured *Vp*, and ρ is the mass density of the concrete; it is equal to m/2πrL. *m*, *r*, and *L* are the mass, radius, and length of the specimens, respectively. A Poisson's ratio (ν) of 0.2 was used, which is the typical value for ordinary concrete.

**Figure 2.** Methods for measuring (**a**) ultrasonic pulse velocity using a P-wave transducer (MK 954) and (**b**) ultrasonic shear-wave velocity using an S-wave transducer (ACS T1802).

The S-wave velocity *(Vs)* was determined using the measurement procedure for *Vp*. The measurement of *Vs* was similar to that of *Vp*, except that a pair of S-wave transducers (ACS T1802, ACS Group, Saarbrücken, Germany) were used. The signal driven using the pulsar was converted to a pulse in the transverse mode by the transducer and passed through the specimen. The signal measured using the receiving transducer was digitized using the oscilloscope. Figure 2b presents the method of measuring *Vs* and the ultrasonic signal measured using the S-wave receiver. The arrival of a stress wave through the specimen was determined based on the signals measured using a modified threshold method [32]. In this method, the approximate arrival time was first obtained using a threshold method [33]. Thereafter, the exact arrival time required to fit the line to a single datum was calculated. The S-wave travel time was defined at the intersection between the calculated zero signal level and the fitting line. Finally, *Vs* was calculated by dividing the length of the specimen (*L*) by the travel time (*t*) (*Vs* = *L*/*t*). In this study, the *Ed* based on *Vs* is expressed as Equation (2):

$$Ed.Vs = 2(1+\nu)\rho V\_s^2\tag{2}$$

where *Ed*.*Vs* is the *Ed* of the concrete specimen for the measured *Vs*, and ν is the Poisson's ratio.

### *2.4. Resonance Frequency Tests for Calculating Dynamic Elastic Modulus*

The fundamental longitudinal and transverse resonance frequencies of the concrete specimens were determined to calculate the *Ed* value according to the ASTM C215-14 guidelines (Figure 3) [5]. A steel ball hammer with a diameter of 10 mm was used to generate stress waves in the concrete specimens through impact. The use of the steel ball hammer was effective in generating significantly low to 20 kHz frequency signals during the resonance frequency tests. The dynamic responses of the concrete specimens were measured using an accelerometer (PCB 353B16, PCB, Erie County, NY, USA) with a resonance frequency of approximately 70 kHz and an error of 5%, within the range of 1 to 10 kHz. The signals measured using the accelerometer were stabilized using a signal conditioner (PCB 482C16, PCB, Erie County, NY, USA) and digitized at a sampling frequency of 1 MHz using an oscilloscope (NI-PXIe 6366). The time signal was transformed into the frequency domain through a fast Fourier transform algorithm. The resonance frequency had the largest amplitude in the amplitude spectrum, and the frequency corresponding to the largest amplitude was considered as the fundamental resonance

frequency in the longitudinal and transverse modes. The *Ed* based on this resonance frequency is defined using Equations (3) and (4):

$$Ed.LT = \alpha\_{LT} m f\_{LT}^2 (Pa) \tag{3}$$

$$\text{Ed.TR} = \alpha\_{TR} \mathfrak{m} f\_{TR}^2 (Pa) \tag{4}$$

where *Ed.LT* and *Ed.TR* are calculated using *fLT* and *fTR*, respectively, as the fundamental resonance frequencies. α*LT* has a constant value depending on the dimensions of the specimen (5.093 (*L*/*d*2)), where *L* is the length and d is the diameter. α*TR* has a constant value, and its value depends on the +Poisson's ratio and specimen dimensions (1.6067 (*L*3*T*/*d*4)), where *T* is the correction factor of the Poisson's ratio according to ASTM C215-14 [5], and m is the mass of the specimen in kg.

**Figure 3.** Resonance frequency test for (**a**) longitudinal mode and (**b**) transverse mode.

### **3. ML Techniques**
