Effect of Moisture Distribution on Velocity and Waveform of Ultrasonic-Wave Propagation in Mortar

materials

Article Effect of Moisture Distribution on Velocity and Waveform of Ultrasonic-Wave Propagation in Mortar

Shinichiro Okazaki 1,* , Hiroma Iwase 2, Hiroyuki Nakagawa 3, Hidenori Yoshida 1 and Ryosuke Hinei 4

1 Faculty of Engineering and Design, Kagawa University, 2217-20 Hayashi, Takamatsu, Kagawa 761-0396, Japan; [email protected] 2 Chuo Consultants, 2-11-23 Nakono, Nishi-ku, Nagoya, Aichi 451-0042, Japan; [email protected] 3 Shikoku Research Institute Inc., 2109-8 Yashima, Takamatsu, Kagawa 761-0113, Japan; [email protected] 4 Building Engineering Group, Civil Engineering and Construction Department, Shikoku Electric Power Co., Inc., 2-5 Marunouchi, Takamatsu, Kagawa 760-8573, Japan; [email protected] * Correspondence: [email protected]

Abstract: Considering that the ultrasonic method is applied for the quality evaluation of concrete, this study experimentally and numerically investigates the effect of inhomogeneity caused by changes in the moisture content of concrete on ultrasonic wave propagation. The experimental results demonstrate that the propagation velocity and amplitude of the ultrasonic wave vary for different moisture content distributions in the specimens. In the analytical study, the characteristics obtained experimentally are reproduced by modeling a system in which the moisture content varies between the surface layer and interior of concrete.

Keywords: concrete; ultrasonic; water content; elastic modulus

Citation: Okazaki, S.; Iwase, H.; 1. Introduction Nakagawa, H.; Yoshida, H.; Hinei, R. Effect of Moisture Distribution on As many infrastructures deteriorate at an early stage, long-term structure management Velocity and Waveform of is required. If structural deterioration can be detected as early as possible, the scale of Ultrasonic-Wave Propagation in repair can be reduced, decreasing maintenance costs [1]. In recent years, nondestructive Mortar. Materials 2021, 14, 790. testing has been employed to estimate the cause of deterioration and objectively evaluate https://doi.org/10.3390/ma14040790 the progress of deterioration without compromising the durability of the structure. There are various nondestructive testing methods, including the impact elastic wave method [2,3], Academic Editor: Mikołaj Mi´skiewicz X-ray transmission [4,5], electromagnetic radar [6–8], and acoustic emission [9–11]. The Received: 7 January 2021 ultrasonic test method is also used for concrete inspection [12–14], taking advantage of its Accepted: 29 January 2021 better propagation when the object is densely concentrated, and the density distribution Published: 7 February 2021 is stable. The propagation properties of elastic waves in a material vary depending on the Publisher’s Note: MDPI stays neutral density and elastic modulus [15,16], and the propagation velocity correlates with the qual- with regard to jurisdictional claims in ity and strength of the material [17]. Therefore, the propagation properties of ultrasonic published maps and institutional affil- waves can be used to estimate the internal state of the target material, and this method iations. is attracting attention as an effective method for measuring internal defects in the field of concrete inspection [18–20]. However, concrete is an inhomogeneous material, which contains several voids, cracks, and coarse aggregates, and its density distribution is nonuniform [21,22]. In addition, ultrasonic waves propagate in a complicated pattern due to Copyright: © 2021 by the authors. reflection, confusion, diffraction, interference, etc., when they approach discontinuities [23]. Licensee MDPI, Basel, Switzerland. Therefore, the propagation of ultrasonic waves in concrete has not been clarified, and This article is an open access article the range of application and usefulness of the ultrasonic method for concrete inspection distributed under the terms and remains unclear. Thus, there are many problems to be solved for improving the defect and conditions of the Creative Commons quality evaluation of concrete using the ultrasonic method. Attribution (CC BY) license (https:// The enhancement of the measurement accuracy of the ultrasonic method, which has a creativecommons.org/licenses/by/ relatively high detection accuracy, has been extensively researched [18–20]. In concrete, the 4.0/).

Materials 2021, 14, 790. https://doi.org/10.3390/ma14040790 https://www.mdpi.com/journal/materials Materials 2021, 14, 790 2 of 14

relationship between elastic-wave propagation and the Young’s modulus has been widely reported because concrete is strongly affected not only by chemical degradation such as alkali-aggregate reactions [24], but also by changes in the mechanical properties such as long-term increase in the strength, drying shrinkage, and increase in creep deformation. There are two types of ultrasonic test methods: the transmission method, which utilizes the wave propagation time through concrete, and the reflection method, which utilizes the propagation time of the diffracted waves. In the transmission method, the relationship between the propagation velocity of longitudinal waves and the Young’s modulus has been widely reported. Recently, a method for calculating the Poisson’s ratio and Young’s modulus of a specimen based on the propagation velocity of longitudinal and transverse waves has been investigated [25]. Furthermore, Abeele et al. reported the variation of the Young’s modulus and Poisson’s ratio of concrete with time, from a young age [26]. The Young’s modulus of concrete increases linearly with the increase in water content [27,28]. Furthermore, Whitman et al. reported that the Young’s modulus of hardened cement decreases with the decrease in the equilibrium relative humidity, reaches a minimum value at a specific relative humidity, and increases again at lower humidity [29]. Sereda et al. reported that the Young’s modulus of hardened cement does not change at relative humidity ranging from 0–50% during the adsorption process but increases in the high- humidity region [30]. Maruyama and Igarashi et al. measured the Young’s modulus through ultrasonic and direct tensile testing by placing specimens in different equilibrium relative humidity environments and decreasing the relative humidity [31,32]. It was confirmed that the Young’s modulus decreased accordingly. Ultrasonic testing showed a minimum value around 40% relative humidity, the Young’s modulus increased again in the region below 40%, and the Si-O chain length of CSH increased due to drying in the solid phase. Thus, there is currently no unified view on the change in the Young’s modulus of concrete and hardened cement with drying. Therefore, the effect of the internal state and heterogeneity of concrete, due to changes in the moisture content, on the propagation of ultrasonic waves remains unclear. As concrete is a composite material containing voids, cracks and coarse aggregates, several factors can affect the propagation of ultrasonic waves. Hence it is necessary to clarify whether the change in the ultrasonic-wave propagation properties is due to the water content, coarse aggregate, or voids, and understand the effect of the heterogeneity within concrete on the ultrasonic-wave propagation properties. In this study, mortar specimens without coarse aggregate were prepared and ultrasonic testing was performed. The objective of this study was to understand the effect of the water content of the specimen on the propagation characteristics of ultrasonic waves by storing the specimen in a thermostatic dryer and conducting ultrasonic tests during the transition from the saturated to dry state. In addition, by simulating the propagation of ultrasonic waves through finite element analysis with the numerical values obtained from ultrasonic testing, the effect of the internal and boundary conditions of concrete on the propagation characteristics of ultrasonic waves was investigated, and applicability of this method to concrete was examined.

2. Experimental Study 2.1. Materials and Specimen Preparation Concrete is a composite material comprising cement hydrates, aggregates, and voids, which affect ultrasonic-wave propagation. In this study, a mortar sample without coarse aggregate, which affects ultrasonic-wave propagation, was used mainly to investigate the relationship between the ultrasonic-wave propagation velocity and water content of the sample. Figure1 shows the mortar cylinder specimen ( ϕ 100 mm × 200 mm) used in the experiment. As materials, ordinary Portland cement (3.15 g/cm3) and crushed sandstone (2.60 g/cm3) were mixed at a volume ratio of 1:3.8 and W/C of 70%. To investigate the effect of internal voids on the ultrasonic propagation velocity and vibration reception waveform, the airﬂow of the sample was adjusted with an air-entraining agent, and the air content was set to 5%, 10%, and 14.5%, respectively. Materials 2021, 14, x FOR PEER REVIEW 3 of 15

(2.60 g/cm3) were mixed at a volume ratio of 1:3.8 and W/C of 70%. To investigate the effect of internal voids on the ultrasonic propagation velocity and vibration reception waveform, the airflow of the sample was adjusted with an air-entraining agent, and the air content was set to 5%, 10%, and 14.5%, respectively. The aim of this experiment is to understand the ultrasonic propagation properties of concrete with varying moisture content. Therefore, ultrasonic measurements were performed during a process where the specimen changed from wet to completely dry. The specimens were initially placed in water for at least a week, and the mass and ultrasound were measured after the specimens were wet. Further, the specimens were placed in a constant temperature drying oven at 40 °C, and ultrasonic measurements were performed periodically for a week until the specimens were completely dry. The moisture content of the specimens was calculated under wet and absolutely dry conditions. After removing the specimens from the constant-temperature drying oven to prevent the specimen temperature from affecting the ultrasonic measurements, the specimens were placed in a con- Materials 2021, 14, 790 stant-temperature oven at 20 °C for 24 h, and measurements were performed after3 ofthe 14 specimen temperature was constant. Each ultrasonic wave propagation test was repeated twice.

Figure 1. Test specimens.

2.2. WaveThe aimPropagation of this experimentMeasurement is to understand the ultrasonic propagation properties of concreteThe measuring with varying device moisture shown in content. Figure 2 Therefore,was used for ultrasonic the ultrasonic measurements measurements. were performedThe pendulum-based during a process generator where with the an specimen outer diameter changed of from 40 mm wet toand completely covibration dry. of The 0.5 specimensMHz was attached were initially to the placed sample in surface water forwith at gl leastycerin a week, paste. and It was the connected mass and ultrasoundto a PC for were measured after the specimens were wet. Further, the specimens were placed in a recording the ultrasonic-wave propagation◦ velocity and vibration reception waveform. constantThe applied temperature voltage was drying 30 V oven and atthe 40 samplinC, andg ultrasonic frequency measurements was 4096 times. were As performedultrasonic periodicallywaves are detected for a week at the until probe the specimenscenter, the weredistance completely used for dry. velocity The moisture measurement content was of the specimens was calculated under wet and absolutely dry conditions. After removing the the center distance between the two probes. Ultrasonic waves generate vibrations due to specimens from the constant-temperature drying oven to prevent the specimen temperature the piezoelectric effect, and the obtained vibration reception waveform is the electrical from affecting the ultrasonic measurements, the specimens were placed in a constant- variation (V). temperature oven at 20 ◦C for 24 h, and measurements were performed after the specimen temperature was constant. Each ultrasonic wave propagation test was repeated twice. 2.3. Experimental Results 2.2.2.3.1. Wave Effect Propagation of Air Content Measurement on Wave Propagation TheTable measuring 1 summarizes device the shown weight, in Figuremoisture2 was content, used forultrasonic-wave the ultrasonic propagation measurements. ve- Thelocity, pendulum-based and arrival timegenerator of the first with ultrasonic an outer wave diameter for each of air 40 content mm and of the covibration specimens. of 0.5Herein, MHz the was arrival attached time to was the defined sample surfaceas the time with from glycerin the generation paste. It was of the connected wave from to a PCthe fortransmitter recording to the the ultrasonic-wave arrival of the first propagation wave at the velocity pendulum. and vibration The time reception of the onset waveform. of the Thefirst appliedwave, obtained voltage wasat the 30 pendulum, V and the samplingwas measured frequency visually. was Ultrasonic-wave 4096 times. As ultrasonic propaga- wavestion testing are detected was performed at the probe on the center, same theday distance for the three used specimens for velocity with measurement different air was the center distance between the two probes. Ultrasonic waves generate vibrations due to Materials 2021, 14, x FOR PEER REVIEW the piezoelectric effect, and the obtained vibration reception waveform4 of is 15 the electrical

variation (V).

(a) (b)

FigureFigure 2. Measurement 2. Measurement (a) setup (a and) setup (b) test and specimen. (b) test specimen.

content, with a total of six measurements. Measurement day 1 was under the wet condition, whereas date 2–6 were during the subsequent drying process. Even on the same measurement day, the ultrasonic propagation velocity differed between samples with different air contents. The propagation velocity decreased in the order of 5%, 10%, and 14.5% of the specimen air content, and the same trend was observed on all the measurement days. However, even on the same measurement day, the moisture content of each specimen was slightly different. Comparing specimens with the same moisture content, it was determined that the ultrasonic-wave propagation velocity tended to decrease with the air content in the specimen. If the air content in the sample is more, there are more pores in the ultrasonic-wave propagation path, and the wave may be reflected and scattered in the voids and attenuated. Figure 3a,b displays the waveforms of the test specimens obtained on date 1 and 6, respectively. There were no significant differences in the vibration reception waveforms of the three specimens due to different airflow on the measurement days. This is because a mortar specimen was used in this experiment, which did not contain coarse aggregate that would affect the propagation of ultrasonic waves. In the case of concrete, reflection and scattering may occur because of the arrangement of coarse aggregates with different Young’s moduli, and the vibration receiving waveform tends to be different for each specimen; however, in this experiment, the internal structure of each specimen is almost the same. It is considered that the same vibration receiving waveform was obtained by the mortar.

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2.3. Experimental Results 2.3.1. Effect of Air Content on Wave Propagation Table1 summarizes the weight, moisture content, ultrasonic-wave propagation velocity, and arrival time of the first ultrasonic wave for each air content of the specimens. Herein, the arrival time was defined as the time from the generation of the wave from the transmitter to the arrival of the first wave at the pendulum. The time of the onset of the first wave, obtained at the pendulum, was measured visually. Ultrasonic-wave propagation testing was performed on the same day for the three specimens with different air content, with a total of six measurements. Measurement day 1 was under the wet condition, whereas date 2–6 were during the subsequent drying process. Even on the same measurement day, the ultrasonic propagation velocity differed between samples with different air contents. The propagation velocity decreased in the order of 5%, 10%, and 14.5% of the specimen air content, and the same trend was observed on all the measurement days. However, even on the same measurement day, the moisture content of each specimen was slightly different. Comparing specimens with the same moisture content, it was determined that the ultrasonic-wave propagation velocity tended to decrease with the air content in the specimen. If the air content in the sample is more, there are more pores in the ultrasonic-wave propagation path, and the wave may be reflected and scattered in the voids and attenuated. Figure3a,b displays the waveforms of the test specimens obtained on date 1 and 6, respectively. There were no significant differences in the vibration reception waveforms of the three specimens due to different airflow on the measurement days. This is because a mortar specimen was used in this experiment, which did not contain coarse aggregate that would affect the propagation of ultrasonic waves. In the case of concrete, reflection and scattering may occur because of the arrangement of coarse aggregates with different Young’s moduli, and the vibration receiving waveform tends to be different for each specimen; however, in this experiment, the internal structure of each specimen is almost the same. It is considered that the same vibration receiving waveform was obtained by the mortar.

Table 1. Experimental results.

Air Content Weight Water Content Propagation Velocity Arrival Time Lapsed Day Date (%) (g) (%) (m/s) (µs) 0 3263.7 10.5 3919.8 51.0 1 7 3065.5 4.7 3730.9 53.6 2 13 3009.2 2.9 3679.2 54.4 3 5 20 2974.0 1.8 3600.8 55.5 4 29 2945.1 0.8 3466.4 57.7 5 35 2936.4 0.5 3434.4 58.2 6 0 3181.8 10.7 3911.6 51.1 1 7 2961.7 4.1 3693.8 54.1 2 13 2912.8 2.4 3636.0 55.0 3 10 20 2878.5 1.3 3545.8 56.4 4 29 2856.9 0.5 3447.1 58.0 5 35 2849.5 0.3 3434.4 58.2 6 0 3140.5 10.7 3862.8 51.8 1 7 2930.7 4.4 3679.2 54.4 2 13 2873.6 2.4 3607.8 55.4 3 14.5 20 2839.1 1.3 3512.3 56.9 4 29 2815.9 0.5 3428.0 58.3 5 35 2809.3 0.2 3415.4 58.6 6 Materials 2021, 14, x FOR PEER REVIEW 5 of 15

Table 1. Experimental results.

Air Content Weight Water Content Propagation Velocity Arrival Time Lapsed Day Date (%) (g) (%) (m/s) (μs) 0 3263.7 10.5 3919.8 51.0 1 7 3065.5 4.7 3730.9 53.6 2 13 3009.2 2.9 3679.2 54.4 3 5 20 2974.0 1.8 3600.8 55.5 4 29 2945.1 0.8 3466.4 57.7 5 35 2936.4 0.5 3434.4 58.2 6 0 3181.8 10.7 3911.6 51.1 1 7 2961.7 4.1 3693.8 54.1 2 13 2912.8 2.4 3636.0 55.0 3 10 20 2878.5 1.3 3545.8 56.4 4 29 2856.9 0.5 3447.1 58.0 5 35 2849.5 0.3 3434.4 58.2 6 0 3140.5 10.7 3862.8 51.8 1 7 2930.7 4.4 3679.2 54.4 2 13 2873.6 2.4 3607.8 55.4 3 14.5 20 2839.1 1.3 3512.3 56.9 4 Materials 2021, 14, 790 5 of 14 29 2815.9 0.5 3428.0 58.3 5 35 2809.3 0.2 3415.4 58.6 6

30,000 30,000 Air void ratio Air void ratio 5% 20,000 20,000 5% 10% 10% 14.5% 10,000 10,000 14.5%

0 0

-10,000 -10,000 Amplitude (mV)

-20,000 Amplitude-20,000 (mV)

-30,000 -30,000 0 50 100 150 200 0 50 100 150 200 Time (μsec) Time (μsec)

(a) (b)

Figure 3. Measured waveforms: (a) date 1 and (b) date 6.6.

2.3.2. Effect of Moisture Content on Wave PropagationPropagation Materials 2021, 14, x FOR PEER REVIEW 6 of 15 As shown in Table1 1,, thethe ultrasonicultrasonic velocityvelocity decreasesdecreases withwith thethe decreasedecrease inin waterwater content in in all all the the specimens, specimens, indicating indicating that that there there is a is relationship a relationship between between the water the water contentcontent and and ultrasonic ultrasonic velocity. velocity. Comparing Comparing the the propagation propagation velocities velocities of of the the wet wet and and dry specimens,Figure the5a–c difference compares in the velocityvelocity vibration waswas approximatelyapproximatelywaveforms of 480480specimens m/sm/s for withspecimens 5%, 10%, with and 5% and14.5% 10% air aircontent content, on measurement and approximately day 1 450(wet m/s condition) for for the the specimen specimenand day 6with with (dry 14.5% 14.5%condition). air air content. content. In the Figurewaveforms 44 shows shows for each thethe relationship relationshipair void ratio, betweenbetween there is the thea difference ultrasonic-waveultrasonic-wave of about propagationpropagation 10% in the water velocityvelocity content andand thebetween moisture day content.1 and day The The 6, andpropagation this effect velocity varies the increases arrival with time theof the increase ultrasonic. in moisturemoisture In each content,figure, the but but propagation the the gradient gradient velocity of of increase increase of the decreases decreases received when waveform when the the moisture decreases moisture content contentwith theexceeds exceeds decrease 2%. 2%. inIt isItmoisture isconfirmed conﬁrmed content. that that there In there addition, is no is nolinear linearthe relationwave relationship ampshiplitude between between of the the first, themoisture moisture second content and content third and and thewaves thede- creasedecreasehave increased. in inultrasonic ultrasonic This velocity. indicates velocity. However, that However, the differe as as th thereerence isin is a the alack lack moisture of of data data content in in the 5–10%of the specimen moisture contentaffects not range only in the this propagation experiment, velocity it is necessarynecess butary also to the conﬁrmconfirm wave thetheamplitude. trendtrend withinwithin thisthis range.range.

4000

3900

3800

3700

3600 Airvoid ratio=5% Airvoid ratio=10% 3500 Airvoid ratio=14.5% Propagation velocity Propagation (m/s)

3400 024681012 Water content (%)

Figure 4. Relationship between the water contentcontent and propagationpropagation velocity.velocity.

30,000 Figure5a–c30,000 compares the vibration waveforms of30,000 specimens with 5%, 10%, and 14.5%

20,000 air content on20,000 measurement day 1 (wet condition)20,000 and day 6 (dry condition). In the 3rd wave Day1 3rd wave Day1 3rd wave Day1 1st wave waveformsDays6 for each1st wave air void ratio, thereDays6 is a difference of about1st wave 10% in the waterDays6 content 10,000 10,000 10,000 between day 1 and day 6, and this effect varies the arrival time of the ultrasonic. In each 0 ﬁgure, the propagation0 velocity of the received waveform0 decreases with the decrease in -10,000 -10,000 -10,000

moisture content. In addition, the wave amplitudeAmplitudeof (mV) the ﬁrst, second and third waves Amplitude (mV) Amplitude-20,000 (mV) -20,000 -20,000 2nd wave 2nd wave 2nd wave -30,000 -30,000 -30,000 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 Time (μsec) Time (μsec) Time (μsec) (a) (b) (c) Figure 5. Comparison of the measured waveform on date 1 and 6: (a) 5%, (b) 10%, and (c) 14.5% air void ratio.

Figure 6a–c shows the relationship between the moisture content and amplitudes of the first to third vibration waveforms obtained in the experiment. The amplitude decreases with the decrease in moisture content and reaches a minimum value at approximately 1% moisture content. The amplitude increases in the range below 1%, and in the dry state, the amplitude increases to a value equal to or higher than that of the wet state. In particular, the amplitude is large in the wet and dry states, suggesting that the moisture content within the sample has an effect. As a characteristic of ultrasonic waves, reflection and scattering occur when the waves approach materials with unstable density distributions or discontinuities. Therefore, it is inferred that the moisture within the sample is unevenly distributed due to drying, and boundary surfaces with different densities and Young’s moduli are generated in the sample, causing some of the ultrasonic waves to be reflected and scattered, affecting the amplitude.

Materials 2021, 14, x FOR PEER REVIEW 6 of 15

Figure 5a–c compares the vibration waveforms of specimens with 5%, 10%, and 14.5% air content on measurement day 1 (wet condition) and day 6 (dry condition). In the waveforms for each air void ratio, there is a difference of about 10% in the water content between day 1 and day 6, and this effect varies the arrival time of the ultrasonic. In each figure, the propagation velocity of the received waveform decreases with the decrease in moisture content. In addition, the wave amplitude of the first, second and third waves have increased. This indicates that the difference in the moisture content of the specimen affects not only the propagation velocity but also the wave amplitude.

4000

3900

3800

3700

3600 Airvoid ratio=5% Airvoid ratio=10% 3500 Airvoid ratio=14.5%

Materials 2021, 14, 790 velocity Propagation (m/s) 6 of 14

3400 024681012 Water content (%) have increased. This indicates that the difference in the moisture content of the specimen affectsFigure not 4. Relationship only the propagation between the velocity water co butntent also and the propagation wave amplitude. velocity.

30,000 30,000 30,000

20,000 20,000 20,000 3rd wave Day1 3rd wave Day1 3rd wave Day1 1st wave Days6 1st wave Days6 1st wave Days6 10,000 10,000 10,000

0 0 0

-10,000 -10,000 -10,000 Amplitude (mV) Amplitude (mV) Amplitude-20,000 (mV) -20,000 -20,000 2nd wave 2nd wave 2nd wave -30,000 -30,000 -30,000 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 Time (μsec) Time (μsec) Time (μsec) (a) (b) (c)

FigureFigure 5. 5.Comparison Comparison of of the the measured measured waveform waveform on on date date 1 and1 and 6: 6: (a ()a 5%,) 5%, (b ()b 10%,) 10%, and and (c ()c 14.5%) 14.5% air air void void ratio. ratio.

FigureFigure6a–c 6a–c shows shows the the relationship relationship between between the the moisture moisture content content and and amplitudes amplitudes of of thethe first first to to third third vibration vibration waveforms waveforms obtained obtained in the in experiment. the experiment. The amplitude The amplitude decreases de- withcreases the decreasewith the indecrease moisture in contentmoisture and content reaches and a minimumreaches a minimum value at approximately value at approxi- 1% moisturemately 1% content. moisture The content. amplitude The increases amplitude in the increases range below in the 1%, range and below in the 1%, dry state,and in the the amplitudedry state, increasesthe amplitude to a value increases equal to to a orvalue higher equal than to or that higher of the than wet that state. of In the particular, wet state. theIn particular, amplitude the is large amplitude in the is wet large and in the dry we states,t and suggestingdry states, suggesting that the moisture that the contentmoisture withincontent the within sample the has sample an effect. has an As effect. a characteristic As a characteristic of ultrasonic of ultrasonic waves, waves, reflection reflection and scatteringand scattering occur whenoccur thewhen waves the waves approach approach materials materials with unstable with unstable density density distributions distribu- or discontinuities.tions or discontinuities. Therefore, Therefore, it is inferred it is that inferred the moisture that the within moisture the samplewithin the is unevenly sample is distributedunevenly distributed due to drying, due andto drying, boundary and surfacesboundary with surfaces different with densities different and densities Young’s and Materials 2021, 14, x FOR PEER REVIEWmoduli are generated in the sample, causing some of the ultrasonic waves to be reflected7 of 15 Young’s moduli are generated in the sample, causing some of the ultrasonic waves to be andreflected scattered, and affectingscattered, the affecting amplitude. the amplitude.

15,000 35,000 25,000 Air void ratio=5% Air void ratio=5% Air void ratio=5% Air void ratio=10% 30,000 Air void ratio=10% Air void ratio=10% 12,000 20,000 Air void ratio=14.5% Air void ratio=14.5% Air void ratio=14.5% 25,000

9,000 20,000 15,000

15,000 6,000 10,000 Amplitude (mV) Amplitude (mV) Amplitude (mV)

× 10,000

× 3,000 (-1) 5,000

5,000 (-1)

0 0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 Water content (%) Water content (%) Water content (%) (a) (b) (c)

FigureFigure 6.6.Comparison Comparison ofof thethe amplitudeamplitude andand waterwater content:content: ((aa)) ﬁrst,first, ( b(b)) second, second, and and ( c(c)) third third wave. wave.

3.3. AnalyticalAnalytical StudyStudy 3.1.3.1. ModelModel SetupSetup TheThe wavewave propagation propagation characteristics characteristics in an in inhomogeneous an inhomogeneous ﬁeld are field validated are validated through numericalthrough numerical analysis. Inanalysis. this study, In this the study, analytical the analytical model for model concrete for is concrete regarded is asregarded an elastic as body.an elastic The body. numerical The numerical integration integration method in meth whichod thein which equation the ofequation motion of is motion numerically is nu- integratedmerically integrated at small time at small intervals time intervals to obtain to the obtain solution, the solution, and the and mode the polymerization mode polymer- methodization method in which in the which linear the response linear ofresponse a multiple of a degree-of-freedom multiple degree-of-freedom system is expressed system is byexpressed the superposition by the superposition of each order of ofeach the order natural of vibration the natural mode vibration are typical mode methods are typical for analyzingmethods for the analyzing wave response. the wave In this response. study, aIn numerical this study, integration a numerical method integration was used. method The Newmark-was used. βThemethod, Newmark- whichβ method, is most extensivelywhich is most used extensively in seismic used response in seismic analysis, response was usedanalysis, for numericalwas used for integration. numerical The integration. ﬁnite element The finite model element (Figure model7a) and (Figure the ultrasonic7a) and the testultrasonic specimen test ( φspecimen100 mm (×ϕ 100200 mm mm) ×employed 200 mm) employed in the experiment in the experiment were used were for analysis. used for analysis. Because the diameter of the ultrasonic sensor (transducer and pendulum) used in the experiment was 40 mm, the range of the receiver and oscillator in the analysis was set to 40 mm. As the input waveform to the oscillator, based on the waveform input to the specimen in the ultrasonic test, a half-wavelength sinewave with a frequency of 200 kHz (see Figure 7b) was provided as a compression wave at the position corresponding to the oscillator, and the displacement was output at the position corresponding to the pendulum. In finite element analysis, the analysis results are highly dependent on the time increment dt per step of the analysis. Considering the computer performance and analysis time, we used the minimum number of steps without affecting the analysis accuracy. Based on the results of various investigations, we selected 0.2 µs per step. To simplify the problem, the attenuation of ultrasonic waves was not considered. In this study, we did not focus on reproducing the experimental data but on understanding the sensitivity of the effect of porosity and water content on elastic-wave propagation in concrete.

0.8 mm) -5

10 0.6 ×

0.4 Amplitude ( Amplitude

0.2

0 0246810 Time (μs) (a) (b) Figure 7. Analysis condition: (a) Model and (b) Input waveform.

Materials 2021, 14, x FOR PEER REVIEW 7 of 15

9,000 20,000 15,000

15,000 6,000 10,000 Amplitude (mV) Amplitude (mV) Amplitude (mV)

× 10,000 × 3,000 (-1) 5,000

5,000 (-1)

0 0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 0 0.0 2.0 4.0 6.0 8.0 10.0 12.0 Water content (%) Water content (%) Water content (%) (a) (b) (c) Figure 6. Comparison of the amplitude and water content: (a) first, (b) second, and (c) third wave.

3. Analytical Study 3.1. Model Setup The wave propagation characteristics in an inhomogeneous field are validated through numerical analysis. In this study, the analytical model for concrete is regarded as an elastic body. The numerical integration method in which the equation of motion is numerically integrated at small time intervals to obtain the solution, and the mode polymerization method in which the linear response of a multiple degree-of-freedom system is expressed by the superposition of each order of the natural vibration mode are typical

Materials 2021, 14, 790 methods for analyzing the wave response. In this study, a numerical integration method7 of 14 was used. The Newmark-β method, which is most extensively used in seismic response analysis, was used for numerical integration. The finite element model (Figure 7a) and the ultrasonic test specimen (ϕ 100 mm × 200 mm) employed in the experiment were used for analysis.Because Because the diameter the diameter of the ultrasonicof the ultras sensoronic sensor (transducer (transducer and pendulum) and pendulum) used inused the inexperiment the experiment was 40was mm, 40 mm, the rangethe range of the of receiverthe receiver and and oscillator oscillator in thein the analysis analysis was was set setto to 40 40 mm. mm. As As the the input input waveform waveform to to thethe oscillator,oscillator, basedbased on the waveform input input to to the the specimenspecimen in in the the ultrasonic ultrasonic test, test, a a half-wavel half-wavelengthength sinewave sinewave with with a afrequency frequency of of 200 200 kHz kHz (see(see FigureFigure 7b)7b )was was provided provided as as a a compression compression wave wave at at the the position position corresponding corresponding to to the the oscillator,oscillator, and and the the displacement waswas outputoutput atat the the position position corresponding corresponding to to the the pendulum. pendulum.In ﬁnite In finite element element analysis, analysis, the analysis the analysis results results are highly are highly dependent dependent on the on time the increment time in- crementdt per step dt per of thestep analysis. of the analysis. Considering Considering the computer the computer performance performance and analysis and analysis time, we time,used we the used minimum the minimum number of number steps without of step affectings without the affecting analysis the accuracy. analysis Based accuracy. on the Basedresults on of the various results investigations, of various investigations we selected, 0.2we µselecteds per step. 0.2 Toµs simplifyper step. theTo simplify problem, the the problem,attenuation the ofattenuation ultrasonic of waves ultrasonic was notwaves considered. was not considered. In this study, In we this did study, not focuswe did on notreproducing focus on reproducing the experimental the experimental data but on data understanding but on understanding the sensitivity the ofsensitivity the effect of of theporosity effect of and porosity water contentand water on elastic-wavecontent on elastic-wave propagation propagation in concrete. in concrete.

0.8 mm) -5

10 0.6 ×

0.4 Amplitude ( Amplitude

0.2

0 0246810 Time (μs) (a) (b)

FigureFigure 7. 7. AnalysisAnalysis condition: condition: (a (a) )Model Model and and (b (b) )Input Input waveform. waveform.

3.2. Parameter Setting The Young’s moduli and densities of the specimens were calculated based on the experimental results, and applied in the numerical analysis. In this study, even though the experimental results indicated that the different air content in the specimen affected the wave propagation velocity in concrete, the data of the specimen with 10% air content was used as a representative value in the analysis because the different air contents showed the same velocity reduction and amplitude increase/decrease trends. In addition, because mortar was used in this experiment, the effect of ﬁne aggregate was assumed to be negligible with respect to the size of the ﬁnite element mesh, and parameters with the same density and Young’s modulus were used. The applied analysis parameters are listed in Table2. The dynamic modulus of elasticity depicted in Table2 was calculated using the following Equation (1) obtained based on the classical theory of elasticity with the experimentally obtained density ρ and wave velocity CL, and the most commonly used assumption of a Poisson ratio ν = 0.2. s E 1 − v C = (1) L ρ (1 + v)(1 − 2v)

3.3. Result Table3 presents the analysis results. Similar to the experimental results, the arrival time of the ﬁrst wave reduces as the water content decreases, i.e., as the dynamic modulus and density decrease. This is because the Young’s modulus was calculated based on the experimental results using Equation (1). However, compared to the arrival time of the ﬁrst Materials 2021, 14, 790 8 of 14

wave in the experiment, the analytical results show a time difference of approximately 1.0 µs in all the cases, which is approximately 80 m/s faster than the propagation velocity.

Table 2. Parameters used in the simulation.

Analysis Air Content Young’s Modulus Mass Density Poisson’s Case (%) (N/mm2) (kg/mm3) Ratio 1 2.79 × 107 2.03 × 10−6 2 2.32 × 107 1.89 × 10−6 3 2.21 × 107 1.85 × 10−6 10% 0.2 4 2.07 × 107 1.83 × 10−6 5 1.95 × 107 1.82 × 10−6 6 1.93 × 107 1.81 × 10−6

Table 3. Simulation results.

Analysis Propagation Velocity Arrival Time First Wave Amplitude Case (m/s) (µs) (mm) 1 4000.0 50.0 4.36 × 10−6 2 3773.6 53.0 4.37 × 10−6 3 3724.4 53.7 4.38 × 10−6 4 3610.1 55.4 4.39 × 10−6 5 3508.8 57.0 4.40 × 10−6 6 3508.8 57.0 4.41 × 10−6

Further, Figure8 compares the experimental and analytical results for Case 1, Case 4, and Case 6. Note that the vertical axes of the graphs are different for the vibration waveforms obtained experimentally and the response displacement obtained through numerical analysis. Comparing these responses, the arrival intervals of the first, second, and third waves are almost identical, but the waveforms of the later waves, i.e., the waves reflected after arriving at the receiver, exhibit different shapes. In the analysis, the arrival time of the waves was affected by changes in the parameters, whereas the congruent-shaped waves moved in parallel and did not reproduce the amplitude change with the decreasing water content obtained in the experiment. This is probably due to the assumption that the used analytical model is homogeneous and does not consider the effects of the reflection and diffraction of waves due to changes in the water content [23].

3.4. Analysis of Nonuniform Water Content 3.4.1. Parameter Settings In this section, we develop an analytical model that considers the change in the moisture content distribution with material drying. Previous studies have indicated that the Young’s modulus decreases with the decrease in water content during ultrasonic testing. Therefore, the elements of the analytical model are classiﬁed into two types: wet (mortar 1) and dry (mortar 2), and the analytical parameters are set as shown in Table4. Materials 2021, 14, x FOR PEER REVIEW 9 of 15

waves are almost identical, but the waveforms of the later waves, i.e., the waves reflected after arriving at the receiver, exhibit different shapes. In the analysis, the arrival time of the waves was affected by changes in the parameters, whereas the congruent-shaped waves moved in parallel and did not reproduce the amplitude change with the decreasing Materials 2021, 14, 790 9 of 14 water content obtained in the experiment. This is probably due to the assumption that the used analytical model is homogeneous and does not consider the effects of the reflection and diffraction of waves due to changes in the water content [23].

(a-1) (a-2)

(b-1) (b-2)

(c-1) (c-2)

FigureFigure 8. 8. Measured waveform: (a (a-1-1) )measured measured waveform waveform on on date date 1, ( 1,a-2) (a-2 Analysis) Analysis result result on case on case1, (b-1) 1, (measuredb-1) measured wave- waveformform on date on date 4, (b 4,-2) (b-2 Analysis) Analysis result result on case on case 4, (c 4,-1) ( c-1measured) measured waveform waveform on date on date 6, (c 6,-2)Analysis (c-2) Analysis result result on case on case 6 6.

3.4. Analysis of Nonuniform Water Content Table 4. Parameters used in the simulation. 3.4.1. Parameter Settings Young’s Modulus (N/mm2) Mass Density (kg/mm3) DryIn Depth this section, we develop an analytical model that considers the changePoisson’s in the moisture(mm) content distributionMortar 1 with material Mortar 2 drying. Mortar Previous 1 studies Mortar have 2 indicatedRatio that the Young’s1 modulus decreases with the decrease in water content during ultrasonic testing. Therefore,2 the elements of the analytical model are classified into two types: wet (mortar 1) and dry (mortar 2), and the analytical parameters are set as shown in Table 4. 3 2.79 × 107 1.93 × 107 2.03 × 10−6 1.81 × 10−6 0.2 4 5 6

From saturated conditions, structural concrete gradually dries from the center of the specimen to the surface. Therefore, this two-phase model does not simulate the continuous change of the moisture content in concrete. The investigation of this two-phase model Materials 2021, 14, 790 10 of 14

intended to clarify the wave propagation behavior in an inhomogeneous ﬁeld and is a model with no signiﬁcant differences from actual concrete. The Young’s modulus and density in the wet condition for mortar 1 and in the dry condition for mortar 2 were set based on the experimental results (Table1) at 10% air content in order to reproduce the moisture content distribution in the specimens. To Materials 2021, 14, x FOR PEER REVIEWconsider the effect of increasing the dry depth, these areas were set at 5 mm, 10 mm, 2011 of mm, 15 30 mm, 40 mm, and 45 mm from the surface of the specimen, as shown in Figure9a–f.

(a) (b)

(e) (f)

FigureFigure 9. 9. MeasuredMeasured waveform: waveform: ( (aa)) analysis analysis model model (dry (dry depth depth = = 5 5 mm), mm), ( (bb)) analysis analysis model model (dry (dry depth depth = = 10 10 mm), mm), ( (cc)) analysis analysis model (dry depth = 20 mm), (d) analysis model (dry depth = 30 mm), (e) analysis model (dry depth = 40 mm), and (f) model (dry depth = 20 mm), (d) analysis model (dry depth = 30 mm), (e) analysis model (dry depth = 40 mm), and (f) analysis model (dry depth = 45 mm). analysis model (dry depth = 45 mm). 5 3.4.2. Analysis Results for Non-Uniform Moisture Content 4 The propagation velocity, arrival time, and amplitude of the first wave obtained through3 analysis are shown in Table5, and a comparison of the response displacement with the expansion of the dry region is displayed in Figure 10. In addition, the displacement mm) 2 distribution-6 is depicted in Figure 11(a-1),(c-3) in increments of 20 µs up to 60 µs. Table5 indicates10 that the arrival time of the first wave reduces with the expansion of the dry depth. × 1 This is because the proportion of the area with a low Young’s modulus increases with the expansion0 of the dry depth. Further, from Table5 and Figure 10, it can be confirmed that 50 52 54 56 58 60 62 64 66 68 70 the amplitude of the first wave decreases. When the wave enters mortar 2 (wet region).

Amplitude ( -1 0mm 5mm -2 10mm 20mm 30mm 40mm -3 45mm -4 Time (μs)

Figure 10. Analysis results of the waveforms.

Materials 2021, 14, x FOR PEER REVIEW 11 of 15

(a) (b)

Materials 2021, 14, 790 11 of 14

(cTable) 5. Simulation results. (d)

Dry Depth Propagation Velocity Arrival Time First Wave Amplitude (mm) (m/s) (µs) (mm) 5 3992.0 50.1 4.14 × 10−6 10 3960.4 50.5 4.05 × 10−6 20 3898.6 51.3 3.67 × 10−6

30 3838.8 52.1 2.81 × 10−6 (e) (f) 40 3745.3 53.4 2.02 × 10−6 Figure 9. Measured waveform: (a) analysis model (dry depth = 5 mm), (b) analysis model (dry depth = 10 mm), (c) analysis × −6 model (dry depth = 20 mm), (d) analysis45 model (dry depth = 30 3669.7 mm), (e) analysis model 54.5 (dry depth = 40 mm),2.74 and10 (f) analysis model (dry depth = 45 mm).

mm) 2 -6 10

× 1

0 50 52 54 56 58 60 62 64 66 68 70

Amplitude ( -1 0mm 5mm -2 10mm 20mm 30mm 40mm -3 45mm -4 Materials 2021, 14, x FOR PEER REVIEW Time (μs) 12 of 15

Figure 10. Analysis results of the waveforms. Figure 10. Analysis results of the waveforms.

(a-1) (a-2) (a-3)

(b-1) (b-2) (b-3)

(c-1) (c-2) (c-3)

FigureFigure 11. 11.Analysis Analysis results results of of the the two-dimensional two-dimensional waveforms: waveforms: (a-1 (a-1) dry) dry depth depth = 5= mm5 mm at at 20 20µ s,µs, (a-2 (a-2) dry) dry depth depth = 5= mm5 mm at at 40 µs, 40 µs, (a-3) dry depth = 5 mm at 60 µs, (b-1) dry depth = 30 mm at 20 µs, (b-2) dry depth = 30 mm at 40 µs, (b-3) dry depth (a-3) dry depth = 5 mm at 60 µs, (b-1) dry depth = 30 mm at 20 µs, (b-2) dry depth = 30 mm at 40 µs, (b-3) dry depth = 30 mm = 30 mm at 60 µs, (c-1) dry depth = 45 mm at 20 µs, (c-2) dry depth = 45 mm at 40 µs, and (c-3) dry depth = 45 mm at 60 µs. at 60 µs, (c-1) dry depth = 45 mm at 20 µs, (c-2) dry depth = 45 mm at 40 µs, and (c-3) dry depth = 45 mm at 60 µs. Table 5. Simulation results.

Dry Depth Propagation Velocity Arrival Time First Wave Amplitude (mm) (m/s) (μs) (mm) 5 3992.0 50.1 4.14 × 10−6 10 3960.4 50.5 4.05 × 10−6 20 3898.6 51.3 3.67 × 10−6 30 3838.8 52.1 2.81 × 10−6 40 3745.3 53.4 2.02 × 10−6 45 3669.7 54.5 2.74 × 10−6

3.4.3. Discussion The moisture content of the analytical model was approximated and compared between the ultrasonic test and numerical analysis. For the analytical model, the moisture content was calculated as the ratio of the area of mortar 1 to a saturated moisture content of 10.7%, which was determined through ultrasonic testing when all the elements were in mortar 1 (wet state). Figure 12 shows the relationship between the amplitude of the initial wave, and the moisture content of the ultrasonic test and numerical analysis results. The graph in the figure is normalized to a value of 10.7% moisture content and depicts the extent to which the amplitude changes with the change in the moisture content. Although there are certain mismatches between the experimental and analytical values, it is possible to reproduce the tendency of the amplitude decrease with the increase in moisture content from approximately 0% and the amplitude increase again from approximately 1%. Figure 13 displays the relationship between the ultrasonic velocity and moisture content for the ultrasonic test and numerical analysis. As shown in the previous figure, the experimental values are greater than the numerical ones probably owing to the very simplistic nature of the model. However, the arrival time tends to increase with the increase

Materials 2021, 14, 790 12 of 14

3.4.3. Discussion The moisture content of the analytical model was approximated and compared be- Materials 2021, 14, x FOR PEER REVIEWtween the ultrasonic test and numerical analysis. For the analytical model, the moisture13 of 15

content was calculated as the ratio of the area of mortar 1 to a saturated moisture content of 10.7%, which was determined through ultrasonic testing when all the elements were inin mortarmoisture 1 (wet content state). and Figure the linear 12 shows increase the is relationship reproduced. between This analysis the amplitude model does of thenot initialconsider wave, the andcracks the and moisture voids contentwithin ofthe the spec ultrasonicimen and test does and not numerical reflect the analysis reflection results. and Thescattering graph inof theultrasonic ﬁgure iswaves, normalized which tomay a value have ofcaused 10.7% the moisture differences content between and depicts the exper- the extentimental to values which theand amplitude analysis results. changes However, with the the change results in the of this moisture study content. show that Although the dif- thereference are in certain moisture mismatches content near between the surface the experimental layer and andwithin analytical the concrete, values, i.e., it is the possible differ- toence reproduce in material the tendencyproperties, of was the amplitudethe dominant decrease factor with in describing the increase the in wave moisture propagation content from approximately 0% and the amplitude increase again from approximately 1%. phenomenon in concrete.

1.2 Materials 2021, 14, x FOR PEER REVIEW 13 of 15 1

0.8 in moisture content and the linear increase is reproduced. This analysis model does not 0.6 consider the cracks and voids withinExperiment the specimen and does not reflect the reflection and scattering of ultrasonic waves, whichAnalysis may have caused the differences between the exper- 0.4 imental values and analysis results. However, the results of this study show that the dif-

ferenceNormalized amplitude (-) 0.2 in moisture content near the surface layer and within the concrete, i.e., the difference in material properties, was the dominant factor in describing the wave propagation phenomenon0 in concrete. 0.0 2.0 4.0 6.0 8.0 10.0 12.0 Water contetnt ratio (%) 1.2 FigureFigure 12.12.Relationship Relationship betweenbetween thethe moisturemoisture content content ratio ratio and and normalized normalized amplitude. amplitude. 1 1.05Figure 13 displays the relationship between the ultrasonic velocity and moisture 0.8 content1 for the ultrasonic test and numerical analysis. As shown in the previous ﬁgure,

the0.60.95 experimental values are greater than the numerical ones probably owing to the very simplistic nature of the model. However,Experiment the arrival time tends to increase with the increase 0.9 Analysis in moisture0.4 content and the linear increase is reproduced. This analysis model does not 0.85 consider the cracks and voids within the specimen and does not reﬂect the reﬂection

Normalized amplitude (-) Experiment 0.20.8 and scattering of ultrasonic waves,Analysis which may have caused the differences between the experimental0.75 values and analysis results. However, the results of this study show that Normalized velocity (-) 0 0.7 the difference0.0 2.0 in moisture 4.0 6.0 content 8.0 near 10.0 the surface 12.0 layer and within the concrete, i.e., the0.65 difference in materialWater contetnt properties, ratio (%) was the dominant factor in describing the wave propagation phenomenon in concrete. Figure0.6 12. Relationship between the moisture content ratio and normalized amplitude. 0.0 2.0 4.0 6.0 8.0 10.0 12.0 Water contetnt ratio (%) 1.05 Figure1 13. Relationship between the moisture content ratio and normalized velocity. 0.95 4. Conclusions 0.9 The ultrasonic method is applied for the quality evaluation of concrete. In this study, 0.85 the effect of inhomogeneity causedExperiment by the change in the moisture content of concrete on 0.8 ultrasonic-wave propagation wasAnalysis investigated experimentally and numerically. The fol- 0.75

lowingNormalized velocity (-) conclusions were obtained: 1. 0.7The results of ultrasonic testing confirmed that the elastic-wave velocity tended to 0.65decrease with the increase in the air content of the specimen. In addition, the elastic- 0.6wave velocity exhibited a decreasing trend as the moisture content of the specimen decreased0.0 2.0 with 4.0 drying. 6.0 8.0 10.0 12.0 Water contetnt ratio (%) 2. As the moisture content of the specimen decreased, the amplitude of the vibration Figurewaveform 13. Relationship changed. between The theamplitude moisture decreased contentcontent ratioratio with andand thenormalizednormalized decrease velocity.velocity. in moisture content and reached a minimum value at approximately 1% moisture content; however, the 4. Conclusions amplitude exhibited an increasing trend at lower moisture content. 3. TheThe ultrasonicnumerical method analysis is reflectedapplied for the the decrease quality evaluationin the elastic of concrete.modulus Inwith this thestudy, de- the effectcrease of ininhomogeneity moisture content caused in theby theanalytical change model,in the moisture and the resultscontent reproduced of concrete theon ultrasonic-wave propagation was investigated experimentally and numerically. The following conclusions were obtained: 1. The results of ultrasonic testing confirmed that the elastic-wave velocity tended to decrease with the increase in the air content of the specimen. In addition, the elastic- wave velocity exhibited a decreasing trend as the moisture content of the specimen decreased with drying. 2. As the moisture content of the specimen decreased, the amplitude of the vibration waveform changed. The amplitude decreased with the decrease in moisture content and reached a minimum value at approximately 1% moisture content; however, the amplitude exhibited an increasing trend at lower moisture content. 3. The numerical analysis reflected the decrease in the elastic modulus with the decrease in moisture content in the analytical model, and the results reproduced the

Materials 2021, 14, 790 13 of 14

4. Conclusions The ultrasonic method is applied for the quality evaluation of concrete. In this study, the effect of inhomogeneity caused by the change in the moisture content of concrete on ultrasonic-wave propagation was investigated experimentally and numerically. The following conclusions were obtained: 1. The results of ultrasonic testing confirmed that the elastic-wave velocity tended to decrease with the increase in the air content of the specimen. In addition, the elastic- wave velocity exhibited a decreasing trend as the moisture content of the specimen decreased with drying. 2. As the moisture content of the specimen decreased, the amplitude of the vibration waveform changed. The amplitude decreased with the decrease in moisture content and reached a minimum value at approximately 1% moisture content; however, the amplitude exhibited an increasing trend at lower moisture content. 3. The numerical analysis reflected the decrease in the elastic modulus with the decrease in moisture content in the analytical model, and the results reproduced the increasing and decreasing trends of the amplitude obtained through ultrasonic testing. It is considered that ultrasonic waves were attenuated at the boundary between regions with different parameters, and that the amplitude initially decreased as the boundary increased with the expansion of the dry region; however, this reverted to an increasing trend as the boundary decreased when the dry region exceeded a certain range. Although the present study was carried out in using mortar, it is necessary to consider the effect of the presence of coarse aggregate on the reflection and diffraction of waves in concrete for the study in actual structures. However, the understanding of wave propagation phenomena in concrete with inhomogeneous water content, as in the present study, is essential for actual field measurements for precise prediction of parameters such as concrete strength and permeability, and will be necessary in the future.

Author Contributions: Conceptualization: S.O., H.N. and R.H.; methodology: S.O., H.N. and H.Y.; software: H.Y.; validation: S.O., H.I., and H.N.; formal analysis: H.I., H.N., and H.Y.; investigation: S.O. and H.I.; resources: H.N. and H.Y.; data curation: H.I.; writing—original draft preparation: S.O. and H.I.; writing—review and editing: S.O.; visualization: H.I.; supervision: H.N., H.Y. and R.H.; project administration: S.O., H.N. and R.H.; funding acquisition: S.O. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by the Ministry of Land, Infrastructure, Transport and Tourism, Construction Technology Research and Development Grant Program (CRD). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The data are not publicly available due to privacy restrictions. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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