# The Measurement of P-, S-, and R-Wave Velocities to Evaluate the Condition of Reinforced and Prestressed Concrete Slabs

Authors: Young Hak Lee; Taekeun Oh
Journal: Advances in Materials Science and Engineering
 (2016)

---

## Abstract

The traditional P-wave ultrasonic measurement has been used for the condition assessment of general reinforced concrete structures for a long time, but the effects of prestressing applied to concrete structures such as long-span buildings and bridges on ultrasonic pulse velocity have not been studied clearly. Therefore, this study analyzed the statistical distribution of P-wave ultrasonic pulse velocities in reinforced and prestressed concrete slabs of 3000 × 3000 mm with a thickness of 250 mm. In addition, we measured S- and R-waves to identify experimental consistency by statistical analysis using the Kolmogorov-Smirnov goodness-of-fit test. The experimental results show that the P-, S-, and R-wave velocities increased slightly (2-3%) when prestressing was applied. As expected, the S- and R-wave measurements show better statistical reliability and potential for in situ evaluation than the P-wave because they are less sensitive to confinement and boundary conditions. The experimental results in this study can be used when assessing the condition of prestressed concrete structures through the velocities of elastic waves.


---

## Body

## 1. Introduction

The accurate measurement of concrete properties, such as elasticity, strength, and Poisson’s ratio, is important in terms of the quality assurance (Q/A) and quality control (Q/C) of concrete structures [1]. The Q/A and Q/C require numerous tests in the laboratory. In the field, obtaining core samples consumes a lot of time, budget, and labor and can deteriorate the structure itself. Therefore, nondestructive testing is needed to eliminate problems in both the laboratory and the field.One of the most effective nondestructive evaluation methods for the assessment of concrete structures is ultrasonic measurement [2]. It has been popularly used in both reinforced and prestressed concrete structures to determine material properties, detect defects, and assess deterioration. Recent failures of prestressed concrete structures have highlighted the need to improve inspection and maintenance in the United States and Europe. However, the field application of ultrasonic methods to prestressed concrete structures should be cautious because the effects of prestressing on the ultrasonic methods have not been clearly validated. These effects are analogous to the acoustoelastic effects that the ultrasonic wave velocity of a solid medium changes with the stress state of the medium [3, 4]. Even though many researchers have developed the health monitoring techniques for steel structures based on the acoustoelasticity [5], only few studies have been related to reinforced or prestressed concrete structural members because of a few limitations; for example, the inelastic characteristics and the small relative velocity change over stress change in a concrete medium [6]. The theoretical study of elastic waves in an infinite prestressed solid that is homogeneous and isotropic is well-advanced [7, 8], but the deduced analytical equations offer no practically effective applications for nonhomogeneous and inelastic materials such as concrete under an inconsistent stress field. Thus, it is necessary to experimentally investigate and analyze the distribution of ultrasonic velocities in prestressed concrete structures in the field.Generally, ultrasonic testing methods assess material conditions and deterioration by comparing velocity, attenuation, frequency, and energy against reference values such as ultrasonic pulse velocity (UPV) determined using laboratory specimens. The ratio of field UPV to the reference UPV indicates the level of material condition [9]. Traditionally, the pressure wave (P-wave) pulse velocity has been popularly applied to concrete structures for its easy generation and measurement. However, the statistical stability of experimental data for P-wave velocity is weaker than for shear (S-) or Rayleigh (R-) waves because the energy of a P-wave is much less than that of S- and R-waves [10]. Furthermore, the P-wave depends on the presence of pore water in the concrete. Therefore, S- and R-wave pulse velocities have recently been applied to various structures.For this study, we measured and analyzed P-, S-, and R-wave velocities in both reinforced and prestressed concrete slabs to investigate the statistical distribution of each wave velocity with and without prestressing. The experimental results present practical guidelines for applying the ultrasonic methods to reinforced and prestressed concrete structures.


## 2. Ultrasonic Pulse Velocity and Its Measurement

In an elastic and stress-free solid medium, body waves travel within the body (P- and S-waves), and surface waves (R-waves) travel along the free surface of the material. The velocities of wave propagation depend on elastic constants and the mass density of the material. The relations among P-, S-, and R-wave velocities can be expressed by the following equations [15]:(1)
V
P
=
E
1
-
v
ρ
1
+
v
1
-
2
v
,
V
S
=
E
1
-
v
2
ρ
1
+
v
,
V
R
=
0.87
+
1.12
v
1
+
v
E
ρ
1
2
1
+
v
,where V
P, V
S, and V
R are the velocities of P-, S-, and R-waves, respectively, and E, ρ, and v are dynamic elasticity, density, and Poisson’s ratio, respectively.V
P typically ranges from 3500 m/s to 4500 m/s and V
R from 1800 to 2500 m/s for sound concrete [16]. The motion resulting from R-waves is restricted to a region near the surface and decreases exponentially in amplitude away from the surface. The R-wave penetration depth is inversely related to the frequency of the wave. R-waves are easily generated in a solid by a transient point source and more readily sensed than P- and S-waves because of their large amplitude. The only limitation of R-waves is caused by the limited penetration depth; the disturbances are confined to the surface region of thickness, approximately twice the wavelength, λ
R. Figure 1 shows the wave pressure field generated by a harmonic normal load applied at the interface. The propagating P-, S-, and R-waves in the concrete have 7, 26, and 67% of the source energy, respectively [11].Figure 1
Distribution of displacement and energy in P-, S-, and R-waves from a harmonic normal load on a half-space forv
=
0.25 [11].


### 2.1. P-Wave (Pressure Wave) Measurement

The P-wave ultrasonic measurement mainly uses the arrival time of a stress wave and has two types of methods: direct (pulse-echo and through-transmission) and indirect transmission, as illustrated in Figure2 [12]. The direct transmission uses the transfer of P-wave energy passing through a cross section between the transmitter and receiver. In the pulse-echo method, the transmitter/receiver transducer performs both sending and receiving of the pulsed waves reflected from the back wall of specimen. In the through-transmission, a transmitter sends ultrasound waves through one surface, and a receiver detects them on the opposite surface. On the other hand, the indirect transmission uses the P-wave path near surface. It is mainly used when only one face of the concrete is accessible or when the depth of a surface crack is to be determined. It is the least sensitive of the transducer arrangement for a given path. The surface response caused by the arrival of reflected or transmitted waves is monitored by the same or a different transducer acting as a receiver. The receiver output is displayed on an oscilloscope as a time-domain waveform. The round-trip travel time of the pulse can be calculated by determining the time from the transmitted pulse to the reflected echo. If the wave speed in the material is known, this travel time can be used to compute the depth of the reflecting interface. Transducers associated with short-duration, low-frequency (50–200 kHz) focused waves are generally used for testing concrete.Figure 2
Schematic of ultrasonic direct and indirect transmission method [12].


### 2.2. S-Wave (Shear Wave) Measurement

One of the most effective ways to measure S-wave velocity is with MIRA equipment that generates shear wave tomography [13]. The MIRA also operates on the basic ultrasonic pulse-echo principle. Unlike other pulse-echo methods, the MIRA device does not require a coupling agent with a spring-loaded design. Interactive postprocessing software uses the synthetic aperture focusing technique (SAFT) to generate 2D and 3D images of the test results [13] (Figure 3). The generated S-waves have particle motion that propagates perpendicular to the direction of the wave front with a velocity about 60 percent that of P-waves [11]. Samokrutov et al. [17] showed that using S-waves instead of P-waves reduces the amount of backscattering and signal attenuation in the direction parallel to the propagating wave.Figure 3
Schematic representation of the digitally focused array signal capturing scheme [13].Recent advances have improved the MIRA transducer, which can now create a 3D tomography of internal defects that might be present in a concrete element, with penetration depths up to about 2.0 m [13]. MIRA is based on the ultrasonic pitch-catch method and uses an antenna of dry point contact transducers that emit shear waves into the concrete with a nominal center frequency of 50 kHz. Using an array of point transducers rapidly produces 180 transit time measurements during each test. The antenna is composed of a 4 by 12 array of point transducers and a control unit that operates the transducers, as illustrated in Figure 4 [14]. The transducers act as transmitters and receivers in a sequential mode. The use of very high frequencies with the pulse-echo method could be beneficial in terms of improved defect resolution.Figure 4
Illustration of low-frequency ultrasonic tomography (MIRA) [14].


### 2.3. R-Wave (Rayleigh Wave) Measurement

The conventional measurement of R-wave velocity uses the time difference between the first or second significant peaks in two R-waves from two receivers [18, 19]. However, system errors in catching the peak points can occur. The best way to make up for that shortcoming uses the dispersion curve of Lamb waves in the plate with MASW (multichannel analysis of surface waves) [20, 21].MASW data collection is based onN-wave signals collected on the surface along a linear array of sensed points equally spaced (with spacing d
x) from the wave source, such as the impact event illustrated in Figure 5. The impact event for wave generation must be provided by a high frequency impactor (small contact area). Multiple data are processed as individual signals obtained by each sensor. Data are transformed from the offset time-domain to the frequency-phase velocity domain using a 2D Fourier transform, producing a phase velocity that is usually called the dispersion curve.Figure 5
A scheme for an MASW test, in whichX
i is the near offset, d
x is the sensor spacing, and L is the offset range.MASW has been commonly applied to the surface wave testing of pavements, and the experimentally computed dispersion curve is interpreted to represent R-waves. Several modes of guided dispersive waves propagating in a pavement structure can be measured at the surface and used for material characterization, including the A0 and S0 Lamb modes used to determine Poisson’s ratio, R-wave velocity, and plate thickness [22]. An example of a dispersion curve in a concrete slab with 30 cm depth is presented in Figure 6. It is obtained by using MASW wave transformation in the following equation [20]:(2)
S
ω
,
c
P
=
∫
e
-
i
ω
/
c
P
x
U
x
,
ω
d
x
,where U
(
x
,
ω
) is the normalized complex spectrum obtained from the Fourier transformation of u
(
x
,
t
), which is multichannel record at different offsets. ω is the angular frequency, and c
P is the phase velocity.Figure 6
Phase velocity dispersion curves determined by MASW (based on the FE simulation of a concrete slab with a thickness of 0.3 m). A density of 2250 kg/m3, an elasticity of 23 GPa, and a fixed Poisson’s ratio of 0.167 are assumed for the concrete slab.


## 2.1. P-Wave (Pressure Wave) Measurement

The P-wave ultrasonic measurement mainly uses the arrival time of a stress wave and has two types of methods: direct (pulse-echo and through-transmission) and indirect transmission, as illustrated in Figure2 [12]. The direct transmission uses the transfer of P-wave energy passing through a cross section between the transmitter and receiver. In the pulse-echo method, the transmitter/receiver transducer performs both sending and receiving of the pulsed waves reflected from the back wall of specimen. In the through-transmission, a transmitter sends ultrasound waves through one surface, and a receiver detects them on the opposite surface. On the other hand, the indirect transmission uses the P-wave path near surface. It is mainly used when only one face of the concrete is accessible or when the depth of a surface crack is to be determined. It is the least sensitive of the transducer arrangement for a given path. The surface response caused by the arrival of reflected or transmitted waves is monitored by the same or a different transducer acting as a receiver. The receiver output is displayed on an oscilloscope as a time-domain waveform. The round-trip travel time of the pulse can be calculated by determining the time from the transmitted pulse to the reflected echo. If the wave speed in the material is known, this travel time can be used to compute the depth of the reflecting interface. Transducers associated with short-duration, low-frequency (50–200 kHz) focused waves are generally used for testing concrete.Figure 2
Schematic of ultrasonic direct and indirect transmission method [12].


## 2.2. S-Wave (Shear Wave) Measurement

One of the most effective ways to measure S-wave velocity is with MIRA equipment that generates shear wave tomography [13]. The MIRA also operates on the basic ultrasonic pulse-echo principle. Unlike other pulse-echo methods, the MIRA device does not require a coupling agent with a spring-loaded design. Interactive postprocessing software uses the synthetic aperture focusing technique (SAFT) to generate 2D and 3D images of the test results [13] (Figure 3). The generated S-waves have particle motion that propagates perpendicular to the direction of the wave front with a velocity about 60 percent that of P-waves [11]. Samokrutov et al. [17] showed that using S-waves instead of P-waves reduces the amount of backscattering and signal attenuation in the direction parallel to the propagating wave.Figure 3
Schematic representation of the digitally focused array signal capturing scheme [13].Recent advances have improved the MIRA transducer, which can now create a 3D tomography of internal defects that might be present in a concrete element, with penetration depths up to about 2.0 m [13]. MIRA is based on the ultrasonic pitch-catch method and uses an antenna of dry point contact transducers that emit shear waves into the concrete with a nominal center frequency of 50 kHz. Using an array of point transducers rapidly produces 180 transit time measurements during each test. The antenna is composed of a 4 by 12 array of point transducers and a control unit that operates the transducers, as illustrated in Figure 4 [14]. The transducers act as transmitters and receivers in a sequential mode. The use of very high frequencies with the pulse-echo method could be beneficial in terms of improved defect resolution.Figure 4
Illustration of low-frequency ultrasonic tomography (MIRA) [14].


## 2.3. R-Wave (Rayleigh Wave) Measurement

The conventional measurement of R-wave velocity uses the time difference between the first or second significant peaks in two R-waves from two receivers [18, 19]. However, system errors in catching the peak points can occur. The best way to make up for that shortcoming uses the dispersion curve of Lamb waves in the plate with MASW (multichannel analysis of surface waves) [20, 21].MASW data collection is based onN-wave signals collected on the surface along a linear array of sensed points equally spaced (with spacing d
x) from the wave source, such as the impact event illustrated in Figure 5. The impact event for wave generation must be provided by a high frequency impactor (small contact area). Multiple data are processed as individual signals obtained by each sensor. Data are transformed from the offset time-domain to the frequency-phase velocity domain using a 2D Fourier transform, producing a phase velocity that is usually called the dispersion curve.Figure 5
A scheme for an MASW test, in whichX
i is the near offset, d
x is the sensor spacing, and L is the offset range.MASW has been commonly applied to the surface wave testing of pavements, and the experimentally computed dispersion curve is interpreted to represent R-waves. Several modes of guided dispersive waves propagating in a pavement structure can be measured at the surface and used for material characterization, including the A0 and S0 Lamb modes used to determine Poisson’s ratio, R-wave velocity, and plate thickness [22]. An example of a dispersion curve in a concrete slab with 30 cm depth is presented in Figure 6. It is obtained by using MASW wave transformation in the following equation [20]:(2)
S
ω
,
c
P
=
∫
e
-
i
ω
/
c
P
x
U
x
,
ω
d
x
,where U
(
x
,
ω
) is the normalized complex spectrum obtained from the Fourier transformation of u
(
x
,
t
), which is multichannel record at different offsets. ω is the angular frequency, and c
P is the phase velocity.Figure 6
Phase velocity dispersion curves determined by MASW (based on the FE simulation of a concrete slab with a thickness of 0.3 m). A density of 2250 kg/m3, an elasticity of 23 GPa, and a fixed Poisson’s ratio of 0.167 are assumed for the concrete slab.


## 3. Experiments

### 3.1. Test Specimens

To simulate the effects of prestressing on UPV into a concrete slab, we carried out a series of ultrasonic tests on the three types of concrete slab (S1, S2, and S3) shown in Figure7. All of the specimens are 3000 mm × 3000 mm with a nominal thickness of 250 mm, and they all contain transverse and longitudinal 13 mm diameter reinforcements with 560 mm spacing at 20 and 230 mm depths, respectively. We prestressed the S2 and S3 slabs in the two and one ways, respectively. Five 12.7 mm diameter strands with 350 mm spacing were applied in each direction. The details of the prestress strand are summarized in Table 1.Table 1
Information on the prestress strand.
Tendon type
Diameter (mm)
Area (mm2)
Elongation (%)
Tensile strength (MPa)
Jacking force (kN)
SWPC7B
12.7
98.7
3.5
1860
128.5Figure 7
The plan and side views of specimens S1, S2, and S3. All dimensions in millimeters.The specified w/c of the concrete mixture was 0.48 with 6% entrained air content. The mixture contained Type I cement and limestone aggregates with a maximum coarse aggregate size of 25 mm. At the time of concrete placement, slump was measured as 150 mm and density as 2250 kg/m3. The specimens were moist-cured for 7 days by covering them with saturated burlap with a bleed hose and plastic sheeting. Beyond the eighth day, the specimens were kept in laboratory air.We determined the concrete’s mechanical properties using tests performed on ten 150 mm × 300 mm standard cylinders prepared from the same batch of concrete. For the same conditions as the S1, S2, and S3 slabs, we air-cured the standard specimens for 28-day strength, static modulus, and Poisson’s ratio. We determined the compressive strength using ASTM C-39 [23] and conducted the modulus of elasticity E
c and Poisson’s ratio tests (v) from ASTM C-469 [24]. The average results for the 28-day tests were 14.84 MPa for strength, 17.68 MPa for the modulus of elasticity, and 0.16 for Poisson’s ratio. Also, the dynamic modulus E
d was 21.30 GPa, found by following the empirical relationship proposed by Lydon and Balendran [25]:(3)
E
c
=
0.83
E
d
G
P
a
.


### 3.2. Test Methods

#### 3.2.1. P-Wave Measurement

We measured the P-wave velocity of concrete,V
P, according to BS 1881 [26] using a pair of P-wave transducers (MK-954 transmitters and receivers) connected to a pulse-receiver (Ultracon-170). The transmitter was driven by a 200 V square pulse, generating a transverse ultrasonic pulse of 52 kHz. The receiver measured the transient stress waves through the surface of each slab (Figure 8).Figure 8
P-wave measurement in a grid on the concrete slab surface.We performed the P-wave measurements with a digital scope board synchronized with the pulser-receiver unit; therefore, data collection started at the time of pulse application. Measurement of flight time was affected by the electrical noise superimposed with the waveform. Therefore, to minimize random errors associated with identifying the arrival time, we performed wave averaging of 128 waveforms. The first step in identifying the flight time from the waveform was establishing the baseline. Afterward, the waveform was further smoothed using a 10-point moving average filter.We made a total of 40 indirect measurements on each concrete slab using a coordinate system drawn on the slab surface (Figure9). The coordinate system consisted of a primary grid at 353 × 100 mm spacing. The gridlines were labeled along the width of the specimens as axes A, B, C, D, E, F, G, and H and along the length of the specimens as axes I, II, III, IV, and V. We made indirect measurements longitudinally along the lettered axes. We placed the transmitter and receiver transducers at the grid nodes and measured the average P-wave velocity between them. For example, at A-I test position, upper and bottom circles represent the transducers (transmitter and receiver), and cross marks indicate the average P-wave velocity between two transducers.Figure 9
A plan view of the 353 × 100 mm test point grid for the P-wave measurement. The test was carried out on the grid locations. The ∘ (circle) and × (cross mark) indicate the positions of the transducers and average measurements, respectively.We acquired the transmitter and conditioned receiver signals using a high-speed (1 MHz sampling rate) analog to digital data acquisition board. We developed a computer algorithm based on a fixed threshold level to determine the time of flight using the digitally acquired waveforms. Figure10 presents a typical signal of the transmitter and receiver transducers.Figure 10
Procedure for determining P-wave time of flight at the A-II point in slab S1.


#### 3.2.2. MIRA Test for the S-Wave Measurement

For effective S-wave measurement, we used MIRA equipment that was verified in both Europe and the United States. The procedure is simple: a trigger button on the MIRA board starts reception of all possible combinations of pulse reflections from each test point location through the appropriate filtering and space-time processing based on the SAFT algorithm. Eventually, the digital display presents a B-scan image with the S-wave velocity.We made a total of 20 direct S-wave measurements on each concrete slab using the same coordinate system as for the P-wave measurement. However, we conducted these tests only in the areas shaded in Figure11. We labeled the gridlines along the width of the specimens as axes AB, CD, EF, and GH and those along the length of the specimens as axes I, II, III, IV, and V. We carried out direct measurements at a single position because the MIRA uses the pulse-echo method (Figure 12).Figure 11
A plan view of the 353 × 100 mm test point grid for the S-wave measurement. The test was carried out at the shaded areas in the grid system.Figure 12
S-wave measurement in the grid on concrete slab surface.Figure13 shows the result of the MIRA testing at the EF-V point on the S1 slab. The reconstructed B-scan image depicts an average transverse cross section (90° from the transducer array travel path). In the view, the center of the bright red color represents reflections from the back of the slab, which corresponds to a nominal thickness of 250 mm. Additional reverberations from the bottom of the slab, at approximately twice the thickness of each consecutive step, are observed at the 500 mm depth. Also, the average S-wave velocity computed by the SAFT algorithm is displayed in the left corner.Figure 13
B-scan image from MIRA at the EF-V point in slab S1.


#### 3.2.3. MASW Test for R-Wave Measurement

We applied an MASW testing configuration for the identification of R-wave velocity consistently to the three test specimens along the 12 paths shown in Figure14.Figure 14
A plan view of the 12 test paths for the R-wave measurement. The ∘ marks indicate the sensor positions in each path, and the arrows show the direction of each test.We used a steel ball with an 18 mm diameter as the impact source for each MASW test. The forcing function associated with the impact exhibits consistent and broad spectral content, ranging from DC to 15 kHz. We used 5 accelerometers (PCB 353B16), with a±
5
% frequency range of 1 to 10 kHz and a resonance frequency around 70 kHz, in even 10 cm spacing along the test line to detect the surface vibrations generated by the ball impact event. For a rapid test, we mounted the 5 accelerometers to the frame, as shown in Figure 15. We stabilized the signals using a signal conditioner (PCB 482C16) and digitized them at a sampling frequency of 1 MHz using an NI-PXI 5105 oscilloscope.Figure 15
MASW test for the R-wave measurement along predefined paths on the concrete slab surface.The multichannel record consists of 5 time series (called traces) from the receivers in an ordered manner. MASW data processing consists of three steps:(
1
) detection of surface waves, (
2
) construction of the dispersion image and extraction of the signal dispersion curve, and (
3
) identification of the several Lamb wave modes and R-wave velocity. All these steps can be fully automated. The detection of surface waves examines the recorded seismic waves in the most probable range of frequencies and phase velocities. Construction of the phase velocity image is accomplished through a 2D (time and pace) wave field transformation method. This transformation eliminates all the ambient noise from human activities as well as source-generated noise such as scattered waves. The necessary dispersion curve, such as that of the A0, A1, S0, or S1 fundamental-mode, is then extracted from the accumulation pattern. The extracted dispersion curve is finally used as a reference to identify the R-wave velocity. For each test, we obtained time signals of 10 ms duration. Because the amplitude of the input forcing function at each test point across the concrete surface is inherently inconsistent, we normalized the amplitude of each time signal with respect to the early-arriving negative peak of the R-wave pulse arrival within that signal, which provides more consistent MASW data.Figure16 shows the experimental results along path 6 in the S2 slab and exhibits dispersion images and curves up to 12 kHz. The Lamb wave curves in the single layer must be fit to one of the responses. The A0 and S0 modes beyond 10 kHz converge to about 2000 m/s phase velocity, corresponding to the R-wave. Also, the impact-echo mode (thickness mode), which is identical to the S1 mode, shows that 7.5 kHz corresponds to a nominal thickness of 250 mm.Figure 16
MASW results along the 6th path in slab S2. The computed A0, A1, S0, and S1 Lamb modes corresponding to the slab depth overlap on the dispersion curve image.
(a)
The signals in the time domain
(b)
Dispersion curve


## 3.1. Test Specimens

To simulate the effects of prestressing on UPV into a concrete slab, we carried out a series of ultrasonic tests on the three types of concrete slab (S1, S2, and S3) shown in Figure7. All of the specimens are 3000 mm × 3000 mm with a nominal thickness of 250 mm, and they all contain transverse and longitudinal 13 mm diameter reinforcements with 560 mm spacing at 20 and 230 mm depths, respectively. We prestressed the S2 and S3 slabs in the two and one ways, respectively. Five 12.7 mm diameter strands with 350 mm spacing were applied in each direction. The details of the prestress strand are summarized in Table 1.Table 1
Information on the prestress strand.
Tendon type
Diameter (mm)
Area (mm2)
Elongation (%)
Tensile strength (MPa)
Jacking force (kN)
SWPC7B
12.7
98.7
3.5
1860
128.5Figure 7
The plan and side views of specimens S1, S2, and S3. All dimensions in millimeters.The specified w/c of the concrete mixture was 0.48 with 6% entrained air content. The mixture contained Type I cement and limestone aggregates with a maximum coarse aggregate size of 25 mm. At the time of concrete placement, slump was measured as 150 mm and density as 2250 kg/m3. The specimens were moist-cured for 7 days by covering them with saturated burlap with a bleed hose and plastic sheeting. Beyond the eighth day, the specimens were kept in laboratory air.We determined the concrete’s mechanical properties using tests performed on ten 150 mm × 300 mm standard cylinders prepared from the same batch of concrete. For the same conditions as the S1, S2, and S3 slabs, we air-cured the standard specimens for 28-day strength, static modulus, and Poisson’s ratio. We determined the compressive strength using ASTM C-39 [23] and conducted the modulus of elasticity E
c and Poisson’s ratio tests (v) from ASTM C-469 [24]. The average results for the 28-day tests were 14.84 MPa for strength, 17.68 MPa for the modulus of elasticity, and 0.16 for Poisson’s ratio. Also, the dynamic modulus E
d was 21.30 GPa, found by following the empirical relationship proposed by Lydon and Balendran [25]:(3)
E
c
=
0.83
E
d
G
P
a
.


## 3.2. Test Methods

### 3.2.1. P-Wave Measurement

We measured the P-wave velocity of concrete,V
P, according to BS 1881 [26] using a pair of P-wave transducers (MK-954 transmitters and receivers) connected to a pulse-receiver (Ultracon-170). The transmitter was driven by a 200 V square pulse, generating a transverse ultrasonic pulse of 52 kHz. The receiver measured the transient stress waves through the surface of each slab (Figure 8).Figure 8
P-wave measurement in a grid on the concrete slab surface.We performed the P-wave measurements with a digital scope board synchronized with the pulser-receiver unit; therefore, data collection started at the time of pulse application. Measurement of flight time was affected by the electrical noise superimposed with the waveform. Therefore, to minimize random errors associated with identifying the arrival time, we performed wave averaging of 128 waveforms. The first step in identifying the flight time from the waveform was establishing the baseline. Afterward, the waveform was further smoothed using a 10-point moving average filter.We made a total of 40 indirect measurements on each concrete slab using a coordinate system drawn on the slab surface (Figure9). The coordinate system consisted of a primary grid at 353 × 100 mm spacing. The gridlines were labeled along the width of the specimens as axes A, B, C, D, E, F, G, and H and along the length of the specimens as axes I, II, III, IV, and V. We made indirect measurements longitudinally along the lettered axes. We placed the transmitter and receiver transducers at the grid nodes and measured the average P-wave velocity between them. For example, at A-I test position, upper and bottom circles represent the transducers (transmitter and receiver), and cross marks indicate the average P-wave velocity between two transducers.Figure 9
A plan view of the 353 × 100 mm test point grid for the P-wave measurement. The test was carried out on the grid locations. The ∘ (circle) and × (cross mark) indicate the positions of the transducers and average measurements, respectively.We acquired the transmitter and conditioned receiver signals using a high-speed (1 MHz sampling rate) analog to digital data acquisition board. We developed a computer algorithm based on a fixed threshold level to determine the time of flight using the digitally acquired waveforms. Figure10 presents a typical signal of the transmitter and receiver transducers.Figure 10
Procedure for determining P-wave time of flight at the A-II point in slab S1.


### 3.2.2. MIRA Test for the S-Wave Measurement

For effective S-wave measurement, we used MIRA equipment that was verified in both Europe and the United States. The procedure is simple: a trigger button on the MIRA board starts reception of all possible combinations of pulse reflections from each test point location through the appropriate filtering and space-time processing based on the SAFT algorithm. Eventually, the digital display presents a B-scan image with the S-wave velocity.We made a total of 20 direct S-wave measurements on each concrete slab using the same coordinate system as for the P-wave measurement. However, we conducted these tests only in the areas shaded in Figure11. We labeled the gridlines along the width of the specimens as axes AB, CD, EF, and GH and those along the length of the specimens as axes I, II, III, IV, and V. We carried out direct measurements at a single position because the MIRA uses the pulse-echo method (Figure 12).Figure 11
A plan view of the 353 × 100 mm test point grid for the S-wave measurement. The test was carried out at the shaded areas in the grid system.Figure 12
S-wave measurement in the grid on concrete slab surface.Figure13 shows the result of the MIRA testing at the EF-V point on the S1 slab. The reconstructed B-scan image depicts an average transverse cross section (90° from the transducer array travel path). In the view, the center of the bright red color represents reflections from the back of the slab, which corresponds to a nominal thickness of 250 mm. Additional reverberations from the bottom of the slab, at approximately twice the thickness of each consecutive step, are observed at the 500 mm depth. Also, the average S-wave velocity computed by the SAFT algorithm is displayed in the left corner.Figure 13
B-scan image from MIRA at the EF-V point in slab S1.


### 3.2.3. MASW Test for R-Wave Measurement

We applied an MASW testing configuration for the identification of R-wave velocity consistently to the three test specimens along the 12 paths shown in Figure14.Figure 14
A plan view of the 12 test paths for the R-wave measurement. The ∘ marks indicate the sensor positions in each path, and the arrows show the direction of each test.We used a steel ball with an 18 mm diameter as the impact source for each MASW test. The forcing function associated with the impact exhibits consistent and broad spectral content, ranging from DC to 15 kHz. We used 5 accelerometers (PCB 353B16), with a±
5
% frequency range of 1 to 10 kHz and a resonance frequency around 70 kHz, in even 10 cm spacing along the test line to detect the surface vibrations generated by the ball impact event. For a rapid test, we mounted the 5 accelerometers to the frame, as shown in Figure 15. We stabilized the signals using a signal conditioner (PCB 482C16) and digitized them at a sampling frequency of 1 MHz using an NI-PXI 5105 oscilloscope.Figure 15
MASW test for the R-wave measurement along predefined paths on the concrete slab surface.The multichannel record consists of 5 time series (called traces) from the receivers in an ordered manner. MASW data processing consists of three steps:(
1
) detection of surface waves, (
2
) construction of the dispersion image and extraction of the signal dispersion curve, and (
3
) identification of the several Lamb wave modes and R-wave velocity. All these steps can be fully automated. The detection of surface waves examines the recorded seismic waves in the most probable range of frequencies and phase velocities. Construction of the phase velocity image is accomplished through a 2D (time and pace) wave field transformation method. This transformation eliminates all the ambient noise from human activities as well as source-generated noise such as scattered waves. The necessary dispersion curve, such as that of the A0, A1, S0, or S1 fundamental-mode, is then extracted from the accumulation pattern. The extracted dispersion curve is finally used as a reference to identify the R-wave velocity. For each test, we obtained time signals of 10 ms duration. Because the amplitude of the input forcing function at each test point across the concrete surface is inherently inconsistent, we normalized the amplitude of each time signal with respect to the early-arriving negative peak of the R-wave pulse arrival within that signal, which provides more consistent MASW data.Figure16 shows the experimental results along path 6 in the S2 slab and exhibits dispersion images and curves up to 12 kHz. The Lamb wave curves in the single layer must be fit to one of the responses. The A0 and S0 modes beyond 10 kHz converge to about 2000 m/s phase velocity, corresponding to the R-wave. Also, the impact-echo mode (thickness mode), which is identical to the S1 mode, shows that 7.5 kHz corresponds to a nominal thickness of 250 mm.Figure 16
MASW results along the 6th path in slab S2. The computed A0, A1, S0, and S1 Lamb modes corresponding to the slab depth overlap on the dispersion curve image.
(a)
The signals in the time domain
(b)
Dispersion curve


## 3.2.1. P-Wave Measurement

We measured the P-wave velocity of concrete,V
P, according to BS 1881 [26] using a pair of P-wave transducers (MK-954 transmitters and receivers) connected to a pulse-receiver (Ultracon-170). The transmitter was driven by a 200 V square pulse, generating a transverse ultrasonic pulse of 52 kHz. The receiver measured the transient stress waves through the surface of each slab (Figure 8).Figure 8
P-wave measurement in a grid on the concrete slab surface.We performed the P-wave measurements with a digital scope board synchronized with the pulser-receiver unit; therefore, data collection started at the time of pulse application. Measurement of flight time was affected by the electrical noise superimposed with the waveform. Therefore, to minimize random errors associated with identifying the arrival time, we performed wave averaging of 128 waveforms. The first step in identifying the flight time from the waveform was establishing the baseline. Afterward, the waveform was further smoothed using a 10-point moving average filter.We made a total of 40 indirect measurements on each concrete slab using a coordinate system drawn on the slab surface (Figure9). The coordinate system consisted of a primary grid at 353 × 100 mm spacing. The gridlines were labeled along the width of the specimens as axes A, B, C, D, E, F, G, and H and along the length of the specimens as axes I, II, III, IV, and V. We made indirect measurements longitudinally along the lettered axes. We placed the transmitter and receiver transducers at the grid nodes and measured the average P-wave velocity between them. For example, at A-I test position, upper and bottom circles represent the transducers (transmitter and receiver), and cross marks indicate the average P-wave velocity between two transducers.Figure 9
A plan view of the 353 × 100 mm test point grid for the P-wave measurement. The test was carried out on the grid locations. The ∘ (circle) and × (cross mark) indicate the positions of the transducers and average measurements, respectively.We acquired the transmitter and conditioned receiver signals using a high-speed (1 MHz sampling rate) analog to digital data acquisition board. We developed a computer algorithm based on a fixed threshold level to determine the time of flight using the digitally acquired waveforms. Figure10 presents a typical signal of the transmitter and receiver transducers.Figure 10
Procedure for determining P-wave time of flight at the A-II point in slab S1.


## 3.2.2. MIRA Test for the S-Wave Measurement

For effective S-wave measurement, we used MIRA equipment that was verified in both Europe and the United States. The procedure is simple: a trigger button on the MIRA board starts reception of all possible combinations of pulse reflections from each test point location through the appropriate filtering and space-time processing based on the SAFT algorithm. Eventually, the digital display presents a B-scan image with the S-wave velocity.We made a total of 20 direct S-wave measurements on each concrete slab using the same coordinate system as for the P-wave measurement. However, we conducted these tests only in the areas shaded in Figure11. We labeled the gridlines along the width of the specimens as axes AB, CD, EF, and GH and those along the length of the specimens as axes I, II, III, IV, and V. We carried out direct measurements at a single position because the MIRA uses the pulse-echo method (Figure 12).Figure 11
A plan view of the 353 × 100 mm test point grid for the S-wave measurement. The test was carried out at the shaded areas in the grid system.Figure 12
S-wave measurement in the grid on concrete slab surface.Figure13 shows the result of the MIRA testing at the EF-V point on the S1 slab. The reconstructed B-scan image depicts an average transverse cross section (90° from the transducer array travel path). In the view, the center of the bright red color represents reflections from the back of the slab, which corresponds to a nominal thickness of 250 mm. Additional reverberations from the bottom of the slab, at approximately twice the thickness of each consecutive step, are observed at the 500 mm depth. Also, the average S-wave velocity computed by the SAFT algorithm is displayed in the left corner.Figure 13
B-scan image from MIRA at the EF-V point in slab S1.


## 3.2.3. MASW Test for R-Wave Measurement

We applied an MASW testing configuration for the identification of R-wave velocity consistently to the three test specimens along the 12 paths shown in Figure14.Figure 14
A plan view of the 12 test paths for the R-wave measurement. The ∘ marks indicate the sensor positions in each path, and the arrows show the direction of each test.We used a steel ball with an 18 mm diameter as the impact source for each MASW test. The forcing function associated with the impact exhibits consistent and broad spectral content, ranging from DC to 15 kHz. We used 5 accelerometers (PCB 353B16), with a±
5
% frequency range of 1 to 10 kHz and a resonance frequency around 70 kHz, in even 10 cm spacing along the test line to detect the surface vibrations generated by the ball impact event. For a rapid test, we mounted the 5 accelerometers to the frame, as shown in Figure 15. We stabilized the signals using a signal conditioner (PCB 482C16) and digitized them at a sampling frequency of 1 MHz using an NI-PXI 5105 oscilloscope.Figure 15
MASW test for the R-wave measurement along predefined paths on the concrete slab surface.The multichannel record consists of 5 time series (called traces) from the receivers in an ordered manner. MASW data processing consists of three steps:(
1
) detection of surface waves, (
2
) construction of the dispersion image and extraction of the signal dispersion curve, and (
3
) identification of the several Lamb wave modes and R-wave velocity. All these steps can be fully automated. The detection of surface waves examines the recorded seismic waves in the most probable range of frequencies and phase velocities. Construction of the phase velocity image is accomplished through a 2D (time and pace) wave field transformation method. This transformation eliminates all the ambient noise from human activities as well as source-generated noise such as scattered waves. The necessary dispersion curve, such as that of the A0, A1, S0, or S1 fundamental-mode, is then extracted from the accumulation pattern. The extracted dispersion curve is finally used as a reference to identify the R-wave velocity. For each test, we obtained time signals of 10 ms duration. Because the amplitude of the input forcing function at each test point across the concrete surface is inherently inconsistent, we normalized the amplitude of each time signal with respect to the early-arriving negative peak of the R-wave pulse arrival within that signal, which provides more consistent MASW data.Figure16 shows the experimental results along path 6 in the S2 slab and exhibits dispersion images and curves up to 12 kHz. The Lamb wave curves in the single layer must be fit to one of the responses. The A0 and S0 modes beyond 10 kHz converge to about 2000 m/s phase velocity, corresponding to the R-wave. Also, the impact-echo mode (thickness mode), which is identical to the S1 mode, shows that 7.5 kHz corresponds to a nominal thickness of 250 mm.Figure 16
MASW results along the 6th path in slab S2. The computed A0, A1, S0, and S1 Lamb modes corresponding to the slab depth overlap on the dispersion curve image.
(a)
The signals in the time domain
(b)
Dispersion curve


## 4. Results and Discussion

### 4.1. The Experimental Data for P-, S-, and R-Wave Velocities

To minimize the random errors associated with identifying the arrival time, we averaged the times for 128 waveforms for the P-wave measurement. For the S-wave measurement, we repeated the MIRA tests at each point until we identified a clear reflection from the back of the slab. We also carried out the MASW test on a single path until the computed dispersion image showed a distinct A0 mode. All the data for the P-, S-, and R-wave velocities are summarized in Tables2–4.Table 2
P-wave velocities (m/s) at test grid points in slabs S1, S2, and S3.
Test point
S1
S2
S3
I
II
III
IV
V
I
II
III
IV
V
I
II
III
IV
V
A
3002
3301
3295
3326
3231
3411
3258
3400
3183
3391
3253
3320
3348
3358
3244
B
3136
3333
3283
3331
3308
3333
3433
3395
3285
3691
3211
3733
3630
3300
3401
C
3254
3197
3281
3350
3322
3275
3335
3287
3287
3358
3316
3409
3367
3256
3260
D
3429
3339
3318
3340
3429
3329
3333
3297
3348
3246
3301
3256
3283
3301
3337
E
3130
3268
3104
3472
3378
3166
3398
3300
3474
3160
3554
3337
3435
3341
3406
F
3108
3268
3300
3391
3374
3374
3528
3280
3524
3260
3320
3458
3130
3279
3371
G
3191
3207
3207
3234
3275
3277
3312
3295
3540
3343
3358
3329
3367
3379
3371
H
3334
3374
3271
3333
3363
3255
3400
3793
3818
3316
3316
3497
3444
3442
3447
Min
3002
3160
3130
Max
3472
3818
3733
Avg (m/s)
3285
3367
3362
Std (m/s)
97
146
110
Avg = average velocity and Std = standard deviation.Table 3
S-wave velocities (m/s) at test grid points in slabs S1, S2, and S3.
Test point
S1
S2
S3
AB
CD
EF
GH
AB
CD
EF
GH
AB
CD
EF
GH
I
1830
1870
2020
1800
2270
1790
1830
2320
1910
1930
1890
1900
II
1950
1870
1840
1780
1800
1790
2070
1800
1930
1810
1900
2030
III
1880
1840
1840
1900
1780
1800
1830
2050
1960
2040
1950
2010
IV
1890
2160
1890
1890
1840
2070
2150
1920
1890
1980
1970
2050
V
2020
1890
2010
2040
2110
2040
2040
1920
1890
2010
2010
1970
Min
1780
1780
1810
Max
2160
2320
2050
Avg (m/s)
1911
1961
1952
Std (m/s)
95
169
62
Avg = average velocity and Std = standard deviation.Table 4
R-wave velocities (m/s) along 12 paths in slabs S1, S2, and S3.
Slab
Path
1
2
3
4
5
6
7
8
9
10
11
12
Min
Max
Avg
Std
S1
1768
1855
1913
1753
1951
1835
1988
1894
1882
1921
1917
1882
1753
1988
1880
69
S2
2025
1951
1874
1988
2006
1992
1894
2043
1855
1795
1932
1855
1795
2043
1934
79
S3
1853
1988
1970
1917
1992
1894
1855
1971
1845
1932
2006
1888
1845
2006
1926
75
Avg = average velocity and Std = standard deviation.The ranges for P-, S-, and R-wave velocities are 3002–3472 m/s, 1780–2160 m/s, and 1753–1988 m/s, respectively, for the reinforced concrete slab (S1). The data distribution for each type of wave is reasonably comparable to the theoretical velocity values of 3174, 1851, and 1827 m/s computed by (1) with Poisson’s ratio (0.16), dynamic elasticity (21.3 MPa), and density (2250 kg/m3). The difference between the maximum and minimum velocities in slab S1 tends to be smaller than those in S2 and S3, which have prestressing in two and one ways, respectively, because the stress field in the reinforced concrete slab is more consistent than those in the prestressed slabs.


### 4.2. Statistical Analysis

We conducted our statistical analysis on the UPV data mathematically to evaluate variation in the experimental data from the reinforced and prestressed concrete slabs. We used the sample size, mean, and standard deviation of the UPV from slabs S1, S2, and S3 for the basic input, as summarized in Table5.Table 5
The results of statistical analysis for slabs S1, S2, and S3.
Type of measurement
Type of slab
Statistics
⁢Goodness-of-fit test
Sample size
Avg(σ)∗ m/s
Std(μ)∗
∗ m/s
COV∗
∗
∗
D
m
a
x
D
5
%
p value
Probability distribution
P-wave
S1
40
3285
97
0.030
0.16
0.21
0.20
Normal
S2
40
3367
146
0.043
0.20
0.21
0.05
Normal
S3
40
3362
110
0.033
0.19
0.21
0.09
Normal
S-wave
S1
20
1911
95
0.049
0.23
0.29
0.18
Normal
S2
20
1961
169
0.086
0.24
0.29
0.17
Normal
S3
20
1952
62
0.032
0.20
0.29
0.33
Normal
R-wave
S1
12
1880
69
0.037
0.18
0.37
0.76
Normal
S2
12
1934
79
0.041
0.20
0.37
0.65
Normal
S3
12
1918
75
0.039
0.22
0.37
0.51
Normal
Avg(σ)∗ = average velocity; Std(μ)∗
∗ = standard deviation; COV∗
∗
∗ = coefficient of variable (=σ
/
μ
×
100 (%)).Generally, for an ultrasonic wave at 50 kHz with a wavelength of approximately 90 mm, the time of flight between the transmitter and receiver transducers can be influenced by the nonuniformity of coarse aggregate distribution, which creates a basic data error in the concrete material [26]. The statistical data show that the standard deviations and COVs of R- and S-waves are usually less than those of P-wave because of the two reasons. Firstly, P-wave has the highest velocity among all the ultrasonic waves. Secondly, the R- and S-waves depend less on boundary conditions and water pore pressure than P-waves. Therefore, it is possible to measure more distinct flight time, resulting in the more accurate wave velocity. Moreover, the MASW and MIRA tests for R- and S-wave measurements use improved algorithms to minimize noise signals from the multiple-sensor measurements. Thus, P-wave measurement of a single wave path associated with a single sensor has more systematic and electrical errors than R- and S-wave measurements.All the COVs of the UPV data in the field concrete specimen are good (4.0 to 5.0) or very good (3.0 to 4.0), according to ACI 214R [27], except for the S-wave measurement on slab S2. The large COV (0.086) in the S-wave measurement might be caused by unstable convergence in the SAFT algorithm on the rough surface of the concrete slab or by the inconsistent stress field in the prestressed concrete slab, even though we repeated the MIRA tests several times.In all the UPV tests, the COV tends to grow larger as the prestressing becomes stronger because the stress field in prestressed slabs is inconsistent, and the analytical characterization of ultrasonic waves in the inconsistent stress field of a nonhomogeneous material is almost impossible. Thus, our purpose in this study was to experimentally identify the statistical variations in UPV data from prestressed slabs and suggest practical recommendations.We also applied the Kolmogorov-Smirnov goodness-of-fit test [28] to all the cases to check the statistical distribution of the UPV measurements. In this test (as shown in Figures 17–19), we assumed an empirical stepwise cumulative frequency distribution function and plotted the cumulative normal distribution function for each of the variables presented in Table 5. The observed D-statistic, D
m
a
x, was less than the critical value corresponding to the commonly used 5% level of significance (Table 5). Therefore, the null hypothesis that the data have a normal distribution cannot be rejected at the 5% level of significance. The p value represents the probability that the observed sample statistic is equal to or more extreme than a statistical hypothesis, which means that the null hypothesis can be more accepted as the p value becomes larger than the level of significance. For all the data, the null hypothesis was satisfied. Also, the experimental data for the R-wave are more statistically significant than those for the S- and P-waves.Figure 17
Cumulative normal distribution function of P-wave velocities.Figure 18
Cumulative normal distribution function of S-wave velocities.Figure 19
Cumulative normal distribution function of R-wave velocities.To sum it all up, our inference is that all the types of UPV data can be represented as normally distributed variables with their respective means and standard deviations.


### 4.3. Comparison with the Dynamic Modulus from Static Test

We checked the accuracy of our experimental data by comparing the dynamic moduli from the measured UPV to one determined from the static modulus. Table6 shows the comparison of the dynamic moduli for S1, S2, and S3. The error range for slab S1 (without prestressing) is 5–7%, and the R-, S-, and P-waves, in that order, have smaller errors compared with the dynamic modulus from the static test. However, the error increases 12% for S2 and S3 regardless of the wave type, even though error between S2 and S3 is below 2%. Thus, prestressing affects all the types of wave velocities and increases the dynamic modulus by more than 10% based on the wave velocity.Table 6
Comparison of dynamic moduli from ultrasonic and static tests.
Measurement
Slab
Ultrasonic test
Static test
Error
Avgm/s
Edu∗ (GPa)
v
fck∗
∗ (Mpa)
E
c (GPa)
E
d (GPa)
P-wave
S1
3285
22.80
0.16
14.84
17.68
21.30
7.01%
S2
3367
23.96
0.16
14.84
17.68
21.30
12.46%
S3
3362
23.88
0.16
14.84
17.68
21.30
12.09%
S-wave
S1
1910
22.67
0.16
14.84
17.68
21.30
6.43%
S2
1960
23.87
0.16
14.84
17.68
21.30
12.07%
S3
1950
23.63
0.16
14.84
17.68
21.30
10.93%
R-wave
S1
1880
22.55
0.16
14.84
17.68
21.30
5.86%
S2
1934
23.87
0.16
14.84
17.68
21.30
12.06%
S3
1918
23.46
0.16
14.84
17.68
21.30
10.15%
Edu∗: dynamic modulus by ultrasonic test, fck∗
∗: 28-day compressive strength.


## 4.1. The Experimental Data for P-, S-, and R-Wave Velocities

To minimize the random errors associated with identifying the arrival time, we averaged the times for 128 waveforms for the P-wave measurement. For the S-wave measurement, we repeated the MIRA tests at each point until we identified a clear reflection from the back of the slab. We also carried out the MASW test on a single path until the computed dispersion image showed a distinct A0 mode. All the data for the P-, S-, and R-wave velocities are summarized in Tables2–4.Table 2
P-wave velocities (m/s) at test grid points in slabs S1, S2, and S3.
Test point
S1
S2
S3
I
II
III
IV
V
I
II
III
IV
V
I
II
III
IV
V
A
3002
3301
3295
3326
3231
3411
3258
3400
3183
3391
3253
3320
3348
3358
3244
B
3136
3333
3283
3331
3308
3333
3433
3395
3285
3691
3211
3733
3630
3300
3401
C
3254
3197
3281
3350
3322
3275
3335
3287
3287
3358
3316
3409
3367
3256
3260
D
3429
3339
3318
3340
3429
3329
3333
3297
3348
3246
3301
3256
3283
3301
3337
E
3130
3268
3104
3472
3378
3166
3398
3300
3474
3160
3554
3337
3435
3341
3406
F
3108
3268
3300
3391
3374
3374
3528
3280
3524
3260
3320
3458
3130
3279
3371
G
3191
3207
3207
3234
3275
3277
3312
3295
3540
3343
3358
3329
3367
3379
3371
H
3334
3374
3271
3333
3363
3255
3400
3793
3818
3316
3316
3497
3444
3442
3447
Min
3002
3160
3130
Max
3472
3818
3733
Avg (m/s)
3285
3367
3362
Std (m/s)
97
146
110
Avg = average velocity and Std = standard deviation.Table 3
S-wave velocities (m/s) at test grid points in slabs S1, S2, and S3.
Test point
S1
S2
S3
AB
CD
EF
GH
AB
CD
EF
GH
AB
CD
EF
GH
I
1830
1870
2020
1800
2270
1790
1830
2320
1910
1930
1890
1900
II
1950
1870
1840
1780
1800
1790
2070
1800
1930
1810
1900
2030
III
1880
1840
1840
1900
1780
1800
1830
2050
1960
2040
1950
2010
IV
1890
2160
1890
1890
1840
2070
2150
1920
1890
1980
1970
2050
V
2020
1890
2010
2040
2110
2040
2040
1920
1890
2010
2010
1970
Min
1780
1780
1810
Max
2160
2320
2050
Avg (m/s)
1911
1961
1952
Std (m/s)
95
169
62
Avg = average velocity and Std = standard deviation.Table 4
R-wave velocities (m/s) along 12 paths in slabs S1, S2, and S3.
Slab
Path
1
2
3
4
5
6
7
8
9
10
11
12
Min
Max
Avg
Std
S1
1768
1855
1913
1753
1951
1835
1988
1894
1882
1921
1917
1882
1753
1988
1880
69
S2
2025
1951
1874
1988
2006
1992
1894
2043
1855
1795
1932
1855
1795
2043
1934
79
S3
1853
1988
1970
1917
1992
1894
1855
1971
1845
1932
2006
1888
1845
2006
1926
75
Avg = average velocity and Std = standard deviation.The ranges for P-, S-, and R-wave velocities are 3002–3472 m/s, 1780–2160 m/s, and 1753–1988 m/s, respectively, for the reinforced concrete slab (S1). The data distribution for each type of wave is reasonably comparable to the theoretical velocity values of 3174, 1851, and 1827 m/s computed by (1) with Poisson’s ratio (0.16), dynamic elasticity (21.3 MPa), and density (2250 kg/m3). The difference between the maximum and minimum velocities in slab S1 tends to be smaller than those in S2 and S3, which have prestressing in two and one ways, respectively, because the stress field in the reinforced concrete slab is more consistent than those in the prestressed slabs.


## 4.2. Statistical Analysis

We conducted our statistical analysis on the UPV data mathematically to evaluate variation in the experimental data from the reinforced and prestressed concrete slabs. We used the sample size, mean, and standard deviation of the UPV from slabs S1, S2, and S3 for the basic input, as summarized in Table5.Table 5
The results of statistical analysis for slabs S1, S2, and S3.
Type of measurement
Type of slab
Statistics
⁢Goodness-of-fit test
Sample size
Avg(σ)∗ m/s
Std(μ)∗
∗ m/s
COV∗
∗
∗
D
m
a
x
D
5
%
p value
Probability distribution
P-wave
S1
40
3285
97
0.030
0.16
0.21
0.20
Normal
S2
40
3367
146
0.043
0.20
0.21
0.05
Normal
S3
40
3362
110
0.033
0.19
0.21
0.09
Normal
S-wave
S1
20
1911
95
0.049
0.23
0.29
0.18
Normal
S2
20
1961
169
0.086
0.24
0.29
0.17
Normal
S3
20
1952
62
0.032
0.20
0.29
0.33
Normal
R-wave
S1
12
1880
69
0.037
0.18
0.37
0.76
Normal
S2
12
1934
79
0.041
0.20
0.37
0.65
Normal
S3
12
1918
75
0.039
0.22
0.37
0.51
Normal
Avg(σ)∗ = average velocity; Std(μ)∗
∗ = standard deviation; COV∗
∗
∗ = coefficient of variable (=σ
/
μ
×
100 (%)).Generally, for an ultrasonic wave at 50 kHz with a wavelength of approximately 90 mm, the time of flight between the transmitter and receiver transducers can be influenced by the nonuniformity of coarse aggregate distribution, which creates a basic data error in the concrete material [26]. The statistical data show that the standard deviations and COVs of R- and S-waves are usually less than those of P-wave because of the two reasons. Firstly, P-wave has the highest velocity among all the ultrasonic waves. Secondly, the R- and S-waves depend less on boundary conditions and water pore pressure than P-waves. Therefore, it is possible to measure more distinct flight time, resulting in the more accurate wave velocity. Moreover, the MASW and MIRA tests for R- and S-wave measurements use improved algorithms to minimize noise signals from the multiple-sensor measurements. Thus, P-wave measurement of a single wave path associated with a single sensor has more systematic and electrical errors than R- and S-wave measurements.All the COVs of the UPV data in the field concrete specimen are good (4.0 to 5.0) or very good (3.0 to 4.0), according to ACI 214R [27], except for the S-wave measurement on slab S2. The large COV (0.086) in the S-wave measurement might be caused by unstable convergence in the SAFT algorithm on the rough surface of the concrete slab or by the inconsistent stress field in the prestressed concrete slab, even though we repeated the MIRA tests several times.In all the UPV tests, the COV tends to grow larger as the prestressing becomes stronger because the stress field in prestressed slabs is inconsistent, and the analytical characterization of ultrasonic waves in the inconsistent stress field of a nonhomogeneous material is almost impossible. Thus, our purpose in this study was to experimentally identify the statistical variations in UPV data from prestressed slabs and suggest practical recommendations.We also applied the Kolmogorov-Smirnov goodness-of-fit test [28] to all the cases to check the statistical distribution of the UPV measurements. In this test (as shown in Figures 17–19), we assumed an empirical stepwise cumulative frequency distribution function and plotted the cumulative normal distribution function for each of the variables presented in Table 5. The observed D-statistic, D
m
a
x, was less than the critical value corresponding to the commonly used 5% level of significance (Table 5). Therefore, the null hypothesis that the data have a normal distribution cannot be rejected at the 5% level of significance. The p value represents the probability that the observed sample statistic is equal to or more extreme than a statistical hypothesis, which means that the null hypothesis can be more accepted as the p value becomes larger than the level of significance. For all the data, the null hypothesis was satisfied. Also, the experimental data for the R-wave are more statistically significant than those for the S- and P-waves.Figure 17
Cumulative normal distribution function of P-wave velocities.Figure 18
Cumulative normal distribution function of S-wave velocities.Figure 19
Cumulative normal distribution function of R-wave velocities.To sum it all up, our inference is that all the types of UPV data can be represented as normally distributed variables with their respective means and standard deviations.


## 4.3. Comparison with the Dynamic Modulus from Static Test

We checked the accuracy of our experimental data by comparing the dynamic moduli from the measured UPV to one determined from the static modulus. Table6 shows the comparison of the dynamic moduli for S1, S2, and S3. The error range for slab S1 (without prestressing) is 5–7%, and the R-, S-, and P-waves, in that order, have smaller errors compared with the dynamic modulus from the static test. However, the error increases 12% for S2 and S3 regardless of the wave type, even though error between S2 and S3 is below 2%. Thus, prestressing affects all the types of wave velocities and increases the dynamic modulus by more than 10% based on the wave velocity.Table 6
Comparison of dynamic moduli from ultrasonic and static tests.
Measurement
Slab
Ultrasonic test
Static test
Error
Avgm/s
Edu∗ (GPa)
v
fck∗
∗ (Mpa)
E
c (GPa)
E
d (GPa)
P-wave
S1
3285
22.80
0.16
14.84
17.68
21.30
7.01%
S2
3367
23.96
0.16
14.84
17.68
21.30
12.46%
S3
3362
23.88
0.16
14.84
17.68
21.30
12.09%
S-wave
S1
1910
22.67
0.16
14.84
17.68
21.30
6.43%
S2
1960
23.87
0.16
14.84
17.68
21.30
12.07%
S3
1950
23.63
0.16
14.84
17.68
21.30
10.93%
R-wave
S1
1880
22.55
0.16
14.84
17.68
21.30
5.86%
S2
1934
23.87
0.16
14.84
17.68
21.30
12.06%
S3
1918
23.46
0.16
14.84
17.68
21.30
10.15%
Edu∗: dynamic modulus by ultrasonic test, fck∗
∗: 28-day compressive strength.


## 5. Conclusion

We conducted a series of experimental UPV tests to explore the variation of P-, S-, and R-wave velocities in a reinforced concrete slab and two prestressed concrete slabs. For the S- and R-wave measurements, we applied the MIRA and MASW tests, respectively, and verified that they are robust, promising test methods for wave velocity measurement. All of our experimental data are statistically stable and significant. Based on the data presented in this study, we draw the following conclusions.(i)
First, all the experimental UPV data are in the reasonable range theoretically computed from the physical properties found in the static test. The experimental data for the R-, S-, and P-waves, in that order, are statistically stable because of differences in energy magnitude, effects of confinement, and improvements in the measurement equipment and analysis associated with the various sensors.
(ii)
The statistical analysis by COV and goodness-of-fit test showed good or very good data distribution rates, according to ACI 214R, and all the data represent the normal distribution at the 5% level of significance. Thus, all of the data can be trusted, statistically.
(iii)
The ultrasonic velocities in the prestressed concrete, regardless of wave type, are 2-3% faster than those in the reinforced concrete slab. Also, the dynamic moduli from the UPV data in the PSC slab are 5–7% higher than those in the RC slab.
(iv)
We obtained statistically reliable data using promising methods and showed the variation of elastic waves in PSC and RC slabs. Our experimental results offer practical guidelines for the application of ultrasonic methods to PSC structures.



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*Source: 1548215-2016-09-08.xml*