# Evaluation of Condition of Concrete Structures Using Ultrasonic Pulse Velocity Method
## 3 Ultrasonic Pulse Velocity Method
\[V_{p}=\sqrt{\frac{M}{\rho}}=\sqrt{\frac{E(1-v)}{\rho(1+v)(1-2v)}} \tag{1}\]  
where,  
\(V_{p}\): Velocity (m/s)  
\(M\): Constrained modulus (MPa)  
\(E\): Young's modulus (MPa)  
\(\rho\): Density (kg/m\({}^{3}\))  
\(v\): Poisson's ratio  
As can be seen from Equation (1), the fundamental components of concrete that affect the wave velocity are the elastic modulus and density. The wave velocity is proportional to the square root of the elastic modulus and inversely proportional to the square root of the density. Factors affecting the wave velocity other than the strength are the water content and rebar. As for the water content, when concrete is changed from the dried state to the saturated state, the wave velocity increases by approximately 5%. As for rebar, correction factors of 0.9 and 0.8 for the measured ultrasonic pulse velocity are proposed for perpendicular and parallel cases to the wave path, respectively. When a stress wave is propagated along a medium with the cylindrical shape in which axial displacement is allowed, the rod-wave velocity (\(V_{c}\)) can be determined by Equation (2). \[V_{c}=\sqrt{\frac{E}{\rho}} \tag{2}\]  
As opposed to the P wave, the S wave causes only shear deformation without volume deformation, and the direction of the medium particle motion is perpendicular to the propagation direction. The velocity of the S wave (\(V_{s}\)) in Equation (3) is determined by the shear elastic modulus and density of the medium. \[V_{s}=\sqrt{\frac{G}{\rho}} \tag{3}\]  
where \(G=\frac{E}{2(1+v)}\): Shear elastic modulus (MPa)  
The medium particles of Rayleigh waves propagating along the surface of a semi-infinite medium show their behavior in the form of a retrograde ellipse, and the behavior is opposite to the propagation direction of the wave on top of the ellipse. The velocity of the R wave (\(V_{R}\)) in Equation (4) is a function of Poisson's ratio and can be obtained from the velocity of the S wave. \[V_{R}=\frac{0.83+1.12v}{1+v}V_{s} \tag{4}\]  
The ultrasonic pulse velocity method comprises direct, indirect, and angle beam methods according to the placement of the transmitter and receiver. The direct method is the most reliable one. When the characteristics of materials are evaluated by measuring the ultrasonic pulse velocity, the measurement accuracy must be very high. This means that testing equipment capable of generating appropriate pulses and accurately measuring the transit time through the tested material must be used. When the path lengths of pulses in a material are measured, the pulse velocity can be calculated using Equation (5). \[\text{Pulse velocity}=\frac{\text{Path length}}{Transit time} \tag{5}\]  
The typical equipment used for testing includes a pair of flexible data port channel (FDPC) platforms for recording and analyzing the original velocity, and receiver transducers (54 kHz) for displaying the pulse velocity energy detected by the receiver. In the ultrasonic pulse velocity method inspection source, the receiver (54-kHz resonant transducer concrete) compressional wave and the ultrasonic pulse are included when transferring the distance known through waves, concrete, or wood. The signal is recorded by the computer, which is capable of amplifying, filtering, and viewing the signal. The computer also records the execution time and voltage amplitude. The pulse velocity is calculated by dividing the pulse path length by the transit time in concrete. The number shown on the measuring instrument represents the velocity passing from the transmitting transducer (Tx) to the receiving transducer (Rx) when Tx and Rx are located at the appropriate positions on the surface of a member, and it is the value for the earliest pulse.