# Study on Impact-Echo Response of Concrete Column near the Edge
## 2 Background
### Numerical Models  
Because in the actual detection process, the knock position, the sensor placement position, and the intensity of each knock are slightly different, it affects the received signal. Therefore, it is necessary to carry out numerical analysis to understand the transient impact response of the concrete column. The strain generated by the shock wave on the concrete surface is deficient. Therefore, the linear elastic material model suits concrete with low strain levels. In the impact-echo test, the excitation of the stress wave is generated by a small steel ball (17 mm in diameter) falling onto the surface of the concrete. In this paper,  
Figure 1: (**a**) SPC-MATS instrument; (**b**) impact–echo instrument.  
to accurately simulate the actual impact load, ABAQUS/Explicit was used to simulate and analyze the transient impact process of a steel ball falling from a certain height on the surface of a concrete column (in the simulation, the falling process of a steel ball was simplified as a semi-periodic harmonic force [27]). The displacement of particles on the surface of concrete members was collected near the impact point so as to obtain the propagation information of stress waves in concrete members. On this basis, the time domain diagram of the harmonic motion was transformed into a frequency spectrum diagram via fast Fourier transform (FFT) for specific analysis. In this paper, the response of stress waves under the boundary condition of the concrete column is studied and the influence of boundary conditions on the signal is discussed. The ABAQUS finite element simulation was used to simulate the signal received by the signal sensor when the steel ball was knocked near the boundary of the concrete column, then the signal was extracted by Origin software to perform Fourier transform in order to obtain the spectrum diagram, and the change in its predominant frequency was analyzed. The impact form is shown in Formula (3).  
\[F(t)=\left\{\begin{array}{c}F_{max}\sin\left(\frac{\pi t}{t_{c}}\right)0 \leq t\leq t_{c}\\ 0\text{ }t>t_{c}\end{array}\right. \tag{3}\]  
The maximum simulated concentrated force was 30 N. The duration of shock action was calculated by the formula (12-74 \(\upmu\)s) [28; 29]. The signal was collected every 2 \(\times\) 10\({}^{-6}\) s, and the corresponding sampling frequency was 500 kHz. The maximum effective frequency generated by the small steel ball was about 17.1 kHz because the density of concrete was 2400 kg/m\({}^{3}\), the elastic modulus was 3.25 \(\times\) 10\({}^{10}\) Pa, Poisson's ratio was 0.2, the wave velocity calculated by Formula (2) was 4000 m/s, and the wavelength was approximately 23.39 cm when calculated. Then, according to Formula (4), the maximum mesh size was estimated to be 10 mm. The unit type was C3D8R, where C is the entity, 3D represents three dimensions, 8 is the number of nodes of the unit, R is the reduced integral unit, and the grid is divided by sweeping.  
\[L_{min}\leq\frac{\lambda_{min}}{20} \tag{4}\]  
The end surfaces of concrete columns often cause many frequency peaks to appear in the spectra of the simulation results, and this is because a reflection phenomenon occurs when the stress wave reaches the end surface of the concrete column during the propagation process. This paper creates an infinite element on the end surface of the concrete column, extending the column's end surface infinitely so that the waves inside the member are not affected by the influence of the end surface. At the edge, 5 cm is used as the node for impact, from the middle of the column to the boundary, and 5 cm above the impact point is used as the signal receiving point. When entering the mutation range, the node accurately arranges an impact point for each 1 cm. The model is shown in Figure 3.  
Figure 2: (**a**) details of the detection area; (**b**) field testing at the boundary.