# The Dynamic Response of an Arch Dam During a Record Low-Intensity Earthquake
## 4 Behavior During the Low-Intensity Earthquake  
The analysis of the dam's dynamic behavior during the low-intensity earthquake was performed with the numerical model calibrated with the experimental results for the full reservoir condition. Due to the finite size of the numerical model, absorbing boundaries have to be employed to simulate the continuity of the foundation rock mass, thus avoiding the reflection of seismic waves at the numerical boundaries, which would affect the dynamic behavior of the dam. The free field conditions applied to the four lateral boundaries of the model sides are intended to provide the dynamic stresses resulting from the vertically propagating wave. The formulation implemented in 3 DEC [13; 21] (Figure 9a) follows the same principles of the direct finite element models [1; 6]. At the lateral boundaries, the free-field meshes are connected by viscous elements to the main model, providing the intended non-reflecting conditions (Figure 9b). The issue of the appropriate size of numerical models has been discussed in the literature [1]. Comparisons of models with different sizes have been presented [7]. In standard practice, the boundaries are placed at a distance larger than the dam height [5; 6]. In the present model, the dam height is 123 m; thus, in the vertical direction, the lower boundary is placed 200 m below the dam, and the lateral boundaries are about 150 m away from the abutments. The dynamic input is applied at the model base, a standard viscous boundary, by means of a stress record. Figure 8: Natural frequencies determined with the numerical model (NUM), forced vibration tests (FVTs), and average curve for the CDMS for different elevations of the Baixo Sabor reservoir. The seismic monitoring system (SMS) implemented at the Baixo Sabor dam has recorded the occurrence of several low-intensity earthquakes. The event on 3 October 2020 at 12:29 was chosen, whose epicenter was located about 8 km from the dam and had a magnitude of approximately 2.0. Based on the records of the seismometers installed along the dam's foundation, the velocities to be applied to the base of the numerical model were determined. These velocities were converted into dynamic stress histories based on the characteristics of the rock mass (specific mass and propagation velocities of the shear and pressure waves) for application in the numerical model. This conversion is based on the assumption of a vertically propagating plane wave, thus not taking into account the geometry of the valley. Therefore, the stress record applied at the model base has to be calibrated to approximate the measured velocities at the SM3 monitoring point. For this purpose, the dynamic stresses were multiplied by a factor of 1.8 in the direction perpendicular to the river and by 1.2 in the other two directions. Figure 10 shows the velocities obtained at the base of the numerical model in the simulation of the event by the application of these stress records. Figure 11 presents the comparison of the results of the numerical model and the values observed at point SM3 (base of the dam) in terms of velocities and frequency content. The good agreement of the results, particularly the in-frequency content, shows that the numerical model is capable of reproducing the field conditions. Figure 10: Velocities obtained in the numerical simulation at a point under the dam axis in the lower boundary of the model. Figure 9: Numerical model for the study of seismic action: (**a**) schematic of the adopted boundary conditions (_free field_) and (**b**) view of the numerical model. Figure 12 shows the velocities obtained in the foundation (SM1 and SM6) and near the crest (SM2 and SM5) in the numerical model and in the SMS. There is generally good agreement between the peak values obtained with the numerical model and the observed values. For the points on the dam crest, in the radial direction, the numerical model displays faster attenuation after the peak values than the monitoring records.