## 1 Introduction  
The accurate safety inspection technology is required to prevent safety accidents of infrastructures, and various studies have been actively conducted to inspect the structural safety of bridges [1; 2; 3; 4; 5; 6]. Bridge bearings are especially important due to their connections which accommodate the longitudinal deformations generated by environmental loads and support the traffic and wind loads. Among them, the seismic isolation bearings safely protect the bridge from seismic events by shifting the natural period of the structure under the occurrence of an earthquake, dissipating the seismic energy and enabling the recovery of eventual displacements [7; 8; 9; 10]. These features highlight the crucial role played by the bridge bearings in the structural stability by connecting the superstructure and substructure as well as the importance of their accurate design and construction for letting them fulfill their original functions. In particular, the bearing must be adequately anchored to the substructure by anchor bolts embedded with the required length to be able to transmit the loads [11; 12; 13]. However, these anchor bolts are often not meeting such a design requirement during their construction or replacement, which may result in the collapse of the whole structure due to the occurrence of problems like the rupture, loosening, damage of anchor bolts or the cracking of the pedestal as shown in Figure 1[14; 15; 16; 17; 18]. Moreover, in view of the peculiarities of the bridge bearing, it is difficult to verify the soundness of the anchor bolt before the failure of the concrete at the support. Accurately estimating the embedment depth of the anchor bolt using non-destructive testing (NDT) methods is thus necessary to solve such problems. The application of NDT methods such as ultrasonic, impact-echo, impulse thermography, radar, and acoustic emission is being extensively studied because of the possibility to inspect internal damages in the structure without mutilating it while preserving the quality [19; 20; 21]. Among these methods, those using ultrasonic pulses offer easier measurement as well as easier analysis that make them widely utilized for estimating the strength, analyzing the durable performances and evaluating the setting time of concrete according to various mix conditions and ages as well as detect defects and cracks occurring at the surface [21; 22; 23; 24; 25]. [PERSON] et al. proposed a model estimating the compressive strength of concretes with various mix conditions by using the measured ultrasonic velocity as input data [22]. [PERSON] and [PERSON] utilized the amplitude attenuation method in ultrasonic testing to evaluate the corrosion damage of the steel reinforcement in concrete. These authors experimentally proved the existence of a relationship between the average amplitude attenuation, the circuit potential values, the instantaneous corrosion rate, and the thickness loss [23]. [PERSON] et al. evaluated the corrosion-induced crack and rebar corrosion by ultrasonic testing and revealed that the ratio of the propagation distance was characterized by the attenuation, which was correlated with the damage of rebar corrosion [24]. [PERSON] et al. experimentally demonstrated that the crack width at the surface of the concrete could be detected by ultrasonic techniques [25]. The aforementioned studies focused mainly on the detection of cracks at the surface of concrete or on the evaluation of the material properties. In addition, the method using guided ultrasonic pulses  
Figure 1: Defects occurring in bridge bearings due to the insufficient embedment depth of anchor bolts: (**a**) rupture of anchor bolt; (**b**) loosening of anchor bolt; (**c**) damage of anchor bolt; (**d**) cracking of bridge bearing pedestal [14]. can be seen as representative for estimating the embedded length of steel bars like anchor bolts [26; 27; 28].