# Evaluation of Unfilled Sheath in Concrete Structures Using Response Waveform in Time Domain
## 1 Introduction  
### Non-Destructive Testing for Concrete Structures  
Concrete is one of the most common construction materials. It is widely used for the construction of structures because the unit price of materials is low and on-site construction is easy [1]. For the asset management of the concrete structures, quality control during the construction and maintenance after the construction are significant roles. The soundness evaluations are performed for the objectives, and the results are used for the preventive maintenance as well. Although the visual inspection and hammering test are frequently conducted for the soundness evaluation, the techniques investigate only the surface of the structures, and it is difficult to evaluate the internal condition. In addition, it is known that the results of these techniques depend on the ability of the inspector. Hence, the results of the investigations might be unreliable if the inspector is unskilled. Therefore, the use of NDT and micro-destructive test are considered in order to guarantee the accuracy of the investigations [2; 3]. The IEW method is one of the NDT techniques of concrete structures [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. It has been applied to evaluate the thickness and internal defects of the target structure based on the dominant frequency of the response wave that is formed by the repeated reflections in the thickness direction. Furthermore, it is suitable for testing concrete structures because the frequency of the excitation is relatively low, and the elastic wave emitted by the excitation is not easily attenuated [4; 8]. In the field of NDT of concrete structures using IEW, [PERSON] et al. [4; 5; 6]. elucidated the response characteristics of elastic waves in the concrete structures and established a method to evaluate the thickness and internal defects of the concrete structures based on the frequency of standing waves that are formed bythe reflection of the elastic waves in the structures [4; 5; 6; 7; 8; 9; 10]. The elastic wave is reflected at a boundary where the acoustic impedance changes discontinuously. As a consequence, standing waves are formed between the boundaries, and the dominant frequency of the standing waves is determined by the distance between the boundaries. If the structure is sound, the boundaries are the surfaces of the structure and the dominant frequency is determined by the thickness of the structure. On the other hand, if the structure has internal defects, the boundaries are the surface of the structure and internal surface at the defect, and the dominant frequency is determined by the depth of the defect as a consequence. This evaluation method is called \"Impact-Echo\", and research on this technique has been actively conducted [12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. However, generally speaking, evaluation using Impact-Echo would be difficult if the size of the defect is relatively small or the location of the defect is deep since the multiple reflections are not formed clearly under the conditions [7; 21]. Further, if the structures are not able to be considered plate-like structures, it is difficult to apply the Impact-Echo because standing waves are not formed between the surfaces [22; 23; 24; 25]. The configuration of the plate-like structures in which Impact-Echo is applicable is defined in \"ASTM-C1383-04\" [26]. According to the definition, the lateral dimensions are at least six times the thickness so that the standing waves are correctly formed in the thickness direction. On the other hand, [PERSON] and [PERSON] proposed a technique that evaluates the internal defects in the members of a rectangular cross-section [22; 23]. This technique evaluates the soundness by using changes of the frequency characteristic of the members of the same configuration. However, if applied to existing structures, the evaluation indexes are the frequency characteristics of the members considered to be sound, and there is no guarantee that these indexes are sound.