# Seismic Performance of Dam Piers Retrofitted with Reinforced Polymer Cement Mortar
## 3 Outline of Seismic Response Analysis for Dam Piers of Existing Dams  
### Shape and Modeling of the Target Dam Piers  
To investigate the influence of the structural characteristics of dam piers on the reinforcing effect of the SRS method, we targeted the dam piers of four existing dams. In this study, they are called TYPE-A, -B, -C and -D, respectively. Figure 11 shows their shapes and dimensions, as well as the FEM model. As shown in Figure 11a, TYPE-A has dimensions such as a height of approximately 17.5 m, a length in the upstream and downstream directions of approximately 10 m, and a thickness in the dam axis direction (this becomes a weak axis direction) of approximately 2 m. For reinforcement, D16 was used as the main reinforcement, and D13 was used as the shear reinforcement. The bar arrangement interval was 600 mm for the main bar and 600 mm for the shear reinforcing  
Figure 10: Load\(-\)strain relationship of each of the reinforcing bars: (**a**) compression strain of the rebar in the concrete; (**b**) tensile strain of the rebar in the concrete; (**c**) compression strain of the rebar in the PCM layer; (**d**) tensile strain of the rebar in the PCM layer. Figure 9: Comparison of the load-displacement relationship. bar. Next, as shown in Figure 11b, TYPE-B has a height of approximately 25 m, a length in the upstream and downstream directions of approximately 20 m, and a thickness in the dam axis direction of approximately 3 m. It is a dam pier that is larger than the TYPE-A model in both thicknesses. Regarding the reinforcement, D22 and D19 were used as the main reinforcements, and D13 was used as the shear reinforcement in the upper part. The bar arrangement interval was 158 mm for the main bar and 2000 mm for the shear reinforcing bar. At the bottom, D25 was arranged as the main reinforcement, and D16 was arranged as the shear reinforcement. The bar arrangement interval was 181 mm for the main bar and 500 mm for the shear reinforcing bar. Figure 11: FEM analysis models of dam pier: (**a**) TYPE-A dam pier; (**b**) TYPE-B dam pier; (**c**) TYPE-C dam pier; (**d**) TYPE-D dam pier. The major difference between the four types of dam piers is the shape and amount of the reinforcement. TYPE-A has a low and thick shape, and TYPE-B has a high and thin shape. In addition, TYPE-A has sparse reinforcement, and TYPE-B has dense reinforcement. As shown in Figure 11c, TYPE-C has dimensions such as a height of approximately 12.1 m, a length in the upstream and downstream directions of approximately 10 m and a thickness in the dam axis direction of approximately 2.5 m. For reinforcement, D25 is used as the main reinforcement, and D16 is used as the shear reinforcement. The bar arrangement interval was 450 mm for the main bar and 800 mm for the shear reinforcing bar. TYPE-C is lower and thicker than the TYPE-A and -B models, so it has a chunky shape overall. As shown in Figure 11d, TYPE-D has dimensions such as a height of approximately 15.4 m, a length in the upstream and downstream directions of approximately 10 m and a thickness in the dam axis direction of approximately 2.5 m. For reinforcement, D16 is used as the main reinforcement, and D12 is used as the shear reinforcement. The bar arrangement interval was 500 mm for the main bar and 1000 mm for the shear reinforcing bar. The TYPE-D model has the sparsest reinforcement among the four dam types. The differences in the structural characteristics of these four dam piers are shown for the slenderness ratio and natural frequency. Figure 12 shows the slenderness ratio of the four dams and the amount of reinforcing bar in the existing part. The slenderness ratio is defined by Equation (1). Here, \(i\) is the radius of gyration of area, \(A\) is the cross-sectional area, \(B\) is the horizontal width of the cross-section and \(H\) is the vertical width of the cross-section. In addition, the amount of reinforcing bars in the existing part is defined by the total cross-sectional area of the reinforcing bars included in the unit length.