## 5 Numerical Analysis Results  
Figure 12 shows the finite element analysis results for a hardfill dam body with three slopes (1:0.6, 1:0.8, 1:1) and a height of 50 m. It shows the stress distribution of the cross-section of the dam body when the maximum compressive stress and maximum tensile stress occur in the dam body, and the three types of seismic waves in Figure 5 are applied. The location where the maximum compressive stress occurs in the dam body differs according to the type of seismic wave. The maximum compressive stress occurs at the lower part of the upstream side (left side) of the dam body with a 1:0.6 slope for the Hachinohe wave, at the upper part of the downstream side (right side) of the dam body with a 1:0.8 slope for the Ofunato wave, and at the upper side of the dam body with a 1:1.0 slope in the case of an artificial wave. Meanwhile, the maximum tensile stress occurs similarly at the lower part of the upstream side for all three types of seismic waves, as shown similarly in a previous study [13]. Figure 13 shows the changes in the maximum compressive stress and maximum tensile stress according to the change in the slope of the dam body for the three types of seismic waves. The maximum compressive stress is the largest at 2.14 MPa in the hardfill dam body, with the steepest slope of 1:0.6 when the artificial wave with the largest maximum acceleration is applied. However, it rapidly decreases to 1.3 MPa when the slope is relaxed to 1:0.8. The maximum compressive stresses under the action of the Hachinohe and Ofunato  
Figure 12: Results of FE analysis (stress distributions). (**a**) Compressive stress of Hachinohe wave (1:0.6); (**b**) tensile stress of Hachinohe wave (1:0.6); (**c**) compressive stress of Ofunato wave (1:0.8); (**d**) tensile stress of Ofunato wave (1:0.8); (**e**) compressive stress of artificial seismic wave (1:1.0); (**f**) tensile stress of artificial seismic wave (1:1.0). waves are 1.07 MPa and 1.14 MPa in the hardfill dam body with a slope of 1:0.6, respectively, i.e., significantly lower than that of the artificial wave. Subsequently, all of them gradually decrease as the slope is relaxed. The largest value of the maximum tensile stress occurs in the hardfill dam body with a slope of 1:0.6 when the artificial wave is applied, as in the case of the maximum compressive stress. However, the magnitude is only 0.1 MPa, i.e., significantly lower than that of the compressive stress. Furthermore, the maximum tensile stress tends to decrease overall as the slope of the dam body is relaxed. However, the decrease is relatively insignificant or increases in some parts (the dam body with a slope of 1:0.8 in the Hachinohe wave). Figure 13: Results of FE analysis (maximum compressive and tensile stresses). (**a**) Maximum compressive stress. (**b**) Maximum tensile stress. The hardfill comprising the dam body must have sufficient strength to resist the maximum compressive stress and maximum tensile stress occurring in the dam body. In this study, the stability of the hardfill dam body was evaluated by applying a safety factor of 1.5 to the maximum stress values shown in Figure 13. That is, the value obtained by multiplying the safety factor of 1.5 by the larger value of the maximum compressive stress and the compressive stress converted into seven times the maximum tensile stress was set as the minimum compressive strength of hardfill required to maintain the stability of the hardfill dam body (i.e., required hardfill strength) [3]. This was compared with the uniaxial compressive strengths of the large hardfill specimens through indoor laboratory tests described in Section 3 and the uniaxial compressive strengths of the field-compacted hardfill cores described in Section 4. The results are shown in Figure 14. The required hardfill strengths of the three inclined hardfill dam bodies for the three seismic waves are displayed as bar graphs.