# Failure Analysis of a Concrete Anchor under Severe Seismic Action
## 4 Dynamic Simulation under DS-0050
The yield and ultimate strength of the steel column (SS400) are 235 and 400 MPa, respectively; the corresponding values for the high-tension anchor bolt (M24, M36, M48) are 250 and 400 MPa. The compressive and tensile strengths are 30 and 2 MPa, respectively. The progressive tension and compression damage were used as shown in Figure 5. The surface interaction between concrete bed and anchor plate was modeled a master-slave surface interaction with friction (\(\mu=\)0.4) and no overlapping is allowed. Since no reinforcement was model in concrete bed, the interaction property between steel anchor and concrete bed was modeled a master-slave surface interaction with tie option. Data for the Gyeongju earthquake (Richter scale = 5.8) occurring in South Korea in 2016 were analyzed after tuning to a maximum PGA of 0.3 g (Figure 16). The input motion changed on initial zero padding of the time axis. This reduced the correlations among the three different directional inputs when the input motions were simultaneously applied. Correlations among the motions were calculated using Equation (13) and were 0.4%, 0.048%, and 0.043% for \(X\) vs. \(Y\), \(Y\) vs. \(Z\), and \(X\) vs. \(Z\), respectively. Therefore, the three orthogonal input motions are almost completely decoupled. Below, we discuss the structural responses to these simultaneously input motions and the ASCE 7 100:40:40 combination of individual input motions. \[\delta(\%)=\frac{1}{N}\sum_{i=1}^{N}\frac{\left(X_{i}-\overline{X}\right) \left(Y_{i}-\overline{Y}\right)}{s_{X}\cdot s_{Y}}\times 100 \tag{13}\]  
Figure 17 shows the pushover simulation results obtained with M24 anchors and regular (intact) steel supplements; we present the lateral force-displacement curves associated with different failure mechanisms. The inelastic behaviors (all of which are nonlinear) exhibit much lower reactions than the elastic restoring forces. The case in Figure 17 highlights the large difference. The mass of the structure is lumped at a single reference point (the center of gravity) and the structure is rigid. The ductility is derived from only the anchors and their supplements. Figure 17b indicates that the elastic, ductile design load limits are 586 and 398 kN, respectively. The nonlinear pushover simulation reveals a lateral force of 200 kN when the lateral displacement is about 15 mm, which is considerably less than the load design limits. The longitudinal tensile forces acting on each anchor are shown in Figure 18.  
Figure 13:0 The measured Gyeongju earthquake data (scaled to a maximum of 0.3 g). The elastic pushover simulation reveals that the independent (100:40:40) and simultaneous motions are associated with average anchor forces of 225 and 180 kN, respectively; the elastic design limit is 170 kN. Therefore, the M24 anchor is unsatisfactory. However, using a ductile design, the average anchor force is around 50 kN, which is satisfactory; the design limit is 141 kN. Figure 19 shows that all of the anchor shear forces satisfy both the elastic and ductile design limits. Figure 13:1 Anchor forces under shear (M24, pushover analyses). Figure 13:2 Pushover simulation of the entire model. (**a**) Simulation with different failure mechanisms. (**b**) Zoomed-in view of (**a**). Figure 13:3 Anchor forces under tension (M24, pushover analyses). During elastic/nonlinear time history analyses, simultaneous input motions (x: 0.3 g, y: 0.3 g, z: 0.15 g) were applied in three orthogonal directions. The time histories of inertial forces and displacement at the center of gravity (elevation from concrete bed = 0.6 m) are shown in Figure 13:4  
The lateral inertial force at the center of gravity was calculated via finite element analysis. Figure 21 shows the horizontal earthquake load; \(Q_{E}\) = 586 kN bounds both the elastic and ductile behaviors of the system. The lateral displacement is about 12-13 mm (Figure 22). Figure 13:5 Lateral inertial forces at the center of gravity (M24, dynamic analyses).