# Failure Analysis of a Concrete Anchor under Severe Seismic Action
## 3 Pushover Simulation to Quantify the Factors of Interest  
Figure 4 shows the anchorage of an arbitrary structure with a wide-flanged steel column (H \(\times\) B \(\times\)\(t_{w}\)\(\times\)\(t_{f}\):100 \(\times\) 100 \(\times\) 5 \(\times\) 8 mm) and four M8 anchor bolts. Although localized plastic behavior may differ by system (structure) ductility, redundancy, overstrength, and damping, we focus on the anchor zone shown in Figure 4 to explore variations in base shear forces during the different failure mechanisms of structural  
Figure 4: Anchor zone modeling for the pushover test. Figure 3: Load combinations when the primary load is an earthquake. (**a**) Redundancy factor. (**b**) Overstrength factor. elements. The base PL steel plate has dimensions of 300 \(\times\) 300 \(\times\) 10 mm and the concrete bed has dimensions of 1000 \(\times\) 1000 \(\times\) 200 mm; the anchor embedment is \(h_{ef}\) = 72.75 mm. The distance between the anchors is \(c_{a}\) = 150 mm. The yield and ultimate strength of the steel column (SS400) are 235 and 400 MPa, respectively; the corresponding values for the high-tension M8 anchor bolt are 250 and 400 MPa. The bilinear hardening law is applicable to the steel elements. We employ a damage-plasticity model (modified Drucker-Prager model) (Figure 5). The compressive and tensile strengths are 30 and 2 MPa, respectively. The strain softening model for plain concrete is used and the damage along the inelastic strain is defined as strength deterioration. In Figure 6, the anchor zone design is explored in terms of ductile failure (a). ASCE-7 permits other types of ductile failure, i.e., anchor supplement failure (b) and failure of the main structure or non-structural components (c). We applied a pushover test to the anchor zone using different failure mechanisms, to determine if the response modification and overstrength factors change. The parametric analyses consider five scenarios: anchor ductile failure, column ductile failure, concrete brittle failure, elastic/inelastic behavior, and all elastic/inelastic materials (Figure 7). Figure 5: (a) Inelastic material behavior of compressive concrete. (b) Variations in tensile strength and damage. Figure 8a shows the lateral force vs. displacement curve under various failure scenarios. The brittle failure of concrete beds is associated with a high horizontal reaction with a small displacement. During ductile failure, column yielding is much greater than anchor yielding. In addition, both cracked and non-cracked concrete beds influence ductile behavior in terms of stiffness and strength. In Figure 8b, the material overstrength factor is apparent when comparing the strain-hardening and perfectly plastic behaviors, and by examining the inelastic energy absorption factor \(R_{\mu}\). Figure 9 shows the maximum von-Mises anchor stress as the yield strength and elastic modulus of the steel column vary. As the anchor yield strength is 250 MPa and the anchor is elastic, the main structure experiences swinging vibration. If the structure is stiffer and stronger, the anchor must be larger in diameter and the embedded length must increase; thus, elastic anchors are expensive. The data can be interpreted as the equivalency between the elastic energy \(U_{e}\) and inelastic energy \(U_{i}\) in the lateral force-displacement curve (Figure 2). Figure 10 illustrates the importance of the anchor ductile yield under large lateral displacements; it reduces the reaction (base shear force) of the structure. Figure 11a shows the von-Mises stress contour of the model (ductile anchor yielding in tension) and Figure 11b illustrates the brittle concrete damage (crack) in the vicinity of the steel anchor. Figure 12 shows the measured response modification factor \(R\) (5.0) and overstrength factor (material overstrength factor; 1.65). Thus, the inelastic energy absorption factor \(R_{\mu}\) is 3.0. Figure 8: Pushover simulations. (**a**) Lateral force vs. lateral displacement under different failure scenarios.