## 4 Numerical Calculation Results and Analysis
### Discussion of Seismic Time-History Response Results
#### 4.3.2 Deformation and Stress of the Tank Wall  
Seismic damage to steel storage tanks may take several forms. Large axial compressive stresses due to the beam-like bending of the tank wall can lead to \"elephant-foot\" buckling of the wall [19], as shown in Figure 7a. In this study, the \"elephant-foot\" deformation of the tank wall is also obtained by the numerical simulation method, as shown in Figure 7b. It can be seen that the numerical simulation results in this study are consistent with the actual earthquake damage phenomenon. The tank is axisymmetric, and the earthquake action is not axisymmetric, so the horizontal displacement along the circumference of the tank body is different at a certain height from the bottom of the tank. In the analysis, for different excitation directions, the locations of the measured nodes are different, as shown in Figure 5. Compared with the unidirectional X excitation, the vertical component will not affect the location of the measurement points, while the horizontal Y component will change the positions of the measurement nodes. The peak displacements comparison along the tank wall under El Centro ground motion is shown in Figure 8a. The horizontal displacements of the tank wall are nearly symmetrical along the height of the tank. The displacement response of the tank wall is near the bottom of the plate, referred to as the \"elephant-foot\" deformation, and exhibits the largest displacement. The horizontal deformation of the tank wall suddenly decreases after the deformation of the \"elephant-foot\" and then continues  
Figure 6: Comparison of the peak normalization of the seismic response of the tank under El Centro ground motion. to increase; that is, 1.8 m away from the bottom of the tank, the tank wall shows discernible relative shrinkage deformation. As shown in Table 3 and Figure 8a, the \"elephant-foot\" obtained under the X + Y + Z excitation increased notably compared to that of the X-direction excitation. The axial compressive stress distribution on the tank wall is shown in Figure 8b. In accordance with the Chinese national standard \"Code for design of vertical cylindrical welded steel oil tanks\" (GB50341-2014), the stress of the tank wall should be less than the allowable critical axial compressive stress. According to the design specifications, the allowable critical stress of the tank wall under earthquake conditions should be calculated by \([\sigma_{\sigma}]=0.22E\frac{t}{D}\), where \(E\) is the elastic modulus of the tank at the design temperature; \(t\) is the effective thickness of the bottom shell; and \(D\) is the inner diameter of the tank. The calculated allowable critical stress is 28.77 MPa. It should be noted that the maximum stress at this time has not reached the limit value of the yield stress of the material. From Table 3, the maximum hoop tensile stress is 123.10 MPa, and the maximum Mises stress is 119.97 MPa, and both of them are lower than the yield stress of 235 MPa of the tank. As shown in Table 3, the most obvious axial compressive stress appears in the tank under the El Centro ground motion. The maximum axial compressive stress of the tank is 31.72 MPa and 34.11 MPa under bi-directional horizontal X + Y excitation and tri-directional X + Y + Z excitation, respectively. Both the results exceed the allowable axial compressive stress of the code, indicating that the deformation of the \"elephant-foot\" position has reached a buckling failure state. In this case, the tank structure may be in a more dangerous state under the excitation of X + Y + Z seismic waves. It is necessary to consider the influence of both the vertical and bi-directional horizontal components of ground motion. Figure 8: Distribution of the seismic response results along the height of the tank wall under El Centro ground motion: (**a**) horizontal displacement; (**b**) axial stress.