# On the Modeling and Analysis of Brittle Failure in Existing R/C Structures Due to Seismic Loads
## 3 Example Application of the Proposed Numerical Simulation Procedures
### Evaluation of the Analyses Results  
In order to evaluate the accuracy of the results obtained from a third-tier seismic assessment of substandard R/C buildings simulated according to the proposed modeling procedures, the computed response of the FE building model of the SPEAR building is compared to the actual response recorded at ELSA-JRC during the testing. To demonstrate the significance of simulating the brittle mechanisms of failure in substandard R/C buildings, these comparisons considered modifications in the structural response as follows: (i) a first FE building model of the SPEAR building accounted only for the inelastic flexural response of the R/C structural elements, while (ii) in a second FE building model, zero-length elements simulating mechanism [M2-M5] along column lines according to Section 2 were also included. Figures 8-13 present a comparison between the computed time histories of the horizontal displacements along with the \(X\) and \(Y\) plan directions, \(U_{X}\) and \(U_{Y}\), versus those recorded at ELSA-JRC during the s10, s11, and s12 pseudo-dynamic tests (black lines). Specifically, the numerical responses obtained from the time-history dynamic analyses of the FE building model using the proposed simulation procedure (dark grey lines) and those of the FE building model, accounting only for an inelastic flexural response, are plotted concurrently (light gray lines). These displacements correspond to the vibration of the center of mass  
(_CM_) of the three floors of the SPEAR building. Note that the overestimation of flexural stiffness leads to very low estimates of displacements and a stiffer overall structure, i.e., a lower natural period leading to unconservative results for the displacement demands and the anticipated damage. In the s11 earthquake case, the displacement demands estimated from analysis of the FE building model accounting only for inelastic flexural response are downgraded by 24% to 58% in the \(X\) plan direction and by 16% to 37% in the \(Y\) plan direction as compared to the response of the test building. In the case of the s12 earthquake case, the estimated displacement demands according to the analysis results of the same FE building model are downgraded by 32% to 61% and by 51% to 57% in the \(X\) and \(Y\) plan directions, respectively, as compared to the actual building response. On the other hand, the addition of the zero-length elements seem to have lengthened the natural period, leading to convergence of the displacement response and damage as compared to the response of the test building. Decisions made based on these two bounding estimates respectively would lead to little or no retrofit in the former case, and excessive and invasive retrofit in the latter case. It is also noted that as the intensity of shaking and damage accumulation from previous shaking increases in the structure, the waveforms of the more compliant model where all mechanism formations have been activated converge to the experimental response. This primarily occurs during the duration of the response pulses, which suggests convergence in the fundamental period computation.