# Faster Post-Earthquake Damage Assessment Based on 1D Convolutional Neural Networks
## 4 Case Study  
### Benchmark Building and NLTHA  
A benchmark building analyzed by [49] was selected as the case study structure. This benchmark building was designed as a hypothetical four-story office building based on the 2003 International Building Code (IBC). The building was located in a typical high-seismic urban region of California. The design incorporated a perimeter-frame system with four perimeter frames mainly providing the lateral resistance for the building. Figure 4 shows a 2D nonlinear finite element model of one perimeter frame of the benchmark building in OpenSEES [50]. In Figure 4a, the symbols of \"b\", \"h\", and \"bar #\" are the width (m), depth (m), and steel rebar diameter (mm) of the beams and columns. The symbol \"\(\rho\)\" means the reinforcement ratio of the columns, and the symbols \"\(\rho_{\text{bot}}\)\" and \"\(\rho_{\text{top}}\)\" are the bottom and top reinforcement ratios of the beams. In this study, all the columns were fixed at the base since their support conditions had little effect on seismic responses. Figure 4b represents the fiber-distributed plasticity element to simulate the nonlinearity of the beams and the columns of the frame. Each structural element consisted of five integration points. The material characteristics of concrete (with a nominal compressive strength of 34.5 MPa) and steel (with an expected yield strength of 462 MPa) were captured by the Concrete02 and Steel02 material models in OpenSEES, respectively. The stress-strain relationships (left) and the hysteretic behavior (right) of Concrete02 (top) and Steel02 (bottom) are found in Figure 4c. Additional details regarding these two materials were referenced in [51,52]. The dynamic analysis was conducted on the computational model of the benchmark building. The fundamental period for the fixed-base perimeter frame, in Figure 4a, was 0.724 s, slightly lower than the 0.75 s of the flexible-base model in [49] due to the stiffness increment of the fixed base. Using the maximum interstory drift ratio (MIDR) as the damage index in [49], the frame would fail at an MIDR range of 0.07-0.12, and 39% failure scenarios formed the mechanism at the first story while approximately 61% of the scenarios caused the mechanism to form at the third story. For the GMRs with a typical design basis exceedance probability (10% in 50 years), the MIDRs of the frames ranged from 0.005-0.02, which satisfied the design limits set by the design code. For the task of seismic damage assessment, a flexible number of damage states were defined to describe the building's damage conditions. Two damage classes--namely, the collapse class and the non-collapse class--were defined in the machine learning-based approaches to predict the collapse of ductile r/c building frames [53]. Five damage states of r/c buildings in neural network-based approaches were used to classify the seismic structural damage  
Figure 3: The architectures of three neural network models: (**a**) the 1D CNN model; (**b**) the 2D CNN model; and (**c**) the FNN model. states [16; 17; 23]. Three damage states were used to evaluate the performance of r/c buildings after earthquake events in [22; 25; 54], following the guidelines of the Applied Technology Council (ATC)-20 [55] and ATC-40 [56]. Three damage states, i.e., safe (green placard), limited entry (yellow placard), and unsafe (red placard), were defined in this study, following ATC tag rules. Based on the MIDR limits in [49], GMRs with MIDRs < 0.02 were labeled with green placards, GMRs with 0.02 \(\leq\) MIDRs < 0.05 were labeled with yellow placards, and GMRs with 0.05 \(\leq\) MIDRs were labeled with red placards. Particularly, the lower bound of 0.05 for the red tag was determined by the mean value minus three times the standard deviation of all GMRs in the collapse range of 0.07-0.12, which was identified in [49] to be conservative in the evaluation of unsafe structures.