Seismic fragility analysis of elevated RC tanks based on IDA and machine learning

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Aziz Al-Ayoubi, Varatharajan Thirumurugan, K. S. Satyanarayanan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6690906/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 30 Jun, 2025 Read the published version in Asian Journal of Civil Engineering → Version 1 posted 6 You are reading this latest preprint version Abstract Elevated reinforced concrete (RC) water tanks are critical lifeline structures whose seismic performance is governed by complex fluid–structure interaction (FSI) effects and slender staging systems. Conventional fragility assessment via incremental dynamic analysis (IDA) yields probabilistic insights but entails extensive nonlinear time history simulations that limit practical application. This study presents a hybrid framework that couples IDA with machine learning (ML) to expedite the generation of seismic fragility curves for three Indian Standard–compliant RC tank configurations (75 m 3 , 320 m 3 , 1008 m 3 ). Validated finite element (FE) models in SAP2000 incorporate Housner’s added mass formulation to represent hydrodynamic demands. IDA under 22 far-field ground motions produces 738 nonlinear response samples characterized by ground motion characteristics and key geometric parameters. Support vector regression (SVR) and multilayer perceptron (MLP) regressors are trained to predict peak inter-story drift ratio (IDR), with hyperparameters optimized via Bayesian search and interpretability assessed through SHapley Additive exPlanations (SHAP) analysis. MLP achieves superior fidelity (test R 2 = 0.990, RMSE = 0.0009) compared to SVR (R 2 = 0.953, RMSE = 0.0021), maintaining errors below 6% for collapse-level exceedance probabilities. ML-derived fragility curves closely match IDA baselines, capturing threshold transitions and dispersion. The proposed approach enables rapid, code-compliant fragility evaluation—bridging probabilistic rigor and computational efficiency—and supports performance-based seismic design, retrofit prioritization and resilience planning for RC water infrastructure in seismically active regions. Machine learning Fragility curves Fluid-structure interaction Elevated RC tanks Seismic risk assessment Incremental dynamic analysis (IDA) Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 1. Introduction Elevated reinforced concrete (RC) water tanks are critical lifeline structures, essential for maintaining water supply continuity during and after seismic events. Their seismic performance is governed by complex fluid-structure interaction (FSI) effects, dynamic sloshing, and the inherent vulnerability of slender staging systems, making them prone to damage under strong ground motions. Traditional seismic fragility assessment methodologies, such as Incremental Dynamic Analysis (IDA), provide probabilistic insights into structural performance but require computationally intensive nonlinear time-history analyses, particularly for systems with varying geometries and hydrodynamic complexities. While finite element (FE) modeling and code-based approaches have been widely adopted to evaluate the seismic behavior of liquid-retaining structures, the integration of machine learning (ML) to accelerate fragility curve development remains underexplored, especially for elevated RC tanks designed under Indian Standard codes. Although FE modeling and code-based evaluations have been widely used for assessing liquid-retaining structures, efforts to integrate ML with fragility assessment for elevated tanks remain limited. Prior studies have explored ML applications in predicting seismic response metrics; (Al-Ayoubi et al., 2025 ) employed hybrid models combining Housner’s two-mass formulation with SVR and CatBoost to predict base shear and displacements for RC tanks. Similarly, (Naeim et al., 2024) applied HGB models to steel tanks, identifying liquid height and intensity measures as key predictors. These efforts, however, focused on deterministic parameters and did not extend to fragility analysis. For conventional building structures, ML-assisted fragility estimation has been more developed. Salmi et al. (2023) applied classification-based ML models to RC moment-resisting frames and achieved discrepancies below 10% compared to stripe-based analysis. Gondaliya et al. (2023) highlighted IDA’s accuracy over pushover methods in fragility estimation. Xu et al. (2024) used ensemble learning and neural networks trained on IDA outputs to produce fragility curves for RC frames with errors under 10%. Yazdanpanah et al. (2023) adopted boosted tree models for rapid fragility evaluation of eccentrically braced frames using system identification outputs. These studies demonstrate ML’s potential for probabilistic assessment but are primarily focused on building systems. Elevated RC tanks pose additional challenges due to FSI effects, sloshing, and dynamic interaction between tanks and staging, which remain underrepresented in these models. This study addresses these gaps by introducing a hybrid framework that integrates IDA with ML to generate seismic fragility curves for three RC tank configurations. Validated FE models in SAP2000 incorporate Housner’s added mass approach and undergo IDA under far-field ground motions, yielding 738 nonlinear response samples. SVR and MLP models are trained to predict peak inter-story drift ratios (IDR) from ground motion intensity measures and structural parameters. The framework extends prior ML applications by explicitly incorporating FSI effects and staging dynamics, while SHAP analysis quantifies feature importance. The proposed approach supports rapid, code-compliant fragility evaluation, offering a balance between computational efficiency and probabilistic accuracy for performance-based assessment of elevated RC tanks. 2. Methodology 2.1 Finite element model and parameters The finite element models of the three elevated RC water tanks were developed in SAP2000 v26 following Indian Standard codes IS 1893 (Part 2): 2014 and IS 3370: 2021 (Bureau of Indian Standards, 2014 , 2021 ). The staging systems, composed of reinforced concrete columns and horizontal braces, were modeled using frame elements with rigid end zones to simulate joint stiffness. Shell elements discretized the container walls and base slabs to capture bending and membrane behavior (Moslemi et al., 2011 ). Material properties adhered to IS 456: 2000 specifications: M25 concrete for the 75 m 3 tank and M30 concrete for the 320 m 3 and 1008 m 3 tanks, with Fe415 steel reinforcement (Bureau of Indian Standards, 2000 ; Computers and Structures, 2024 ). Damping was applied as follows: 5% of critical damping was assigned to all structural vibration modes associated with the reinforced concrete components, consistent with typical RC damping values. For the convective (sloshing) mode governed by hydrodynamic effects, a reduced damping ratio of 0.5% was applied, reflecting the low energy dissipation inherent to water motion. This bifurcation aligns with Housner’s theory, which distinguishes impulsive and convective liquid responses (Rai, 2003 ). The impulsive mass, representing water rigidly coupled to the tank structure, was modeled as static nodal loads, while the convective mass—associated with sloshing—was simulated using a spring-mass analog (Fig. 1 ). Spring stiffness for the convective mode ( \(\:{K}_{c}\) ) was derived from Housner’s formulations to replicate sloshing dynamics (Housner, 1963 ). The SAP2000 models (Fig. 2 ) were geometrically configured per Table 1 . For instance, the 320 m 3 tank features a 5×4 m staging grid, 200 mm slab/wall thicknesses, and column widths of 800 mm. Boundary conditions assumed fixed column bases, Nonlinear hinges at column bases followed ASCE 41 − 13 to simulate inelastic behavior under seismic demands ( Seismic Evaluation and Retrofit of Existing Buildings , 2014). Table 1 Structural properties of elevated RC tanks Tank Volume (m 3 ) Length (m) Tank Height (m) Concrete Strength Column width (mm) Tank Slab/Wall Thickness (mm) Staging 75 5 3 M25 350 200 5 x 4 m 320 8 5 M30 800 1008 12 7 M30 1250 2.2 Validation of finite element modelling methods To ensure the reliability of the SAP2000 models, a validation process was conducted for all three elevated tanks using manual response spectrum analyses adhering to IS 1893 (Part 2): 2014 guidelines (Bureau of Indian Standards, 2014 ). Dunkerley’s method was applied to approximate the fundamental vibration periods of each tank-staging system, accounting for the combined stiffness of columns, braces, and hydrodynamic interactions (Kumar et al., 2024 ). Hydrodynamic Masses: Impulsive and convective masses were derived using Housner’s formulations, with water sloshing effects quantified for each tank geometry. For base shear calculations, Seismic coefficients and design spectrum ordinates (Zone IV, 5% damping) were applied to compute theoretical base shear values for all tanks. The SAP2000 models were subjected to identical seismic inputs, and results for impulsive natural periods ( \(\:{T}_{i}\) ) and base shear \(\:{V}_{b}\:\) were compared with manual calculations as shown in Table 1 . For instance, \(\:{T}_{i}\) value of the 1008 m 3 tank was theoretically computed as 1.604 s, while the SAP2000 model yielded 1.539 s (4% error); this difference arises in part because the manual procedure neglects modal coupling between sloshing and structural modes and employs lumped-mass approximations for hydrodynamic effects, whereas the finite-element model captures higher-mode interaction and stiffness continuity more accurately (Sarokolayi et al., 2014). Similarly, the 320 m 3 tank’s manual \(\:{V}_{b}\) of 480.02 kN aligned closely with the SAP2000 result of 493.56 kN (2.7% error) (Housner, 1963 ). Table 2 Comparison of manual and SAP2000-derived natural periods and base-shear values Tank Capacity (m 3 ) \(\:{T}_{i}\) (s) \(\:{V}_{b}\) (kN) Manual SAP2000 Manual SAP2000 75 1.517 1.414 137.50 143.69 320 1.562 1.497 480.02 493.56 1008 1.604 1.539 1345.1 1381.15 2.3 Selection of Ground Vibration Records and Incremental Dynamic Analysis The selection of ground motion records and the execution of incremental dynamic analysis (IDA) are pivotal to ensuring the reliability of seismic fragility assessments. For this study, 22 pairs of far-field ground motion records were selected from the Pacific Earthquake Engineering Research (PEER) Center database, adhering to the methodology outlined in FEMA P-695 (Federal Emergency Management Agency, 2009 ; Pacific Earthquake Engineering Research Center (PEER), 2023 ). These records were chosen to represent a broad spectrum of seismic scenarios, encompassing varying magnitudes, distances, and site conditions consistent with the seismic hazard characteristics of the target region as shown in Table 3 . The FEMA P-695 methodology ensures that the selected records adequately capture the variability in ground motion intensity and frequency content, thereby enhancing the robustness of the subsequent nonlinear dynamic analyses. The selected ground motions are characterized by a suite of intensity and spectral parameters that together capture the amplitude, energy content, and frequency characteristics most relevant to elevated RC tanks. Each record’s peak ground acceleration (PGA) quantifies the maximum inertial demand, while Peak ground velocity (PGV) provides insight into the potential for permanent deformation and damage to non-structural components. Arias intensity (AI) is used to assess the cumulative energy input into the structure, and Housner intensity (HI) highlights the spectral energy within the 0.1–2.5 s period band that is critical for flexible systems such as elevated water tanks (Baltay et al., 2019 ; Campbell & Bozorgnia, 2023 ). The predominant period (TP) of each motion is compared against the fundamental period of the tank model to ensure coverage of resonance effects, and significant duration (SD) that covers between 5% and 95% of AI (Kempton & Stewart, 2006 ). By ensuring that ground motion characteristics span the ranges observed in the target seismic hazard, the IDA results yield fragility curves that robustly reflect both amplitude‐driven and frequency‐driven failure modes. Table 3 Selected ground-motion records and their key intensity and spectral parameters EQ ID PEER-NGA Number PGA (g) PGV (m/s) AI (m/s) HI (cm) TP (s) SD (s) 120111 953 0.416 58.948 3.073 238.905 0.52 9.21 120121 960 0.410 42.973 1.913 171.610 0.58 6.26 120411 1602 0.728 56.444 3.723 212.841 0.32 8.51 120521 1787 0.266 28.557 0.830 102.806 0.22 11.65 120611 169 0.238 26.001 2.397 109.872 0.48 51.05 120621 174 0.364 34.437 1.958 135.998 0.24 8.705 120711 1111 0.509 37.288 3.352 146.999 0.46 9.72 120721 1116 0.243 37.795 0.826 116.825 0.66 10.32 120811 1158 0.312 58.853 1.085 156.812 0.38 11.79 120821 1148 0.219 17.695 0.289 36.739 0.16 11.015 120911 900 0.245 51.408 0.924 150.309 0.68 17.62 120921 848 0.283 25.648 1.215 78.883 0.26 10.435 121011 752 0.529 35.014 4.374 188.174 0.28 11.915 121021 767 0.555 35.684 2.087 96.154 0.2 6.365 121111 1633 0.515 42.468 4.656 136.111 0.16 28.92 121211 721 0.358 46.360 1.063 138.720 0.22 16.05 121221 725 0.446 35.711 2.093 120.783 0.46 13.81 121321 829 0.385 43.805 1.523 141.661 0.24 15.34 121411 1244 0.353 70.653 2.319 163.614 0.16 30.385 121421 1485 0.474 36.700 1.396 108.211 0.44 11.275 121511 68 0.210 18.874 0.650 77.416 0.24 10.49 121711 125 0.351 22.036 0.780 73.931 0.26 4.24 Nonlinear behavior of the elevated tank structures was modeled in SAP2000, with a focus on simulating the inelastic response of critical structural components. Column-beam hinges were explicitly defined in accordance with ASCE 41 − 13 guidelines, incorporating failure condition II to account for combined flexural and shear failure mechanisms (Federal Emergency Management Agency, 2009 ; Seismic Evaluation and Retrofit of Existing Buildings , 2014). The hinge properties were calibrated to reflect the expected nonlinear deformation capacities and degradation characteristics under seismic time-history loading, ensuring an accurate representation of post-yield behavior and collapse mechanisms. This approach aligns with performance-based engineering principles, enabling the quantification of structural damage progression under increasing seismic demands (Chopra, 1995 ; Bertero & Bertero, 2002 ). IDA was conducted to evaluate the structural response across a range of ground motion intensities. Each ground motion record was scaled incrementally using the spectral acceleration at the fundamental period of the structure Sa as the intensity measure (IM) (Luco & Cornell, 2007 ; Vamvatsikos & Cornell, 2002 ). The scaling process continued until global collapse was observed, defined as the point where the structure undergoes excessive lateral drift or hinge failures lead to numerical instability. The histogram of IM (Sa) collapse values (Fig. 3 ), derived from the IDA results, was used to determine the median ground shaking intensity index corresponding to collapse, this median value serves as a probabilistic benchmark for assessing the seismic fragility of the elevated tanks. Figure 4 shows the response spectra of all selected ground motion records with 5% damping, with the mean spectrum highlighted to illustrate the range of spectral demands imposed on the models. The IDA results were post-processed to extract engineering demand parameters (EDPs), including maximum lateral displacements and hinge rotation demands. These parameters were statistically analyzed to establish probabilistic relationships between ground motion intensity and structural response (Fan & Zhang, 2014 ). The use of 22 far-field records ensured a comprehensive representation of seismic uncertainty, while the nonlinear modeling framework provided insights into the failure mechanisms governing the seismic performance of the elevated tanks. The integration of FEMA P-695 guidelines, ASCE 41 − 13 nonlinear hinge modeling, and IDA methodology collectively ensures a rigorous and reproducible approach to seismic fragility evaluation (Taflanidis & Beck, 2006 ). 3. Machine Learning Models In this study, seismic fragility assessment of RC elevated tanks is augmented by two complementary machine learning algorithms—SVR and MLP—selected for their documented efficacy in resolving nonlinear seismic response prediction challenges. SVR is widely adopted in structural engineering for its ability to model high-dimensional relationships between ground motion parameters and structural demands while maintaining computational efficiency, as demonstrated in hybrid frameworks for liquid-retaining systems (Al-Ayoubi et al., 2025 ). MLP, conversely, is prioritized for its capacity to capture intricate fluid-structure interactions and staging system nonlinearities, a capability validated in prior studies on elevated tanks subjected to hydrodynamic and seismic coupling (Pourbagheri et al., 2017 ). The models are trained on a database of 738 response samples generated via elastic-plastic time-history analyses under IDA. Ground-motion intensity measures (Sa, PGV, HI, AI, and TP), together with key structural attributes (tank height (H), tank length (L), and column width (Col)), constitute the input feature set. 3.1 Dataset Composition and Feature Engineering The predictive database comprises 738 distinct IDA sample points, each representing a unique combination of scaled far-field ground motion record and tank geometry. Box–Cox transformations were applied to AI, SD and to reduce skewness, as these features exhibited non-Gaussian distributions, all features were subsequently standardized to zero mean and unit variance to expedite algorithm convergence and mitigate scale-driven bias (Box & Cox, 1964 ). Table 4 summarizes the input and output feature definitions, facilitating reproducibility of the modeling exercise. Table 4 Definitions of ML input features and model parameters Input Parameters Output Parameter Ground motion parameters Structural parameters Sa HI L IDR PGV TP H AI SD Col Hyperparameter selection critically influences both model accuracy and generalization. Rather than exhaustive grid search, Bayesian optimization framework (BayesSearchCV) was employed to iteratively evaluate and update a probabilistic surrogate model of the validation loss surface to efficiently identify optimal hyperparameter combinations (Bergstra et al., 2011 ; Kaveh, 2024 ). At each iteration, the acquisition function balances exploration of poorly sampled regions against exploitation of promising configurations, reducing the total number of evaluations required to converge on the global optimum. This approach was applied to both SVR and MLP, tuning parameters such as the RBF-kernel coefficient γ and regularization parameter C for SVR, and hidden‐layer widths, learning rate, and L₂‐regularization strength for MLP. The 5‐fold cross‐validation process used throughout hyperparameter search is illustrated in Fig. 5 , where data splits are shown along with corresponding validation‐set performance trajectories (Kaveh et al., 2021 ; Lundberg & Lee, 2017 ). All computations were performed on a Ryzen 7-5800H CPU, 32 GB RAM, and an NVIDIA RTX 3050 Laptop GPU, with MLP leveraging GPU acceleration for training. 3.2 Structural Response Prediction Using SVR The SVR model employs a radial basis function kernel to nonlinearly project the input feature space, enabling the capture of complex IM–structural response relationships. Optimal hyperparameters determined via BayesSearchCV (C = 100, ε = 0.0183) balance bias–variance trade-offs and constrain margin violations (Tao et al., 2024 ). The database was randomly partitioned into 80% training and 20% testing subsets; a 5‐fold cross‐validation scheme was embedded within the training set to guard against overfitting. Model performance is evaluated by the coefficient of determination (R 2 ), which measures the proportion of variance in the observed collapse IDR explained by the predictions Eq. ( 1 ); the root‐mean‐square error (RMSE), which represents the square root of the average squared prediction deviations and thus indicates overall predictive dispersion Eq. ( 2 ); the mean‐absolute error (MAE), which quantifies the average absolute bias between predicted and actual values Eq. ( 3 ); and the mean‐absolute‐percentage error (MAPE), which expresses the average relative error as a percentage of observed values Eq. ( 4 )—together offering a multifaceted view of predictive fidelity (Kaveh & Khavaninzadeh, 2023 ). Scatter plots comparing actual versus predicted collapse IDR for each tank configuration under SVR (Fig. 6 ) demonstrate good alignment along the 1:1 line for low‐rise tanks, with modest dispersion emerging in the taller 1008 m 3 configuration. $$\:{R}^{2}=1-\frac{{\sum\:}_{i=1}^{n}{({y}_{i}-\widehat{{y}_{i}})}^{2}}{{\sum\:}_{i=1}^{n}{({y}_{i}-\stackrel{-}{y})}^{2}}$$ 1 $$\:RMSE=\:\sqrt{\frac{1}{n}{\sum\:}_{i=1}^{n}{({y}_{i}-\widehat{{y}_{i}})}^{2}}$$ 2 $$\:MAE=\frac{1}{n}{\sum\:}_{i=1}^{n}\left|{y}_{i}-\widehat{{y}_{i}}\right|$$ 3 $$\:MAPE=\frac{100\%}{n}{\sum\:}_{i=1}^{n}\left|\frac{{y}_{i}-\widehat{{y}_{i}}}{{y}_{i}}\right|$$ 4 Where \(\:n\) is the total number of observations in the measured set, \(\:{y}_{i}\) ​ is the actual IDR for the \(\:i\) th sample, \(\:\widehat{{y}_{i}}\) is the ML-predicted collapse IDR for the \(\:i\) th sample, and \(\:\stackrel{-}{y}\) is the mean of the observed IDR values. 3.3 Structural Response Prediction Using MLP The MLP framework developed for predicting IDR consists of an input layer aligned with the dimensionality of the selected ground motion and structural features, followed by two hidden layers of 256 neurons each. This configuration was selected based on hyperparameter optimization using Bayes Optimizer, which systematically explored candidate architectures by balancing accuracy and training efficiency (Yoo et al., 2021 ). The ReLU activation function was applied to all hidden layers to enable nonlinearity while addressing vanishing gradient issues (Nair & Hinton, 2010 ). He normal initialization was used to ensure stable gradient propagation. The model incorporated L₂ regularization with a coefficient of 1.05×10⁻⁴ to constrain weight magnitudes and mitigate overfitting. The optimizer adopted was Adam, with a learning rate of 1.69×10⁻3, identified through Bayesian search (He et al., 2015 ). This optimizer dynamically adjusted learning rates based on first and second moment estimates of the gradients. Learning rate decay was implemented by halving the rate upon stagnation of validation loss over five consecutive epochs. Early stopping was triggered when no improvement in validation MSE was observed for ten epochs, using a 10% holdout from the training partition, and training was capped at 500 epochs (Kingma & Ba, 2014). Convergence typically occurred by epoch 120. The selected architecture reflects a trade-off achieved through Bayesian search: it offers sufficient depth and capacity to capture nonlinear interactions among input features—particularly those arising from fluid–structure coupling—without incurring excessive computational cost or overfitting. Figure 7 illustrates the model structure, and Fig. 8 shows the resulting predictive performance on test data, confirming that MLP achieves closer alignment with actual IDR values across all tank configurations relative to SVR. 3.4 Comparative Model Performance and Computational Efficiency The reported test metrics (Table 5 ) reflect performance on a 20% held-out set not used in training or tuning, confirming model generalization. Both SVR and MLP exhibit strengths and limitations that must be weighed when selecting an algorithm for seismic fragility assessment. As shown in Table 5 , SVR completed training in 0.894 s and inference in 0.019 s, whereas MLP required 21.203 s for training and 0.004 s for inference. This disparity reflects the underlying computational complexity: SVR solves a convex quadratic program whose cost scales between O(n 2 ) and O(n 3 ) with the number of samples, while MLP back-propagation over 50,000 weights entails repeated gradient updates proportional to network size and epochs (Smola & Schölkopf, 2004 ). For reference, a single IDA run for one tank configuration required approximately 2 hours on similar hardware, underscoring the computational efficiency. Despite the longer runtimes, MLP yielded higher predictive fidelity: test R2 improved from 0.953 (SVR) to 0.990 (MLP), and RMSE decreased from 0.0021 to 0.0009, with corresponding MAE and MAPE reductions (from 0.0010 to 0.0007 and from 7.73–4.93%, respectively). These gains align with broader findings that neural networks often outperform SVR in capturing complex, nonlinear mappings when sufficient data are available, at the expense of increased risk of overfitting and heavier computational demands. Conversely, SVR’s reliance on support vectors (often a small subset of the training set) confers robust generalization under limited data conditions. Moreover, SVR’s unique global optimum (due to convexity) ensures reproducible results across runs, while MLP training on a nonconvex loss surface may converge to different local minima unless multiple random restarts or advanced optimizers are employed. Inference speed also favors SVR when the number of support vectors remains modest, but MLP can leverage GPU acceleration and batch processing to mitigate latency in high-throughput applications (Rumelhart et al., 1986 ). Both SVR and MLP serve as efficient surrogates for IDA, with distinct trade-offs. SVR delivers rapid, reliable estimates for high- to moderate-probability damage states (e.g., IO, LS) with errors under 5%, while MLP provides superior fidelity across all damage thresholds—including CP—with maximum error below 6%. These trade-offs underscore MLP’s suitability for scenarios demanding precise collapse-level predictions, provided computational resources and overfitting controls are prioritized. Table 5 Comparative performance metrics and computational times for SVR and MLP models Model Dataset R 2 MAE RMSE MAPE Time (s) SVR Train 0.9911 0.000345 0.000892 2.065% 0.894 Test 0.9529 0.001019 0.002087 7.728% 0.019 MLP Train 0.9931 0.000460 0.000791 2.861% 21.203 Test 0.9897 0.000653 0.000938 4.934% 0.004 3.5 Model Interpretability and SHAP Analysis SHapley Additive exPlanations (SHAP) was used to interpret the predictions made by both the SVR and MLP models by attributing each prediction to its input features. For the SVR model, the SHAP summary plot (Fig. 9 ) identifies PGV and HI as the most influential predictors. Their SHAP values are distributed around zero, indicating that their contributions to the predicted IDR vary depending on the specific input scenario. Sa and TP also contribute meaningfully, whereas AI, SD, and geometric features such as Length, Height, and Col show lesser but non-negligible influence. The color gradients in the SHAP plot suggest that higher PGV and HI values are typically associated with increased IDR, reflecting their role in amplifying structural demand (Lundberg & Lee, 2017 ). For the MLP model, the SHAP summary (Fig. 10 ) shows a broader range of feature contributions. PGV and HI again dominate the input space, but Sa and AI also have significant positive associations with higher predicted IDR. Unlike SVR, the MLP model assigns greater importance to structural parameters, particularly Col, which is not prominent in the SVR interpretation. TP and SD also show increased relevance. This redistribution of feature importance is indicative of MLP’s capacity to learn complex nonlinear interactions, in which both dynamic and geometric characteristics jointly influence seismic response. Length and Height show limited direct influence, implying that their effects may be indirectly captured through interactions with other parameters. The observed emphasis on Col in the MLP model likely stems from its ability to model coupled effects of geometry and dynamic response, suggesting improved sensitivity to FSI-related behaviors compared to SVR. 4. Comparative Analysis of Seismic Fragility Curves 4.1 Fragility Curve Development For each tank, the collapse IM samples from IDA—scaled from 0.1 g to 2.0 g—were fit with log-normal distributions to define median Sa and dispersion β for the Immediate Occupancy (IO), Life Safety (LS), and Collapse Prevention (CP) limit states (Vamvatsikos & Cornell, 2002 ). The damage‐state thresholds are set at IDR = 0.01 for IO, IDR = 0.02 for LS, and the median collapse IDR values for CP are taken as 0.0340, 0.0295, and 0.0309 for the 75 m 3 , 320 m 3 , and 1008 m 3 tanks respectively (Baker, 2015 ). SVR and MLP then predicted exceedance probabilities at these same IM values, using the trained regression mapping from Sa to peak IDR. The resulting ML‐based fragility curves maintain the characteristic S‐shape of the IDA baseline, capturing both the threshold and the spread of the damage probability (Sudret et al., 2014 ). 4.2 Comparison of SVR and MLP Predictions Against IDA The fragility curves predicted by both SVR and MLP models capture the general trends of IDA-derived probabilities across all three damage states as shown in Fig. 11 and Fig. 12 , but each exhibits systematic biases that vary with tank volume and damage threshold. For the 75 m 3 tank, SVR closely replicates the IO median capacity near Sa = 0.3g, yet modestly overpredicts the slope of the LS curve, resulting in a slightly steeper transition than IDA and a median at roughly 0.85g compared to 0.8g. Its CP prediction is conservative, underestimating the IDA median by nearly 0.2g, which may reflect limited sensitivity to high‐drift behavior in sparse training data. MLP, by contrast, yields IO and LS medians within 0.05g of IDA and aligns more closely with the observed dispersion for both states, but underestimates CP capacity by approximately 0.25g and produces a gentler slope, indicating a tendency to smooth extreme responses. In the 320 m 3 tank, SVR again matches IO capacity within measurement uncertainty yet overestimates LS by about 0.1g; its CP fit improves, reducing the IDA offset to roughly 0.15g MLP outperforms SVR for LS and CP in this case, with median predictions within 0.1g of IDA and similar lognormal dispersion, though it slightly overpredicts the fragility slope for IO. For the 1008 m 3 tank, the two ML approaches converge in performance: SVR and MLP both reproduce IO medians at 0.4g and LS medians near 1.2g, deviating from IDA by less than 0.05g. However, SVR maintains a marginally steeper LS slope, while MLP more accurately mirrors the gradual increase in CP probability, underestimating the IDA median by only 0.1g. Across volumes, SVR exhibits greater consistency in IO predictions but tends toward conservative CP estimates, whereas MLP offers balanced accuracy in LS and CP at the expense of slightly overestimating IO dispersion. These discrepancies underscore the importance of model selection based on targeted damage states: SVR may be preferred for initial yield assessments, while MLP more reliably predicts advanced damage probabilities (Basterrechea-Arévalo et al., 2023 ; Sainct et al., 2018 ). 4.3 Probability Analysis and Error Assessment Table 6 , Table 7 and Table 8 compare exceedance probabilities and absolute errors between IDA, SVR, and MLP. For the CP limit state, SVR exhibits an 11.5% error in the 75 m 3 tank, reflecting reduced accuracy in collapse-level predictions compared to MLP (5.6% error). This discrepancy highlights SVR’s limitations in capturing nonlinear collapse mechanisms, particularly for smaller tanks where geometric and FSI interactions intensify. While SVR maintains sub-5% errors for IO and LS states across all tanks, MLP achieves lower errors (≤ 5.6%) for CP, demonstrating enhanced reliability for collapse assessments. The results align with MLP’s capacity to model complex FSI-coupled responses, as evidenced by SHAP interpretations. For practical applications, SVR remains viable for rapid IO/LS evaluations, but MLP is recommended for CP scenarios requiring precise collapse probability estimates. Table 6 Exceedance probabilities and absolute errors for the 75 m 3 tank. Damage State Sa(g) IDA SVR MLP P P Error % P Error % IO 0.6 0.9643 0.9688 0.472 0.9596 0.490 LS 0.9 0.7806 0.7765 0.522 0.7732 0.946 CP 1.5 0.6415 0.5679 11.470 0.6058 5.562 Table 7 Exceedance probabilities and absolute errors for the 320 m 3 tank. Damage State Sa(g) IDA SVR MLP P P Error % P Error % IO 0.4 0.7768 0.8125 4.601 0.7998 2.968 LS 0.75 0.5595 0.5631 0.645 0.5798 3.631 CP 1.5 0.7788 0.7692 1.233 0.7538 3.208 Table 8 Exceedance probabilities and absolute errors for the 1008 m 3 tank. Damage State Sa(g) IDA SVR MLP P P Error % P Error % IO 0.35 0.9964 0.9928 0.360 0.9964 0 LS 1 0.9364 0.9321 0.466 0.9541 1.892 CP 1.5 0.8083 0.7823 3.212 0.8177 1.163 5. Conclusions This study presented a hybrid framework integrating IDA with ML to expedite seismic fragility analysis of elevated RC tanks, addressing the computational limitations of conventional IDA while preserving probabilistic rigor. Three Indian Standard-compliant tank configurations (75 m 3 , 320 m 3 , 1008 m 3 ) were modeled in SAP2000, incorporating FSI effects via Housner’s added mass formulation. IDA under 22 far-field ground motions generated 738 nonlinear response samples, forming the dataset for training SVR and MLP models to predict peak IDR. Hyperparameter optimization via Bayesian search and SHAP-based interpretability analysis ensured model fidelity and transparency. MLP demonstrated superior predictive accuracy (test R 2 = 0.99, RMSE = 0.0009) compared to SVR (R 2 = 0.95, RMSE = 0.0021), with errors below 6% even at collapse-level thresholds. SHAP analysis identified PGV and HI as dominant predictors, while MLP uniquely captured interactions between structural parameters (e.g., column width) and dynamic demands, reflecting its capacity to resolve FSI-driven complexities. Fragility curves derived from ML predictions aligned closely with IDA baselines, particularly for MLP, which replicated threshold transitions and dispersion with minimal deviation. SVR exhibited conservatism at higher damage states, whereas MLP maintained consistency across all limit states (IO, LS, CP), achieving errors under 6% for CP probabilities. The framework enables rapid fragility curve generation without sacrificing the probabilistic foundations of IDA, reducing computational costs from hours per IDA run to seconds for ML inference. This efficiency facilitates code-compliant seismic risk assessments, particularly in regions requiring urgent evaluation of existing water infrastructure. Applications include performance-based design of new tanks, retrofit prioritization for vulnerable assets, and resilience planning for lifeline systems in seismically active zones. By bridging computational efficiency with rigorous fragility quantification, the approach supports data-driven decision-making for disaster mitigation and resource allocation. The study underscores MLP’s viability as a surrogate model for IDA in systems governed by FSI and geometric nonlinearities, offering a template for extending ML-aided fragility analysis to other liquid-retaining structures. Future work could explore ensemble methods or physics-informed ML to further enhance generalizability across broader tank typologies and hazard scenarios. The findings contribute to advancing ML’s role in performance-based earthquake engineering, emphasizing its potential to transform traditional workflows into scalable, resource-efficient solutions for critical infrastructure resilience. Declarations Competing interests The authors declare no competing interests. Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. Author Contribution A. A.: conceptualization, writing original draft,formal analysis, investigation, visualization. V. T.: supervision, reviewand editing. S.S.: methodology, review and editing. Data Availability Data and code are available from the corresponding author upon reasonable request References Al-Ayoubi, A. A., Thirumurugan, V., & Satyanarayanan, K. S. (2025). 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E., Hinton, G. E., & Williams, R. J. (1986). Learning representations by back-propagating errors. Nature , 323 (6088), 533–536. https://doi.org/10.1038/323533a0 Sainct, R., Feau, C., Martinez, J.-M., & Garnier, J. (2018). Efficient Seismic fragility curve estimation by Active Learning on Support Vector Machines . https://doi.org/10.48550/arXiv.1810.01240 Smola, A. J., & Schölkopf, B. (2004). A tutorial on support vector regression. Statistics and Computing , 14 (3), 199–222. https://doi.org/10.1023/B:STCO.0000035301.49549.88 Sudret, B., Mai, C., & Konakli, K. (2014). Assessment of the lognormality assumption of seismic fragility curves using non-parametric representations . https://doi.org/10.48550/arXiv.1403.5481 Taflanidis, A. A., & Beck, J. L. (2006). Analytical approximation for stationary reliability of certain and uncertain linear dynamic systems with higher-dimensional output. 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Cite Share Download PDF Status: Published Journal Publication published 30 Jun, 2025 Read the published version in Asian Journal of Civil Engineering → Version 1 posted Reviewers agreed at journal 31 May, 2025 Reviewers agreed at journal 30 May, 2025 Reviewers invited by journal 30 May, 2025 Editor assigned by journal 19 May, 2025 Submission checks completed at journal 19 May, 2025 First submitted to journal 18 May, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6690906","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":464567895,"identity":"6963258c-e468-4d91-b759-f5c742ab032a","order_by":0,"name":"A. 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model\u003c/p\u003e","description":"","filename":"1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/a904880d83b86ae86e5d1692.jpeg"},{"id":83824412,"identity":"30b4cd40-b773-41fc-841b-41bc5f58112f","added_by":"auto","created_at":"2025-06-03 09:40:46","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":54417,"visible":true,"origin":"","legend":"\u003cp\u003eFinite-element models of the 75 m\u003csup\u003e3\u003c/sup\u003e (a), 320 m\u003csup\u003e3 \u003c/sup\u003e(b), 1008 m\u003csup\u003e3\u003c/sup\u003e (c) tanks in SAP2000\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/6a2a43766d812d081097be86.jpg"},{"id":83824419,"identity":"bee503db-6621-4c15-b792-9a36ec1be1d4","added_by":"auto","created_at":"2025-06-03 09:40:46","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":175088,"visible":true,"origin":"","legend":"\u003cp\u003eHistogram of collapse Sa values obtained from IDA\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/f5a40a9539d874a42e2bce9f.png"},{"id":83824697,"identity":"d9fbd17d-582c-4925-8677-362e2d4bd230","added_by":"auto","created_at":"2025-06-03 09:48:46","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":798129,"visible":true,"origin":"","legend":"\u003cp\u003eResponse spectra (5% damping) of selected ground motions, with the mean spectrum highlighted\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/32a5e22a1199d1b0637324f5.png"},{"id":83824695,"identity":"d940ca4a-406b-47fd-9bee-2785550d982b","added_by":"auto","created_at":"2025-06-03 09:48:46","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":191323,"visible":true,"origin":"","legend":"\u003cp\u003e5-fold cross-validation diagram\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/f2c819e8526a566dae57df57.png"},{"id":83824415,"identity":"a9e1785b-8d56-47d6-9bb7-698c46cc59fc","added_by":"auto","created_at":"2025-06-03 09:40:46","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":40548,"visible":true,"origin":"","legend":"\u003cp\u003eScatter plots of actual IDR vs SVR predicted IDR for the 75 m\u003csup\u003e3\u003c/sup\u003e (a), 320 m\u003csup\u003e3\u003c/sup\u003e (b), and 1008 m\u003csup\u003e3 \u003c/sup\u003e(c) tank\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/9e29f43318a54f791aee621e.jpg"},{"id":83824696,"identity":"a53f0976-a8e5-45f7-bbbc-89df3dd89f79","added_by":"auto","created_at":"2025-06-03 09:48:46","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":3028321,"visible":true,"origin":"","legend":"\u003cp\u003eArchitecture of the MLP model\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/1a3c122843bc5320397f52a8.png"},{"id":83824417,"identity":"a4c69c28-a0e6-451b-a7b5-3b2c68e94374","added_by":"auto","created_at":"2025-06-03 09:40:46","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":38878,"visible":true,"origin":"","legend":"\u003cp\u003eScatter plots of actual IDR vs MLP predicted IDR for the 75 m\u003csup\u003e3\u003c/sup\u003e (a), 320 m\u003csup\u003e3\u003c/sup\u003e (b), and 1008 m\u003csup\u003e3 \u003c/sup\u003e(c) tanks\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/f14530248cf3ed170801273c.jpg"},{"id":83824421,"identity":"3c252a97-d719-4c72-ad21-2db10ca3f28e","added_by":"auto","created_at":"2025-06-03 09:40:46","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":430949,"visible":true,"origin":"","legend":"\u003cp\u003eSHAP summary for the IDR predictions using SVR models\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/ffdda8b3624f285f1657ca03.png"},{"id":83824423,"identity":"b0b4e846-1aec-42d7-b8fa-2642d04f8aa3","added_by":"auto","created_at":"2025-06-03 09:40:46","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":369677,"visible":true,"origin":"","legend":"\u003cp\u003eSHAP summary for the IDR predictions using MLP models\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/3f536f4d19ed2040390ca7ac.png"},{"id":83824426,"identity":"43869408-c5a5-4cf1-9858-230c52cb6e57","added_by":"auto","created_at":"2025-06-03 09:40:46","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":58412,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of IDA-derived and SVR-predicted fragility curves for the 75 m\u003csup\u003e3\u003c/sup\u003e (a), 320 m\u003csup\u003e3\u003c/sup\u003e (b), and 1008 m\u003csup\u003e3\u003c/sup\u003e (c) tank.\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/1e9c886283f9adf2dfc6167b.jpg"},{"id":83825409,"identity":"121fe5dd-efba-4ab5-a6d7-7d6c64cfa493","added_by":"auto","created_at":"2025-06-03 09:56:46","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":58272,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of IDA-derived and MLP-predicted fragility curves for the 75 m\u003csup\u003e3\u003c/sup\u003e (a), 320 m\u003csup\u003e3\u003c/sup\u003e (b), and 1008 m\u003csup\u003e3\u003c/sup\u003e (c) tank.\u003c/p\u003e","description":"","filename":"12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/4f5a5a913d18817880b0063b.jpg"},{"id":86172742,"identity":"aab7a0a0-01a6-40c5-af70-55aebcdbbe85","added_by":"auto","created_at":"2025-07-07 14:45:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":5679949,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6690906/v1/0d9c22d9-1f99-454c-9468-7bcbea767309.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Seismic fragility analysis of elevated RC tanks based on IDA and machine learning","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eElevated reinforced concrete (RC) water tanks are critical lifeline structures, essential for maintaining water supply continuity during and after seismic events. Their seismic performance is governed by complex fluid-structure interaction (FSI) effects, dynamic sloshing, and the inherent vulnerability of slender staging systems, making them prone to damage under strong ground motions. Traditional seismic fragility assessment methodologies, such as Incremental Dynamic Analysis (IDA), provide probabilistic insights into structural performance but require computationally intensive nonlinear time-history analyses, particularly for systems with varying geometries and hydrodynamic complexities. While finite element (FE) modeling and code-based approaches have been widely adopted to evaluate the seismic behavior of liquid-retaining structures, the integration of machine learning (ML) to accelerate fragility curve development remains underexplored, especially for elevated RC tanks designed under Indian Standard codes.\u003c/p\u003e \u003cp\u003eAlthough FE modeling and code-based evaluations have been widely used for assessing liquid-retaining structures, efforts to integrate ML with fragility assessment for elevated tanks remain limited. Prior studies have explored ML applications in predicting seismic response metrics; (Al-Ayoubi et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2025\u003c/span\u003e) employed hybrid models combining Housner\u0026rsquo;s two-mass formulation with SVR and CatBoost to predict base shear and displacements for RC tanks. Similarly, (Naeim et al., 2024) applied HGB models to steel tanks, identifying liquid height and intensity measures as key predictors. These efforts, however, focused on deterministic parameters and did not extend to fragility analysis.\u003c/p\u003e \u003cp\u003eFor conventional building structures, ML-assisted fragility estimation has been more developed. Salmi et al. (2023) applied classification-based ML models to RC moment-resisting frames and achieved discrepancies below 10% compared to stripe-based analysis. Gondaliya et al. (2023) highlighted IDA\u0026rsquo;s accuracy over pushover methods in fragility estimation. Xu et al. (2024) used ensemble learning and neural networks trained on IDA outputs to produce fragility curves for RC frames with errors under 10%. Yazdanpanah et al. (2023) adopted boosted tree models for rapid fragility evaluation of eccentrically braced frames using system identification outputs. These studies demonstrate ML\u0026rsquo;s potential for probabilistic assessment but are primarily focused on building systems. Elevated RC tanks pose additional challenges due to FSI effects, sloshing, and dynamic interaction between tanks and staging, which remain underrepresented in these models.\u003c/p\u003e \u003cp\u003eThis study addresses these gaps by introducing a hybrid framework that integrates IDA with ML to generate seismic fragility curves for three RC tank configurations. Validated FE models in SAP2000 incorporate Housner\u0026rsquo;s added mass approach and undergo IDA under far-field ground motions, yielding 738 nonlinear response samples. SVR and MLP models are trained to predict peak inter-story drift ratios (IDR) from ground motion intensity measures and structural parameters. The framework extends prior ML applications by explicitly incorporating FSI effects and staging dynamics, while SHAP analysis quantifies feature importance. The proposed approach supports rapid, code-compliant fragility evaluation, offering a balance between computational efficiency and probabilistic accuracy for performance-based assessment of elevated RC tanks.\u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cp\u003e2.1 Finite element model and parameters\u003c/p\u003e \u003cp\u003eThe finite element models of the three elevated RC water tanks were developed in SAP2000 v26 following Indian Standard codes IS 1893 (Part 2): 2014 and IS 3370: 2021 (Bureau of Indian Standards, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The staging systems, composed of reinforced concrete columns and horizontal braces, were modeled using frame elements with rigid end zones to simulate joint stiffness. Shell elements discretized the container walls and base slabs to capture bending and membrane behavior (Moslemi et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Material properties adhered to IS 456: 2000 specifications: M25 concrete for the 75 m\u003csup\u003e3\u003c/sup\u003e tank and M30 concrete for the 320 m\u003csup\u003e3\u003c/sup\u003e and 1008 m\u003csup\u003e3\u003c/sup\u003e tanks, with Fe415 steel reinforcement (Bureau of Indian Standards, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Computers and Structures, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eDamping was applied as follows: 5% of critical damping was assigned to all structural vibration modes associated with the reinforced concrete components, consistent with typical RC damping values. For the convective (sloshing) mode governed by hydrodynamic effects, a reduced damping ratio of 0.5% was applied, reflecting the low energy dissipation inherent to water motion. This bifurcation aligns with Housner\u0026rsquo;s theory, which distinguishes impulsive and convective liquid responses (Rai, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2003\u003c/span\u003e). The impulsive mass, representing water rigidly coupled to the tank structure, was modeled as static nodal loads, while the convective mass\u0026mdash;associated with sloshing\u0026mdash;was simulated using a spring-mass analog (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Spring stiffness for the convective mode (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{K}_{c}\\)\u003c/span\u003e\u003c/span\u003e) was derived from Housner\u0026rsquo;s formulations to replicate sloshing dynamics (Housner, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1963\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe SAP2000 models (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) were geometrically configured per Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. For instance, the 320 m\u003csup\u003e3\u003c/sup\u003e tank features a 5\u0026times;4 m staging grid, 200 mm slab/wall thicknesses, and column widths of 800 mm. Boundary conditions assumed fixed column bases, Nonlinear hinges at column bases followed ASCE 41\u0026thinsp;\u0026minus;\u0026thinsp;13 to simulate inelastic behavior under seismic demands (\u003cem\u003eSeismic Evaluation and Retrofit of Existing Buildings\u003c/em\u003e, 2014).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eStructural properties of elevated RC tanks\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTank Volume (m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eLength (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTank Height (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eConcrete Strength\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eColumn width (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eTank Slab/Wall Thickness (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eStaging\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eM25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e350\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e5 x 4 m\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eM30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e800\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eM30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1250\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e2.2 Validation of finite element modelling methods\u003c/p\u003e \u003cp\u003eTo ensure the reliability of the SAP2000 models, a validation process was conducted for all three elevated tanks using manual response spectrum analyses adhering to IS 1893 (Part 2): 2014 guidelines (Bureau of Indian Standards, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Dunkerley\u0026rsquo;s method was applied to approximate the fundamental vibration periods of each tank-staging system, accounting for the combined stiffness of columns, braces, and hydrodynamic interactions (Kumar et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). Hydrodynamic Masses: Impulsive and convective masses were derived using Housner\u0026rsquo;s formulations, with water sloshing effects quantified for each tank geometry. For base shear calculations, Seismic coefficients and design spectrum ordinates (Zone IV, 5% damping) were applied to compute theoretical base shear values for all tanks. The SAP2000 models were subjected to identical seismic inputs, and results for impulsive natural periods (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{T}_{i}\\)\u003c/span\u003e\u003c/span\u003e) and base shear \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{b}\\:\\)\u003c/span\u003e\u003c/span\u003ewere compared with manual calculations as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. For instance, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{T}_{i}\\)\u003c/span\u003e\u003c/span\u003e value of the 1008 m\u003csup\u003e3\u003c/sup\u003e tank was theoretically computed as 1.604 s, while the SAP2000 model yielded 1.539 s (4% error); this difference arises in part because the manual procedure neglects modal coupling between sloshing and structural modes and employs lumped-mass approximations for hydrodynamic effects, whereas the finite-element model captures higher-mode interaction and stiffness continuity more accurately (Sarokolayi et al., 2014). Similarly, the 320 m\u003csup\u003e3\u003c/sup\u003e tank\u0026rsquo;s manual \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{b}\\)\u003c/span\u003e\u003c/span\u003e of 480.02 kN aligned closely with the SAP2000 result of 493.56 kN (2.7% error) (Housner, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1963\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of manual and SAP2000-derived natural periods and base-shear values\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eTank Capacity (m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{T}_{i}\\)\u003c/span\u003e\u003c/span\u003e (s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{V}_{b}\\)\u003c/span\u003e\u003c/span\u003e (kN)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eManual\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSAP2000\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eManual\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSAP2000\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.517\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.414\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e137.50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e143.69\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e320\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.562\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e480.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e493.56\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1008\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.604\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.539\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1345.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1381.15\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e2.3 Selection of Ground Vibration Records and Incremental Dynamic Analysis\u003c/p\u003e \u003cp\u003eThe selection of ground motion records and the execution of incremental dynamic analysis (IDA) are pivotal to ensuring the reliability of seismic fragility assessments. For this study, 22 pairs of far-field ground motion records were selected from the Pacific Earthquake Engineering Research (PEER) Center database, adhering to the methodology outlined in FEMA P-695 (Federal Emergency Management Agency, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Pacific Earthquake Engineering Research Center (PEER), \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). These records were chosen to represent a broad spectrum of seismic scenarios, encompassing varying magnitudes, distances, and site conditions consistent with the seismic hazard characteristics of the target region as shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The FEMA P-695 methodology ensures that the selected records adequately capture the variability in ground motion intensity and frequency content, thereby enhancing the robustness of the subsequent nonlinear dynamic analyses. The selected ground motions are characterized by a suite of intensity and spectral parameters that together capture the amplitude, energy content, and frequency characteristics most relevant to elevated RC tanks. Each record\u0026rsquo;s peak ground acceleration (PGA) quantifies the maximum inertial demand, while Peak ground velocity (PGV) provides insight into the potential for permanent deformation and damage to non-structural components. Arias intensity (AI) is used to assess the cumulative energy input into the structure, and Housner intensity (HI) highlights the spectral energy within the 0.1\u0026ndash;2.5 s period band that is critical for flexible systems such as elevated water tanks (Baltay et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Campbell \u0026amp; Bozorgnia, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). The predominant period (TP) of each motion is compared against the fundamental period of the tank model to ensure coverage of resonance effects, and significant duration (SD) that covers between 5% and 95% of AI (Kempton \u0026amp; Stewart, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2006\u003c/span\u003e). By ensuring that ground motion characteristics span the ranges observed in the target seismic hazard, the IDA results yield fragility curves that robustly reflect both amplitude‐driven and frequency‐driven failure modes.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSelected ground-motion records and their key intensity and spectral parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEQ ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePEER-NGA Number\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003ePGA (g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePGV (m/s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAI (m/s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHI (cm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTP (s)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eSD (s)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120111\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e953\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.416\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e58.948\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e238.905\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.52\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e9.21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120121\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e960\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.410\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e42.973\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.913\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e171.610\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120411\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1602\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.728\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e56.444\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.723\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e212.841\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e8.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120521\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1787\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.266\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28.557\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.830\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e102.806\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e11.65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120611\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e169\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.238\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e26.001\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.397\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e109.872\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e51.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120621\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e174\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e34.437\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.958\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e135.998\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e8.705\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120711\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1111\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.509\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e37.288\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.352\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e146.999\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e9.72\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120721\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1116\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.243\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e37.795\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.826\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e116.825\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.66\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10.32\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120811\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1158\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.312\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e58.853\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.085\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e156.812\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e11.79\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120821\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.219\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e17.695\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.289\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e36.739\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e11.015\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120911\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.245\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e51.408\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.924\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e150.309\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e17.62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e120921\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e848\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.283\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25.648\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.215\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e78.883\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10.435\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e121011\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e752\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.529\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35.014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.374\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e188.174\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e11.915\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e121021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e767\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.555\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35.684\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.087\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e96.154\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e6.365\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e121111\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1633\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.515\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e42.468\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.656\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e136.111\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e28.92\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e121211\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e721\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.358\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e46.360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.063\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e138.720\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e16.05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e121221\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e725\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.446\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35.711\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.093\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e120.783\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e13.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e121321\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e829\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.385\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e43.805\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.523\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e141.661\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e15.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e121411\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1244\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.353\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e70.653\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e2.319\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e163.614\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e30.385\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e121421\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1485\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.474\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e36.700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.396\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e108.211\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e11.275\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e121511\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.210\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e18.874\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.650\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e77.416\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e10.49\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e121711\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.351\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e22.036\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.780\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e73.931\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e4.24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eNonlinear behavior of the elevated tank structures was modeled in SAP2000, with a focus on simulating the inelastic response of critical structural components. Column-beam hinges were explicitly defined in accordance with ASCE 41\u0026thinsp;\u0026minus;\u0026thinsp;13 guidelines, incorporating failure condition II to account for combined flexural and shear failure mechanisms (Federal Emergency Management Agency, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; \u003cem\u003eSeismic Evaluation and Retrofit of Existing Buildings\u003c/em\u003e, 2014). The hinge properties were calibrated to reflect the expected nonlinear deformation capacities and degradation characteristics under seismic time-history loading, ensuring an accurate representation of post-yield behavior and collapse mechanisms. This approach aligns with performance-based engineering principles, enabling the quantification of structural damage progression under increasing seismic demands (Chopra, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e1995\u003c/span\u003e; Bertero \u0026amp; Bertero, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2002\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIDA was conducted to evaluate the structural response across a range of ground motion intensities. Each ground motion record was scaled incrementally using the spectral acceleration at the fundamental period of the structure Sa as the intensity measure (IM) (Luco \u0026amp; Cornell, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Vamvatsikos \u0026amp; Cornell, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). The scaling process continued until global collapse was observed, defined as the point where the structure undergoes excessive lateral drift or hinge failures lead to numerical instability. The histogram of IM (Sa) collapse values (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), derived from the IDA results, was used to determine the median ground shaking intensity index corresponding to collapse, this median value serves as a probabilistic benchmark for assessing the seismic fragility of the elevated tanks. Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the response spectra of all selected ground motion records with 5% damping, with the mean spectrum highlighted to illustrate the range of spectral demands imposed on the models.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe IDA results were post-processed to extract engineering demand parameters (EDPs), including maximum lateral displacements and hinge rotation demands. These parameters were statistically analyzed to establish probabilistic relationships between ground motion intensity and structural response (Fan \u0026amp; Zhang, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). The use of 22 far-field records ensured a comprehensive representation of seismic uncertainty, while the nonlinear modeling framework provided insights into the failure mechanisms governing the seismic performance of the elevated tanks. The integration of FEMA P-695 guidelines, ASCE 41\u0026thinsp;\u0026minus;\u0026thinsp;13 nonlinear hinge modeling, and IDA methodology collectively ensures a rigorous and reproducible approach to seismic fragility evaluation (Taflanidis \u0026amp; Beck, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2006\u003c/span\u003e).\u003c/p\u003e"},{"header":"3. Machine Learning Models","content":"\u003cp\u003eIn this study, seismic fragility assessment of RC elevated tanks is augmented by two complementary machine learning algorithms\u0026mdash;SVR and MLP\u0026mdash;selected for their documented efficacy in resolving nonlinear seismic response prediction challenges. SVR is widely adopted in structural engineering for its ability to model high-dimensional relationships between ground motion parameters and structural demands while maintaining computational efficiency, as demonstrated in hybrid frameworks for liquid-retaining systems (Al-Ayoubi et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2025\u003c/span\u003e). MLP, conversely, is prioritized for its capacity to capture intricate fluid-structure interactions and staging system nonlinearities, a capability validated in prior studies on elevated tanks subjected to hydrodynamic and seismic coupling (Pourbagheri et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The models are trained on a database of 738 response samples generated via elastic-plastic time-history analyses under IDA. Ground-motion intensity measures (Sa, PGV, HI, AI, and TP), together with key structural attributes (tank height (H), tank length (L), and column width (Col)), constitute the input feature set.\u003c/p\u003e \u003cp\u003e3.1 Dataset Composition and Feature Engineering\u003c/p\u003e \u003cp\u003eThe predictive database comprises 738 distinct IDA sample points, each representing a unique combination of scaled far-field ground motion record and tank geometry. Box\u0026ndash;Cox transformations were applied to AI, SD and to reduce skewness, as these features exhibited non-Gaussian distributions, all features were subsequently standardized to zero mean and unit variance to expedite algorithm convergence and mitigate scale-driven bias (Box \u0026amp; Cox, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1964\u003c/span\u003e). Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e summarizes the input and output feature definitions, facilitating reproducibility of the modeling exercise.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDefinitions of ML input features and model parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003eInput\u003c/p\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eOutput Parameter\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eGround motion parameters\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStructural parameters\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eIDR\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePGV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eH\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCol\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eHyperparameter selection critically influences both model accuracy and generalization. Rather than exhaustive grid search, Bayesian optimization framework (BayesSearchCV) was employed to iteratively evaluate and update a probabilistic surrogate model of the validation loss surface to efficiently identify optimal hyperparameter combinations (Bergstra et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2011\u003c/span\u003e; Kaveh, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). At each iteration, the acquisition function balances exploration of poorly sampled regions against exploitation of promising configurations, reducing the total number of evaluations required to converge on the global optimum. This approach was applied to both SVR and MLP, tuning parameters such as the RBF-kernel coefficient γ and regularization parameter C for SVR, and hidden‐layer widths, learning rate, and L₂‐regularization strength for MLP. The 5‐fold cross‐validation process used throughout hyperparameter search is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, where data splits are shown along with corresponding validation‐set performance trajectories (Kaveh et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Lundberg \u0026amp; Lee, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). All computations were performed on a Ryzen 7-5800H CPU, 32 GB RAM, and an NVIDIA RTX 3050 Laptop GPU, with MLP leveraging GPU acceleration for training.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e3.2 Structural Response Prediction Using SVR\u003c/p\u003e \u003cp\u003eThe SVR model employs a radial basis function kernel to nonlinearly project the input feature space, enabling the capture of complex IM\u0026ndash;structural response relationships. Optimal hyperparameters determined via BayesSearchCV (C\u0026thinsp;=\u0026thinsp;100, ε\u0026thinsp;=\u0026thinsp;0.0183) balance bias\u0026ndash;variance trade-offs and constrain margin violations (Tao et al., \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). The database was randomly partitioned into 80% training and 20% testing subsets; a 5‐fold cross‐validation scheme was embedded within the training set to guard against overfitting. Model performance is evaluated by the coefficient of determination (R\u003csup\u003e2\u003c/sup\u003e), which measures the proportion of variance in the observed collapse IDR explained by the predictions Eq.\u0026nbsp;(\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e); the root‐mean‐square error (RMSE), which represents the square root of the average squared prediction deviations and thus indicates overall predictive dispersion Eq.\u0026nbsp;(\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e); the mean‐absolute error (MAE), which quantifies the average absolute bias between predicted and actual values Eq.\u0026nbsp;(\u003cspan refid=\"Equ3\" class=\"InternalRef\"\u003e3\u003c/span\u003e); and the mean‐absolute‐percentage error (MAPE), which expresses the average relative error as a percentage of observed values Eq.\u0026nbsp;(\u003cspan refid=\"Equ4\" class=\"InternalRef\"\u003e4\u003c/span\u003e)\u0026mdash;together offering a multifaceted view of predictive fidelity (Kaveh \u0026amp; Khavaninzadeh, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Scatter plots comparing actual versus predicted collapse IDR for each tank configuration under SVR (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) demonstrate good alignment along the 1:1 line for low‐rise tanks, with modest dispersion emerging in the taller 1008 m\u003csup\u003e3\u003c/sup\u003e configuration.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{R}^{2}=1-\\frac{{\\sum\\:}_{i=1}^{n}{({y}_{i}-\\widehat{{y}_{i}})}^{2}}{{\\sum\\:}_{i=1}^{n}{({y}_{i}-\\stackrel{-}{y})}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:RMSE=\\:\\sqrt{\\frac{1}{n}{\\sum\\:}_{i=1}^{n}{({y}_{i}-\\widehat{{y}_{i}})}^{2}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:MAE=\\frac{1}{n}{\\sum\\:}_{i=1}^{n}\\left|{y}_{i}-\\widehat{{y}_{i}}\\right|$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:MAPE=\\frac{100\\%}{n}{\\sum\\:}_{i=1}^{n}\\left|\\frac{{y}_{i}-\\widehat{{y}_{i}}}{{y}_{i}}\\right|$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u003c/span\u003e is the total number of observations in the measured set, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{y}_{i}\\)\u003c/span\u003e\u003c/span\u003e​ is the actual IDR for the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003eth sample,\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\widehat{{y}_{i}}\\)\u003c/span\u003e \u003c/span\u003e is the ML-predicted collapse IDR for the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:i\\)\u003c/span\u003e\u003c/span\u003eth sample, and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\stackrel{-}{y}\\)\u003c/span\u003e\u003c/span\u003e is the mean of the observed IDR values.\u003c/p\u003e \u003cp\u003e3.3 Structural Response Prediction Using MLP\u003c/p\u003e \u003cp\u003eThe MLP framework developed for predicting IDR consists of an input layer aligned with the dimensionality of the selected ground motion and structural features, followed by two hidden layers of 256 neurons each. This configuration was selected based on hyperparameter optimization using Bayes Optimizer, which systematically explored candidate architectures by balancing accuracy and training efficiency (Yoo et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The ReLU activation function was applied to all hidden layers to enable nonlinearity while addressing vanishing gradient issues (Nair \u0026amp; Hinton, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). He normal initialization was used to ensure stable gradient propagation. The model incorporated L₂ regularization with a coefficient of 1.05\u0026times;10⁻⁴ to constrain weight magnitudes and mitigate overfitting. The optimizer adopted was Adam, with a learning rate of 1.69\u0026times;10⁻3, identified through Bayesian search (He et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). This optimizer dynamically adjusted learning rates based on first and second moment estimates of the gradients. Learning rate decay was implemented by halving the rate upon stagnation of validation loss over five consecutive epochs. Early stopping was triggered when no improvement in validation MSE was observed for ten epochs, using a 10% holdout from the training partition, and training was capped at 500 epochs (Kingma \u0026amp; Ba, 2014). Convergence typically occurred by epoch 120. The selected architecture reflects a trade-off achieved through Bayesian search: it offers sufficient depth and capacity to capture nonlinear interactions among input features\u0026mdash;particularly those arising from fluid\u0026ndash;structure coupling\u0026mdash;without incurring excessive computational cost or overfitting. Figure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e illustrates the model structure, and Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the resulting predictive performance on test data, confirming that MLP achieves closer alignment with actual IDR values across all tank configurations relative to SVR.\u003c/p\u003e \u003cp\u003e3.4 Comparative Model Performance and Computational Efficiency\u003c/p\u003e \u003cp\u003eThe reported test metrics (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e) reflect performance on a 20% held-out set not used in training or tuning, confirming model generalization. Both SVR and MLP exhibit strengths and limitations that must be weighed when selecting an algorithm for seismic fragility assessment. As shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, SVR completed training in 0.894 s and inference in 0.019 s, whereas MLP required 21.203 s for training and 0.004 s for inference. This disparity reflects the underlying computational complexity: SVR solves a convex quadratic program whose cost scales between O(n\u003csup\u003e2\u003c/sup\u003e) and O(n\u003csup\u003e3\u003c/sup\u003e) with the number of samples, while MLP back-propagation over 50,000 weights entails repeated gradient updates proportional to network size and epochs (Smola \u0026amp; Sch\u0026ouml;lkopf, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). For reference, a single IDA run for one tank configuration required approximately 2 hours on similar hardware, underscoring the computational efficiency.\u003c/p\u003e \u003cp\u003eDespite the longer runtimes, MLP yielded higher predictive fidelity: test R2 improved from 0.953 (SVR) to 0.990 (MLP), and RMSE decreased from 0.0021 to 0.0009, with corresponding MAE and MAPE reductions (from 0.0010 to 0.0007 and from 7.73\u0026ndash;4.93%, respectively). These gains align with broader findings that neural networks often outperform SVR in capturing complex, nonlinear mappings when sufficient data are available, at the expense of increased risk of overfitting and heavier computational demands. Conversely, SVR\u0026rsquo;s reliance on support vectors (often a small subset of the training set) confers robust generalization under limited data conditions. Moreover, SVR\u0026rsquo;s unique global optimum (due to convexity) ensures reproducible results across runs, while MLP training on a nonconvex loss surface may converge to different local minima unless multiple random restarts or advanced optimizers are employed. Inference speed also favors SVR when the number of support vectors remains modest, but MLP can leverage GPU acceleration and batch processing to mitigate latency in high-throughput applications (Rumelhart et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e1986\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eBoth SVR and MLP serve as efficient surrogates for IDA, with distinct trade-offs. SVR delivers rapid, reliable estimates for high- to moderate-probability damage states (e.g., IO, LS) with errors under 5%, while MLP provides superior fidelity across all damage thresholds\u0026mdash;including CP\u0026mdash;with maximum error below 6%. These trade-offs underscore MLP\u0026rsquo;s suitability for scenarios demanding precise collapse-level predictions, provided computational resources and overfitting controls are prioritized.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparative performance metrics and computational times for SVR and MLP models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDataset\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMAE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eMAPE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eTime (s)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSVR\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTrain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9911\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.000345\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.000892\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.065%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.894\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9529\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.001019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.002087\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e7.728%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.019\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eMLP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTrain\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9931\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.000460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.000791\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e2.861%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e21.203\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTest\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9897\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.000653\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.000938\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e4.934%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e3.5 Model Interpretability and SHAP Analysis\u003c/p\u003e \u003cp\u003eSHapley Additive exPlanations (SHAP) was used to interpret the predictions made by both the SVR and MLP models by attributing each prediction to its input features. For the SVR model, the SHAP summary plot (Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e) identifies PGV and HI as the most influential predictors. Their SHAP values are distributed around zero, indicating that their contributions to the predicted IDR vary depending on the specific input scenario. Sa and TP also contribute meaningfully, whereas AI, SD, and geometric features such as Length, Height, and Col show lesser but non-negligible influence. The color gradients in the SHAP plot suggest that higher PGV and HI values are typically associated with increased IDR, reflecting their role in amplifying structural demand (Lundberg \u0026amp; Lee, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor the MLP model, the SHAP summary (Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e) shows a broader range of feature contributions. PGV and HI again dominate the input space, but Sa and AI also have significant positive associations with higher predicted IDR. Unlike SVR, the MLP model assigns greater importance to structural parameters, particularly Col, which is not prominent in the SVR interpretation. TP and SD also show increased relevance. This redistribution of feature importance is indicative of MLP\u0026rsquo;s capacity to learn complex nonlinear interactions, in which both dynamic and geometric characteristics jointly influence seismic response. Length and Height show limited direct influence, implying that their effects may be indirectly captured through interactions with other parameters. The observed emphasis on Col in the MLP model likely stems from its ability to model coupled effects of geometry and dynamic response, suggesting improved sensitivity to FSI-related behaviors compared to SVR.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"4. Comparative Analysis of Seismic Fragility Curves","content":"\u003cp\u003e4.1 Fragility Curve Development\u003c/p\u003e \u003cp\u003eFor each tank, the collapse IM samples from IDA\u0026mdash;scaled from 0.1 g to 2.0 g\u0026mdash;were fit with log-normal distributions to define median Sa and dispersion β for the Immediate Occupancy (IO), Life Safety (LS), and Collapse Prevention (CP) limit states (Vamvatsikos \u0026amp; Cornell, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2002\u003c/span\u003e). The damage‐state thresholds are set at IDR\u0026thinsp;=\u0026thinsp;0.01 for IO, IDR\u0026thinsp;=\u0026thinsp;0.02 for LS, and the median collapse IDR values for CP are taken as 0.0340, 0.0295, and 0.0309 for the 75 m\u003csup\u003e3\u003c/sup\u003e, 320 m\u003csup\u003e3\u003c/sup\u003e, and 1008 m\u003csup\u003e3\u003c/sup\u003e tanks respectively (Baker, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). SVR and MLP then predicted exceedance probabilities at these same IM values, using the trained regression mapping from Sa to peak IDR. The resulting ML‐based fragility curves maintain the characteristic S‐shape of the IDA baseline, capturing both the threshold and the spread of the damage probability (Sudret et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e4.2 Comparison of SVR and MLP Predictions Against IDA\u003c/p\u003e \u003cp\u003eThe fragility curves predicted by both SVR and MLP models capture the general trends of IDA-derived probabilities across all three damage states as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e, but each exhibits systematic biases that vary with tank volume and damage threshold. For the 75 m\u003csup\u003e3\u003c/sup\u003e tank, SVR closely replicates the IO median capacity near Sa\u0026thinsp;=\u0026thinsp;0.3g, yet modestly overpredicts the slope of the LS curve, resulting in a slightly steeper transition than IDA and a median at roughly 0.85g compared to 0.8g. Its CP prediction is conservative, underestimating the IDA median by nearly 0.2g, which may reflect limited sensitivity to high‐drift behavior in sparse training data. MLP, by contrast, yields IO and LS medians within 0.05g of IDA and aligns more closely with the observed dispersion for both states, but underestimates CP capacity by approximately 0.25g and produces a gentler slope, indicating a tendency to smooth extreme responses. In the 320 m\u003csup\u003e3\u003c/sup\u003e tank, SVR again matches IO capacity within measurement uncertainty yet overestimates LS by about 0.1g; its CP fit improves, reducing the IDA offset to roughly 0.15g MLP outperforms SVR for LS and CP in this case, with median predictions within 0.1g of IDA and similar lognormal dispersion, though it slightly overpredicts the fragility slope for IO. For the 1008 m\u003csup\u003e3\u003c/sup\u003e tank, the two ML approaches converge in performance: SVR and MLP both reproduce IO medians at 0.4g and LS medians near 1.2g, deviating from IDA by less than 0.05g. However, SVR maintains a marginally steeper LS slope, while MLP more accurately mirrors the gradual increase in CP probability, underestimating the IDA median by only 0.1g. Across volumes, SVR exhibits greater consistency in IO predictions but tends toward conservative CP estimates, whereas MLP offers balanced accuracy in LS and CP at the expense of slightly overestimating IO dispersion. These discrepancies underscore the importance of model selection based on targeted damage states: SVR may be preferred for initial yield assessments, while MLP more reliably predicts advanced damage probabilities (Basterrechea-Ar\u0026eacute;valo et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Sainct et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e4.3 Probability Analysis and Error Assessment\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e compare exceedance probabilities and absolute errors between IDA, SVR, and MLP. For the CP limit state, SVR exhibits an 11.5% error in the 75 m\u003csup\u003e3\u003c/sup\u003e tank, reflecting reduced accuracy in collapse-level predictions compared to MLP (5.6% error). This discrepancy highlights SVR\u0026rsquo;s limitations in capturing nonlinear collapse mechanisms, particularly for smaller tanks where geometric and FSI interactions intensify. While SVR maintains sub-5% errors for IO and LS states across all tanks, MLP achieves lower errors (\u0026le;\u0026thinsp;5.6%) for CP, demonstrating enhanced reliability for collapse assessments. The results align with MLP\u0026rsquo;s capacity to model complex FSI-coupled responses, as evidenced by SHAP interpretations. For practical applications, SVR remains viable for rapid IO/LS evaluations, but MLP is recommended for CP scenarios requiring precise collapse probability estimates.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExceedance probabilities and absolute errors for the 75 m\u003csup\u003e3\u003c/sup\u003e tank.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eDamage State\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSa(g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIDA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eSVR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eMLP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eError %\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eError %\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9643\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9688\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.472\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9596\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.490\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7806\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7765\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.522\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.7732\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.946\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.6415\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5679\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e11.470\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.6058\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e5.562\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExceedance probabilities and absolute errors for the 320 m\u003csup\u003e3\u003c/sup\u003e tank.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eDamage State\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSa(g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIDA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eSVR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eMLP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eError %\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eError %\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7768\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.8125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e4.601\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.7998\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e2.968\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.5595\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5631\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.645\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.5798\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3.631\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7788\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7692\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.233\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.7538\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e3.208\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExceedance probabilities and absolute errors for the 1008 m\u003csup\u003e3\u003c/sup\u003e tank.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eDamage State\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eSa(g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eIDA\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eSVR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c7\" namest=\"c6\"\u003e \u003cp\u003eMLP\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eError %\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eError %\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIO\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9964\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9928\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.360\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9964\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLS\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.9364\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9321\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.466\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9541\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.892\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCP\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.8083\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.7823\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e3.212\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.8177\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1.163\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThis study presented a hybrid framework integrating IDA with ML to expedite seismic fragility analysis of elevated RC tanks, addressing the computational limitations of conventional IDA while preserving probabilistic rigor. Three Indian Standard-compliant tank configurations (75 m\u003csup\u003e3\u003c/sup\u003e, 320 m\u003csup\u003e3\u003c/sup\u003e, 1008 m\u003csup\u003e3\u003c/sup\u003e) were modeled in SAP2000, incorporating FSI effects via Housner\u0026rsquo;s added mass formulation. IDA under 22 far-field ground motions generated 738 nonlinear response samples, forming the dataset for training SVR and MLP models to predict peak IDR. Hyperparameter optimization via Bayesian search and SHAP-based interpretability analysis ensured model fidelity and transparency.\u003c/p\u003e \u003cp\u003eMLP demonstrated superior predictive accuracy (test R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.99, RMSE\u0026thinsp;=\u0026thinsp;0.0009) compared to SVR (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.95, RMSE\u0026thinsp;=\u0026thinsp;0.0021), with errors below 6% even at collapse-level thresholds. SHAP analysis identified PGV and HI as dominant predictors, while MLP uniquely captured interactions between structural parameters (e.g., column width) and dynamic demands, reflecting its capacity to resolve FSI-driven complexities. Fragility curves derived from ML predictions aligned closely with IDA baselines, particularly for MLP, which replicated threshold transitions and dispersion with minimal deviation. SVR exhibited conservatism at higher damage states, whereas MLP maintained consistency across all limit states (IO, LS, CP), achieving errors under 6% for CP probabilities.\u003c/p\u003e \u003cp\u003eThe framework enables rapid fragility curve generation without sacrificing the probabilistic foundations of IDA, reducing computational costs from hours per IDA run to seconds for ML inference. This efficiency facilitates code-compliant seismic risk assessments, particularly in regions requiring urgent evaluation of existing water infrastructure. Applications include performance-based design of new tanks, retrofit prioritization for vulnerable assets, and resilience planning for lifeline systems in seismically active zones. By bridging computational efficiency with rigorous fragility quantification, the approach supports data-driven decision-making for disaster mitigation and resource allocation.\u003c/p\u003e \u003cp\u003eThe study underscores MLP\u0026rsquo;s viability as a surrogate model for IDA in systems governed by FSI and geometric nonlinearities, offering a template for extending ML-aided fragility analysis to other liquid-retaining structures. Future work could explore ensemble methods or physics-informed ML to further enhance generalizability across broader tank typologies and hazard scenarios. The findings contribute to advancing ML\u0026rsquo;s role in performance-based earthquake engineering, emphasizing its potential to transform traditional workflows into scalable, resource-efficient solutions for critical infrastructure resilience.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThe authors declare that no funds, grants, or other support were received during the preparation of this manuscript.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eA. A.: conceptualization, writing original draft,formal analysis, investigation, visualization. V. T.: supervision, reviewand editing. S.S.: methodology, review and editing.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData and code are available from the corresponding author upon reasonable request\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAl-Ayoubi, A. A., Thirumurugan, V., \u0026amp; Satyanarayanan, K. S. (2025). A machine learning framework for predicting seismic behavior in elevated reinforced concrete tanks. \u003cem\u003eAsian Journal of Civil Engineering\u003c/em\u003e. Advance online publication. https://doi.org/10.1007/s42107-025-01356-1\u003c/li\u003e\n\u003cli\u003eAmerican Society of Civil Engineers (2014).\u003cem\u003e Seismic Evaluation and Retrofit of Existing Buildings\u003c/em\u003e. American Society of Civil Engineers. https://doi.org/10.1061/9780784412855\u003c/li\u003e\n\u003cli\u003eBaker, J. W. (2015). 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Seismic Ground Response Prediction Based on Multilayer Perceptron. \u003cem\u003eApplied Sciences\u003c/em\u003e, \u003cem\u003e11\u003c/em\u003e(5), 2088. https://doi.org/10.3390/app11052088\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"asian-journal-of-civil-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Asian Journal of Civil Engineering](https://www.springer.com/journal/42107)","snPcode":"42107","submissionUrl":"https://submission.nature.com/new-submission/42107/3","title":"Asian Journal of Civil Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Machine learning, Fragility curves, Fluid-structure interaction, Elevated RC tanks, Seismic risk assessment, Incremental dynamic analysis (IDA)","lastPublishedDoi":"10.21203/rs.3.rs-6690906/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6690906/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eElevated reinforced concrete (RC) water tanks are critical lifeline structures whose seismic performance is governed by complex fluid\u0026ndash;structure interaction (FSI) effects and slender staging systems. Conventional fragility assessment via incremental dynamic analysis (IDA) yields probabilistic insights but entails extensive nonlinear time history simulations that limit practical application. This study presents a hybrid framework that couples IDA with machine learning (ML) to expedite the generation of seismic fragility curves for three Indian Standard\u0026ndash;compliant RC tank configurations (75 m\u003csup\u003e3\u003c/sup\u003e, 320 m\u003csup\u003e3\u003c/sup\u003e, 1008 m\u003csup\u003e3\u003c/sup\u003e). Validated finite element (FE) models in SAP2000 incorporate Housner\u0026rsquo;s added mass formulation to represent hydrodynamic demands. IDA under 22 far-field ground motions produces 738 nonlinear response samples characterized by ground motion characteristics and key geometric parameters. Support vector regression (SVR) and multilayer perceptron (MLP) regressors are trained to predict peak inter-story drift ratio (IDR), with hyperparameters optimized via Bayesian search and interpretability assessed through SHapley Additive exPlanations (SHAP) analysis. MLP achieves superior fidelity (test R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.990, RMSE\u0026thinsp;=\u0026thinsp;0.0009) compared to SVR (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.953, RMSE\u0026thinsp;=\u0026thinsp;0.0021), maintaining errors below 6% for collapse-level exceedance probabilities. ML-derived fragility curves closely match IDA baselines, capturing threshold transitions and dispersion. The proposed approach enables rapid, code-compliant fragility evaluation\u0026mdash;bridging probabilistic rigor and computational efficiency\u0026mdash;and supports performance-based seismic design, retrofit prioritization and resilience planning for RC water infrastructure in seismically active regions.\u003c/p\u003e","manuscriptTitle":"Seismic fragility analysis of elevated RC tanks based on IDA and machine learning","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-03 09:40:42","doi":"10.21203/rs.3.rs-6690906/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"43918802175337170361061375615803453439","date":"2025-05-31T13:28:13+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"199686641999039408051930811786387193829","date":"2025-05-30T12:25:44+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-05-30T12:18:25+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-05-19T12:34:03+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-05-19T11:57:07+00:00","index":"","fulltext":""},{"type":"submitted","content":"Asian Journal of Civil Engineering","date":"2025-05-18T09:26:11+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"asian-journal-of-civil-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Asian Journal of Civil Engineering](https://www.springer.com/journal/42107)","snPcode":"42107","submissionUrl":"https://submission.nature.com/new-submission/42107/3","title":"Asian Journal of Civil Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"c40509f3-1dfb-482e-8ca6-c11e9563a010","owner":[],"postedDate":"June 3rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2025-07-07T14:45:44+00:00","versionOfRecord":{"articleIdentity":"rs-6690906","link":"https://doi.org/10.1007/s42107-025-01420-w","journal":{"identity":"asian-journal-of-civil-engineering","isVorOnly":false,"title":"Asian Journal of Civil Engineering"},"publishedOn":"2025-07-01 00:00:00","publishedOnDateReadable":"July 1st, 2025"},"versionCreatedAt":"2025-06-03 09:40:42","video":"","vorDoi":"10.1007/s42107-025-01420-w","vorDoiUrl":"https://doi.org/10.1007/s42107-025-01420-w","workflowStages":[]},"version":"v1","identity":"rs-6690906","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6690906","identity":"rs-6690906","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}