The multi-strip method is often used to establish a demand model for fragility analysis. Using the multi-strip method to scale the ground motion record may cause uncertainty and bias in structural response calculation and fragility assessment. It is necessary to analyze the effect of differences in the amplitude scaling range in different strips on structural seismic response calculation and seismic fragility assessment. In this paper, the multi-strip method was used to analyze the seismic demand bias based on four multi-story reinforced concrete frame structures subjected to eight ground motion record sets. The bias, variance, and coefficient of variation in different strips in each group of ground motion records were obtained. The effect of different strips on the demand bias was investigated by analysis of variance (ANOVA). Uncertainty quantification of structural demand and fragility curves was carried out using the bootstrap sampling method. The results for structures in different ground motion record sets verify that the differences between the demand bias for different strips by amplitude scaling are statistically insignificant for a 95% confidence level. These findings will contribute to the use of scaling methods for ground motion record sets in a probabilistic seismic demand assessment, allowing for a more reliable prediction of structural seismic fragility.

It is necessary to evaluate the reliability of the water supply network, when the water supply network is damaged by an earthquake. Therefore, this paper researched the feasibility and characteristics of the surplus power entropy as the reliability index of the water supply network, and established a scheme framework for optimizing and improving the reliability of the water supply network. This paper developed a reliability evaluation model for the water supply network after an earthquake. Combined with the Monte Carlo stochastic simulation hydraulic analysis, this model is also based on the pressure-driven nodes water demand model. In the case study, the surplus power entropy method was applied to test the reliability of the model. The statistical curves of the surplus power entropy of nodes and pipe networks, the distribution of the surplus power entropy with different intensities in pipe networks, and the comparison results of three reliability improvement schemes, before and after, were obtained. The influence factors of the surplus power entropy were obtained from the data analysis. The high consistency between the surplus power entropy and flow entropy verifies the feasibility of the surplus power entropy as a reliability index. The three schemes show that the surplus power entropy index can be used as a beneficial supplement to the reliability evaluation index of the pipe network.

The dynamic shear modulus ratios and dynamic damping ratios of soil are critical parameters for soil seismic response analyses and seismic safety evaluation of engineering sites. This study utilized dynamic triaxial test and resonant column test data of 5208 soil samples collected from more than 2500 boreholes across the Beijing-Tianjin-Hebei (BTH) region. Statistical analyses were conducted for five typical soil types (silty clay, clay, silt, silty sand, and fine sand), focusing on their dynamic shear modulus ratios and dynamic damping ratios. Key parameters representing the characteristics of soil dynamics, including the reference strain, the maximum damping ratio, and the damping ratio nonlinearity coefficient, were statistically evaluated. Median values, as well as the values corresponding to 84% and 16% exceedance probabilities, were provided. The median values of the reference strain, the maximum damping ratio, and the damping ratio nonlinearity coefficient were 13.43 × 10⁻⁴, 0.2155, and 0.7799 for silty clay; 16.47 × 10⁻⁴, 0.2266, and 0.7722 for clay; 10.64 × 10⁻⁴, 0.2012, and 0.7856 for silt; 11.98 × 10⁻⁴, 0.1842, and 0.7911 for silty sand; and 12.73 × 10⁻⁴, 0.1803, and 0.8064 for fine sand. Based on these statistics, the influence of various factors on the reference shear strain, maximum damping ratio, and damping ratio nonlinearity coefficient were investigated. The results showed considerable variability, and weak correlations were observed between these parameters and site-related factors such as sampling depth, shear wave velocity at sampling depth, overburden thickness, 30 m average shear wave velocity (V_S30), and 20 m equivalent shear wave velocity (V_se). The coefficients of determination for the linear regressions considering each factor were between 0.001 and 0.274, which were sufficiently close to 0 and indicated a weak predictive ability of the model considering only one factor. Furthermore, multivariate linear regression models incorporating all five influencing factors also achieved a slight reduction in standard deviation compared with directly adopting the mean values—by <5.5% for the reference shear strain, <3.9% for the maximum damping ratio, and <7.3% for the damping ratio nonlinearity coefficient. A case study was conducted to demonstrate the impact of the variability in soil dynamic parameters on both site seismic response and structural seismic response. For the selected ground motion inputs, site model, and structural model, differences in soil dynamic parameters led to variations in structural seismic response up to 54.5%. Comparative analyses with recommended values from existing studies indicate that the dynamic parameters of the five typical soil types in the BTH region investigated exhibited distinct regional characteristics: the dynamic shear modulus ratios were significantly lower, while the dynamic damping ratios were significantly higher. Comparisons with results from other studies on soil dynamic parameters in China showed that the dynamic shear modulus ratios derived from this study were noticeably smaller, while the dynamic damping ratios were significantly larger. At least one of the three soil dynamic parameters for each soil type failed to pass two-side t-tests, which indicated that the statistical data were from two distributions, that is, soil dynamic properties were intrinsically linked to sedimentary environments, exhibiting distinct regional specificity. Therefore, for boreholes lacking laboratory dynamic test data of soil in the BTH region, it was recommended to use the median values of reference shear strains, maximum damping ratios, and damping ratio nonlinearity coefficients provided in this study for the estimation of dynamic shear modulus ratios and dynamic damping ratios, while their variability must be taken into consideration.

A significant challenge in probabilistic seismic demand analysis lies in selecting appropriate intensity measures and investigating their relationships with demand parameters to ensure accurate seismic fragility predictions. A single ground motion intensity measure is insufficient to capture the complex characteristics of ground motion, leading researchers to focus on compound intensity measures. It is essential to investigate the selection of ground motion features and the number of features included in the construction of compound intensity measures, as these measures cannot comprise an unlimited set of ground motion features. This study focused on machine learning feature selection methods to select ground motion features for compound intensity measures, utilizing mutual information for feature selection. Considering the symmetry and asymmetry requirements of this process, optimized features were selected. Based on the selected features, the compound ground motion intensity measure was constructed to evaluate structural seismic fragility. The compound ground motion intensity measure was evaluated against scalar intensity measure in terms of correlation, efficiency, practicality, proficiency, and sufficiency. A comprehensive comparative analysis demonstrates the applicability of the compound intensity measure. The study’s findings support fragility analysis and performance evaluation using compound intensity measures. The corresponding results can be applied in the risk analysis aspect of performance-based earthquake engineering.