Accurate structural health monitoring (SHM) is crucial for ensuring safety and preventing catastrophic failures. However, conventional parameter identification methods often assume a fixed-base foundation, neglecting the significant influence of soil-structure interaction (SSI) on the dynamic response, leading to inaccurate damage assessments, especially under seismic loading. Therefore, we introduce a novel approach that explicitly incorporates SSI effects into parameter identification for frame structures, utilizing an optimized variational mode decomposition (VMD) technique. The core innovation is the application of the Subtraction Average-Based Optimizer (SABO) algorithm, coupled with permutation entropy as the fitness function, to optimize the critical VMD parameters. This SABO-VMD method was rigorously validated through a shaking table test on a 12-story frame structure on soft soil. Comparative analysis with EMD and conventional VMD demonstrated that SABO-VMD provides a superior time-frequency representation of the structural response, capturing non-stationary characteristics more effectively. A novel energy entropy index, derived from the SABO-VMD output with SSI, was developed for quantitative damage assessment. It revealed 8.1% lower degree of structural damage compared to the fixed-base assumption. The proposed SABO-VMD-based approach, by explicitly accounting for SSI, offers a substantial advancement in SHM of frame structures, leading to more reliable safety evaluations and improved seismic resilience.

Fractional calculus is a powerful mathematical tool for solving mechanical modeling problems. It is used to simulate soils between ideal solids and fluids. Using Riemann-Liouville's fractional calculus operator and theory, fractional order viscous element, nonlinear viscous element and viscoplastic body are connected in series to establish a fractional nonlinear creep damage model, which is used to simulate the nonlinear gradient process of rock creep under different water content conditions. The constitutive equation of the model is constructed. The parameters of creep damage model are identified based on the principle of least squares. The results show that the correlation between theoretical model and experimental data is more than 0.98, which can simulate the creep characteristics of rock well. The effect of model parameters on deformation is further explored, so that the effectiveness of model parameters can be analyzed and verified, and the applicability of the model in other complex stress environments is increased. The research results can provide theoretical basis for stability analysis and disaster prevention of soft rock slopes.

A numerical model was established in earlier work to investigate the macroscale critical state, which determines the mechanical behavior of sheared granular materials. This paper explores the behavior of this model by conducting a parametric study that varies the constitutive parameters over a wide range. This study is essential to define the combination of material parameters that will lead to the emergence of critical state along the classical response. According to the typical critical state behavior, while the material volume and stress remain unchanged under large shear deformation, the material continues to deform. The critical state concept is examined using a granular micromechanics approach within a numerical framework. In this model, elastic and dissipation energies for a generic grain-pair interaction are adapted using a hemivariational principle. Karush-Kuhn-Tucker-type conditions are derived through a hemivariational principle, providing evolution equations for damage and plastic irreversible phenomena. The coupled damage and plasticity, which are crucial for material strength properties, are associated with grain-pair contact loss and irreversible deformation. Notably, damage-elastoplastic spring elements are described in order to link the micro and macro mechanisms, using orientationally based grain-pair interactions, decomposed into normal and tangential directions. The material properties of specimens with different initial density states are adapted according to dilatancy/compaction characteristics to achieve the idealized critical state behavior. The present model is then applied to simulate the stress and volumetric strain behaviors under varying characteristic compression constitutive parameters.

The soft interlayer, often considered the weak link of slopes, poses a significant threat to slope stability. This study focuses on the Permian carbonaceous shale soft interlayer commonly found in Southwest China. The creep characteristics of the soft interlayer were investigated, and a graded shear creep test was conducted in addition to conventional shear tests to analyze the shear deformation behavior of the soft interlayer comprehensively. The long-term strength of the soft interlayer was determined using the steady-state creep rate method. Building upon the Riemann-Liouville fractional order integral theory and statistical damage theory, an improved model based on the traditional Nishihara model was developed. The accuracy of the model was verified using the adaptive differential evolution algorithm in combination with the weak interlayer shear creep test curve, followed by a parameter sensitivity analysis. The results demonstrate that the improved model adequately describes the three stages of creep in the weak interlayer. The creep curve is influenced by the differential order., the shape parameter m, and the proportional parameter F-0. Parameter m reflects the brittle characteristics of the soft interlayer, while parameter F-0 characterizes its physical and mechanical strength. The research results can provide a theoretical basis for disaster prevention monitoring and stability analysis of slopes with weak interlayer.

Multiple research studies and seismic data analyses have shown that multi-directional long-period ground motion affects crucial and intricate large-scale structures like oil storage containers, long-span bridges, and high-rise buildings. Seismic damage data show a 3-55% chance of long-period ground motion. To clarify, the chance of occurrence is 3% in hard soil and 83% in soft soil. Due of the above characteristics, the aseismic engineering field requires a realistic stochastic model that accounts for long-period multi-directional ground motion. A weighted average seismic amplification coefficient selected NGA database multi-directional long-period ground motion recordings for this study. Due to the significant low-frequency component in the long-period ground motion, this research uses empirical mode decomposition (EMD) to efficiently decompose it into a composite structure with high- and low-frequency components. Given the above, further investigation is needed on the evolutionary power spectrum density (EPSD) functions of high- and low-frequency components. Analyzing the recorded data will reveal these functions and their corresponding parameters. Proper orthogonal decomposition (POD) is needed to simulate samples of high- and low-frequency components in different directions. These samples can be combined to illustrate multi-directional long-period ground motion. Representative samples exhibit the seismic characteristics of long-period multi-directional ground motion, as shown by numerical examples. This proves the method's engineering accuracy and usefulness. Moreover, this study used incremental dynamic analysis (IDA) to apply seismic vulnerability theory. This study investigated whether long-period ground motions in both x and multi-directional directions could enhance the seismic response of a high-rise frame structure. By using this method, a comprehensive seismic economic loss rate curve was created, making economic loss assessment clearer. This study shows that multi-directional impacts should be included when studying seismic events and calculating structure economic damages.