Soil-structure cluster dynamic interaction (SSCI) has a significant effect on structural responses as well as ground motions for soft soil, while investigations on the latter remain limited. In this paper, four test models, including the free field model, soil-single structure model, soil-equal height structure cluster model, and soil-multiple height structure cluster model, were manufactured and investigated through large scale shaking table tests. The effect of structure numbers, layouts, structural dynamic characteristics and seismic spectrum characteristics on the ground motions was discussed. On this basis, finite element analysis and wavelet packet decomposition were employed to further investigate the evolution rule of cluster effect. The results manifested that, due to the structure cluster, the predominant period of the original free field could be elongated notably and earthquake response spectrum in the long period domain was amplified, especially under the excitation of seismic waves with abundant low-frequency components. The influence of SSCI on ground motions is chiefly reflected in the variation of site predominant period and the soil damping during the vibration. In addition, the cluster effect on ground motion presents a monotonous degressive trend with the increase of the structural spacing, and its attenuation rate is negatively correlated with structural height, while the difference in ground motion due to different structure numbers becomes insignificant with the increase of structural spacing.
In this article, a two-stage robust model is proposed to solve the crude oil scheduling problem under uncertain conditions. The first stage of the model is developed using chance-constrained programming and fuzzy programming that can be transformed into the deterministic counterpart problem, whereas the second-stage is scenario-based. Through the combination of the approaches, the two-stage model can deal with uncertain parameters with both continuous and discrete probability distributions within a finite number of scenarios. The model was tested on several small examples and an industrial-size case. Uncertainties were introduced in ship arrival times and fluctuating product demands. The computational results demonstrate the effectiveness and robustness of the proposed approach. The tradeoff between solution robustness and model robustness was also analyzed.
This study conducted the parametric and quantitative analysis of the influence of soil-structure cluster interaction (SSCI) on ground motion. Based on the results of the shaking table test and numerical simulation, the changes in the characteristics of ground motion with the alterations of multiple factors are explored via wavelet packet decomposition. The results indicated that: (a) structure cluster reduces the site eigenfrequency, thereby amplifying the low-frequency components of ground motion and attenuating the high-frequency components. Ground can capture more of the high-frequency seismic energy coming from the bedrock through the long piles; (b) homogeneous structures inhibit the ground motion component with a frequency close to the structural eigenfrequency. The effect is more significant with increasing the number of structures and is gradually transformed into the energy dissipation effect acted in the wideband with increasing the damping ratio of structures; (c) the peak ground acceleration gradually diminishes from the center of the homogeneous structure cluster outward and this spatial variation is more pronounced under the excitation with high-frequency seismic waves. Furthermore, the energy variation index and coefficient of variation are employed to quantify the influence of SSCI on ground motion. The mass density of the structure cluster is the crucial variable for affecting the holistic variation of free-field ground motion. The spatial variation of ground motion attenuates significantly with increasing the thickness, shear wave velocity of subsoil, structural spacing, and homogeneity of structure cluster. The spacing between the structures required for the degeneration of SSCI into soil-structure interaction is chiefly related to the site condition and the structural frequency, which is enlarged with the decrease in soil shear wave velocity and structural frequency.
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