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The regression analysis method is being widely adopted to analyse the tunnel strain, most of which ignore the strain-softening effect of the rock mass and fail to consider the influence of support pressure, initial stress state, and rock mass strength classification in one fitting equation. This study aims to overcome these deficiencies with a regression model used to estimate the tunnel strain. A group of geological strength indexes (GSI) are configured to quantify the input strength parameters and deformation moduli for the rock mass with a quality ranging from poor to excellent. A specific semi-analytical procedure is developed to calculate the tunnel strain around a circular opening, which is validated by comparison with those using existing methods. A nonlinear regression model is then established to analyse the obtained tunnel strain, combining twelve fitting equations to relate the tunnel strain and the factors including the support pressure, GSI, initial stress state, and critical softening parameter. Particularly, three equations are for the estimation of the critical tunnel strain, critical support pressure, and tunnel strain under elastic behaviour, respectively; and the other nine equations are for the tunnel strain with different strain-softening behaviours. The relative significance between the GSI, the initial stress and the support pressure on the tunnel strain is assessed.

A wind tunnel test of synchronized pressure measurement on a spring-suspended sectional model of a flat closed box deck at a large scale of 1/20 was carried out by taking Xiangshan Harbour Bridge in China as background. The chordwise correlation of the fluctuating aerodynamic pressures (FAP) on the surface of the box deck was then investigated at both stationary state and vortex-induced resonance (VIR) states of the deck model. Afterwards, an approximate approach was developed for estimating the spanwise correlation coefficients of pure vertical vortex-shedding force (VSF) on the deck under VIR state. On this basis, the spanwise correlation coefficients of both the integrated total vertical fluctuating aerodynamic force (FAF) and the pure vertical VSF on the flat box deck were then studied and compared to each other quantitatively at the stationary state as well as the VIR states at various wind speeds. Finally, the spanwise correlation coefficients of the surface FAP at some typical positions on the deck cross section were calculated and compared with that of the total vertical FAF and the vertical VSF. The results show that the chordwise correlation of the FAP on stationary deck is not strong at most part of the deck surface, however, can be enhanced with the increase of incident wind speed. The chordwise correlation of FAP can also be enhanced quite significantly by the deck oscillation under VIR states, but is still imperfect. Furthermore, the spanwise correlations of FAP at different positions on the deck cross section are clearly different from each other, and much weaker than that of the total vertical FAF, for both the stationary state and the VIR states of the deck. However, they are generally much stronger than that of the pure VSF in cases of notable VIR, and much weaker in the cases of slight VIR, such as near the onset of VIR. The spanwise correlation characteristics of both the pure vertical VSF and the total vertical FAF are hence very different from those of the surface pressures. Moreover, the spanwise correlation of the total vertical FAF on cross sections can be greatly intensified by the VIR because of the existence of a large portion of vortex-induced self-excited force (VISEF). On the other hand, the spanwise correlation of the vertical VSF under the VIR states is much weaker than that of total vertical FAF as well as that of the pure vertical VSF under the stationary state at same wind speeds. Finally, the variations of the spanwise correlation of both the total vertical FAF and the pure vertical VSF with the response displacement of VIR is quite complicated. The most violent VIR, the most correlated total FAF and the most correlated VSF occur generally at different wind speeds.

By taking Xiangshan Harbor Bridge located in Ningbo of Zhejiang Province in China, a steel cable-stayed bridge with a main span of 688 m, as a background, the nonlinear vortex-induced vertical force (VIVF) force on the flat closed-box deck was investigated in this study via wind tunnel tests of spring-suspended sectional model at a large scale of 1/20. In the tests, the signals of the dynamic forces acting on the outer cladding of the model at various wind speeds within the lock-in range of vortex-induced resonance (VIR) were measured using four single-component force balances installed in the box of the deck model while the corresponding signals of the dynamic displacement and acceleration responses of the model were measured simultaneously using four laser displacement sensors and four accelerometers. A nonlinear least square fitting (NLSF) method was then applied on the time histories of the VIVFs extracted from the measured dynamic forces to identify the relevant parameters of the Scanlan′s empirical nonlinear model and a new nonlinear mathematic model proposed in this paper for the VIVFs. By comparing both the displacement responses of and the VIVF on the sectional model computed based on the identified model parameters with the corresponding tested results, it was found that the proposed nonlinear mathematical model is adequate, whilst the Scanlan′s empirical nonlinear model may not suitable, for describing the VIVF acting on flat closed-box decks.

Third Nanjing Bridge over Yangtze River in China is a long-span steel cable-stayed bridge with a main span of 648 m and a closed streamline cross-section of single box. The flutter and buffeting performances of the bridge under yaw winds were investigated via a wind tunnel test of full bridge aeroelastic model at a geometric scale of 1:120. The service state and three key construction states including the longest single-cantilever state, the longest double-cantilever state with a temporary pier, and the longest double-cantilever state without any temporary pier, were considered in the test. The test was conducted in both smooth and simulated boundary layer wind fields with various combinations of wind yaw angle and inclination angle. The model was elaborately designed and manufactured, and the modal properties of the service-state model were checked before the test. The natural frequencies and mode shapes were identified automatically using a self-developed special software from the acceleration signals recorded in an ambient vibration test, where an “artificial” turbulent wind with lower mean speed of 1 m/s was used as a major ambient excitation addition to the “natural” one from the slight ground trembling. The modal damping ratios were checked using free-decay vibration approach. The testing results show that the bridge has enough aerodynamic stability for all structural states and wind directions concerned, and the most unfavorable buffeting responses often occur in yaw wind case with a yaw angle between 5° and 30°.