Immersed tube tunnels are usually placed on soft soil layers in cross-sea tunnelling engineering. Owing to the influence of stratum conditions and slope design, the longitudinal distribution of substratum layers is generally uneven. Thus, the inhomogeneous deformation of the element-joint becomes the key factor in the failure of the immersed tube tunnel. Therefore, a corresponding calculation method for joint deformation is needed to explore the deformation law of immersed tube tunnels. By constructing a three-section immersed tube tunnel analysis model (TTM), the relationship between the two types of deformation of the immersed tube tunnel structure in a longitudinal nonuniform soft soil foundation is described, and the deformation characteristics of the immersed structure under different boundaries are discussed. Based on the mechanical behaviour of the joint and foundation, according to the Timoshenko beam on the Vlasov two-parameter foundation (VTM), considering the tidal cyclic load during the operation and maintenance period, an example analysis is given. Moreover, the deformation characteristics and development trend of the immersed tube tunnel under the influence of different soil layers are discussed. The obtained results have a certain guiding significance for the deformation calculation of immersed tube tunnels.
The short-term evolution of spheroidal galaxies has been explored by S. Chandrasekhar et al. and G. S. Sunder et al. In this paper, we study their long-term evolution with Laskar's method of frequency analysis. The main new results are as follows: (1) There exists a unique equilibrium, which is spherically symmetric. This equilibrium has a critical linear stability. (2) Generally speaking, the semi-axes exhibit quasiperiodic or nearly quasi-periodic (in a time scale longer than a Hubble time) oscillations around the radius of the above-mentioned equilibrium, so the equilibrium is practically stable. (3) There are cases in which one of the semi-axes tends fast to zero while the other to some finite value. The limit state is generally planar rather than linear, i.e. it is the symmetric semi-axis that tends to zero. This implies that some disk galaxies may have originated from spheroidal pregalaxy material. 相似文献