Analytical solutions for nonlinear consolidation of soft soil around a shield tunnel with idealized sealing linings     

《Computers and Geotechnics》2014

This paper presents the analytical solutions for nonlinear consolidation of soft soil around a shield tunnel with idealized sealing linings. By introducing the empirical relation between permeability and compressibility, along with the conformal transformation, the governing equations of nonlinear consolidation are established, and the corresponding analytical solutions are derived. Then, the Terzaghi consolidation solutions are derived from the degenerate governing equation of nonlinear consolidation. Through the predictions of different consolidation theories in both completely permeable and impermeable lining conditions, the influences of a tunnel acting as a drain and impacting the dissipation of pore pressure, degree of consolidation, long-term ground settlements and ground settlement rates are investigated. During the early stages of consolidation, the case studies reveal that the predictions made by this study strongly agree with the field data when a completely permeable lining is applied. This study confirms that a tunnel acting as a drain can accelerate the consolidation of soil and enlarge soil deformation due to consolidation. During long term consolidation, a notable nonlinearity of the soil consolidation is exhibited by a small and gradually decreasing settlement rate, showing agreement with the tendency of field data from the impermeable conditions.  相似文献   

A steady state of the disc dynamo     

Ladislav Kvasz  Dmitry Sokoloff  Anvar Shukurov 《地球物理与天体物理流体动力学》2013,107(1-4):231-244

Abstract

We discuss the steady states of the αω-dynamo in a thin disc which arise due to α-quenching. Two asymptotic regimes are considered, one for the dynamo numberD near the generation thresholdD ₀, and the other for |D| ? 1. Asymptotic solutions for |D—D ₀| ? |D ₀| have a rather universal character provided only that the bifurcation is supercritical. For |D| ? 1 the asymptotic solution crucially depends on whether or not the mean helicity α, as a function ofB, has a positive root (hereB is the mean magnetic field). When such a root exists, the field value in the major portion of the disc is O(l), while near the disc surface thin boundary layers appear where the field rapidly decreases to zero (if the disc is surrounded by vacuum). Otherwise, when α = O(|B|^?s) for |B| → ∞, we demonstrate that |B| = O(|D|^1/s ) and the solution is free of boundary layers. The results obtained here admit direct comparison with observations of magnetic fields in spiral galaxies, so that an appropriate model of nonlinear galactic dynamos hopefully could be specified.  相似文献   

静力平衡近似下大气中非线性对称运动的稳定性、分岔和突变     

彭晓林  罗德海 《成都信息工程学院学报》1991,(Z1)

本文在考虑基本气流具有非线性切变情况下,导出了对称运动所满足的非线性常微分方程,并用非线性系统的稳定、分岔、突变理论,严格地讨论了非线性对称运动的稳定性、分岔和突变问题,获得了一个推广的对称不稳定判据,找到了突变产生的条件。  相似文献   

扩展SSH　Hubbard模型的晶格振动矩阵     

杨进 《成都信息工程学院学报》1996,(Z1)

在计及最近邻电子相互作用的扩展ＳＳＨＨｕｂｂａｒｄ模型时，得到了晶格振动矩阵，它对电子的正负自旋态对称和非对称的各类非线性元激发情形均适用。  相似文献   

非线性Lyapunov稳定性及Stern''''s Modons的稳定性判据     

罗德海 《成都信息工程学院学报》1993,(4)

本文在构造正压大气运动的浅水波模式的Hamilton守恒量和积分不变的Casimir泛函的基础上,建立了一个积分不变的Lyapunov函数,通过使用变分法,找出了正压旋转流体运动的非线性Lyapunov稳定性判据,并进一步讨论了Stern's Modons的稳定性。  相似文献   

Cross-equatorial structures of equatorially trapped nonlinear Rossby waves     

《Dynamics of Atmospheres and Oceans》2013

Analysis of the Sea Surface Height (SSH) from satellite altimeters has shown that equatorially trapped Rossby waves exhibit asymmetric cross-equatorial structures; their northern extrema are much larger in magnitude than their southern counterparts. Such asymmetry is inconsistent with the classical theory for the first baroclinic, first meridional equatorially trapped Rossby mode, which predicts that SSH and zonal velocity are symmetric in latitude and the meridional velocity is latitudinally antisymmetric (Matsuno, 1966). Chelton et al. (2003) attributed the observed asymmetry to the mean-shear-induced modifications of first meridional mode Rossby waves. The present paper examines nonlinear rectification of cross-equatorial wave structures in the presence of different zonal mean currents. Nonlinear traveling Rossby waves embedded in shears are calculated numerically in a 1.5-layer model. Nonlinearity is shown to increase the cross-equatorial asymmetry substantially making the northern extrema even more pronounced. However, nonlinearity only slightly increases the magnitude of the westward phase speed.  相似文献   

往复活塞式制冷压缩机性能系数的曲面回归方程     

关志强 《广东海洋大学学报》1994,(2)

采用非线性二乘法对国产１２．５系列往复活塞式制冷压缩机的实测性能数据进行拟合，得出描述该系列制冷压缩机性能系数与运行工况之间相关关系的曲面回归方程，为制冷系统的数值计算、动态特性模拟和优化设计提供数学模型。  相似文献   

Low correlation between redshift and intrinsic brightness for quasars and galaxies in a de sitter universe     

John B. Miller  Thomas E. Miller 《Astrophysics and Space Science》1995,227(1-2):53-60

Since the discovery of quasars, it has been recognized that these objects must have either an extraordinary intrinsic brightness or a nonlinear redshift. The most widely accepted current belief incorporates a linear (Hubble) redshift- distance relation and time evolution within a Big Bang model. We reconsider the possibility of a nonlinear (de Sitter) redshift-distance relation and find quasar intrinsic brightness to be not at all extraordinary. Given a de Sitter law, intrinsic brightness is found to be independent of redshift over five orders of magnitude.  相似文献   

An approximated method for the solution of elliptic problems in thin domains: Application to nonlinear internal waves     

A. Scotti  S. Mitran   《Ocean Modelling》2008,25(3-4):144-153

Realistic numerical simulations of nonlinear internal waves (NLIWs) have been hampered by the need to use computationally expensive nonhydrostatic models. In this paper, we show that the solution to the elliptic problem arising from the incompressibility condition can be successfully approximated by a few terms (three at most) of an expansion in powers of the ratio (horizontal grid spacing)/(total depth). For an n dimensional problem, each term in the expansion is the sum of a function that satisfies a one-dimensional second-order ODE in the vertical direction plus, depending on the surface boundary condition, the solution to an n-1 dimension elliptic problem, an evident saving over having to solve the original n-dimensional elliptic problem. This approximation provides the physically correct amount of dispersion necessary to counteract the nonlinear steepening tendency of NLIWs. Experiments with different types of NLIWs validate the approach. Unlike other methods, no ad hoc artificial dispersion needs to be introduced.  相似文献   

地形作用下有限振幅Rossby波的稳定性分析     

周定文  彭晓林  罗德海 《成都信息工程学院学报》1990,(Z1)

本文用微分方程定性理论方法分析了地形对有限振幅Rossby波的稳定性影响。结果表明:地形北坡有利于波动出现不稳定,南坡使波动稳定;西坡使导式波动不稳定但使曳式波动稳定,东坡使导式波动稳定但使曳式波动不稳定。  相似文献