A critical state model for sands dependent on stress and density

An elastoplastic model for sands is presented in this paper, which can describe stress–strain behaviour dependent on mean effective stress level and void ratio. The main features of the proposed model are: (a) a new state parameter, which is dependent on the initial void ratio and initial mean stress, is proposed and applied to the yield function in order to predict the plastic deformation for very loose sands; and (b) another new state parameter, which is used to determine the peak strength and describe the critical state behaviour of sands during shearing, is proposed in order to predict simply negative/positive dilatancy and the hardening/softening behaviour of medium or dense sands. In addition, the proposed model can also predict the stress–strain behaviour of sands under three-dimensional stress conditions by using a transformed stress tensor instead of ordinary stress tensor. Copyright © 2004 John Wiley & Sons, Ltd.     

Elastic solutions for stresses in a transversely isotropic half‐space subjected to three‐dimensional buried parabolic rectangular loads

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd.     

Robe's restricted three-body problem revisited

Robe's restricted three-body problem is reanalyzed with a view to incorporate a new assumption, namely that the configuration of the fluid body is that described by an hydrostatic equilibrium figure (Roche's ellipsoid). In the concomitant gravitational field a full treatment of the buoyancy force is given. The pertinent equations of motion are derived, the linear stability of the equilibrium solution is studied and the connection between the effect of the buoyancy forces and a perturbation of the Coriolis force is pointed out.     

The Expansion of the Distance Between Two Arbitrary Gravitating Points as Applied to Specific Models of Celestial Bodies

For the complete system of biharmonic functions a suitable representation in spheroidal coordinates is found. It is used for expanding the distance between two arbitrary gravitating points and its inverse quantity in appropriate series. Such expansions can be of interest and useful in a number of problems of celestial mechanics and stellar dynamics.     

On the practice of estimating fractal dimension

Coastlines epitomize deterministic fractals and fractal (Hausdorff-Besicovitch) dimensions; a divider [compass] method can be used to calculate fractal dimensions for these features. Noise models are used to develop another notion of fractals, a stochastic one. Spectral and variogram methods are used to estimate fractal dimensions for stochastic fractals. When estimating fractal dimension, the objective of the analysis must be consistent with the method chosen for fractal dimension calculation. Spectal and variogram methods yield fractal dimensions which indicate the similarity of the feature under study to noise (e.g., Brownian noise). A divider measurement method yields a fractal dimension which is a measure of complexity of shape.     

岩体三维节点偶对分析及其应用

本文讨论了节点偶对分析的三维扩展。节点偶对分析是针对摩擦滑动节理单元的约束边界进行的序列矢量判定。在三维节理单元的分析中,几何约束和相应的力学判据极为复杂,采用节点偶对等效结合力方法才能迎刃而解。文中对三维转向节理模型的分析得到合理的结果,它表明本文所提出的方法可成功地应用于节理岩体的有限元分析。     

Influence of Structural Non-Stationarity of Surface Roughness on Morphological Characterization and Mechanical Deformation of Rock Joints

Summary Structural non-stationarity of surface roughness affects accurate morphological characterization as well as mechanical behaviour of rock joints at the laboratory scale using samples with a size below the stationarity threshold. In this paper, the effect of structural non-stationarity of surface roughness is investigated by studying the scale dependence of surface roughness and mechanical behaviour of rock joints. The results show that the structural non-stationarity mainly affects the accurate characterization of the surface roughness of the fracture samples. It also controls the amount and location of the contact areas during shear tests, which in turn affects the mechanical properties and asperity degradation of the samples. It is concluded that for accurate determination of the morphological and mechanical properties of rock joints at laboratory and field scales, samples with size equal to or larger than the stationarity threshold are required. Author’s address: Nader Fardin, Rock Mechanics Group, Department of Mining Engineering, Faculty of Engineering, University of Tehran, P.O. Box: 11365/4563, Tehran, Iran     

P-III分布参数的概率权重矩法S函数计算

概率权重矩法是一种估计统计分布参数的方法.本文根据不完全Γ函数在无限区间积分,推导了P-Ⅲ分布参数的S函数的计算公式.通过现有计算公式比较,其计算结果具有较高的计算精度,避免了的大量的数值积分计算.文中公式只要借助于计算编程进行求解,给定超几何函数项一定的截断误差,其运算具有较高的运行速度.文中计算公式是一种P-Ⅲ分布参数S函数的计算途径.     

The linearisation of three dimensional drag force in random seas with current

A frame invariant linearisation method for three-dimensional drag force in random seas with current is presented. Numerical results are compared with those obtained from a commonly used linearisation method which is based on a non-frame invariant approximation to the drag force. Significant differences are discovered and the present method is found to show closer agreement with computed time histories of the true drag force.