Self‐similar solution of a plane‐strain fracture driven by a power‐law fluid     

J. I. Adachi  E. Detournay 《国际地质力学数值与分析法杂志》2002,26(6):579-604

This paper analyses the problem of a hydraulically driven fracture, propagating in an impermeable, linear elastic medium. The fracture is driven by injection of an incompressible, viscous fluid with power‐law rheology and behaviour index n?0. The opening of the fracture and the internal fluid pressure are related through the elastic singular integral equation, and the flow of fluid inside the crack is modelled using the lubrication theory. Under the additional assumptions of negligible toughness and no lag between the fluid front and the crack tip, the problem is reduced to self‐similar form. A solution that describes the crack length evolution, the fracture opening, the net fluid pressure and the fluid flow rate inside the crack is presented. This self‐similar solution is obtained by expanding the fracture opening in a series of Gegenbauer polynomials, with the series coefficients calculated using a numerical minimization procedure. The influence of the fluid index n in the crack propagation is also analysed. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

Explicit solutions for the instantaneous undrained contraction of hollow cylinders and spheres in porous elastoplastic medium     

A. Giraud  F. Homand  V. Labiouse 《国际地质力学数值与分析法杂志》2002,26(3):231-258

In this article we present closed‐form solutions for the undrained variations in stress, pore pressure, deformation and displacement inside hollow cylinders and hollow spheres subjected to uniform mechanical pressure instantaneously applied to their external and internal boundary surfaces. The material is assumed to be a saturated porous medium obeying a Mohr–Coulomb model failure criterion, exhibiting dilatant plastic deformation according to a non‐associated flow rule which accounts for isotropically strain hardening or softening. The instantaneous response of a porous medium submitted to an instantaneous loading is undrained, i.e. without any fluid mass exchange. The short‐term equilibrium problem to be solved is now formally identical to a problem of elastoplasticity where the constitutive equations involve the undrained elastic moduli and particular equivalent plastic parameters. The response of the model is presented (i) for extension and compression undrained triaxial tests, and (ii) for unloading problems of hollow cylinders and spheres through the use of appropriately developed closed‐form solutions. Numerical results are presented for a plastic clay stone with strain hardening and an argilite with strain softening. The effects of plastic dilation, of the strain softening law and also of geometry of the cavity on the behaviour of the porous medium have been underlined. Analytical solutions provide valuable benchmarks enabling various numerical methods in undrained conditions with a finite boundary to be verified. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

Kinematic wave solutions for pollutant transport over an infiltrating plane with finite‐period mixing and mixing zone     

V. P. Singh 《水文研究》2002,16(12):2441-2477

Kinematic wave solutions are derived for transport of a conservative non‐point‐source pollutant during a rainfall‐runoff event over an infiltrating plane for two cases: (i) finite‐period mixing and (ii) soil‐mixing zone. Rainfall is assumed to be steady, uniform and finite in duration, and it is assumed to have zero concentration of pollutants. Infiltration is assumed constant in time and space. Prior to the start of rainfall, the pollutant is distributed uniformly over the plane. In the first case, when rainfall occurs, the mixing of pollutant in the runoff water occurs in a finite period of time. In the second case, the chemical concentration is assumed to be a linearly decreasing function of rainfall intensity and overland flow. The solute concentration and discharge are found to depend on the flow characteristics as well as the solute concentration parameters. The characteristics of solute concentration and discharge graphs seem to be similar to those reported in the literature and observed in laboratory experiments. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

On Motions Near the Lagrange Equilibrium Point L 4 in the Case of Routh's Critical Mass Ratio     

Boris Bardin 《Celestial Mechanics and Dynamical Astronomy》2002,82(2):163-177

We deal with the planar restricted circular problem of three bodies. We study trajectories in a small neighborhood of the Lagrange equilibrium point L ₄ when mass ratio is close to Routh's value. In particular, we show that the case of proper degeneracy takes place and for most initial conditions trajectories are conditionally-periodic. We obtain an approximate representation of families of periodic solution emanating from the equilibrium point L ₄. We also show that in the case of instability of L ₄ the trajectories starting in a vicinity of L ₄ remain in a finite domain forever. We give an upper bound of this domain. To carry out our investigation, we analyze the dynamics of a general Hamiltonian system with two degrees of freedom in the case of 1 : 1 resonance in detail.This revised version was published online in October 2005 with corrections to the Cover Date.  相似文献   

A complex analytic solution for the attitude motion of a near-symmetric rigid body under body-fixed torques     

P. Tsiotras  J. M. Longuski 《Celestial Mechanics and Dynamical Astronomy》1991,51(3):281-301

Although analytic solutions for the attitude motion of a rigid body are available for several special cases, a comprehensive theory does not exist in the literature for the more complicated problems found in spacecraft dynamics. In the present paper, analytic solutions in complex form are derived for the attitude motion of a near-symmetric rigid body under the influence of constant body-fixed torques. The solution is very compact, which enables efficient and rapid machine computation. Numerical simulations reveal that the solution is very accurate when applied to typical spinning spacecraft problems.  相似文献   

An analytical assessment on the impact of covers on the onset of air convection in mine wastes     

Ning Lu 《国际地质力学数值与分析法杂志》2001,25(4):347-364

If a mine waste pile is left open, an active chemical reaction of oxidation is often found due to the commonly high content of pyritic materials. The oxidation of pyrites is an exothermic process and the released heat will promote the flow of fresh oxygen from the surrounding atmosphere into the waste dump. As a result, oxidation reaction will accelerate and temperature within the dump can increase to as high as 60°C above the ambient temperature. The oxidation process also releases sulphuric acid and hydrogen ions into ground water to cause water contamination. Low‐permeability covers such as clay liners have been recently proposed to abate the oxidation process in mine wastes. The effectiveness of using low‐permeability materials to cover mine wastes in order to suppress the pyrite oxidation is examined. By conducting the theoretical analysis of the onset of convective air flow within waste rocks, the conditions under which soil gas flow is significant are identified. By comparing the results with previous field measurements and theoretical analysis for the uncovered conditions, it is shown that low‐permeability covers can effectively suppress soil gas flow and slow down the pyrite oxidation process in mine wastes. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

一阶可变号非线性奇异初值问题     

杨光崇 《成都信息工程学院学报》2005,20(2):213-218

获得了一类一阶可变号非线性奇异初值问题的新结果。  相似文献   

用正行列式解瓶颈指派问题     

由雷  岳中亮 《广东海洋大学学报》2007,27(6):67-70

用正行列式作为工具，给出了瓶颈指派问题新的解法，并利用正行列式的值求出了瓶颈指派问题的全部最优解。最后通过一个实例说明该算法的实用和有效性。  相似文献   

用正行列式解瓶颈指派问题     

由雷  岳中亮 《广东海洋大学学报》2007,27(6):67-70

用正行列式作为工具,给出了瓶颈指派问题新的解法,并利用正行列式的值求出了瓶颈指派问题的全部最优解。最后通过一个实例说明该算法的实用和有效性。  相似文献   

On the Centre Manifold of Collinear Points in the Planar Three-Body Problem     

Regina Martínez  Anna Samà 《Celestial Mechanics and Dynamical Astronomy》2003,85(4):311-340

We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.  相似文献