Extension of the Griffith's fracture criteria to saturated clays

Inglis [1] has solved the problem of distribution of stress in an elastic plate around an elliptical hole. His works clarify the role of cracks in the failure of an elastic material. However, his solution cannot be applied to saturated clay because he considers only total stresses, while, in saturated clay, the criterion of rupture should be expressed in terms of effective and not total stresses. The solution of Atkinson and Craster [2] using Biot's poroelasticity theory, shows that there is no high pore pressure in the vicinity of the crack tips for saturated clay. The major difference between this approach and the Biot's theory of is that, in saturated clay, strain is a function of the variation of the effective stress [3], while, in poroelastic media, strain is only a function of the variation of the total stress [4, Equation 2.2]. Also in their solution there is continuity between the pore fluid and the inner fluid in the crack. Their solution is valid for poroelastic media involving a movement of the pore fluid. In our solution there is no movement of the pore fluid (Undrained condition). In this paper we have solved the same problem as Inglis [1], but for the particular case of saturated clay obeying elastic law. By solving this problem we obtained the expressions for pore pressure, effective stress, total stress and displacements. The results show that not only the total stress but also the pore pressure and the effective stress are also high in the vicinity of the crack tips. A new failure criterion, based on Griffith's strain energy principle [5] and maximum tensile stress [6], valid for saturated clay is developed in this paper. Copyright © 2003 John Wiley & Sons, Ltd.     

Displacement‐controlled method and its applications to material non‐linearity

For the analysis of non‐linear problems, the displacement‐controlled method (DCM) has a more extensive application scope and more powerful abilities than the load‐controlled method (LCM). However, difficulties of the DCM's procedure not amenable to most finite element implementations of the conventional LCM have restricted its applications in geomechanics. By means of Sherman–Morrison's theorem, the solution of DCM is improved. The improved procedure is characterized by high efficiency, good numerical stability and a programme structure similar to LCM. Two aspects of applications of DCM are illustrated. The first application is to compute the response of a structure under a given load level like the conventional finite element analysis. The second application is to trace the equilibrium path of a structure under a given load distribution type. A simple but effective algorithm is presented for automatically adjusting the step length in tracing the equilibrium path. Examples illustrate that the proposed procedures are suited for modelling complicated non‐linear problems in geomechanics. Copyright © 2005 John Wiley & Sons, Ltd.     

The role of non-thermal electrons in the hydrogen and calcium lines of stellar flares

There is observational evidence showing that stellar and solar flares occur with a similar circumstance, although the former are usually much more energetic. It is expected that the bombardment by high-energy electrons is one of the chief heating processes of the flaring atmosphere. In this paper we study how a precipitating electron beam can influence the line profiles of Ly α , H α , Ca  ii K and λ 8542. We use a model atmosphere of a dMe star and make non-LTE computations taking into account the non-thermal collisional rates owing to the electron beam. The results show that the four lines can be enhanced to different extents. The relative enhancement increases with increasing formation height of the lines. Varying the energy flux of the electron beam has different effects on the four lines. The wings of Ly α and H α become increasingly broad with the beam flux; change of the Ca  ii K and λ 8542 lines, however, is most significant in the line centre. Varying the electron energy (i.e. the low-energy cut-off for a power-law beam) has a great influence on the Ly α line, but little on the H α and Ca  ii lines. An electron beam of higher energy precipitates deeper, thus producing less enhancement of the Ly α line. The Ly α /H α flux ratio is thus sensitive to the electron energy.     

Effect of property variation and modelling on convection in a fluid overlying a porous layer

An accurate computational analysis is presented for the onset of thermal convection in a two‐layer system which is comprised of a saturated layer of porous material described by Darcy's law, over which lies a layer of the same saturating fluid. The two‐layer system is heated from below and the upper (fluid) surface is allowed to be fixed or stress free. The onset of convection may have a bi‐modal nature in which convection may be dominated by the porous medium or by the fluid depending on the depths of the relative layers, but this is strongly controlled by material parameters. The effect of variation of relevant fluid and porous material properties is investigated in detail, as is the effect of the interface boundary condition between the fluid and the porous medium. Copyright © 2001 John Wiley & Sons, Ltd.     

A two-zone model for the broad iron line emission in MCG–6-30-15

We reanalyse the ASCA and BeppoSAX data of MCG–6-30-15, using a double-zone model for the iron line profile. In this model, the X-ray source is located around ≈10 Schwarzschild radii and the regions interior and exterior to the X-ray source produce the line emission. We find that this model fits the data with a similar reduced χ ² to the standard single-zone model. Thus we show that the presence of a broad iron line feature does not necessarily require that the X-ray source be located close to the last stable orbit or in the disc rotation axis.
Within the framework of this model, the best-fitting inclination angle of the source     for the intermediate-intensity ASCA data set is compatible with that determined by earlier modelling of optical lines. The observed variability of the line profile with intensity can be explained as variations of the X-ray source size. That several active galactic nuclei with broad lines have the peak centroid near 6.4 keV can be explained under certain conditions.
We also show that the simultaneous broad-band observations of this source by BeppoSAX rule out the Comptonization model which was an alternative to the standard inner-disc one. We thereby strengthen the case that line broadening occurs as a result of the strong gravitational influence of a black hole.     

An iterative technique for solving equations of statistical equilibrium

Superlevel partitioning is combined with a simple relaxation procedure to construct an iterative technique for solving equations of statistical equilibrium. In treating an N -level model atom, the technique avoids the N ³ scaling in computer time for direct solutions with standard linear equation routines and also does not fail at large N due to the accumulation of round-off errors. As a consequence, the technique allows detailed model atoms with N ≳10³ , such as those required for iron peak elements, to be incorporated into diagnostic codes for analysing astronomical spectra. Tests are reported for a 394-level Fe  ii ion and a 1266-level Ni  i – iv atom.