Physical properties of a horizon of a white hole and a Kruskal wormhole

The possible application of a Rindler type reference frame for studies of physical processes near the horizons of black and white holes is considered. New similar reference frames inside black and white holes in the region T of a Kruskal wormhole are introduced.     

Gamma-ray bursts as a result of the interaction of a shock from a supernova and a neutron-star companion

A supernova explosion in a close binary system in which one of the components is a compact magnetized object (neutron star or white dwarf) can form a narrow “tail” with length l _t ～10⁹ cm, width h _t ～10⁸ cm, and magnetic field B _t ～10⁶, due to the resulting shock wave flowing around the magnetosphere of the compact object. The energy released by the reconnection of magnetic field lines in this tail can accelerate electrons to relativistic speeds (γ≈10⁴), creating the conditions required for powerful synchrotron radiation at energies from hundreds of keV to several MeV, i.e., for a gamma-ray burst (GRB). The duration of this radiation will depend on the power of the shock that forms during the supernova. If the shock is not sufficiently powerful to tear off the magnetosphere tail from the compact object, the duration of the GRB will not exceed l _t /V _A ≤1 s, and the conditions necessary for an “afterglow” at softer energies will not arise. If the shock is more powerful, the tail can be torn from the magnetosphere, forming a narrow ejection, which is perceived in its relativistic motion toward the observer(Γ～10⁴) as an afterglow whose duration grows from tens of seconds at gamma-ray energies to tens of days in the optical. This may explain why afterglows are observed only in association with long GRBs (T ₉₀>10 s). Very short GRBs (T ₉₀<0.1 s) may be local, i.e., low-power, phenomena occurring in close pairs containing compact, magnetized objects, in which there is again an interaction between the magnetosphere of the compact object and a shock wave, but the shock is initiated by a flare on the companion, which is a red-dwarf cataclysmic variable, rather than by a supernova.     

Coupled consolidation of a porous medium with a cylindrical or a spherical cavity

This paper presents a theoretical approach to analyse coupled, linear thermoporoelastic fields in a saturated porous medium under radial and spherical symmetry. The governing equations account for compressibility and thermal expansion of constituents, heat sink due to thermal dilatation of water and thermal expansion of the medium, and thermodynamically coupled heat–water flow. It has been reported in the literature that thermodynamically coupled heat–water flows known as thermo-osmosis and thermal filtration have the potential to significantly alter the flow fields in clay-rich barriers in the near field of a underground waste containment scheme. This study presents a mathematical model and examines the effects of thermo-osmosis and thermal-filtration on coupled consolidation fields in a porous medium with a cavity. Analytical solutions of the governing equations are presented in the Laplace transform space. A numerical inversion scheme is used to obtain the time-domain solutions for a cylindrical cavity in a homogeneous or a non-homogeneous medium. A closed form time-domain solution is presented for a spherical cavity in a homogeneous medium. Selected numerical solutions for homogeneous and non-homogeneous media show a significant increase in pore pressure and displacements due to the presence of thermodynamically coupled flows and a negligible influence on temperature. © 1998 John Wiley & Sons, Ltd.     

Propagation of a shear crack in a compressed plane with a circular hole

The problem of the equilibrium of a plane with a circular hole and a shear crack is considered to model failure of an excavation (borehole or circular opening) in rocks weakened by discontinuities (planes of weakness). It is assumed that sliding occurs in a part of the plane of weakness when the Mohr–Coulomb friction criterion is satisfied due to the stress redistribution caused by the excavation. The method of singular integral equations is employed to solve the boundary value problem. Geomechanical problems concerning borehole breakout and rockburst caused by fault-opening interaction are discussed. © 1998 John Wiley & Sons, Ltd.     

Spreading of a NAPL lens in a double-porosity medium

Spreading of a non-aqueous phase liquid (NAPL) denser than water (DNAPL) lens (mound) in the unsaturated zone of double-porosity aquifer above an impervious plane boundary is investigated. The double-porosity aquifer is conceptualized as a fracture network surrounding pervious blocks. Vertical gravity equilibrium is assumed to prevail in each one of the two media, fractures and blocks. Through vertical integration, two coupled partial differential equations for the DNAPL content in each medium are obtained. The mass exchange rate between high- and low-permeability media is considered as a function of NAPL content. The dominant effect is gravity, whereas capillary forces are negligible. Analytical solutions for one-dimensional and axisymmetric problems of mound spreading are obtained.     

Phase space of a two-dimensional model of a Parker dynamo

The dependences of the magnetic-field strength, variations of the magnetic field, and the multipole level on the amplitudes of the α and ω effects are considered using a two-dimensional model for a Parker dynamo in a spherical layer. Calculations have been carried out for both traditional spatial distributions of α and ω and geostrophic regimes obtained from three-dimensional modeling of thermal convection. Two-dimensional distributions of the dynamo-wave velocities in the zone where magnetic field is generated are presented. Comparisons with the solar and planetary dynamos are considered.     

Locating a point on a spherical surface relative to a spherical polygon of arbitrary shape

An algorithm for determining if any given point,P, on the surface of a sphere is located inside, outside, or along the border of an arbitrary spherical polygon,S, is described. The polygon is described by specifying coordinates of its vertices, and coordinates of some pointX which is known to lie withinS. The algorithm is based on the principle that an arc joiningX andP will cross the border ofS an odd number of times ifP lies outsideS, and an even number of times ifP lies withinS. The algorithm has been implemented as a set of FORTRAN subroutines, and a listing is provided. The algorithm and subroutine package can be used with spherical polygons containing holes, or with composited spherical polygons.     

Scattering of a plane wave by a lined cylindrical cavity in a poroelastic half-plane

The focus of this contribution is to develop a complex variable function method to solve the two-dimensional scattering of plane waves by a lined cylindrical cavity in the poroelastic half-plane. The poroelastic half-plane is based on Biot’s dynamic theory, and the governing equations are solved by reduction to three Helmholtz equations. The lining structure can be treated as an elastic material and decoupled into two Helmholtz equations. Here, the large circle assumption is applied to simulate the half-plane boundary. By using appropriate boundary conditions and continuity conditions, the unknown coefficients in the potentials can be determined. Selected numerical results are presented in this paper.     

Bearing capacity of a strip foundation on a sand layer overlying a smooth rigid stratum

The effect of a smooth rigid stratum, located beneath a dense sand layer, on the bearing capacity and settlement of surface and shallow strip footings is investigated using an advanced experimental model. A theoretical analysis is presented for the bearing capacity of surface footings. The results indicate that the bearing capacity reaches a minimum value at a specific sand-layer thickness. Any increase in the layer thickness above this value causes an increase in the bearing capacity up to that corresponding to a continuous media.Notation H= thickness of the sand layer - B= foundation width - N _q and N = bearing capacity factors for a semi-infinite layer - N _qs and N _s= bearing capacity factors for a finite layer - H _o /B= limiting depth - D _r= relative density - = angle of soil internal friction - M= model width - D= depth of surcharge - q= bearing stress, pressure applied on the footing - q _u= bearing capacity - = unit weight of sand     

Toward a definition of a mineral sample in geology

Summary Any rock may be regarded as an aggregate of mineral species frequency distributions, thus opening up a new method of analyzing the problems of the nature of these discrete distributions.Based on theorems in mathematical probability, a subrock sample is defined as a probability sample under the conditions that every mineral species' distribution function in this subrock converges probabilistically to one and the same distributions the nature of which is immaterial at this point.For obvious reasons, the situation is excluded if the sample size approaches infinity, i.e., Chebyshev's theorem (Chebyshev, 1867).     

Strain analysis of a shear zone in a granodiorite

A ductile shear zone in a late Precambrian granodiorite, from the Rouergue (southwest part of the French Massif Central) has been studied.A single episode of deformation is responsible for the formation of a foliation and a well-defined lineation which are localized into an elongated zone, a few decimeters wide.The strain features can be attributed to a simple-shear mechanism (Ramsay and Graham, 1970), so that the main parameters of the deformation are defined.At stages of increasing deformation, the quartz isotropic sub-fabric of the undeformed host rock is progressively transformed into an anisotropic fabric composed of a single oblique girdle while the subgrain size progressively decrease and the dislocation density remains constant. It is suggested that the gliding planes of quartz are the basal plane (0001) and a predominant prismatic plane 101&#x0304;0 the slip directions may be a for both glide-planes.The results obtained in this investigation provide a basis for a high voltage electron microscope (H.V.E.M.) study which shows that the fabrics development may be related to dislocation processes. The difference of strain rates in the host rock and in the shear zone is calculated from the dislocation microstructures.     

TEM investigation of a microcline from a nepheline syenite

Chess-board (“tiled”) microcline crystals from a nepheline-bearing syenite from Ilimaussaq, W. Greenland, were investigated using transmission electron microscopy (TEM) and were found to consist of a mosaic of slightly misoriented domains, which bear no obvious relationship to the optical microstructure. Part of the misorientation of most pairs of neighbouring domains involves a small rotation about c. However, some are related to adjacent domains by the albite twin law, the pericline law, or diagonal association. This microcline could have crystallized with triclinic symmetry which could account for the differences between the microstructure of this microcline and M-twinned microcline. Metasomatism may explain both the optical microscope and TEM scale structures of this microcline. Examination of the electron diffraction patterns of areas of microcline which contain both diagonally associated and twinned domains draw attention to the fact that each of the few orientations in an M-twinned crystal is related to one of the other orientations by diagonal association. The formation of common cross-hatch twinned microstructures are discussed with reference to diagonal association.     

On a nonlinear hybrid method for multiscale analysis of a bearing-capacity test of a real-scale segmental tunnel ring

A nonlinear hybrid method is developed for multiscale analysis of a bearing-capacity test of a real-scale segmental tunnel ring subjected to point loads. The structural analysis consists of two parts. Part I refers to modeling of bending-induced tensile cracking of the segments, resulting from the external loading. The segments are subdivided into elements, according to the crack spacing. Each element is either intact or contains one central crack band, flanked by lateral undamaged domains. A multiscale model for tensile softening of concrete is used to describe the progressive deterioration of the crack bands. After iterative determination of their state of damage, the effective bending and extensional stiffnesses of the corresponding elements are quantified by means of Voigt-Reuss-Hill estimates. The effective stiffnesses are used for linear-elastic simulations of the segmental tunnel ring. Part II refers to the relative rotation angles at the joints, which are estimated from monitoring data, using the Bernoulli-Euler hypothesis. Since the validity of this hypothesis is questionable for neck-like joints, the relative rotation angles are post-processed such that they refer to rigid body displacements of the segments. The following conclusions are drawn: The presented approach yields good estimates of crack widths. Relative rotation angles at the joints mainly result in rigid body displacements of the segments, governing the convergences. Because realistic interface models are lacking, hybrid analysis based on displacement-monitoring data allows for performing ultimate-load analysis of segmental tunnel rings.     

承压含水层非完整反滤回灌井的稳定流计算

反滤回灌井是地下水库中一种有效的回灌设施,它由回灌井和井口反滤层组成。非完整反滤回灌井井流运动由砂反滤层的竖向流和非完整回灌井井流组合而成。文中提出了承压含水层非完整反滤回灌井稳定流的计算方法,分析了反滤层、井损和回灌堵塞等因素对回灌量的影响,并结合实例证明了反滤回灌井回灌量大大低于普通回灌井的回灌量。     

Response of a tunnel deeply embedded in a viscoelastic medium

This paper presents a three‐dimensional energy‐based solution for the time‐dependent response of a deeply embedded and unsupported semi‐infinite tunnel of circular cross‐section. The tunnel is taken to be excavated quasi‐instantaneously from an infinite rock body that initially exhibits an isotropic stress state and that is made up of a homogeneous, isotropic and viscoelastic material. The viscoelastic behaviour is modelled by means of Burger's model, and the rock is taken to behave volumetrically linear elastic and to exhibit exclusively deviatoric creep. This viscoelastic problem is transformed into the Laplace domain, where it represents a quasi‐elastic problem. The displacement fields in the new solution are taken to be the products of independent functions that vary in the radial and longitudinal directions. The differential equations governing the displacements of the system and appropriate boundary conditions are obtained using the principle of minimum potential energy. The solutions for these governing equations in the Laplace domain are then obtained analytically and numerically using a one‐dimensional finite difference technique. The results are then transformed back into the time domain using an efficient numerical scheme. The accuracy of the new solution is comparable with that of a finite element analysis but requires much less computation effort. Copyright © 2011 John Wiley & Sons, Ltd.     

双层地基水平受荷桩受力变形分析

基于双层地基中的水平受荷桩的特性,对其受力变形进行了分析。将水平受荷桩视为竖直放置的弹性地基梁,基于Winkler弹性地基梁理论,考虑桩土共同工作得到水平受荷桩位移控制微分方程及其幂级数解答,进而根据内力与位移的连续条件得到了由桩顶受力及变形条件表示任一深度处桩身的水平位移、转角、弯矩及剪力的计算矩阵表达式。通过一具体算例将幂级数解计算结果与《公路桥涵地基与基础设计规范》推荐的简化计算公式计算结果进行了比较。结果表明：当第1层地基土的厚度在某一定值时,《规范》简化计算方法所得结果与幂级数解接近;但当层厚不在该值附近时,两个方法计算结果存在差异。     

Finite element analysis of a centrifuge model of a retaining wall embedded in a heavily overconsolidated clay

The current study is aimed at the behaviour right upto collapse of a retaining wall embedded in overconsolidated clay. It is found that the excess pore pressures generated due to the excavation are fairly well simulated. The rupture lines on the passive side in the centrifuge model test were closely matched by two lines along which the stress state was reaching the critical state in the analysis. The displacements on the active side were not well matched especially the vertical settlements near to the wall. The bending moments were significantly overpredicted. The prop force due to excavation was also overpredicted. This is to be expected because the prop was modelled as rigid in the analysis.     

Numerical Study of a Failure of a Reinforced Earth Retaining Wall

The case history of a failure of a RE wall has been presented. The wall failed immediately upon completion due to the overestimation of the strengths of the foundation clay layers and due to the underestimation of the self weight of the fill materials. A typical cross-section of the wall along with the stabilizing embankment and the foundation are modeled numerically by the limit equilibrium method and by a finite element method. The strengths of the foundation soils are determined by field tests done after the failure of the wall. Both the analyses predicted failure of the wall. The deformations predicted by the finite element method are found to be comparable to the observed field data. The numerical analyses further indicate that by consolidating a foundation clay layer to a minimum undrained strength of 45 kPa, the required factor of safety for the wall along with the road embankment can be achieved theoretically. Accordingly, prefabricated vertical drains are used to expedite the drainage and consolidation of the foundation clay layers. After the field tests confirm that the required minimum undrained strength is achieved, the RE wall and the embankment have been rebuilt successfully and now in full operation.     

Validity of a sharp-interface model in a confined coastal aquifer

 The problem of seawater intrusion is considered for the case of a confined coastal aquifer in which there is steady seaward flow of fresh water. Using the GWCH2O model, the problem is solved first for the case of no dispersion where a distinct interface exists separating the fresh water from the salt water. The problem is solved next by taking into account dispersion and diffusion of the salt-water component, along with the density effect. In this respect, a two-dimensional finite-element model, 2D-VDTRAN, is developed to simulate density-dependent solute transport. To investigate the limitation of the sharp-interface approach in coastal aquifers for conditions of both steady state and unsteady state, the problem is solved twice using the two models with different parameter values. These parameters are combined in dimensionless form, resulting in four named parameters: seepage factor (A); dispersion-to-advection ratio (B); geometry ratio (C); and time-scale factor (T). Using the density-dependent model, the dimensionless width of the transition zone (W/L) is determined for different values of A, B, C, and T. Steady-state simulations show that the sharp-interface approach is valid only when the system is dominated by advection, i.e., when 0<B≤5% for all values of A and C, or when A≥65% for all values of B and C. However, the unsteady-state analysis shows that the applicability of the sharp-interface approach is sufficiently accurate at early times. Received, October 1997 Revised, June 1998, October 1998 Accepted, November 1998