Nonlinear evolution of a layered stratified shear flow

We investigate numerically and theoretically the nonlinear evolution of a parallel shear flow at moderate Reynolds number which has embedded within it a mixed layer of intermediate fluid. The two relatively thin strongly stratified density interfaces are centered on the edges of the shear layer. We are particularly interested in the development of primary and secondary instabilities. We present the results of a stability analysis which predicts that such flows may be unstable to stationary vortical disturbances which are a generalization of an inviscid instability first considered by G.I. Taylor. We investigate the behavior of these “Taylor billows” at finite amplitude through two-dimensional numerical simulations. We observe that the braid regions connecting adjacent primary Taylor billows are susceptible to secondary, inherently two-dimensional instabilities. We verify that these secondary instabilities, which take the form of small elliptical vortices, arise due to a local intensification of the spanwise vorticity in the braid region.     

Scattering of SH-wave by multiple circular cavities in half space

In this paper, an analytic method is developed to address steady SH-wave scattering and perform dynamic analysis of multiple circular cavities in half space. The scattered wave function used for scattering of SH-waves by multiple circular cavities, which automatically satisfies the stress-free condition at the horizontal surface, is constructed by applying the symmetry of the SH-wave scattering and the method of multi-polar coordinates system. Applying this scattered wave function and method of moving coordinates, the original problem can be transformed to the problem of SH-wave scattering by multiple circular cavities in the full space. Finally, the solution of the problem can be reduced to a series of algebraic equations and solved numerically by truncating the infinite algebraic equations to the finite ones. Numerical examples are provided for case with two cavities to show the effect of wave number, and the distances between the centers of the cavities and from the centers to the ground surface on the dynamic stress concentration around the cavity impacted by incident steady SH-wave.     

Reflection of<Emphasis Type="Italic">P</Emphasis> and<Emphasis Type="Italic">SV</Emphasis> waves at the free surface of a monoclinic elastic half-space

The propagation of plane waves in an anisotropic elastic medium possessing monoclinic symmetry is discussed. The expressions for the phase velocity ofqP andqSV waves propagating in the plane of elastic symmetry are obtained in terms of the direction cosines of the propagation vector. It is shown that, in general,qP waves are not longitudinal andqSV waves are not transverse. Pure longitudinal and pure transverse waves can propagate only in certain specific directions. Closed-form expressions for the reflection coefficients ofqP andqSV waves incident at the free surface of a homogeneous monoclinic elastic half-space are obtained. These expressions are used for studying numerically the variation of the reflection coefficients with the angle of incidence. The present analysis corrects some fundamental errors appearing in recent papers on the subject.     

Ultimate collapse of cross-jointed,thinly bedded,horizontal roof strata

Summary Small scale physical model studies of the collapse of mine roofs excavated in horizontally bedded strata containing uniformly spaced, rough, vertical cross-joints revealed a new type of failure mechanism, of which the classic Voussoir arch is shown to be a special case. The mechanism involves vertical displacement of a central section about two peripheral hinges. Hence, the author has called it the 2-hinge collapse mechanism.A numerical model of the mechanism was developed, which allows for progressive rock failure at the hinge points and for external loadings across the roof span. Results from this analysis show that the collapse mechanism is very sensitive to bed thickness and rock strength. Failure by this mode is more likely to develop in weak, thinly laminated beds with low horizontal stresses.It is deduced from this investigation that, in a geological environment where this type of failure is likely, bolts installed close to the sides (ribs) of openings should have high shear stiffness, for example full column, resin bolts. Bolts in the central region, where vertical movement predominates, need adequate pull-out resistance and, if some corrosion protection is necessary, may be grouted with a less expensive cement or plaster-based grout.     

计算分层介质中位错点源静态位移场的广义反射、透射系数矩阵和离散波数方法

本文将计算合成地震图的广义反射、透射系数矩阵和离散波数方法应用于静态问题,给出了分层介质中位错点源产生的静态位移场的计算方法。该方法保留了反射、透射矩阵方法的原有优点,通过将数值结果与解析解的对比表明,该方法具有较高的数值精度,可用于研究地震断层活动造成的地表形变。     

Estimation of Elastic Moduli in a Compressible Gibson Half-space by Inverting Rayleigh-wave Phase Velocity

A Gibson half-space model (a non-layered Earth model) has the shear modulus varying linearly with depth in an inhomogeneous elastic half-space. In a half-space of sedimentary granular soil under a geostatic state of initial stress, the density and the Poisson’s ratio do not vary considerably with depth. In such an Earth body, the dynamic shear modulus is the parameter that mainly affects the dispersion of propagating waves. We have estimated shear-wave velocities in the compressible Gibson half-space by inverting Rayleigh-wave phase velocities. An analytical dispersion law of Rayleigh-type waves in a compressible Gibson half-space is given in an algebraic form, which makes our inversion process extremely simple and fast. The convergence of the weighted damping solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method. Calculation efficiency is achieved by reconstructing a weighted damping solution using singular value decomposition techniques. The main advantage of this algorithm is that only three parameters define the compressible Gibson half-space model. Theoretically, to determine the model by the inversion, only three Rayleigh-wave phase velocities at different frequencies are required. This is useful in practice where Rayleigh-wave energy is only developed in a limited frequency range or at certain frequencies as data acquired at manmade structures such as dams and levees. Two real examples are presented and verified by borehole S-wave velocity measurements. The results of these real examples are also compared with the results of the layered-Earth model.     

Quasi-static deformation of a poroelastic half-space with anisotropic permeability by two-dimensional surface loads

An analytical solution is obtained of the fully coupled diffusion–deformation system of equations governing the quasi-static plane strain deformation of a poroelastic half-space with anisotropic permeability and compressible constituents. The stresses and the pore pressure are taken as the basic state variables. Displacements are obtained by integrating the coupled constitutive relations. The problem of surface loads is discussed in detail. Explicit analytical solutions are derived for normal line loading, shear line loading and normal strip loading. The permeability anisotropy is found to have a significant effect on the quasi-static deformation of the half-space. However, in the drained and undrained limits, the anisotropy has no effect. The stresses in the drained and undrained states are independent of the poroelastic parameters. Numerical computation of the pore pressure indicates that ignoring permeability anisotropy may lead to an overestimation of the pore pressure at points vertically below the point of normal loading. Further, anisotropy in permeability may lead to a dilution in the theoretical prediction of the Mandel–Cryer Effect.     

淤砂层模拟方法对上层理想流体动力反应的影响——平面P波入射

采用解析法,以弹性半空间-淤砂层-理想流体层为对象,分别将淤砂层模拟为固体介质和流体介质,分析了平面P波入射时上层理想流体的动力反应特性。通过算例分析,比较了将淤砂层模拟为弹性固体、黏弹性固体、理想流体和黏性流体介质时与将淤砂层模拟为两相多孔介质时计算结果的差异。研究表明当渗透系数很小时,多孔介质可以近似简化为黏弹性固体,甚至线弹性固体。这一分析研究对于在高坝-库水-淤砂-地基系统地震反应分析的数值模型中采用合理的淤砂层模型,提高计算效率具有重要参考意义,而且还可以用于校核数值模型的合理性。