Inclined plane

About: Inclined plane is a research topic. Over the lifetime, 2450 publications have been published within this topic receiving 27852 citations. The topic is also known as: ramp.

Role of fluid pressure in mechanics of overthrust faulting: I. Mechanics of fluid-filled porous solids and its application to overthrust faulting

Abstract: Promise of resolving the paradox of overthrust faulting arises from a consideration of the influence of the pressure of interstitial fluids upon the effective stresses in rocks. If, in a porous rock filled with a fluid at pressure p, the normal and shear components of total stress across any given plane are S and T, then are the corresponding components of the effective stress in the solid alone. According to the Mohr-Coulomb law, slippage along any internal plane in the rock should occur when the shear stress along that plane reaches the critical value where σ is the normal stress across the plane of slippage, τ 0 the shear strength of the material when σ is zero, and ϕ the angle of internal friction. However, once a fracture is started τ 0 is eliminated, and further slippage results when This can be further simplified by expressing p in terms of S by means of the equation which, when introduced into equation (4), gives From equations (4) and (6) it follows that, without changing the coefficient of friction tan ϕ , the critical value of the shearing stress can be made arbitrarily small simply by increasing the fluid pressure p. In a horizontal block the total weight per unit area S zz is jointly supported by the fluid pressure p and the residual solid stress σ zz ; as p is increased, σ zz is correspondingly diminished until, as p approaches the limit S zz , or λ approaches 1, σ zz approaches 0. For the case of gravitational sliding, on a subaerial slope of angle θ where T is the total shear stress, and S the total normal stress on the inclined plane. However, from equations (2) and (6) Then, equating the right-hand terms of equations (7) and (8), we obtain which indicates that the angle of slope θ down which the block will slide can be made to approach 0 as λ approaches 1, corresponding to the approach of the fluid pressure p to the total normal stress S . Hence, given sufficiently high fluid pressures, very much longer fault blocks could be pushed over a nearly horizontal surface, or blocks under their own weight could slide down very much gentler slopes than otherwise would be possible. That the requisite pressures actually do exist is attested by the increasing frequency with which pressures as great as 0.9 S zz are being observed in deep oil wells in various parts of the world.

The motion of a finite mass of granular material down a rough incline

Abstract: Rock, snow and ice masses are often dislodged on steep slopes of mountainous regions. The masses, which typically are in the form of innumerable discrete blocks or granules, initially accelerate down the slope until the angle of inclination of the bed approaches the horizontal and bed friction eventually brings them to rest. The present paper describes an initial investigation which considers the idealized problem of a finite mass of material released from rest on a rough inclined plane. The granular mass is treated as a frictional Coulomb-like continuum with a Coulomb-like basal friction law. Depth-averaged equations of motion are derived; they bear a superficial resemblance to the nonlinear shallow-water wave equations. Two similarity solutions are found for the motion. They both are of surprisingly simple analytical form and show a rather unanticipated behaviour. One has the form of a pile of granular material in the shape of a parabolic cap and the other has the form of an M-wave with vertical faces at the leading and trailing edges. The linear stability of the similarity solutions is studied. A restricted stability analysis, in which the spread is left unperturbed shows them to be stable, suggesting that mathematically both are possible asymptotic wave forms. Two numerical finite-difference schemes, one of Lagrangian, the other of Eulerian type, are presented. While the Eulerian technique is able to reproduce the M-wave similarity solution, it appears to give spurious results for more general initial conditions and the Lagrangian technique is best suited for the present problem. The numerical predictions are compared with laboratory experiments of Huber (1980) involving the motion of gravel released from rest on a rough inclined plane. Although in these experiments the continuum approximation breaks down at large times when the gravel layer is only a few particle diameters thick, the general features of the development of the gravel mass are well predicted by the numerical solutions.

Granular flow down an inclined plane: Bagnold scaling and rheology

Abstract: We have performed a systematic, large-scale simulation study of granular media in two and three dimensions, investigating the rheology of cohesionless granular particles in inclined plane geometries, i.e., chute flows. We find that over a wide range of parameter space of interaction coefficients and inclination angles, a steady-state flow regime exists in which the energy input from gravity balances that dissipated from friction and inelastic collisions. In this regime, the bulk packing fraction (away from the top free surface and the bottom plate boundary) remains constant as a function of depth z, of the pile. The velocity profile in the direction of flow vx(z) scales with height of the pile H, according to vx(z) proportional to H(alpha), with alpha=1.52+/-0.05. However, the behavior of the normal stresses indicates that existing simple theories of granular flow do not capture all of the features evidenced in the simulations.

Stability of Liquid Flow down an Inclined Plane

Abstract: The stability of a liquid layer flowing down an inclined plane is investigated. A new perturbation method is used to furnish information regarding stability of surface waves for three cases: the case of small wavenumbers, of small Reynolds numbers, and of large wavenumbers. The results for small wavenumbers agree with Benjamin's result obtained by the use of power series expansion, and the results for the two other cases are new. The results for large wavenumbers, zero surface tension, and vertical plate contradict the tentative assertion of Benjamin. The three cases are then re‐examined for shear‐wave stability, and the results compared with those for confined plane Poiseuille flow. The comparison serves to indicate the vestiges of shear waves in the free‐surface flow, and to give a sense of unity in the understanding of the stability of both flows. The case of large wavenumbers also serves as a new example of the dual role of viscosity in stability phenomena.The topological features of the ci curves for...