Geology topics

B. Amadei

Publications and source records attributed to B. Amadei.

6 recordsLinked to original sources

USGS2001

An analytical solution for transient flow of Bingham viscoplastic materials in rock fractures

We present below an analytical solution to model the one-dimensional transient flow of a Bingham viscoplastic material in a fracture with parallel walls (smooth or rough) that is subjected to an applied pressure gradient. The solution models the acceleration and the deceleration of the material as the pressure gradient changes with time. Two cases are considered: A pressure gradient applied over a finite time interval and an applied pressure gradient that is constant over time. The solution is expressed in dimensionless form and can therefore be used for a wide range of Bingham viscoplastic materials. The solution is also capable of capturing the transition that takes place in a fracture between viscoplastic flow and rigid plug flow. Also, it shows the development of a rigid central layer in fractures, the extent of which depends on the fluid properties (viscosity and yield stress), the magnitude of the pressure gradient, and the fracture aperture and surface roughness. Finally, it is shown that when a pressure gradient is applied and kept constant, the solution for the fracture flow rate converges over time to a steady-state solution that can be defined as a modified cubic law. In this case, the fracture transmissivity is found to be a non-linear function of the head gradient. This solution provides a tool for a better understanding of the flow of Bingham materials in rock fractures, interfaces, and cracks. ?? 2001 Elsevier Science Ltd. All rights reserved.

International Journal of Rock Mechanics and Mining↗

USGS1994

Gravitational stresses in long symmetric ridges and valleys in anisotropic rock

The effect of topography and rock mass anisotropy on gravitational stresses in long isolated symmetric ridges and valleys is modeled using an analytical method proposed earlier by the first two authors. The rock mass deforms under a condition of plane strain. A parametric study is presented on the effect of (1) topography, (2) orientation of anisotropy and (3) degree of anisotropy on the magnitude and distribution of gravitational stresses in transversely isotropic rock masses with planes of anisotropy striking parallel to the ridge or valley axis. It is found that compressive stresses develop near ridge crests and that tensile stresses develop in valley bottoms and valley walls. The magnitude of the gravitational stresses is of the order of the characteristics stress ??{variant}g??b?? where ??{variant} is the rock density, g is the gravitational acceleration and ??b?? is the height of the ridge or depth of the valley. ?? 1994.

International Journal of Rock Mechanics and Mining↗

USGS1992

On the state of stress in the near-surface of the earth's crust

Five models for near-surface crustal stresses induced by gravity and horizontal deformation and the influence of rock property contrasts, rock strength, and stress relaxation on these stresses are presented. Three of the models-the lateral constraint model, the model for crustal stresses caused by horizontal deformation, and the model for the effects of anisotropy-are linearly elastic. The other two models assume that crustal rocks are brittle or viscoelastic in order to account for the effects of rock strength and time on near-surface stresses. It is shown that the lateral constraint model is simply a special case of the combined gravity-and deformation-induced stress field when horizontal strains vanish and that the inclusion of the effect of rock anisotropy in the solution for crustal stresses caused by gravity and horizontal deformation broadens the range for predicted stresses. It is also shown that when stress levels in the crust reach the limits of brittle rock strength, these stresses become independent of strain rates and that stress relaxation in ductile crustal rocks subject to constant horizontal strain rates causes horizontal stresses to become independent of time in the long term. ?? 1992 Birkha??user Verlag.

Pure and Applied Geophysics PAGEOPH↗

USGS1991

Analysis of borehole expansion and gallery tests in anisotropic rock masses

Closed-form solutions are used to show how rock anisotropy affects the variation of the modulus of deformation around the walls of a hole in which expansion tests are conducted. These tests include dilatometer and NX-jack tests in boreholes and gallery tests in tunnels. The effects of rock anisotropy on the modulus of deformation are shown for transversely isotropic and regularly jointed rock masses with planes of transverse isotropy or joint planes parallel or normal to the hole longitudinal axis for plane strain or plane stress condition. The closed-form solutions can also be used when determining the elastic properties of anisotropic rock masses (intact or regularly jointed) in situ. ?? 1991.

International Journal of Rock Mechanics and Mining↗

USGS1988

Gravity-induced stresses in stratified rock masses

This paper presents closed-form solutions for the stress field induced by gravity in anisotropic and stratified rock masses. These rocks are assumed to be laterally restrained. The rock mass consists of finite mechanical units, each unit being modeled as a homogeneous, transversely isotropic or isotropic linearly elastic material. The following results are found. The nature of the gravity induced stress field in a stratified rock mass depends on the elastic properties of each rock unit and how these properties vary with depth. It is thermodynamically admissible for the induced horizontal stress component in a given stratified rock mass to exceed the vertical stress component in certain units and to be smaller in other units; this is not possible for the classical unstratified isotropic solution. Examples are presented to explore the nature of the gravity induced stress field in stratified rock masses. It is found that a decrease in rock mass anisotropy and a stiffening of rock masses with depth can generate stress distributions comparable to empirical hyperbolic distributions previously proposed in the literature. ?? 1988 Springer-Verlag.

Rock Mechanics and Rock Engineering↗

USGS1987

Gravitational stresses in anisotropic rock masses

This paper presents closed-form solutions for the stress field induced by gravity in anisotropic rock masses. These rocks are assumed to be laterally restrained and are modelled as a homogeneous, orthotropic or transversely isotropic, linearly elastic material. The analysis, constrained by the thermodynamic requirement that strain energy be positive definite, gives the following important result: inclusion of anisotropy broadens the range of permissible values of gravity-induced horizontal stresses. In fact, for some ranges of anisotropic rock properties, it is thermodynamically admissible for gravity-induced horizontal stresses to exceed the vertical stress component; this is not possible for the classical isotropic solution. Specific examples are presented to explore the nature of the gravity-induced stress field in anisotropic rocks and its dependence on the type, degree and orientation of anisotropy with respect to the horizontal ground surface. ?? 1987.

International Journal of Rock Mechanics and Mining↗