Stability of a Penny-Shaped Geothermal Reservoir in the Earth’s Crust

1982 ◽  
Vol 104 (2) ◽  
pp. 93-95 ◽  
Author(s):  
H. Abe´ ◽  
H. Sekine ◽  
S. Kitada
Keyword(s):  
Critical Pressure ◽  
Three Dimensional ◽  
Tectonic Stress ◽  
Theory Of Elasticity ◽  
Surrounding Rock ◽  
Geothermal Reservoir ◽  
Earth’S Crust ◽  
Dimensional Theory ◽  
Opening Mode ◽  
Earth's Crust

The theoretical analysis of a penny-shaped geothermal reservoir in the earth’s crust subject to linear tectonic stress gradients has been made on the basis of the three-dimensional theory of elasticity. The condition for stability of a reservoir requires K1 < Kc, where K1 and Kc are, respectively, the stress intensity factor for the opening mode and the fracture toughness of the surrounding rock. From this condition the upper critical pressure being necessary for the reservoir stability is obtained and is shown graphically.

Three-Dimensional Elasticity Solution of a Composite Beam

1967 ◽  
Vol 1 (2) ◽  
pp. 122-135 ◽  
Author(s):  
Staley F. Adams ◽  
M. Maiti ◽  
Richard E. Mark
Keyword(s):  
Three Dimensional ◽  
Solid Wood ◽  
Theory Of Elasticity ◽  
Orthotropic Materials ◽  
Stress And Strain ◽  
Cantilever Beams ◽  
Dimensional Theory ◽  
Reinforced Plastics ◽  
Three Dimensional Elasticity ◽  
Moduli Of Elasticity

This investigation was undertaken to develop a rigorous mathe matical solution of stress and strain for a composite pole con sisting of a reinforced plastics jacket laminated on a solid wood core. The wood and plastics are treated as orthotropic materials. The problem of bending of such poles as cantilever beams has been determined by the application of the principles of three- dimensional theory of elasticity. Values of all components of the stress tensor in cylindrical coordinates are given for the core and jacket. Exact values for the stresses have been obtained from computer results, using the basic elastic constants—Poisson's ratios, moduli of elasticity and moduli of rigidity—for each ma terial. A comparison of the numerical results of the exact solu tion with strength of materials solutions has been completed.

A Refined Theory of Elastic, Orthotropic Plates

1958 ◽  
Vol 25 (4) ◽  
pp. 437-443 ◽  
Author(s):  
S. J. Medwadowski
Keyword(s):  
Body Force ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Refined Theory ◽  
System Of Equations ◽  
Order Partial Differential Equation ◽  
Type Solution ◽  
Orthotropic Plates ◽  
Dimensional Theory ◽  
Nonlinear System Of Equations

Abstract A refined theory of elastic, orthotropic plates is presented. The theory includes the effect of transverse shear deformation and normal stress and may be considered a generalization of the classical theory of von Karman modified by the refinements of the Levy-Reissner-Mindlin theories. A nonlinear system of equations is derived directly from the corresponding equations of the three-dimensional theory of elasticity in which body-force terms have been retained. Next, the system of equations is linearized and reduced to a single sixth-order partial differential equation in a stress function. A Levy-type solution of this equation is discussed.

Metamorphic Rocks

2018 ◽  
Author(s):  
Alex Maltman
Keyword(s):  
Metamorphic Rock ◽  
Central Area ◽  
Tectonic Stress ◽  
Earth’S Crust ◽  
Metamorphic Rocks ◽  
Tectonic Plates ◽  
The Earth ◽  
Two Factors ◽  
Earth's Crust ◽  
Increased Pressure

We come now to the metamorphic rocks, the result of modifications to already existing rock. I’m well aware that this can all seem a bit mysterious. After all, no one has ever seen the changes take place; no one has ever witnessed a metamorphic rock form—the processes are imperceptibly slow, and they happen deep in the Earth’s crust, way out of sight. Why should these changes happen? Well, they are primarily driven by increases in pressure and temperature, so we begin with a look at these two factors. There are sites in the Earth’s crust where material becomes progressively buried. It happens, for example, where a tectonic plate is driving underneath another one, taking rocks ever deeper as it descends. It can happen in the central area of a plate that is stretching and sagging, allowing thick accumulations of sediment. It’s pretty self-evident that as buried material gets deeper, because of the growing weight of rocks above bearing down due to gravity, it becomes subjected to increasing burial pressure. Less intuitive, though, is the fact that this pressure acts on a volume of rock equally in all directions. Imagine a small volume of rock at depth. It’s bearing the weight of the rocks above it, and so it responds by trying to move downward and to spread out laterally. Of course, it can’t because it’s constrained all around by other volumes of rock that are trying to do exactly the same thing. And so the downward gravity is translated into an all-around pressure. It’s the same effect as diving down to the bottom of a swimming pool. You feel the increased pressure owing to the weight of water above, but you feel it equally in all directions. All-round pressure like this can cause things to change in volume, through changing their density, but it can’t change their shape. However, there can be another kind of pressure as well, and this does have direction, and it can cause change of shape. In the Earth, we call it tectonic stress. It comes about through heat-driven motions in the Earth, including the movement of tectonic plates.

Geo-Stress Measurement and its Application in the Yangchangwan Coal Mine

2013 ◽  
Vol 353-356 ◽  
pp. 398-402
Author(s):  
Xiao Yu Zhang ◽  
Feng Ming Liu ◽  
Gang Chen
Keyword(s):  
Stability Analysis ◽  
Coal Mine ◽  
Basic Parameter ◽  
Stress Measurement ◽  
Three Dimensional ◽  
Stress Relief ◽  
Tectonic Stress ◽  
Surrounding Rock ◽  
Support Design ◽  
Rock Stability

The initial stress of rock is a basic parameter, which can be used for surrounding rock stability analysis, exploitation and support design. By utilizing stress relief method of hollow inclusion with its characters of high precision and obtaining three dimensional stress at one time, we have measured three dimensional stress magnitude and direction in north wing roadway (-850m) and 710 open-off cut (-1000m), respectively. The results show that the horizontal tectonic stress is obvious in this coal area.

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