## Masters Theses

#### Abstract

"The purpose of this investigation is to search for a method by which the strength properties of a rock may be described.

For this purpose, an attempt has been made to find out some relationship by which the rooks may be classified or described. For the solution of problems of mine stability, the mechanical properties of a rock should be known, i.e., hardness, toughness and strength. It is difficult to make a study of some method of classification or description of a rock without knowledge of these properties.

With a view to achieve the solution of a general classification for rocks from the strength characteristics, many organizations have obtained information regarding the mechanical properties of rooks. These properties were obtained by different methods and various technicians and seem to give comparable results; but no correlation has been carried out between the fundamental properties to evolve a relationship which will describe a rock. However, it is extremely difficult to find a single property of a rook which will describe every other rock, and it is not easy to determine several such properties which will form a key to describe a rock at different locations. The strength properties of a rock is determined from standardized experimental procedures and specifications. The experimental results differ much from the calculated theoretical values. This is due to the fact that the strength properties were determined on many assumptions. It Is assumed to establish the theory of elasticity that a material Is elastic, Isotropic, and homogeneous; Infinitely divisible without change In properties; and that It conforms to Hook's law, which states that "stress is proportional to strain." Actually none of these assumptions are true. Very careful experiments show that there is some permanent deformation, and Hook's law is not perfectly true for any stress, however small. This shows deviations from the values calculated by a theory and the results obtained by observed data.

The objective of finding a relationship by which a rock can be described has considerable importance, as we are confronted with problems which are difficult to control. Hence a predetermination of conditions are necessary for solution of a particular problem.

Some of the strength properties of a rock can be determined from the stress-strain diagram of the rook. With a view to find a common property which may describe a rook, stress-strain diagrams of different rocks were plotted. It was found that the stress-strain diagrams have different shapes. The diagrams of the same shape are grouped into one family; then, in a similar way, two other families were formed. Then equations of curves of these families were determined by applying the theory of measurements. It was found that each family gives approximately an equation of one kind. From these equations, and applying the general methods of mechanics, the centroid of the area beneath each diagram has been determined. This point, which is always a fixed point, gave hints as to the nature of deformations and the energy absorbed by the rooks at the point of failure. It will be discussed later in the paper how the positions of the centroids of areas beneath different curves and the equations are used to make a correlation of describing a rock"--Introduction, pages 1-3.

#### Advisor(s)

Vine, William A.

#### Department(s)

Mining and Nuclear Engineering

#### Degree Name

M.S. in Mining Engineering

#### Publisher

Missouri School of Mines and Metallurgy

#### Publication Date

1953

#### Pagination

vi, 58 pages

#### Note about bibliography

Includes bibliographical references (pages 56-57).

#### Rights

© 1953 Muhammed Abdul Waheb, All rights reserved.

#### Document Type

Thesis - Open Access

#### File Type

text

#### Language

English

#### Library of Congress Subject Headings

Rock deformation

Plasticity -- Mathematical models

Strength of materials -- Mathematical models

#### Thesis Number

T 1054

#### Print OCLC #

5151223

#### Electronic OCLC #

953453283

#### Link to Catalog Record

#### Recommended Citation

Waheb, Muhammed Abdul, "Plastic deformation of rocks" (1953). *Masters Theses*. 2211.

https://scholarsmine.mst.edu/masters_theses/2211

*Stress-Strain Diagram of Rocks*

Waheb_Muhammed_1953_Fig_2.tif (155197 kB)

*Stress-Strain Diagram of Rocks showing Equations and Areas*

Waheb_Muhammed_1953_Fig_3.tif (25916 kB)

*Sketch Showing the Method of Determining Center of Gravity of a Body*

Waheb_Muhammed_1953_Fig_4.tif (150630 kB)

*Diagrammatic Sketch Showing the Method of Determining the Canter of an Area*

Waheb_Muhammed_1953_Fig_5.tif (18301 kB)

*Skeleton Diagrams Used in Deriving the Formula for Energy*

Waheb_Muhammed_1953_Fig_6.tif (124493 kB)

*Three Cycles Double Log Paper Used in Plotting Curve Number 2 for Determination of an Equation*

Waheb_Muhammed_1953_Fig_7.tif (106481 kB)

*Semi-log Paper Used in Plotting Curve Number 11 for Determination of an Equation*