## Doctoral Dissertations

#### Abstract

"The adverse effects of faults on the stability of underground openings has long been realized. To date, however, discontinuities and most other types of geologic heterogeneities have not been amenable to mathematical analysis using the classical theories of elasticity and plasticity. This investigation examines the stress distribution around a single discontinuity and compares the experimental and numerical methods used for the analysis. The theory of elasticity, employing the equations of compatibility, equilibrium etc., was used to determine a stress function for the stress distribution around a circular hole loaded in a centrifugal field. The analysis was terminated after the stress function had been derived due to the intractability of the solution obtained. A photoelastic stress freezing technique was used to determine the fringe patterns in centrifugally loaded models containing a single discontinuity. Stress trajectories were obtained for all the models, but no absolute determination of stress was possible as the fringe orders in the models could not be determined. The finite element method was used to solve for the stress distribution around discontinuities. Some finite element models were similar in geometric arrangement to the photoelastic models to allow a direct comparison of results. The method employed assumes a finite number of triangular shaped elements joined only at the corners. The stiffness of each element is derived and from these the overall stiffness of the system can be obtained. From the applied loads and known matrix relationships the displacements of the element corners, or nodal points, can be calculated. These displacements can then be translated into element and nodal point stresses. Stress vector diagrams were made for all the finite element models run. The analysis showed a high stress concentration to exist at the lower end of the discontinuity. The magnitude of the stresses in this concentration and their components, whether tension or compression, was a function of the degree of restraint, the friction along the fault, the dip of the fault, and Poisson's ratio. In the neighborhood of the fault, away from the stress concentration at the lower end, the principal stress direction and ratio varied in the close proximity of the fault. The degree of variation depended upon the friction along the fault and the degree of lateral restraint. The finite element technique proved a more versatile means of analysis for this type problem, particularly when a systematic variation of parameters was required. However, some limitations were imposed on the analysis due to the boundary conditions"--Abstract, page ii-iii.

Clark, George Bromley, 1912-

#### Committee Member(s)

Schwanke, Alfred E.
Haas, Charles J.
Beveridge, Thomas R. (Thomas Robinson), 1918-1978
Davidson, Robert F., 1911-1971

#### Department(s)

Mining Engineering

#### Degree Name

Ph. D. in Mining Engineering

#### Publisher

University of Missouri at Rolla

1967

#### Pagination

xiv, 144 pages

Includes bibliographical references (pages 122-124).

#### Document Type

Dissertation - Open Access

text

#### Language

English

Elastic analysis (Engineering)
Fault-tolerant computing
Faults (Geology)

T 2031

9525027

#### Electronic OCLC #

780551259

http://merlin.lib.umsystem.edu/record=b1487865~S5

COinS