SCHOOL OF SCIENCES Group: 1

1. KUORWEL NGANG JACOB 2013/AUG/BPMM/B11865/DAY

2. NYAKATO JUSTINE 2014/AUG/BPMM/B14040/DAY

3. KANDOLE GEORGE 2014/AUG/BPMM/B12982/DAY

4. TUMUSIIME RONALD 2014/AUG/BPMM/B14171/DAY

5. AMPUMUZA JERVIS

a) Discuss what you understand by Mohr tress diagram

b) Discuss the importance/significance of the Mohr stress (MSD) in structural geology

c) Write a detailed notice using sketch diagrams where necessary on the following types of faults

Normal fault Reverse fault Strike-slip fault Diapirs

Introduction

Introduced by Otto Mohr in 1882, Mohr's Circle illustrates principal stresses (Normal stress) and stress transformations via a graphical format. Mohr's Circle was the leading tool used to visualize relationships between normal and shear stresses., and to estimate the maximum stresses before the hand-held calculators became popular. Even today, Mohr's Circle is still widely used by engineers all over the world.

Three Fundamental Principles of Mohr Circles

•Directions of planes are always represented by their poles

•Angles on the Mohr Circle are double the corresponding angles in real life.

•Always measure angles in the same sense in both real life and on Mohr Circles

Since angles are doubled on the Mohr Circle, any angles in real life greater than 180 degrees will be equal to 360 on the Mohr Circle simply because they repeat themselves. Even if you perform stress calculations for a plane oriented at 180 degrees from the plane, the results remain identical.

SYMBOL NO TYPE OF STRESS

1 1= Sigma Maximum Compressive Stress

2 2= Sigma Intermediate Compressive Stress

3 3= Sigma Minimum Compressive Stress

Theta Angle formed by an inclined plane with the

maximum and minimum compressive stress

directions, and measured from the minimum stress

position.

n n= Normal Stress Oriented perpendicular to a plane

s s= Shear Stress Oriented parallel to a plane in question

Given the above diagram, the two principal stresses are shown in red, and the maximum shear stress is shown in orange. Recall that the normal stresses equal the principal stresses when the stress element is aligned with the principal directions, and the shear stress equals the maximum shear stress when the stress element is rotated 45° away from the principal directions. As the stress element is rotated away from the principal (or maximum shear) directions, the normal and shear stress components will always lie on Mohr's Circle. A force applied to an area (stress) may be resolved into a normal force (Fn) perpendicular to a plane and a shear force (Fs), parallel to a plane in question.

PLOTTING MOHR'S CIRCLE:

Mohr's circle is plotted on two perpendicular axes: The vertical axis (ordinate) depicts

shear stress and the horizontal axis (abscissa) depicts normal stress.

On a Mohr’s Diagram, the following shear conventions apply:

Sinistral (counter-clockwise) shear is Positive (+)

Dextral (clockwise) shear is Negative (-).

Angles theta associated with planes experiencing sinistral shear plotted in the upper

hemisphere as well as planes experiencing dextral shear plot in the lower hemisphere

Note that the axes of Mohrs diagram do not have a geographic orientation. However,

prior to constructing Mohrs diagram, it is useful to sketch a block diagram of the

orientations of the principal stress axes and the plane in question to ascertain the

relative sense of shear & orientation of principal stress axes.

Two points on the horizontal axis define the diameter of a circle. The Circle is plotted on the abscissa

These points establish a radius (R) whereby:

The center (C) is then plotted:

We can determine the normal and shear stress on any plane oriented at an angle theta from the abscissa, as measured counter-clockwise from the minimum compressive stress direction. Because of the properties of a circle, the angle between Point P, the center of the circle and the maximum compressive stress direction =2 theta, as measured counter-clockwise from the center of the circle.

Importance of Mohr Circle in Structural GeologyDetermination of elasticity states for lithospheric stressElementary elasticity is appropriate because many in-situ stress measurement techniques capitalize on the elastic behavior of rocks. Furthermore, many notions concerning state of stress in the lithosphere arise from the assumption that the upper crust behaves as a linear elastic body.

Understanding two reference states of stressStress generated by plate tectonic processes make the difference in the earth. Geologically, reference states are those expected in 'young' rocks shortly after lithification. Indication of Lithostatic stress. Lithostatic stress will develop if a rock has no long-term shear strength. Although some rocks such as weak shales and halite have very little shear strength, experiments suggest that all rocks support at least a small differential stress

Determination of forces. Since most stresses in structural geology are compressional,

many workers prefer to define compression as positive and tension as negative hence indicating the direction of

forces.

Maximum shear stress occurs on planes oriented 45O to the

maximum and minimum compressive stress directions; thus, these points plot at the

top and bottom of Mohr's Circle as denoted on the

diagram below.

Importance of Mohr Circle in Structural Geology ..Cont..

• Determination of stress and strain values. • Depicts the attitude of planes along which shear stress is the

greatest for a given stress state • Facilitates a quick, graphical determination of stresses on planes

of any orientation. • Mohr diagrams are excellent for visualizing the state of stress

although difficult for calculating stress tensors which are used to calculate stress.

• Determination of effective stress & fluid pore pressure

Importance of Mohr Circle in Structural Geology ..Cont..

In geology, a fault is a planar fracture or discontinuity in a volume of rock across which there has been significant displacement along the fractures as a result of rock mass movement. Large faults within the Earth's crust result from the action of plate tectonic forces form which result in the formation of boundaries between the plates, such as subduction zones or transform faults. Energy release associated with rapid movement on

active faults is the cause of most earthquakes

Diapir (from Greek diapeirein, “to pierce”), geological structure consisting of mobile material that was forced into more brittle surrounding rocks, usually by the upward flow of material from a parent stratum.

Conclusion:Traditionally, tectonic stresses are associated with stress arising from the largest-scale natural sources such as plate-boundary tractions, radioactivity and convection current but cause a lot of deformation rocks even at the surface.

THANK YOU.