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GE 5471 ROCK ENGINEERING CH 5 – Stress
Dr. Norbert H. Maerz
Missouri University of Science and Technology
(573) 341-6714
norbert@mst.edu
Instructional Objectives
1. Explain the consequences of stress release.2. Propose engineering solutions to the problems of stress
release.3. Define stress and strain in 3-dimensions.4. Define principal stresses and special states of stress.5. Calculate vertical stresses based on material properties.6. Explain Fossil stresses.7. Describe how stress is measured using the overcoring, strain
nulling, and hydrofracturing methods, and solve stresses using calculations.
8. Solve using calculations , problems involving unconfined compressive strength, forces and stresses, stress in the earth, stress in underground rooms, and shear stresses.
IS STRESS BAD? Examples of Stress Release
• Earthquakes
• Rockbursts
• Rockfalls
• Pop-ups
• Squeezing
Pop-ups
Photo from the collection of Dr. J. A. Franklin
Stress release
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Stress ReleaseENGINEERING SOLUTIONS TO STRESS (RELEASE) RELATED
PROBLEMS
• Catastrophic– Understand and
manage stress
– Design to remove stress concentrations
– Learn to monitor and predict rockbursts
• Non-catastrophic– Design for movement
What is stress
• Applied force per unit area
• Shear stress
• Normal stress
• (Newton is a unit of force)
2m
N
2m
N
2sec
.mkgmaN
Practical Rock Mechanics (Hencher)
Relationship between normal and shear stress
Practical Rock Mechanics (Hencher)
Stress is 3-D with 9 componentsStress Tensor
zzyzx
yzyyx
xzxyx
zyzxz
yzyxy
xzxyx
Practical Rock Mechanics
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Principal Stresses
• σ1 = maximum principle stress
• σ2 = intermediate principle stress
• σ3 = minimum principle stressz
y
x
00
00
00
Special States of Stress
• Uniaxial Stress
• Biaxial Stress
• Triaxial Stress
• Hydrostatic Stress
Worked Example – Column of 1 m blocks – how high could we stack these?
Worked Example – Column of 1 m blocks – how high could we stack these?
Stress Distribution Around Openings
Practical Rock Mechanics (Hencher) Practical Rock Mechanics
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Stress Distribution Around Openings Stress with Depth
Strain Worked Example – Column of 1 m blocks – what is thestrain?
Horizontal Stresses
• “Virgin” basin
• Tectonism
• Rock anisotropy
• Topography
• “Fossil” Stresses
Fossil Stresses
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Stress with Depth
Methods of Stress Measurement
• Overcoring
• Strain Nulling
• Hydrofracturing
Overcoring:Strain-ReliefMethod
South AfricanDoorstopper
DoorstopperStressMeasurement
Photos from the collection of Dr. J. A. Franklin
CSIR Triaxial Cell
Picture courtesy of Roctest.
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CSIRO Stress Cell
Photos from the collection of Dr. J. A. Franklin
USBM Stress Gauge
Photos from the collection of Dr. J. A. Franklin
LisbonStressMeter
Photos from the collection of Dr. J. A. Franklin
Biaxial Modulus Chamber
Photos from the collection of Dr. J. A. Franklin
Undercoring
https://www.onepetro.org/download/conference-paper/ISRM-EUROCK-2012-009?id=conference-paper%2FISRM-EUROCK-2012-009
Strain Nulling:Flat Jack
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Goodman (Flat) Jack Method FlatjackStress
Measurement
Photos from the collection of Dr. J. A. Franklin
HydrofracturingHydrofracturingStress Measurement
Photos from the collection of Dr. J. A. Franklin
Photos from the collection of Dr. J. A. Franklin
Calculations
• Tensile strength τo =Pf – Pr
• ’min = 3 = Ps – P0
• ’max = 1 = τ + 3Ps – Pf – P0
• ’max = 1 = 3Ps – Pr – P0
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Orientation of Fractures
Photos from the collection of Dr. J. A. Franklin
Strain Relief Methods
• PROS
– Can get all values σ1, σ2, σ3
– Can get the orientation of the principal stresses
– Deep borehole not required
• CONS
– Can’t get too deep into the rock, partially disturbed
– Difficult test, especially in wet and long boreholes
– Need a good stress-strain relationship
Strain Nulling Methods
• PROS
– simple, inexpensive tests– easy accessibility– measures tangential stress
in an opening
• CONS
– measures stress in one direction only per test
– very shallow penetration, consequently operating in “disturbed” stress fields (stress concentration; stress relaxation)
– need numerical solutions to get σ1, σ2, σ3
Hydrofracturing Methods
• PROS
– Good for getting magnitudes of σ1 and σ3
– Deep, deep reach in borehole
– Reaches undisturbed stress fields
• CONS
– No σ2
– Stress orientation somewhat fuzzy.
– Expensive test, especially if you need to bore a deep hole
Slide Show
• Stress manifestation
• Stress measurement
• Stress distribution
Stress Manifestation
Photos from the collection of Dr. J. A. Franklin
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Convergeance
Photos from the collection of Dr. J. A. Franklin
FailedRockbolt
Photos from the collection of Dr. J. A. Franklin
Breakout
Photos from the collection of Dr. J. A. Franklin
Disking
Photos from the collection of Dr. J. A. Franklin
StressRelief
Sliding
Photos from the collection of Dr. J. A. Franklin
Rock Movement
Photos from the collection of Dr. J. A. Franklin
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Convergeance
Photos from the collection of Dr. J. A. Franklin
Popups
Photos from the collection of Dr. J. A. Franklin
Exfoliation Joints
Floor Heave
Photos from the collection of Dr. J. A. Franklin
Stress Distribution
Photos from the collection of Dr. J. A. Franklin
StressDistribution
Photos from the collection of Dr. J. A. Franklin
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Gonzales and Ferrer Gonzales and Ferrer
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