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GE 6477 DISCONTINUOUS ROCK7. Shear Strength of Discontinuities

Dr. Norbert H. Maerz

Missouri University of Science and Technology

(573) 341-6714

norbert@mst.edu

Instructional Objectives

1. Explain the differences between a simple frictional model of sliding between and the Mohr Colomb model for sliding on a discontinuity.

2. Explain the difference between peak and residual shear strength and justify the use of either model.

3. Critique the advantages and disadvantages in using triaxial vs direct shear test to establish the Mohr-Coulomb parameters.

4. Describe the shortcomings of the Mohr-Columb shear strength criterion, and how these are overcome in the Patton and Barton criteria.

5. Predict the effect of a) dilation and b) shear displacement on the fidelity of the measurements of the shear strength parameters.

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Instructional Objectives

6. Justify the Patton and Barton criteria in terms of the physical representation of the roughness representations.

7. Explain what the Barton criterion has that is missing in the Patton criterion.

8. Suggest why the other shear strength models presented in this section are not widely used.

9. Predict how the scale effect would affect the behavior of rock discontinuities in shear.

Image(s) from the collection of Dr. John Franklin.

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Shear Strength of Joints

• Largely frictional property

• Some influence of cohesion

• Very sensitive to normal or confining stress

• Principle of peak vs. residual strength

Simple Friction Model

0

1

0 1

F

R

6.02.0 R

F

6.02.0'

''

R

F

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Rock shear strength model

Triaxial tests on discontinuities

Image(s) from the collection of Dr. John Franklin.

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Triaxial tests on discontinuities

Traixial tests on discontinuities

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c

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Direct shear tests

Direct shear tests

Image(s) from the collection of Dr. John Franklin.

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Direct shear tests

• Review of stress- strain relationships

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Direct shear test results

Big direct shear tests

Image(s) from the collection of Dr. John Franklin.

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Mohr-Coulomb model

n

c

tannc

M-C model vs. data

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Picture(s) from Gonzales de Vallejo and Ferrer

What makes a good model?

1. Accurate, faithful.2. Simple – If no one understand it, it goes

nowhere.3. Lowest possible number of parameters – If

there are too many it is too difficult.4. Critical parameters are ones that are not

easy to measure or estimate, and the model is especially sensitive to them.

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Bilinear failure criteria

• What happens during shearing of rough surfaces?

1. Dilation.

2. Destruction of asperities.

Bilinear failure criteria: Pattons i-angle

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Bilinear failure criteria: Pattons i-angle

• For low normal stress

• For high normal stress

iunp tan

rnjp S tan

Picture(s) from Gonzales de Vallejo and Ferrer

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Dilation

Dilation

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Barton’s curvilinear failure criterion

• Empirical, curilinear three-parameter empirical shear strength model

• Uses Joint Roughness Coefficient, Joint (wall) Compressive Strength, and a base friction angle

b

nn

JCSJRC

10logtan

• JRC (Joint roughness coefficient).

• Typically estimated, or calculated from a digitized profile.

• Range 0-20.

Picture(s) from Gonzales de Vallejo and Ferrer

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JCS (Joint wall Compressive Strength) from Schmidt Hardness

Image(s) from the collection of Dr. John Franklin.

Base angle of friction

• Tilt test on core

• Typical guess = 30 degrees

tan155.1tan 1b

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Barton Model

Barton vs Patton

b

nn

JCSJRC

10logtan

ubn

iJCS

JRC

10log

un i tan

ub IF

iJCS

JRCn

10log

Equating

THEN

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Barton Model

Roughness

• Directional.

• Can be thought of as a waveform.

• No direct relationship between roughness and shear strength.

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Roughness

• Amplitude, wavelength, slope.

• Ratio of filling thickness to amplitude.

Roughness to shear strength

• 1) Generate roughness profiles.

• 2) Measure some parameters on profile, such as average slope, use in Patton’s model.

• 3) Empirical relationship to a parameter that can be used in a model, such as JRC, use in Barton’s model.

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Shadow Profilometry

Image(s) from the collection of Dr. John Franklin.

Principle of shadow profilometry

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• Angle of shadow profile

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Shadow Profilometry

• Roughness Profile with Z2 (root mean square of the first derivative), i (average micro inclination angle), Rp (roughness profile index)

Shadow Profilometry

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Shadow profilometry

Image(s) from the collection of Dr. John Franklin.

Precision of shadow profilometry

• Greater accuracy and precision

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Roughness to shear strength: Barton type curves

1401 pRJRC

Roughness to shear strength, tilt tests on cores

1411 pRJRC

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Shadow profilometry paper

• http://web.mst.edu/~norbert/pdf/jointroughness.pdf

Ladanyi and Archambault model

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Denby and Scoble Model

BnA

Reeves Model

• Uses Z2 (root mean square of the first derivative) and empircal constants C, n to fit a power law curve.

tn tan

nt ZC 2tan

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Models superimposed

Other models:

• Abound in literature,

• Suffer from obscurity.

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Roughness scale effect

• Corrugated cardboard • Rock joint surface

Roughness scale effect

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Shear strength scale effect

Picture(s) from Gonzales de Vallejo and Ferrer

Resolving shear scale effects

• Small portable shear machines - core sized

• Large lab shear machines -300 mm on side

• Field shearing machines -several m on end

• Use small tests to get residual or ultimate or base friction.

• Use roughness (whichever measure) on the scale of the potential failure.

• Use back analysis

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Time Dependent behavior of joints - rheological elements

Time Dependent behavior of joints - rheological model