The document discusses shear strength of discontinuities in rock masses. It introduces concepts like shear strength of planar surfaces, shear strength of rough surfaces, Barton's estimate of shear strength which relates shear strength to joint roughness coefficient (JRC) and joint compressive strength (JCS). It discusses estimating JRC and JCS in the field and how these parameters are influenced by scale. It also summarizes the shear strength of filled discontinuities and the influence of water pressure on shear strength.

1. Chapter 4
Shear strength of discontinuities

2. Mountain Climber
Katie Brown
Fisher Towers, Utah
https://www.youtube.com/watch?list=RDCIjGaDUp6FY&v=p-
hW4AOC0c4&feature=emb_rel_end

3. Pictured Rocks National Lakeshore
Miner’s Castle

4. Where did the
first Miner’s
Castle Block go?

5. Miners Castle before and after April 13, 2006, rockfallNPS photos
On Thursday morning, April 13, 2006, the northeast turret of Miners Castle collapsed. One
turret remains on Miners Castle, the best-known feature of Pictured Rocks National
Lakeshore. The collapse was reported via cell phone by fisherman in the area, according to
chief ranger Larry Hach.
Most of the rock fell north and into Lake Superior, and there were no injuries. The lower
overlook platform near Miners Castle appears to be unaffected.
While the rockfall at Miners Castle on April 13 was startling, such events are not rare along
the Pictured Rocks escarpment. At least five major falls have occurred over the past dozen
years: 1) two different portions of Grand Portal Point, 2) the eastern side of Indian Head just
east of Grand Portal Point, 3) Miners Falls just below the (now modified) viewing platform,
and 4) beneath the lip of Munising Falls (along the former trail that went behind the
cascade).
All the rockfalls involved the same rock unit, the Miners Castle Member of the Munising
Formation. Rock units are named for places where they were first technically described.
The Miners Castle Member consists of crumbly cross-bedded sandstone that is poorly
cemented by secondary quartz, according to U.S. Geological Survey Research Ecologist
Walter Loope.
Rockfalls along the cliffs typically occur in the spring and fall due to freezing and thawing
action of Mother Nature.
Miners Castle Turret Collapses
https://www.youtube.com/watch?v=RxpHIeBTFOc

6. Shear strength of discontinuities
• Introduction
• Shear strength of planar surfaces
• Shear strength of rough surfaces
• Barton’s estimate of shear strength
• Field estimates of JRC
• Field estimates of JCS
• Influence of scale on JRC and JCS
• Shear strength of filled discontinuities
• Influence of water pressure

7. Introduction
• All rock masses contain
discontinuities such as bedding
planes, joints, shear zones and
faults.
• At shallow depth, where
stresses are low, failure of the
intact rock material is minimal
and the behavior of the rock
mass is controlled by sliding on
the discontinuities.

8. 123

9. Mohr-Coulomb: 𝜏𝜏 = 𝑐𝑐 + 𝜎𝜎𝑛𝑛 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

10. Shear strength of planar surfaces

11. φpeak = φp Peak Shear Strength
φresidual = φr Residual Shear Strength
φBasic = φb Basic Shear Strength
φb ≈ φr Basic friction assumes perfectly smooth
surfaces and is essentially the friction angle of the
mineral, e.g., quartz or smooth granite blocks
Three Basic Shear Strengths:
Peak, Residual, and Basic Friction Angle

12. 1. In shear tests on soils, the stress levels are generally an order of magnitude lower
than those involved in rock testing and the cohesive strength of a soil is a result of
the adhesion of the soil particles.
2. In rock mechanics, true cohesion occurs when cemented surfaces are sheared.
3. However, in many practical applications, the term cohesion is used for convenience
and it refers to a mathematical quantity related to surface roughness, as discussed
in a later section.
4. Cohesion is simply the intercept on the τ axis at zero normal stress.
What is cohesion, C?
𝜏𝜏 = 𝜎𝜎𝑛𝑛 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 Assume c = 0

13. Shear strength of rough surfaces
Asperities
• Increase friction
• Increase dilation
(upward movement
of the block)

14. Shear strength of rough surfaces
• A natural discontinuity surface in hard rock is never as smooth as a sawn
or ground surface of the type used for determining the basic friction
angle.
• The undulations and asperities on a natural joint surface have a
significant influence on its shear behavior.
• Generally, this surface roughness increases the shear strength of the
surface, and this strength increase is extremely important in terms of
the stability of excavations in rock.
• Patton (1966) demonstrated this influence by means of an experiment in
which he carried out shear tests on 'saw-tooth' specimens such as the
one illustrated in Figure 4.

15. 𝜏𝜏 = 𝜎𝜎𝑛𝑛 tan 𝜙𝜙𝑏𝑏 + 𝑖𝑖 (5)
• φb is the basic friction angle of the surface and
• i is the angle of the saw-tooth face.
• Note that “c” is now part of the term i
Patton’s
Equation

16. Barton’s estimate of shear strength
• Equation (4) is valid at low normal stresses where shear displacement
is due to sliding along the inclined surfaces.
• At higher normal stresses, the strength of the intact material will be
exceeded and the teeth (asperities) will tend to break off, resulting in
a shear strength behavior which is more closely related to the intact
material strength than to the frictional characteristics of the surfaces.
• While Patton’s approach has the merit of being very simple, it does
not reflect the reality that changes in shear strength with increasing
normal stress are gradual rather than abrupt.
• Barton (1973, 1976) studied the behavior of natural rock joints and
proposed that equation (4) could be re-written as:

17. 𝜏𝜏 = 𝜎𝜎𝑛𝑛 𝑡𝑡𝑡𝑡𝑡𝑡 𝜙𝜙𝑏𝑏 + 𝐽𝐽 𝐽𝐽𝐽𝐽𝑙𝑙𝑙𝑙 𝑙𝑙10
𝐽𝐽𝐽𝐽𝐽𝐽
𝜎𝜎𝑛𝑛
(6)
• JRC is the Joint Roughness Coefficient
• JCS is the joint wall compressive strength
• Note – the equation used the φb ≈ φr
Barton’s Equation with a Joint Roughness Coefficient
(JRC) and a Joint Compressive Strength (JCS)
φ

18. 𝜏𝜏 = 𝜎𝜎𝑛𝑛 𝑡𝑡𝑡𝑡𝑡𝑡 𝜙𝜙𝑟𝑟 + 𝐽𝐽 𝐽𝐽𝐽𝐽𝑙𝑙𝑙𝑙 𝑙𝑙10
𝐽𝐽𝐽𝐽𝐽𝐽
𝜎𝜎𝑛𝑛
(7)
Since the “basic friction is approximately equal to the residual
friction angle Barton substitutes φb ≈ φr

19. Field estimates of JRC
Note: That the length of
the joint is based on a
length (Lo) = 10 cm (100
mm)

20. Another method to
determine JRC using
field measurements
Example: Assume you have a 1 m
length surface with 10 mm
asperities, the JRC ≈ 4

21. Field estimates of JCS
Schmidt rebound hammer

22. Schmidt rebound hammer

23. Influence of scale on JRC and JCS
• Extensive size effects testing reported by Bandis et al (1981) suggest
that both JRC and JCS reduce with increasing block size.
• Greatest reductions in these parameters occur with the roughest joint
surfaces due to the marked change in size of the individual contact
points between opposed asperities.
Lo

24. From “Effects of Block Size
on the Shear Behavior of
Jointed Rock”
By
Nick Barton and Stavros
Bandis

25. From “Effects of
Block Size on the
Shear Behavior of
Jointed Rock”
By
Nick Barton and
Stavros Bandis

26. • Increased joint size:
• Reduced asperity strength
• Reduced dilation
• Increased displacement to mobilize peak
strength
Note: From “Effects
of Block Size on the
Shear Behavior of
Jointed Rock”
By
Nick Barton and
Stavros Bandis
Peak Strength

27. From “Effects of Block Size on the
Shear Behavior of Jointed Rock”
By
Nick Barton and Stavros Bandis

28. Note: From “Effects of Block Size on
the Shear Behavior of Jointed Rock”
By
Nick Barton and Stavros Bandis
Peak Displacement, δpeak

29. Influence of scale on JRC – Joint Roughness Coefficient
• On the basis of extensive testing of joints, joint replicas, and a review
of literature, Barton and Bandis (1982) proposed the scale corrections
for JRC defined by the following relationship:
𝐽𝐽 𝐽𝐽 𝐽𝐽𝑛𝑛 = 𝐽𝐽 𝐽𝐽 𝐽𝐽𝑜𝑜
𝐿𝐿𝑛𝑛
𝐿𝐿𝑜𝑜
−0.02𝐽𝐽𝐽𝐽𝐽𝐽𝑜𝑜
• where JRCo, and Lo (length) refer to 100 mm laboratory scale samples and
• JRCn, and Ln refer to in situ block sizes.

30. Influence of scale on JCS – Joint Compressive
Strength
• Because of the greater possibility of weaknesses in a large surface, it
is likely that the average joint wall compressive strength (JCS)
decreases with increasing scale. Barton and Bandis (1982) proposed
the scale corrections for JCS defined by the following relationship:
𝐽𝐽𝐽𝐽𝐽𝐽𝑛𝑛 = 𝐽𝐽𝐽𝐽𝐽𝐽𝑜𝑜
𝐿𝐿𝑛𝑛
𝐿𝐿𝑜𝑜
−0.03𝐽𝐽𝐽𝐽𝐽𝐽𝑜𝑜
• where JSCo, and Lo (length) refer to 100 mm laboratory scale samples and
• JSCn, and Ln refer to in situ block sizes.
• Note: that you can simple use the compressive strength, σc, of the rock
mass if the joint does not have an infilling.
Note: JRC not JCS

31. Example of scaling a JRC and a JCS:
• Assume that a joint has the following JRC and JCS values:
• JRC = 12
• JCS = 80 MPa
• The length of the joint is 1 m; Lo = 100 mm & Ln = 20 m
𝐽𝐽 𝐽𝐽 𝐽𝐽𝑛𝑛 = 𝐽𝐽 𝐽𝐽 𝐽𝐽𝑜𝑜
𝐿𝐿𝑛𝑛
𝐿𝐿𝑜𝑜
−0.02𝐽𝐽𝐽𝐽𝐽𝐽𝑜𝑜
= 12
1
0.1
−0.02(12)
= 6.9
𝐽𝐽𝐽𝐽𝐽𝐽𝑛𝑛 = 𝐽𝐽𝐽𝐽𝐽𝐽𝑜𝑜
𝐿𝐿𝑛𝑛
𝐿𝐿𝑜𝑜
−0.03𝐽𝐽𝐽𝐽𝐽𝐽𝑜𝑜
= 80
1
0.1
−0.03(12)
= 34.9
JRCn = 7 JRCo = 12
JCSn = 35 Mpa JCSo = 80 MPa
Scaled JRC & JCS

32. Shear strength of filled discontinuities (Barton, 1974)
• The discussion presented in the previous sections has dealt with the shear
strength of discontinuities in which rock wall contact occurs over the entire
length of the surface under consideration.
• This shear strength can be reduced drastically when part or all of the
surface is not in intimate contact, but covered by soft filling material such
as clay gouge.
• For planar surfaces, such as bedding planes in sedimentary rock, a thin clay
coating will result in a significant shear strength reduction.
• For a rough or undulating joint, the filling thickness has to be greater than
the amplitude of the undulations before the shear strength is reduced to
that of the filling material.

33. Shear strength of filled discontinuities
(From Barton, 1974)

35. A comprehensive review of the shear strength of filled discontinuities was prepared
by Barton (1974) and a summary of the shear strengths of typical discontinuity
fillings, based on Barton's review, is given in Table 1.

37. Influence of water pressure
𝜏𝜏 = 𝜎𝜎𝑛𝑛 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡
𝜏𝜏 = 𝜎𝜎𝑛𝑛 − 𝑢𝑢 𝑡𝑡𝑡𝑡𝑡𝑡 𝜙𝜙𝑟𝑟 + 𝐽𝐽 𝐽𝐽 𝐽𝐽𝑙𝑙𝑙𝑙 𝑙𝑙10
𝐽𝐽𝐽𝐽𝐽𝐽
𝜎𝜎𝑛𝑛
𝜏𝜏 = 𝜎𝜎𝑛𝑛 − 𝑢𝑢 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

38. Instantaneous cohesion and friction