Rock Engineering Practice & Design.pdf

Rock Engineering Practice & Design Lecture 4: Kinematic Ki ti A Analysis l i I (Slopes)

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Erik Eberhardt – UBC Geological Engineering

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Author’s Note: The lecture slides provided here are taken from the course “Geotechnical Engineering Practice”, which is part of the 4th year Geological Engineering program at the University of British Columbia (V (Vancouver, Canada). C d ) The Th course covers rock k engineering i i and d geotechnical design methodologies, building on those already taken by the students covering Introductory Rock Mechanics and Advanced Rock Mechanics. Mechanics Although the slides have been modified in part to add context, they of course are missing the detailed narrative that accompanies any l lecture. It is also l recognized d that h these h lectures l summarize, reproduce and build on the work of others for which gratitude is extended. Where possible, efforts have been made to acknowledge th vvarious the ri us ssources, urc s with ith a list of f references r f r nc s being b in provided pr vid d att the th end of each lecture. Errors, omissions, comments, etc., can be forwarded to the author at: [email protected] 2 of 36


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Rock Slope – Continuum or Discontinuum Discontinuum? ? In a moderately d l jointed d rock k mass, slope l failure f l is generally ll dictated d d directly by the presence of discontinuities, which act as planes of weakness within the rock mass. These interact to control the size and the direction of movement of the slope failure. planar failure

wedge failure 3 of 36


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Discontinuity Mapping Hudsson & Harrisson (1997)

Scanline mapping

Window mapping

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Discontinuity Mapping

Wyllie & Mah (2004) 5 of 36


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Discontinuity Mapping – Remote Sensing Strouth & Eberhardt (2006)

Remote sensing techniques like LiDAR and phtogrammetry, provide a means to collect rock mass data from slopes that would otherwise be inaccessible or dangerous. dangerous Discontinuity orientation orientation, persistence persistence, and spacing data can be extracted from the 3-D point cloud of the scanned surface. 6 of 36


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Stereonets – Pole Plots Plotting dip and dip direction, direction pole plots provide an immediate visual depiction of pole concentrations. All natural discontinuities have a certain variability in their orientation that results in scatter of the pole plots. However, by contouring the pole plot, the most highly concentrated areas of poles, representing the dominant discontinuity sets, can be identified.

It must be remembered though, that it may be difficult to distinguish which set a particular discontinuity belongs to or that in some cases a single discontinuity may be the controlling factor as opposed to a set of discontinuities. 7 of 36


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Pole Plots & Modes of Slope Instability Typical pole plots for different modes of rock slope failure.

Wyllie & Mah (2004) 8 of 36


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Discontinuity Persistence Persistence refers to the areal extent or size of a discontinuity plane within a plane. Clearly, the persistence will have a major influence on the shear strength developed in the plane of the discontinuity, where the intact rock segments g are referred to as ‘rock bridges’. g

rock k bridge

increasing persistence 9 of 36


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Discontinuity Persistence Together with spacing, discontinuity persistence helps to define the size of blocks that can slide from a rock face. Several procedures have been developed to calculate persistence by measuring their exposed trace lengths on a specified area of the face. scan line t

c t

Step 2: count the total number of discontinuities (N’’)) of a specific set with dip  in this area, (N area and the numbers of these either contained within (Nc) or transecting (Nt) the mapping area defined.

c c

c

L1

t c

t



Step 1 1: define a mapping area on the rock face with dimensions L1 and L2.

L2 Pahl (1981) 10 of 36

For example, in this case: N’’ = 14 Nc = 5 Nt = 4


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Discontinuity Persistence Step 1: define a mapping area on the rock face with dimensions L1 and L2.

Pahl (1981)

t

c t

c c

c

L1

t c

t



Step 2: count the total number of discontinuities (N’’) of a specific set with dip  in this area, and the numbers of these either contained within (Nc) or transecting (Nt) the mapping area defined. Step 3: calculate the approximate length, l, of the discontinuities using the equations below.

L2 Again, for this case: If L1 = 15 m, L2 = 5 m and  = 35°, then H’ = 4.95 m and m = -0.07. From this, this the average length/persistence of the discontinuity set l = 4.3 4 3 m. m 11 of 36


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Discontinuity Spacing Spacing is a key parameter in that it controls the block size distribution related to a potentially unstable mass (i.e. failure of a massive block or unravelling-type failure).

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Discontinuity Roughness

Barto on & Choube ey (1977)

From the practical point of view of quantifying joint roughness, only one technique has received some degree of universality – the Joint Roughness Coefficient (JRC). This method involves comparing discontinuity surface profiles l to standard roughness curves assigned numerical values.

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Dilatancy and Shear Strength

Wyllie & Mah (200 04)

In the h case of f sliding ld of f an unconstrained block of rock from a slope, dilatancy will accompany shearing of all but the smoothest discontinuity surfaces. If a rock block is free to dilate, then the second-order asperities will have a di i i h d effect diminished ff t on shear h strength. t th

By increasing the normal force across a shear surface by adding tensioned rock bolts, dilation can be limited and interlocking along the sliding surface maintained, allowing the second-order asperities to contribute to the shear strength strength. 14 of 36


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Wylllie & Mah (2 2004)

Mechanical Properties of Discontinuities

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Discontinuity Data – Probability Distributions Discontinuity properties can vary over a wide range, even for those belonging to the same set. The distribution of a property can be described by means of probability distributions. distributions A normal distribution is applicable where a particular property’s mean value is the most commonly occurring. This is usually the case for dip and dip direction. direction

A negative exponential distribution is applicable for properties of discontinuities, such as spacing and persistence, which are randomly distributed. Negative exponential function:

Wyllie & Mah (2004) 16 of 36


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Discontinuity Data - Probability Distributions

Negative N i exponential function:

Wyllie & Mah (2004)

From this this, the probability that a given value will be less than dimension x is given by: For example, for a discontinuity set with a mean spacing of 2 m, the probabilities b bl that h the h spacing will ll be b less l than: h 1 m 5 m 17 of 36


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StructurallyStructurally -Controlled Instability Mechanisms Structurally-controlled instability means that blocks formed by discontinuities may be free to slide from a newly excavated slope face under a set of body forces (usually gravity). To assess the lik lih d of likelihood f such h failures, f il an analysis l i of f the th kinematic ki m ti admissibility dmi ibilit of potential wedges or planes that intersect the excavation face(s) can be performed.

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Kinematic Analysis – Planar Rock Slope Failure To consider the kinematic admissibility of plane instability, instability five necessary but simple geometrical criteria must be met: (i)

The plane on which sliding occurs must strike ik near parallel ll l to the h slope face (within approx. ±20°).

(ii) Release surfaces (that provide n li ibl resistance negligible sist nc tto slidin sliding)) must be present to define the lateral slide boundaries. (iii) The sliding plane must “daylight” daylight in the slope face. (iv) The dip of the sliding plane must be greater than the angle of friction. friction (v) The upper end of the sliding surface either intersects the upper slope, or terminates in a tension crack. Wyllie & Mah (2004) 19 of 36


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Kinematic Analysis – Rock Slope Wedge Failure Similar to planar failures, failures several conditions relating to the line of intersection must be met for wedge failure to be kinematically admissible : (i)

The dip of the slope must exceed the dip of the line of intersection of the two wedge forming di discontinuity ti it planes. l

(ii) The line of intersection must “daylight” on the slope face. (iii) The dip of the line of intersection must be such that the strength of the two planes are reached. ( ) Th (iv) The upper end d of f the h line l of f intersection either intersects the upper slope, or terminates in a tension crack. Wyllie & Mah (2004) 20 of 36


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Kinematic Analysis – Daylight Envelopes Daylight Envelope: Zone within which all poles belong to planes that daylight, and are therefore potentially unstable.

Lisle (2004)

slope faces

daylight d li ht envelopes 21 of 36


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Kinematic Analysis – Friction Cones

Harriison & Hudso on (2000)

Friction Cone: Zone within which all poles belong to planes that dip at angles less than the friction angle, and are therefore stable.

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Pole Plots - Kinematic Admissibility

friction cone

slope face

daylight envelope

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Having determined from the daylight envelope whether block failure is kinematically permissible, a check is then made to see if the dip angle of the failure surface (or li line of f intersection) i i ) iis steeper than the with the friction angle.

Thus, for poles that plot inside the daylight y g envelope, p , but outside the friction circle, translational sliding is possible.


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Pole Plots - Kinematic Admissibility  < f



 > f

Wyllie y & Mah (2004)

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Wedge Failure – Direction of Sliding

Example scenario #2: If the dip directions of one plane (e.g. Plane A) lies within the included angle between i (trend of the line of intersection) and f (dip direction of face), the wedge will slide on only that plane. plane

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Wylllie & Mah (2 2004)

Scenario #1: If the dip directions of the two planes lie outside the included angle between i (trend of the line of intersection) and f (dip direction of face), face) the wedge will slide on both planes.

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Couurtesy - B. F Fisher (Kleinf felder)

Case History: Rock Slope Stabilization

A rock slope p with a history of block failures is to be stabilized through anchoring. To carry y out the design, g a back analysis of earlier block failures is first performed to obtain jjoint shear strength g properties. 26 of 36


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Courrtesy - B. Fissher (Kleinfe elder)


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Case History: Rock Slope Stabilization Assume: Water in tension crack @ 50% the tension crack height & water along discontinuity. discontinuity

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Courrtesy - B. Fissher (Kleinfe elder)


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Case History: Rock Slope Stabilization Given: • • • • •

Unstable Rock Slope 40 ft tall t ll About 55 degrees Joint Set Dips 38 degrees ’ + i ~ 38 - 40 degrees  55 deg slope

From previous back analysis of failed block below bridge abutment.

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Case History: Rock Slope Stabilization 1. “Worst case” tension crack distance is 8.6 ft for a “dry” condition condition.

9.9’

2. Assume 50% saturation for tension crack. 3. Estimate “super bolt” tension given desired bolt inclination.

55 deg slope

4. Distribute “super bolt” tension over slope face based on available bolts. 5. Make sure and “bolt” all unstable blocks.

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Case History: Rock Slope Stabilization Results: 1. 22 kips tension/ft required at 5 deg d d downward d angle l f for F = 1.5 2. Slope face length is equal to:

9.86’

V

55 deg slope

U

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Case History: Rock Slope Stabilization Recommendations: 1. 8 rows of bolts (40/5 = 8) 2. Try to bolt every block 3. Grout length determined by contractor 4. Rule of thumb, grout length; UCS/30 < 200 psi adhesion

55 deg slope

5. Contractor responsible l for f testing or rock bolts 6. Engineer responsible to “sign off” ff” on Contractors tests

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Courttesy - B. Fish her (Kleinfellder)


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ComputerComputer -Aided Planar Analysis

(R cscience – RocPlane) (Rocscience R cPlane)

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Lecture References Barton, NR & Choubey, V (1977). The shear strength of rock joints in theory and practice. Rock Mechanics 10: 1–54. Hoek, E, Kaiser, PK & Bawden, WF (1995). Support of Underground Excavations in Hard Rock. Balkema: Rotterdam. Hudson, JA & Harrison, JP (1997). Engineering Rock Mechanics – An Introduction to the Principles . Elsevier Science: Oxford. Lisle, RJ (2004). Calculation of the daylight envelope for plane failure of rock slopes. Géotechnique 54: 279-280. 279 280 Pahl, PJ (1981). Estimating the mean length of discontinuity traces. International Journal of Rock Mechanics & Mining Sciences & Geomechanics Abstracts 18: 221-228. ) The use of LiDAR to overcome rock slope p hazard data collection Strouth,, A & Eberhardt,, E ((2006). challenges at Afternoon Creek, Washington. In 41st U.S. Symposium on Rock Mechanics: 50 Years of Rock Mechanics, Golden. American Rock Mechanics Association, CD: 06-993. Wyllie, DC & Mah, CW (2004). Rock Slope Engineering (4th edition). Spon Press: London. W lli DC & Norrish, Wyllie, N i h NI (1996). (1996) Rock R k strength t th properties ti and d their th i Measurement. M t In I Landslides: L d lid Investigation and Mitigation – Special Report 247. National Academy Press: Washington, D.C., pp. 372390.

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Rock Engineering Practice & Design.pdf

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