1. Lecture 12
Yield Zones
Deep Excavations and
Rock Burst Conditions

2. Triaxial (Compression) Test1
cell
2= 3
Rubber sleeve
specimen
Hoek Triaxial Cell

3. Triaxial (compression) test

4. Deformation mechanisms
After Rutter, The Mechanics of Natural rock Deformation. In Comprehensive Rock Engineering, Pergamon Press. Vol.1, pp

5. Rock-support interaction analysis
Where n is the gradient of the 3 versus 1 plot (poisson’s ratio).

6. Yield Zone

7. Yield zone width
Zone
Yield criterion
Elastic
1 = C0 + b3
Fractured
1 = d3
(1)
(2)
For the hydrostatic case the radial and circumferential stresses are given by:
(3)
(4)

8. Since the problem is axisymmetric, there is one differential equation of equilibrium:
(5)

9. substituting (7) in (6) gives:
This simplifies to:
(6)
From (2) we can see that:
(7)
substituting (7) in (6) gives:
(8)

10. Integrating this expression and introducing the boundary condition, r = Pi when r = a, yields the stress distribution relations:
(9)
(10)
Equations (9) and (10) are satisfied throughout the fractured domain and on its boundaries. At the outer limit of the yield zone, fractured rock is in equilibrium with the intact, elastic rock. If P is the equilibrium radial stress at the outer boundary, R: or
(11)
(12)

11. Simple superposition indicates that the stress distribution in the elastic zone is defined by:
(13)
and,
(14)
Therefore, at the inner boundary of the elastic zone (r = R), the state of stress is given by:
(15)
and,
(16)

12. substituting in (12) gives:
This state of stress must represent the limiting state for intact rock. Substituting in (1) gives:
(17)
and,
(18)
substituting in (12) gives:
(19)

13. Alternative models #
Elastic
Fractured
R/a 1 2 3

14. Alternative models #
Elastic
Fractured
R/a 4 5

15. where, = triaxial stress factor c = Unconfined compressive strength cr = Residual strength of broken rock t = tensile strength a = Radius of excavation R = Radius of yield zone perimeter pi = Support pressure B, b define the curvature of the failure envelope for broken rock

17. Rock A
c=30 MN m-2, kp=4,
t=10 MN m-2, B=4.82, b=0.709
Rock B
c=10 MN m-2
kp=2.5,
t=1 MN m-2, B=4.07,
b=0.74

18. Volumetric closure
It is possible to estimate the extent of excavation closure by measuring the volumetric expansion of laboratory specimens at a confining stress representative of the average level in the yield zone = 0.250.  = estimated bulking factor

19. Rock bursts
“A sudden and violent failure of overstressed rock resulting in the instantaneous release of large amounts of accumulated energy.”

20. Rock bursts in tunnelling
Although originally identified in deep mines in South Africa, India, Canada and USA, problems associated with rock burst conditions are becoming increasingly common in civil engineering projects.
Tunnels through mountain ranges are often at depths of 1000 m to 2000 m below ground level and there rock bursts pose a significant risk.
Rock bursts have occurred in civil engineering tunnels in Chile, China, Norway, Canada and the Andes.

21. Olmos trans-Andean tunnel
A 5.3 m-dia. Robbins unshielded main beam TBM.
13.8 km-long tunnel through the Andes.
Complex geology consisting of quartz porphyry, andesite, and tuff from 60 to 225 MPa UCS.
One of the deepest tunnelling projects in the world with 1,931 metres of overburden at its deepest point.

22. The Jinping II Hydropower Station
After C. Zhang, X. Feng, H. Zhou, S. Qiu & W. Wu, Case Histories of Four Extremely Intense Rockbursts in Deep Tunnels. Rock Mech. Rock Eng. Pub.online

26. Key Factors Rock bolt reinforcement too short
Location and orientation of local faults
High in situ stress
Brittle rock - marble

27. After C. Zhang, X. Feng, H. Zhou, S. Qiu & W. Wu, 2011
After C. Zhang, X. Feng, H. Zhou, S. Qiu & W. Wu, A Top Pilot Tunnel Preconditioning Method for the Prevention of Extremely Intense Rockbursts in Deep Tunnels Excavated by TBMs. Rock Mech. Rock Eng. Pub. online

28. Laerdal Tunnel, Norway 24.5 km long
www. hannekevanwell.web-log.nl

29. Laerdal Tunnel, Norway
Tunnel excavated by conventional drill and blast methods.
Support comprised galvanised steel rockbolts (2m to 5m long) and fibre reinforced shotcrete.

30. http://www. engineering
The Laerdal tunnel excavated through with Pre-Cambrian gneiss at depths of up to 1400 metres below surface.
Rock burst conditions were present due to the high in situ rock stresses.

31. Seymour-Capilano Tunnels, Vancouver
TBM’s excavating the Seymour-Capilano twin tunnels in Vancouver were stopped in January 2008 due to concerns regarding tunnel safety.
At a depth of approximately 550m below ground level the TBM’s encountered weak rock which fell from the tunnel crown.
Although the failure was not of an explosive nature there was evidence of stress relief.

32. Seymour-Capilano Tunnels

33. Seymour-Capilano Tunnels

34. Rock burst Conditions
Generally found in deep excavations in brittle rocks.
Much research into rock bursts has been carried out in South Africa in the deep gold mines, where the development tunnels are excavated in very strong, brittle quartzite.
Large in situ rock stress either through depth or large horizontal stresses.

35. Rock burst in brittle rock under very high stress
E.Hoek

36. Cause of rock bursts
Failures known as spalling, popping or rock burst are caused by overstressing of brittle, massive rocks at depth.
These failures can also be induced at shallower depth where high horizontal stresses or strongly anisotropic stresses are acting.

37. Microcrack development
Compare Griffith theory
In tunnels, results from removal of confining stress and increased tangential stress. Cracks extend parallel to the excavation wall.

38. 3-D crack growth in uniaxial compression
After A. V. Dyskin, E Sahouryeh, L. N. Germanovich
cross-section
plan

39. Unconfined Compression Test
Crack growth typically starts around 0.3–0.5 sc &
increases until macroscopic failure takes place.

40. “Around an underground opening, this behaviour is significantly modified. Instead of a simple monotonic loading path, the rock mass in the field undergoes a specific stress–strain history, which causes the stress level for crack coalescence to drop to a much lower value. Typically, in massive and moderately jointed hard rock masses, brittle failure occurs around 0.3–0.5 sc, i.e. near or slightly above the stress level required for damage initiation.”
F. Rojat,V. Labiouse, P. K. Kaiser & F. Descoeudres, Brittle Rock Failure in the Steg Lateral Adit
of the Lo¨tschberg Base Tunnel. Rock Mech Rock Eng 42:341–359

41. - Hoek and Brown
F. Rojat,V. Labiouse, P. K. Kaiser & F. Descoeudres, Brittle Rock Failure in the Steg Lateral Adit
of the Lo¨tschberg Base Tunnel. Rock Mech Rock Eng 42:341–359

42. After M. S. Diederichs, P,K,Kaiser, E. Eberhardt, 2004
After M.S. Diederichs, P,K,Kaiser, E.Eberhardt, Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation. Int.J.Rock Mech.& Min.Sci., 41, pp

43. Kaiser PK, Diederichs MS, Martin CD, Sharp J, Steiner W (2000) Underground works in hard rock
tunnelling and mining. In: Keynote lecture at GeoEng2000, Melbourne, Australia Technomic
Publishing Co., Melbourne, Australia, p 841–926
Relationship between depth of failure, stress level and Barton’s stress reduction factor (SRF)

44. Overstressed weaker rocks
Squeezing can occur both in massive (weak and deformable) rocks and in highly jointed rock masses as a result of overstressing.
It is characterized by yielding under the redistributed state of stress during and after excavation.
The squeezing can be very large; deformations as much as l7% of the tunnel diameter have been reported in India.

45. Influence of discontinuities on rock bursts
Buckling of rock slabs is driven by the release of gravitational and elastic potential energy (A).

46. A weak discontinuity can dramatically increase the amount of energy released, resulting in a more hazardous
rock burst (B).

47. Assessment of rock burst risks
Various attempts have been made to quantify the likelihood of rock bursts occurring.
Hoek and Brown produce a simple relationship between the uniaxial compressive strength of the rock and the vertical applied load
This work was largely based on tunnels of square cross section in brittle quartzites.

48. Assessment of rock burst risks
Vertical applied stress = pz
Uniaxial compressive strength = sc
pz /sc = stable unsupported tunnel
pz /sc = minor sidewall spalling
pz /sc = severe sidewall spalling
pz /sc = heavy support required
pz /sc = possible rock burst conditions

49. Assessment of rock burst risks
The Rock Mass index (RMi) characterises the strength of rock masses and can be applied directly in stability analyses.
The competency factor (Cg) expressed as the ratio between rock mass strength and the tangential stress (sq) around the opening (Cg = RMi/ sq) is applied to indicate whether the ground is overstressed or not.

50. Assessment of rock burst risks
The rock mass index is given as
RMi = sc .JP where JP, the jointing parameter, is a measure for the intensity of jointing (given as block size) and the joint characteristics (Palmström).
In massive rock where the jointing parameters
JP = 1, the rock mass index is RMi = fs. sc and
Cg = RMi/ sq = fs. sc/sq
fs is the scale effect for the compressive strength given as fs = (50/d) 0.2
(d is the block diameter measured in mm).
In highly jointed and crushed rock masses Cg = sc .JP /sq
Cg = RMi/ sq

51. Rock burst risk based on tangential stress and point load strength
A. Palmström, Characterizing Rock Burst and Squeezing by the Rock Mass Index. Design & Construction of Underground Structures, New Dehli.pp.10.

52. Assessment of rock burst risks
Palmström, 1995

53. Palmström, 1995

54. Empirical criterion
After Kumar, Reported in B.Singh & R.K.Goel, Tunnelling in Weak Rocks.Elsevier. P.489

55. Overstressing in weak rocks
In weaker materials high in situ stresses cause squeezing of the tunnel perimeter.
The squeezing can occur not only in the roof and walls, but also in the floor of the tunnel.
Squeezing is related to time-dependent shearing i.e. shear creep.
A general opinion is that squeezing is associated with volumetric expansion (dilation), as the radial inward displacement of the tunnel surface develops.

56. Modes of squeezing failure
Aydan Ö., Akagi T. andKawamoto T The squeezing potential of rocks around tunnels;theory and prediction. Rock Mech. Rock Engn, No. 26, pp quoted in Palmstrom 1995

57. Estimating squeezing potential
For straight line fits:
NS = no squeeze
LS = light squeeze
FS = fair squeeze
HS = high squeeze
Aydan Ö., Akagi T. andKawamoto T The squeezing potential of rocks around tunnels;theory and prediction. Rock Mech. Rock Engn, No. 26, pp quoted in Palmstrom 1995

58. Avoiding rock bursts ‘Perfect support’
Reduce rate of advance – rock absorb strain energy through creep.
Destressing by inducing yield zone around opening with radius >b.
Support system should be slow and ductile.
Support pressure:
After Kumar, Reported in B.Singh & R.K.Goel, Tunnelling in Weak Rocks.Elsevier. P.489
f = correction factor for H
Q = post-construction rock mass quality