Rock slope failure along non persistent joints insights from fracture mechanics approach
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1 Rock slope failure along non persistent joints insights from fracture mechanics approach Louis N.Y. Wong PhD(MIT), BSc(HKU) Assistant Professor and Assistant Chair (Academic) Nanyang Technological University, Singapore Slope Stability First Principle of Slope Engineering All slopes are potentially unstable.
2 Stability is controlled by Material type and properties of rock slope Geological structures (faults, joints, etc) Geometry of slope External factors (weather, water, seismic events, blasting, excavation, etc) Rock slopes are predominantly structurally controlled (discontinuities) design.co.uk/wp content/uploads/2010/06/ting Kau Bridge Approach Road Rock Slopes Hong Kong.jpg 3 Tennessee Rock Slope Failure 4
3 Failure Modes of Rock Slopes 5 Plane (Planar) rock slope failure Sliding of a rock mass along a relatively planar failure surface. Why meta stable? Shear strength of rock joint Rock bridge strength 6
4 Rock Joint Survey - Important geomechanical properties of discontinuities Orientation Spacing Persistence Roughness Aperture Filling Wall strength Seepage Number of sets Block size 7 Joint Persistence 8
5 Plane Failure Analysis based on water filled critical tension crack depth Other forces: Surcharge on top of slope Ground water (pushing and reduction in normal force) Reinforcement (tension, load capacity) Earthquakes (horizontal acceleration) Hoek: Practical Rock Engineering 9 Analytical approach (a, b) 10 Jennings, J.E. (1970) A Mathematical theory for the calculation of the stability of slopes in open cast mines. in Planning of Open Pit Mines, Proceedings, Johannesburg;
6 Analytical approach (c) Jaeger, J.C. (1971) Friction of rocks and stability of rock slopes. Geotechnique; 21: tensile tensile Enchelon cracking trajectory 12
7 Typical Stress-Strain Curve in Rock (lab scale) σ 1 σ1 ε 2 ε 1 Micro-crack Crack coalescence?? Habib, P. (1983) An outline of soil and rock mechanics, Cambridge University Press. 13 Fracture Mechanics Approach Two scenarios Initiation of new cracks in intact material Propagation from existing crack tip Let s see the mechanics 14
8 Fracture Mechanics Approach new crack initiation in intact material For shear crack For tensile crack σ 1 σ c cos σ + = i φ i + σ sin φ i, σ3 > σ t 2 2 σ = σ 3 t where c i and φ i are the cohesion and friction angle of the intact material σ 1 and σ 3 are the maximum principal stress and the minimum principal stress, respectively 15 Fracture Mechanics Approach Propagation from existing crack tip θ θ 3 K K θ = K cos ( 0 I cos II sin 0) IC where K I and K II are the mode I and mode II stress intensity factors respectively K IC is the mode I fracture roughness and the propagation angle θ 0 can be obtained by the following equation: 2 2 KI KI + 8KII 2arctan( ) KII = 0 θ0 = 4KII 0 KII 0 16
9 Slope geometry 17 slope containing one pre existing discontinuity crack initiation crack coalescence with the slope surface slope failure 18
10 slope containing four pre existing discontinuities crack coalescence Further crack coalescence slope failure 19 SF calculation is based on successively increasing the acceleration of gravity until the slope fails. Factor of Safety (SF) SF = g trial g 0 g 0 = acceleration of gravity in the initial state g trial = acceleration of gravity at failure Li, L.C., C.A. Tang, W.C. Zhu, and Z.Z. Liang (2009) Numerical analysis of slope stability based on the gravity increase method. Computers and Geotechnics; 36:
11 Factor of Safety (SF) continuous discontinuity. Displacement-dependent cohesion reduction method (Wang et al. 2013) - cohesion between the discontinuity surfaces degrades with increasing movement along the surfaces. - enables relative movements between contact pairs and the removal of the cohesion based on the accumulated relative sliding Wang, L.Z., et al. (2013) Development of discontinuous deformation analysis with displacementdependent interface shear strength. Computers and Geotechnics; 47: Factor of Safety (SF) coplanar non persistent discontinuity 22
12 Factor of Safety (SF) stepped non persistent discontinuity 23 Experimental study Geometry representation L β α, e.g. 2a a = half flaw length 24
13 Carrara Marble Water Abrasive Jet Flaw length 13mm (0.5 ) Flaw aperture 1.3mm (0.05 ) 25 OMAX water abrasive jet 26
14 Uniaxial Compression Loading Test High Speed Camera 27 Normal Speed vs High Speed videos Normal speed video σ 1 High speed video L = 2a 2000 frames per second (-500) Video played at 45 times slower 28
15 Results generalized crack types Type 1 tensile crack (tensile wing crack) Type 2 tensile crack Type 3 tensile crack Mixed tensile-shear crack Type 1 shear crack Type 2 shear crack Type 3 shear crack 29 Next Step Fundamental Crack Types Coalescence Patterns 30
16 Results coalescence categories (1) No coalescence (2) Indirect coalescence (3) Type 2 shear crack(s) (4) Type 1 shear crack(s) (5) Mixed sheartensile crack(s) (3) (9) Direct coalescence (6) Type 2 tensile crack(s) (7) Type 1 tensile cracks (8) Tensile crack (type not assigned) (9) Type 3 tensile cracks 31 Conclusions Progressive rock slope failure requires the consideration of two factors slide plane development internal rock mass deformation/degradation Fracture mechanics approach Crack tip Intact rock Conventional approach Assumed to be persistent Failed when tensile strength or shear strength is overcome 32
17 Thank you Louis N.Y. Wong PhD(MIT), BSc(HKU) Nanyang Technological University, Singapore
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