Increases in Slope Stability of Rock/Soil Mixtures Due to Tortuosity of Failure Surfaces Around Rock...
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Transcript of Increases in Slope Stability of Rock/Soil Mixtures Due to Tortuosity of Failure Surfaces Around Rock...
Increases in Slope Stability of Increases in Slope Stability of
Rock/Soil Mixtures Due to Rock/Soil Mixtures Due to Tortuosity of Failure Surfaces Tortuosity of Failure Surfaces
Around Rock BlocksAround Rock BlocksEd Medley and Pablo Sanz RehermannEd Medley and Pablo Sanz Rehermann
Exponent Failure Analysis Associates, Menlo Park, CAExponent Failure Analysis Associates, Menlo Park, CA
GSA Conference Seattle WA November 2, 2003GSA Conference Seattle WA November 2, 2003
VER 00G64000 0000 1201 EM63
decomposed granite, Hwy 50, California
A rock/soil mixture (block-A rock/soil mixture (block-in- matrix rocks - bimrocks)in- matrix rocks - bimrocks)
soil
Corestones, (blocks)
Franciscan Complex melange
Shears in matrix negotiate around blocks
Geological engineering Geological engineering problems of block-in-matrix problems of block-in-matrix
rocks (bimrocks)rocks (bimrocks)• Often severe spatial variabilityOften severe spatial variability
• Heterogeneity in propertiesHeterogeneity in properties
• Design and construction shortcomings of Design and construction shortcomings of geo-characterizations cost $$$$geo-characterizations cost $$$$
• Not readily analyzed by current rock Not readily analyzed by current rock mechanics OR soil mechanics techniquesmechanics OR soil mechanics techniques
• Not a hot research topicNot a hot research topic
Landslide in Franciscan Landslide in Franciscan melange…melange…
block-rich melange at toe resisted block-rich melange at toe resisted movementmovement
..leading to back-facing ..leading to back-facing scarpsscarps
Blocks added strength to Blocks added strength to matrix: but matrix: but HOW MUCH??HOW MUCH??
(a motivation for this (a motivation for this analysis)analysis)
Failed physical model melangesFailed physical model melanges150 mm diameter Tx specimens 150 mm diameter Tx specimens (Lindquist, 1994)(Lindquist, 1994)
failure surfaces tortuously negotiate blocksfailure surfaces tortuously negotiate blocks
Tortuosity of failure surfaces Tortuosity of failure surfaces influenced by low block influenced by low block proportion and vertical proportion and vertical
orientationorientation
Tortuosity influenced by high Tortuosity influenced by high proportion but horizontal proportion but horizontal
orientationorientation
Tortuosity influenced by Tortuosity influenced by Block Size Distribution Block Size Distribution (BSD) and block shapes(BSD) and block shapes
Uniform BSD Graded BSD
Analyses AssumptionsAnalyses Assumptions
• matrix : Φ = 25º c = 10 kPa (~200 psf)
• block strengths not considered
• no block/matrix contact strengths
• no water
Analyses Assumptions Analyses Assumptions (cont.)(cont.)
• BSD = part 2D Franciscan (~2n 1.3)
• horizontal block orientations
• random arrays of blocks
• Areal = Volumetric block proportions
• failure surfaces pass around blocks
• 2D analyses suffice (for now…)
Model AssumptionsModel Assumptions
horizontal rectangular blocks
BSD= partial Franciscan
Random arraystrial surfaces negotiate blocks, tortuosity reflects many factors
AA=VV
5m
Some Random Block Some Random Block ArraysArrays50%
25%
50% 50%
25% 25%
13% 13% 13%
Matrix only:Matrix only: Critical failure Critical failure surfacesurface
Φ = 25º c = 10 kPa
FS ~ 1.26
1.263
Using Slope/W
Factor of Safety (FS)Factor of Safety (FS)
1.263
x
R
S
WFS= Resisting Moment
Driving Moment
RSL
Wx= L
50% block proportion 50% block proportion tortuosity lengthens failure tortuosity lengthens failure
surfacessurfaces
Critical surface for matrix only
50% block proportion: 50% block proportion: FS for a tortuous trial FS for a tortuous trial
surfacesurface
1.760
FS ~ 1.65
1.430
25% block proportion: 25% block proportion: FS for a tortuous trial FS for a tortuous trial
surfacesurface
FS ~ 1.40
13% block proportion: 13% block proportion: FS for a tortuous trial FS for a tortuous trial
surfacesurface
1.380
FS ~ 1.27
““First cut”: Slope stability First cut”: Slope stability increases with block proportionincreases with block proportion
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
0% 10% 20% 30% 40% 50% 60% 70% 80%
Block Proportion
Fac
tor
of
Saf
ety
(Jan
bu
)
μ?
μ-σ ?
μ+σ ?
threshold 15% -25%?
Conclusion: Need MANY more iterations …
Shortcomings and good Shortcomings and good intentionsintentions• Must incorporate block/matrix
contact strengths
• Must generalize procedures for other block shapes, orientations, etc.
• Must perform Monte Carlo-type analyses
• Need 3D numerical modeling to incorporate blocks
Epilogue: Recall Lindquist Triaxial Epilogue: Recall Lindquist Triaxial ModelsModels
>120 multi-stage >120 multi-stage Triaxial tests Triaxial tests performed on 150mm performed on 150mm diameter specimens diameter specimens of model melangesof model melanges
-5
0
5
10
15
20
25
30
0 20 40 60 80 100
Volumetric Block Proportion (%)
Incr.. Friction Angle, degrees
Scott Dam melange
Physical modelsIrfan and Tang, 1993
conservative trend (Lindquist 1994a)
Scott Dam melange
Bimrock strength increases with Bimrock strength increases with block proportion (>~15%-25% block proportion (>~15%-25%
VVvv))
BUT……BUT……
•Q: How does one estimate Block Proportions and their uncertainty based on the usual tools of mapping and drilling???
•A: That is stereological story (already partly told …)
Complex geological mixtures Complex geological mixtures of rock/soil (bimrocks)of rock/soil (bimrocks)
Matrix
Matrix
Willis, 2000; after Medley, 2000
Complex Geologic Mixture Complex Geologic Mixture – – As Mapped, or as drilled As Mapped, or as drilled and coredand cored
Matrix
Matrix
Willis, 2000
ConclusionsConclusions
• Slope stability of a bimrock (as Slope stability of a bimrock (as indicated by FS) depends on block indicated by FS) depends on block proportionproportion
• Increases in FS are due to Increases in FS are due to increased tortuosity related to increased tortuosity related to orientation, shape, BSD, block orientation, shape, BSD, block proportion, etc.proportion, etc.
• Current 2D analytical tools are very Current 2D analytical tools are very limited for investigationlimited for investigation
• Need Monte Carlo-type analyses Need Monte Carlo-type analyses with 3D numerical modelingwith 3D numerical modeling