Increases in Slope Stability of Rock/Soil Mixtures Due to Tortuosity of Failure Surfaces Around Rock Blocks Increases in Slope Stability of Rock/Soil Mixtures Due to Tortuosity of Failure Surfaces Around Rock Blocks Ed Medley and Pablo Sanz Rehermann Exponent Failure Analysis Associates, Menlo Park, CA GSA Conference Seattle WA November 2, 2003 VER 00G EM63

decomposed granite, Hwy 50, California A rock/soil mixture (block-in- matrix rocks - bimrocks) soil Corestones, (blocks)

Franciscan Complex melange Shears in matrix negotiate around blocks

Geological engineering problems of block-in-matrix rocks (bimrocks) Often severe spatial variability Often severe spatial variability Heterogeneity in properties Heterogeneity in properties Design and construction shortcomings of geo-characterizations cost $$$$ Design and construction shortcomings of geo-characterizations cost $$$$ Not readily analyzed by current rock mechanics OR soil mechanics techniques Not readily analyzed by current rock mechanics OR soil mechanics techniques Not a hot research topic Not a hot research topic

Landslide in Franciscan melange…

block-rich melange at toe resisted movement

..leading to back-facing scarps

Blocks added strength to matrix: but HOW MUCH?? (a motivation for this analysis)

Failed physical model melanges 150 mm diameter Tx specimens (Lindquist, 1994) failure surfaces tortuously negotiate blocks

Tortuosity of failure surfaces influenced by low block proportion and vertical orientation

Tortuosity influenced by high proportion but horizontal orientation

Tortuosity influenced by Block Size Distribution (BSD) and block shapes Uniform BSDGraded BSD

Analyses Assumptions matrix : Φ = 25º c = 10 kPa (~200 psf) block strengths not considered no block/matrix contact strengths no water

Analyses Assumptions (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 Assumptions horizontal rectangular blocks BSD= partial Franciscan Random arrays trial surfaces negotiate blocks, tortuosity reflects many factors A A =V V 5m

Some Random Block Arrays 50% 25% 50% 25% 13%

Matrix only: Critical failure surface Φ = 25º c = 10 kPa FS ~ 1.26 Using Slope/W

Factor of Safety (FS) x R S W FS = Resisting Moment Driving Moment RSL Wx = L

50% block proportion tortuosity lengthens failure surfaces Critical surface for matrix only

50% block proportion: FS for a tortuous trial surface FS ~ 1.65

25% block proportion: FS for a tortuous trial surface FS ~ 1.40

13% block proportion: FS for a tortuous trial surface FS ~ 1.27

“First cut”: Slope stability increases with block proportion μ? μ-σ ? μ+σ ? threshold 15% -25%? Conclusion: Need MANY more iterations …

Shortcomings and good intentions 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 Models >120 multi-stage Triaxial tests performed on 150mm diameter specimens of model melanges

Bimrock strength increases with block proportion (>~15%-25% V v )

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 of rock/soil (bimrocks) Matrix Willis, 2000; after Medley, 2000

Complex Geologic Mixture – As Mapped, or as drilled and cored Matrix Willis, 2000

Conclusions Slope stability of a bimrock (as indicated by FS) depends on block proportion Slope stability of a bimrock (as indicated by FS) depends on block proportion Increases in FS are due to increased tortuosity related to orientation, shape, BSD, block proportion, etc. Increases in FS are due to increased tortuosity related to orientation, shape, BSD, block proportion, etc. Current 2D analytical tools are very limited for investigation Current 2D analytical tools are very limited for investigation Need Monte Carlo-type analyses with 3D numerical modeling Need Monte Carlo-type analyses with 3D numerical modeling