Ed Medley and Pablo Sanz Rehermann Exponent Failure Analysis Associates, Menlo Park, CA

1. 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

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

3. Franciscan Complex melange Shears in matrix negotiate around blocks

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

5. Landslide in Franciscan melange…

6. block-rich melange at toe resisted movement

7. ..leading to back-facing scarps

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

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

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

11. Tortuosity influenced by high proportion but horizontal orientation

12. Uniform BSD Graded BSD Tortuosity influenced by Block Size Distribution (BSD) and block shapes

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

14. 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…)

15. horizontal rectangular blocks BSD= partial Franciscan Random arrays trial surfaces negotiate blocks, tortuosity reflects many factors Model Assumptions AA=VV 5m

16. 50% 50% 50% 25% 25% 25% 13% 13% 13% Some Random Block Arrays

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

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

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

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

21. 25% block proportion: FS for a tortuous trial surface FS ~ 1.40

22. 13% block proportion: FS for a tortuous trial surface FS ~ 1.27

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

24. 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

25. Epilogue: Recall Lindquist Triaxial Models >120 multi-stage Triaxial tests performed on 150mm diameter specimens of model melanges

26. 30 Scott Dam melange 25 Physical models Irfan and Tang, 1993 20 Scott Dam melange 15 10  Incr.. Friction Angle, degrees 5 conservative trend 0 (Lindquist 1994a) -5 0 20 40 60 80 100 Volumetric Block Proportion (%) Bimrock strength increases with block proportion (>~15%-25% Vv)

27. 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 …)

28. Matrix Matrix Complex geological mixtures of rock/soil (bimrocks) Willis, 2000; after Medley, 2000

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

30. Conclusions • Slope stability of a bimrock (as indicated by FS) appears to depend on block proportion • 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 • Need Monte Carlo-type analyses with 3D numerical modeling