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

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) appears to depend indicated by FS) appears to depend on block proportionon block proportion

• 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