8 slope stability

10
Slope Stability updated June 7, 2007 Haryo Dwito Armono, M.Eng, Ph.D

Transcript of 8 slope stability

Page 1: 8 slope stability

Slope Stability

updated June 7, 2007

Haryo Dwito Armono, M.Eng, Ph.D

Page 2: 8 slope stability

Types of Slope FailuresTypes of Slope Failures

FallsFalls

Topless

Slides

Spreads

Flows

Falls

Slope failures consisting

Topless

Similar to a fall,p gof soil or rock fragments that droprapidly down a l

except that it begins with a mass of rock of stiff l t ti fslope

Most often occur in steep rock slopes

clay rotating away from a vertical joint

steep rock slopes

Usually triggered by water pressure orwater pressure or seismic activity

Page 3: 8 slope stability

Slides

Slope failures that

Spreads

Similar to translational pinvolve one ore more blocks of earth that

d l b

slides except that the block separate and

t th lmove downslope by shearing along well defined surfaces or thin

move apart as they also move outward

Can be very destructivedefined surfaces or thin shear zones

Can be very destructive

Flows

Downslope movement of

Types of Slides

Rotational slidespearth where earth resembles a viscous fl id

Most often occur in homogeneous materials such as fills or soft claysfluid

Mudflow can start with a snow avalanche or be in

such as fills or soft clays

Translational slidesMove along planar shearsnow avalanche, or be in

conjuction with flooding

Move along planar shear surfaces

Compound slides

Complex and composite slides

Page 4: 8 slope stability

The driving force (gravity) overcomes the g (g y)resistance derived from the shear strength of the soil along the rupture surfaceg p

Slope stability analysisSlope stability analysis

Calculation to check the safety of naturalCalculation to check the safety of natural slopes, slopes of excavations and of

t d b k tcompacted embankments.

The check involves determining and comparing the shear stress de elopedcomparing the shear stress developed along the most likely rupture surface to the shear strength of soil.

Page 5: 8 slope stability

Factor of SafetyFactor of Safetyf

sd

Fττ

=

factor of safety with respect to strength

average shear strength of the soil

average shear stress developed along the potential failure surface

d

f

d

Fs

ττ

==

= a e age s ea st ess de e oped a o g t e pote t a a u e su ace

tan

cohesion

d

f c

c

τ

τ σ φ= +

= cohesion

angle of friction

av

c

φσ

== erage normal stress on the potential failure surface

tan

subscript 'd' refer to potential failure surfaced d d

similarly

cτ σ φ= +

s

p p

tanF =

tand d

c

c

σ φσ φ

++

when Fs = 1, the slope is in a state of impending of failured dφ

.

In general Fs > 1.5 is acceptable

Stability of SlopeStability of Slope

Infinite slope without seepageInfinite slope without seepage

Infinite slope with seepage

Finite slope with Plane Failure Surface (Cullman's Method)(Cullman s Method)

Finite slope with Circular Failure Surface(Method of Slices)

Page 6: 8 slope stability

Infinite slopeInfinite slope

β

L

β

L tancFs

φ= +β

WF

B

d

a

T

Na

β

WF

B

d

a

T

Na

2cos tan tanFs

Hγ β β β= +

For granular soils c=0 Fs is independent

βR

F

H

A

c

b

Ta

Tr

NrβR

F

H

A

c

b

Ta

Tr

Nr

For granular soils, c 0, Fs is independent of height H, and the slope is stable as long as β < φ

RR

LL

W

Direction of seepage

d

a

N

L

W

Direction of seepage

d

a

N

L

' tancF

γ φ

β

H

B

c

b

Ta

Na

Trβ

H

B

c

b

Ta

Na

Tr

2cos tan tansat sat

FsH

γ φγ β β γ β

= +

β βRA

r

Nr

β βRA

r

Nr

Finite slope with Plane Failure SurfaceFinite slope with Plane Failure Surface

W

B C

β φ+W

Ta

Na

tan

unit weight of soil

f cτ σ φγ

= +=H

2d

cr

β φθ

+=

RTr Nr

Aβ θ

unit weight of soil γ=

4 sin cos

1 cos( )cr

cH

β φγ β φ

⎡ ⎤= ⎢ ⎥− −⎣ ⎦A ( )γ β φ⎣ ⎦

Page 7: 8 slope stability

Finite slope with Circular Failure SurfaceFinite slope with Circular Failure Surface

Slope Failure Shallow Slope FailureSlope Failure Shallow Slope FailureO

Toe Circle

Firm Base

OBase Failure

L L

O

L L

Slope Circle

Firm Base

Midpoint circle

Firm BaseFirm Base Firm Base

Slopes in Homogeneous Clay (φ=0)Slopes in Homogeneous Clay (φ=0)For equilibrium, resisting and driving moment about O:

M M OOR d

2d 1 1 2 2

1 1 2 2

M = M

c r W l W l

W l W l

θ = −

O

Radius = r

C Dθ

O

Radius = r

C Dθf ucτ =

1 1 2 2d 2

cr

c

W l W l

θ= l2 l1

A B

FW1

cdH

l2 l1

A B

FW1

cdH

u

d d

c

c c

critical when Fs is minimum, trials to find critical plane

fFsτ

= =

→E

W2

cd cd

Nr (normal reaction)E

W2

cd cd

Nr (normal reaction)

solved analitically by Fellenius (1927) and Taylor (1937)

cucr

cH =

m

presented graphically by Terzaghi &Peck, 1967 in Fig 11.9 Braja

γ

m is stability number

Page 8: 8 slope stability

Swedish Slip Circle Method

Slopes in Homogeneous Clay (φ>0)Slopes in Homogeneous Clay (φ>0)tanf cτ σ φ= +f φ

( )dc , , ,H fγ α β θ φ⎡ ⎤= ⎣ ⎦

( ), , ,c

f mH

α β θ φ= =( )

where m is stability numbercrHγ

Page 9: 8 slope stability

Method of SlicesMethod of Slices

For equilibrium

α= cosr n nN W

( )α φ=

=

Δ +=

∑1

cos tann p

n n nn

c L WFs

α=

=

=

∑1

sinn p

n nn

FsW

αΔ ≈ th where b is the width of n slice

cosn

nn

bL

n

Bishop MethodBishop MethodBishop (1955) refine solution to the previous method of slices.In his method, the effect of forces on the sides of each slice are accounted for some degree .

= 1n p

( )α

φ

α

=

=

+=

∑1 ( )

1tan

sin

n p

n nn n

n p

n n

cb Wm

FsW

φ αα

=

= +

∑1

tan sincos

n nn

n

where

mα α= +( ) cosn nmFs

The ordinary method of slices is presented as learning tools It is rarely used because is toolearning tools. It is rarely used because is too conservative

Page 10: 8 slope stability

Computer ProgramsComputer Programs

STABLSTABL

GEO-SLOPE

etc

BibliographyBibliographyHoltz, R.D and Kovacs, W.D., “An Introduction to GeotechnicalHoltz, R.D and Kovacs, W.D., An Introduction to Geotechnical

Engineering”

Das, B.M., “Soil Mechanics”

Das, B.M., “Advanced Soil Mechanics”