# Stability of rock blocks - .Influence of water on slope stability EPFL -LMR Sliding stability of

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1

COLE POLYTECHNIQUEFDRALE DE LAUSANNE

L M RRock mechanics

LABORATOIRE DEMCANIQUE DES ROCHES

V. Labiouse, J. Abbruzzese

Stability of rock blocks

EPFL - LMR

Stability of rock blocks

1. Stability of one block

2. Stability of a column

3. Stability of two blocks

4. Stability of several blocks (fauchage)

5. Influence of water on slope stability

EPFL - LMR

Sliding stability of a block

W cos

W sin

W = N/A = W cos /A

b h

res = tan + c*

sol = T/A = W sin /A

EPFL - LMR

W cos

W sin

W

b h

W sin /A < (W cos /A) tan + c* sol < res = tan + c*

Stable if

Sliding stability of a block

2

EPFL - LMR

Safety Factor with respect to sliding :

solsol

ress

ctanF

+=

=

W

b h

+

=

sinWAc

tantanFs

+=

sinAW

ctancosAW

Fs

Sliding stability of a block

EPFL - LMR

>

<

=

Sliding

Stable

Stability limit

Sliding of a block on a smooth plane (c* = 0)

EPFL - LMR

SlidingStable

tan

b/h

> <

tan

Sliding of a block on a smooth plane (c* = 0)

EPFL - LMR

W cos

W sin

W

Mdestabilizing,0 = W sin . h/2 b

h

Toppling stability of a block

Toppling instability occurs if the direction line of the weight vector Wintersects the slope surface beyond the base of the column.

destab,0 < stab,0Stable if

0

Mstabilizing,0 = W cos . b/2

tan < b/h

3

EPFL - LMR

W cos

W sin

W

b

h

Safety Factor with respect to toppling :

==

tanhb

MM

F0,dstab

0,stabs

Toppling stability of a blockEPFL - LMR

b/h < tan

b/h > tan b/h = tan

Toppling

Stable

Stability limit

b

h

Toppling stability of a block

EPFL - LMR

Toppling

Stable

tan

b/h

b/h < tan

b/h > tan

b / h= t

an

Toppling stability of a blockEPFL - LMR

Sliding and toppling stability of a block on a smooth plane (c* = 0)

Sliding

Stable

tan

tan

b/h

b / h= t

an

Slidingand

Toppling

Toppling

4

EPFL - LMR

Safety Factor with respect to sliding :

A

+

=

sinWAc

tantanFs

res = tan + c*

WCG

Sliding stability of a columnEPFL - LMR

==

tanhb

MMF

CG

CG

dstab

stabsCG

bCG

hCG

Toppling instability occurs if the direction line of the weight vector Wintersects the slope surface beyond the base of the column.

Toppling stability of a column

Safety Factor with respect to toppling :

EPFL - LMR

Sliding and toppling stability ofrock columns

EPFL - LMR

Stability of two blocks

Toppling of the two blocks

Toppling and sliding

Stability of the two blocks

5

EPFL - LMR

The fauchage phenomenon

Toppling in layered or

fractured rocks

characterized by a

system steeply dipping

into the slope EPFL - LMR

b

huu = w h cos

Pressure distributions for allowed seepage

0

Hypotheses:1. Hydrostatic along the

rear fracture2. Flow with constant

gradient in the basaldiscontinuity

u0 = 0

V

UV = w h2 cos U = w h b cos

EPFL - LMR

W cos

W

b

h

res = tan + c* V

U

W sin

= N/Asol = T/A

Sliding stability for allowed seepage

0N = W cos - UT = W sin + V

Stable if sol < res

Stability highly endangered

EPFL - LMR

W cos

W

b

h

V

U

W sin

Toppling stability for allowed seepage

0

Mdestabilizing,0 = W sin . h/2 + V. h/3 + U. 2b/3

destab,0 < stab,0Stable if

Mstabilizing,0 = W cos . b/2

Stability highly endangered

6

EPFL - LMR

Pressure distributions if no outflow possible

b

h

V

U

u0

u = w h cos

Hypotheses:1. Hydrostatic along the

rear fracture2. No outflow at the toe of

the basal discontinuity

u0 = w (h cos + b sin )

V = w h2 cos U = w b (2h cos + b sin )

COLE POLYTECHNIQUEFDRALE DE LAUSANNE

L M RRock mechanics

LABORATOIRE DEMCANIQUE DES ROCHES

V. Labiouse, J. Abbruzzese

Plane slide

EPFL - LMR

Stability of a plane slide

1. Kinematical conditions

2. Sliding along a plane

3. Sliding along a plane, with a rear tension crack

4. Stabilising measures

Control of water

Pre-tense anchors (active)

Grouted bar bolts (passive)

EPFL - LMR

Plane slide on the D526 roadconnecting Mens and Clelles (Isre France)

http://www.irma-grenoble.com/

7

EPFL - LMR

Plane slide in layered rocksin Sylans (France)

EPFL - LMR

When is a sliding mechanism possible ?

Yes No

NoNoautomatic detection of potential sliding planes, based on the use

of DTM25.

examplefor plane sliding

EPFL - LMR

Slide on a single plane joint: dry slope

Factor of safety:max. shear strengthapplied shear stressFS =

- applied shear stress:sol = (T/A) = W/A sin

A = L x 1 (m)= (N/A) = W/A cos = (T/A) = W/A sin c*= 0

=

=tantan

sinWtancosWFS

- max. shear strength:res = tan + c*

= (N/A) tan

W cos W

W sin

L

EPFL - LMR

U

Hw

Slide on a single plane joint: role of water

U = resultant of the pore water pressure distribution, as a function of the hydraulic conditions

( )

=

sinWtanUcosWFS

res = ( - u) tan res =[ (Wcos-U)/ ] tan

The maximum shear strength on the failure surface is reduced

W cos W

W sin

L

8

EPFL - LMR

Slide on a single joint (with tension crack)

Seepage allowedActions due to water presence:

1. Hydrostatic pressure in the tension crack;

2. Seepage through the joint at the base.

at the toe of the tension crack:u = w hw

L

V

UW cos

W

W sin u

hw

2ww h2

1V = Lh21U ww=

EPFL - LMR

Slide on a single joint (with tension crack)

Seepage allowedstability against sliding

: = W cos U V sin : = W sin + V cos

( )+

+=

cosVsinWA*ctansinVUcosWFS

Shear strength reduced and applied forces increasedstability highly endangered.

L

V

UW cos

W

W sin u

hw

EPFL - LMR

Slide on a single joint (with tension crack)

No outflow possible (at 0)Actions due to water presence:

1. Hydrostatic pressure inthe tension crack;

2. No water flow; Hydrostatic pressure in the failure plane.

at the toe 0 of the basal plane:u = w (hw+ L sin)

L

V

UW cos

W

W sin u

hw

0

2ww h2

1V = ( )2

sinLh2LU ww +=

EPFL - LMR

1. Surface drainage(cut-off ditch)

2. Pumping from wells3. Gravity drainage of

the rear tension crack4. Gravity drainage of

the basal plane5. Drainage gallery and

radial drains

Methods to control water in jointed rock slopes

1.2.

3.

4.

9

EPFL - LMR

Support methods: active measures

Pre-tension active anchors

Free length

Spiral winding cables or rodsGrouted zone

Fixed anchor length

EPFL - LMR

: = Wcos - U - Vsin + Pa sin( + ) : = Wsin + Vcos - Pa cos( + )

V

UW cos

W

W sin

Pa

Pa cos( + )

Pa sin( + )

Support methods: active measures

EPFL - LMR

V

UW cos

W

W sin

Pa

Pa cos( + )

Pa sin( + )

Support methods: active measures

( )( )( )++

++=

cosPcosVsinWtansinPsinVUcosWFS

a

a

The pre-tension of anchors both increases N and

decreases T, thus improving the stability of the slope.

EPFL - LMR

Support methods: passive measures

Grouted boltsGrouting all along the bars length

Thread bar Grouted zone

Passive anchors increasethe rock mass cohesion(Bjurstrm, 1974):

f

ca

aa S

SC

=

Sa = area of bars transversal sectionS = area of the surface reinforced by boltsa = shear strength of the bar (a 0.6 f)c = rocks compressive strengthf = yielding stress of the bars material (steel)

! Take care that there is also tension in the bolts in addition to bending and shear stresses

10

EPFL - LMR

Support methods: passive measures

: = Wcos - U - Vsin : = Wsin + Vcos

V

UW cos

W

W sin T

ScS*ctanNFS a ++=

! either c*S or caS(do not add contributions)

EPFL - LMR

Support methods: passive measures

TS*ctanNFS +=

( )+

+=

cosVsinWSCtansinVUcosWFS a

V

UW cos

W

W sin

COLE POLYTECHNIQUEFDRALE DE LAUSANNE

L M RRock mechanics

LABORATOIRE DEMCANIQUE DES ROCHES

V. Labiouse, J. Abbruzzese

Wedge slide

EPFL - LMR

Wedge slide above the road of Cogne (Italy)

http://www.crealp.ch/

Wedge sliding on

two intersecting

discontinuities

11

EPFL - LMR

Wedge sliding stability

Vertical plane Transverse section to i direction

Sliding failure of a rock wedge on the S1 and S2planes, which define an intersection line