Geology 3.pdf

7/30/2019 Geology 3.pdf

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Geology 229Engineering and Environmental

GeologyLecture 26

Mass Movement andLandslides (Cont. see Ch. 14)


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Quantitative Analysis of Landslides

1. Definition of slip (sliding)2. Translational slip

3. Rotational slip

4. Analysis of factor of safety (FS)5. Surface subsidence and sinkholes


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Feb. 18, 2006 Philippine Landslide


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Movement by slip (sliding)

- Movement occurs as a displacement along onedistinct surface of failure (or a narrow zone of

failure). This is in contrast with flow.

-Using the limit equilibrium approach: equating thedriving forces to the resisting forces on the slipping

plane at the time of failure.

-The failure surface is idealized into either a planeror circular plane.

-Failure occurred on the planar surface istranslational;

-Failure occurred on the circular plane is

rotational;


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Driving force: WsinResisting force: Wcos

Wcos


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The factor of safety (FS) for the

translational slip is defined as

tantan

sincos ===

WW

FFFSD

R

Clearly, when the dipping angle is smallerthan the angle of friction , the resistingforce FR is greater than the driving force FD,and the factor of safety (FS) is greater than

1, and vice versa. When FS > 1, safe; FS = 1,

onset of failure; and FS < 1, failed.


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The slope failure (slump)

Slope failure is also called a slump;

Circular surface of failure is commonfor considering essentiallyhomogeneous materials (soils, looseor weak materials);

As indicated by the TRB

Classification, slump occurs with thepresence of earth, debris, weak rockmatters, etc.


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Three types of slump failure

Slope failure: weak near surface materials;toe failure: extended slope or additional excavation;Base failure: f lat weak zone at depth.

slope failure

toe failure

base failure


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Slumps usually occur in humid areas, groundwater

plays an important role in slump failure. In

springtime, after the thawing, after heavy rainfall,slump failures are very common in all natural

slopes, road cuts, out slopes, and embankments.


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Factor of safety (FS) analysis for

slump failureParallel to the FS analysis we have done for slipalong a planar plane, the analysis is similar butwith several exceptions. (1), the slip is occurringalong a circular plane, not a planar plane anymore.(2), the mass movement is not a simple

translational motion, but with rotation component.To analyze a case like this, we need a help fromrigid body mechanics whose treatment is suitablefor analyzing rotations. Thus, instead of using the

force balance approach, we need using a balanceof moment. The moment is defined as the forcetimes the arm length to the shaft of the rotation.


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The factor of safety (FS) now is defined as

DD

RR

D

R

armF

armF

M

MFS

==


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where MR is the resisting moment and MD is the

driving moment. If the resisting moment is larger

than the driving moment it is a safe slope, slip

would not happen. The FS is greater than one for

this case. In the case if FS is close to unity, itimplies that the driving moment is close to the

resisting moment, the slope is close to fail.


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Driving Moment


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i

n

i

iiD WrM sin1

=

=

Wisini is the driving force on the i-th portion of thefailure plane, parallel to the failure plane towards

downward. After multiplying the driving force withthe arm of rotation ri the quantity is the driving

moment from that portion, or the contribution from

the i-th sub-block. The arm length ri is taken as theradius of the circular failure plane (an arc).


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Recall the Coulomb-Mohr criterion for shear failure, for eachsub-block we have

)(tan)(iniinii

PCPC +=+= where

i is the shear stress;

ni is the normal stress; and

iP is the pore pressure;

is the angle of friction;C is the cohesion;

inieff p= is the effective stress.


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The above formula is in stress format, multiplication of it

with A i, the area underneath each sub-block on the

slipping plane results in the resisting force

)cos(tan iiiiiRi PAWCAF +=

then the total resisting moment is

)]cos(tan[

1

iiiiii

n

i

R PAWCArM +==


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So that the Factor of Safety FS is

i

n

i

ii

iiiiii

n

i

D

R

Wr

PAWCAr

M

MFS

sin

)]cos(tan[

1

1

=

=+

==

For a practical calculation we can further simplified by

approximating the slipping plane to be circular, so thearm lengths for all the sub-blocks are the same distance

r. We can also take the contact area on the slipping

plane as the length l i times a unity thickness d. Finally,


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So that the Factor of Safety FS is

FS=M

R

MD

=dCL + tan (Wi cosi dPili )

i=1

N

Wi

sini

i=1

N

=

=

==

=

n

1i

i

n

1i

i

AAdL

L l

with

This formula can be

practically implemented.


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Now we can integrate the discussion of slip and

toppling.

The question is: under what conditions the block

has toppling and under what conditions it has

slip?


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(West, Fig. 14.8)

< >

No slippingNo toppling

Toppling

No slipping

SlippingNo toppling

Slippingtoppling

b/h=tan


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Surface subsidence and sinkholes


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Form of a sinkhole (West, Fig. 14.3)


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Lowering the land surface by a verticaldownward movement is called Subsidence.

The mechanisms of subsidence include:compaction;

consolidation;

plastic outflow of weak layers (organic, siltylayer near surface, etc.);

collapse of subsurface openings.

Underground Opening Collapse


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Underground Opening Collapse

When the opening width W is sufficiently small or the

rock above the cave is massive (strong, or containing

few and widely spaced joints), the void would not

migrate upward, but instead, form an arch-shaped roof,

no surface subsidence at all.

Analogy:

When you drive on Route 15 to New York, you mightnoticed many crossover bridges crossing the highway

above Route 15, and they are all in arch shaped

structure, with wide-span. The weight of the bridge issupported by the arch.

Reason: Compression developed in the arch, the weight

of the bridge is transferred to the abutments.

A h h d b id


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Arch-shaped bridge

Subsurface opening

W

Zhaozhou Bridge (built ~600 AD, Hebei, China)


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Zhaozhou Bridge (built 600 AD, Hebei, China)

Subsurface opening

W


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Angle depends on the rock type and the jointspacing.

Rock type and joint spacing together determines

the effective strength of the country rock in which

the subsurface opening exists.

However, when the width W is large enough,

surface subsidence will occur.


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Surface expression a sinkhole (West, Fig. 14.2)

o


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Refer to Figure 14.2:

Angle of break :On which slide likely to occur;

= /2+45 is the angle of friction, a physical property of therocks.

Angle of draw :Angle of draw is measured from vertical, from the

point the plane of draw meeting the groundsurface, the mass moves inward. Practically this

point (F) is taken as the location where 5% of the

maximum vertical displacement occurs.


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The plane of draw is always more horizontal than

the plane of break; i.e, the plane of draw isalways outside of the plane of break.

Point B:

vertically above the boundary of the opening: the

inflection point on subsidence curve. It

corresponds to point D, the zero-point on strain

curve.

Usually, OB = OF/2.5. OF = W/2.


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Point C:

C is the point with maximum tensile strain. Itcorresponds to point A on the break plane, so it is

the likely plane of break to occur (cracks).

BA ~ 3BF.The values:Rock type valueRock, hard clay 11-26Stiff or soft clay 26-50

Sand below water table >50

Clearly soft or loose materials have large value,Means broader effect area.

A good landslide introduction web:


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g

http://www.eos.ubc.ca/public/resources/landslideimages

Geology 3.pdf

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