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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