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Page 1
1 Introduction
1.1 Principle Theory of Slope Failure
Every year there are approximately a thousand slope failure cases around the globe.
On average, death tolls of many thousands of people, as well as economic losses related tolandslide events are common. Therefore, it is evident that there is a clear need to investigate
the cause of devastating slope failures.
Slope failure is related to various causes, these include: the rise of ground water table,
soil properties and geological characteristics of slopes. These causes of slope failures are
often interrelated and can influence each other, collectively deteriorating the stability of the
slope. The combination of these failure modes forms the principle elements related to slope
failure.
Slope failure is driven by slope slip surface which is caused by gravitational andseepage forces that push the slip surface and causes slope instability (Ortigao, 2004)
According to Abramson (2002), there are various types of slope failure which are driven by
slip surfaces, namely: circular/rotational slip, non-circular slip, translational slip and
compound slip.
(a)Circular slip surface
(b) Non Circular slip surface
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(c) Translation slip surface
(d) Rotational slip surface
Figure 1: Types of slip surfaces (Das, 2006)
Figure 2: Rain water flow and seepage on slope (Murthy, 2000)
The most common type of slope failure mode is circular/rotational slip. This is
described as a circular shaped slip surface which is mobilised across a homogenous &
isotropic soil condition, whereas a non-circular slip surface is mobilized in a non-
Rain
Surface runoff
Seepage
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homogenous condition (Ortigao, 2004). On the other hand, according to Ortigao, (2004)
described that slope failure driven by translational and compound slip surface is developed
due to the presence of a rigid layer (for example a bedrock layer), or the presence of
discontinuities such as fissures and pre-existing slips.
1.2 Factors Affecting the Slope Stability
There are many factors which affects the slope stability. According to Ortigao,
(2004) described that one of the main factors is the geometrical changes. This is described
as a change in the gravitational force. The main force responsible for movement is gravity.
Gravity is the internal force that acts on body, pulling mass object in a direction toward the
center of the earth. If the object is on a flat surface then the gravitational force will act
downward. In another words, if the objects is located on the flat surface it will not move
under the gravity force.
However, in the case of a sloping ground, according to Ortigao (2004) described
that the force of gravity can be divided into two vector components, one component isacting normal to the slope and the other component is acting tangent to the slope. The slope
gains its stability from the strength properties of the soil. These include the shear strength,
frictional resistance and cohesion among the soil particles that make up the soil mass
(Ortigao, 2004). As the applied shear stress which occurs under gravitational force
becomes greater than the combination of forces holding the soil mass on the slope, the
object will move down the slope. In geotechnical engineering, this movement is called
slope failure or landslide.
Thus, this slope movement is favoured by steeper slope angles which increase the
shear stresses on the soil. The slope stability is threatened by anything that reduces the
shear strength, such as lowering the cohesion among the particles or lowering the frictional
resistance. The tenancy of slope failure is expressed in terms of the ratio of shear strength
to shear stress, which is known as Safety Factor (Cornforth, 2005).
Safety Factor = Shear Strength/Shear stress.
If the safety factor becomes less than 1.0, slope failure is expected.
The other factor that causes slope failure is an increase in water pressure. This is
caused by the increase in groundwater level. Consequently, an increase of water pressure
adds an increased internal water force inside the slope. Although water is not alwaysdirectly involved as the transporting medium in mass-wasting processes (Ortigao, 2004), it
does play an important role. For exemplary reasons, a sand castle on the beach may be
used. If the sand is dry, it is impossible to build a steep face like a castle wall. If the sand is
wet, vertical wall can be build. If the sand is too wet, then it flows like a fluid and cannot
stay as a wall.
For the case of dry sand, the sand can form a slope with a slope angle relative to the
flat ground that is equal to its Friction angle. The friction angle is the steepest angle at
which the sand slope can remain stable (Liu, 2008). In this case, the stability of the sand
slope is purely dictated by the frictional contact between the soil grains. In general, the
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friction angle increases with increasing grain size. However, different soil types contain
different soil friction angles. This mechanical soil parameter can be usually obtained from
experiments, for example, Triaxial test and direct shear test.
In the partially saturated soil, water particle and the sand particle are interlocked by
an internal suction force between them. This suction force assists in building up apparent
cohesion in cohesionless material. It should be noted that, excessive water will break the
suction force between the soil particles.
The other factor that affects the slope stability is the additional loads (surcharge)
applied on the top of the slope. This external loading can increase the disturbing force and
cause slope instability.
Another reason that affecting slope stability is water pressure. Water pressure is
common on a general slope where a water table might usually exist. When water pressure
increases, the effective stresses, shear strength decrease and can lead to slope failure. An
increase in the water pressure may be due to many uncertain reasons. Usually, the most
common reasons that cause slope failure relate to water pressure increases due to elevated
rainfall intensity and increases in the water content in slope, such as water pipe leakage.
These are the main factors that can affect the slope stability. These are also the
main items which one has to focus on when dealing with reducing the presence of slope
instability.
There is another factor that can induce instability to a slope, which is an
earthquake. However this factor is relatively uncommon when compared to the otherfactors mentioned above. Slope instability caused by an earthquake only happens during
earthquakes in active earthquake zones, such as in China and Japan. This factor causes
slope displacement and changes the gravity condition of slope material. During the
displacement and change of gravity of slope, the body of slope mass no longer is in a
balance condition, and slope will no longer be in a stable condition.
In many seismic regions of the world, slope displacements caused by earthquakes
have led to disaster situations. Examples of magnitude 7.8 earthquake-induced landslides
are the landslide events in the area of Sichuan in China, which were caused by a major
earth movement event near the belt of Sichuan region in May 2008.
According to CEDD (2008) & Ortigao, (2004), the causes of slope instability can
be summarised as follows:
External force that causes slope instability:
Geometrical changes (Undercutting, erosion, changes in slope height, length andsteepness)
Surcharge (Addition of material, Increase in slope height and increasedevelopment at slope crest)
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Shocks and vibrations (earth quake) Drawdown (lowering of water in lake or reservoir) Change in water regime ( rainfall , increase in weight , pore pressure )
Internal forces that causes slope instability:
Progressive failure (following lateral expansion of fissuring and erosion) Weathering (reduction of cohesion, desiccation) Seepage erosion (solution , piping)
Moreover, there are some other non-natural factor cause slope instability:
Removal of vegetation; Interference with, or changes to, natural drainage; Modification of slopes by construction of roads, railways, buildings, etc; Overloading slopes; Mining and quarrying activities; Vibrations from heavy traffic, blasting, etc; and Excavation or displacement of rocks.
1.3 Slope Failure Hazard
The term "landslide" describes a wide variety of processes that result in the
downward and outward movement of slope-forming materials including rock, soil,
artificial fill, or a combination of these. The materials may move by falling, toppling,
sliding, spreading, or flowing.
The various types of landslides (Highland & Bobrowaky, 2008) can be
differentiated by the kinds of material involved and the mode of movement. A
classification system based on these parameters is shown in (Figure 3). Other classification
systems incorporate additional variables, such as the rate of movement and the water, air,
or ice content of the landslide material.
Although landslides are primarily associated with mountainous regions, they can
also occur in areas of generally low relief. In low-relief areas, landslides occur as cut-and-fill failures (roadway and building excavations), river bluff failures, lateral spreading
landslides, collapse of mine-waste piles (especially coal), and a wide variety of slope
failures associated with quarries and open-pit mines. The most common types of landslides
are described as follows and are illustrated in (Figure 3).
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Table 1: Type of landslides (Highland & Bobrowaky, 2008)
Types of movement Bedrock Engineering soil
Falls Rock fall Debris fall Earth fall
Topples Rock Topple Debris Topple Earth Topple
slides RotationalRock Slide Debris Slide Earth Slide
Translational
Lateral spreads Rock Spread Debris Spread Earth Spread
Flows Rock Flow
(Deep Creep)
Debris Flow Earth Flow
(Soil Creep)
Complex Combination of two or more types of movement
(a)Falls (b)Topples (c)Debris flow
(d)Debris avalanche (e) Earth flow (f) CreepFigure 3: Types of landslides (Highland & Bobrowaky, 2008)
FALLS
Falls are abrupt movements of masses of geologic materials, such as rocks and boulders,
that become detached from steep slopes or cliffs (Figure 3a). Separation occurs along
discontinuities such as fractures, joints, and bedding planes and movement occurs by free-
fall, bouncing, and rolling. Falls are strongly influenced by gravity, mechanical
weathering, and the presence of interstitial water.
Tilted pole
Curved tree trunk
Fence out of
alignment
Soil ripples
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TOPPLES
Toppling failures are distinguished by the forward rotation of a unit or units about some
pivotal point, below or low in the unit, under the actions of gravity and forces exerted by
adjacent units or by fluids in cracks (Figure 3b).
FLOWS
There are five basic categories of flows that differ from one another in fundamental ways.
(a) Debris flow
A debris flow is a form of rapid mass movement in which a combination of loose soil,
rock, organic matter, air, and water mobilize as slurry that flows down slope (Figure 3c).
Debris flows include
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where movement is within the depth of soil affected by seasonal changes in soil moisture
and soil temperature; (2) continuous, where shear stress continuously exceeds the strength
of the material; and (3) progressive, where slopes are reaching the point of failure as other
types of mass movements. Creep is indicated by curved tree trunks, bent fences or
retaining walls, tilted poles or fences, and small soil ripples or ridges (Figure 3f).
1.4 Landslide hazard identification
According to Highland & Bobrowaky (2008), the identification of landslide hazard
involved following procedure:
Desk study- An aerial photograph is an important aspect of landslide hazardidentification. The study of aerial photographs assists in cataloguing of historical
landslides, describing and evaluating the geomorphology and determining the site
history particularly with respect to human activities on natural slopes.
Engineering geological reconnaissance Mapping- The mapping providedadditional landslide information data which was not visible on the aerial photos and
enables ground truthing of some of the geomorphologic interpretations made from
aerial photographs.
Ground Investigation - In order to understand the ground model better, groundinvestigation was carried out to explore the soil properties and the condition of the
groundwater regime.
Site investigation - site visits and field measurements were taken of the slopegeometry (eg. Slope height, angle, seepage). Therefore, the collected data can be used
to provide the most precise information and representative the real slope geometry
for further design.
Engineering Geological synthesis - An engineering geological synthesis of thefinding from the desk study, engineering geological mapping, ground investigation
fieldwork, site investigation fieldwork and laboratory tests was conducted to
produce a geological model and representative geological sections.
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1.5 India Landslide Risk Zone Category
Figure 4: Landslide risk zone category of India (Sarkar, 2005)
1.6 Methods of Slope Failure Prevention
A number of factors and parameters such as soil properties, pore water
pressure resume, slope geometry, earthquake, and vibration can influence the slope
stability. Engineering slope stabilization is generally referred to stop or decrease the
possible of instability process of slopes. Preventing the movement of a slope or
increasing the safety factor (SF) is possible by using structural or geotechnical
methods. Among techniques which increase resisting forces and basically act
externally on the soils or rocks sliding are geometrical methods (USDA, 1994),
hydraulic improvement, surface and subsurface drainage (USDA, 1994), structural
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barriers such as rigid walls and piles (Hassiotis et al., 1997; Ausilio et al., 2001),
physical and mechanical improvement (Komak Panah, 1994), chemical improvement
(Ghazav, 2008), reinforcement with geosynthetics (Jorge and Zornberg, 2002; Kousik
Deb et al., 2007), soil nailing (Turner and Jensen, 2005; Sugawara, 2006), etc.
Before 1990, chuman surface and non-reinforcing shotcrete surfaces were a
common use of material for slope stability improvement. For some steep slopes, a
stone pitching surface was most widely used, or masonry facing for rigid surface
cover. Some of them were installed weep holes to reduce the pore water pressure
inside the slope. However, the main purpose of this was to achieve an impervious
interface for prevention of the surface erosion and the rainfall entry into the slope in
order to reduce the pore water pressure inside the slope. This method is easy in terms
of construction and maintenance and was also cost efficient.
However, if the slope had inherent instability due to internal soil, shear failure
and sliding would still occur. This method would not provide an enough structural
external force against the movement of the slope failure wedge. On the other hand,
this method usually uses a concrete or stone base construction material, which is
usually grey or white in colour. This triggers an environmental problem, as the finish
is very inconsistent with the surrounding natural landscape.
1.6.1 Shotcrete surface method
Shotcrete is a process where concrete is sprayed onto slope surface using ashotcrete feeder gun to form rigid surface. Usually, shotcrete surface slopes have
approximate 50-150 mm thick and provide wire mash reinforcement to prevent surface
crack and shrinkage.
(a) Laying of wire mesh (b)Spreading of concreteFigure 5: Shotcrete surface (Jade, 1993)
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1.6.2 Masnory surface method
Use stone pitching as a rigid surface cover for prevent erosion and surface runoff. This
method is easy for maintenance and construction.
(a) (b)
Figure 6: Masonry surface (Cheng, 2008)
1.6.3 Chuman surface metod
Use of cement sand mix material for surface protection. No reinforcement and wire
mash required. Poor crack and shrinkage resistance.
Figure 7: Chuman surface (Cheng, 2008)
1.6.4 Soil Nailing
It is a new technique in which soil slopes, excavations or retaining walls are
reinforced by the insertion steel reinforcing bars. According to Ortigao (2004) noted that
the first use of the soil nailing application was in 1972 and now this method is a well-
established technique around the world. Sometimes, soil nailing can combine different type
of retaining methods such as soil nailing on retaining walls and with greening surfaces.
Soil nailing can provide a cost efficient, quick and standard technique for slope
improvement solution.
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Figure 8: Typical Soil nailing method (Tommy, 1988)
1.6.5 Bio-Engineering
Itis one of the most innovative technologies for slope improvements in the world.
According to Ducan et al. (1987) described that Bio-Engineering includes the use of tree
roots or plant roots to retain shallow slope failure. This method has an advantage as it is
natural and environmental friendly (Ducan et al., 1987). However, many factors can
influence the effectiveness of Bio-engineering for slope stabilisation. This method is in an
early stage of development, and needs a period of time for technology proving and
development.
Figure 9: Vetiver Grass System (Greenwood, 2008)
1.6.6 Soil Re-Compaction and No-fine Replacement
For some loose material slopes such as fill slope, soil nailing is not a suitable
stabilisation method. Some technologies such as soil re-compaction and soil re-placement
are more suitable and are usually applied. Soil re-compaction involves the excavation of
the loose soil, backfilling and re-compacting to improve the friction angle. However, the
soil re-compaction method has some restrictions such as every backfill and re-compaction
has to be carried out in a 300mm thick layer (NAS, 2004), layer by layer, and every single
layer needs an individual soil test for compaction ratio checking. Moreover, this method is
highly influenced by weather conditions. The soil has to be placed in thinner lifts and
requires moisture control for compaction. As a result, this method will increase the
construction cost and time period.
The other method is the soil replacement method. This design approach includes
using other materials such as no-fine concrete or gravel to replace the loose soil. Removalof the original loose soil on the slope is carried out, then forming a slope with a design
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slope angle by backfilling with no-fine concrete or gravel. After that, a thin layer of soil
with hydroseeding is applied to the surface as a cover and for landscaping. This method
can reduce the construction period, hence alleviating labour costs and operation costs
which then compare with the soil re-compaction method.
However, these replacement and re-compaction methods are constrained in that the
construction sequence has to be scheduled for the dry season when the groundwater levels
are lower than they were at the time of active landsliding. Alternatively, temporary
groundwater lowering through the use of a raking drain may be needed prior to, and during
construction work.
(a)No-Fine concrete replacement (b) Completed no-fine replacement slopeFigure 10: Soil Re-Compaction and No-fine Replacement (NAS, 2004)
1.6.7 Subsurface Drainage
Of all stabilisation methods considered for the prevention of landslides, a reduction
of pore water pressure behind the slope is the most important. According to
Cornforth(2005) described that the subsurface drainage method can reduce the
destabilising hydrostatic and seepage water pressures on the slope as well as the risk of
sliding or flow.
Figure 11: Subsurface drainage (Cornforth, 2005)
For large, unstable slopes, a drainage tunnel can be applied to draw down the water table
and minimise the risk of slope failure. In Hong Kong, the Lung Fu Shan drainage tunnel
and vertical drainage system is under construction. This drainage tunnel can prevent the
failure of a 200m high natural slope which could be triggered by water pressure. Other
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subsurface drainage methods include: Drain blanket, Trenches, Cut-off drains, Horizontal
Drains, Relief Drains and Raking Drains.
1.6.8 Shear Piles
According to Cornforth, (2005) described that shear piles are reinforced concretecylindrical piles that pass through the slide plant and anchored at lower end stable soils or
bedrock. This shear pile anchorage can provide lateral bearing resistance near the base of
ground movement (Cornforth, 2005).
Figure 12: Shear pile for slope stability (Saroglou, 2008)
This method is effective for a large instability zone and can provide the flexibility of
selecting an installation location. However, this method has limitations such as being
costly and cannot be installed in moving landslide.
1.6.9 Stone Columns
Based on Cornforth, (2005) described that this ground improvement method can
increase the average shear resistance of soil along a potential slip surface by replacing or
displacing the in situ soil with a series of closely spaced and large diameter columns of
compacted stone. However, this method requires the use of a boring machine and material
delivery, which would result in an access problem if the slope is inaccessible.
Stone columns (Barksdale & Bachus, 1983; Cheung, 1998; Kousik Deb et al., 2007;Ambily, 2007) are another method for slope stabilization. Such columns have been used
since 1950 normally for cohesive soil improvement. It is a hole with circular section which
is filled by gravel, rubble and etc and is an effective method to increase the shear strength
on the slip surface of clayey slopes. The most important cases for utilizing stone columns
(Barksdale & Bachus, 1983) are:
1) Improving slopes stability of both embankment and natural slopes2) Increasing the bearing capacity of shallow foundations constructed on soft soils3) Reducing total and differential settlements4) Decreasing the liquefaction potential of sandy soils
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Figure 13: Slope prevention by stone column (Saroglou, 2008)
The performance of stone columns for reinforced and improved soil is easier and cheaper
than other methods such as geotextile, grouting, and compaction (Barksdale & Bachus,m
1983). The diameter of stone column usually varies between 0.3 to 1.2 m and their intervals
between 1.5 to 3 m. Stone columns are normally constructed in multiple rows, depending on
the soil condition.
2 Design of stone column for slope stability prevention
2.1 Methods for slope stability analysis with stone column
Generally, for the analysis of slope treated with the stone column, two methods are applied:
The profile method and the average shear strength method.
(1) In the profile method (or discrete soil-stone column element method), each row of the
stone columns (Christoulas et al., 1997) is converted into an equivalent continuous strip.
Each strip of granular and cohesive soils is then analyzed using its actual geometry and
material properties. The stress concentration in the stone columns results in an increase in
resisting shear force.
Figure 14: Plan of grouped stone columns (Barksdale & Bachus, 1983)
Row 1 2 3 4
S
R2
S
S
Equivalent stone column strip
Stone column
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(2) In the average shear strength method, the weighted average material properties are
calculated for the material within the unit cell. The soil having the fictitious weighted
material properties is then used in a stability analysis. It is important to remember that
stone columns must actually be located over the entire zone of material having weighted
shear properties through which the circular arc passes.
To evaluate the factors of safety of the treated soil (after the installation of the
columns) composite values of unit weight, , and strength parameters c, and were used,
replacing the real composite material (soft soilstone columns) with a homogeneous
material of equivalent strength behaviour. The values of , c, were determined by the
formulae proposed by Dimaggio (1978):
csss aa 1
csss cacac 1
csss aa
tantan1tan
A
Aa
ss
Where;
sa = replacement ratio
= unit weight of composite material
s = unit weight of untreated soilc = unit weight of stone column material
c = cohesion of composite material
cs = cohesion of untreated soil
cc = cohesion of stone column material
= angle of internal friction of composite material
s = angle of internal friction of untreated soil
c = angle of internal friction of stone column material
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2.2 Closed form solution for slope stability analysis
(1)Factor of safety equation for un-reinforced slope (F.S. no-col):
Figure 15: Static slope stability analysis of untreated soil (Das, 2006)
Figure 16: Force exerted on the strip of soil (Das, 2006)
A
B
C
D
Ws
Ts
NS
USs
hs
l
b
O
A
B
C
D
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Ws = Weight of soil slice
NS = Total normal force on the failure surface of soil slice
Ts = Total tangential force on the failure surface of soil slice
US = Pore water pressure on the base of soil slice = usl
s = Inclination of failure surface of soil slice to the horizontal
hs = Height of soil slice between surface of slope and slip surface
Ws = sat,s hs b
Where; sat,s = saturated unit weight of soil slice
NS = Wscoss
= sat,s hsb coss
TS = Wssins
= sat,s hsb sins
s = Normal stress on the base of soil slice
s = Shear stress on the base of soil slice
1
lNSs =
lbh ssssat cos,
=l
bh ssssat cos,
= sssat b 2, cos
1
l
NSs =
l
bh ssssat sin, =
l
bh ssssat sin, = sssat b 2, sin
The equation of shear strength of soil slice, Ss is;
'''tan sssCss
'sC
= effective cohesion of soil
's = effective normal stress on soil
's = effective angle of internal friction of soil
''tan)( ssss uCss
Resisting force on the base of the soil slice is ( ss l = FR,s)
FR,s = '
11
'
tan)(ssss ll uC
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s
bl
cos
FR,s ='
sec'
tan)coscos
coscos
(22
, ssssb ss
ws
s
ssats
bh
bhC
Driving force on the base of the soil slice is FD,S
FD,S = Wssins= sat,s hsb sins
F.S. no-col =F
,sF
D,S
R
=ss
sssss
bh
hbC
sat,s
sb
sin
tan)cos(''
sec'
(2) Factor of safety equation for reinforced slope (F.S. soil-col):
Figure 17: Static slope stability analysis of soil reinforced with a row of stone column
Wc = sat,c hc b
Nc = Wccosc = sat,c hcS
R2cosc
Tc = Wcsinc = sat,c hcS
R2
sinc
GH =S
R2
ccos
1
O
E
F
G
H
Stone column strip
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Figure 18: Force exerted on the strip of soil-column system
1
cos
12
c
c
c
S
R
N
=
1cos
1
cos
2
2
,
c
ccsat
S
R
hS
Rc
= cccsat h 2, cos
1cos
1
T2
c
c
c
S
R
=
1cos
1
sin
2
2
,
c
ccsat
S
R
hS
Rc
= ccccsat h sincos,
Resisting force offered by soil-column system is
FR = FR,s + FR,c
FR,c = Resisting force offered by stone column
FR,c ='
tantan)( cGHusc
'tan
cos
1)coscos(
222
, c
c
scwsccsat
S
Rhh
= '' tan)cos(2
cccc
S
Rh
FR = FR,s + FR,c
S
R2
Wc
Tc
Nc
Ucc
hc
E
F
G
H
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3 Parametric studies
Parametric study is carried out to find the factor of safety for untreated as well as
for treated slope using the software Slide of Rocscience Inc. Factor of safety of treated
slope is found out by discrete soil element method considering the effect of single as well
as multiple row of stone column. Factor of safety of untreated soil comes out equal to0.926 by Fellenius method. (Table 2 & 3) shows the factor of safety with respect to
distance from the crest of the slope for single and multiple row of stone column.
Figure 19: Location of single row of stone column
Table 2: Effective location of stone column for single row
Distance: x (m) F.S. soil-col
30.24 0.928
0 0.956
22.68 0.990
7.56 1.012
15.12 1.024
Table 3: Effective location of stone column for multiple rows
Distance: x (m) F.S. soil-col
0, 30.24 0.944
15.12, 30.24 1.015
0, 15.12 1.047
15.12, 22.68 1.089
7.56, 15.12 1.097
0, 7.56, 15.12 1.12
7.56, 15.12, 22.68 1.165
15.12, 18.9, 22.68 1.176
7.56, 11.34, 15.12 1.181
L
x
Stone column
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Figure 20: Factor of safety v/s distance for single row
Parametric study is being carried out to locate the position of stone column for single row
of stone column. From the (Figure 20), it is shown that the effective location of stone
column is about x=0.5L, if single row of stone column is being used.
Figure 21: Factor of safety of soil column system v/s distance for multiple rows
Factor of safety is also being found out considering the multiple rows (Figure 21) of stone
columns. According to Cornforth (2005), permissible limit for the factor of safety for
natural slope range between 1.1 to 1.2 and that for engineered slope in the range of 1.5 to2.
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Figure 22: Spacing of stone column v/s Factor of safety of soil column system
The effect of spacing on the factor of safety is depicted in the (Figure 22), considering the
different value of cohesion of the untreated soil with multiple rows of stone columns at
distances 0.25L, 0.37L & 0.50L from the crest of the slope. Factor of safety increases
about 80% if the cohesion of untreated soil increases 50%.
Figure 23: Factor of safety of soil column system v/s Spacing of stone column
Effect of angle of internal friction on factor of safety is as shown in the (Figure 23).
Considerable increase in safety factor is observed for higher angle of internal friction of
stone column material.
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Figure 24: Angle of slope v/s Factor of safety of soil column system
A considerable increase in safety factor (Figure 24) is observed for gentle slope. For higher
value of slope, large decrease in safety factor occurs. Around 32% increase in factor of
safety occurs if slope angle decrease from 40 to 10.
4 Concluding remark
Through the parametric study, it is concluded that the effective location of a single
row of stone column is at a distance of 0. 50L from the crest and that for three rows of
stone column is 0.25L, 0.37L, 0.50L having factor of safety within permissible limit. Both
shear parameters of untreated soil and stone column having a significant effect on
stabilization of slope. For a gentle slope higher factor of safety is achieved than of steeper
slope.
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Notation
Ws
= Weight of soil slicesat,s
= Saturated unit weight of soil slice
NS = Total normal force on the failure surface of soil sliceTs
= Total tangential force on the failure surface of soil slice
US
= Pore water pressure on the base of soil slice
s
= Inclination of failure surface of soil slice to the horizontalhs
= Height of soil slice between surface of slope and slip surface
FR,c = Resisting force offered by stone column
FR,s = Resisting force offered by stone column
'sC
= Effective cohesion of soil
's
= Effective normal stress on soil
's
= Effective angle of internal friction of soil
sa
= Replacement ratio = Unit weight of composite material
c = Submerge unit weight of stone column material
s = Submerge unit weight of untreated soil
s
= Unit weight of untreated soilc
= Unit weight of stone column material
c
= Cohesion of composite materialcs
= Cohesion of untreated soilcc = Cohesion of stone column material
= Angle of internal friction of composite material
s = Angle of internal friction of untreated soil
c = Angle of internal friction of stone column material
F.S. soil-col = Factor of safety of soil column system
F.S. no-col = Factor of safety of untreated soil
S = Spacing of stone column
x = Distance of stone column row from the crest of slope
= Angle of slopeb = Width of soil slice
l = Width of soil slice along the slope angle
L = Horizontal length of slope
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References
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