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John Curran, Ph.D, P.EngCEO and Founder, Rocscience Inc.
R.M. Smith Professor Emeritus, University of Toronto
February 28-29, 2012, Perth, Australia
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About Us
Established in 1996, based on 15+years research and developmentwork
20 full-time staff in Toronto, mostwith advanced engineeringdegrees
Over 6000 customers, in 110+
countries; user base includesconsulting firms of every size, andabout 200 universities
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Our Unique Offering
Competitively priced software
return on investment is rapid
Free technical support provided by engineers who developed programs
We have software from a few different companies and I just wanted to let you
know that your customer support blows all theirs out of the water.
Thank you very much! Free evaluation copy and 30-day money back
guarantee
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Our Unique Approach
Highly user-friendly programs
CAD tools
Similar interface between our 13 programs Rapid learning
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Our Software
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Examine
3D
analysis of underground
excavations
Phase2
finite element analysis
of excavations & slopes
Unwedgewedge analysis for
underground excavations
RocSupportsupport estimation using
ground reaction curves
Our Software - Excavation Design
http://www.rocscience.com/Anon/RocSupportDemo2.exehttp://www.rocscience.com/roc/software/Phase2.htmhttp://www.rocscience.com/roc/software/Examine3D.htm7/24/2019 Slide Workshop Introduction
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Dipsgraphical and statistical
analysis of orientation data
RocFallstatistical analysis of rockfalls
RocDatarock mass, soil & discontinuity
strength analysis
Our Software - Geotechnical Tools
Settle3D
Settle3D
3D analysis of settlements and
consolidation
http://www.rocscience.com/roc/software/Examine3D.htmhttp://www.rocscience.com/roc/software/Examine3D.htmhttp://www.rocscience.com/roc/software/Examine3D.htmhttp://www.rocscience.com/roc/software/RocFall.htmhttp://www.rocscience.com/roc/software/Dips.htm7/24/2019 Slide Workshop Introduction
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Our Software Philosophy
Modeling goals:
Gain insight
Explore potential trade-offs and alternatives
To achieve goals:
Allow designers to focus on engineering
Leave tedious/mundane tasks to program
Facilitate speedy modelling
Compute as fast as possible
Make it easy and fast to create models
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Part I
Introduction to slope stability
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Objectives
Goals of slope stability analysis
Basic slope stability analysis
Identifying different slope failure mechanisms
Identifying conditions under which particularmechanisms occur
Overview of slope stabilization methods
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Aims of Slope Stability Analysis
Assess equilibrium
conditions (natural slopes)
Evaluate methods for
stabilizing slope
Evaluate impact/role of
geometric and physical
parameters on stability
Discontinuity strength Height
Slope angle, etc.
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Aims of Slope Stability Analysis
Determine impact of
seismic shock on
stability
Back analyze forprevailing conditions
at failure
Shear strength
Groundwater conditions
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Aims of Slope Stability Analysis
Determine optimal staged
excavation or construction
sequence
Design slopes that reliably
maintain stability at
reasonable economic
costs
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Parametric Analysis
Uncertainties regarding material
properties and physical
conditions
Variability of properties from
location to location
Difficulties in measurement
Required to evaluate physical
and geometrical factorsaffecting stability
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Slope Stability Analysis
Components of analysis
Slope under consideration (geometry, geology, soil
properties, groundwater, etc.)
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Slope Stability Analysis
Components of analysis
Slope geometry
Geologic model
Groundwater Loadings on slope
Failure criterion
Failure analysis
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Failure Modes
Slope failure modes/mechanisms
Ways in which slide masses move
Identifies critical failures that should be eliminated or
minimized
Used proactively to permit early design improvements and
at less cost than is possible by reactive correction of
problems
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Failure Modes
Three major classes
Slides: Mass in contact
with parent/underlying
material moving along
discrete boundary (shear
surface)
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Failure Modes
Three major classes
Falls: Steep faces,
immediate separation of
moving mass from parent
material, intermittent
contact thereafter
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Failure Modes
Three major classes
Flows: Moving mass
disaggregates,
displacement not
concentrated on
boundary
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Failure Modes
Slides (dictated by unbalanced shear
stress along one or more surfaces)
Rotational
Translational
Compound/
Combination
Planar
Wedge Toppling
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Failure Modes
Rotational (rock and soil)
Sliding along curved surface
Common cause: erosion at base of slope
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Failure Modes
Rotational (rock and soil)
Original Surface
Failure Surface
Circular Shallow Noncircular
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Failure Modes
Rotational (rock and soil)
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Failure Modes
Translational
Slides move in contact with underlying surface
Sliding surface commonly a bedding plane,
can also be fault/fracture surface
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Failure Modes
Translational
Block slide Slab slide
Failure Surface
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Failure Modes
Translational
Block Slide Slab Slide
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Failure Modes
Aspect ratio of sliding mass
Rotational: 0.15 < D/L < 0.33
Translational: D/L
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Failure Modes
Compound
Competent stratum
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Side Relief Planes
Upper Slope Surface
Slope Face
Failure Plane
Failure Modes
Planar (rock and soil)
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Failure Modes
Planar
Movement controlled by geologic structure
Surfaces of weakness (discontinuities joints, faults, bedding
planes, etc.)
Contact between overlying weathered material and firm bedrock
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Failure Modes
Geometric conditions
necessary for planar
failure
Failure plane strikes parallel
or approximately parallel(within 20o) to slope face
Failure plane daylights into
slope face
Dip of the failure plane >friction angle of failure
plane
Upper Slope Surface
Slope Face
Slope Height
TensionCrack
Sliding Block or
Mass (Wedge)
Failure or SlidingSurface
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Failure Modes
Presence of release surfaces at
lateral boundaries of sliding
block
> >
Dip of the
slope faceDip of the
discontinuity
Angle of
friction for the
rock surface
Upper Slope Surface
Slope Face
Slope Height
Tension
Crack
Sliding Block or
Mass (Wedge)
Failure or
Sliding Surface
Failure or Sliding Surface
Release Surfaces
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Failure Modes
Forces acting on failure
block:
Weight of block, W
Normal water pressure, U
Tension crack water pressure, V
Surcharge, F
Seismic forces, S
Forces from artificial support, B
W
S
B
F
V
U
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Failure Modes
Wedge (rock)
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Failure Modes
Wedge (rock)
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Failure Modes
Wedge Geometry
1,2= Failure planes (2
intersecting joint sets)
3= Upper ground surface
4= Slope face
5= Tension crack
H1= Slope height referred
to plane 1
L= Distance of tension crackfrom crest, measured along
the trace of plane 1.
15
3
2
4
H1
L
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Failure Modes
Wedge (rock)
2 discontinuities striking obliquely across slope face
Line of intersection daylights in slope face
Dip of line of intersection > friction angle of discontinuities
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Failure Modes
General conditions for wedge failure
Plunge of line of intersection > angle of friction for rock
surface
Plunge of line of intersection < dip of slope face
Trend of line of intersection approximately parallel to dip
direction of slope face and daylights in slope face
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Failure Modes
Wedges fail if strength is exceeded
> >
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Failure Modes
Wedges cannot fail
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Failure Modes
Wedge (rock)
Active Wedge
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Failure Modes
TopplingUndercutting Discontinuities
Low-Dip Base
Plane Daylighting
in Slope Face
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Failure Modes
Toppling (blocky rock masses)
Weight vector of block resting on incline falls outside base
of block
Often occurs in undercutting beds
Goals of toppling analysis
Determine mechanism (path) and factor of safety against
toppling
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Geologic factors controlling failure modesGeologic Conditions Potential Failure Surface
Cohesionless soils
Residual or colluvial soils over shallow rock
Stiff fissured clays and marine shales within
upper, highly weathered zone
Translational with small
depth/length ratio
Sliding block
Interbedded dipping rock or soil
Faulted or slickensided material Intact stiff to hard cohesive soil
Single planar surface
Sliding blocks in rocky masses
Weathered interbedded sedimentary rocks
Clay shales and stiff fissured clays
Stratified soils
Multiple planar surfaces
Thick residual and colluvial soil layers
Soft marine clays and shales
Soil to firm cohesive
Highly altered and weathered rocks
Rotational (circular slopes with
homogeneous material, non-
circular slopes of heterogeneous
material)
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Objectives
Overview of principles of
Limit equilibrium analysis
Method of slices
Review of assumptions of different methods
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Limit Equilibrium Analysis
General approaches for analysis of slopes
Limit equilibrium
Finite element, finite difference
Back analysis
Keyblock concept (rock)
Probabilistic methods
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Limit Equilibrium Analysis
Attraction of limit equilibrium
Most common slope analysis method
Relatively simple formulation
Useful for evaluating sensitivity of possible failure
conditions to input parameters
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Limit Equilibrium Analysis
Fundamental concepts
All points along slip surface are on verge of failure
At this point in time
Driving forces (D) = Resisting forces (R)
Factor of safety(FS) = 1
D > R FS < 1
D < R FS > 1
Limiting equilibrium perfect equilibrium between forcesdriving failure and those resisting failure
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Limit Equilibrium Analysis
Fundamental concepts Factor of safety (factor of ignorance)
Quantitative measure of degree of stability
Accounts for uncertainty
Guards against ignorance about reliability of input parameters Lower quality site investigationhigher desired factor of safety
Higher quality site investigationlower desired factor of safety
Empirical tool to establish suitable economic bounds on design
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Limit Equilibrium Analysis
Uncertainties accounted for by factor of safety Uncertainty in shear strength due to soil variability, relationship
between lab strength and field strength
Uncertainty in loadings (surface loading, unit weight, porepressures, etc.)
Modelling uncertainties: including possibility critical failuremechanism SLIGHTLY different from that identified, model is notconservative
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Limit Equilibrium Analysis
Factor of safety DOES NOT account for possibility of grosserrors such as bad choice of failure mechanism
e.g. ignoring presence of existing shear surfaces in slope
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Limit Equilibrium Analysis
Fundamental concepts
Two steps for calculating factor of safety
Compute shear strength required along potential failure surface
to maintain stability
Compare required shear strength to available shear strength(which is assumed constant along failure surface)
For Mohr-Coulomb
=
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Limit Equilibrium Analysis
Planar failure
W
W sin
N
W cos
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Limit Equilibrium Analysis
Planar failure
W
W sin
N
W cos
tan
sin tan
cAFS
W
= +
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Limit Equilibrium Analysis
Rotational failure method of slices
Used by most computer
programs
Readily accommodates
complex slope
geometries, variable soil
and groundwater
conditions & variableexternal loads
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Limit Equilibrium Analysis
Rotational failure method of slices
N slices
Zi
n Number of Slices
Number of unknowns (6n 2)
n Normal forces on base
n Shear forces on base
n Lines of action (Zi)
n-1 Interslice normal forces
n-1 Interslice shear forces
n-1 Lines of action (Zh)
1 Factor of Safety
FS?
Zh
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Limit Equilibrium Analysis
Rotational failure method of slices
N slices
Zi
n Number of Slices
Total number of equations (4n)
n Moment equilibrium of slice
n Force equilibrium in X
n Force equilibrium in Y
FS?
n Mohr-Coulomb
relationship between shear
strength and normaleffective stress
M = 0
Fx= 0
Fy= 0
Zh
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Limit Equilibrium Analysis
Rotational failure method of slices
N slices
Zi
Common assumption
Zi= base length of slice
i.e. normal force on slice base acts at
midpoint of base
n 2unknowns remain to make
problem determinate
These assumptions characterize
different slope stability methods
d
Zi = d/2
Zh
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Limit Equilibrium Analysis
Slope stability analysismethods
Ordinary (Fellenius)
Bishop simplified
Janbu simplified
Janbu corrected
Lowe-Karafiath
Corps of Engineers (I, II)
Spencer
Morgenstern-Price
General Limit Equilibrium
(GLE)
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Limit Equilibrium Analysis
Rotational failure method of slices
Thrust line: connects points of application of interslice
forces
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Limit Equilibrium Analysis
Rotational failure method of slices
Location of thrust line
May be assumed
May be calculated from rigorous analysis that satisfies complete
equilibrium (Spencer, Morgenstern-Price, GLE)
Simplified methods (Bishop, Janbu, Lowe-Karafiath, Army Core)
neglect location of interslice force because complete equilibrium
is not satisfied
l b l
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Limit Equilibrium Analysis
Slope stability analysis methods Many methods available
Methods are similar
Difference only in:
Which static equations satisfied
Which interslice forces included
Relationship between interslice
and shear normal forces
l b l
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Limit Equilibrium Analysis
Methods of slicesassumptions
Ordinary (Fellenius)
Assumes circular slip
surface Neglects all interslice forces
(shear and normal)
Only satisfies moment
equilibrium
One of the simplest
procedures
( tan )
sin
c l
FS
W
+
=
i i ilib i l i
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Limit Equilibrium Analysis
EXAMPLE:
Determine the factor
of safety for the slip
circle shown
35
c = 20k Pa
= 20
6.1 m
Li i E ilib i A l i
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Limit Equilibrium Analysis
Solution for slip circle Subdivide sliding sector (4)
Find area of each slice
(mid-height x breadth)
Determine weight (unitweight x area)
Find tangential and normal
force components on
sliding surface
Repeat for each slice &
sum up
12
34
N= ?T= ?
Li i E ilib i A l i
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Limit Equilibrium Analysis
Solution for slip circle - Ordinary
12
3
4
Tangential
T [kN]
Normal
N [kN]
Weight
W [kN]
Area
]m2[
Slice
no.
-771723.71
421631688.72
11619122411.63
1061041487.74
N= 529 T= 257
c = 20k Pa
= 20tan 529*0.364 192
7620*10.7*( ) 284180
tan 284 1921.85
257
N kN
cr kN
cr NFS
T
= =
= =
+ += = =
Li i E ilib i A l i
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Limit Equilibrium Analysis
Methods of slicesassumptions
Bishop (1955) simplified
Assumes interslice shear
forces = 0 (reduces # ofunknowns by (n-1))
Moment eq. about centre
and vertical force eq. for
each slice are satisfied
Overdetermined soln(horizontal force eq. not
satisfied for one slice)
( tan )
sin
c l
FS
W
+
=
Li i E ilib i A l i
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Limit Equilibrium Analysis
Methods of slicesassumptions
Janbu simplified
Assumes interslice shear
forces = 0 (reduces # ofunknowns by (n-1))
Overall horizontal force eq.
and vertical force eq. for
each slice
Overdetermined solution(moment equilibrium not
completely satisfied)
( tan )
sin
c l
FS
W
+
=
Li it E ilib i A l i
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Limit Equilibrium Analysis
Methods of slicesassumptions
Janbu corrected
Assumes interslice shear
forces = 0 (reduces # ofunknowns by (n-1))
Overdetermined solution
(moment equilibrium not
completely satisfied)
Correction factor,f0,accounts for interslice shear
force inadequacy
Li it E ilib i A l i
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Limit Equilibrium Analysis
Methods of slicesassumptions
Lowe and Karafiath
Assumes interslice force
inclined at angle = (groundsurface angle + slope base
angle)/2
Horizontal and vertical force
equilibrium are satisfied for
each slice Overdetermined solution
(moment equilibrium not
satisfied)
Li it E ilib i A l i
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Limit Equilibrium Analysis
Methods of slicesassumptions
Corps of Engineers I
Assumes interslice force
inclined at angle = groundsurface angle
Horizontal and vertical force
are eq. satisfied for each
slice
Overdetermined solution(moment equilibrium not
satisfied)
Li it E ilib i A l i
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Limit Equilibrium Analysis
Methods of slicesassumptions
Corps of Engineers II
Assumes interslice force
inclined at angle = averageslope angle between left
and right points of failure
surface
Horizontal and vertical force
are eq. satisfied for eachslice
Li it E ilib i A l i
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Limit Equilibrium Analysis
Methods of slicesassumptions
Spencer
Assumes all interslice forces
inclined at constant, butunknown, angle
Complete equilibrium
satisfied
Li it E ilib i A l i
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Limit Equilibrium Analysis
Methods of slicesassumptions
Morgenstern-Price
Similar to Spencers
assumes all interslice forcesinclined at constant, but
unknown, angle
Inclination assumed to vary
according to portion of
arbitrary function Satisfies complete
equilibrium
Li it E ilib i A l i
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Limit Equilibrium Analysis
Methods of slices
Force Equilibrium Moment
Method Horizontal Vertical Equilibrium
Ordinary No No Yes
Bishop simplified No Yes Yes
Janbu simplified Yes Yes No
Lowe-Karafiath Yes Yes No
Corps of Engineers Yes Yes No
Spencer Yes Yes YesGLE (Morgenstern-Price) Yes Yes Yes
I f C iti l S f S h
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Issue of Critical Surface Search
Example: centre of criticalfailure surface may not be
located inside grid
Probabilistic Slope Analysis
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Probabilistic Slope Analysis
Under ideal conditions FS= 1 should ensure safe design Uncertainty forces use of higher FSs
Based on past experience FS= (1.3 1.5)
Use of single FSvalue does not accurately reflect site
investigation quality Good site characterization should be lower FS
Poor site characterization should be higher FS
Often though same FS used
Slope Stabilization Methods
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Slope Stabilization Methods
Reduction of slope height Reduction/flattening of slope angle
Incorporation of benches
Application of support elements (bolts, piles, buttresses,
berms, etc.) Installation of drainage
Use of excavation techniques that minimize dynamicshocks and rock mass damage
Removal of unstable or potentially unstable materials
Slope Stabilization Methods
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Slope Stabilization Methods
Slope Stabilization Methods
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Slope Stabilization Methods
Slope Stability References
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Slope Stability References
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