Post on 20-Feb-2017
Seismic Stability Analysis Of
Nailed Slopes
Dhanaji S. Chavan
Asst.Prof., TKIET, Warananagar
1Dhanaji S. Chavan
Dynamic Analysis-Earthquake
Loading
We can deal with problems such as:
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Soil Slope
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Soil-Well-Pier System
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Bridge Abutment-Soil System
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Bridge Abutment-Soil System6
Problem for today’s discussion
Stability analysis of nailed soil slopes subjected to
earthquake loading
Same philosophy is applicable to other two problems
with a little modification.
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For a successful analysis……..
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We must understand:
How to apply earthquake loading and where
How to define boundary conditions
How to define interface connectivity
How to carry out analysis
Which elements to be used
Validation of model
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Boundary conditions
We have to model only limited domain of
actual problem. Hence, we need to cut it from
rest of the region
When we cut it from rest of the region how to
model boundaries
We must model boundaries in such a way that
it will simulate the actual problem
Remember: for any software garbage in
garbage outDhanaji S. Chavan
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Boundary conditions
it is not necessary that results result we get from a
software are always correct.
Results will be correct only when we model our
problem correctly
To model a problem correctly we have to first
understand the physics of the problem
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Science
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EQ
Surface Waves
Fault Rupture
Body Waves
Structure
Soil
Geologic Strata
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Seismic Waves…
Body Waves
Direction of Energy Transmission
P-Waves
Side to side
Up and down
Push and pull
S-Waves
CompressionExtension
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Surface WavesLove Waves
Rayleigh Waves
Sideways in horizontal plane
Elliptic in vertical plane
Direction of Energy Transmission
Seismic Waves…
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Boundary conditions
Analysis is carried out in two stages:
1. Gravity analysis
Side boundaries are restrained in horizontal
direction and kept free in vertical direction
Base boundary is fixed in both directions
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2. Dynamic analysis
Restraints in the gravity analysis are
removed and reactions from Gravity analysis
are applied.
Radiation dampers are provided at side and
base boundaries
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Radiation dampers at boundaries
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Details at boundaries
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Application of the earthquake motion
Applied at the base in the form of equivalent nodal
shear force in horizontal direction
Shear force proportional to the velocity of incident
shear wave
Expression for the equivalent shear force obtained
from the 1-D propagation of shear wave in the
vertical direction through linear, isotropic and
undamped soil material
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The shear stress induced at any point in the material is given by the following expression
Where is the velocity of soil particle and is the velocity of incident wave
Av
xtuCtxuCF
Av
xtuvAtxuvF
v
xtuvtxuvtx
s
i
s
iss
s
iss
)(2),(
)(2),(
)(2),(),(
),( txu )(s
iv
xtu
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The first term represents the viscous resistance offered by horizontal dashpot. Hence it is replaced with a horizontal dashpot with a dashpot coefficient C equal to
It is found that when vertical shear wave propagates through an undamped, linear and isotropic semi infinite half space, the outcrop motion is twice the motion at any point within the half space. So the second term represents the equivalent shear force at outcrop. To apply it at the base of the model it is scaled down by 2. Hence, the equivalent nodal shear force applied at the base of the model is is uAv )(
Avs
),( txuC
iuC 2
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Analysis Procedure
Analysis is carried out in two stages-
Gravity analysis and
Dynamic analysis
Gravity analysis:
Side boundaries are fixed in horizontal direction and
kept free in vertical direction.
Base boundary is kept fixed in either directions.
Self weight of material is applied and gravity analysis
is performed
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Analysis Procedure
Dynamic analysis:
Once the gravity analysis is over, the restraints at the
boundaries are replaced with the reactions.
Radiation dampers are provided to take care of
reflection of shear waves.
The earthquake motion is applied at the base nodes in
the form of equivalent shear force.
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Material modeling
Constitutive behavior of soil
Pressure dependent multi-yield material model
Nonlinear material model, Drucker-Prager yield
surfaces as yield criteria
Captures liquefaction of soil as well. However in
present study only dry soil considered. Hence
parameters defining liquefaction set to zero.
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Elements used for soil
Quad element
- Four node quadrilateral element, with four Gauss points,
Two degrees of freedom at each node, both translational
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Maximum dimension in the direction of wave
propagation
120
8
8
max
max
max
minmax
s
s
vl
f
vl
l
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Modeling of Nail
Followed equivalent plate approach
Equivalent plate approach (Hsien 2003)Dhanaji S. Chavan
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Nails replaced with a plate
Basic concept- axial stiffness of nail and plate are
same when unit spacing is considered
In present study-elastic-beam column element, 3
dof, 2 translational, 1 rotational
nnpp EAEA
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Soil-Nail Connectivity
Case 1- Perfect bonding
Se
Se
Me
Soil
Soil
Nail
Me: Master node in equal degree of freedom constraint
Se: Slave node in equal degree of freedom constraint
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Case-2 Interface elements
Mi
Si and Se
Si
Mi and Se
Me
Mi: Master node in interface element
Me: Master node in equal degree of freedom constraint
Si: Slave node in interface element
Se: Slave node in equal degree of freedom constraint
Soil
Soil
Nail
Dummy nodes
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Verification of OpenSees model
OpenSees model is verified with Shake2000 model
Shake2000 used for equivalent 1-D Linear analysis
Material used- elastic isotropic, is set to be 1 for all strain values , negligible amount of damping 0.001% is defined
Discretization of OpenSees model and soil column in Shake2000 is same, total 46 layers
Peak horizontal acceleration profile across the depth and acceleration time history at the centre of model(and zero depth) are verified
maxGG
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Models used in present study
Total 3 slopes 300, 450 and 600
Each slope has height 12 m
Each slope modeled for 3 cases:
Case 1: slope without nail
Case 2: slope with nail, perfect bonding contact
Case 3: slope with nail, with interface elements
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Medium sand
Medium -dense sand
Dense sand
12m
20 m
30 m
200 m
Schematic of the model used in the present study
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Strain contours-at the end of gravity
analysis(slope 600)
(a) Case 1- without nail (b) Case 2- perfect bonding (c) Case 3- interface elements
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At the end of dynamic analysis
(a) Case 1- without nail (b) Case 2- perfect bonding (c) Case 3- interface elements
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Displacements at crest
Displacement at the end of gravity
analysis(mm)
Displacement at the end of
dynamic analysis(mm)
X Y X Y
Case 1- without
nail
4.7 60.7 5689.9 6259.2
Case 2- perfect
bonding
1.5 57.7 311.9 537.6
Case 3- interface
elements
3.7 60.9 937.0 1409.4
Displacement at the crest of the slope (600)
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Strain contours at the end of dynamic
analysis- slope 450
(a) Case 1- without nail (b) Case 2- perfect bonding (c) Case 3- interface elements
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Displacement at the end of dynamic analysis
(mm)
X Y
Case 1- without nail 1443.6 1781.1
Case 2- perfect bonding 214.2 305.5
Case 3- interface elements 255.6 327.8
Displacements at the crest of the slope (450)
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Strain contours at the end of seismic
analysis-slope 300
(a) Case 1- without nail (b) Case 2- perfect bonding (c) Case 3- interface elements
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Displacement at the end of dynamic
analysis(mm)
X Y
Case 1- without nail 50.0 164.2
Case 2- perfect bonding 0.2 95.5
Case 3- interface elements 10.9 103.2
Displacement at the crest of the slope (300)
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Permanent displacement at the toe
Case Displacement (mm)
Approximate method 16.9
FEM-without nail 91.6
FEM-with nail (perfect bonding) 21.9
FEM-with nail (interface) 15.0
Comparison of permanent displacement at toe (slope-600, Kc =0.2)
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Comparison of permanent displacement at toe (slope-450, Kc =0.1)
Case Displacement (mm)
Approximate method 63.5
FEM-No Nail 44.1
FEM-With Nail-Perfect Bonding 17.3
FEM-With Nail-Interface 14.7
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Case Permanent Toe Displacement(cm)
Approximate method 64.3
FEM-No Nail 14.6
FEM-With Nail-Perfect Bonding 14.3
FEM-With Nail-Interface 12.4
Comparison of permanent displacement at toe (slope-300, Kc =0.1)
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Explanation of mass distribution for toe
displacement
(a) Deformation pattern for perfect
bonding case
(b) Deformation pattern for interface case
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Perfect bonding versus interface
elements
Displacement in case of
interface elements (mm)
Displacement in case of
perfect bonding (mm)
X Y X Y
Nail-1 30.0 1543.0 7.9 588.8
Nail-2 23.5 1276.6 12.2 557.0
Nail-3 18.7 978.6 13.0 475.7
Nail-4 15.6 585.3 13.3 351.8
Nail-5 12.1 184.3 13.3 133.0
Deformation of nail tips(a) perfect bonding (b) Interface elements
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Variation of overburden pressure
along nail
(a) overburden pressure along nail-1 and nail-3 at 5.121 second
Nail- 1Nail- 3
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(b) overburden pressure along nail-1 and nail-3 at 10.318 second
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(c) overburden pressure along nail-1 and nail-3 at 15.322 second
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Increase per length(kPa) Percent increase per length
Nail-1 Nail-3 Nail-1 Nail- 3
5.121 second 2.64 6.75 18.29 7.62
10.318 second 1.70 2.10 11.75 2.37
15.322 second 1.92 3.64 13.31 4.11
20.443 second 2.62 9.48 18.15 10.70
25.567 second 3.70 16.54 25.64 18.67
30.621 second 3.59 9.58 24.87 10.81
35.703 second 3.84 8.86 26.54 10.01
40.754 second 3.37 7.58 23.29 8.56
45.754 second 2.98 9.36 20.60 10.57
Change in the overburden pressure
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Average increase in the overburden pressure is 10%
This increase in the overburden pressure will increase
the pull-out capacity of nail which in turn will add to the
stability of slope
Seismic design of nailed soil slope can be carried out
with static overburden pressure on the nail. However this
will result into conservative design and may add to the
cost of structure. Hence it is suggested that static
overburden pressure should be increased by 10% and
then used in the design
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Conclusions
In the design of nailed soil slopes by approximate method, it was assumed that the failure surface passes through the toe of the slope. The failure surface observed from the finite element analysis also passed through the toe of the slope
The failure surface was assumed to be log-spiral in the design of nailed soil slope by approximate method. However, it was observed from the finite element analysis of nailed soil slopes that the failure surface was planer
Overall deformation of nailed soil slope is more when soil-nail interface is defined with interface elements
The deformation at the toe of the nailed soil slope is more in case of perfect bonding contact in comparison with interface elements
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The change in the overburden pressure during seismic shaking,
along the nail length, was studied. It was found that there was
about 10 to 20% of increase in the overburden pressure over
the static overburden pressure when the slope is subjected to
seismic loading
Approximate method gives lower value of permanent
displacement at toe for higher critical acceleration and vice
versa
The permanent displacement, at the toe of the nailed soil
slope, obtained from the finite element analysis was found to
be smaller than that obtained from the approximate method,
irrespective of the slope angle and critical acceleration
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Scope for the future study
In the present study, nailed soil slopes without berm has been
considered. presence of berm may affect the failure surface,
nail forces and the permanent displacement at toe. Hence, the
finite element analysis of nailed soil slopes with berm,
subjected to earthquake loading, can be taken as the
extension of present work
In the present study,2-D finite element analysis has been
carried out. The seismic response of the 3-D model of nailed
soil slopes can be studied in the future
In the present study, nails of equal length were considered.
The effect of variable nail length, on the seismic response of
the nailed soil slopes, can be considered as the future task
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Scope for the future study
Nails with uniform spacing were considered in the present
study. The effect of variable spacing on the seismic behavior
of the nailed soil slopes can be taken as the extension of
present work
In the present study, only dry soil is considered. The effect of
saturated soil on seismic behavior of nailed soil slope can be
taken as the future task
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References
Al-Hussaini, M. M. and L. D. Johnson (1978). Numerical analysis of a reinforced earth wall, ASCE.
Cai, Z. and R. Bathurst (1996). "Deterministic sliding block methods for estimating seismic displacements of earth structures." Soil Dynamics and Earthquake Engineering 15(4): 255-268.
Chen, W. F. and J. T. P. Y. Fellows (1984). "Seismic displacements in slopes by limit analysis." Journal of Geotechnical Engineering 110: 860.
Fan, C. C. and C. C. Hsieh (2010). "The mechanical behaviour and design concerns for a hybrid reinforced earth embankment built in limited width adjacent to a slope." Computers and Geotechnics.
Fan, C. C. and J. H. Luo (2008). "Numerical study on the optimum layout of soil-nailed slopes." Computers and Geotechnics 35(4): 585-599.
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References
Al-Hussaini, M. M. and L. D. Johnson (1978). Numerical analysis of a reinforced earth wall, ASCE.
Cai, Z. and R. Bathurst (1996). "Deterministic sliding block methods for estimating seismic displacements of earth structures." Soil Dynamics and Earthquake Engineering 15(4): 255-268.
Fan, C. C. and C. C. Hsieh (2010). "The mechanical behaviour and design concerns for a hybrid reinforced earth embankment built in limited width adjacent to a slope." Computers and Geotechnics.
Fan, C. C. and J. H. Luo (2008). "Numerical study on the optimum layout of soil-nailed slopes." Computers and Geotechnics 35(4): 585-599.
Michalowski, R. L. (1998). "Soil reinforcement for seismic design of geotechnical structures." Computers and Geotechnics 23(1-2): 1-17.
Michalowski, R. L. and L. You (2000). "Displacements of reinforced slopes subjected to seismic loads." Journal of geotechnical and geoenvironmental engineering 126: 685.
Newmark, N. M. (1965). "Effects of earthquakes on dams and embankments." Geotechnique 15(2): 139-160.
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Thank You
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Meshing
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Mesh convergence
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Load-defection for interface element
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Interface element behavior
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Penetration convergence
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Sliding convergence
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