OpenSees: Seismic stability of nailed soil slopes

Seismic Stability Analysis Of

Nailed Slopes

Dhanaji S. Chavan

Asst.Prof., TKIET, Warananagar

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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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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


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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


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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


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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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Case Displacement (mm)


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)


FEM-No Nail 14.6

FEM-With Nail-Perfect Bonding 14.3

FEM-With Nail-Interface 12.4


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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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OpenSees: Seismic stability of nailed soil slopes

Engineering

Transcript of OpenSees: Seismic stability of nailed soil slopes