Dr. Arindam Dey Presentations/2021/Dey...05-01-2021 Short Course, NIT Warangal 17 •Modelling...

Dr. Arindam DeyAssociate Professor

Geotechnical Engineering Division

Department of Civil Engineering

IIT Guwahati

Short Course

Finite Element Analysis of Static and Dynamic

Soil-structure Interaction of Geosystems

Department of Civil Engineering, NIT Warangal

Introduction• Growing habitation and urbanization on hilly terrains

• Foundations on or near the edges of slopes

Examples of such practice

Buildings or roads constructed in hilly regions

Electric transmission towers built on mountain slopes

Foundations for bridge abutments

• Foundations on slope or near the slope

Reduction in ultimate bearing capacity

Incomplete formation of passive zone

Lack of resistance of outward lateral movement

05-01-2021 Short Course, NIT Warangal 2

Foundations on Horizontal Ground

• Hosseini (2014)

Carried out experimental and numerical investigation

Bearing capacity estimation of square footing

Comparison of results with conventional theories

• Khan et al. (2006), Cerato and Lutenegger (2006) and Nareeman (2012)

Carried out experimental investigation

Increased bearing capacity of square footing

Increase of footing width

• Cerato and Lutenegger (2007)

Carried out Experimental investigation

Enhanced bearing capacity of square footing

Significant effect of relative density of soil

• Khan et al. (2006), Pusadkar et al. (2013), Lavasan and Ghazavi (2014)

Inteference effect of square footing

Bearing capacity increased

Interfering footing than isolated footing

• Asaduzzaman and Iftiarul (2014), Dhatrak and Farukh (2014), Belal and Ahmed (2015)

Reinforcing soil bed

Enhanced bearing capacity


Foundations on Sloping Ground

• Shields et al. (1977), Bauer et al. (1981), Kumar and Ilampurthy(2009), Castelli and Lentini (2012), Keskin and Laman (2013)

Strip footing on dry cohesionless sandy slope

Ultimate bearing capacity and bearing capacity factor

Effecting various parameter (Setback distance, relative density, slope angle, load inclination)

• Castelli and Lentini (2012)

Square footing on cohesionless sandy slope

Bearing capacity and bearing capacity factor

• Azzam and Farouk (2010)

Skirted strip footing resting on the crest of sandy slope

Ultimate bearing capacity

• Clark et al. (1988)

Field test with anchored inclined footing

Overall response

• Alamshahi and Hataf (2009), Yoo (2001)

Geosynthetic inclusion

Enhanced bearing capacity of strip footing by altering the reinforcing parameter


Codal Provisions

• IS-1904 (1986)

Provided various design guidelines

The construction of shallow footing resting on slope face

• AASHTO (2012)

Provide various design charts

Shallow footings resting on or near the sandy or clayey slope


0.5u cq qq cN BN

Bearing Capacity of Square Footing Resting on Crest of c-φ Slope


Numerical Finite Element Modelling

05-01-2021 Short Course, NIT Warangal

• PLAXIS 3D

Three-dimensional analysis

Deformation

Stability

Ground water flow in geotechnical engineering

Equipped with features

Various aspects of complex geotechnical structures

• PLAXIS 3D Analysis

Geometry

Two types of model geometry

Horizontal ground surface or footing below horizontal ground surface

Footing on slope crest or on the slope face

The dimensions of the models

“0.1q” significant stress contour

Not to be intersected by the side and bottom edges of the model

The outermost significant stress isobar

Effect of the applied load

Considered to be negligible

7

Numerical Finite Element Modelling Boundary Conditions

Vertical edges of the model

Horizontal fixity

Slope of the model

No fixity

Bottom edge

Both vertical and horizontal fixities

Assumed to be non-yielding

This boundary condition

“Standard fixity”

Meshing

Finite element calculation

Discretized into smaller finite number of tetrahedral elements

10-noded tetrahedral elements

Five basic meshing schemes

Very coarse, coarse, medium, fine, and very fine

User-defined refinements

Special conditions

Mesh should be sufficiently fine

Accurate numerical results

Avoid very fine mesh

Excessive time

Convergence study05-01-2021 Short Course, NIT Warangal 8

Numerical Finite Element Modelling

• Geometry

‘0.1 q’ stress isobar

• Boundary condition

Standard fixities

• Meshing

10-node

Tetrahedrons

• Location

Footings

Various setback distance

Embedment depth


Development of Numerical Model

• Material

Soil (Keskin and Laman 2013)

M-C model

Associated flow rule

Footing (Boushehrian and Hataf 2002)

M20 concrete

Linear elastic model

Rinter = 1 (Nasr 2014)

Newton-Cotes integration

• The failure mechanism generated beneath the footing

Resting on horizontal ground

Postulated by Terzaghi (1943)

Assumption that the base of the footing is rough


Unit weight (γ)

(kN/m3)

Modulus of elasticity E

(GPa)Poisson's ratio (ν)

25 22 0.15

Results and Discussions• Validation study

Castelli and Lentini (2012)

Same soil properties

Domain size

B = 0.08 m (square)

b = 0.12 m

• Convergence study

Fine mesh

Significant match

Numerical

Experimental outcomes


Results and Discussions


• Convergence study

Various slope angles

Embedment depth

Fine mesh

Opted for analysis

• Parametric investigation

Variation of c


Shear strength increases

Increase of c

Variation of φ


Confinement increases

Increase of φ



• Variation of unit weight (γ)

Insignificant effect

On ultimate bearing capacity (qu)

• Variation of width of footing (B)

Significant effect

Bearing capacity (qu) increased

Increasing B

Larger soil domain

Support the incumbent load



• Variation of slope angle (β)

Ultimate bearing capacity decreased (qu)

Smaller zone of passive resistance

Increase of β

• Variation of Embedment depth (Df)

Ultimate bearing capacity increased (qu)

Higher confinement effect

Restricting the soil movement


• Failure mechanism

Setback ratio (b/B) = 0

• Formation of passive zone

One-directional

Curtailed by the slope

Dominant free deformation

• Setback ratio increases

Influencing effect of the slope

Gradually diminishes

• Setback ratio (b/B)critical = 4

Footing behaves

Resting on horizontal ground


Acharyya R, Dey A (2017) Finite element investigation of the bearing capacity of

square footings resting on sloping ground. INAE Letters 2(3): 97-105.

Acharyya R, Dey A, Kumar B (2018) Finite element and ANN-based prediction ofbearing capacity of square footing resting on the crest of c-φ soil slope. InternationalJournal of Geotechnical Engineering DOI: 10.1080/19386362.2018.1435022.

Bearing Capacity of Strip Footing Located on Crest of c-φ Slope


Numerical Modelling


• Modelling

Plaxis 2D

• Meshing

15-node

Triangular element

• Geometry and boundary condition

• Material model (Soil and Footing)

Same as considered

Square footing on slope



0 1 2 3 4 5 6 7 8 9 10 110

20

40

60

80

100

120

140

qu/

Hs

Setback ratio (b/B)

c = 10 kPa

c = 30 kPa

c = 50 kPa

, B = 2m, D

f/B = 0

0 2 4 6 8 10

8

16

32

64

128

ckPa = , D

f/B = 0, B = 2 m

Setback ratio (b/B)

qu/

Hs


• Failure mechanism

Various setback distances

b = 6B (B = width of footing)

Behaves footing on horizontal surface


Acharyya R, Dey A (2018) Assessment of bearing capacity for strip

footing located near sloping surface considering ANN-model.

Neural Computing and Applications DOI: 10.1007/s00521-018-

3661-4.

Interaction Mechanism of Strip Footings Resting on a Horizontal Ground


Interfering Foundations on Horizontal Ground

• Stuart (1962) is the first

Given the concept of interference of shallow footings

Efficiency factors were added in

The ultimate bearing capacity expression given by Terzaghi (1943)

To show the effect of interference

On Terzaghi’s bearing capacity factors

• Saran and Agarwal (1973)

Laboratory investigation done

For two dimensional and three dimensional cases

Bearing capacity factor and settlement characteristics

Results are matched

Stuart (1962)

Bearing capacity decreased

For increasing of spacing of footing



• Das and Larbi Cherif (1983)

Experimental Investigation

Ultimate bearing capacity of closely spaced strip footings

Obtained values compared

Stuart (1962)

Bearing capacity decreased

For increasing of spacing of footing

• Kumar and Kouzer (2007)

upper bound limit analysis in conjunction with finite elements

linear computer programming

Results given

In terms of ‘Efficiency factor’ (ξ )

When two footings having no gap

The magnitude of ξ is 2.0



• For the validation

The experimental studies done by Das and Larbi Cherif (1983)

Two different numerical models have been developed

One model was formed for strip footing resting on surface of horizontal ground

Other model was made for footing resting on horizontal ground with embedment depth

Dry sand having relative density of (Dr) of 54%

Dry density of 15.88 kN/m3

And angle of internal friction (φ) of 38°

medium mesh has been used to discretize the model


Results and Interpretations

• Numerical simulations

Conducted for varying spacing of the footings,

Ranging from 1B to 10B,

Where B is the width of an individual footing

The interaction reduces

The increase in spacing between the footings,

Non-overlapping displacement and stress contours



• Total displacement and vertical stress distribution



• Incremental deviatoric strain



• Footings spaced

Distance of 6B can be

Considered to have mutual influences

On their stress and settlement characteristics

Termed as closely-spaced interfering footings.

Beyond this spacing

The interaction effects of the footings cease to exist

The footings can be considered as isolated footings


S/B = 1 S/B = 1.5

S/B = 2 S/B = 3

S/B = 4 S/B = 5

S/B = 6 S/B = 10



S/B = 1 S/B = 1.5

S/B = 2 S/B = 3

S/B = 4 S/B = 5

S/B = 6 S/B = 10

Response of Interfering Footings Located on Crest and Face of Slope


Interfering Foundations on Slopes

• Interference on sloping ground

No documentation observed

• From practical point of view

The mechanism of a single footing

Not represent the mechanism of building footings

Due to the presence of various types of multiple footings within a small region

• Common in hilly regions

Find most of the houses

Resting either on the slope face or on the slope crest

Most of these inhabitations

Comprises of buildings resting on shallow footing


Interfering Foundations on Slopes


Mechanism of Footings Located on a Slope Crest

• Investigate the basic mechanism

The interaction effect of strip footing

Resting on or near the slope

Basic difference of mechanisms of interaction

For strip footings resting on horizontal surface

And strip footings resting on or near the slope

A sloping model of homogeneous dense sandy soil,

developed in PLAXIS 2D


Mechanism of Footings Located on a Slope Crest


• Footings are kept over the crest of the slope

Nominal setback distance and spacing,

Mass movement of the soil occurs towards the slope face

Lack of passive resistance from the slope boundary

• This behaviour is different in comparison

Footings resting on horizontal ground with a nominal spacing

The total displacement was downwards

Rather than one directional


• Geometry

‘0.1q’ stress isobar

Not intersected by boundaries of domain

• Boundary condition

Standard fixities


• Meshing

10-node

Tetrahedrons

Fine mesh

Used in analysis


• Material

Soil (Nader and Hataf 2014)

Associated flow rule

(Drescher and Detournay1993)

Footing

M20 concrete

Interface

Rough

Rinter = 1


Soil typesCohesion

(c) (kPa)

Angle of

internal

friction

(φ)°

Unit

weight (γ)

(kN/m3)

Modulus

of

elasticity

(E) (kPa)

Poisson's

ratio (ν)

Soil-A 10 40

8000 0.3Soil-B 30 30 17

Soil-C 80 10

Unit weight (γ)

(kN/m3)

Modulus of elasticity E

(GPa)

Poisson's ratio

(ν)

25 22 0.15

• Validation

Das and Larbi-Cherif (1983)

Experimental Investigation

Geometrical and geotechnical properties

Same taken

Numerical analysis

Dry sand having relative density of (Dr) of 54%,

Dry density of 15.88 kN/m3

Angle of internal friction (φ) of 38°

Fine mesh

Used to discretize the model

Results and Discussion

• Variation of Spacing

Bearing capacity

Increased

up to S/B = 1.5

Decreased

Up to S/B = 3

Isolated strip footing

Resting on crest of slope

Slope angle increased

Bearing capacity

Decreased


0 2 4 6 8 10

1500

2000

2500

3000

3500

4000

4500

s/B

qu (

kP

a)

b/B = 2, Soil-A

ß=10°

ß=20°

ß=30°

ß=40°


• Setback distance (b)

Bearing capacity

Increased

Increasing

Setback distance



• Variation of Footing Width (B)

Bearing capacity

Increased

Larger soil domain

Support the incumbent load


• Variation soil type

Soil-A

S/B = 3

Soil-B

S/B = 3

Soil-C

S/B = 2

Bearing capacity

Increased

Increasing angle of internal friction (φ)

Results and Discussion• Failure mechanism

(b/B) = 3

β = 30°

Soil-A

(S/B) critical = 3

Isolated strip footing


Acharyya R, Dey A (2018) Assessment of bearing

capacity of interfering strip footings located near

sloping surface considering Ann-technique. Journal

of Mountain Science 15(12): 2766–2780

Mechanism of a Footing on a Slope Face

• The mechanism for a strip footing located in a slope

Plane strain approach taken for

Assessment of mechanism

Through PLAXIS 2D

A 60 m high hill slope with sloping angle of 30°

A 2 m wide strip footing has been considered

Located on the hill-slope having

A minimum embedment depth of 1 m from the slope face

A homogeneous medium dense sandy soil

To make the hill slope and

A vertical failure load given over the footing

The numerical investigation

Natural hill-slopes will not be a purely sandy medium

And will comprise of other soil constituents as well

However, to keep the problem simple for understanding

The pre-failure and failure mechanisms of the footing and the slope

The simulation has been carried out

Considering only homogeneous cohesionless medium.



• A 55m high hill slope

Modelled in the PLAXIS 2D

Represent a typical field slope geometry

The failure displacement

Given to the strip footing

As 20% of the footing width (B)



• While evaluating the stress and deformation mechanisms

The shallow strip footing resting on slope face

Observed that at failure load

The footing exhibits rotation

Initially, it has been believed

Such rotation is bound to be exhibited due to

The outward movement of the soil mass owing to the lack of passive resistance

From the slope face

Illustrates the mechanism developed

Terms of the incremental displacement, incremental deviatoric strain and soil displacement vectors

It can be easily deducted that the soil displacement

Beneath the footing has occurred predominantly

Towards the slope face, resulting in the tilting of the footing

It was supposedly assumed that such tilting of footing should not occur

For a footing resting on horizontal ground in a symmetric numerical model and subjected to a symmetric loading



• Plaxis 2D output


Interaction Mechanism of Footings on a Slope Face

• 2D simulation

• The degree of interaction

Quantified by the overlap of the 0.1Bdisplacement contour

Termed as ‘significant displacement contour

Produced by the adjacent footings

Highlights the significant displacement contour

Produced by the loading of the benchmark footing

The region bounded by the significant displacement contour

Susceptible to substantial movement upon loading of the footing

Any other footing present in this region,

Simultaneously loaded till failure

Result in further drastic movement of the soil in the bounded region


Interaction Mechanism of Footings on Slope Face


Interaction Mechanisms of Footings on Slope Face



• Numerical simulation of the interference effects of footings

Resting on horizontal ground has been carried out

And validated against the existing theories.

Interaction effect of the footings, resting on a slope

Not be according to the conventional theories of interference of footings

Resting on horizontal ground.

Based on intensive studies, the interaction effects of footing

Resting on a hill-slope have been efficiently illustrated



• habitations in the hilly terrains

Most of the urbanization

Taken place on the hill slopes

Slope angle within the range of 20° to 40°


As a benchmark problem The response of an

isolated strip footing investigated;

This problem is termed as ‘h = 0B’ condition


• 3D simulation

• In order to investigate

• The effect of analysis type on the obtained understanding

3D simulation has been done by PLAXIS 3D v2015

To investigate the interference effect of strip footings resting on hill slope

A 25° hill slope

Dense sand

The width of the slope

such a way that the boundary effect should not come in the analysis

The height was taken same as taken in 2D analysis

The length of the footing has been taken as 9 times of the footing width (B)

The footing should behave like strip footing

Plain strain condition is maintained

Failure load imposed over the footing



• Displacement iso-surfaces


Application of Artificial Neural Networks in Predicting Bearing Capacity of

Foundations on Slopes


Overview of ANN

• Neural networks

Bio-mimetic data mining structures

Containing several simple

Highly interrelated

Processing elements

Termed as artificial neurons

In a complex architecture

Used to develop correlation maps

Between the contributory parameters

Inputs

The model outcomes

Outputs


Neural Network

Learning Algorithm

Error feedback

Error

Desired output

Input Output

Change

parameters to

reduce error

Modelling of ANN

• Normalization of data

Input

Output

(Rukhaiyar et al. 2017)

and are before and after normalization magnitude

and are the maximum and minimum magnitude


min

max min

2( )1

( )

a

n i i

i

i i

P PP

P P

a

iPn

iP

max

iPmin

iP

• ANN

Architecture

• Network

Feed-forward cum back-propagation

• Training function

Levenberg-Marquardt's


• ANN models (Square footing on slope)

Number of neurons

Hidden layer

Varied

The mean square error (MSE)

Achieves a minimum (0.0126)

Ten neurons

Hidden layer

7 input nodes

(c, φ, γ, B, b/B, β and Df/B)

10 hidden-layer neurons

A single (1) output node

(qu)

The architecture

7–10–1


2

1

1( )

N

Simulation ANN

i

MSE O ON

Nd = Number of data

OSimulation = Numerically simulated values

OANN = Predicted values of the same entity


• ANN architecture

Training

Testing

Validation

80% of the total data

used for training

20% of the total data

Validation of the ANN architecture

Training dataset

Further divided, where

70% of the data

Used for actual training

Remaining 30% of the data

Used as the testing

Das and Basudhar 2006



• Table

Weight

Biases


N

X

Hidden

N1

Hidden

N2

Hidden

N3

Hidden

N4

Hidden

N5

Hidden

N6

Hidden

N7

Hidden

N8

Hidden

N9

Hidden

N10

c (X1) 0.55 -0.67 -0.26 0.84 -0.54 0.95 0.58 -3.58 0.004 -0.12

φ (X2) -0.56 -0.33 8.43 1.30 -0.64 -7.25 1.27 -5.25 -0.29 -0.91

γ (X3) 0.32 0.03 0.02 0.16 -0.09 0.03 0.09 -0.75 -0.01 0.04

B (X4) 0.24 0.11 0.15 0.46 -0.52 -0.06 0.46 4.79 -0.13 -0.13

b/B (X5) 1.45 0.0008 2.05 0.14 0.07 -1.74 -0.51 2.64 0.02 2.01

β (X6) -0.38 -0.01 -0.47 -0.04 -0.01 0.51 0.11 -0.67 0.004 -0.46

Df/B(X7) 1.30 0.57 -0.66 0.72 -0.35 0.66 0.42 6.50 -0.09 -0.05

N

Y

Hidden

N1

Hidden

N2

Hidden

N3

Hidden

N4

Hidden

N5

Hidden

N6

Hidden

N7

Hidden

N8

Hidden

N9

Hidden

N10

Output 0.06 -2.16 0.52 1.91 2.01 0.53 0.83 2.32 -3.58 0.97

Hidden layer biases

(bhN)

Output layer biases

(bO)

1.16

-0.61

-0.48

-0.66

-2.16

1.34

0.03

-1.79

-5.15

-0.03

3.03

Biases

Hidden-Output weights

Input-Hidden weights


• Sensitivity analysis

Garson’s algorithm (1991)


10

71

1

XN

X

N

ZN

Z

HiddenInput

Hidden

(Garson’s algorithm)

N

Z

Hidden

N1

Hidden

N2

Hidden

N3

Hidden

N4

Hidden

N5

Hidden

N6

Hidden

N7

Hidden

N8

Hidden

N9

Hidden

N10

c (X1) 0.04 1.45 -0.13 1.61 -1.09 0.50 0.48 -8.31 0.02 -0.12

φ (X2) -0.04 0.71 4.40 2.49 -1.29 -3.83 1.06 -12.18 1.03 -0.88

γ (X3) 0.02 -0.07 0.01 0.31 -0.19 0.02 0.08 -1.73 0.02 0.04

B (X4) 0.02 -0.24 0.08 0.87 -1.04 -0.03 0.38 11.10 0.48 -0.12

b/B (X5) 0.09 0.0018 1.07 0.26 0.14 -0.92 -0.43 6.13 -0.07 1.94

β (X6) -0.02 0.03 -0.24 -0.08 -0.01 0.27 0.09 -1.55 0.01 -0.45

Df/B (X7) 0.08 -1.23 -0.34 1.37 -0.69 0.35 0.35 15.09 0.32 -0.05

Product of the input-hidden and hidden-output

connection weights

Shahin et al. 2002; Das et al. 2012;

Mishra et al. 2016

19%

35%16%

11%

7%12%

c

φ

B

b/B

β

Df/B

Square footing

Strip footing

12%8%

7%

25%25%

23%

c

φ

B

b/B

S/B

β

Interfering strip footing

Results and Discussions• Predicting Expression (Goh 1994; Das and Basudhar 2006; Das and Basudhar 2008)

(Square footing on slope)


1 0.56 0.32 0.24 10.55( ) ( ) ( ) .45( / ) ( )0.38 1.30 / 6( ) 1.1fA c B b B D B

10 0.12 0.91 0.04 0.13( ) ( ) ( ) ( / )2.01 0.46 0.05 3( ) ( / .) 03fA c B b B D B

1 1

1 11 (0. )06

A A

A A

e eB

e e

10 10

10 1010 0 (7 ).9

A A

A A

e eB

e e

1 1 2 3 4 5 6 7 8 9 100.61C B B B B B B B B B B 1 1

1 1

( ) ( )C C

u n C C

e eq

e e

max min min( ) 0.5[( ) 1][( ) ( ) ] ( )u u n u u uq q q q q

Acharyya R, Dey A, Kumar B (2018) Finite element and ANN-based prediction of bearing capacity of square footing resting on the crest of c-φ soil slope. International Journal of Geotechnical Engineering DOI: 10.1080/19386362.2018.1435022.

Acharyya R, Dey A (2018) Assessment of bearing capacity for strip footing located near sloping surface considering ANN-model. Neural

Computing and Applications DOI: 10.1007/s00521-018-3661-4.

1 1

( ) { [ ( )]}h m

un Sig O N Sig hN iN i

N is

qf b w f b w X

H

Typical Design Example using ANN • Design example for square footing resting on crest of a slope

• The initial step in the assessment of bearing capacity

Normalize the input and output parameters between 1 to -1

Equations in previous slide

The normalized output [(qu)n] magnitude

-0.307

The actual magnitude of qu Equation in previous slide

The ultimate bearing capacity of square footing (qu) for current design problem has been found as 6.1 MPa


Parameters Range

c (kPa) 0-80

φ (°) 10-40

B (m) 0.08-2

b/B 0-10

β (°) 10-40

qu (MPa) 0.25-17.14

0.5 ( 0.307 1) (17.14 0.25) 0.25 6.1 MPauq

Relevant References

• Acharyya R, Dey A (2017) Finite element investigation of the bearing capacity of square footings resting on sloping ground. INAE Letters 2(3): 97-105.

• Acharyya R, Dey A, Kumar B (2018) Finite element and ANN-based prediction of bearing capacity of square footing resting on the crest of c-φ soil slope. International Journal of Geotechnical Engineering DOI: 10.1080/19386362.2018.1435022.

• Acharyya R, Dey A (2018) Assessment of failure mechanism of a strip footing on horizontal ground considering flow rules. Innovative Infrastructure Solution DOI: 10.1007/s41062-018-0150-7.

• Acharyya R, Dey A (2018) Importance of dilatancy on the evolution of failure mechanism of a strip footing resting on horizontal ground. INAE Letters DOI: 10.1007/s41403-018-0042-3.

• Acharyya R, Dey A (2018) Assessment of bearing capacity for strip footing located near sloping surface considering ANN-model. Neural Computing and Applications DOI: 10.1007/s00521-018-3661-4.

• Acharyya R, Dey A (2018) Assessment of bearing capacity of interfering strip footings located near sloping surface considering Ann-technique. Journal of Mountain Science 15(12): 2766–2780.

• Acharyya R, Dey A (2018) Assessment of bearing capacity and failure mechanism of single and interfering strip footings on sloping ground. International Journal of Geotechnical Engineering. DOI: 10.1080/19386362.2018.1540099


Acknowledgment


Dr. Rana Acharyya

Assistant Professor

Dehradun Institute of Technology

Uttarakhand

Further Interaction

http://www.iitg.ac.in/arindam.dey/homepage/index.html


https://www.researchgate.net/profile/Arindam_Dey11

http://www.iitg.ac.in/arindam.dey/homepage/index.htmlhttps://www.researchgate.net/profile/Arindam_Dey11


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