modelling techniques in geotechnical engineeering

7/30/2019 Modelling techniques in geotechnical engineeering

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Geotechnical and Geoenvironmental Aspect of Waste

and their Util ization in I nf rastructure Project

Modeling Techniques in Geotechnical

Engineering

V. A. Sawant

Associate Professor

Department of Civil Engineering

IIT Roorkee


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PHYSICAL MODELING

NUMERICAL MODELING

STATISTICAL ANALYSIS- DEVELOPMENT OFEMPIRICAL RELATIONSHIPS


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PHYSICAL MODELING

CENTRIFUGE MODELING

NUMERICAL MODELING

RELIABILITY BASED ANALYSIS

ARTIFICIAL NEURAL NETWORKS


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Physical Modeling

Studies on scaled models are resorted to in engineering

disciplines in order to understand the behaviour of thereal full-scale structures called prototypes.

A physical model involves a real object subjected to

forces or displacements and physical quantities such as

resulting responses are measured.

From the physical measurements made on the model,

the corresponding quantities are predicted for the

prototype.


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Scaled models in GE seriously lack similitude

because stress levels in the model do not matchthose in the prototype.

There are two major factors which need to be

considered in modeling of GE structures Theseare :

Body force due to gravity which is often the

actuating force and

Soil properties such as strength and stiffness

which are highly stress dependent.


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CENTRIFUGE MODELINGWhen studies are undertaken to understand the

behavior of real structures through scaled models, it isfound impossible to simulate the body forces in the

normal 1 g field.

It has been realized that this deficiency can beovercome with the use of centrifuge technique in which

models are subjected to predetermined, high

acceleration levels to produce similarity conditions

satisfactorily in most situations.


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Centrifuge modeling is now firmly established as a

dependable research tool that can provide solutions to

many of the intractable problems in GE.Some of the important problems relating to earth dams

tunnels, offshore foundations, geo-environmenta

problems, problems of nuclear waste disposal, seismicstudies of earth structures and foundations can be

tackled using centrifuge modeling.


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Two systems are said to behave similarly when

corresponding physical quantities are related by

equations of the type Rm=Rpwhere Rm and Rp are same physical quantity pertaining

to the model and the prototype

is the proportionality constant.Different physical quantities may be related by

different proportionality constants. The linearity of the

relationship is a necessity.

When two systems behave similarly :

knowledge of the behaviour of one will enable us to

determine what the behaviour of the other must be.


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Modeling of clay slope

Consider the stability of a

clay slope shown in Figure

having a slope angle i under

undrained conditions.

An estimate of the

maximum stable height maybe based on the slip circle

method of analysis.

Based on Taylor's stabilitychart the maximum stable

height of slope Hc for i =

60 can be estimated.


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Suppose if this estimate is to be verified, how

could one proceed to carry out a scaled model

study by reducing the linear dimension by afactor, say of 50 %.

If experiments are envisaged in 1-g field it

becomes necessary to produce a model material

having a value of cu/=0.02 for the value of theprototype material.

It is indeed almost impossible to produce a

material corresponding to this value of cu/.


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Table 3 Scaling Laws

Quantity Prototype Model

Length n 1

Area n2

1Volume n3 1

Velocity 1 1

Acceleration 1 n

Mass n3 1

Force n2 1

Energy n3 1Stress 1 1

Strain 1 1

Mass density 1 1

Energy density 1 1

Time (dynamic) n 1

Time (diffusion) n2 1Time (creep) 1 1

Frequency 1 n


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ANNs are a data driven artificial intelligence approach

that attempts to mimic, cognition capability of humanbrain.

ANNs learn by examples of data inputs and outputs

presented to them so that the subtle functionalrelationships among the data are captured, even if the

underlying relationships are unknown or the physical

meaning is difficult to explain.

This is in contrast to most traditional empirical andstatistical methods, which need prior knowledge about

the nature of the relationships among the data.

ARTIFICIAL NEURAL NETWORKS


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The input from each PE in the previous layer xi is multiplied by

an adjustable connection weight wji. At each PE, the weighted

input signals are summed and a threshold value j is added.

This combined input Ij is then passed through a nonlineartransfer function f(Ij) to produce the output of the PE yj . The

output of one PE provides the input to the PEs in the next layer.

The propagation of information in an ANN starts at the input

layer, where the input data are presented. The network adjustsits weights on the presentation of a training data set and uses a

learning rule to find a set of weights that will produce the

input/output mapping that has the smallest possible error. This

process is called learning or training.Once the training phase of the model has been successfully

accomplished, the performance of the trained model needs to

be validated using an independent testing set.


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Figure 2 Main steps in ANN model development


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Liquefaction during earthquakes is one of the very dangerous

ground failure phenomena that can cause a large amount of

damage to most civil engineering structures. Although theliquefaction mechanism is well known, the prediction of

liquefaction potential is very complex. This fact has attracted many

researchers to investigate the applicability of ANNs for predicting

liquefaction. Hanna et al (2007) reported evaluation of liquefaction

potential of soil deposits using artificial neural networks. The

prediction capabilities of the ANN model was compared to a set of

data that were not used during model training and testing. The

validation data was randomly selected from both Kocaeli and Chi-

Chi earthquakes, and corresponds to approximately 12 percent of

the data set collected. The results are presented in graphical form

in Figure 3. The results produced by the proposed ANN model

compare well with the field data.


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Figure 3 Network performance on soil liquefaction potential (Hanna et al 2007)


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NUMERICAL MODELINGMathematical and computational techniques have been developed for

design, analysis, and prediction of the behavior of soil and rock, as well

as structural elements in contact with the soil, when subjected tovarious internally or externally applied boundary conditions.

Models are not meant to be an exact representation of reality, but

rather to mimic the essential characteristics of the elements of the

prototype as necessary for design or prediction.

Status in Basic and Applied Engineering Research

Numerical modeling is the subject of many basic and applied research

efforts in civil engineering. Such efforts often involve the use of FDM,

FEM, BEM, and DEM in conjunction with sophisticated nonlinear

elastic, elastoplastic, viscoplastic, crystal plasticity, and

micromechanical constitutive models. Constitutive models have

increased rapidly in sophistication in recent decades.


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Subgrade Reaction Approach

Elastic Continuum Approach

Finite Element Analysis

Analysis of Pile (LLP)

S i l i l FEM


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In the SAFE approach, variations of loading anddisplacements in the direction of revolution are

expressed in the form of Fourier series.

Displacements in the plane forming solid ofrevolution are expressed using shape functions, as

employed in 2-D FE formulation.

Semi-analytical FEM

L

n

n

L

n

n

L

n

n

L

n

n

L

n

n

L

n

n

nwnww

nvnvv

nunuu

10

01

10

sincos

cossin

sincos


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Semi-analytical FEM

Pile & soil media 8 node continuum element

Interface between pile and soil 6 node interface

element


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Eight Noded Element

84

112

1

62

112

1

7,5,3,1

1)1)(1(4

1

2

2

andifor

N

andifor

N

ifor

N

ii

ii

iiiii


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Stress strain relationship is given as,

DD

z

r

rz

z

r

z

r

rz

z

r


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215.000000

0215.00000

00215.0000

0001

0001

0001

)1)(21(

ED


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Element stiffness matrix, [K]e, is given by

Load vector, {F}, for uniformly distributed load,

qz, acting on the element can be obtained as,

1

1

1

1

2 ddrJBDBkT

e

2

0

1

1

0

sin

cos

ddrNqaFT

e

Stiffness matrix of and interface element

V S

f

T

f dsBDBk


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Geometry and Material

Properties

Pile E=0.3605108 kPa

= 0.15

Soil Es=4267 kPa

Load 1000 kN

Dia (m) 0.4, 0.6, 0.8, 1.0

L/D Ratio 10, 15, 20, 25

z/D

r/D

Finite Element Mesh


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Deflection Curves for different Dia & L/D ratio

Z/L

Non-dimensional Displacement

0.4-25

0.6-25

0.8-25

1.0-25

0.4-20

0.4-15

0.4-10

M/HT


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Z/L

M/HT

25 20

15 10

Bending Moment along the length of pile

Depth of max. moment 0.33, 0.3, 0.25, 0.2 (L/D 10, 15, 20, 25)

i l ( )


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Top-Displacement (mm)

L/D Dia 0.4 Dia 0.6 Dia 0.8 Dia 1.0

10 186.660 123.025 91.435 72.582

15 159.468 105.436 78.557 62.489

20 155.309 102.769 76.618 60.977

25 155.131 102.658 76.538 60.916


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Pile Top Displacement (mm)

Top-Displacement(m

m)

L/D

0.4 0.6

0.8 1

EI


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Non-dimensional Top-Displacement


10 0.50831 0.50253 0.49799 0.49413

15 0.43426 0.43068 0.42785 0.42542

20 0.42293 0.41979 0.41729 0.41513

25 0.42245 0.41933 0.41685 0.41471

3TH

EI


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Non-dimensional Pile Top Displacement

Non-DimensionalDisplacement

L/D

0.4 0.6

0.8 1

M M t (kN )


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Max. Moment (kNm)


10 566.465 848.613 1129.925 1410.425

15 707.483 1057.121 1404.825 1750.825

20 731.766 1092.167 1450.161 1806.061

25 733.780 1095.050 1453.869 1810.558


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Maximum Moment in Pile (kNm)

Max.

Moment(kNm)

L/D

0.4 0.6

0.8 1

M


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Non-dimensional Max-Moment


10 0.22190 0.22162 0.22131 0.22100

15 0.27714 0.27607 0.27516 0.27434

20 0.28665 0.28522 0.28404 0.28300

25 0.28744 0.28598 0.28476 0.28370

TH

MM max


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Non-dimensional Max. Moment in Pile

Non-D

imensionalMaxM

oment

L/D

0.4 0.6

0.8 1

Observations


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1. Top Displacement (absolute and non-dimensional) is

decreasing with increase in pile diameter and L/D ratio.

However after L/D=20 it approaches a constant value(0.42 in non-dimensional).

2. Absolute Max. Moment in Pile is increasing with

increase in pile diameter and L/D ratio. However after

L/D=20 it approaches a constant value.

3. Non-dimensional Max. Moment in Pile is decreasing

with increase in pile diameter, but increasing with L/D

ratio (0.22 to 0.28). However after L/D=20 it approaches

a constant value (0.287).

4. Depth of max. moment decreases with L/D ratio from

0.33 (for L/D=10) to 0.2(for L/D=25).


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3-D F ini te Element Analysis

Pile, pile cap and soil aredescretized using 20 nodeisoparametric continuumelements

Interface between the pileand soil is modeled using 16node isoparametric surfaceelement.

The analysis, further, takesinto consideration theinteraction between the pile

cap and underlying soil,generally the most neglectedparameter in the analysis ofpile group.

ddVVBDBK

dddJBDBK

f

T

fe

T

e

1

1

1

1_

1

1

1

1

1

1


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Pile was hollow circular with diameter of 1.6. However, for the sake of convenience, the

hollow circular section of pile is converted into an equivalent solid circular section of 1.6

An equivalent modulus of elasticity of sand

modulus was approximately computed from the relation E= Jz Terzaghi (1943)

where z is the depth from surface and J is the dimensionless parameter. Lateral load of

magnitude 2.75 lb

Table 1 : Properties of Pile Soil

Pile Soil

Mild Steel Medium Dense sand

Ep =43520 lb.inch2 Density =120 lb/cft

= 0.20 = 0.25

J = 350


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0

4

8

12

16

20

24

-0.002 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016

Depth(inch)

Displacement (inch)

Figure 2 Comparioson of Top Displacement of Pile

FEM Expt

Figure 3 Comparison of Bending Moment distribution in Pile


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Figure 3 Comparison of Bending Moment distribution in Pile

0

4

8

12

16

20

24

-0.5 0.5 1.5 2.5 3.5 4.5 5.5

Depth(i

n)

Moment (lb-in)

FEM

Expt


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From the Figure 2 and Figure 3, quite a good

agreement is seen in the results obtained by FEMand experiment.

Variation obtained in displacement between either

result is in the range of 4-10 % and that in moment

in is in the range of 3- 8%.This indicates close agreement in the results.

Displacement (m)


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D

epth(m)

FirstSecond

Third

Spacing 3D

Depth(m)

Moment (kNm)

First

Second

Third

Spacing 3D

Granular Pile (GP)


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In this section, a single GP whose modulus of

deformation increases with depth is analyzed.

If (z, ) are vertical and shear stress on anyelement, then from the equilibrium of vertical

forces on the elementdzd

d z 4

ZEZE 10

Assuming the modulus of deformation E(Z) of the GP

to increase linearly with depth as

where is the rate of increase of the modulus with the

normalized depth Z=z/LStress strain relation for the GP


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d

wWand

Ed

Lkwhere

WZdWd

ZdWdZ

Ed

wk

zd

wd

Lzd

wdZ

dwk

zdwdLE

zdwdZE

zd

wdZEZE

s

s

s

zz

0

2

2

2

0

2

2

02

2

0

0

4

01

04

1

4/1

1.

Boundary conditions


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Boundary conditions

At top of GP z=Z=0 24

d

Pz

At tip z=L, Z=1,

W=0, if GP is resting on rigid stratumw = z/kt, for deformable stratum


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01

1

01

1

1

22

2

2

2

W

W

Zd

Wd

Zd

WdZ

W

W

Zd

Wd

Zd

WdZ

dkwhere

W

Wdk

m

sisi


51/61

ZnW

WnZnWnZnW

nZWith

WW

ZWW

ZWWWZ

i

iii

i

iiiiii

121

5.015.01

1

012

21

2

2

1

2

1

2

211

211

Consolidation


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222

22

2

2

2

2

2

,,1,,2,,1

,1,,,2,1,

2

,1,,1,11

,,,,

1

z

tjiutjiutjiu

z

u

r

tjiutjiutjiu

r

u

r

tjiutjiu

rr

u

r

t

tjiuttjiu

t

u

formDifferenceFinite

z

uC

r

u

rr

uC

t

u

j

vZvR


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22

,,1,,2,,1

,1,,1,2

,1,,,2,1,,,,,

z

Ctand

r

Ctwhere

tjiutjiutjiu

tjiutjiurr

tjiutjiutjiutjiuttjiu

vZZ

vRR

Z

jR

R

00;0;02

r

urat

z

uHzatudrAt e

Boundary conditions

Reliability


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Reliability is the probability of an system performing its

required function adequately for a specified period of

time under stated conditions.It is the purpose of reliability-based design to produce

an engineered system whose failure would be an event

of very low probability.

Probabilities of failure are the most significant indexesof reliability.

Being objective, they admit directly to comparisons of

the risk of failure of different systems under varying

operating conditions.


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Slope section for the Illustrative example``1

Central factor of safety of the slope using mean values of

the uncertain parameters is 1.243


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Table 1 Soil data for Illustrative Example

Soil Parameter Mean Value COV (%)

Cohesion, c' (kN/m2) 18.00 22.22

Friction Angle, 30.00 10.00

Unit Weight, (kN/m3

)19.50 3.00

Pore Pressure Ratio, ru0.35 50.00

First Order Second Moment (FOSM) Method


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First Order Second Moment (FOSM) Method

FOSM estimates the uncertainty on the FS as a function of the

variances of the random input variables.

, cohesion, and pore pressure u.

It uses Taylor series expansion to estimate the local uncertainty of

the FS

If Y is a function of several random variables,

Y=g(X1, X2, ........, Xn)

One can obtain the mean and variance of Y, using Taylor

series expansion, as follows

n

i

n

jji

ji

n XXCVXX

gXXgYE

1 1

2

21 ,2

1,.......,,X


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in

i i

n

ii

i

n

n

i

n

ijji

jii

n

i i

XVX

gYVandXV

X

gXXgYE

XXCVX

g

X

g

XVX

g

YV

2

112

2

21

1

1 1

2

1

2

1,.......,,X

,2

Rosenblueth's Point Estimate Method (RPEM)


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PEM, suggested by Rosenblueth (1975) and modified by Li

(1992) is widely used.

The versatility of the RPEM is that, it can be used even when

the functional relationships are not given as an explicit

equation. This independence from the type of distribution or

correlations among the basic variables is an advantage.

In RPEM, the original probability density function (PDF) ofthe random variable X is approximated by assuming that the

entire probability mass of X is concentrated at two points x-

and x+.

Calculations are made at two points and Rosenblueth uses the

following notations

X- = -z- and X+ = -z+

xgpxgpYErrr


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1;

2

11

2

1

1

2

zzzwhere

ppandzz

zp

1

1 1121

2,........,,

N

i

N

ijN

ij

ji

N

iiiN

pp


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Table 2 Results of reliability Analysis by RPEM and FOSM

(c',') = 0 (c',') = 0.50 (c', ') = 0.25

RPEM FOSM RPEM FOSM RPEM FOSM

E[FS] 1.242 1.243 1.238 1.243 1.243 1.243

[FS] 0.303 0.291 0.282 0.275 0.315 0.3

() 0.798 0.835 0.843 0.884 0.771 0.811PrFS 1.0 0.2124 0.2018 0.1996 0.1883 0.2203 0.2086

modelling techniques in geotechnical engineeering

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