geotechnical earthquake engineering · 2017. 8. 4. · rowe and davis (1982) finite element...

Geotechnical Earthquake

Engineering

by

Dr. Deepankar Choudhury Humboldt Fellow, JSPS Fellow, BOYSCAST Fellow

Professor

Department of Civil Engineering

IIT Bombay, Powai, Mumbai 400 076, India.

Email: [email protected]

URL: http://www.civil.iitb.ac.in/~dc/

Lecture – 41

IIT Bombay, DC 2

Module – 9

Seismic Analysis and

Design of Various

Geotechnical Structures

IIT Bombay, DC 3

Seismic Design of Pile

Foundation

4

Piles in liquefying soil under lateral loads:

Force method

Non-liquefiable layer

Non Liquefiable layer

HNL

Liquefiable layer

qL =30% of over

burden pressure Pressure

qNL = Passive earth Pressure

HL

JRA (1996): Idealisation for pile

design in liquefying soils

5

Failure theory based on Tokimatsu et al. (1998) :

Prior to the development of pore water pressure, the inertia

force from the superstructure may dominate.

Kinematic forces from the liquefied soil start acting with

increasing pore pressure.

Towards the end of shaking, kinematic forces would dominate

and have a significant effect on pile performance particularly

when permanent displacements occur in laterally spreading soil.

III) Lateral movement

after earthquake

liquefaction

Inertia force

Ground

displacemen

t

I) During Shaking before

liquefaction

Inertia force

Bending

moment

Inertia force

I) During Shaking after

liquefaction

[see Choudhury et al., 2009, Proc. of National Academy of Sciences,

India, Springer, Sec. A]

Case-Specific Design of Pile

Foundations under

Earthquake Conditions

7

Typical Bore hole data for MBH# 1: Mangalwadi site, Mumbai

Layer No. Stratum Layer thickness (m) Depth

below GL

(m)

SPT ‘N’ value

1 Filled up soil 1.5 1.5 10

2 Yellowish loose sand 1.5 3.0 12

1.5 4.5 13

1.5 6.0 16

3 Black clayey soil 2.0 8.0 20

4 Yellowish clayey soil 1.8 9.8 25

5 Greyish hard rock - >9.8

-

EQUIVALENT GROUND

RESPONSE ANALYSIS

See Phanikanth (2011), PhD Thesis, IIT Bombay, Mumbai, India.

8

Amplification of acceleration vs. depth (m)

Typical Results

EQUIVALENT GROUND

RESPONSE ANALYSIS

D. Choudhury, IIT Bombay, India

Model considered for single Pile

passing through liquefied layer

Soil-pile analysis considering

ground deformations

using finite difference technique

ANALYTICAL

MODEL

[Phanikanth et al.

(2013), Int. Jl. of

Geomech., ASCE]


Governing Equations for solving the basic differential equation of

laterally loaded pile in liquefied zone is given below:

y = lateral displacement of pile; z = depth from ground; EI = flexural rigidity of pile.

Sf is scaling factor varying from 0.001 to 0.01 (Ishihara and Cubrinovski,1998)

as compared to normal soil condition where there is no liquefaction .

Tokimatsu et al. 1998

[AIJ ( 2001)]

[Phanikanth et al.

(2013), Int. Jl. of

Geomech., ASCE]


Bending moment in non liquefied and liquefied soil for

free headed single pile with floating tip in Mumbai [Phanikanth, Choudhury and Reddy, 2013, Int. Jl. of Geomech., ASCE]


Typical effect of thickness of liquefiable soil layer on displacement profile

of free headed single pile with floating tip subjected to 2001 Bhuj motion [Phanikanth, Choudhury and Reddy, 2013, Int. Jl. of Geomech., ASCE]

Combined Pile – Raft

Foundation (CPRF)

Under Earthquake Conditions

INTRODUCTION

Piled raft foundation(also called composite foundation) solve:

1. Settlement – through interaction and load sharing.

2. Differential settlement – raft provide stiffness against load.

3. Economical - reducing number of piles.

Poulos et al. (2001) has examined a number of idealized soil profiles, and found that soil profiles consisting of relatively stiff clays and relatively dense sands may be favourable for piled raft foundation.

Construction: 1988 - 1990

Foundation: CPRF

Height: 256 m Messeturm tower, Germany

(Katzenbach et al. 2005)

Foundations of high-rise buildings in Frankfurt am

Main, Germany

The subsoil of Frankfurt am Main mainly consists of non homogeneous, stiff and

over consolidated tertiary ”Frankfurt clay” with embedded limestone bands of

varying thicknesses. 15

(Katzenbach et al. 2005)

Tower

Lower Sections

Hydraulic Jacks

Tower 1

Tower 2

Deutsche Bank · Frankfurt am Main, Germany

Height: 162 m

Settlement: max. 22 cm / min. 10 cm

Katzenbach et al. (2009)

-12.8 m

0.0 m

→ Combined Pile-Raft Foundation (CPRF) Katzenbach et al. (2009)

Settlements calculated for a shallow foundation:

s > 40 cm

z = 0 - 20 m → 75 - 80 %

Messeturm · Frankfurt am Main,

Germany

Settlements:

Messeturm · Frankfurt am Main, Germany

dydxy,x,s)s(R k,raft

m

1j

k,raftj,k,pilek,tot sRsRsR

sRsRsR j,k,sj,k,bj,k,pile

Total resistance of the CPRF:

Pile resistance:

Raft resistance:

Bearing concept of a

Combined Pile-Raft Foundation (CPRF)

Katzenbach et al. (2012)

Analytical study:

19

Katzenbach et al. (1998) had suggested that designing Combined Pile-Raft

Foundations (CPRF) requires the qualified understanding of soil-structure

interaction.

Rtotal,k = ΣRpile,k, j + RRaft, k

Total resistance of the CPRF:

Pile resistance: sRsRsR jksjkbjkpile ,,,,,,

Raft resistance:

dydxyxssR kraft ,,)(,

αCPRF is set between 0.45-0.55

s =

(Katzenbach et al. 1998).

, ,

1

,

( )

( )

m

pile k j

j

CPRF

tot k

R s

R s

CPRF coefficient:

20

Three dimensional view of pile group and pile-raft model in ABAQUS

(Eslami et al. 2011)

Dynamic loading response:

21

Comparison of acceleration and bending moment response of under

sinusoidal accelerations


Input acceleration – 1 m/sec2

Input frequency – 1 Hz

36% decrease in

piled raft model

54 %

decrease in

piled raft

model

Seismic loading response:

• El- centro acceleration time history was chosen.

• Input acceleration and displacement- 4.21m/sec2 and 37.4 cm.

22

Acceleration response

34% reduction


piled raft pile group

9%

reduction

Horizontal displacement response under El- centro seismic

loading

Piled raft pile group

(Eslami et al. 2011) 23

Case Study

Combined Pile – Raft

Foundation (CPRF)

under Earthquake

Conditions

Case study of pile-raft foundation during 2011 Tohoku earthquake

Yamashita et al. (2011):

Building located at JAPAN PROTON ACCELERATOR RESEARCH COMPLEX (JPARC).

25

Pile raft foundation

371 PHC piles

Diameter – 0.6m to 0.8m

Earthquake occurred – 44

month after the end of

construction.

Epicenter -270 km from

the site

Ground acceleration –

3.24 m/s2 and 2.77 m/s2 for

the horizontal and vertical

directions .

Yamashita et al. (2011)

26

Plan of foundation profile with monitoring

devices Profiles of vertical ground displacements

Yamashita et al. (2011) (Yamashita et al. (2012)

Ratio of load carried by pile Pile P1 Pile P2

Decreased from 0.85

to 0.82 after the

earthquake

Decreased from 0.67

to 0.57 after the

earthquake

(Yamashita et al. 2012) 27

International Guideline on CPRF – 2012

by

ISSMGE Technical Committee

TC 212 – Deep Foundations

(www.issmge.org)


IIT Bombay, DC 32

Seismic Design of

Ground Anchors

See, Rangari, S. M. (2013), PhD Thesis, IIT Bombay, Mumbai, India.

33

• To mitigate the effect of earthquake Ground Anchors can be used for structures

subjected to uplift / pullout loads.

• Estimation of Uplift Capacity of Ground Anchor is an application of passive earth

pressure theory.

• Problem is more complex under seismic conditions.

INTRODUCTION

34

Selected Available Studies (Static Condition)

Author Method of Analysis Failure plane Seismic Analysis

Meyerhof and Adams

(1968)

Limit Equilibrium Logspiral No

Rowe and Davis (1982) Finite Element

/Experimental

-- No

Murray and Geddes (1987) Experimental/Limit

equilibrium/limit analysis

--- No

Kumar (1999) Method of slices Logspiral No

Merifield and Sloan (2006) Limit analysis (Upper and

lower bound)

Planar No

Deshmukh et al. (2011) Limit Equilibrium Planar No

Rangari, S.M., Choudhury, D., Dewaikar, D.M. (2011) in ASCE GSP 211, pp. 1821-1831

35

Available Studies

• Scarcity of research and design methods for estimation of vertical uplift capacity of

horizontal and inclined strip anchors under earthquake conditions using both pseudo-

static and pseudo-dynamic approaches.

Author Method of Analysis Failure plane Seismic Analysis

Kumar (2001) Upper bound limit analysis Planar Yes

(Pseudo-static)

Choudhury and Subba

Rao (2004, 2005)

Limit Equilibrium Logspiral Yes

(Pseudo-static)

Ghosh (2009) Upper bound Limit analysis Planar Yes (Pseudo-

dynamic)

Rangari et al. (2012) Limit Equilibrium Planar Yes (Pseudo- static)

36

REVIEW OF LITERATURE

Very few researchers obtained the uplift capacity of obliquely loaded horizontal

strip anchor and all under static conditions;

•

Author Analysis Method Failure plane Seismic Analysis

Meyerhof (1973) Limit equilibrium/ Model test

Logspiral No

Das and Seeley (1975)

Model Test --- No

Rangari, S.M., Choudhury, D., Dewaikar, D.M. (2012) in ASCE GSP 225, pp. 185-194.

37

REVIEW OF LITERATURE

Author Analysis Method Failure plane Seismic Analysis

Meyerhof (1973) Limit Equilibrium Logspiral No

Hanna et al. (1988) Limit Equilibrium

Planar No

Maiah et.al (1986) Empirical relation --- No

Choudhury and Subba Rao (2005)

Limit equilibrium Logspiral Yes (Pseudo-static)

Choudhury and Subba Rao (2007)

Limit equilibrium Logspiral Yes (Pseudo-static)

Ghosh (2010) Upper bound limit analysis

Planar Yes (Pseudo-dynamic)

•It shows the scarcity of research for the obliquely loaded inclined strip

anchors under static condition and yet untouched under the seismic

condition.

38

Kötter’s (1903) equation

Kötter’s (1903) equation gives solution for determining the distribution of soil

reaction on failure plane

Where,

dp = differential reaction pressure on the

failure Surface,

ds = differential length of failure surf ace,

p = uniform pressure on the failure surface

d = differential angle,

= angle of failure plane formed by inclination of tangent at the point of interest

with the horizontal

= unit weight of soil and

= soil friction angle

sintan2ds

dp

ds

dp

39

The total reaction R1 and R3 on

the failure surfaces are computed

by integrating Kötter’s equation;

•W is the weight of failure

soil block,

• Pp d1 and Pp d3 are the

seismic passive

resistances,

• is soil friction angle,

• B is width and H is depth

of anchor

•Qh and Qv are total

seismic horizontal and

vertical inertial forces

respectively.

•Simple Planar failure surface. Hence the

Kötter’s (1903) equation reduces to,

sinp s

Horizontal Strip Shallow Anchor under Seismic Conditions

• Consider failure block above the anchor.

• The mass of the elementary strip is given by;

• The horizontal and vertical acceleration at any depth z and time t below the

ground surface can be expressed as;

• Total horizontal and vertical inertial forces acting within the failure zone

(CDEF) can be expressed as,

40

Proposed Method by Rangari et al. (2013)

γBdzm =

g

( , ) sin and ( , ) sinh h v vs p

H z H za z t a t a z t a t

V V

2 22 22 cos cos and 2 cos cos

4 4

h vh v

Bk BkQ t Q t

Rangari, S.M., Choudhury, D., Dewaikar, D.M. (2013) in Geotechnical and Geological

Engineering , Springer, Vol. 31(2), pp. 569-580.

41

where, =TVs is the wavelength of the vertically propagating shear wave, = TVp

is the wave length of the vertically propagating shear wave,

and

The gross pullout capacity (Pud) is given by;

•The net seismic uplift capacity of anchor, qudnet

Proposed Method of Rangari et al. (2013) contd.

1 3 2 2sin sinud p d p d vP P P W Q

s

Ht

V p

Ht

V

2

22 tan 2 cos cos tan

2

hd p d

kF K t

B

The net seismic uplift capacity factor,

2 20.5

ud vud d

P W Qq BF

B

Where, Embedment ratio, = H/B and Kp d is a net seismic passive earth pressure

coefficient

42

Typical Design Charts (Results) for Seismic Uplift Capacity

Factor of Horizontal Shallow Anchors

a. Using Pseudo-Static approach b. Using Pseudo-Dynamic approach Rangari, S.M., Choudhury, D., Dewaikar, D.M. (2013) in Geotechnical and Geological


43

Comparison of ultimate seismic uplift capacity factor (F E = Pud/ B2) for various

values of kh and kv= 0.5 kh for = 30 , = 4 with H/ =0.3 and H/ =0.16.

kh Ghosh (2009)

Pseudo-

dynamic

Kumar

(2001)

Pseudo-

static

Choudhury and

Subba Rao

(2004)

Pseudo-static

Present study

Pseudo-

static

Pseudo-

dynamic

0.0

13.27

13.27

12.89

13.01

13.01

0.1

12.59

12.48

12.44

12.12

12.08

0.2

11.90

11.71

11.96

11.25

11.29

0.3

11.14

10.90

11.53

10.39

10.61

0.4

10.21

9.81

11.01

9.56

10.05

Comparison of Results

Rangari, S.M., Choudhury, D., Dewaikar, D.M. (2013) in Geotechnical and Geological


44

For a plane failure surface, Kötter’s equation (1903), takes the following form

where,

p = uniform pressure on failure

plane

= unit weight of soil

s = represents the distance of failure plane

as measured from ground surface

The total reaction R1 and R3 on the failure surfaces are computed by integrating

Kotter’s equation;

sinp s

Inclined Strip Shallow Anchor under Seismic Conditions

Rangari, S.M., Choudhury, D., Dewaikar, D.M. (2012) in Disaster Advances, Vol. 5(4), pp. 9-16.

45

For Design, qudnet can is expressed as,

Net seismic uplift capacity factor ( F d) can be obtained as;

where, embedment ratio, and Kp d is net seismic passive earth pressure

coefficient.

Critical angle of failure planes:

The trial value of α1 and α3 are obtained such that the values of Ppγd1 and Ppγd3

should be same obtained from failure wedges CDF and ABE respectively.

B

H

udnet dq 0.5 BF

2 2 2

d P d

v h

F tan 0.25 tan K cos tan tan

2 1 k sin k cos

Inclined Strip Shallow Anchor under Seismic Conditions


46

Typical Design Charts (Results) for Seismic Uplift Capacity

Factor of Obliquely loaded Inclined Shallow Anchors


47

COMPARISION OF RESULTS

Comparison of net SEISMIC uplift capacity factor (F d) with results from

literature for =30 , with = 30 and ε =3.

kh Choudhury and Subba Rao

(2005)

Present study

kv=0.0kh kv=0.5kh kv=1.0kh kv=0.0kh kv=0.5kh kv=1.0kh

0.0 5.85 5.85 5.85 6.28 6.28 6.28

0.1 5.48 5.32 5.16 6.27 5.95 5.61

0.2 5.39 4.76 4.43 6.25 5.62 5.05

0.3 5.28 4.31 3.53 6.13 5.2 4.41

0.4 4.99 3.69 -- 5.94 4.73 --


48

COMPARISION OF RESULTS

Comparison for ultimate SEISMIC uplift capacity factor (F E = Pud / B2) for

=0 , ε =1 and kv = 0.0 with results from literature.

0 kh Kumar

(2001)

Ghosh

(2009)

Present

study

300

0.0 1.577 1.577 1.563

0.1 1.566 1.571 1.481

0.2 1.544 1.533 1.403

0.3 1.499 1.520 1.329

400

0.0 1.839 1.839 1.839

0.1 1.832 1.835 1.709

0.2 1.815 1.821 1.587

0.3 1.786 1.798 1.472

500

0.0 2.192 2.192 2.145

0.1 2.187 2.189 1.952

0.2 2.174 2.179 1.771

0.3 2.155 2.163 1.601


geotechnical earthquake engineering · 2017. 8. 4. · rowe and davis (1982) finite element...

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