geot earthquake eng ch9b walls sh aders 10

14
9. Seismic Design of RETAINING STRUCTURES RIGID WALLS 9. Seismic Design of RETAINING STRUCTURES RIGID WALLS October 2009 Part B: G. BOUCKOVALAS & G. KOURETZIS GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.1

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Page 1: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

9. Seismic Design of

RETAINING STRUCTURES

RIGID WALLS

9. Seismic Design of

RETAINING STRUCTURES

RIGID WALLS

October 2009

Part B:

G. BOUCKOVALAS & G. KOURETZIS

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.1

Page 2: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

Solutions for “perfectly rigid” or “semi-rigid” walls

Problem outline …..

The Mononobe-Okabe method requires that the retaining wall can move freely (slide or rotate) so that active earth pressures

develop behind the wall.

Nevertheless, there are cases where the free movement of the wall is totally or partially restrained (e.g. basement walls, braced

walls, massive walls embeded in rock like formations) .

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.2

Page 3: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

CONTENTSCONTENTS

9.6 PERFECTLY RIGID WALLS (Wood, 1973)

9.7 WALLS WITH LIMITED DISPLACEMENT (Veletsos & Yunan, 1996)

9.8 SEISMIC CODES

Sggested ReadingSggested Reading

Steven Kramer: Chapter 11

Assumptions

1. Pseudo static conditions (Τδιεγερ>>4Η/Vs) – quite usual case (why?)2. plain strain3. Elastic soil4. Smooth & rigid walls

Εwall>>Esoil

Elastic soil between two rigid walls

9.6 PERFECTLY RIGID WALLS (Wood 1973)

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.3

Page 4: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

Analytical Solutions for ……..

dynamic earth pressures

h g

αγια = 1

heq PF F

g

αΔ = γΗ2

=F

p

h

g

α= 1

Analytical Solutions for ……..

Overturning moment and base shear

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.4

Page 5: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

heq PF F

g

αΔ = γΗ2

heq mM F

g

αΔ = γΗ3

=F

p

=F

m

h

g

α= 1

h

g

α= 1

Overturning moment and base shear

Analytical Solutions for ……..

0 1 2 3 4 5 6 7 8 9 10

L/H

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

h/H

Application point of the resultant seismic thrust

h L. για

H H⎛ ⎞≈ >⎜ ⎟⎝ ⎠

0 55 4

eq

eq

hP

ΔΜ=

Δ

Analytical Solutions for ……..

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.5

Page 6: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

Smooth vs. bonded (rough) wall side

Analytical Solutions for ……..

Extension to harmonic base excitation – Base shear

"στατική"λύση

συντονισμός υψίσυχνες διεγέρσεις

excit soil

soil excit

T.

T

ωΩ = = <<

ω1 0

Analytical Solutions for ……..

Static Resonance High frequency excitation

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.6

Page 7: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

excit soil

soil excit

T.

T

ωΩ = = <<

ω1 0

Extension to harmonic base excitation – Overturning Moment

Analytical Solutions for ……..

H

ξηρή άμμοςφ, γν=0.3

This is the main reason why the elastic solutions of Wood (1973) were put aside for more than 30 yaers… (in connection with the fact that very limited wall failures were observed during strong earthquakes)

x3!!

28 32 36 40 44φ (deg)

0

0.2

0.4

0.6

0.8

1

ΔF

eq/[γΗ

2 (ah/

g)]

Wood

Mononobe-Okabe

0 0.1 0.2 0.3 0.4 0.5ah (g)

0

0.2

0.4

0.6

0.8

1

ΔF

eq/[γΗ

2 (ah/

g)]

Wood

Mononobe-Okabe

(ah=0.15g)(φ=36ο)

απλοποίησηSeed & Whitman (kv=0)

απλοποίησηSeed & Whitman (kv=0)

Comparison with Mononobe - Okabe

Dry sand

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.7

Page 8: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

ww

GHd

D=

3

GHd

Rθθ

=2

( )w w

w

w

E tD

v

⎛ ⎞⎜ ⎟=⎜ ⎟−⎝ ⎠

3

212 1

bonded wall-soil mass-less wall5% soil damping2% wall damping

Relative translational rigidity of the wall-fill system

9.7 WALLS WITH LIMITED DISPLACEMENT (displacement & rotation, Veletsos & Yunan, 1996)

Relative rotational rigidity of the wall-fill system

Assumptions

Pseudo-static earth pressures

h

Hη =

(normal. height)

Analytical solutions for …….

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.8

Page 9: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

h

Hη =

Pseudo-static shear forces & bending moments

Analytical solutions for …….

Pseudo static base shearbase shear & & overturning momentoverturning moment

WoodWood

Seed & Whitman

Μ-O

Analytical solutions for …….

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.9

Page 10: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

Pseudo static (?) displacements…

For a flexible (compared to the fill) concrete wall (dw=20) and a seismic excitation with amax=0.3g, the resulting displacement is U/H=0.03%...

[ U=U=0.1%0.1%÷÷0.4%0.4%··HH for active for active ““failurefailure”” →Μ-Ο]

Analytical solutions for …….

"στατική"λύση

συντονισμός υψίσυχνες διεγέρσεις

soil

soil

V

H

ππω = =

Τ12

2

the effect of harmonic excitation frequency on base shear((AF coefficientAF coefficient))

Analytical solutions for …….

High frequency excitation

StaticResonance

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.10

Page 11: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

resonance… (Max AF)

the effect of harmonic excitation frequency on displacements

Analytical solutions for …….

Variation of amplification factor AF for base shear versus the fVariation of amplification factor AF for base shear versus the fundamental soil periodundamental soil period))

(does this remind something to you?)

Numerical solution - El Centro (1940) earthquake

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.11

Page 12: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

Average values of the amplification factor AF for base shear andAverage values of the amplification factor AF for base shear and relative relative displacement displacement

Numerical solution - El Centro (1940) earthquake

1. Tensile cracks, at the top of the wal, are not taken into account(→shear forces and bending moments are over-estimated)

2. Uniform soil is assumed(e.g. a parabolic distribution of G with depth yields zero earth pressures at the top of the wall)

Note: (1) and (2) above have a counteracting effect for walls with rotational flexibility

Limitations . . . .

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.12

Page 13: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

Earth press. at rest

Dynamic earth press.

H

KoγH 0.5αhγH

1.5αhγH

heqM .

g

αΔ = γΗ30 58

heq g

αΔΡ = γΗ3

Wood

EAK

Wood

9.8 SEISMIC CODES

EAK 2002 – Rigid walls

Rigid walls0.05% > U/H

ΥΠΕΧΩ∆Ε-εγκ.39/99 «Guidelines for the design of bridges»

Walls with limited displacement 0.1%>U/H>0.05%

heqM .

g

αΔ = γΗ30 58

H

0.58.H

σE=0.5.α.γ.Η

ΔPE=α.γ.H2

σE=1.5.α.γ.Η

H

H/2

σE=0.7.α.γ.Η

ΔPE=0.75.α.γ.H2

heqM .

g

αΔ = γΗ30 375

reminder:M-O

(U/H>0.1%)

H

0.60H

Δ[email protected].α.γ.H2

heqM .

g

αΔ = γΗ30 225

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.13

Page 14: Geot Earthquake Eng Ch9B WALLS SH ADERS 10

COMPARISON OF DIFFERENT METHODS ……….…

DIFFERENCES CAN BECOME SIGNIFICANT !

0

0.2

0.4

0.6

0.8

1

ΔF

eq/[γΗ

2 (ah/

g)]

Wood

M-O

Veletsos & Younan

EAK 2002-εγκ.39/99

U/H

HWK 9.1:Compute the total base shear force and overturning moment which develops at the base of a 5m high retaining wall during seismic excitation with αmax=0.15g. The wall is vertical and smooth, while the fill consists of sandy gravel with c=0, φ=36ο, γΞ=17kN/m3 and VS=100m/s. The computations will be performed:(α) for rigid wall, (β) for a wall with limited deformation (dw=10, dθ=1), using the V&Y methodology, (γ) for a wall with limited deformation (dw=10, dθ=1), using the seismic code provisions, Note: assume pseudo static conditions and neglect the wall mass.

HWK 9.2Repeat HWK 9.1 for the extreme case of resonance between soil and excitation.

GEORGE BOUCKOVALAS, National Technical University of Athes, Greece, 2011 9B.14