jonathan p. stewart – seismic earth pressures on retaining walls

Seismic Earth Pressures on

Retaining Walls

Jonathan P. Stewart, PhD, PE

Professor and Chair

UCLA Civil & Environmental Engineering Dept.

ASCE Los Angeles Section

Geotechnical Group Dinner Meeting

September 23, 2015

Los Angeles, CA

2

You can observe a lot by just watching.

Geotechnical Interpretation: Observational

method

If you don't know where you are going, you

might wind up someplace else.

Never forget the fundamentals.

I usually take a two hour nap from one to

four.

We’re geotechnical errors, 50% error isn’t

so bad

…when I die, just bury me where you

want. Surprise me.

We’ll miss you.

Yogi Berra (1925-2015):


Retaining Walls


Professor and Chair


ASCE Seattle Section

Geotechnical Group Spring Seminar

May 2, 2015

Seattle, WA


Retaining Walls


Professor and Chair


University of Rome, La Sapienza

Dept. Structural & Geotechnical Engineering

March 27, 2015

Rome, Italy


Retaining Walls


Professor and Chair


University of Rome, Federico II

Civil & Environmental Engineering Dept.

March 25, 2015

Napoli, Italy


Retaining Walls


Professor and Chair


University of Michigan

Civil & Environmental Engineering Dept.

February 19, 2015

Ann Arbor, MI

Acknowledgements

• Scott J. Brandenberg and George Mylonakis

(principal collaborators)

• Ertugrul Taciroglu, Farhang Ostadan, Youssef

Hashash, others (fruitful discussions)

• ATC-83 project. http://www.nehrp.gov/pdf/nistgcr12-917-21.pdf

7

Project Technical Committee

Jonathan P Stewart (Chair)

CB Crouse

Tara Hutchinson

Bret Lizundia

Farzad Naeim

Farhang Ostadan

Working Group Members

Curt Haselton

Fortunato Enriquez

Michael Givens

Silvia Mazzoni

Erik Olstad

Andreas Schellenberg

Review Panel

Craig Comartin

Youssef Hashash

Annie Kammerer

Gyimah Kasali

George Mylonakis

Graham Powell

ATC-83 Project

8

Outline

• Mechanisms for wall-soil interaction

• Current practice & recent research

• Wall-soil interaction springs

• Kinematic wall-soil interaction

• Summary

9

Interaction Mechanisms

Kinematic soil-structure

interaction (SSI)

• Foundation input

motion (FIM)

• No external inertial

forces

• Pressure from

differential wall-soil

movements

10

Physical Basis for Kinematic SSI Effects

Low frequency

Long wavelength

λλλλ = Vs/f

uFIM ≈≈≈≈ ug0

θθθθFIM ≈≈≈≈ 0

Negligible wall pressures

0

11

Physical Basis for Kinematic SSI Effects

High frequency

Short wavelength

λλλλ = Vs/f

uFIM < ug0

θθθθFIM > 0

Large wall pressures

0

12


Inertial SSI

• Inertia in structure

produces base shear

and moment (V & M)

• V & M resisted by soil

reactions (incl. walls)

• Key issue: connectivity

of structural lateral

force resisting system

to walls

13


Important Points:

Both kinematic and inertial effects give rise to

seismic earth pressures

Both produce pressures as a result of relative

movements between wall and soil.

14

Outline





• Summary

15

Current Practice & Recent Research

• Mononobe-Okabe procedure

– Basis for current standards of practice, with

various modifications over time

– Current guideline using M-O: NCHRP (2008)(1)

• Results of recent research

– Centrifuge tests

– Dynamic SSI analysis

16

(1) NCHRP = National Cooperative Highway Research Program.

Report 611. Transportation Research Board, 2008. Available at:

http://www.trb.org/Main/Blurbs/160387.aspx

M-O Approach(1)

• Begin with static earth pressure (e.g., Ka or K0). Resultant PA.

• Limit equilibrium analysis with seismic coefficient kh

(∝ PGA) in Coulomb-type wedge. Produces PE.

• Problem: Seismic earth pressure correlated to acceleration

17(1) Okabe (1924) and Mononobe and Matsuo (1929)

0

Consider case of vertically propagating,

horizontally coherent, SH wave

Acceleration:

Inertia generated by wave resisted by

mobilized shear stresses, τhv(z)

Wave produces no change in normal stresses

on vertical or horizontal planes (absent ∆u)

∴ Horizontal stresses have no fundamental

association with PGA

( ) 2

0 cosi t

g g

S

zu z u e

V

ωωω

= −

&&

z

Centrifuge Tests

• Al Atik and Sitar (2009, 2010)

• U-shaped walls, rigid & flexible. H = 6.5 m and B =

5.3m (prototype)

• D = 19 m

• 3 time series

Al Atik and Sitar, 2010: JGGE20

H

2BD

Centrifuge Tests

Total earth pressures. Below M-O predictions.


Centrifuge Tests

Recommendation: No seismic earth pressure for PGA < 0.4g. M-O over-predicts.


Dynamic SSI Analysis

• Ostadan, 2005

• No wall-soil movement at

base

• H = 9.14m. Broadband

input

• Strong site response due

to rigid base and input

energy at f1=VS/(4H)

Rigid base

Similar results by Wood, 1973;

Veletsos and Younan, 1994;

23

Dynamic SSI Analysis

• Ostadan, 2005

• No wall-soil movement at

base

• H = 9.14m. Broadband

input

• Strong site response due

to rigid base and input

energy at f1=VS/(4H)

• Substantially larger

pressures than M-O

Rigid base

Ostadan, 2005 24

Summary of Recent Studies: Free-

Standing Walls

• Centrifuge tests tend to support pressures

lower than M-O

• Analyses involving a strongly resonant site

condition support higher pressures than M-O

No surprise that there is considerable

confusion in practice surrounding this issue

25

Outline





• Summary

26

Interaction Springs

• Our objective: wall-soil pressures

• Evaluate from relative displacements and

foundation-soil interaction springs

27

Interaction Springs

We have solutions for:

• Stiffness of surface

foundation: Ky, Kxx

28

Interaction Springs



foundation: Ky, Kxx

• Stiffness of embedded

foundation: Ky,emb, Kxx,emb

29

Interaction Springs



foundation: Ky, Kxx



Partition into:

• Stiffness of base slab

30

Interaction Springs



foundation: Ky, Kxx



Partition into:

• Stiffness of base slab

• Wall contributions (our

objective)

31

Partitioning of stiffness values

derived in present work

Interaction Springs

Wall reactions computed

using stiffness intensities:

• Defined as

stiffness/area on wall.

• Notation: kyi and kz

i

Units of Force/Length^3

32

Interaction Springs

Wall reactions computed

using stiffness intensities:

• Defined as

stiffness/area on wall.

• Notation: kyi and kz

i

Units of Force/Length^3

33

Interaction Springs

Approach:

• Develop expressions for kyi and kz

i

• Take as known: Ky, Kxx, Ky,emb, Kxx,emb (literature)

• Use equilibrium to relate (Ky, Kxx) and (kyi, kz

i )

to (Ky,emb, Kxx,emb)

• Thereby derive coupling terms (χy, χxx)

34

Interaction Springs

Approach:

• Develop expressions for kyi and kz

i

• Take as known: Ky, Kxx, Ky,emb, Kxx,emb (literature)

• Use equilibrium to relate (Ky, Kxx) and (kyi, kz

i )

to (Ky,emb, Kxx,emb)

• Thereby derive coupling terms (χχχχy, χχχχxx)

35

Interaction Springs

Stiffness intensity expressions:

• Rigid vertical wall over rigid base at depth H

(Kloukinas et al, 2012: JGGE)

• Rigid vertical wall over finite soil layer, including

interaction effects (this study)

36

Interaction Springs


2

21

(1 )(2 )

i

y y

s

G Hk

H V

π ωχ

πν ν

= −

− −

2

2 21

2 1

i

z xx

s

G Hk

H V

π ν ωχ

ν π

−= −

−

Dynamic stiffness modifiers:

Unity when λλλλ/H → ∞∞∞∞

(common condition)

37

Interaction Springs


2

21

(1 )(2 )

i

y y

s

G Hk

H V

π ωχ

πν ν

= −

− −

Modulus taken from VS

of soil materials

adjacent to walls (not

below foundation).

Adjustments for

nonhomogeneity and

nonlinearity.

38

2

2 21

2 1

i

z xx

s

G Hk

H V

π ν ωχ

ν π

−= −

−

Interaction Springs


2

21

(1 )(2 )

i

y y

s

G Hk

H V

π ωχ

πν ν

= −

− − Coupling factors

39

2

2 21

2 1

i

z xx

s

G Hk

H V

π ν ωχ

ν π

−= −

−

Interaction Springs

40

Coupling terms: why necessary?

Wall-soil reactions affect multiple stiffness terms for

embedded foundation. Examples:

• kyi affects Ky,emb and Kxx,emb

Interaction Springs

41

Coupling terms: why necessary?

Wall-soil reactions affect multiple stiffness terms for

embedded foundation. Examples:

• kyi affects Ky,emb and Kxx,emb

• kzi affects Kz,emb and Kxx,emb

Unfactored base slab

stiffnesses and wall stiffness

intensities combine to

overestimate Ky,emb & Kxx,emb

Interaction Springs

,2

i

y emb y y yK k H Kχ= +

2 2

,2

i i

xx emb y xx xx zK k H K k HBχ= + +

42

Equilibrium equations:

Horizontal:

Rotation:

Where Kj and Kjj stiffness terms are

from the literature

Outline





• Summary

44

Kinematic Interaction Problem

• Formulation of solution

• Kinematic model results

• Synthesis of method

• Comparison to centrifuge tests and SASSI

results

45

Formulation of Solution

• Formulate PE from

integration over depth of

kyi × relative wall

displacement

• Similar expression for ME

• Equations apply for

uniform Vs and rigid wall

46

( )0

0

cos ( )

H

i

E y g wP k u kz u z dz= −∫


• Wall displacement

affected by translation

and rotation

• Wall force balanced by

base shear

( )( )w FIM FIMu z u H zθ= + −

Force on wall, PE Base shear

47

( )0 0

0

cos cos2

H

yi

E y g FIM FIM FIM g

KP k u kz u H z dz u u kHθ = − − − = − ∫


• Wall displacement

affected by translation

and rotation

• Wall force balanced by

base shear

• Similar eqns for ME

• System of eqns solved for

uFIM and θFIM

• PE and ME computed

( )( )w FIM FIMu z u H zθ= + −

48

Base Slab Motions

49

• Ordinate: FIM / ug0 ratios

• Abscissa: λ/H

• Translation decreases for

small λ/H < ∼ 10

• Rotation increases for

same conditions

• Kausel et al. (1978)

model ok for translation,

low for rotation

Kinematic Model Results

• Ordinate: PE/(ug0kyiH)

• Abscissa: λ/H

• Peaks at λ/H = 2.3

• Small for λ/H > ∼10

50


• Ordinate: PE/(ug0kyiH)

• Abscissa: λ/H

• Peaks at λ/H = 2.3

• Small for λ/H > ∼10

• Modest effects of relative

foundation-wall stiffness

Critical finding: interaction

force depends strongly on λλλλ/H

51

0

0.4

0.8

1.2

Normalized Force,

|PE|

ugokyi H

0

0.4

0.8

1.2

Normalized Force,

|PE|

ugokyi H

1 10

Normalized Wavelength, H

0

0.4

0.8

1.2

Normalized Force,

|PE|

ugokyi H

Rigid Base

Ky/kyiH = 100

(a) Kxx (kyiH2/3) = 3

(b) Kxx (kyiH2/3) = 10

(c) Kxx (kyiH2/3) = 100

Rigid Base

Ky/kyiH = 100

Rigid Base

Ky/kyiH = 100

10

3

1

103

1

10

3

1


• Can relax uniform soil

assumptionPeak shifts to right.

Amplitudes decrease.

52Figure: Scott Brandenberg

53

Mode shape for soil displacement behind wall. As

n increases, displaced shape becomes nearly

vertical.


• Can relax rigid wall

assumptionPeak shifts to right.

Amplitudes decrease.

54Figure: Scott Brandenberg

Synthesis

1. Compute FFT of free-field motion,

2. Compute foundation stiffnesses, kyi, kz

i, Ky,

Kxx, Ky_emb, Kxx_emb

3. Solve for FIM in frequency-domain:

4. Solve for PE in frequency-domain:

5. Inverse Fourier transform to PE(t)

( )0ˆ

gu ω

( )ˆFIMu ω ( )ˆ

FIMθ ω

( )ˆEP ω

55

Synthesis: Simplified Approach

1. Estimate mean period, Tm, from GMPE

2. Compute λ/H = VsTm/H

3. Use graphical result for PE/(ug0kyiH) vs. λ/H to

find normalized force

4. Compute kyi

5. Estimate ug0 as PGV/ω, where ω=2π/Tm

6. Solve for maximum value of PE

56

Comparison to Prior Results

SASSI: λλλλ/H=4

Centrifuge:

λλλλ/H = 12

57

In theory there is no difference between theory and practice. In practice there is.

– Yogi Berra

Comparison to Prior Results

Good match Right resultant.

Wrong shape.

58

59

-20 0 20 40 60 80Seismic Earth Pressure Increment (kPa)

6

4

2

0

Depth (m)

Rigid Wall, Constant Vs Profile

PE = 150 kN/m

Flexible Wall, Parabolic Vs profile

PE = 86 kN/m

Mononobe-OkabePE = 180 kN/m

0 100 200 300Vs (m/s)

6

4

2

0

Depth (m)

MeasuredPE = 90 kN/m

Considering profile inhomogeneity…

Figure: Scott Brandenberg

Pending Comparisons to

Experimental Results

60

UCB-UCD-NEESR centrifuge test data (Mikola et al.,

2014)

U. Colorado Boulder centrifuge test data (Hushmand

et al., 2015)

U. Bristol-U. Naples-U. Sannio shake table testing

(Kloukinas et al., 2014)

UCSD-NEESR shake table testing (Wilson and

Elgamal, 2015)

Summary

• Seismic earth pressures on walls result from

relative wall/free-field displacements.

• These relative displacements can arise from

distinct inertial and kinematic mechanisms

• M-O procedures capture neither mechanism

• The seismic earth pressure increment has no

fundamental relationship to PGA.

61

Summary

• Kinematic wall pressures governed by ug0 and

λ/H. Often small for practical conditions.

• Proposed procedures resolves conflicting

findings in literature

• No specialty software required

• Inertial interaction computed using dynamic

analysis of structure with foundation springs.

Wall pressures depend on load path.

62

63

Details in:

Brandenberg SJ, G Mylonakis, and JP Stewart, 2015. Kinematic

framework for evaluating seismic earth pressures on retaining

walls. J. Geotech. & Geoenviron. Eng., 141, 04015031

Java Applet at:

http://uclageo.com/.

64

References

Al Atik, L and N Sitar, 2010. Seismic earth pressures on cantilever retaining structures, J. Geotech. & Geoenv.

Eng., 136, 1324-1333.

Brandenberg SJ, G Mylonakis, and JP Stewart, 2015. Kinematic framework for evaluating seismic earth pressures

on retaining walls. J. Geotech. & Geoenviron. Eng., 141, 04015031

Kausel, E, A Whitman, J Murray, and F Elsabee, 1978. The spring method for embedded foundations, Nuclear

Engineering and Design, 48, 377-392.

Kloukinas, P, M Langoussis, and G Mylonakis, 2012. Simple wave solution for seismic earth pressures on non-

yielding walls, J. Geotech. & Geoenv. Eng., 138, 1514–1519.

Mononobe, N and M Matsuo, 1929. On the determination of earth pressures during earthquakes. Proc. World

Engrg. Congress, 9, 179–187.

National Cooperative Highway Research Program, NCHRP, 2008. Seismic Analysis and Design of Retaining Walls,

Buried Structures, Slopes, and Embankments. Report 611, Prepared by D.G. Anderson, G.R. Martin, I.P. Lam, and

J.N. Wang. Transportation Research Board, National Academies, Washington DC.

National Institute of Standards and Technology, NIST, 2012. Soil-Structure Interaction for Building Structures,

Report NIST GCR 12-917-21, Prepared by NEHRP Consultants Joint Venture, J.P. Stewart, Project Technical

Director. US Dept. of Commerce, Gaithersburg, MD.

Okabe, S, 1924. General theory of earth pressure and seismic stability of retaining wall and dam. J. Japanese

Society of Civil Engineering, 12 (4), 34-41.

Ostadan, F, 2005. Seismic soil pressure for building walls – an updated approach, Soil Dyn. Earthquake Eng., 25,

785-793.

Veletsos, AS and AH Younan, 1994. Dynamic soil pressures on rigid retaining walls. Earthquake Eng. Struct. Dyn.,

23(3), 275-301.

Wood, JH, 1973. Earthquake induced soil pressures on structures, Report No. EERL 73-05, California Institute of

Technology, Pasadena, CA.

When is Inertial Interaction

Important?

yyx k

kh

k

k

T

T2

1

~

++=

Most critical factor for is h/(VST).

The flexibility (period) and damping of the system are

affected.

66

Period Lengthening Trends

Inertial SSI significant if h/(VsT) > 0.1

67

Foundation Damping

Trends:

68

Effects of Period Lengthening

& Damping on Base Shear

69

Response History Recommendations

• Apply bathtub model

(no multi-support

excitation req’d)

• Wall springs can be

evaluated from kyi

• Computed wall spring

forces applied in

combination with

kinematic loads Source: NIST (2012)

Large wall demands from inertial SSI require rigid

foundation or lateral load transfer above base level70

Java Applet Demonstration

71

jonathan p. stewart – seismic earth pressures on retaining walls

Documents