Post on 02-Jan-2017
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):
Seismic Earth Pressures on
Retaining Walls
Jonathan P. Stewart, PhD, PE
Professor and Chair
UCLA Civil & Environmental Engineering Dept.
ASCE Seattle Section
Geotechnical Group Spring Seminar
May 2, 2015
Seattle, WA
Seismic Earth Pressures on
Retaining Walls
Jonathan P. Stewart, PhD, PE
Professor and Chair
UCLA Civil & Environmental Engineering Dept.
University of Rome, La Sapienza
Dept. Structural & Geotechnical Engineering
March 27, 2015
Rome, Italy
Seismic Earth Pressures on
Retaining Walls
Jonathan P. Stewart, PhD, PE
Professor and Chair
UCLA Civil & Environmental Engineering Dept.
University of Rome, Federico II
Civil & Environmental Engineering Dept.
March 25, 2015
Napoli, Italy
Seismic Earth Pressures on
Retaining Walls
Jonathan P. Stewart, PhD, PE
Professor and Chair
UCLA Civil & Environmental Engineering Dept.
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
Interaction Mechanisms
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
Interaction Mechanisms
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
• Mechanisms for wall-soil interaction
• Current practice & recent research
• Wall-soil interaction springs
• Kinematic wall-soil interaction
• 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
19
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.
Al Atik and Sitar, 2010: JGGE21
Centrifuge Tests
Recommendation: No seismic earth pressure for PGA < 0.4g. M-O over-predicts.
Al Atik and Sitar, 2010: JGGE22
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
• Mechanisms for wall-soil interaction
• Current practice & recent research
• Wall-soil interaction springs
• Kinematic wall-soil interaction
• 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
We have solutions for:
• Stiffness of surface
foundation: Ky, Kxx
• Stiffness of embedded
foundation: Ky,emb, Kxx,emb
29
Interaction Springs
We have solutions for:
• Stiffness of surface
foundation: Ky, Kxx
• Stiffness of embedded
foundation: Ky,emb, Kxx,emb
Partition into:
• Stiffness of base slab
30
Interaction Springs
We have solutions for:
• Stiffness of surface
foundation: Ky, Kxx
• Stiffness of embedded
foundation: Ky,emb, Kxx,emb
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
Stiffness intensity expressions:
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
Stiffness intensity expressions:
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
Stiffness intensity expressions:
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
43
Outline
• Mechanisms for wall-soil interaction
• Current practice & recent research
• Wall-soil interaction springs
• Kinematic wall-soil interaction
• 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= −∫
Formulation of Solution
• 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 = − − − = − ∫
Formulation of Solution
• 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
Kinematic Model Results
• 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
Kinematic Model Results
• 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.
Kinematic Model Results
• 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.
65
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