View
264
Download
1
Category
Tags:
Preview:
DESCRIPTION
analisis simico
Citation preview
1
Seismic Slope Instability and Seismic Slope Instability and Slope Displacement ProceduresSlope Displacement Procedures
Jonathan D. Bray, Ph.D., P.E.
Univ. of California at Berkeley
Thanks to Dr. Thaleia Travasarou, Prof. Ellen Rathje, & others, with support from PEER & the Packard Foundation
Seismic Slope DisplacementSeismic Slope Displacement
EERC Slide Collection
Waste Liner Tear, 1994 Northridge EQ
4th Ave. Slide, 1964 Alaska EQ 1999 Chi-Chi, Taiwan EQ
Solid-Waste Landfill
2
Mechanisms Contributing toMechanisms Contributing toSeismic Slope DeformationSeismic Slope Deformation
• Slip along a distinct surface
• Distributed deviatoric shear deformation
• Volumetric deformation
• Combined effects
Use procedures such as Tokimatsu and Seed 1987 for 1D volumetric seismic
compression (e.g., Stewart et al. 2005)
Two Critical Design IssuesTwo Critical Design Issues
• Are there materials that will lose significant strength as a result of cyclic loading? ““Flow SlideFlow Slide””
• If not, will the earth or waste fill system undergo significant deformations that may jeopardize system performance?““Seismically Induced DeformationsSeismically Induced Deformations””
3
TerzaghiTerzaghi (1950) commenting on (1950) commenting on pseudostatic slope stability analysis:pseudostatic slope stability analysis:
“Theoretically a value of FS = 1 would mean a slide but in reality a slope may remain stable in spite of FS being smaller than unity and it may fail at a value of FS > 1, depending on the character of the slope forming materials.”
“The most sensitive materials are slightly cemented grain aggregates such as loess and submerged or partly submerged loose sand.”
PseudoPseudo--Static Stability AnalysisStatic Stability Analysis
1. k = seismic coefficient, constant that represents earthquake loading
2. S = dynamic material strengths and geometry give FS
3. Potential sliding mass is rigid
Selection of acceptable combination of S, k, & FS requires calibration through case histories or consistency with more advanced analyses
4
Static Slope Stability MethodsStatic Slope Stability Methods• Limit equilibrium methods that satisfy all
conditions of equilibrium give FS within +/- 6% (Duncan 1992)– Morgenstern and Price 1965– Spencer 1967– Generalized Janbu 1968
• Focus on these most important issues: – Defining geometry– Shear strengths– Unit weights– Water pressures
Some Prevalent Pseudostatic methodsSome Prevalent Pseudostatic methods(for embankments that do not lose significant (for embankments that do not lose significant
strength from earthquake shaking)strength from earthquake shaking)• Hynes-Griffen & Franklin (1984)
– 20% strength reduction – k = ½ MHA,rock
– FS > 1.0
• Seed (1979)– “appropriate” dynamic strengths– k = 0.15 – FS > 1.15
BUT these methods were calibrated for earth dams where ~ 1 m of displacement is judged to be acceptable
WHAT about other systems and other levels of acceptable displacement?
5
Critical Components of a Critical Components of a Seismic Displacement AnalysisSeismic Displacement Analysis
1. Earthquake Ground Motion
2. Dynamic Resistance of Slope
3. Dynamic Response of Potential Sliding Mass
Earthquake Shaking:Earthquake Shaking:Acceleration Acceleration –– Time HistoryTime History
acce
lera
tion
(g)
-0.50
-0.25
0.00
0.25
0.50
time (s)
0 5 10 15 20 25 30
Izmit (180 Comp) 1999 Kocaeli EQ (Mw=7.4) scaled to MHA = 0.30 g
MHA = 0.3 g Tm = 0.63 s & D5-95 = 15 s
6
Acceleration Response SpectrumAcceleration Response Spectrum(provides response of SDOF of different periods at 5% damping,(provides response of SDOF of different periods at 5% damping,
i.e., indicates frequency content of ground motion)i.e., indicates frequency content of ground motion)
0 1 2 3 4 5Period (s)
0.0
0.5
1.0
1.5Sp
ectral
Acc
eler
atio
n (g
)
5% Damping
Sa at T = 0.5 s
Sa at T = 1.0 s
MHA
Dynamic Resistance:Dynamic Resistance:Simplified Estimates of Yield Coefficient (Simplified Estimates of Yield Coefficient (kkyy))
(seismic coefficient that results in FS=1.0 in pseudostatic stab(seismic coefficient that results in FS=1.0 in pseudostatic stability analysis)ility analysis)
H
β
c = cohesionφ = friction angle
kc
Hy = − +⋅ ⋅ ⋅ + ⋅
tan( )cos ( tan tan )
φ βγ β φ β2 1
1 S2
1 H
L
S1
kFS S H
H S S Lystatic=
− ⋅ ⋅ ⋅⋅ + +
⋅( ) cos sin( )
1 22
1 1 1
1 2
θ θ
( )FS
S H L S HS Hstatic =
⋅ ⋅ ⋅ + + ⋅⋅ ⋅ ⋅
tan coscos sin
φ θθ θ
12
1 2
1 1 1
2 22
with θ11
11= −tan ( )S
Shallow SlidingDeep Sliding
Bray et al. 1998
7
Seed and Martin 1966
Dynamic Response of Potential Sliding Mass
Dynamic Response: Equivalent Acceleration ConceptDynamic Response: Equivalent Acceleration Concept
• accounts for cumulative effect of incoherent motion in deformable sliding block
• In 1-D, HEA = (τh/σv) g
– Calculate shear stress-time history at slide plane depth and divide each value by the total vertical stress acting at that depth
–MHEA = max. HEA value
–Kmax = MHEA/g
H σvτh
Seed and Martin 1966
8
9
10
MHEA depends on stiffness and geometry of the MHEA depends on stiffness and geometry of the sliding mass (i.e., its fundamental period)sliding mass (i.e., its fundamental period)
Ts,1-D = 4 H / Vs
Ts, 1-D = Initial Fundamental Period of Sliding Mass
H = Height of Sliding Mass
Vs = Average Shear Wave Velocity of Sliding Mass
11
Bray & Rathje 1998kmax = MHEA/g
Principal FindingsPrincipal Findings• HEA represents τhf and thus the seismic loading:
HEA = (τh/σv) g; k = HEA/g & kmax = MHEA/g
• MHEA depends primarily on dynamic response of sliding mass (Tfill) and input rock motions (MHA,rock, Tm)
• Development of pseudostatic method has merit due to simplicity; key is the selection of strengths, k & FS
“Use of k = MHEA/g & FS > 1 with conservative strengths is equivalent to calculating no sliding displacement (i.e., max. driving force never exceeds resisting force)”
““Focus on seismically induced permanent displacementsFocus on seismically induced permanent displacements””
12
NewmarkNewmark (1965) Rigid Sliding Block Analysis(1965) Rigid Sliding Block Analysis
• Assumes:– Rigid sliding block – Defined slip surface– Material is rigid-perfectly plastic– Material does not lose strength during shaking– Acceleration-time history defines EQ loading
Key Parameters:• Yield Coefficient (ky) (max. dynamic resistance)• Seismic Coefficient (kmax) (max. seismic loading)• ky/kmax (if > 1 = no displ.; but if < 1 = some displ.)
Rigid DeformableSliding SlidingBlock Block(kmax= (kmax =MHA) MHEA)
13
Decoupled & Coupled Sliding AnalysisDecoupled & Coupled Sliding Analysis
Earth Fill
Potential Slide Plane
Decoupled Analysis
Coupled Analysis
Flexible System
Dynamic Response
Rigid Block
Sliding Response
Flexible SystemFlexible System
Dynamic Response and Sliding Response
Max Force at Base = ky ·W
Calculate HEA-time history
assuming no sliding along base
Double integrate HEA-time
history given kyto calculate U
Decoupled vs. Coupled AnalysisDecoupled vs. Coupled Analysis
From Rathje and Bray (2000)
• Insignificant difference for Udecoupled < 1 cm
• Conservative for Udecoupled > 1 m
• Between 1 cm and 1 m, could be meaningfully unconservative
0.1 1 10 100 1000U (cm)
-40
-20
0
20
40
60
80
100
Dis
plac
emen
t Diff
eren
ce (c
m):
U
- U
decoupled
deco
uple
d
c
oupl
ed
k = 0.05
k = 0.1
k = 0.2
y
y
y
(b)
Dec
oupl
ed C
onse
rvat
ive
14
(Bray & Rathje 1998)
Bray & Rathje 1998
15
SAFE
UNSAFE
??
16
Deep Sliding Case: 1D vs. 2DDeep Sliding Case: 1D vs. 2D
• 1D analysis “averages” accelerations over depth to compute HEA-t history
• 2D analysis “averages” over depth andwidth to compute overall HEA-time history
1D Analysis of 2D Geometry
• Common to analyze large slides as 1D– Large areal extent– Relatively flat slopes
• Use representative SHAKE columns
Rock
Base
Cover
I
III
II
Rock
Base
Cover
I
III
II
Calculate HEA-time history for each column at depth of sliding &calculate mass-weighted average in time of overall HEA-t history
17
Accounting for 2D Shallow Sliding EffectsAccounting for 2D Shallow Sliding Effects
• Topographic Effects – MHAcrest ~ 1.3 MHA1D (Use MHAcrest ~ 1.5 MHA1D for steep slopes (>60o); Ashford and Sitar 2002)
• Localized shallow sliding near crest– MHEA ~ MHAcrest ~ 1.3 MHA1D
• Long shallow sliding surface– MHEA ~ 0.5 MHAcrest ~ (0.5)(1.3) MHA1D ~
0.6 MHA1D
Sliding Displacement ProgramsSliding Displacement Programs• USGS computer program available
– Rigid and simplified decoupled sliding block displacement calculations
– Degrading Ky vs. U– Large catalog of EQ ground motions– Can import HEA-time histories from other programs
(e.g., SHAKE) for decoupled analysis– Jibson & Jibson (2003) O-F Report 03-005
• New USGS program will have coupled nonlinear sliding block analysis– Jibson, Rathje & Jibson (2007)
18
FEA of Shaking Table Test of Clay SlopeFEA of Shaking Table Test of Clay Slope
0 2 4 6 8 10-2.5
-2
-1.5
-1
-0.5
0
0.5
Time (sec)
Dis
plac
emen
t (in
ches
)
Horizontal displacement (D2)
PLAXISRECORD
0 2 4 6 8 10-3
-2
-1
0
1
Dis
plac
emen
t (in
ches
)
Horizontal displacement (D4)
0 2 4 6 8 10-1.5
-1
-0.5
0
0.5
1
Time (sec)
Horizontal displacement (D5)
0 2 4 6 8 10-1.5
-1
-0.5
0
0.5Vertical displacement (D1)
SummarySummary• First question: will earth materials lose strength?
• If not, evaluate seismic slope stability in terms of displacements
• Newmark-type approach with deformable sliding mass captures:
– Earthquake ground motion – Dynamic resistance of slope– Dynamic response of potential sliding mass
• Some Other Issues:
– Decoupled sliding approximation is reasonable, with possible exception of near-fault ground motions case
– 1D analysis is conservative for deep sliding case and can be corrected for topographic effects for shallow sliding case
– Nonlinear FE analysis can lead to better insights but it is difficult to perform well
• With dynamic analyses the full HEA-time history can be calculated for each input rock motion. With ky, the seismic displacement can be calculated.
• Seismic displacement is an index of performance
• Simplified procedures can provide this index of performance
Recommended