-
8/10/2019 139-Strenk
1/20
-
8/10/2019 139-Strenk
2/20
Introduction1
Seismic performance of earth systems requirescomputation of
their dynamic response
Two General
Categories:
Equivalent-Linear
Cyclic Non-Linear
Frequency-domainvs.
Time-domain
Understand how
frequency-
vs. time-domainimplementation affects dynamic response
Objective
-
8/10/2019 139-Strenk
3/20
Equivalent-Linear & Non-Linear 2
Equivalent-Linear Cyclic Non-Linear
G sec
DampingratioMasing (1926)
hypothesis2maxsec
loop
G
A
21
Secant shearmodulus G tanTangent shearmodulus
-
8/10/2019 139-Strenk
4/20
3
Curve-Fitting Process
Equivalent-Linear & Non-Linear
Establish consistency with physically-meaningful
soil properties
-
8/10/2019 139-Strenk
5/20
Dynamic Response Analyses4
AnalysesEquivalent-linear SHAKECyclic non-linear FLAC v.6
(Hysteretic)
SHAKE-FLAC Comparisons
1. Shear strain ( ) and shear modulus (G sec
, G tan
)time histories
2. Acceleration time histories
To understand, at a mechanistic level, how
time-varying stiffness affects dynamic behavior
To understand how time-varying stiffness
translates into differences in ground surfaceaccelerations and
amplification response
-
8/10/2019 139-Strenk
6/20
1D Soil Column5
Soil Column Properties:
Height of 30 m (60 zones/layers)
Shear wave velocity: 250 m/s Unit weight: 20 kN/m 3
Seed & Idriss
(1970) curves
SAND
FLAC fit using [default] function
Histories:
Shear strain ( ) and shear modulusat depth of 5 m
Acceleration at top of soil column
-
8/10/2019 139-Strenk
7/20
Stiffness Reduction & Damping6
Empirical curves in SHAKEreplaced
with FLAC fits
Issue of excess dampingeliminated
Both codes have identical curves!!
-
8/10/2019 139-Strenk
8/20
Input Ground Motions7
Sine motion (f m
= 1.25 Hz)(Ramped, 5 s intense shaking, 10 s quiet shaking)
Earthquake recording (f m
= 1.28 Hz)
(Hollister Hall, USGS 1028, from 1989 Loma Prieta, CA, USA)
Intense 0.2g
Quiet 0.05g
0.2g
-
8/10/2019 139-Strenk
9/20
Strain & Modulus Time Histories8
Single, cycle duringintense
shaking
Single, cycle duringquiet
shaking
-
8/10/2019 139-Strenk
10/20
Observation 19
Difference between FLAC and SHAKE most pronouncedduring interval
of intense shaking
Discrepancy between frequency-domain and time-domainmodels is
sensitive to the magnitude of the induced strains
-
8/10/2019 139-Strenk
11/20
Observation 2
Intense Period
10
FLAC is softer
than SHAKE (phase shift, slower)
Greatest difference when G tan
is a minimum (points b , d )
-
8/10/2019 139-Strenk
12/20
-
8/10/2019 139-Strenk
13/20
Observation 412
Steeper slope;more non-linear
Intense Period
Corresponds to shear modulus that isreducing at a rapid rate
From b to c , strains change rapidly Backbone curve
-
8/10/2019 139-Strenk
14/20
Observation 413
More gentle slope;Less non-linear
Intense Period
Corresponds to shear modulus thatis reducing at a slower
rate
From c to d , strains change slowly Backbone curve
-
8/10/2019 139-Strenk
15/20
Observation 514
Quiet Period
FLAC is stiffer
than SHAKE
Lower induced strains, response is nearly
identical(linear-elastic)
-
8/10/2019 139-Strenk
16/20
-
8/10/2019 139-Strenk
17/20
Hysteresis Loops16
ShakingLevel
G sec
(MPa)
(%)
SHAKE FLAC SHAKE FLAC
Intense 94.1 78.7 5.4 7.4
Quiet 94.1 107.7 5.4 3.4
< Greater
Greater Response
-
8/10/2019 139-Strenk
18/20
Ground Surface Accelerations17
FLAC Peak Accelerations
50% greater
-
8/10/2019 139-Strenk
19/20
Conclusions18
When damping is the same, differences in dynamic
response are attributed to the coupled interactionbetween
time-varying stiffness and shear strain.
Amplification response governed more by time-
varying stiffness than material damping. Time-domain
implementation more effectively
captures peak points
of shaking (e.g. peak groundacceleration, PGA)
Non-linear models more appropriate for large strain situations
(e.g. high intensity motions, soft sites,
resonance)
Frequency-
vs. Time Domain
-
8/10/2019 139-Strenk
20/20
Thank you!
Second International FLAC/DEM Symposium on Numerical
Modeling
