impedance issues in ssi of embedded and deeply … 19, 2016 19 effect of varying wave fields on ssi...
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October 19, 2016
Impedance Issues in SSI of Embedded and Deeply Embedded
Structures
DOE Natural Phenomena Hazards MeetingOctober 19, 2016
Greg MertzCarl J Costantino and Associates
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2October 19, 2016
Outline
● Impedance of deeply embedded structures ● Soil box impedance ● Effect of varying wave fields
Note:● This talk represents a snapshot of work in progress.● Mixed results:
• Some good• Some less than acceptable
● Sharing is encouraged
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3October 19, 2016
Embedded Cylinder Impedance
● Rigid massless cylinder● Embedment=2•radius● Symmetry● Direct solution● Different meshes
f≤Vs10h
f≤Vs6h
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4October 19, 2016
Horizontal Impedance
● Poor comparison for ao>3
● Minor improvement with mesh refinement
● At ao=3, the fine mesh has Vs/21h
● Something besides mesh issues are perturbing the solution
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5October 19, 2016
Vertical Impedance
● Poor comparison for ao>2.5
● Minor improvement with mesh refinement
● Something besides mesh issues are perturbing the solution
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6October 19, 2016
Embedded Cylinder Impedance
● Same problem, with an embedment of 0.5•radius
● Vs/6h model
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7October 19, 2016
Summary of Deeply Embedded Structures
● SASSI V&V project considered embedment depths up to 50% of the effective radius
● Preliminary results for deeper embedment are unsatisfactory– Additional work is required to understand existing results
and path forward
● Engineers are cautioned to ensure that their V&V fully encompasses the full range of parameters being evaluated
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8October 19, 2016
Soil Box Impedance
● Considering implementing time domain SSI– Can we implement, execute and defend analyses?
● Proposed models– Structure– Boundary– Soil box
Structure
Soil Box
Boundary
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9October 19, 2016
Soil Box Impedance
● Linear frequency domain SSI experience– Extensive V&V of soil impedance
● What works ● What doesn't work
● How does the time domain soil impedance compare with frequency domain benchmarks?
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10October 19, 2016
Impedance Comparison Methodology
● Focus on boundaries and soil box size– Omit nonlinear soil models
● Use common damping formulation– Abaqus viscoelastic soil model can be equal to SASSI complex soil damping
● Limited to lumped mass matrix ● Initial comparisons in frequency domain
– Abaqus steady state dynamics with direct option yields complex stiffness and displacement
– Use transmitting boundary (infinite elements) to calibrate soil box size– Rerun with alternate boundaries
● Time domain comparison– Abaqus explicit
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11October 19, 2016
Axisymmetric Modeling
● Exploratory– Quick runs
● Frequency domain● Calibrate damping● Transmitting boundary
– Limited to symmetric load– Asymmetric infinite boundary would be
helpful
● SASSI V&V Task 6 Problem 5– Model parameters
● r= foundation radius ● a= soil box radius
Sym.CL a
rSoil box
Transmitting boundary
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12October 19, 2016
Axisymmetric Modeling
● High frequency behavior is good– Mesh ≈Vs/(10fmax)
– Initial mesh was problematic
● Low frequency behavior is problematic– Wavelength, λ ≈ 0.9Vs/f ≈ 5.6r/ao
● a=2r → λ=a at ao=2.8
● A=6r → λ=a at ao=0.9
– Response degrades when soil box radius, a ≤ λ
● Mesh with infinite elements● Preliminary results
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13October 19, 2016
3D Modeling
● Quarter symmetry– Some frequency domain runs are
slow
● SASSI V&V Task 8 Problem 1– Square rigid massless surface
plate, half-width=a– Uniform half-space
● Cases:– Infinite boundary– Side constraint plus infinite
boundary on base only
Rigid massless
plate½ width=a
SoilBox
½ width=LInfinite
elements
Symmetry
Symmetry/Antisymmetry
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14October 19, 2016
3D Modeling – Frequency Domain
● Horizontal unit load● Investigate soil box size
– Low frequency problems similar to axisymmetric case
– Response degrades when soil box width, L ≤ λ
● L=2a → λ=L at ao=2.8
● L=8a → λ=L at ao=0.7
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15October 19, 2016
3D Modeling – Frequency Domain
● Horizontal unit load● Compare soil box
mesh density– L=8a for all meshes– Each mesh meets λ/5
– Response degrades at frequencies > λ/10
– Note: Response is based on lumped mass matrix
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16October 19, 2016
3D Modeling – Frequency Domain
● Horizontal unit load● Compare
transmitting and restrained boundaries– L=8a
– Each mesh meets λ/5
– Restrained boundary has spurious response due to reflected energy
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17October 19, 2016
Time Domain Response
● Abaqus explicit● Response to unit impulse● Significant reflections in
constrained boundary solution
● To do... – Refine data extraction – Understand high frequency
noise in horizontal response– Extract frequency domain
displacement TF and compare to benchmark
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18October 19, 2016
Summary of Soil Box Impedance Study
● Preliminary results– Work in progress
● Abaqus transmitting boundary– Good comparisons with benchmark– 6-node wedge would be very use full
● Side constraint plus infinite boundary on base only– Reflections from side constraint corrupt solution at L=8a
● Mesh requirements– High frequency: element size < Vs/10h
– Low frequency: soil box size > λ
● Overall, promising results– Additional work needed before implementation on a safety basis project
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19October 19, 2016
Effect of Varying Wave Fields on SSI Loads
● Current practice– Analyze vertically propagating P and S-waves
● Maximize response in a surface or shallowly embedded structure
– Magnitude anchored to input spectra at some elevation
● Actual wave field– Combined body and surface waves
● P-wave, S-wave ● Rayleigh wave, Love wave
● Potential issues– Are P and S wave fields realistic for both shallow and deeply embedded structures?– How do we evaluate alternate wave fields?– Does the actual wave field impact response?
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20October 19, 2016
P and S Wave FieldsVp≈2000 fps
λP=400 ft @ 5hz
Vs=1000 fpsλ
S=200 ft @ 5hz
λP/4
λS/2
● Embedment, e=100', Radius, r=50', e/r=2● Control point at surface● Seismic input averaged over the depth of embedment is much
less than a surface foundation.
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21October 19, 2016
Evaluation of Alternate Wave Field
● Wave field generation– Active R&D – Current study uses PUNCH to generate plane strain waves
● Analysis– Seismic load vector F=K Δ
– Use PUNCH to develop free field displacement, Δ
– Use SASSI for soil impedance, K
– Import frequency dependent load vector into SASSI
– Solve using traditional frequency domain approach
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22October 19, 2016
Wave field generation
Layer 1: Vs=1000 fps; Dens.= 110 pcf; v=0.3
h=200 f
Halfspace: Vs=4000 fps; Dens.= 110 pcf; v=0.25
h=100 f Layer 2: Vs=2000 fps; Dens.= 110 pcf; v=0.25
Unit amplitudesource
Receivers10 wide by 10 deep; 10’ grid
h=150 f
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23October 19, 2016
5 Hz Wave From Vertical Surface Input
● Primarily Rayleigh wave– λR≈180'
– λR/2≈building width
– Input is down on lef size, up on right side with coupled translation
– Direction and amplitude of input changes with phase angle
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24October 19, 2016
2 and 20 Hz Excitation
2 Hz, width≈λR/5 20 Hz, width≈2λ
R
Loads in phase, greater total load than traditional analysis assumptions
Loads out of phase, smaller total load than traditional analysis assumptions
Out of phase loading can have a significant impact on structural response.
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25October 19, 2016
Effect of Wave Fields
● Vertically propagating P-Wave– Analytical idealization
● Yields spurious results in 1D convolution analyses● PSHA & Site studies use empirical V/H ratios
● Surface Waves– Combined vertical and horizontal input
– Coherent building input when λR > building width● More total load for deeply embedded structures
– Incoherent building input when λR < building width● Less total load for all structures at high frequencies● Excite building responses not observed in traditional analyses.
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26October 19, 2016
Summary for Varying Wave Fields on SSI Loads
● Surface waves are a viable alternative to traditional seismic input– Provide better insight into actual seismic response
● Coherent low frequency input ● Incoherent high frequency input
– Superposition of multiple waves could be used to develop ground motions meeting target spectra
● Additional work required to develop design motion
● Surface waves can be evaluated using existing analysis tools