Univ Los Andes Bogota 2005
Transcript of Univ Los Andes Bogota 2005
-
8/22/2019 Univ Los Andes Bogota 2005
1/29
Los
LosAndes
AndesUniversid
ad
Universid
adBogot
2005
Bogot
2005
Bauhaus-Universitt Weimar / Germany
Seismic Site Investigations
for the Application in Geotechnical and
Earthquake Engineering
Dr.-Ing. Hans - Gottfried Schmidt
Bauhaus - University WeimarLaboratory of Soil Mechanics
Content:
Site investigations tasks
and goals
Site specifics in seismic
affected areas
Requirements of the design
Use of strain-dependent
parameters
Strain dependence and
Investigation methods
Use of the Seismic site
investigation methods
Seismic field tests
borehole and surfacemeasurements
Spectral analysis of surface
waves SASW
Inversion of surface wave
data
Examples
-
8/22/2019 Univ Los Andes Bogota 2005
2/29
Los
LosAndes
AndesUniversid
ad
Universid
adBogot
2005
Bogot
2005
Site investigations tasks and goals
Investigation of the variously varying soil structures
Characterization of the natural or reclaimed soildeposits with all uncertainties
+ geometryof soils strata and their spatial variability
+ groundwater conditions+ geostatic stresses and related stress histories
+ characteristics of hydraulic conductivity+ deformation and damping characteristics assessedin the strain range of interest (!)
+ drained and undrained monotonis and cyclic shearstrength for cohesionless and cohesive strata
+ liquefaction potential of the soil deposits
+ direkte Aufschlsse eingeschrnkt einsetzbar
+ ergnzende geophysikalische /seismische Messungen
mglich/notwendig (zerstrungsfrei)
Investigation of disturbances in site conditions: holes,
stones, waste deposits, parts of old buildings
-
8/22/2019 Univ Los Andes Bogota 2005
3/29
Los
LosAndes
AndesUniversid
ad
Universid
adBogot
2005
Bogot
2005
Site Investigations in seismic affected zones
Site investigations related to the Geotechnical Earthquake
Engineering (GEE) aspects
+ depth-dependent velocity- or stiffness profiles, generally for
small strains+ characteristics of the amplification and filter effects of the
sediment layers >>site dependent input motions+ statements to the dominant site frequencies
>> different during main and after shocks ?+ deformation / damping characteristics in a wide range of strains+ shear strength by various conditions+ assessment of the land slides, liquefactions
In GEE:
+ investigation of great affected areas
+ fast and effective investigations
+ use of geophysics to receive realistic soil
parameters, additionally with lab-tests
+ use of all these investigation methods with
consideration of the requirements of thedesign and the risk assessment
-
8/22/2019 Univ Los Andes Bogota 2005
4/29
Los
LosAndes
AndesUniversid
ad
Universid
adBogot
2005
Bogot
200
5
Requirements of the design
Current development: Adjustment of the material parametersCurrent development: Adjustment of the material parameters
to the current strain level of the task of design (see Tatsuoka,to the current strain level of the task of design (see Tatsuoka,
Fahay, Mayne, Burland, Atkinson)Fahay, Mayne, Burland, Atkinson)
10-6 10-5 10-4 10-3 10-2 10-1
G
G0
Earthquakes
Foundations
M achines
Tunnels
Roads
-
8/22/2019 Univ Los Andes Bogota 2005
5/29
Los
LosAndes
AndesUniversid
ad
Universid
adBogot
2005
Bogot
200
5
Use of the strain-dependent soil parameter in the Soil
Dynamics / Geotechnical Earthquake Engineering
Use of a visco-elasto-plastic constitutive law with a definition of one ormore yield surfaces and>> non linear - elastic computations within the yield surface
into a wide range of strains (Tatsuoka, Hamburg 1997)
large acceptance for practical computations in the Dynamics:
>> equivalent linear iteration cycles with the adjustment to thecurrent strain level
>> that means: Hypoelasticity - incremental linear
Hyperbolic law (u.a. Kondner) for the
mean curve (skeleton curve) and the
Masing-Rule for the Hysteretic slope
r
f
-
8/22/2019 Univ Los Andes Bogota 2005
6/29
Los
LosAndes
AndesUniversid
ad
UniversidadBogot
200
5
Bogot
200
5
Use of the strain-dependent soil parameter in the Soil
Dynamics / Amplification Functions
In = Rock motion
Amplificationfunction
Out = Responseof the layer (top)
On the basis of the sufficient knowledge of theOn the basis of the sufficient knowledge of the
material parameters there is a good agreement ofmaterial parameters there is a good agreement of
the dominant site frequencies of various methods:the dominant site frequencies of various methods:
(1) amplification function(1) amplification function (matrix(matrix--reductionreduction--algorithm)algorithm)
(2) H/V(2) H/V technology (Nakamura)technology (Nakamura) (comparing of the(comparing of the
displacements at the ground surface)displacements at the ground surface)
(3) Dispersion curves of the surface waves(3) Dispersion curves of the surface waves
11
22
33
-
8/22/2019 Univ Los Andes Bogota 2005
7/29
Los
Los
Andes
AndesUniversid
ad
UniversidadBogot
200
5
Bogot
200
5
Use of the strain-dependent soil parameter in the Soil
Dynamics / Amplification Functions
GoodGood agreementagreement betweenbetween amplificationamplification
functionfunction (1) and H/(1) and H/VV--ratioratio (3)(3) byby usingusing
thethe samesame soilsoil parameterparameter
Change inChange in thethe frequenciesfrequencies and inand in thethe
sizesize ofofamplitudesamplitudes duedue toto thethe variationvariation ofof
thethe soilsoil stiffnessstiffness// velocitiesvelocities causedcaused byby
differentdifferent inducedinduced strainsstrains ((seesee 1 and 2)!1 and 2)!
11
33
22
-
8/22/2019 Univ Los Andes Bogota 2005
8/29
Los
Los
Andes
AndesUniversidad
UniversidadBogot
200
5
Bogot
200
5
Soil Mechanics - Settlement control
and realistic soil parameters
Measurement of the strains in the soils (relativsettlements)beneath a foundation (Kriegel/Wiesner 1973); Burland 1989
MeasuredSettlements invarious depth z
(e.g. withExtensiometers)
Calculation of thestrains (relative
settlements):* in wide soil regionswe have local strainsunderneath 0,1%
* max. values areabout 0,3%
Reason for differencesof the observed andcalculated settlements
> the most soil deforma-tionen are in the rangelower than 0,1%
> there is a strict nonlinearsoil behaviour over awide range of strains
Consequence:
use of the strain
dependent soil stiffness
and improved
computional algorithm
-
8/22/2019 Univ Los Andes Bogota 2005
9/29
Los
Los
Andes
AndesUniversidad
UniversidadBogot
200
5
Bogot
200
5
Use of strain-dependent Soil Parameters in Routine
Designs of the Soil Mechanics
Increasing tendency: Consideration of the pronounced non-linearity
within the range of small strains (-> WCSMFE 2001)
Goal realistic computations e.g for Settlements(Atkinson 2000, Mayne 2000)>> thatmeans non-linear - elastic computations with strain-dependent
parameters analogue to the Soil Dynamics
LinearLinear
computationcomputation
NonNon--linearlinearcomputationcomputation
FoundationFoundation settlementsettlement:: ComparisonComparison PredictionPrediction (non(non--linear)linear) -- MeasurementMeasurement
S
Qfs
BE=
0,3
0 ult
Qfs
BE 1 (Q /Q )=
-
8/22/2019 Univ Los Andes Bogota 2005
10/29
Los
Los
Andes
AndesUniversidad
UniversidadBogot
200
5
Bogot
200
5
Use of the strain-dependent soil parameter in the Soil
Mechanics / Geotechnical Engineering
Use in routine computations in the soil mechanicse.g. Settlement calculation after Berardi (Diss. 1992)
(Janbu)
(Settlement)
(Loads)
(SPT)Modul factor KE
strain 0,1%
Here arepossibe actualcurves ofmeasurements!
GoalGoal
::
reductionreduction
ofof
thethe
oftenoften
largelarge
differencesdifferences
betweenbetween
thethe
prognosisprognosis
andand
thethe
observationobservation ofofsettlementssettlements!!
-
8/22/2019 Univ Los Andes Bogota 2005
11/29
Los
Los
Andes
AndesUniversidad
UniversidadBogot
200
5
Bogot
200
5
Strain-dependent soil parameter in the Soil Mechanics /
Soil Dynamics / Geotechnical Earthquake Engineering
Degradation ofDegradation ofthethe StiffnessStiffness:: forforstaticstatic loadingsloadings
dehnungsabhdehnungsabhngigngig
beanspruchungsabhbeanspruchungsabhngigngig
Proposals of the Degradation curves for the non-linear Soil Stiffness (after Fahay)
0 r
G 1
G 1=
Degradation ofDegradation ofthethe StiffnessStiffness::
forfordynamicdynamic loadingsloadings
((e.ge.g.. seesee Kramer:Kramer:
GeotechnicalGeotechnical EarthquakeEarthquake Engineering)Engineering)
g
0
G 1 f( )G max
=
-
8/22/2019 Univ Los Andes Bogota 2005
12/29
Los
Los
Andes
AndesUniversidad
UniversidadBogot
200
5
Bogot
200
5
Strain-dependent soil parameter in the Soil Mechanics /
Soil Dynamics / Geotechnical Earthquake Engineering
G0
Static degradation
Dynamic degradation
10-6 10-1
failure
MainMain tasktask forforthatthat descriptionsdescriptions::
++ realisticrealistic maximummaximum valuevalue ofofstiffnessstiffness GmaxGmax ororGG00 forforveryvery smallsmall strainsstrains
++ Adjustment of the stiffness to the current stress / strain of thAdjustment of the stiffness to the current stress / strain of the soile soil
WhatWhat areare thethe possibilitiespossibilities ofofthethe sitesite investigationinvestigation and laband lab methodsmethods??
DifferentDifferent
curvescurves
forfor
differentdifferent loadload regimesregimes !!
There is not only theThere is not only the
one characteristicone characteristic
parameter for a soil.parameter for a soil.
-
8/22/2019 Univ Los Andes Bogota 2005
13/29
Los
Los
Andes
AndesUniversidad
UniversidadBogot
200
5
Bogot
200
5
Geotechnical Site Investigation Methods
How much can material parameters be derivedHow much can material parameters be derived
from a number punch?from a number punch? ((MayneMayne 2001)2001)Is this procedure rational?Is this procedure rational?
What can we begin with seismicWhat can we begin with seismic
measurements?measurements?
Indirect explanations: ProbesDirect explanations (drillings) and samplings: disturbed / undisturbed ?
-
8/22/2019 Univ Los Andes Bogota 2005
14/29
Los
Los
Andes
AndesUniversidad
UniversidadBogot
200
5
Bogot
200
5
Strain Dependence and Investigation Methods
ShearShearstrainstrain
SeismicSeismic boreholeboreholemethodsmethods
SeismicSeismic surfacesurface
methodsmethods
PossibilitiesPossibilities andand limitationslimitations of differentof different investigatioionsinvestigatioions methodsmethods
Advantages of Seismicmeasurements: clear
mechanical relations to othersoil parameters- Schubmodul G0=.vs
2
- Hooke-Modul E0=2(1+)..vs2
(Steifezahl Es=.vp2
- Querdehnzahl =(vp2-2vs
2)/2(vp2-vs
2)
- GeschwindigkeitsverhltnisvR/vs(0862+1,14)/(1+).
-
8/22/2019 Univ Los Andes Bogota 2005
15/29
Los
Los
Andes
AndesUniversidad
UniversidadBogot
200
5
Bogot
200
5
Main focuses for this concept: + determination of the maximal value Go or Eo
+ degradation curve for the non-linear stiffness
Strain Dependence and Investigation Methods
0=0,001%
Main Problem: Conventional Lab- and Field tests cannot provide soil parameters in the demanded lowstrain range (e.g. Burland, Atkinson, Fahay, Tatsuoka)
Consequently we use in the present time
-> Seismic field tests in undisturbed conditions and in a very small strain range
(see 1: < 10-5 )
characteristicalvalue
We focus: In situ - soil parameter should be measured in situ
-
8/22/2019 Univ Los Andes Bogota 2005
16/29
Los
Los
Andes
AndesUniversidad
Universi
dadBogot
200
5
Bogot
200
5
TheoreticalTheoretical backgroundbackground:: wavewave propagationpropagation theorytheory in ain a layeredlayered halfspacehalfspace
Seismic Field Measurements
DifferentDifferent fieldfield measurementmeasurement methodsmethods::
++ BoreholeBorehole measurementsmeasurements:: directdirect measurementmeasurement ofofthethe wavewave velocitiesvelocities
++ MeasurementMeasurement ofofthethe groundground surfacesurface wavewave fieldfield withwith manymany differentdifferentevaluationevaluation methodsmethods:: noninstrusivenoninstrusive indirectindirect measurementmeasurement ofofthethe wavewave velocitiesvelocities
-- Reflexion andReflexion and RefractionRefraction ofofseismicseismic waveswaves -- onlyonly bodybody waveswaves areare usedused
-- DispersionDispersion MethodsMethods dominantdominant surfacesurface waveswaves areare usedused
DispersionDispersion thatthat meansmeans frequencyfrequency dependentdependent wavewave velocitiesvelocities!!
-- H/VH/V techniquetechnique:: measurementmeasurement ofofthethe groundground surfacesurface displacementsdisplacements
andand determinationdetermination ofofthethe dominantdominant sitesite frequencyfrequency
-- Geotomographie: 3DGeotomographie: 3D--detection ofdetection ofnearnearsurfacesurface disturbancesdisturbances
+ Dispersion+ Dispersion MethodsMethods::-- determinationdetermination ofofthethe experimentalexperimental dispersiondispersion curvescurves byby usingusing ofof
differentdifferent mathematicalmathematical correlationcorrelation andand convolutionconvolution// transformationtransformation
techniquestechniques
-- determinationdetermination ofofthethe depthdepth--dependentdependent velocityvelocity ororstiffnessstiffness profileprofile
withwith inversioninversion methodsmethods ((comparisoncomparison ofofthethe experimental andexperimental andtheoreticaltheoretical computedcomputed dispersiondispersion curvecurve))
-
8/22/2019 Univ Los Andes Bogota 2005
17/29
LosLos
Andes
AndesUniversidad
Universi
dadBogot
200
5
Bogot
200
5
Seismic Field Measurements Borehole Methods
Crosshole-, Downhole-, Uphole-Methods
relatively simple, but complex measurements
+ importantly: Contact in the borehole > > balloons+ problem: suitable borehole excitation > > S-wave
further effective developments> Probes with geophones (SCPT)> Pressiometer with geophones
> dilatometers with geophone
CH DH
(Kalinski/Stokoe 2003)
DilatometerDilatometer
-
8/22/2019 Univ Los Andes Bogota 2005
18/29
LosLos
Andes
AndesUniversi
dad
Universi
dadBogot
200
5
Bogot
200
5
Seismic Field Measurements Borehole Methods
Plot ofPlot ofthethe registeredregistered boreholeboreholetimetime historieshistories
ExcitationExcitation byby a horizontala horizontal
polarizedpolarized shearshearwavewave -- ever twoever two
measurements with oppositemeasurements with opposite
direction of the excitationdirection of the excitation
RunningRunning time oftime ofthethe SHSH--wavewave
-
8/22/2019 Univ Los Andes Bogota 2005
19/29
LosLos
Andes
AndesUniversi
dad
Universi
dadBogot
200
5
Bogot
200
5
Ground Surface Wave Field Measurement (1)
SYSCOM / BARTEC
MR 2002 CE-variant
Geophone
Punctual measurements of time historiesPunctual measurements of time histories
from surface wave fieldsfrom surface wave fields
a)a) due to active sources (pulsator, hammer):due to active sources (pulsator, hammer):
usually smaller, linear arraysusually smaller, linear arrays
b)b) due to passive sources (Noise): twodue to passive sources (Noise): two--
dimensional arrays with larger receiverdimensional arrays with larger receiver
distances are possibledistances are possible
The measured time histories possess theThe measured time histories possess the
information of the continuous medium! Theinformation of the continuous medium! The
analysis of these recordings can take placeanalysis of these recordings can take place
with differently strong methods!with differently strong methods!
SledgeSledge
hammerhammer
-- sourcesource
-
8/22/2019 Univ Los Andes Bogota 2005
20/29
LosLos
Andes
AndesUniversi
dad
Universi
dadBogot
200
5
Bogot
200
5
Ground Surface Wave Field Measurement (2)
Direct wave
c
Reflexions / Refraction (only the propagation of P- and S- waves)
DetectionDetection ofofthethe diferentdiferent runningrunning
timestimes ofofthethe differentdifferent waveswaves typestypes
andand derivationderivation ofofthethe wavewavevelocitiesvelocities
Determination of HDetermination of the wave velocities
from the time distance - diagram
linearlinear arrayarray
-
8/22/2019 Univ Los Andes Bogota 2005
21/29
LosLos
Andes
AndesUniversi
dad
UniversidadBogot
200
5
Bogot
200
5
Ground Surface Wave Field Measurement (3)
Rayleigh wave Dispersion Measurement (conventional)
linear array of the Geophones / different spacings /harmonic excitation with various frequencies and detectionof phase differences between e.g. 2 Geophones
PhasePhase velocityvelocity forforeacheach frequencyfrequency
c(fc(f) = Geophon) = Geophon spacingspacing/ Phase/ Phase differencedifference
ResultResult:: DispersionDispersion curvecurve :: cc--ff--curvecurve
vertical particle motion
layer 1
layer 2
half space low freq.high freq
WaveWave lengthlength andand influenceinfluence depthdepth
z
surface
(1/3 . ) RW,1 cRW(f1) or 0,92 cs
StiffnessStiffness profileprofile ofofthethe sitesite:: determineddetermined
velocities arevelocities are
arranged with thearranged with the
(0,3(0,3--0,5)0,5)-- wavelengthwavelength
over the depth!over the depth!
( )RW 1 RW,1 1 1 2 1c (f ) s/ t f s 2 f /= = =
( )RW,1 2 12 s/ =
-
8/22/2019 Univ Los Andes Bogota 2005
22/29
LosLos
Andes
AndesUniversi
dad
UniversidadBogot
200
5
Bogot
200
5
ExperimentalExperimental SurfaceSurface WaveWave FieldField Analysis (1)Analysis (1)
Measurement of wave field with few receivers and with a variable offset!
1. Phase1. Phase DifferenceDifference MethodMethod (linear(lineararrayarray)) -- SASWSASW
Determination ofDetermination ofthethe PhasePhase
differencesdifferences ororthethe PhasePhasevelocitiesvelocities withwith followingfollowing stepssteps
++ FourierFourier--TransformationTransformation fromfrom
thethe TD inTD in thethe FDFD
++ determinationdetermination ofofthethe CrossCross
correlationcorrelation spectrumspectrum ofoftwotwo
measuredmeasured signalssignals++ determinationdetermination of dieof die phasephase
differencedifference withwith ReRe-- andand ImIm--partpart
( ) ( )( )( )( )
ij
s 2 f
c f fa rc tan
ij f
=
Method well been suitable, if only one mode of theMethod well been suitable, if only one mode of the
surface waves, e.g. the fundamental mode issurface waves, e.g. the fundamental mode is
evaluatedevaluated -- >> an averaged dispersion curve resultsan averaged dispersion curve results
(if necessary from many branches)(if necessary from many branches)
Generally a surface wave field possesses severalGenerally a surface wave field possesses several
modes, i.e. at a measuring point several velocitiesmodes, i.e. at a measuring point several velocities
or several wave fields with different velocities existor several wave fields with different velocities exist
> >> > the detection of the higher modes isthe detection of the higher modes is
extremelyextremely importantimportant for the success offor the success ofseismic field investigations!seismic field investigations!
Fundamental modeFundamental mode
HigherHighermodesmodes
AveragedAveraged experimentalexperimental
dispersiondispersion curvecurve
In allIn all casescases:: thethe determinationdetermination ofofthethe dispersiondispersion characteristicscharacteristics ofofthethe sitesite!!
( ) ( ) ( )
( ) ( ) ( )
ij 1 2
ij 1 2
t g g t d
f G f G f
7
= +
=
-
8/22/2019 Univ Los Andes Bogota 2005
23/29
LosLos
Andes
AndesUniversidad
UniversidadBogot
200
5
Bogot
2005
ExperimentalExperimental SurfaceSurface WaveWave FieldField Analysis (2)Analysis (2)
2.2. FrequencyFrequency -- WaveWave numbernumber-- Analysis (Analysis (fkfk -- Analysis)Analysis)
Transformation ofTransformation ofthethe measuredmeasured timetime historieshistories inin thethe FrequencyFrequency -- WaveWave
numbernumber DomainDomain withwith aa doubledouble FourierFourier TransformationTransformation -- techniquetechnique
The distances of the geophones affect the wave number ranges whiThe distances of the geophones affect the wave number ranges which can bech can be
detected and the spatial Aliasing effects; but the analysis is adetected and the spatial Aliasing effects; but the analysis is a durabledurable
procedure with a high resolution!procedure with a high resolution!
Improvement of the technology of evaluating of measured time historiesby consideration of the changes both over the time and the distance
DispersionDispersion analysisanalysis byby usingusing ofofseveralseveral receiversreceivers withwith discretediscrete
signalsignal samplingsampling andand processingprocessing inin thethe timetime-- andand spacespace--domaindomain
( ) ( )c / k =
-
8/22/2019 Univ Los Andes Bogota 2005
24/29
LosLos
Andes
AndesUniversidad
UniversidadBogot
200
5
Bogot
2005
ExperimentalExperimental SurfaceSurface WaveWave FieldField Analysis (3)Analysis (3)
3. Wave3. Wave FieldField TransformationTransformation (Slant Stack Transformation)
( ) ( ), , ixS p P x px e d
= +
-> good method for the evaluation of the higher modes
-> slant stack - that means a linear time-shift and summing of the amplitudesover the outset axis (plane wave decomposition of a wave-field)
-> the mathematical operations: transformation of the wave field in the
p - - domain (a special mapping domain) by two independent lineartransformations: first a slant-stack or special Radon-transformationfollowed of a one-dimensional Fourier-transformation
( )P x,t inputdata
t px;linearmoveout;coordinate transformation
=
1.1. StepStep:: SlantSlant stackstack
p ray-parameter as a inverse of the horizontal phase velocity c
( ) ( )x
P x, px Summationin the p domainS p, + =
SlantSlant stackstack summationsummation
2.2. StepStep: 1D: 1D FourierFourierTransformation ofTransformation ofthethe SlantSlant StackStack SummationSummation
SlownessSlowness spectrumspectrum SS
n R n nc (f )/ f =
-
8/22/2019 Univ Los Andes Bogota 2005
25/29
LosLos
Andes
AndesUniversidad
UniversidadBogot
200
5
Bogot
2005
ExperimentalExperimental SurfaceSurface WaveWave FieldField Analysis (4)Analysis (4)
4.4. ExampleExample forforanan evaluatedevaluated measurementmeasurement
Deposit of an old mining industry:Deposit of an old mining industry:
height 25height 25 -- 30 m30 m
dispersion analysis of the measureddispersion analysis of the measuredwave fieldwave field
(a) time history(a) time history
(b)(b) fkfk -- transformtransform
(c ) slant(c ) slant -- stackstack -- transformtransform
aa
bb
cc
-
8/22/2019 Univ Los Andes Bogota 2005
26/29
LosLos
Andes
AndesUniversidad
UniversidadBogot
2005
Bogot
2005
Theoretical Wave Field Analysis Matrix Methods
1) Thomson-Haskell-Algorithm
relative simple mathematical-physical model
simple numerical realisation
2) Method of the generalized Reflex ion-and Transmission coefficients
numerical stable
7
( ) ( ){ }
( ) ( )
1 1
,
,
z z z zjd
z z z zju
j j j j
j j jj
diag e e
diag e e
=
=
2 2pk k =
2 2sk k =
k c
=
0 0 0
0 0 0
0 0 0
0 0 0
z
z
z
z
e
e
e
e
=
-
8/22/2019 Univ Los Andes Bogota 2005
27/29
LosLos
Andes
AndesUniversidad
UniversidadBogot
2005
Bogot
2005
Inversion of Surface Wave Data
Basis ofBasis ofthethe InversionInversion MethodMethod -- thethe experimentalexperimental dispersiondispersion
curvescurves ofofthethe surfacesurface waveswaves inin thethe FDFD
InversionInversion TechniqueTechnique representsrepresents aa newnew qualityquality ofofthethe
Dispersion Analysis >> Inversion ofDispersion Analysis >> Inversion ofthethe measuredmeasured fieldfield datadata
Goal: Investigation ofGoal: Investigation ofdepthdepth--dependentdependent soilsoil stiffnessstiffness profilesprofiles
M
i ij j
j 1
f (d, m) d Gm 0
d G m=
= =
=
Nonlinear connection between the measuredNonlinear connection between the measured
discrete data d and the material properties mdiscrete data d and the material properties m
with the function Gwith the function G
Solution of the nonSolution of the non--linear Inversion problemlinear Inversion problem
e.g. Use of thee.g. Use of the gradient methodgradient method on basis of theon basis of the linearizationlinearization of aof a nonnon--linearlinear
problemproblem (Taylor(TaylorSeriesSeries expansionexpansion))
d,d,mm difference vectorsdifference vectorsThe number of the iterative cycles depends on the nonThe number of the iterative cycles depends on the non--linearity of the problem andlinearity of the problem and
on the quality of the Input stiffness profile of the siteon the quality of the Input stiffness profile of the site (obtimization problem)
Numerical stabilization of the inversion steps with the use of the weightedMarquardt-Levenberg-Algorithmus
DiscreteDiscrete inversioninversion problemproblem iterativeiterativegoodgood adjustmentadjustment ofofthethe modelmodel vectorvectormm
toto thethe datadata vectorvectordd
T 1 Tm (G WG I) G W d = +
-
8/22/2019 Univ Los Andes Bogota 2005
28/29
LosLos
Andes
AndesUniversidad
UniversidadBogot
2005
Bogot
2005
Inversion of Surface Wave Data
Overview of the Inversion ProcedureOverview of the Inversion Procedure
Theory
Iteration
InversionSite condition
(layers, soil parameters)
j
d
11j
du
j
ud
j
d
j
d
1j
du
j
u
j
du
j
du
T)R~
R(IT~
T~
R~
TRR~
+
=
+=
( ) 0R~R~Idet 1du0ud =( ) (0)EER
~ 1u
1
22
11
21
0
ud
=
N
du
N
du
N
d
N
d
RR~
TT~
=
=
Reflection and Transmission matrixmethod (Chen,Luco)
Experi-
ment
-
8/22/2019 Univ Los Andes Bogota 2005
29/29
LosLos
Andes
AndesUniversidad
UniversidadBogot
2005
Bogot
2005
Inversion of Surface Wave Data
Site investigationSite investigation -- Determination of a soil stiffness Profile (example)Determination of a soil stiffness Profile (example)
Deposit of an old mining industryDeposit of an old mining industry: height 25: height 25 -- 30 m30 m
Inversion of the surface wave dataInversion of the surface wave data Dispersion characteristicsDispersion characteristics
(a) Slant stack dispersion of the site together with theoretical(a) Slant stack dispersion of the site together with theoretical dispersiondispersion
curves of the determined soil profilecurves of the determined soil profile
(b) depth(b) depth--dependent velocity profile (shear wave velocity)dependent velocity profile (shear wave velocity)
aa bb