Micro Seismic Hazard Analysis

Basic physical concepts and definitions• What are site effects?• Effect of the local geology on the thecharacteristics of the seismic wave• Local geology:• “Soft” sediments (overlying bedrock)• Surface topography• The local geology can modify thecharacteristics of the incoming seismic wave,resulting in an amplification or deamplification

Basic physical concepts and definitions(1)• Earthquake signal arriving at the siteaffected by:• Source activation (fault rupture)• Propagation path (attenuation of the signal)• Effect of local geology ((de-)amplification)

Site effects due to low stiffness surfacesoil layers – Soft ground effect (2)• Differences in impedance are important:• If impedance becomes smaller:• Resistance to motion decreases• Law of preservation of energy: Amplitudeincreases -> amplification• However, much of the increased energy isabsorbed due to the damping of the soft soil

Site effects due to low stiffness surfacesoil layers – Soft ground effect (3)• Impedance contrast:C = ρ 2 ·Vs 2 / ρ 1 ·Vs 1Soft sedimentsVs 1 = 200 m/sρ 1 = 18 kN/m 3C = 22 · 1000 / 18 · 200RockC = 6.1Vs 2 = 1000 m/sρ 2 = 22 kN/m 3

Site effects due to low stiffness surfacesoil layers – Soft ground effect• In the Earth, changes in impedance occurprimarily in the vertical direction.• horizontal sedimentary strata near the surface• increase in pressure and temperature with depth• Large impedance contrast between soft soiloverlying bedrock cause also strongreflections:• Seismic waves become “trapped” within the soillayers overlying the bedrock• Trapped waves start interfering with each other,which may result in resonance (at the natural orfundamental frequency of the the soil)

Fundamental frequency andcharacteristic site period• N-th natural frequency of the soil deposit:ωnV s⎛ π ⎞≈ ⎜ + nπ⎟ n = 0,1,2 ,..., ∞H ⎝ 2 ⎠• The greatest amplification factor will occur at thelowest natural frequency: fundamental frequencyπV ω s0=2H

Characteristic site period• The period of vibration corresponding to thefundamental frequency is called thecharacteristic site period2πT = =Sω04HVS• The characteristic site period, which onlydepends on the soil thickness and shear wavevelocity of the soil, provides a very usefulindication of the period of vibration at whichthe most significant amplification can beexpected

Amplification at the fundamentalfrequencyA0=1C+20.5⋅π ⋅ξ• A 0 = amplification at the fundamentalresonant frequency• C = impedance contrast• ξ 1 = material damping of the sediments1

Natural frequency of buildings• All objects or structures have a naturaltendency to vibrate• The rate at which it wants to vibrate isits fundamental period (naturalfrequency)f n=12πKMK= StiffnessM = Mass

Natural frequency of buildings• Buildings tend to have lowernatural frequencies when theyare:• Either heavier (more mass)• Or more flexible (that is less stiff).• One of the main things thataffect the stiffness of a buildingis its height.• Taller buildings tend to be moreflexible, so they tend to have lowernatural frequencies compared toshorter buildings.

Examples of natural frequencies ofbuildingsType of object or structureNatural frequency (Hz)One-story buildings 103-4 story buildings 2Tall buildings 0.5 – 1.0High-rise buildings 0.17Rule-of-thumb:F n = 10/nF n = Natural Frequencyn = number of storeys

(Partial) Resonance• Buildings have a high probability toachieve (partial) resonance, when:• The natural frequency of the ground motioncoincides with the natural frequency of thestructure• Resonance will cause:• Increase in swing of the structure• Given sufficient duration, amplification ofground motion can result in damage ordestruction

Vertical standing waves• Vertical traveling waves will generatestanding waves with discrete frequencies• If the depth range of interference is large, thefrequency will be low.• If the depth range of interference is small thefrequency will be higher.

Inelastic attenuation• Earthquakes: seismic waves with broadrange of frequencies• Inelastic behaviour of rocks cause highfrequencies to be damped out• The farther a seismic wave travels, theless high frequencies it contains:anelastic attenuation

Summarising: building resonance andseismic hazard (1)• Response of a building to shaking at itsbase:• Design and construction• Most important: height of the building

Building resonance and seismichazard (2)• Height determines resonance frequency:• Low buildings: high resonance frequencies (largewavelengths)• Tall buildings: low resonance frequencies (shortwavelengths)• In terms of seismic hazard:• Low-rise buildings are susceptible to damage fromhigh-frequency seismic waves from relatively nearearthquakes and/or shallow depth• High-rise buildings are at risk due to lowfrequencyseismic waves, which may haveoriginated at much greater distance and/or largedepth

Soft ground effect - summary• Soft soil overlying bedrock almostalways amplify ground shaking• Given specific ground conditions andsufficient duration of the quake,resonance can occur, resulting in evenlarger amplifications• If a structure has a natural frequencysimilar to the characteristic site periodof the soil, very large damage or totalcollapse may occur

Soft ground effect - example• 19 Sept. 1985 Michoacan earthquake,Mexico City (M 8.0, MMI IX)• Epicenter far away from city (> 100 km)• PGA’s at rock level 0.04 g - butamplification due to soft ground: 5 x• Greatest damage in Lake Zone: 40-50 m ofsoft clay (lake deposits)• Characteristic site period (1.9-2.8 s) similarto natural period of vibration of 5-20 storeybuildings• Most damaged buildings 8-18 storeys

MichoacanearthquakeCollapsed 21-Story Office Building.Buildings such as the one standing in thebackground met building coderequirementsThe 44-floor Torre Latinoamericana officebuilding in the background on the right,remained almost totally undamaged.

Methods to estimate (1D) soft groundeffects• Theoretical (numerical and analytical)methods• A-priori knowledge of:• Subsurface geometry and geotechnical characteristics• Expected earthquake signal: design earthquake• E.g.: Shake 1D numerical• Experimental-Emperical• A-priori knowledge of geology not needed• E.g.: HVSR, SSR (comparison of spectral ratios ofseismograms of large event or microtremors)

Theoretical methods• Numerical method: one-dimensionalground response analysis (SHAKE)

How do we carry out a ground responseanalysis study? (1)1. Seismic macro hazard analysis: use a‘design earthquake’ that represents theexpected ground motion• Most probable frequency characteristics andrecurrence interval using probabilistic approach• Often, just use the available nearest historicseismic record which caused lots of damageusing deterministic approach• Or, create synthetic seismogram from otherlocation through transfrom using Green’sfunctions

How do we carry out a groundresponse analysis study? (2)2. Quantification of the expected groundmotion• Determining the response of the soildeposit to the motion of the bedrockbeneath it, for a specific location or area

How do we quantify the expectedground motion?• Determining the manner in which theseismic signal is propagating through thesubsurface• Propagation is particularly affected bythe subsurface geology• Large amplification of the signal occursmostly in areas where layers of lowseismic velocity overlies material withhigh seismic velocity

What do we use to quantify theexpected ground motion?• Using peak ground acceleration• Acceleration and force are in directproportion• Peak acceleration often correspond to highfrequencies, which are out of range of thenatural frequencies of most structures• Response spectra analysis• Current standard method for groundresponse analysis• Maximum ground response (amplification)for different frequencies

Example of response spectrum6CCALA NS - Profile N. BrasiliaSa for 5% dampingSpectral acceleration (g)Spectral Acceleration (g)5432100.01 0.1 110(sec)Period (s)

SHAKE• The equivalent linear approach to 1Dground response analysis of layered siteshas been coded into a widely usedcomputer program SHAKE (1972)• Other programs, based on sameapproach:• Shake91• ShakeEdit/Shake2000• ProShake/EduShake

1D ground response analysisAssumptions (1)• Inclined seismic rays are reflected to a nearverticaldirection, because of decrease invelocities of surface deposits

1D ground response analysisAssumptions (2)• All boundaries are horizontal• Response of the soil deposit is caused byShear waves propagating vertically fromthe underlying bedrock• Soil and bedrock are assumed to extendinfinitely in the horizontal direction(half-sphere)

Definitions used in the groundresponse model

Transfer Function as technique for 1Dground response analysis1. Time history of bedrock (input) motionin the frequency domain represented asa Fourier Series using Fourier transform2. Define the Transfer Function3. Each term in the Fourier series ismultiplied by the Transfer Function4. The surface (output) motion is thenexpressed in the time domain using theinverse Fourier transform

Define the transfer function (1)• Solution to the wave equation for auniform single soil layer (simplestcase):u(z,t)=Aei(ωt+k z)k = wave numberA = Amplitude ofB = Amplitude of+Bei(ωt−k z)2πω= =λ Vsshear wave in upward directionshear wavein downward direction

Define the transfer function (2)• For uniform undamped soil:F(ω)=F(ω)=ωH/ Vsuumaxmaxcos( ωHπ= +2(0, t)( H,t)11 1= =cos kH cos( ωH/ Vsnπ⇒/ V(amplification function))F → ∞ (resonance)s)

Transfer function for one-layeruniform undamped soil• Variation of amplification with frequency(for different levels of damping)

Effect of transfer function onAmplitude spectrum0.050N. Brasilia - Layer 1 - CCALA EW0.045Layer No. 10.040Surface levelFourier Amplitude Spectrum0.0350.0300.0250.0200.0150.0100.0050.0000 2 4 6 8Frequency (Hz)Transfer functionFigure 1. Fourier amplitude spectrum for CCALA signal - EW component, surface level.0.050ON Soil profile - Analysis No. 1 - Profile No. 10.045Layer No. 40.040Base level(Bedrock)Fourier Amplitude Spectrum0.0350.0300.0250.0200.0150.0100.0050.0000 2 4 6 8Frequency (Hz)Figure 2. Fourier amplitude spectrum for CCALA signal- EW component,, base level.

Approach to simulate the non-linearbehaviour of soils• Complex transfer function only valid forlinear behaviour of soils• Linear approach must be modified toaccount for the non-linear behaviour ofsoils

Procedure to account for nonlinearity• Linear approach assumes constant:• Shear strength (G)• Damping (ξ)• Non-linear behaviour of soils is well known• The problem reduces to determining theequivalent values consistent with the levelof strain induced in each layer• This is achieved using an iterative procedureon the basis of reference (laboratory) testdata• Modulus reduction curves• Damping curves

Modulus reduction curves andDamping curves• Description of iteration process

General, simplified profile as assumedby the SHAKE program

Experimental-Emperical• Standard Spectral Ratio Technique (SSR)• Depend on reference site (in rock)• Horizontal to Vertical Spectral RatioTechnique (HVSR)• No reference site needed• Analysis of site effects using seismicrecords in the frequency domain

Standard Spectral Ratio Technique (SSR)

Horizontal to Vertical Spectral RatioTechnique (HVSR)

Nakamura’s or H/V method (1)• Summary:• Dividing the Horizontal Response spectrum (H) by theVertical Response spectrum (V) yield a uniform curvein the frequency domain for different seismic events• Assumption: since different seismic event yield thesame H/V curve, it is possible to determine thisusing microtremors• H/V curve show a peak in amplification at thefundamental frequency of the subsurface – that iswhen the resonance occurs• By setting up a dense seismic network measuringthose microtremors it is possible to carry out amicrozonation without intensive borehole surveys

Nakumura’s or H/V method (2)• Establish empirical transfer functions T H andT V on the basis of the horizontal and verticalmicrotremor measurements on soil surfaceand at bedrock level:TH=SSHSHBS HB S VBT H T VTV=SSVSVBBedrockS HSS VSSoilS HBS VB

Nakumura’s or H/V method (3)• Modified site effect function:THSHS⋅SVBTSite= =T S ⋅S• Many observations show that:SSVBHB= 1V⇒HBTSiteVS=SSHSVS• T site shows a peak in the amplification atthe fundamental frequency of the site

Nakumura’s or H/V method (4)• T site or H/V curve shows the same peakirrespective of type of seismic event at F 0

Nakumura’s or H/V method (5)• If F 0 and A 0 are known from the H/V curvesand the seismic velocity of the bedrock (V B )isalso known, bedrock level or soil thickness (H)can be calculated:F0A0⇒VS=4⋅HVB=VH=SV4⋅AB0⋅F0

Site effects due to surface topography• General observation: buildings located on hilltops or close to steep slopes suffer moreintensive damage than those located at thebase• Amplification is larger for the horizontal than forthe vertical• The steeper the slope, the higher the amplification• Maximum effect if the wavelengths are comparableto the horizontal dimension of the topographicfeature• Absolute value of amplification ratio very difficultto quantify due to complex reflections within thegeometry

Site effects due to surface topography• Recorded normalised peak accelerations

Site effects due to surface topography• European Seismic code (EC8-2000)

Liquefaction

Liquefaction – general (1)• Typically occurs in saturated, loose sandwith a high groundwater table• During an earthquake, the shear wavesin the loose sand causes it to compact,creating increased pore water pressure(undrained loading):• Upward flow of water: sand boils• Turns sand layer (temporarily) into aliquefied state - liquefaction

Liquefaction – general (2)• Commonly observed in low-lying areas oradjacent to lakes, rivers, coastlines• Effects:• Settlement• Bearing capacity failure of foundation• Lateral movements of slopes• In practice:• Structures sink or fall over• Buried tanks may float to the surface

Liquefaction – governing factors (1)1. Earthquake intensity and duration(basically a high magnitude)• Threshold values: a max > 0.10 g; M L > 52. Groundwater table• Unsaturated soil above gw table will NOTliquefy3. Soil type: non-plastic cohesionless soil• Fine-medium SAND, or• SAND containing low plasticity fines (SILT)

Liquefaction – governing factors (2)4. Soil relative density (D r )Loosely packedDensely packed5. Grain size distributionPoorly graded(Well sorted)Well graded(Poorly sorted)

Liquefaction – governing factors (3)6. Placement conditions• Hydrologic fills (placed under water)• Natural soil deposits formed in• Lacustrine (Lake)• Alluvial (River)• Marine (Sea) environments7. Drainage conditions• Example: if a gravel layers is on top of theliquefiable layer, the excess pore pressurecan easily dissipate

Liquefaction – governing factors (4)8. Effective stress conditions• If the vertical effective stress (σ v ’)becomes high, liquefaction potentialbecomes lower:stress• Low groundwater table• At larger depth (> 15 m.)depthσ v ’GW level 1GW level 2P 2P 1σ vσ v ’

Liquefaction – governing factors (5)9. Particle shape• Rounded particles tend to densify more easilythan angular particles10. Age, cementation• The longer a soil deposit is, the longer it hasbeen able to undergo compaction and possiblycementation, decreasing liquefaction potential11. History• Soils already undergone liquefaction, will noteasily liquefy again• Pre-loaded sediments (erosion, ice-sheet) will noeasily liquefy

Liquefaction – governing factorssummary• Site conditions:• Site that is close to epicenter or location offault rupture (macro hazard zone)• Soil that has a groundwater table close to thesurface• Soil type:• Loose SAND that is well-sorted and rounded,recently deposited without cementation andno prior loading or seismic shaking

Methods to estimate liquefactionpotential• Most commonly used liquefaction analysis:• “Simplified Procedure” by Seed & Idriss• Using SPT (Standard Penetration Test) data• Procedure:1. Check appropriate soil type (see before)2. Check whether soil below groundwater table(from borehole)3. Determine Cyclic Stress Ratio (CSR):1. Effective stress in soil: thickness, unit weight, GW level2. Earthquake characteristics4. Determine Cyclic Resistance Ratio (CRR)1. Based on SPT data (N-value)5. Calculate Factor of Safety: FoS = CRR/CSR