i earthquakes

8/12/2019 I Earthquakes

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Earthquakes


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Earth is a dynamic planet of a pretty dangerous sort


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Earthquakes occur along faults. A fault is a planar fracture or discontinuity ina volume of rock, across which there has been significant displacement. Largefaults within the Earth's crust result from the action of tectonic forces. Energyrelease associated with rapid movement on active faults is the cause of most

earthquakes. There are three main types of faults:

A normal fault occurswhen the crust is

extended. The hangingwall moves downwardrelative to the footwall

A thrust fault occurswhen the crust is

compressed. Thehanging wall movesupward relative to thefootwall

The fault surface is usuallynear vertical and motionresults from shearing forces.


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An earthquakeis the result of a sudden release of energy in the Earth's crustthat creates seismic waves.The elastic rebound theoryis an explanation forhow energy is spread during earthquakes. As rocks on opposite sides of afault are subjected to force and shift, they accumulate stressenergy and

slowly deform (strain) until their internal strength is exceeded. At that time, asudden movement occurs along the fault, releasing the accumulated energy,and the rocks snap back to their original undeformed shape.

In geology, the elastic rebound theory was the first theory to satisfactorilyexplain earthquakes.


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Following the great 1906 San Francisco earthquake, Harry Fielding Reidexamined the displacement of the ground surface around the San AndreasFault. From his observations he concluded that the earthquake must havebeen the result of the elastic rebound of previously stored elastic stress

energyin the rocks on either side of the fault. In an interseismic period, theEarth's plates move relative to each other except at most plate boundarieswhere they are locked.

Suppose that rocks in the region of the locked fault have bilt up elastic stressenergy in the form of elastic deformation (strain) over a time period of many

years.

When the accumulated strain isgreat enough to overcome thestrength of the rocks,an earthquake occurs on the

fault plane at Time 0.


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During the earthquake, the portions of the rock around the fault that werelocked and had not moved 'spring' back, relieving the strain (accumulatedover several years) in a few seconds. Like an elastic band, the more therocks are strained the more elastic energy is stored and the greater

potential for an event. The stored energy is released during the rupturepartly as heat, partly in damaging the rock, and partly as elastic waves.Modern measurements using GPS largely support Reid"s theory as thebasis of seismic movement, though actual events are often morecomplicated.


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An aftershockis an earthquake that occurs after a previous earthquake,the mainshock. An aftershock is in the same region of the main shock butalways of a smaller magnitude. If an aftershock is larger than the mainshock, the aftershock is redesignated as the main shock and the original

main shock is redesignated as a foreshock. Aftershocks are formed asthe crust around the displaced fault plane adjusts to the effects of themain shock.


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An earthquake's hypocenteris the position where the strain energy stored in the rockis first released, marking the point where the fault begins to rupture. This occurs atthe focal depth below the epicenter.

The epicenteris the point on the Earth's surface that is directly above the hypocenter,the point where an earthquake originates.

There are two types of seismic waves, body wave and surface waves. Bodywavesoriginate in the hypocenter and propagate spherically through theinterior of the Earth. They follow raypaths refracted by the varying densityand modulus (stiffness) of the Earth's interior. The density and modulus, inturn, vary according to temperature, composition, and phase. There aretwo types of body waves: P-waves and S-waves.

Surface wavesare analogous to water waves and travel along the Earth'ssurface. They travel slower than body waves. Because of their lowfrequency, long duration, and large amplitude, they can be the mostdestructive type of seismic wave. There are two types of surface waves:Rayleigh waves and Love waves.


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The P-wave, where P stands for Primary wave or Pressure wave, can travelthrough gases, solids and liquids, including the Earth. It has the highestvelocity (5-8 km/s during an earthquake) and is therefore the first to berecorded, and it is formed from alternating compressions and rarefactions. In

isotropic and homogeneous solids, the polarization of a P-wave is alwayslongitudinal; thus, the particles in the solid have vibrations along (orparallel to) the travel direction of the wave energy.

The velocity of P-waves in ahomogeneous isotropic mediumis given by

where K is the modulus of

incompressibility, #is themodulus of rigidity or shear, $is the density of the materialthrough which the wavepropagates.


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The S-wave, where S stands for Secondary wave orShear wave, moves asa shear or transverse wave, so motion is perpendicularto the direction ofwave propagation: S-waves are like waves in a rope. S-waves can travelonly through solids, as fluids (liquids and gases) do not support shear

stresses. S-waves are slower than P waves, and speeds are typically around60% of that of P waves in any given material.

The velocity of S-waves in ahomogeneous isotropic mediumis given by

where #is the modulus of

rigidity or shear, $is thedensity of the materialthrough which the wavepropagates.


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Nafe-Drake curveP

SAn important empirical relationexists between P and Swaves velocity and density.

P and S velocities increasewith density of medium, i.e., inless dense sedimentary rocks,waves travel slower (blackdots for S waves) than indenser igneous andmetamorphic rocks (white dotsfor S waves).

Seismic waves travel morequickly through densermaterials and thereforegenerally travel morequickly with depth.


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However, as noted from the velocity equations, if density increases, P and

S waves velocity decrease:

However, anomalously hot areas slow down seismic waves. Seismicwaves move more slowly through a liquid than a solid. Molten areas withinthe Earth slow down P waves and stop S waves because in a liquid, rigidityor shear = 0; shearing motion cannot be transmitted through a liquid).

Partially molten areas may slow down the P waves and attenuate orweaken S waves.

Therefore, the actual velocity of P and S waves depends on theinterplay between rock type, depth, and temperature.

Thus, the other properties, incompressibility K and rigidity or shear mustincrease with depth in the Earth at a greater rate than density increases.

This explain the experimantal results illustrated in the Nafe-Drakecurve.


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K = modulo di incompressibilit del mezzo

= modulo di rigidit o di taglio (shear) del mezzo

!= densit del mezzo

Dipendono dalle caratteristiche del mezzo in cui

viaggiano:

Velocit onde P () e onde S (#)

La velocit delle onde S sempre minore della velocitdelle Onde P in quanto manca il termine K. Le onde Pvengono avvertite (arrivano) prima delle S.


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In un mezzo fluido(liquido o gas), K!0, = 0

ovvero i fluidi sono comprimibili ma nonammettono taglio. Quindi:

K

#= 0

Le onde P possono

viaggiare nei solidi, liquidi egas

Le onde S possono

viaggiare nei solidi, ma NONnei liquidi e gas


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La velocit delle onde P e S tende ad aumentareall"aumentare della densit del mezzo(curva diNafe-Drake) poich all"aumentare della densit !di una

roccia i moduli di incompressibilit K e rigidit o shear

della roccia aumentono in proporzione maggiore.

Ci avviene ad esempio all"aumentare della profonditnella crosta: aumenta la pressione litostatica e

l"incompressibilit K e rigidit delle rocce aumentano

maggiormente dell"aumento di densit !


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Ma la velocit delle onde P e S tende a diminuireall"aumentare della temperaturapoich aumentando latemperatura del mezzo i moduli di incompressibilit K e rigidito shear del mezzo diminuiscono maggiormente rispetto alladensit !. Ci avviene ad esempio all"aumentare della

profondit nella crosta (gradiente geotermico).

Dunque l"aumento di velocit in profondit legatoall"aumento di pressione litostatica contrastato dalladiminuzione di velocit causata dall"aumento di

temperatura.

LA VELOCITA"DELLE ONDE E"CONTROLLATA DALLECONDIZIONI GEOLOGICHE #LOCALI"


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Surface waves - Rayleigh and Love waves - are generated by theinteraction of P- and S- waves at the surface of the earth, and travelwith a velocity that is lower than the P-, S- wave velocities.

They emanate outward from the epicenter(surface projection ofhypocenter, where P- and S-waves are generated) of an earthquake.

Rayleigh

Love


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Rayleigh waves, also called ground roll, are surface wavesthat are confinedto the Earth"s surface where they travel as ripples with motions that are similarto those of waves on the surface of water. The surface particles move inellipses in planes normal to the surface and parallel to the direction of

propagation. At the surface and at shallow depths this motion is retrograde(unlike water waves). Particles deeper in the material move in smaller ellipseswith an eccentricity that changes with depth.

The speed of Rayleigh waves on bulk solids, of the order of 25 km/s, is slightlyless than the S-waves velocity.

Rayleigh wave velocity: VR = ~0.9#i.e., ~90% of S-waves


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Love waves travel with a slower velocity VL than P- or S- waves, but faster

than Rayleigh waves: VR< VL< #

Love wavesare surface seismic waves that cause horizontal shifting of the

earth during an earthquake.The particle motion of a Love wave forms ahorizontal line perpendicular to the direction of propagation (i.e. are transversewaves). The amplitude, or maximum particle motion, often decreases rapidly

with depth.


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Body wavesA = f(x-2)

Surface wavesA = f(x-0.5)

A

Ax

x

The amplitude of Surfacewavesdecays as function of

1/sqrt(x)whereastheamplitude of Body wavesdecays as function of1/x2,where x is the radial distancefrom the epicenter for Swaves or from the hypocenterfor Body waves.Surfacewaves therefore decay moreslowly with distance than dobody waves, which spread outin three dimensions from apoint source (hypocenter).

Surface waves thereforetend to be more destructivethan body waves.


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Surficial expression of wavesP waves

S wavesRayleigh waves

Love waves


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Fig. 19.4

Sismografi Wood-AndersonUn terremoto viene registrato attraverso un sismografo che consisteessenzialmente in un pendolo ed un apparato di registrazione. Ilpassaggio dellonda sismica provoca il movimento del supporto delpendolo.


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The differenceof arrival time of P- andS-waves at a seismograph is function ofdistance of earthquake epicenter.

A 11-minute difference equals to adistance of ~8600 km; a 8-minutedifference equals to ~5600 km; a 3-minute difference equals to ~1500 km,and so on.


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The arrival time difference of P- and S-waves measured at threeseismographic stations reveals the location of the epicenterby small-

circles intersection.


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The difference in arrival time between P and S waves is usedIn Japan for the Early Warning System


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Local Magnitude (ML) or Richter scale. The Richter magnitude of anearthquake is determined from the logarithm of the amplitude of wavesrecorded by seismographs (adjustments are included to compensate for thevariation in the distance between the various seismographs and the epicenter

of the earthquake). The original formula is:Richter magnitude ML = log10A - log10A0(%)

Where A is the maximumexcursion of the

seismograph; theempirical correctionfunction A0 depends onlyon the epicentral distanceof the station, %.

The Richter scale isobsoleteand has beenreplaced by the MMSscale.


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= rigidity or shear modulusA= LW= fault plane areaD= mean displacement along fault plane

Seismic moment M0= ADin dyne centimeters (10&7 Nm)

The moment magnitude scale(abbreviated as MMS; denoted as Mw) wasdeveloped in the 1970s to succeed the 1930s-era Richter magnitude scale(ML). The MMS is now the scale used to estimate magnitudes for all modernlarge earthquakes. The magnitude is based on the seismic moment of theearthquake M

0, which is equal to the rigidity of the Earth multiplied by the

average amount of slip on the fault and the size of the area that slipped.

In order to create a moment magnitude scale(Mw) consistent with older

magnitude scales such as the Local Moment (or "Richter") scale the seismicmoment (M0) is converted into a logarithmic scale using the followingequation:

Moment magnitude Mw = 2/3log10(M0) 10.7


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The Moment Magnitude Scale based on the Seismic moment M0andcalculated as Mw = 2/3log10(M0) 10.7 is comparable to the old Richterscale and extends from Mw = 0 to Mw = 10


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Exercise 1


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Exercise 2. Suppose you want to estimate the proportionaldifference f%E in energy releasebetween earthquakes of two

different moment magnitudes Mw1 and Mw2, where Mw1 islarger than Mw2

Starting from the equation of Moment magnitudeMw = 2/3log10(M0) 10.7and solving for M0 we obtain:

log10(M0) = 3/2(Mw + 10.7)

and

M01= 103/2(Mw1 + 10.7)

M02= 103/2(Mw2 + 10.7)

f&E = M01 / M02= (103/2(Mw1 + 10.7)) / (103/2(Mw2 + 10.7))= 103/2(Mw1-Mw2)


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An increase of 1 on the moment magnitude Mw logarithmic scalecorresponds to a 101.5'32 times increase in the amount of energyreleased, an increase of 2 corresponds to a 103= 1000 times increase in

energy, an increase of 3 corresponds to a 10

4.5

= 31622 times increase inenergy etc.

Japan earthquake of Friday, March 11, 2011; Mw1 = 9.0; Depth 32 km L"Aquila earthquake of Monday, April 06, 2009; Mw2 = 6.3; Depth 8.8 km

Mw1-Mw2 = 2.7

fDE = 103/2(2.7) = 11.220 The Japan quake was eleven thousands timesmoreenergetic than the L"Aquila earthquake

The difference f%E in energy releasebetween earthquakes oftwo different moment magnitudes Mw1 > Mw2 is:

f&E = 103/2(Mw1-Mw2)


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Each earthquake has only one magnitude, but the effects of any oneearthquake can vary greatly from place to place. The Modified MercalliIntensity scalegenerally deal with the manner in which the earthquake is feltby people. The higher numbers of the scale are based on observed structural

damage.


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Elastic Rebound

1. Focal mechanisms


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No offset

No offset

Earthquake break

1. Focal mechanisms


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Volumeincrease

(dilation)

Volumedecrease

(compression)

Volumeincrease

(dilation)

Volumedecrease

(compression)

1. Focal mechanisms


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Direction of P-wavefirst motion

1. Focal mechanisms


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Direction of P-wavefirst motion

1. Focal mechanisms


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1. Focal mechanisms

Orientation of fault plane can be represented by beach balls

Normal or riftfaulting


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Different orientations of different faults

1. Focal mechanisms


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La Rete Sismica Nazionale (INGV) registra pi di 2000 terremoti l'anno inItalia. Il catalogo sismico strumentaleriporta circa 35.000 terremotiverificatisi in Italia a partire dal 1975. La sismicit crostalerappresenta lamaggior parte dell'attivit sismica registrata (Fig. 1). Terremoti intermedi eprofondi (Fig.2) avvengono nella zona del Tirreno meridionale verso i 300km di profondit, dove i terremoti possono raggiungere anche M = 7. Questiterremoti suggeriscono un processo di subduzione attiva (Fig. 3).

Fig. 1 Fig. 2

Fig. 3


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Rischio sismico in Italia. Guardando il record storico di terremoti dimedia e forte intensit Mercalli(cio estendendo il record strumentaleindietro nel tempo utilizzando archivi stoirici), risulta che negli ultimi 2500anni, l"Italia stata interessata da pi di 30.000 terremoti di intensit

superiore al IV-V grado Mercalli) e da circa 560 eventi sismici di intensituguale o superiore all"VIII grado della scala Mercalli.

Solo nel XX secolo, ben 7 terremoti hannoavuto una magnitudo uguale o superiorea 6.5 (X e XI grado Mercalli).

La sismicit pi elevata si concentranella parte centro-meridionale dellapenisola lungo la dorsale appenninica(Val di Magra, Mugello, Val Tiberina,Val Nerina, Aquilano, Fucino,Beneventano, Irpinia) - in Calabria

e Sicilia, ed in Friuli e parte del Veneto.


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Peak ground acceleration (PGA)is a measure of earthquake accelerationon the ground. It is not a measure of a quake magnitude (Richter or MMSscales) but rather a measure of how hard the earth shakes in a givengeographic area. The PGA scale ismeasured by accelerographsand it generally correlateswell with the Mercalli scale.

Thanks to the scientists of INGV, we have a detailedPGA Map of Italy


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Prior to the introduction of modern seismic codes in the late 1960s fordeveloped countries (US, Japan) many structures were designed withoutadequate detailing and reinforcement for seismic protection.

Example: Casa dello Studente, L"Aquila


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non sono necessari controlli periodici su palazzi costruiti negli

anni 60 (prima dellentrata in vigore delle normative in materia di

edilizia anti-sismica) in una zona

a classe di massima pericolosit

sismica.


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Professore dica qualcosaSeismic retrofitting is the modification ofexisting structures to make them more resistant to seismic activity,ground motion, or soil failure due to earthquakes. With better understanding ofseismic demand on structures and with our recent experiences with large

earthquakes near urban centers, the need of seismic retrofitting is wellacknowledged. Example from San Francisco:Community ActionPlan for SeismicSafety (CAPSS)

The CAPSS project will make policyrecommendations to the Departmentof Building Inspection (DBI) regardingthe earthquake performance ofmost privately-owned, existing

buildingsin the city. When enacted,these policy recommendations wouldreduce future earthquake damageand facilitate the repair of buildingsdamaged by earthquakes.


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Tsunamican be generated when the sea floor abruptly deforms andvertically displaces the overlying water. When earthquakes occur beneaththe sea, the water above the deformed area is displaced from itsequilibrium position.More specifically, a tsunami can be generated when

thrust faults associated with convergent or destructive plate boundariesmove abruptly, resulting in water displacement, owing to the verticalcomponent of movement involved. Movement on normal faults will alsocause displacement of the seabed, but the size of the largest of such eventsis normally too small to give rise to a significant tsunami.


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Tsunamis in pills:While everyday wind waves have a wavelength (from crest to crest) ofabout 100 metres and a height of roughly 2 metres, a tsunami in the deepocean has a wavelength of about 200 kilometres. Such a wave travels at

well over 800 kilometres per hour over deep water.

As the tsunami approaches the coast and the waters become shallow,wave shoaling compresses the wave and its velocity slows below 80kilometres per hour. Its wavelength diminishes to less than 20 kilometresand its amplitude grows enormously. Since the wave still has the same verylong period (time from crest tocrest), the tsunami maytake minutes to reach fullheight. Except for the verylargest tsunamis,the approaching wave doesnot break, but rather appears

like a fast-moving tidal bore.


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Note the enormous wavelenght (~200 km) of Tsunami waves


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Wave celerity (speed):

Small amplitudetheory for wavecelerity

where gis acceleration of gravity980 cm/sec2

Wave Period, which is the length of time it takes for a wave to pass a fixedpoint (crest to crest), is:

T = L / C


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In the open ocean, a Tsunami typical wave lenght Lis 200 km. Therefore, theterm d/Lis very small, on the order of 0.03; hence, the equation of celerity Cbecomes:

C = = sqrt(980 X 600.000) = 873 km/h (for a 6 km-deep ocean)

T = L / C = 200 / 873 = 14 min

And the Period Tof such a wave is:

T = L / C

Whereas a typical amplitude of a Tsunami is of only about 1 metre.

Long periods and small amplitudes make tsunamis difficult to detectover deep water. Ships rarely notice their passage.


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C == sqrt(980 X 5000) =

80 km/h (for a 50 m-deep ocean)

T = L / C = 20 / 80 = 15 min

As the tsunami approaches the coastand the waters become shallow,wave shoaling compresses the wave and its velocity slows below 80kilometres per hour:

Its wavelength Ldiminishes to lessthan 20 kilometres and its amplitudegrows enormously, whereas hePeriod Tremains the same:

Since the wave still has the same very long period, the tsunami may takeminutes to reach full height. The approaching wave does not usually break,but rather appears like a fast-moving tidal bore.

Si th till h th l i d th hi


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Since the wave still has the same very long period, the approaching wave

appears like a fast-moving tidal bore.The whole ocean is coming upon

land! e.g The 26 Dec 2004 Indian Ocean Mw 9.2 earthquake& tsunami


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A map depicts the Mediterranean Sea (green) and the degree of sea-leveldisplacement caused by a tsunami after the Crete earthqake (magnitude ~8)

that wracked the Mediterranean region in A.D. 365.

Such tsunamis are relatively frequent in the region, striking perhaps as oftenas every 800 years.

Ancient Mediterranean Tsunami May Strike Again


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O b S Gi li di P li ll l b bi i


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31 Ottobre 2001 - San Giuliano di Puglia - crollo scuola: 27 bambinimorti"quella sopraelevazione - ha ricordato il procuratore generale dellaCassazione, Francesco Iacoviello - stata costruita senza rispettare le norme

antisismiche necessarie in una zona, come quella di San Giuliano, ad elevato rischio

sismico e il sindaco non avrebbe dovuto consentire l'apertura di quella scuola senza

nemmeno un certificato di collaudo".

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