PHYSIC EISMIC R

3D SE

Chia

The aim state-of-th The prop wave pro the other systems.

of perfor indicators faults aro for near- correlatio based on It was co estimatio risk asses accurate e

Keywords

1. INTR Seismic populate such stud variabili between seismic earthqua interconn An imp simulatio problem relying o

1 Departm

2 Depa francesco

3 Departm

4 Departm

PHYSIC EISMIC R

SYSTE

ara SMERZIN

of this paper he-art tools fo posed approac opagation prob

hand, of syst The city of T rmance for th s. A couple of ound the city a

-source condi on of ground m

Ground Moti oncluded that n. However, t ssment in larg estimation of

ds: seismic risk

RODUCTIO risk studies ed area, to p

dies are, on o ty (hazard) the hazard a risk assessm ake ground nected system proved asses

ons of grou m, from the fa on Ground M

ment of Civil a artment of o.cavalieri@un ment of Civil E ment of Civil E

S-BASED RISK ASS

EMS: TH

NI¹, Frances

is to develop or the predicti ch makes use, blems to prov temic approac Thessaloniki, i he main wate f rupture scena

are used. The itions, geolog motion. The ri ion Prediction

t the GMPEs the results she ge urban envi spatial correla

k; 3D physics-

ON

are crucial plan effective one hand, a p and, on the and the expe ment studies

motion and ms.

ssment of s und shaking, ault rupture u Motion Pred and Environm Structural niroma1.it Engineering, A Engineering, A

D NUMER SESSMEN HE CASE

sco CAVALI

A a seismic ris ion of earthqu , on one hand vide an accura ches for the ev in Northern G er supply sys arios with ma e results indica gical and site

isk estimates Equations (G s based appro ed light on the ironments and ation of groun

-based numeri

to assess th e actions for proper chara other hand, ected damage at urban sca d for the as seismic haza , reproducin up to the site iction Equat

mental Enginee Geotechnic Aristotle Univ Aristotle Univ

RICAL M NT OF UR E OF THE

IERI², Sotiri

ABSTRACT sk assessment

uake ground m d, of 3D phys

ate description valuation of th Greece, is take

stem are estim agnitude MW e

ated that 3D s e conditions a are compared GMPEs), accou

roach can be e main advant d spatially dis nd motion, wh

rical modeling

he socio-econ r risk mitiga acterization o reliable vul e. The goal o ale using sta ssessment o

ard was ac ng the physi of interest, a tions (GMPE

ering, Politecn cal Enginee

versity of The versity of The

MODELIN RBAN IN ESSALON

s ARGYROU

T

study of urba motion as wel sics-based num

n of spatial v he vulnerabili en as case stud

mated based equal to 6.5 an

simulations ca at local scale d with the one

unting for the used for a p tages of a full stributed syste hich is location

g; systemic vul

nomic impac ation and em of earthquake lnerability m of this work ate-of-the-art

f seismic v chieved usin ics of the w as opposed to Es). 3D num

nico di Milano ering, Sapie

ssaloniki, Gre ssaloniki, Gre

NG AS A NFRASTR NIKI, GR

UDIS³, Kyri

an infrastructu ll as the asses merical simul ariability of g ity of complex dy and the ph

on connectiv nd 7.0, breakin

an efficiently e as well as s obtained usi

spatial variab preliminary a l 3D numerica ems. A major n- and earthqu

lnerability; wa

ct of an eart mergency res e ground mo models to est is to present t tools both vulnerability ng 3D phys whole seismi o convention merical simul

o, Italy, chiara enza Univer eece, sarg@civ eece, kpitilak@

A TOOL F RUCTUR REECE

iazis PITILA

ural systems r ssment of vul lations of sou ground shakin

x, interconnec hysical damag vity based pe ng two major and accuratel for spatial a ing a standard bility of groun and faster sei al modeling f r advantage is uake- specific

ater supply sy

thquake on a sponse. Key otion and of i tablish a rel t a novel app for the pred of complex sics-based n ic wave pro nal empirical lations are su

a.smerzini@p rsity, Rome vil.auth.gr

@civil.auth.gr

FOR RAL

AKIS⁴

relying on nerability.

urce-to-site ng and, on cted urban e and loss rformance hazardous ly account and cross- d approach

nd motion.

ismic loss for seismic s the more

.

ystem

a densely tools for its spatial lationship proach for diction of x, urban, numerical opagation l methods uitable to

olimi.it e, Italy,

r

2

overcome some shortcomings of the GMPEs, which: (i) are poorly constrained for large magnitude events and in near-source conditions that are of concern for the damage of structures; (ii) cannot account for the geological peculiarities of the area under study and the complex site conditions at local scale; (iii) cannot describe the spatial correlation and cross-correlation structure of ground motion.

Referring to point (iii), it is recognized that risk and loss assessment of large urban areas with spatially distributed building portfolios and multiple interconnected infrastructural systems require an accurate description of spatial variability of ground motion intensity at regional scale as well as of cross- correlation of ground motion across different intensity measures, such as response spectral ordinates across different periods (Park et al. 2007; Weatherill et al. 2015; Baker and Jayaram 2008).

As regards damage assessment, state-of-the-art vulnerability models for interconnected infrastructural systems, as developed in SYNER-G (2012) project, were adopted. In particular, SYNER-G developed an innovative methodological framework for the assessment of physical as well as socio-economic seismic vulnerability at the urban/regional level. The built environment was modeled according to a detailed taxonomy into its component systems as close as possible to the European distinctive features of the construction practice, grouped into buildings, transportation and utility networks, and critical facilities. The framework encompasses all aspects in the chain, from regional hazard to fragility assessment of components to the socioeconomic impacts of an earthquake, accounting for relevant uncertainties within an efficient quantitative simulation scheme, and modeling interactions between the multiple component systems in the taxonomy. Fragility curves based on SYNER-G taxonomy were selected, developed and proposed for all elements at risk including damage scales, intensity measures and performance indicators (Pitilakis et al. 2014).

The proposed approach was applied to the city of Thessaloniki, where an abundance of data is available, to estimate the physical damage and loss of performance for the water supply system.

Seismic risk was evaluated for a set of physics-based ground shaking scenarios generated through a large-scale spectral element model including the extended seismic source, the propagation from the source to the site as well as the 3D basin. Numerical simulations were carried out by the high- performance code SPEED (http://speed.mox.polimi.it/) described in Mazzieri et al. (2013). For these ground shaking scenarios, risk of the main water supply system of Thessaloniki was expressed in terms of probability of exceedance of service loss levels, measured by connectivity-based performance indicators. The variability of the expected losses within the urban area was also explored considering a set of different fault rupture scenarios. As an important outcome of this work, the SPEED-based damage and loss of performance estimates were compared with the ones obtained using a standard approach based on GMPEs, but accounting for the spatial variability of ground motion.

2. SEISMIC HAZARD: 3D PHYSICS-BASED NUMERICAL SIMULATIONS

3D numerical simulations of seismic wave propagation were performed using the Discontinuous Galerkin Spectral Elements Method (DGSEM) implemented in the open-source computer package called SPEED - SPectral Element in Elastodynamics with Discontinuous Galerkin (http://speed.mox.polimi.it/). SPEED can handle the simulation of large-scale seismic wave propagation problems including the coupled effect of a seismic fault rupture, the propagation path through Earth’s layers and localized geological irregularities, such as alluvial valleys (Mazzieri et al, 2013). Based on a discontinuous version of the classical spectral element (SE) method, SPEED is naturally oriented to solve multi-scale numerical problems, allowing one to use non-conforming meshes (h-adaptivity) and different polynomial approximation degrees (N-adaptivity) in the numerical model. The code was optimized to run on multi-core computers and large clusters (e.g., Marconi at CINECA), taking advantage of the hybrid MPI-OpenMP parallel programming. Referring to earthquake engineering applications, the main features of the code include: i) different seismic excitation modes, from plane wave propagation to extended kinematic fault source models (as adopted in this work); ii) linear and non-linear visco-elastic soil materials; iii) different anelastic attenuation models with frequency proportional quality factor or frequency constant quality factor.

2.1 3D computational model

Referring to Smerzini et al. (2017) for further details, a large-scale 3D spectral element model was

construc

 g

 k T V

 h

 3 E m (

 n t Note tha an unstr approxim 2.2 Eart In this earthqua earthqua Both fau describe

Figure 1

2.3 Main As show Ground referred (PGA). T ground s reliable o

cted, includin ground topog kinematic so Thessaloniki Volvi earthq horizontally 3D subsoil Eurocode 8 microzonatio (Apostolidis non-linear v the impleme at the mesh e ructured hex mately 60 mi

thquake scen study two ake, M_W6.5, r ake scenario ults are of no fault rupture

1. 3D numeri

in results wn in the foll

Velocity (P to in the fo To obtain ac shaking scen

only in the lo

ng the follow graphy;

ource model i, namely, th quake) and th

layered crus model of th – EC8 (C on geotechn et al. 2004);

isco-elastic s entation detai extends over xahedral co illion. The m narios

earthquake rupturing the

with M_W7.0 ormal type an

e (see superi

ical model ad June

lowing sectio PGV) and th

ollowing as ccurate pred narios have t ow frequency

wing features l of two ma he Gerakaro he Anthemou stal model fo he Thessalon CEN, 2004) nical studies

;

soil behavior ils).

a volume of onforming m maximum freq

scenarios w e Gerakarou 0, occurring nd a k^-2 slip mposed map

dopted to gen e 20^th earthqu

ons, assessm he permanen

PGD, is com dictions of sh

o be produce y range, spec

3 (see Figure ajor seismog ou fault (i.e.

untas fault sy or deep rock m

niki urban a sites B an s (Anastasia

r for top 100

f about 82 km mesh with a

quency of th

were consid fault located along the A distribution ps in Figure 1

enerate the gr uake); Anthe

ment of dama nt ground d

mputed as a hort period i ed starting fr cifically up t

1):

genic faults , the source ystem;

materials;

area with ho nd C, calib adis et al. 2 0 m sedimen

m x 64 km x a total num he numerical

dered: the h d northeast of Anthemounta

(Herrero an 1).

round shakin emountas, M_W

ge to the wa deformation a function o intensity me from the 3D

to 1.5 Hz.

posing a h responsible

omogeneous brated on th

2001) and g nts (see Stup

31 km and w mber of deg

model is abo

historical 19 f Thessalonik s fault syste nd Bernard, 1

ng scenarios:

W7.0.

ater supply sy due to liqu f the Peak G asures, such numerical si

hazard to the e of the M_W

velocity pro he basis of geophysical pazzini et al.

was discretiz grees of fre

out 1.5 Hz.

978 June 20 ki, and a hyp em, south of

1994) was ad

Volvi, M_W6

ystem needs uefaction. Th

Ground Acc h as PGA, b

imulations, w

e city of

W6.5 1978 ofiles for f detailed

analyses 2009 for

zed using edom of

0^th Volvi pothetical f the city.

dopted to

6.5 (1978

the Peak he latter, celeration

roadband which are

For this generate that, for on a da distance main adv studies, i Figure 2 geometri apparent directivi and the A area of T

Figure

3. SYST A softw Framewo (Franchi vulnerab facilities oriented interconn in ordina abstract Objects with the objects f object m class dia and the e the corre several t For insta end-user

purpose, a n e broadband

any location atabase of st

< 35 km), w vantage of su is that spatia shows a sele ic mean of h t the strong c ty/directiona Anthemount Thessaloniki,

2. Spatial di simulatio TEMIC SEI ware platform

ork for Infr in and Caval bility and ri s. The tool, paradigm nected/interd ary or “distu terms, within are instance

same set of from the cla model develo agrams. As a electric powe esponding no types of edge ance, for the r demand nod

novel approa ground moti n, the low pe trong motion which takes a

uch an appro al correlation ection of res horizontal co correlation o ality effects f tas basin. No , highlighted

stribution of ons (SPEED) ISMIC VUL m for quant rastructure M

lieri n.d., 20 sk to earthq coded in MA m (OOP),

dependent in urbed” cond n the OOP, a es (concrete

properties a ass possess) oped within an example, er network (E ode and edge

es and nodes e water supp des, water so

ach based on ions, as desc eriod range o n recordings as input the l oach, especia n of ground m

ults from SP omponents, f of the map of

from the exte ote that risk d with black c

f horizontal P ) for both Vo LNERABILI titative prob Modeling an 013) within S

quakes of an ATLAB^® (T

allows nfrastructure

itions (e.g., a problem is realizations) nd methods) and method SYNER-G a Figure 3 sho EPN) in OOF e classes. Th s within a ne ply system, e

ources or pum 4 n Artificial N cribed in Pao

of the respon s of enginee long period r ally in the pe motion is real PEED in term for both scen f PGV with t ended fault a analyses sho contour in Fi

PGV (geome olvi (left) and ITY: OOFIM

abilistic seis nd Simulatio

SYNER-G ( an urban are The MathWo

to model systems and due to the i described as ) of classes ). Each class ds (actions th and implem ows the class

FIMS. Both he latter, in g etwork, differ

edges can ei mping statio

Neural Netw olucci et al.

nse spectrum ering signifi response spe erspective of listically rep ms of spatial narios (left: V

the focal me and with the own in Secti igure 2.

tric mean) fr d Anthemou MS MODEL smic risk an on (OOFIMS (2012), as a ea including orks 2011) la

and an d sets of build

impact of a s a set of obj

(abstract mo is defined b hat objects f ented in OO s diagram fo

the WSS an eneral, are a rentiated in t ther be pipe ns. The Wat

work (ANN) (2017). We m is predicted

cance (i.e. M ectral ordinat

its use in sei roduced.

distribution o Volvi; right:

echanism of t 3D soil struc ion 4 will be

rom 3D phys ntas (right) s L

nalysis, nam S), has been computation buildings, anguage acc nalyze the

dings, at the natural or m jects that inte odels or tem by its attribut from the clas OFIMS is de

r the water s d EPN classe bstract class terms of prop

s or tunnels er source cla

was adopte limit herein d by an ANN MW=5-7+, e tes from SPE ismic risk as of PGV, com

Anthemoun the source m cture beneath e limited to t

sics-based nu scenarios.

mely Object- n recently d nal tool to a lifelines and cording to th

performa urban/region man-made ha

eract with ea mplates for al tes (propertie ss can perfo escribed by m

supply system es are compo es, since the perties and f , while node ass is an abst

d here to n to recall N trained epicentral EED. The ssessment mputed as ntas). It is model and h the city the urban

umerical

-Oriented developed assess the d critical he object- ance of

nal scale, azard). In ach other.

ll objects es that all orm). The means of m (WSS) osition of ere can be functions.

es can be tract one,

since the water so buried li sources distribut microcom between the distri Uncertai quantitie distribut event or proportio is sampl (with pro and intra are samp then inte on the pr are then geotechn model w in Franc comparis numerica of a dete also in herein. T used in correlati the spati chosen t correlati Europea uncorrel the prim proper c

ere can be b ources. As fa

ines, and th (generators) tion (D) or tr mponents. T them, repres ibution (or tr inty in OOF es or discret tions in a Mo r scenario), t

onal to λ0, i.e ed from the obability dep a-event (the pled to obtai erpolated, fro

rimary IM, a obtained wi nical hazards where landslid chin and Ca son between al ground m erministic sc

the GMPE-b The GMPE b

this work. T on of the in ial correlatio to be the pri

on model. B an strong mot ated, termed mary IM on r

onsideration

Fi

both variable far as the ele here are thre ) and balanc ransformation The two netw sented by the ransformatio FIMS is tre tized random onte Carlo si the source S e., the mean Gutenberg-R pending on th

latter spatia in a chosen p om the close all further IM ith random a

s is finally de and lique avalieri (201 n the GMPE- motion shakin cenario even based simul by Akkar an The model p

tra-event err on structure mary IM, th Based on the

tion database d range, was

rock was set n of spatial co

igure 3. Class

e head (like ectric-power ee node type ce nodes (sla

n/distribution works are sh

e (associatio n/distributio ated with a m fields. Va imulation. C S is sampled

annual rate Richter recur he source mo lly correlated primary IM, est four grid Ms needed in amplification obtained wi faction prob 13). The go -based (i.e., O ng scenarios nt, with fixed

lations, so th nd Bommer (

proposed by ror term. Spe of the intra- hat is, the on e studies per e, in this mo

set to 13.5 k t to 0.5 km, orrelation of

diagram for t

5 elevated tan

network is es: end-user ack buses, o n substations hown in the on) link betw on) class in th

a set of ran alues of suc Concerning th d first, from

of events on rrence law. T odel, uniform d) errors η a

for example d points, to th n fragility mo

n functions. P ith relevant

ability is a fu oal of the p

OOFIMS-ba (i.e., SPEED d magnitude

hat scenario (2010), recen

Jayaram an ecifically, an -event error nly one that

rformed by odel the max

km for PGA which, com

intra-event r

the WSS and E

nks) and con concerned,

demand no one per netw

s (TD). Thes same figure ween the pum

he EPN.

ndom variabl h random v he hazard m

a discrete d n the sources The location L

m for area so and ε in a gr e PGA, on a he vulnerabl odels can be Permanent g models, suc function of su

present work ased) hazard D-based). Sin e and hypoce o-based haza ntly develop nd Baker (20 n exponentia

term associa is sampled o Esposito an imum distan A. The size of mpared to the

residuals.

EPN classes (

nstant head ( edges can b des (load bu work). Load se nodes are

to highlight mping station les that des variables are odel, in each istribution w s. Given the

L is then sam ources). Give

round-motion a square grid

le componen sampled. Su ground deform ch as the FE

urface PGA.

k, as alread model with t nce the latter enter, these q ard scenarios ed for the Eu 009) was ad al model was ated with th on a square g nd Iervolino nce beyond w f the square e adopted ra

Franchin 2014

(like large re be either ove uses), electr buses can assemblies o t the interdep

class in the W scribe single e sampled fr h simulation with probabi

source, mag mpled within en M and L, n prediction d on rock. Su nts’ sites. Co urface intensi mation (PGD EMA/HAZU

Details can dy mentione the 3D phys r is specified quantities w s will be co uropean con dopted for th

s adopted to he GMPEs. P

grid using th (2011; 2012 which the mo grid for pred ange values,

4).

eservoirs) erhead or ric power be either of several

pendence WSS and e random

rom their run (one lity mass gnitude M n source S the inter- equation uch IM is onditional ity values D) due to US (2003)

be found d, is the ics-based d in terms were fixed onsidered ntext, was he spatial describe PGA was he spatial 2) on the otions are diction of allows a

6

Once values for the appropriate IMs at the surface are known at each site, the physical damage state of each component is sampled. This is done differently for point-like and line-like components, with fragility curves used for the former, and Poisson rates as a function of the intensity for the latter. The Poisson rate λ is usually employed to describe the rate of faults (leaks/breaks) per unit length, and is experimentally derived from repair rates obtained in post-earthquake damage surveys. In the WSS model within OOFIMS, only pipelines are considered as vulnerable to earthquakes and the fragility model is given in terms of two Poisson repair rates per kilometer, functions of peak ground velocity (PGV, in cm/s) and PGD (in m), respectively (ALA 2001):

(1)

where K1 and K2 are functions of the pipe material, soil, joint type and diameter and λrepair is returned in km⁻¹. The number of leaks/breaks, NL for the generic pipe is randomly generated using the highest repair rate as the mean of the Poisson distribution. If NL > 0, a number NL of standard uniform numbers is sampled and compared with the rupture probability (a function of λ). If at least one is lower than the rupture probability, the pipe is broken and removed from the network. Since in this study a connectivity-based WSS analysis was carried out, the water outflow from leaks/breaks was not retrieved. In OOFIMS it is possible to carry out a capacitive analysis on the WSS, with computation of flow in pipes and water head at demand nodes.

4. RISK ASSESSMENTS FOR THE WATER SYSTEM OF THESSALONIKI

4.1 Water Supply System of Thessaloniki

The water supply system of the municipality of Thessaloniki includes 20 tanks with total capacity of 91,900 m³. There is also a sedimentation tank of 8,000 m³ capacity and a fire-fighting tank with total capacity of 2,100 m³. The main transmission system has a total length of about 71 km, while the distribution network has a 1,284.1 km approximate length and a supply capacity ranging between 240,000 - 280,000 m³/day. The supplied customers are approximately 420,000 and the total supplied population is about one million. The supplied area is approximately 55 km²; the elevation ranges from 0 to 380 m, and the water pressure between 2 and 5 bars.

For the needs of the present application and due to the complexity and oldness of the system, a simplified, yet realistic, model for Thessaloniki’s main WSS was used (Argyroudis et al. 2014). This network is comprised of 477 nodes and 601 edges (pipes) with total length of about 280 km. The nodes were subdivided into 445 demand nodes, 21 elevated tanks served by pumping stations and 11 constant-head tanks (see Figure 4). Tanks were considered as water sources for the system. Pipelines have 24 different diameter values, ranging between 500-3,000 mm and their construction materials include asbestos cement, cast iron, PVC and welded steel.

The soil formations of the study area were classified according to the EC8 classification scheme (i.e., A, B, C soil classes). The liquefaction susceptibility was defined following the method adopted in HAZUS (FEMA 2003) on the basis of deposit type, age and general distribution of cohesionless loose sediments.

Figure 4

4.2 Perf In order based an performa others ar

• Connec in Eq. (2 (undama demand

• Conne was adap the sum, the wat methodo at node i and to disconne

• Upgrad with SSI expressio system s performa number breakage increase

4. (a) The The tanks and formance me to estimate t nd SPEED-b ance metrics re local, i.e. r ctivity Loss, 2), counting aged) networ

nodes (<···>

ctivity-based pted from a , over the n d ter demands ology, SSIconn

i and the wei 0 otherwise ection of dem

de Benefit In I, in a flow- on was adop serviceability ance. It is de of samples w e given an ea

of SSI_conn gi

essaloniki wat d pumping sta etrics the impact on based) and s were used, referred to th CL (global, the number rk, Nⁱsource,orig

> denotes ave

d System Ser flow-based o demand node s, Qi,0 (deli

n, ranging be ight wi is set e. Such wei mand nodes f

ndex, UBI (l -based analy pted. UBI me y, and is use efined as in E where the i-t arthquake is iven that the

ter supply syst ations, (b) Soil

n the WSS p to carry ou two of whic he single pipe Poljanšek et r of source n , and in the erage).

C

rviceability I one, SSI (W es, of the del vered befor etween 0 and t to 1 if the i-

ght is used from sources

S

ocal, Wang ysis. In this easures the im

d to identify Eq. (4), wher th pipe is int

significantly i-th pipe is u

7 tem used as c l classification

performance ut a compari

ch are global es. The metr t al. 2012). C nodes conne

damaged ne

CL1 N_sourcⁱ N_sourcⁱ

Index, SSIcon

ang and O’R livered water re the earth d 1, is defined -th demand n d to reduce

s.

SSI_conn



i



et al. 2010).

work, UBI mpact of the y critical pipe ere m₁ is the

tact. By “upg y smaller than

upgraded.

(a)

ase study; ele n in the study

due to the co ison between l, i.e. referre rics are defin CL, ranging ected to the etwork, Nⁱsourc

ce,dam ce,orig i

nn (global, C Rourke 2008 r flows after hquake). In

d as in Eq. (3 node is conn

the total d

Q_i,0w_i Q_i,0

1

This metric was comput e upgrade of es that signif total number grade” it is m n its value be

ments can be area accordin

onsidered haz n them, fou ed to the who

ed as follow between 0 a i-th demand

ce,dam, and the

avalieri et a ), which is d

an earthquak the curren 3), where Qi,0

nected to at le delivered wa

c was first de ted with SSI f an individua ficantly affec r of simulati meant that th

efore upgrad

pipes, deman ng to EC8.

azard models ur connectiv ole system, w ws:

and 1, is com d node in the hen averaging

al. 2014). Th defined as th ake, Qi,s, to th nt connectiv

0 is the water east one sou ater flow in

efined for ap I_conn, but the al pipe on th ct the system ion runs and he probabilit de. UBI_i is th

d nodes,

(GMPE- vity-based

while the mputed as e original g over all

(2)

his metric e ratio of he sum of vity-based r demand urce node, n case of

(3)

pplication e original he overall m seismic m₂ is the ty of pipe he percent

(b)

8 UBI_iE SSI _conn| pipe i upgradeE SSI _conn

1E SSI _conn  1

m₂



1

SSI_conn,k

k1 m₁



1 1

m₁



• Damage Consequence Index, DCI (local, Wang et al. 2010). Like UBI, this metric was first defined for application with SSI, and here it has been computed with SSIconn, while keeping the original expression. DCI is a measure of the impact of a pipe breakage on the overall system serviceability. It is defined as in Eq. (5), where m1 is the total number of simulation runs and m3 is the number of samples where the i-th pipe is broken. DCIi is the percent reduction of SSIconn given that the i-th pipe is broken.

DCI_iE SSI _conn E SSI _conn| pipe i broken

1E SSI _conn  1

m₁



3

SSI_conn,j

j1 m₃



1 1

m₁



4.3 Results and discussion

Four Monte Carlo simulations were carried out, to allow the combinations of the two considered ground motion scenarios (Volvi and Anthemountas, see Section 2.2) and the two different hazard models (SPEED-based and GMPE-based). To investigate the sensitivity of results to the spatial correlation of IMs, two more simulations were added, one per scenario, employing the GMPE-based model in which the spatial correlation of primary IM values was disregarded. In the GMPE-based case, the IMs of interest (i.e., PGV and PGD) were computed by the procedure outlined in Section 3 (and implemented in OOFIMS). On the other hand, when defining the hazard by means of physics- based simulations, PGA and PGV were provided by the offline SPEED broadband computations (see Section 2.3). Note that liquefaction-induced PGD is not provided as an output by SPEED and hence it was retrieved by the OOFIMS geotechnical hazard module in which it is derived based on the PGA estimates from SPEED using empirical relationships. All simulations consisted of just 1,000 runs each, given the reduced uncertainty in the hazard models: in fact, the IMs from SPEED are constant in all simulation runs, while in the GMPE-based approach magnitude and hypocenter were fixed, so that only the epistemic uncertainty in the motion attenuation, amplification and geotechnical hazard was considered. The epistemic uncertainty associated with vulnerability assessment is also present (see Section 3), and is the same for all the simulations.

Figure 5 shows the comparison between the Cumulative Distribution Functions (CDFs) of CL and SSIconn, from the SPEED-based simulation, for both events. It is noted that, although in the Volvi scenario more significant directivity effects were found to occur, the Anthemountas scenario results to be the most damaging, in terms of both connectivity loss and serviceability, owing mainly to the higher magnitude and smaller source-to-site distance.

Results were also retrieved at the component (i.e., pipe) level, using the two local performance metrics adopted, namely UBI and DCI. Due to page limit, only the results in terms of UBI are reported here, given the more relevance of this index compared to DCI: in fact, UBI is the primary index in seismic mitigation, and critical links are pipes with relatively large UBI values (Wang et al. 2010). Figure 6 shows UBI maps, from the SPEED-based simulation, for both events. UBI values exist at pipe centroid sites. Instead of interpolating and extrapolating values, both figures are presented as Voronoi diagrams, in which each pipe is assigned a uniformly colored Voronoi cell, collecting all points for which the centroid of that pipe is the closest point. In this representation, UBI values for a pipe are extended to its entire Voronoi cell: moreover, adjacent cells with the same color are merged. The maps indicate the presence of critical links, meaning pipes that result to be damaged in the simulation and whose upgrade will benefit more the system serviceability. Looking at the maps, it appears clear that the Anthemountas scenario causes more pipes to be damaged and thus attain a UBI value larger than zero (see Figure 6(b)). It is also noted that most damage is expected towards south-east of the city,

which is system-l Volvi ev expected

Figu

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mbination o jection of th n empirical e empirical r ysics-based e” in terms o ce-to-site azim at the results

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ntas scenario.

based simul S

ented a seism ction of eart n systems. T at Politecnic de for 3D ph for infrastr test the feas water supply cs-based grou ardous active

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that a GMPE mate of seis

simulation d worse netwo ceability. The

CDFs of (a) C lations, the lat

mic risk asse thquake grou To achieve th

co di Milano hysics-based ructure mod sibility of th y system of und shaking e faults aroun nly two seism e model, it h ave propagat

scale. At t zard is recog

ccounting ex o enhance th g an expone strong motio atial correlati Infantino et m at extendi

e scenarios.

luded in can still be u ding the com e to reduce ation, amplif

10 E/spatial cor smic loss. On

does not aff ork performa e sensitivity

CL and (b) SS tter with and w

essment stud und motion his aim, the n o and at the

numerical m deling and s he proposed

the city of T scenarios, w nd the city (V mic rupture has been de tion have be the level of

gnized main xplicitly for his point, Fi ential model) on recording ion structure al. 2018) an ing the anal

this contr used for a qu mparison bet

the epistem fication) and

rrelation/amp n the other h fect significa

ance, due to of the result

SIconn provided without spatia

dy at urban s and assessm numerical co University modeling of simulation (O

approach, t Thessaloniki with M_W equ Volvi and An scenarios, ne monstrated t ecome matu f a city, the nly in its su the specifici gure 8 show ) for PGV as s) and deriv e is location- nd this may lysis and co ribution su uick and mor tween the tw mic uncertain

d then weigh

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d by the SPEE l correlation.

scale combin ment of syste odes develop of Rome La ground shak OOFIMS), h he physical

has been est ual to 6.5 an nthemountas)

eglecting the that 3D phy re enough t impact of uperiority to

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- and earthqu play a majo mparison wi uggest that re affordable wo approach nty by consi hting them, f

model can stil nsideration o ults in this p e damage, in

tial correlatio

ED-based and

ning latest-g emic vulnera ped independ a Sapienza, n king (SPEED have been u damage and timated cons nd 7, originat

).

e aleatory un ysics-based n to be incorp

using phys describe th geological c parison of th n OOFIMS (

EED results uake-specific or role in sei with the GMP

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Figure 8.

derived 6. ACK This rese FP7/200 Center is 7. REFE Akkar S, Europe, t ALA (A Guideline Anastasia basis for Apostolid using mic Argyroud (eds) SYN and critic Baker JW Earthq Sp Cavalieri of power 607.

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