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1 De Risi, January 10, 2018
Scenariobased seismic risk assessment for buried transmission 1
gas pipelines at regional scale 2
3
Raffaele De Risi1, Flavia De Luca2, OhSung Kwon3, Anastasios Sextos4 4
5
1 Research Associate, Department of Civil Engineering, Queen’s Building, University Walk, 6
University of Bristol, BS8 1TR, UK; Email: raffaele.derisi@bristol.ac.uk
7
2 Lecturer, Department of Civil Engineering, Queen’s Building, University Walk, University 8
of Bristol, BS8 1TR, UK; Email: flavia.deluca@bristol.ac.uk
9
3 Associate Professor, Department of Civil Engineering, 35 St. George St., University of 10
Toronto, Toronto, Ontario, M5S 1A4, Canada, Email: os.kwon@utoronto.ca
11
4 Reader/Associate Professor, Department of Civil Engineering, Queen’s Building, University 12
Walk, University of Bristol, BS8 1TR, UK; Email: a.sextos@bristol.ac.uk
13
& Department of Civil Engineering, Aristotle University of Thessaloniki, Greece 14
15
16
17
18
Submitted to: 19
Journal of Pipeline Systems Engineering and Practice 20
21
22
Corresponding author: 23
Raffaele De Risi 24
Emai: raffaele.derisi@bristol.ac.uk
25
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2 De Risi, January 10, 2018
ABSTRACT 26
Buried gas pipelines in seismicprone regions may suffer leaks or breaks as a consequence of 27
an earthquake, especially if the pipeline is subjected to large differential displacements due to 28
geotechnical failures (e.g., landslide, liquefaction). This paper presents a methodology to assess 29
the risk of a gas pipeline infrastructure at regional level in the aftermath of a seismic event. 30
Once earthquake characteristics, such as magnitude and epicentre, are known, seismic intensity 31
measures (IMs), such as peak ground acceleration (PGA) and peak ground velocity (PGV), are 32
estimated at the location of each pipe through a simulationbased procedure. The potential 33
updating from realtime data coming from accelerometric stations is considered. These IMs are 34
then used to study the cascading landslide and liquefaction hazards providing a hybrid 35
empiricalmechanicalbased estimation of permanent ground displacements (PGD). 36
With the aid of literature damage and fragility functions, loss figures and damage maps are 37
derived as decisionsupport tools for network managers and stakeholders. Losses provide a 38
preliminary estimation of repair costs, while damage maps support the prioritisation of 39
inspections in the aftermath of the event. 40
The risk methodology is a novel combination of cuttingedge and consolidated approaches. 41
Firstly, different crosscorrelation models between PGA and PGV are included. Secondly, a 42
new threephase backtoback geotechnical approach is provided for both landslide and 43
liquefaction, representing (i) the susceptibility, (ii) the triggering, and (iii) the PGD estimation 44
phases. The 1976 Friuli earthquake and the highpressure gas network of NorthEast Italy are 45
assumed as testbed scenario for the risk methodology aimed at emphasising pros and cons of 46
the different alternative options investigated. 47
48
Keywords: shake map; landslide risk; liquefaction risk; crosscorrelated intensity measures, 49
loss curve; damage map; Decision Support Systems. 50
3 De Risi, January 10, 2018
INTRODUCTION 51
Earthquakes can severely damage buried gas transmission networks (O'Rourke and Palmer 52
1996). As a result, reliable damage assessment in the aftermath of an earthquake and the 53
development of enhanced fragility models are among the main challenges to be undertaken in 54
seismic engineering of buried pipelines (PinedaPorras and Najafi 2010). In the last decades, 55
great efforts have been done for the improvement of methodologies for pipelines vulnerability 56
assessment. For example, Lanzano et al. (2015) compiled one of the most extensive database 57
of observed damage to pipelines after earthquakes, providing an excellent base for the creation 58
of empirical fragility models. It has been emphasized that buried gas transmission pipelines are 59
particularly vulnerable to geotechnical failures such as landslides and liquefaction phenomena, 60
since they generate large ground deformations creating large stress concentrations at the joints 61
(Wham and O’Rourke 2016). A detailed description of observed damage in the aftermath of an 62
earthquake to pipeline systems of different materials can be found in Edkins et al. (2016). 63
Damage to gas lifelines can lead to issues in the energy production; if the connection with 64
thermoelectric power stations is interrupted, it can affect everyday life stopping energy flow to 65
homes. Moreover, the damage can trigger major cascading accidents, such as fires and 66
explosions, also known as Natural Hazard Triggering Technological Disasters. Thus, there is 67
pressing need for the development of a reliable riskbased Decision Support System (DSS) that 68
can generate loss figures and damage maps of infrastructure immediately after an earthquake 69
event. Such information can then be used to prioritise inspections and interventions to 70
rehabilitate the gas transmission service as fast as possible (Elsawah et al. 2016). 71
Several relevant studies are available in literature on the seismic risk assessment for buried 72
pipelines. Initially, only scenariobased ground shaking was considered (Hwang et al. 2004, 73
Toprak and Taskin 2007). Subsequently, the importance of geotechnical failures has been 74
emphasized and geotechnical models have been incorporated in the risk methodologies 75
4 De Risi, January 10, 2018
(Mousavi et al. 2014, among the others). O'Rourke et al. (2014) were among the first in 76
emphasizing the importance of having reliable underpinning data to have robust and 77
comprehensive risk figures. Finally, Esposito et al. (2015) emphasised the importance of 78
correlation models among intensity measures and envisaged the possibility of adopting 79
simulationbased hazard assessment procedures. 80
Building upon the seminal researches mentioned above, this paper presents a MonteCarlo 81
simulationbased methodology that can generate preliminary information about the status of a 82
buried gas pipeline infrastructure after a seismic event. Several novelties are introduced herein 83
with respect to previous works. First, the intensity measures at several locations are 84
investigated considering different forms of geographical correlations and crosscorrelations 85
between intensity measures (i.e., peak ground acceleration and peak ground velocity). Second, 86
a procedure to anchor the ground shaking simulations to observed values is presented. Third, 87
more refined largescale geotechnical procedures are developed through a threephase study of 88
(i) susceptibility, (ii) triggering, and then (iii) ground displacements caused by both landslide 89
and liquefaction. It is noted that previous works focused mainly on landslides and adopted the 90
simplified procedure recommended in HAZUS (FEMA 2004). Finally, existing empirical 91
vulnerability and fragility functions are used to compute loss curves and damage maps, 92
respectively. The representation of the earthquake consequences on gas lifelines as expected 93
damage maps is here presented for the first time, and it is considered to be a key deliverable 94
for informed decisionmaking. 95
In the following, the methodology is described and then, it is applied to a “virtual” case study; 96
a portion of the highpressure gas transmission system in the NorthEast region of Italy is 97
analysed under the effect of the 1976 Italian Friuli event. This case study is virtual because the 98
pipeline network considered herein (based on 2013 information) was not completely built at 99
the time of the earthquake event (i.e., 1976). The combination, however, of the model of a real 100
5 De Risi, January 10, 2018
gas network with an actual seismic scenario is deemed to be a useful platform to demonstrate 101
the efficiency and limitations of the methodology. 102
METHODOLOGY 103
The risk assessment for spatiallydistributed infrastructures, such as road networks and buried 104
pipeline systems, requires (i) the identification of the main properties of critical components of 105
the infrastructure, their failure mechanisms and the associated vulnerability models, (ii) the 106
acquisition of the underlying data complementary to the infrastructure (e.g., the soil 107
geotechnical properties), (iii) a hazard assessment procedure capable of providing seismic 108
intensity measures at regional scale, and finally, (iv) a risk quantification procedure consisting 109
in the convolution of hazard and vulnerability models. Figures 1 and 2 provide a graphical 110
representation of the framework developed in this study involving the steps to assess the 111
network hazard (Fig. 1) and risk (Fig. 2), respectively. 112
For a buried gas pipeline system, specific information is needed (Fig. 1a): the geometry of the 113
system, the buried depth, the service pressure, the diameters, materials and joint typologies of 114
the pipes. Such characteristics are necessary for choosing a suitable vulnerability model among 115
those available in literature (e.g., ALA 2001; Piccinelli and Krausmann 2013; Lanzano et al. 116
2015, among the others). 117
Once the system geometry is available, a discretization of the pipeline is needed; specifically, 118
each element of the system is divided in segments with length (L), which is small enough to 119
neglect behaviour/properties variability along the segment. Therefore, each pipeline segment 120
is represented by its midpoint. Complementary data to the infrastructure is all the information 121
necessary to define the topographic, geologic and geotechnical problem of the buried system 122
(Fig. 1b): the digital elevation model (DEM) map, the slope map, the shear wave velocity map 123
of the upper 30m of soil (Vs,30), the geolithology map, representing the local lithology from 124
6 De Risi, January 10, 2018
which, in absence of detailed surveys, it is possible to obtain the geotechnical properties 125
(friction angle
f
, cohesion c, and selfweight
g
) and finally, the groundwater table map. 126
For a postevent seismic risk assessment, information on the earthquake are also necessary 127
(Fig. 1c). Essential data are the event magnitude and the epicentre location, or the fault plane, 128
which are normally publically available soon after the event. Additional data, allowing the 129
refinement of the hazard model, are the strong motion records from seismic stations. Once 130
earthquake data are available, the hazard model can be developed based on predefined ground 131
motion prediction equations (GMPEs), see Fig. 1d. The hazard model is then used to generate 132
the seismic IMs: the peak ground acceleration (PGA) and the peak ground velocity (PGV). For 133
buried infrastructural systems also the permanent ground displacement (PGD) is required; this 134
is the IM typically adopted for the interpretation of geotechnical failures and should not be 135
confused with peak ground displacement. This study presents a new backtoback threephase 136
geotechnical model allowing the quantification of the PGD due to landslide and liquefaction 137
phenomena. 138
Seismic hazard model 139
To account for the uncertainty in seismic actions due to a specific earthquake, a stochastic 140
simulationbased procedure is adopted in this study to estimate seismic IMs (in terms of PGA 141
and PGV) at the midpoint of each pipeline segment
( )
IM
. Specifically, IMs are assumed to 142
follow joint lognormal distribution, with central values
( )
IM
computed by a GMPE and 143
covariance calculated with a correlation model. The following formulation is adopted: 144
( )
( )
( )
2
log N log , I
s
×
(
(
(
(
N log
(
(
IM IM C
(1)
where
s
I is the intraevent standard error of the selected GMPE, C is the correlation matrix and 145
the product
s
I 2·C is the covariance matrix (
S
) of the lognormal distribution. Such approach is 146
7 De Risi, January 10, 2018
largely adopted to predict IMs probabilistically due to a specific earthquake scenario (e.g., 147
Wald et al. 2006). 148
In this study, three main correlation models have been investigated (Fig. 1e): (C1) uncorrelated 149
IMs, (C2) IMs spatially correlated according to Goda and Hong (2008), (C3) IMs correlated 150
and crosscorrelated according to Weatherill et al. (2014). The spatial correlation provides the 151
correlation between the same IM (i.e., PGA or PGV) at different geographical locations. The 152
crosscorrelation provides the correlation between values of PGA and PGV. For the first case, 153
C1, the correlation matrix is equal to the identity matrix, therefore IMs at different locations 154
will be completely uncorrelated. For C2, terms of the correlation matrix (
r
i,j) are obtained as a 155
function of the sitetosite distances (Ri,j) between the midpoints of segment i and segment j: 156
( )
( )
, ,
, ,
1
1
i j i j
j i i j
R
R
r
r
é ù
ê ú
ê ú
ê ú
ê ú
ë û
C =
(2)
Several equations for calculating the correlation coefficients are available in literature (e.g., 157
Goda and Atkinson 2010; Esposito and Iervolino 2011; 2012 among the others). The functions 158
to compute
r
i,j are different for PGA and PGV and they differ for different geographical region 159
and seismogenetic contexts. Correlation terms are equal to 1 if the interdistance is equal to 160
zero, and they decrease to zero for very large values of Ri,j. 161
Finally, for C3, the correlation matrix contains both spatial and cross correlation terms: 162
,
,
;
PGA PGA PGV
PGA PGV PGV
é ù
ê ú
ë û
C C
C =
C C
(3)
where CPGA and CPGV are obtained according to Eq. 2, and the generic term of the matrix 163
CPGA,PGV is equal to: 164
( ) ( )
, ,
, , , ,
i j i j
i j PGA PGV PGA i j PGV i j
R R
r r r r
= × ×
(4)
8 De Risi, January 10, 2018
where
r
PGA,PGV is the correlation term between PGA and PGV and can be estimated by 165
bespoken statistical analyses based on recorded data in a given geographical region. 166
If information from seismic stations is available, the hazard model can be furtherly refined 167
updating the probability model with the observed IM values. To demonstrate this possibility, 168
correlation models C2 and C3 are modified according to procedure described in Miano et al. 169
(2016), in order to consider available information from seismic stations. These two additional 170
models are named C4 and C5 in the following which correspond to C2 and C3, respectively. 171
In both C4 and C5 cases, the central values of the distribution and the covariance matrix are 172
defined according to Eq. 5. 173
11 1, 2
2, 1 2
2
é ù é ù
= =
ê ú ê ú
ê ú ë û
ë û
IM IM IM
IM IM IM
IM
IM
IM
SS
SS S
(5)
In Eq.5,
1
IM
is the intensity measure calculated with the GMPE for the points of interest (e.g., 174
the midpoint of the pipes in this study) and
2
IM
is that calculated for the seismic stations. 175
Analogously,
1IM
S
and
2IM
S
are the covariance matrixes for the points of interest and for the 176
seismic stations, respectively. Finally,
1, 2IM IM
S
is the crosscovariance matrix between the 177
points of interest and the seismic stations’ locations. Let X indicate the intensity measure 178
acquired at the seismic stations; the statistics of the joint distribution of the IMs at the sites of 179
interest, updated with the acquired data X can be computed according to Eq. 6 and 7. 180
( ) ( )
( )
( )
1
12 1 2
1, 2 2
log log log log
é ù
= + × × 
ë û
IM IM IM
IM IM X IMS S
(6)
1
1 2 1 1, 2 2 2, 1

=  × ×
IM IM IM IM IM IM IM IM
S S S S S
(7)
Therefore
12
IM
and
1 2IM IM
S
can be used in Eq. 1 to simulate IMs fields that are anchored to 181
real observations. 182
183
9 De Risi, January 10, 2018
Geotechnical model 184
For each of the five correlation models described above (Fig. 1e), it is possible to obtain 185
simulated intensity measure fields of PGA and PGV (Fig. 1f), however, such IMs are not 186
enough for the case of buried infrastructural systems. This is due to the fact that, for such kind 187
of infrastructure, PGD is also required since several vulnerability/fragility models are 188
expressed in these terms. PGD cannot be calculated by GMPEs but it is inferred from PGA and 189
PGV since none of the GMPEs predicts PGD. This is mainly due to a lack of confidence in 190
lowfrequency content of recorded ground motions leading to lack of confidence in peak 191
ground displacements and consequently PGD to which the latter is strongly correlated 192
(Malhotra 2015). PGD is the combination of three main contributions: (a) coseismic, (b) 193
landslide, and (c) liquefaction displacements. Coseismic effects are neglected in this study 194
since, in general, they do not present localized differential displacements that can influence 195
pipelines; obviously additional studies are necessary to better understand if there are specific 196
conditions affecting buried pipelines. 197
Herein, two new geotechnical models for landslide and liquefaction phenomena are developed. 198
These two models have a similar algorithm consisting of three assessment phases: (a) the 199
analysis of the susceptibility to landslides and liquefaction (b) the probabilistic assessment of 200
the triggering, and (c) the estimation of the resulting PGD. The susceptibility analysis is based 201
on empirical failure domains; such domains are functions of magnitude of the earthquake and 202
sitetosource/epicentral distance and they discriminate if a geotechnical failure can or cannot 203
occur according to historical observations. The triggering assessment is conducted for those 204
locations indicated as susceptible and it is performed adopting physicalbased or semi205
empirical largescale methodologies. Finally, PGD is calculated adopting empirical 206
formulations for those locations in which the geotechnical failure is triggered. For each point 207
of interest, the final PGD is the maximum value between the PGD values, due to landslide and 208
10 De Risi, January 10, 2018
liquefaction, respectively. The two new geotechnical models are described in more detail 209
below. 210
Landslide model 211
The landslide susceptibility analysis is based on the empirical failure domains proposed by 212
Keefer (1984) that defined three empirical domains corresponding to three different landslide 213
typologies (Fig. 1g). If information on the landslide typologies is not available, the more 214
conservative domain can be adopted (i.e., the red line in Fig. 1g). In case that the couple 215
magnitudeepicentral distance falls into the domain of potential failure, then the triggering 216
phenomenon is analysed; conversely, outside the failure domain, the landslide is deemed 217
negligible and PGD due to landslide is equal to zero. 218
In this study, the triggering is analysed only with reference to the translational landslide, i.e., 219
landslides displacing along a planar or undulating surface of rupture, sliding out over the 220
original ground surface (Varnes 1978); rotational landslides are neglected since their safety 221
factor (SF) is generally higher than the SF for planar landslides (Ferentinou et al. 2006). The 222
triggering is analysed with the Newmark’s method (Newmark 1965). In this model, the 223
landslide is treated as a rigid block that slides on an inclined plane (Fig. 1h) when the critical 224
acceleration ac (i.e., the threshold base acceleration required to overcome the resistance and 225
initiate sliding) is exceeded. For analyses at regional level, a simple limitequilibrium model 226
of an infinite slope in material having both friction and cohesive strength can be applied; under 227
these hypotheses, the factor of safety, SF, is given by Eq. 8. 228
tan '
' tan '
sin tan tan
w
u
c
SF t
g f
f
g a a g a
× ×
= + 
× × ×
(8)
In Eq. 8,
f
’, c’, and
g
are the effective friction angle, effective cohesion, and soil unit weight, 229
respectively; u is the saturation ratio and
g
w is the unit weight of water; finally,
a
and t are the 230
slope angle and the slopenormal thickness of the failure slab. Parameters t and u are the most 231
11 De Risi, January 10, 2018
difficult to estimate at large scale; in the following u is studied as a parameter, meanwhile, in 232
absence of detailed information, t can be estimated using models that correlate topographic 233
characteristics with slab depth (Saulnier et al. 1997; Tesfa et al. 2009; Catani et al. 2010; 234
Shafique et al. 2011). 235
Once the SF is computed, the critical acceleration ac can be calculated according to Eq. 9: 236
( )
1 sin
c
a SF g
a
=  × ×
(9)
In Eq. 9, g is the acceleration of gravity. For a given site of interest, if the simulated acceleration 237
exceeds ac, then the block sliding initiates, the landslide is triggered and the PGD can be 238
calculated be means of a proper empirical formulation (Fig. 1i). In this study, the formulation 239
proposed by Saygili and Rathje (2008), presenting the lowest predictive error, is adopted (see 240
Eq. 10). The regression coefficients adopted are a1=1.56, a2=4.58, a3=20.84, a4=44.75, a5=241
30.5, a6=0.64, and a7=1.55. 242
2 3 4
1 2 3 4 5 6 7
lnPGD ln ln
c c c c
a a a a
a a a a a a PGA a PGV
PGA PGA PGA PGA
æ ö æ ö æ ö æ ö
= + + + + + +
ç ÷ ç ÷ ç ÷ ç ÷
è ø è ø è ø è ø
(10)
Liquefaction model 243
Several liquefaction susceptibility domains are available in literature for different geographical 244
regions (Papadopoulos and Lefkopoulos 1993; Papathanassiou et al. 2005; Martino et al. 2014). 245
In this study, the liquefaction susceptibility analysis is conducted according to the three failure 246
domains proposed by Galli (2000), based on Italian data and suitable for the case study 247
discussed below. The envelope of the three domains presented in Galli (2000), is adopted (i.e., 248
the red line in Fig. 1j). For a given seismic event and for a specific site, the triggering analysis 249
can be carried out only if the magnitude and the epicentral distance falls in the failure domain. 250
The triggering analysis (Fig. 1k) is performed through the wellconsolidated semiempirical 251
method proposed initially by Seed and Idriss (1971) and subsequently improved in several 252
studies in order to create a shearwave velocitybased liquefaction triggering assessment (Goda 253
12 De Risi, January 10, 2018
et al. 2011; Kayen et al. 2013). An example of application of such methodology to largescale 254
is presented in Goda et al. (2011). Herein, the probabilistic formulation proposed by Kayen et 255
al. (2013) is adopted. Specifically, the safety factor for liquefaction can be calculated as: 256
CSR
SF CRR
=
(11)
where CSR is the Cyclic Stress Ratio and CRR is the Cyclic Resistance Ratio. According to 257
Seed and Idriss (1971) the CSR at a given depth z is given by: 258
( )
( )
( )
0.65 ' ( )
vd
v
zr z
PGA
CSR g z MSF M
s
s
= × × ×
(12)
In Eq. 12, the PGA is the result of the simulations discussed in Seismic Hazard Model (Fig. 259
1f),
s
’v (z) and
s
v (z) are the vertical effective and total stress at depth z. MSF(M) is the 260
magnitude scaling factor defined by Youd et al. (2001) equal to (M/7.5)2.56; rd(z) is the shear261
stress reduction factor and it is given by Kayen et al. (2013) according to the following 262
expression: 263
( )
( )
,12
,12
,12
,12
23.013 2.949 0.999 0.0525
116.258 0.201 exp 0.341 0.0785 7.586
( ) 23.013 2.949 0.999 0.0525
116.258 0.201 exp 0.341 0.0785 7.586
s
s
d
s
s
PGA M V
z V
r z PGA M V
V
  × + × + ×
+é ù
+ × ×  + × +
ë û
=  × + × + ×
+é ù
+ × × × +
ë û
(13)
where
,12s
V
is the average shear wave velocity in the upper 12m of the soil column, obtained 264
from the available
,30s
V
through the methodology proposed by Boore (2004). According to 265
Kayen et al. (2013) the CRR is given as: 266
( ) ( ) ( )
2.8011 1
1
0.0073 2.6168ln 0.0099 ln ' 0.0028 0.4809
exp 1.946
v L
Vs M FC P
CSR
s

ì ü
é ù
  +  F
ï ï
ë û
=í ý
ï ï
î þ
(14)
where Vs1 is the stresscorrected shear wave velocity defined by Eq. 15: 267
13 De Risi, January 10, 2018
0.25
1 ,12 min ,1.5
'
a
s
v
P
Vs V
s
é ù
æ ö
ê ú
= × ç ÷
ê ú
è ø
ë û
(15)
and Pa is the reference stress equal to 100 kPa. It is noted that in Eq. 14, FC is the percentage 268
of fines content, F1(•) indicates the operator inverse of a cumulative normal distribution and 269
PL is liquefaction probability term. Several formulations of PL are available in literature (Juang 270
et al. 2002; Kayen et al. 2013); in this study, the PGAbased formulation proposed by Santucci 271
de Magistris et al. (2013) is adopted as it is based on Italian data. 272
It is then possible to conclude the triggering analysis calculating the Liquefaction Potential 273
Index (LPI) that is an indicator that succinctly captures the potential liquefaction damage to 274
subsurface structures. LPI was originally proposed by Iwasaki et al. (1978) and is calculated 275
according to Eq. 16, where w(z) = 100.5z and SF is set equal to 0 if SF is greater than 1. 276
( )
20
0
( )LPI SF z w z dz= × ×
ò
(16)
Once the liquefaction potential is computed, then the liquefactioninduced PGD required for 277
the risk and loss analysis can be calculated (Fig. 1l). Toprak and Holzer (2003) identified 278
specific values of LPI corresponding to specific damage scenario. If LPI is lower than 5, then 279
the liquefaction is not triggered and the PGD due to liquefaction is equal to 0. If LPI is between 280
5 and 1215 (in this study 13.5 is assumed as boundary limit) sand boiling and consequently 281
vertical settlements are expected, therefore PGD is equal to the vertical settlement. Finally, if 282
LPI is greater than 1215, also lateral spread is expected to occur, and the PGD is calculated as 283
the square root of sum of square (SRSS) of the vertical settlements and the lateral spread 284
displacements. 285
The vertical settlement due to sand boiling can be computed according to Tanabe and Takada 286
(1988), see Eq. 17, where H is the thickness of the liquefiable layer and N is the number from 287
14 De Risi, January 10, 2018
the Standard Penetration Test. In absence of detailed information N can be empirical correlated 288
to the friction angle (Schmertmann 1978): 289
0.3 2
Settlement
PGA
PGD H N
= × × +
(17)
The lateral spread is calculated as proposed by Bardet et al. (1999), see Eq. 18, where the 290
regression coefficients are b0=7.586, b1=1.109, b2=0.233, b3=0.025, b4=0.477, and b5=0.579. 291
( )
( ) ( ) ( )
0 1 2 3 4 5
ln 0.01 ln ln ln
Lateral Spread
PGD b b M b R b R b b H
a
+ = + + + + +
(18)
The threephase geotechnical model 292
It is worth noting that the threephase geotechnical approach for landslides and liquefaction 293
assessment brings together wellestablished methodologies with recently developed 294
probabilistic formulations specialised for the Italian geographical context. Given the 295
modularity of the approach, if new models are available for each phase or for different 296
geographical contexts, then the procedure can be further improved and adapted to other areas. 297
Such versatility of the procedure is one of the main novelty of this work and it fits perfectly 298
within the performancebased engineering framework and its general principle of de299
constructing of the risk problem. 300
RISK ASSESSMENT 301
For each of the five correlation cases (i.e., C1 to C5) presented in Seismic Hazard Model, PGA 302
and PGV are simulated for all the pipeline segments (Fig. 2a). Then, the geotechnical 303
approaches for landslide and liquefaction allow the calculation of the PGD (i.e., the maximum 304
among the two geotechnical phenomena). The three IMs are then convoluted with vulnerability 305
and fragility models. Specifically, vulnerability models relate directly the IM with the losses 306
(e.g., number of breaks and leaks); while fragility functions relate the IM with the probability 307
of exceeding a specific level of damage. In this research, empirical vulnerability and fragility 308
models from literature are adopted. Vulnerability functions (Fig. 2b) are convoluted with the 309
15 De Risi, January 10, 2018
hazard to obtain loss curves (Fig. 2c), i.e., curves representing the probability of reaching or 310
exceeding a specified level of loss; instead, fragility functions (Fig. 2d) are adopted in a non311
traditional manner to build damage maps (Fig. 2e) aimed at supporting the infrastructure 312
manager in deciding where to deploy inspection teams to verify potential damage to the system 313
in the aftermath of an event. 314
Vulnerability functions and loss curves for natural gas pipelines 315
HAZUS manual (FEMA 2004) identifies two damage states for pipelines: (i) leak and (ii) 316
break. Such damage states can be induced both by transient actions, also known as Strong 317
Ground Shaking (SGS), and by Ground Failure (GF) phenomena, such as earthquakeinduced 318
landslides and liquefactions. According to HAZUS, if the damage is induced by GF then the 319
percentage of leaks and breaks are estimated as 20% and 80%, respectively. Conversely, if the 320
pipeline is damaged by SGS, then the percentage of leaks and breaks is reversed, being 80% 321
and 20%, respectively. 322
The American Lifeline Alliance (ALA 2001) provides damage functions for buried pipes that 323
take into consideration different damage sources (i.e., SGS and GF), materials, diameters, and 324
joint typologies. Such functions permit the calculation of the repair rate (RR) expressed in terms 325
of normalized length (1/km) as follows: 326
, 1 0.002416
R SGS
R K PGV= × ×
(19)
0.319
, 2 11.223
R GF
R K PGD= × ×
(20)
where, for example, K1 and K2 for iron continuous pipelines are both equal to 0.15. Eq. 19 and 327
20 correspond to SGS and GF, respectively; therefore, according to HAZUS indications, the 328
expected number (#) of leaks and breaks along the infrastructure can be calculated as per Eq. 329
21 and 22, where Li is the length of the ith segment of the infrastructure. 330
16 De Risi, January 10, 2018
( )
, ,
# 0.8 0.2
R SGS i R SGS ii
i
R Rof leaks L+= × × ×
å
(21)
( )
, ,
# 0.2 0.8
R SGS i R SGS i
i
i
of brea R Rks L= × × ×+
å
(22)
The empirical complementary cumulative distribution function of the numbers of leak and 331
breaks (Fig. 2c) obtained from the simulations of IMs will be the first result available to the 332
infrastructure managers. This is a novel result available to infrastructure managers who 333
typically make use only of the PGA shakemaps provided by national geological survey services 334
(e.g., United States Geological Survey, Italian National Institute of Geophysics and 335
Volcanology, among the others). As depicted in Fig. 2, each simulation produces the values of 336
PGA, PGV and consequently PGD (through the threestep geotechnical module) for each 337
pipeline segment. These values are used in Eqs 19 and 20 to obtain the repair rate for SGS and 338
GF. Repair rates are transformed into breaks and leaks according to Eqs. 21 and 22 and then 339
summed up for the all network considered. The simulation results are then represented as 340
empirical complementary cumulative distribution function of breaks and leaks over the whole 341
portion of network considered, representing the probability of exceeding a specific number of 342
breaks or leaks, respectively. 343
If the repair cost for each damage typology is available, loss curves can be derived multiplying 344
Eqs. 21 and 22 by the respective repair costs. As an example, in the HAZUS manual (FEMA 345
2004), a repair cost of 1000 US Dollars for break, is suggested for a welded steel pipe with gas 346
welded joints (category NGP1). More recent figures can be found in literature (e.g., INGAA, 347
2016). For each simulation, the total number of breaks and leaks can be transformed into costs 348
and the empirical complementary cumulative distribution function for losses can be provided. 349
Fragility functions and damage maps for natural gas pipelines 350
Several fragility curves are available in the literature (Piccinelli and Krausmann, 2013); in this 351
study models proposed by Lanzano et al. (2014) are adopted given their large and uptodate 352
17 De Risi, January 10, 2018
underpinning database. The latter research presents lognormal and logistic fragility functions 353
for different joint typologies and for SGS and GF corresponding to three damage states (DS), 354
namely: DS0, corresponding to no damage, DS1, corresponding to longitudinal and 355
circumferential cracks and potential compression joint breaks, and finally DS2, for tension 356
cracks along continuous pipelines and joint loosening in segmented ones. Fragilities for SGS 357
and GF are function of PGV and PGA, respectively. In general, fragility functions are 358
convoluted with the hazard to obtain the risk of the system; in this study fragilities are adopted 359
to draw damage maps. In particular, for each scenario simulation, i.e., for each PGA and PGV 360
simulated in the hazard module for the specific pipeline segment, it is possible to calculate the 361
probability of reaching DS0, DS1, and DS2 for both SGS and GF according to Lanzano et al. 362
(2014), see Fig. 2d. The specific segment of the infrastructure will be characterized by the 363
damage state having the highest probability of occurrence. The simulations will provide the 364
frequency of damage for each segment of pipeline and the modal value among all the 365
simulations will identify the expected DS for the specific segment, finally resulting in a map 366
of the expected damage states on the infrastructure (Fig. 2e) that can be used as tool to prioritize 367
the inspections in the aftermath of an earthquake. 368
Critical notes on the risk assessment 369
It is noted that the above risk assessment represents a cuttingedge enhancement of alternative 370
literature methodologies for pipeline networks (e.g., Esposito et al. 2015) since it includes, for 371
the first time, different correlation and crosscorrelation models between IMs, and it adopts 372
two threephase mirrored geotechnical approaches for landslides and liquefaction, respectively. 373
Moreover, the adoption of fragility functions to generate damage maps is an innovative 374
adaptation of the fragility tool to the DSS context. 375
In its current development stage, the methodology includes the treatment of uncertainties 376
related to the hazard and the vulnerability through the employment of Monte Carlo simulation 377
18 De Risi, January 10, 2018
based on the GMPE and the fragility curves, respectively. The threestep geotechnical model 378
and the costs do not include the implementation of uncertainties at this stage. 379
To demonstrate the efficiency of the methodology and quantify the significance of the novel 380
aspects introduced, a detailed case study is employed and is presented in the following sections. 381
CASE STUDY 382
The Italian gas pipeline network 383
The Italian gas pipeline network is formed by the national transmission network (spanning 384
along approximately 8,800 km) and by the regional distribution networks, which extend along 385
more than 22,600 km. Figure 3a shows in red the Italian transmission network and in green the 386
regional distribution one. The first plays a vital role since it is the backbone of the gas flow 387
imported from abroad; in particular, gas is injected in the national network systems through 388
eight terminals, five import points (Gela, Gorizia, Mazzara del Vallo, Passo Gires, and 389
Tarvisio, represented as red triangles in Fig. 3a) and three regasification stations (Cavarzere, 390
Livorno, and Panigaglia, represented as yellow triangles in Fig. 3a). Pipelines belonging to the 391
national network are characterized by large diameters, buried depth larger than 90cm (on 392
average 1.5 m), and nominal and operating pressures of 70 kPa and 50 kPa, respectively 393
(Vianello and Maschio 2014). 394
This study focuses on the national network crossing the Friuli Venezia Giulia region 395
(highlighted in yellow in Fig. 3a); this region is simultaneously a strategic one due to the 396
presence of the Tarvisio and Gorizia import points, and also an area of high seismic activity. 397
Figure 3b shows the portion of national gas pipelines network analysed in this study. The total 398
pipeline length is about 510 km, and diameters span from 26 inches (about 660 mm) to 48 399
inches (about 1220 mm). 400
The geometry of the system is realistic and is provided publically by the company managing 401
the network (Snam Rete Gas S.p.A., http://www.snamretegas.it). For the purposes of sampling,
402
19 De Risi, January 10, 2018
the pipelines have been discretized into 10,975 segments having an average length of about 403
50m. 404
Figure 3b shows also the topography of the region. It is worth noting that the connection from 405
Tarvisio takes advantage of a valley to cross the Alps; from the Tarvisio input point the pipeline 406
network has three parallel branches, from Gorizia only one branch. The higher number of 407
parallel branches increases the redundancy and therefore the resilience of the system (Golara 408
and Esmaeily 2016). 409
The 1976 Friuli earthquake 410
To assess the risk of the casestudy network, the Mw 6.4 earthquake occurred in Friuli on the 411
6th of May, 1976, is employed as the base scenario. This event is used because it is the strongest, 412
instrumentally recorded event in the North Italy region (Moratto et al. 2011). Ten seismic 413
stations recorded the event across Italy, and measurements are freely accessible at 414
http://itaca.mi.ingv.it (Pacor et al 2011); four of the ten stations are represented as red triangles
415
in Fig. 3b. On the same figure, the fault plane it is also depicted as defined by the Italian 416
database of individual seismogenic sources (http://diss.rm.ingv.it/diss/).
417
For the MonteCarlo simulation, the GMPE proposed by Bindi et al. (2011) has been adopted 418
(Fig. 1df), being the most suitable and recent GMPEs based on the Italian event database. 419
Bindi et al. calibrated an intraevent standard deviation for PGA and PGV equal to 0.29 and 420
0.27, respectively. 421
Available data 422
Several maps have been collected for the case study and a geodatabase has been assembled in 423
a geographical information system (GIS) framework: first, a 30m resolution digital elevation 424
model (DEM) for the analysed region (Fig. 3b) was obtained from the Shuttle Radar 425
Topography Mission (SRTM) project (Farr et al. 2007). Then, based on DEM data, the map of 426
slopes (Fig. 3c) has been calculated. For the Vs,30 (Fig. 3d), the USGS globalVs30map server 427
20 De Risi, January 10, 2018
is used (Wald and Allen 2007) in combination with the soil map adopted by the Italian Institute 428
of Geophysics and Volcanology (INGV, Michelini et al. 2008). Finally, maps of soil friction 429
angle (Fig. 3e), cohesion (Fig. 3f), and unit weight (Fig. 3g) are synthesized on the basis of the 430
1:500,000 Italian geological map (http://www.pcn.minambiente.it/GN/) and to the 1:150,000
431
regional geolithological map (http://irdat.regione.fvg.it/WebGIS/GISViewer.jsp). This
432
information needs to be gathered in advance for the area of interest to have the postearthquake 433
risk assessment tool up and running when an event occurs. A fair amount of information is 434
often available to the network manager and it can be employed for the setup of the risk 435
assessment tool. 436
RESULTS 437
10,000 simulations are needed to obtain stable low/high percentiles of final losses. The entire 438
simulation procedure and the generation of the loss curves and the damage maps requires less 439
than twenty minutes to be performed, therefore it is very suitable for a postevent DSS. 440
Loss curves 441
Figure 4 shows the loss curves obtained considering the five different correlation structures 442
(C1  C5) and two different values of soil saturation (u). Specifically, curves represent the 443
number of leaks (Fig. 4a) and breaks (Fig. 4b) along the studied network, and the corresponding 444
repair (Fig. 4c) and replacement costs (Fig. 4d) based on unit repair costs (USD 20k) and 445
replacement costs (USD 130k) that are obtained from the Interstate Natural Gas Association of 446
America (INGAA, 2016). These values are assumed for each leak and break respectively as 447
obtained from the simulations and summed up to obtain the complementary cumulative 448
distribution function of losses. 449
Focusing on the cost estimates of Figure 4, from a geotechnical point of view, an increase in 450
soil saturation (i.e., from 50% to 100%) leads to an increase of the expected losses given its 451
significant influence on both landslide and liquefaction. Therefore, it is very important to have 452
21 De Risi, January 10, 2018
detailed information on the soil saturation along the infrastructure route (e.g., Lillesand et al. 453
2014). 454
From a statistical point of view, it is interesting to observe that neglecting the correlation 455
(model C1, i.e., blue lines in Fig. 4) leads to large underestimation of the final losses, as also 456
observed by other studies for other typologies of infrastructures (e.g., Miano et al. 2016). 457
Moreover, when the spatial correlation and the crosscorrelation between IMs are taken into 458
account, the dispersion of losses tends to reduce with respect to C1, leading to a more accurate 459
estimation. For this case study, the results obtained considering the spatial correlation and 460
neglecting the updating (i.e., case C2) tend to slightly underestimate the losses with respect to 461
the case which includes the updating (C4). Difference observed between case C3 and C5 are 462
negligible; when both spatial correlation and crosscorrelation are considered, the further 463
updating with real data did not improve the final assessment. Thus, neglecting the cross464
correlation of the intensity measures may lead to a underestimation of postearthquake losses. 465
Damage maps 466
Figure 5 shows the maps of potential damage induced by SGS and GF. The predominant 467
damage state is DS1 and the localization of the damage is mainly in the projection of the fault 468
plane (the black rectangle in Fig. 5). 469
In this study, it is extremely rare to attain DS2 for such kind of infrastructure under earthquake 470
actions, as also emphasized by the European Gas pipeline Incident data Group on the annual 471
report on gas pipeline incidents (EGIG, 2015). Nonetheless, regional network can be more 472
susceptible to earthquakes and potentially reach major damage (DS2). On the same map, 473
historical observations of landslides and liquefaction, according to the Italian CEDIT database 474
(Martino et al. 2014), are also plotted. It is possible to observe that all the geotechnical failures 475
historically recorded (red and cyan points, corresponding to landslide and liquefaction, 476
respectively) are very close to pipelines locations characterized as damaged (DS1) according 477
22 De Risi, January 10, 2018
to the methodology. In the future, the proposed damage maps can be integrated with satellite 478
survey of geotechnical failures (that is more and more available nowadays and often adopted 479
in postearthquake recognition Sextos et al. 2017) in order to increase the level of confidence 480
in the localization of potential damage. 481
CONCLUSIONS 482
This paper presents a methodology to quantify losses in terms of repair costs, leaks and breaks 483
and to localize the damage of a gas transmission infrastructure in the first critical period after 484
a major earthquake. The methodology is composed of a Monte Carlo simulationbased 485
procedure for the generation of plausible intensity measures fields that are spatially correlated 486
and crosscorrelated, of two new backtoback threephase geotechnical approaches accounting 487
for (i) susceptibility, (ii) triggering and (iii) ground dislocation due to landslide and liquefaction, 488
and finally of a risk approach based on two different literature vulnerability and fragility 489
models. The application to a real case study verified the coherence and computational 490
efficiency of the methodology, while led to the following conclusions. 491
1. Considering spatial correlation and crosscorrelation of the Intensity Measures required 492
to assess the seismic risk of natural gas pipeline networks, leads to a more reliable 493
estimate of losses, avoiding potential underestimation that is observed when the 494
Intensity Measures are taken as fully uncorrelated or simply spatially correlated. 495
2. The updating of the Intensity Measures’ fields from accelerometric station in real time, 496
if available after the earthquake, is beneficial since it allows anchoring the calculations 497
to real observations. 498
3. The methodology presented herein provides the infrastructure stakeholder with a 499
breakdown of costs and type of interventions required in case of damage in the 500
aftermath of the earthquake event. 501
23 De Risi, January 10, 2018
4. Maps localizing the expected damage are also resulting from this methodology, thus 502
facilitating the inspection missions and reducing the recovery time in the aftermath of 503
a seismic event. 504
Further study is needed for the implementation of coseismic effects considering stochastic 505
simulation of the fault slip, as recently suggested by Goda (2017). New vulnerability models 506
are also required to better reflect the damage typology, potentially using machine learning 507
algorithms. This work can be also extended combining the damage maps with (nearly) real 508
time data on landslides that can be retrieved through satellite imagery and remote sensing 509
capabilities. 510
ACKNOWLEDGMENTS 511
This work is funded by the Horizon 2020 MSCARISE2015 project No. 691213 entitled 512
“ExchangeRisk” (www.exchangerisk.eu). 513
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W.D.L., Harder Jr., L.F., Hynes, M.E., Ishihara, K., Koester, J.P., Liao, S.S.C., Marcuson 669
III, W.F., Martin, G.R., Mitchell, J.K., Moriwaki, Y., Power, M.S., Robertson, P.K., Seed, 670
R.B. and Stokoe II, K. H. (2001). Liquefaction resistance of soils: Summary report from the 671
30 De Risi, January 10, 2018
1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of 672
soils, J. Geotech. Geoenviron. Eng. 127, 817–833. 673
674
Station
(a) Infrastructure
Segment
Joint
L
• Geometry
• Diameters
• Pressure
• Materials
• Joints
• Burial depth
(b) Maps
• DEM
• Slope
• Vs30
• Geolithology
• I, c, J
• Groundwater
(c) Event
Fault plane
• Magnitude (M)
Faulttosite
distance (D)
Sitetosite
distance (Ri,j)
(d) GMPE (e) IMs correlation models (f) PGA & PGV
Distance
Seismic intensity measure
M
Central estimate
Intraevent variability
Basic
Information
• C1) IMs uncorrelated;
• C2) IMs spatially correlated
(Goda & Hong 2008);
• C3) IMs spatially correlated and
crosscorrelated
(Weatherill et al. 2014);
• C4) IMs spatially correlated and
updated with station data;
• C5) IMs spatially correlated and
crosscorrelated
updated with station data.
[ PGAi, PGVi ]
• Stochastic simulations
• Shakemaps
(g) Susceptibility (h) Triggering (i) Landslideinduced PGD
(j) Susceptibility (k) Triggering (l) Liquefactioninduced PGD
4 5 6 7 8 9
0.1
0.2
0.5
1
2
5
10
20
50
100
200
500
1000
Magnitude
Distance (km)
Domain of
potential failures
Type 1
Type 2
Type 3
• Keefer 1984
4 5 6 7 8 9
1
2
5
10
20
50
100
200
500
1000
Eq. 12
Eq. 13
Eq. 14
Envelope
• Galli 2000
Magnitude
Distance (km)
Domain of
potential failures
0.1
0.2
0.5
• Planar landslides:
Newmark’s method
slope (D)
tan '
' tan '
sin tan tan
w
u
c
SF t
J I
I
J D D J D
1 sin
c
a SF g
D
• Safety factor:
• Critical acceleration:
• Semiempirical method:
Seed & Idriss 1971
thickness (t)
CSR
SF
CRR
Cyclic Stress Ratio
Cyclic Resistance Ratio
• Vs30based approach:
Goda et al. 2011; Kayen et al. 2013
20
0
( )LPI SF w z dz
³
• Liquefaction Potential Index
• 0 ÷ 5; Failure potential LOW
• 5 ÷15; Failure potential HIGH
• >15; Failure potential VERY HIGH
PGD
• Empirical function of PGA and PGV:
Saygili & Rathje 2008
• LPI: 0 ÷ 5 ĺ PGD = 0
• Takada & Tanabe 1988
PGD
• LPI: > 15 ĺ Sand Lateral Spread
• Bardet et al. 1999
PGD
• LPI: 5 ÷ 15 ĺ Sand Boiling
Settlements
Stochastic
simulations
Threephase
geotechnical
models Landslide modelLiquefaction model
• e.g. Bindi et al. 2011
• PGA: Peak Ground Acceleration
• PGV: Peak Ground Velocity
Segment i
Segment j
PGD = PGD Settlements
PGD2=(PGD2Settlements
+ PGD2Lateral Spread)
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(a) PGA, PGV & PGD
[ PGAi, PGVi, PGDi ](d) Fragility Functions
(b) Vulnerability Functions
(e) Damage maps
(c) Loss curves
Repair rate (1/km)
Repair rate (1/km)
PGDPGV
• ALA 2001
• Strong Ground Shaking (SGS)
• Ground Failure (GF)
SGS GF
• Leaks: 0.8 SGS + 0.2 GF
• Breaks: 0.2 SGS + 0.8 GF
Probability
Probability
PGAPGV
PDS2
PDS1
PDS0
PDS2
PDS1
PDS0
SGS GF
ds(SGS) =
max(PDS0,PDS1,PDS2)
ds(GF) =
max(PDS0,PDS1,PDS2)
Probability
Probability
# of breaks# of leaks
Probability
Probability
repair costrepair cost
ds0ds0
ds1
ds2
Expected damage states
&OLFNKHUHWRGRZQORDG)LJXUH)LJSGI
Gorizia
Tarvisio
Fault
Tarvisio
Gorizia
Passo
Gries
Mazzara del Vallo
Gela
Panigaglia
Livorno
Cavarzere
National network (Transmission)
Regional network (Distribution)
LNG regasification terminals
Import points
(a) (b)
(c) (d)
(e) (g)(f)
&OLFNKHUHWRGRZQORDG)LJXUH)LJSGI
240 260 280 300 320
NB  number of breaks
10 4
10 3
10 2
10 1
10 0
P(N B>n B)
60 65 70 75 80 85
NL  number of leaks
10 4
10 3
10 2
10 1
10 0
P(N L>n L)
31 34 37 40 42
C0  Expected replacement cost (106 $)
10 4
10 3
10 2
10 1
10 0
P(C 0>c 0)
1.2 1.3 1.4 1.5 1.6 1.7
CR  Expected repair cost (106 $)
10 4
10 3
10 2
10 1
10 0
P(C R>c R)
(a) (b)
(c) (d)
C1
C2
C3
C4
C5 u = 100%
u = 50%
&OLFNKHUHWRGRZQORDG)LJXUH)LJSGI
(a) (b)
Historical landslides
Historical liquefactions
&OLFNKHUHWRGRZQORDG)LJXUH)LJSGI
1 De Risi, January 10, 2018
FIGURE CAPTIONS 1
2
Fig. 1. Computational framework for scenariobased seismic hazard. 3
4
Fig. 2. Scenariobased seismic risk assessment in terms of loss curves and damage maps: (a) 5
hazard simulation in terms of PGA, PGV and PGD, (b) vulnerability functions, (c) loss curves, 6
(d) fragility functions, (e) damage maps. 7
8
Fig. 3. Maps of (a) the Italian gas pipeline network, (b) transmission gas pipeline network in 9
Friuli Venezia Giulia overlaid on the DEM and the 1976 earthquake fault, (c) slopes, (d) Vs,30 10
values, (e) friction angles, (f) cohesion values and (g) unit weight of the soil formations. 11
12
Fig. 4. Loss curves in terms of number of (a) leaks and (b) breaks, and in terms of (c) expected 13
repair cost CR and (d) replacement cost C0, considering a saturation of the soil of 50% (dashed 14
lines) or 100% (continuous lines), respectively. 15
16
Fig. 5. Damage maps corresponding to (a) SGS and (b) GF for the case of IMs spatially 17
correlated and crosscorrelated obtained considering the updating from accelerometric stations 18
(C5). 19
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