Flood-related hazard criteria during the human evacuation of underground spaces through stairs: a state-of-the-art review

Vol.:(0123456789)
Na u al Haza ds
h ps://doi.o g/10.1007/s11069-024-07002-4
REVIEW ARTICLE
Flood‑ ela ed haza d c i e ia du ing hehuman e acua ion
o unde g ound spaces h oughs ai s: as a e‑o ‑ he‑a
e iew
Ca losH.Apa icioU ibe1 · BeniaminoRusso1 · JacksonTéllez‑Ál a ez1,2 ·
Edua doMa ínez‑Goma iz1,3
Recei ed: 29 Feb ua y 2024 / Accep ed: 27 Oc obe 2024
© The Au ho (s) 2024
Abs ac
Due o he inc easing u banisa ion end and mo e ecu en lood e en s wo ldwide ha
a e a ec ing exposed habi able a eas like unde g ound spaces. This s a e-o - he-a e iew
p esen s a comp ehensi e analysis o he a ailable li e a u e ha ocuses on de ining ins a-
bili y c i e ia o haza d assessmen du ing human e acua ion o unde g ound looded
s ai s. The s udies a e ou lined in h ee main g oups: heo e ical, expe imen al campaigns
and nume ical app oaches. Se e al me hods o de ining speci ic c i e ia we e ound, mos
o hese c i e ia we e desc ibed as a unc ion o wa e dep h (D) alone o in combina ion
wi h eloci y (V) highligh ing he impo ance o hese wo wa e - ela ed pa ame e s o
lood- ela ed haza d e alua ion. Succinc ly, he mos ele an indings and limi a ions o
hese s udies a e discussed and summa ised in ables. A compa ison wi h o he lood-
ela ed haza d c i e ia in plain and mild-slope a eas is p esen ed. Finally, po en ial u u e
in es iga ion lines a e p oposed. Thus, his s a e-o - he-a e iew could o e a comp e-
hensi e o e iew o he opic and s imula e new explo a o y s udies in his esea ch ield
yielding aluable insigh s ha can be easily ansmi ed o s akeholde s o non-expe s and
os e u ban esilience du ing loods.
Keywo ds Flood- ela ed haza d assessmen · Ins abili y c i e ia· U ban esilience·
Unde g ound space· Human e acua ion· Flooded s ai s
* Ca los H. Apa icio U ibe
ca los.humbe o.apa [email p o ec ed]
* Beniamino Russo
beniamino. [email p o ec ed]
1 Flumen Resea ch Ins i u e, Uni e si a Poli ècnica de Ca alunya – Cen e In e nacional de Mè odes
Numè ics en Enginye ia, Campus No d, Ca e de Jo di Gi ona, 1-3, B0 S1, 08034Ba celona,
Spain
2 Conso ci Besòs To de a, A eneu San Julià, 241, Ob es i Enginye ia, 08403G anolle s, Spain
3 Aigües de Ba celona, Emp esa Me opoli ana de la Ges ió del Cicle de l’Aigua, C/Gene al Ba e
1-7, 08028Ba celona, Spain
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1 In oduc ion
O e he las decade, loods ha e been he mos ecu en global na u al disas e (CRED-
UNDRR 2020). An agg a a ion o ex eme wea he condi ions due o clima e change is
expec ed in he upcoming yea s leading o inc easing e en s such as lash and la ge-scale
i e loods (K očka e al. 2016; Monjo e al. 2023). Besides, acco ding o he bookle
The Wo ld’s Ci ies (Uni edNa ions 2018) “mo e han wo- hi ds o he wo ld’s popula-
ion will li e in u ban a eas by 2050”. This g owing concen a ion o people is a end ha
causes signi ican en i onmen al dis up ions (Apa icio U ibe e al. 2022). U banisa ion
modi ies soil su ace wo sening he impac o loods due o impe meabilisa ion ha d as i-
cally educes wa e in il a ion (Ribei o e al. 2021). Mo eo e , he densi ica ion o habi -
able a eas consequen ly igge s he de elopmen o unde g ound spaces o supply oom
o human ac i i ies such as comme cial malls, pa king lo s, subway, and me o sys ems.
In his apid u banisa ion end and global clima e change con ex , many ci ies wo ld-
wide expe ience mo e equen and in ense loods (Ma ínez-Goma iz e al. 2019). Thei
unde g ound spaces could be conside ed highly exposed lood-p one a eas (Lyu e al. 2018;
Yu e al. 2019; Fo e o-O iz e al. 2020a, b; Fo e o-O iz and Ma ínez-Goma iz 2020; and
Iagua Magazine 2021). Be ween 2021 and 2023 se e al cases could illus a e his; in he
Chinese p o ince o Henan, a o al o 25 people died a e a eco d-b eaking ain all o
624mm wi h 208mm alling in jus one hou . Mo eo e , in Zhengzhou, he p o ince capi-
al, he unde g ound ailway unnels we e looded apping passenge s and esul ing in 12
dea hs (BBC News 2021a). In New Yo k Ci y, USA a eco d ain all caused by he opical
s o m Ida made au ho i ies decla e a s a e o eme gency, he anspo sys em collapsed and
mos o he ci y’s subway was looded (BBC News 2021b). In Seoul, Sou h Ko ea’s capi al,
au ho i ies epo ed he wo s p ecipi a ion in he las 80yea s ha esul ed a e 100mm
o ain in jus one hou . The public anspo sys em collapsed and he au ho i ies con-
i med 8 a ali ies and 6 missed people (El Mundo News 2022a). In Pa is, F ance’s capi al
he public anspo sys em collapsed du ing one single ain on 16 Augus , wi h 40mm o
ain in jus 90min ep esen ing almos 70% o he mon hly o al ain du ing a no mal sea-
son be ween he yea s 1991 and 2020 (El Mundo News 2022b). In Mad id, Spain’s capi al
unde g ound me o lines L2 and L7 cancelled ope a ions due o wa e in usion a e a ain-
all o a ound 50mm pe hou (To es and Olaizola 2023).
Wi h his p essing backg ound, an app op ia e esponse o he unde g ound u ban-asso-
cia ed in as uc u e du ing ex eme wea he e en s is an essen ial equi emen o gua an-
ee u ban esilience (Russo e al. 2020a, b). The aim o p ese ing his in as uc u e in
such c isis episodes is o main ain he p o ided se ices and a he same ime use s’ sa e y.
Unde g ound spaces can be signi ican ly c owded du ing peak hou s and i c ea es a po en-
ial scene y o inciden s ha could esul in a ali ies. In addi ion, unde g ound in as uc-
u e plays a c ucial ole in he ca go anspo , inancial s eng h, secu i y, and s abili y o
people and ci ies (A ci and Ozbulu 2018). Thus, a be e unde s anding o hei ulne -
abili y and how i a ec s use s will enhance hei esilience (Lyu e al. 2018).
Conside ing ha human ac i i y in lood-p one a eas is ine i able (Cox e  al. 2010;
Russo e al. 2013), a deep comp ehension o people’s capabili ies du ing loods is impo -
an o ensu e hei sa e y and explo e haza d mi iga ion measu es du ing e acua ions
(Dias e al. 2021). Many s udies abou human s abili y in la o mild-slope a eas ha e been
p esen ed in he li e a u e (e.g., Fos e and Cox 1973; Lo e e al. 1989; Takahashi e al.
1992; Témez 1992; Nanía 1999; Ka onen e al. 2000; Yee 2003; Cox e al. 2004; Goméz
2008; Jonkman and Penning-Rowsell 2008; Russo 2009; Shand e al. 2010; Xia e al. 2014;
Na u al Haza ds
Ma ínez-Goma iz e al. 2016; and Okamo o e al. 2022). Howe e , ega ding human s a-
bili y in looded s ai s, a ailable in o ma ion is limi ed. The e o e, i is pa amoun o ana-
lyse low pa e ns in such en i onmen s accoun ing o hei singula i ies (Hou e al. 2022).
Also, a mo e accu a e unde s anding o a ious aspec s o lood haza ds o pedes ians is
necessa y (Musolino e al. 2020). Thus, ha ing in mind unde g ound s ai s wi h hei si e-
speci ic cons ain s and how hey a ec human- low in e ac ions, u he esea ch should
be add essed.
A e he in oduc ion (1), he me hodological app oaches will be men ioned (2) s a -
ing om heo e ical app oaches (2.1) hen, con inuing wi h he expe imen al campaigns
on s aigh - un s ai s (acco ding o BUEDRI 2005; ICC 2011; MOHURD 2013) he mos
commonly used s ai s o m in unde g ound space en ances (see Fig.1) and s aigh - un
s ai s wi h es pla o m (2.2). A e wa ds, esea ch based on nume ical models will be
p esen ed (2.3). Finally, a discussion compa ing he di e en app oaches and sugges ing
u u e s udies and some conclusions will be gi en (3).
2 Me hodological app oaches
As men ioned in he in oduc ion he haza dous condi ions in looded u ban a eas ha e
been o in e es o se e al decades. None heless, he e is no ex ensi e e ision je ocus-
ing onspeci ic s a e o he a abou lood- ela ed haza dous condi ions du ing he e acu-
a ion o unde g ound spaces and hei p oposed sa e y c i e ia. The e o e, he goal o his
e iew is o conduc a ho ough examina ion o he a ailable li e a u e, p o iding a con-
sul ing esou ce on he opic. This is highly aluable because o he consolida ion o he
exis ing knowledge and he iden i ica ion o gaps ha should be ocused on in he coming
yea s. Mos o he ci ed s udies ha e been accessed om exis ing indexed da abases (i.e.
Web o Science, Scopus, e c.) o pee - e iewed/ e e eed a icles and hei espec i e ci a-
ions. These con ibu ions ha e been di ided in o h ee g oups ollowing speci ic esea ch
app oaches: heo e ical, expe imen al and nume ical.
The heo e ical s udies include analyses ha used concep ual o ma hema ical app oaches
wi hou elying on empi ical o expe imen al da a. The expe imen al app oaches e e o all
s udies ha conduc ed es s o explo e he e en s. Finally, he nume ical app oaches eso o
algo i hms o ob ain app oxima e solu ions o he s udied phenomena. The e ms sa e e acu-
a ion and c i ical e acua ion will be men ioned equen ly. The i s one e e s o a condi ion
Fig. 1 S ai s’ o ms: s aigh - un (a), s aigh - un wi h es pla o m (b), L-shape (c), U-shape (d), and
s aigh - un wi h junc ion in he es pla o m (e)
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in which he e acuee could e acua e wi hou any help, and he second e e s o a condi ion in
which he pe son apped would no be able o e acua e, a leas wi hou any help o ex e nal
in e en ion.
2.1 Theo e ical app oaches
2.1.1 Mechanics‑based analysis o human ins abili y ins ai s
Conside ing human in e ac ions in loods he e a e h ee po en ial ins abili y mechanisms:
sliding, oppling and loa ing. This las one can occu when he wa e dep h exceeds he body
heigh , bu in p ac ice loa ing p obabili y is small conside ing ha human densi y is sligh ly
g ea e han wa e densi y (Xia e al. 2014). Focusing on sliding and oppling mechanisms
acco ding o Li e al. (2022), he o ces ac ing on a human body imme sed in a lood (Fig.2)
a e: he d ag o ce o he low FD, he ic ional o ce be ween human ee and s ep su ace FR,
he g a i a ional o ce Fg, he buoyancy o ce Fb, he human li o ce FL, and he no mal eac-
ion o ce om he g ound FN. Human heigh is hp and he lowing wa e dep h o e he ee
on he s ep is h . The angle o o ce FL in he e ical di ec ion is θ. The geome ic pa ame e s
o he human body we e simpli ied as a p ism o heigh hp wid h w’ and leng h d (Lind e al.
2004). Consequen ly, he ac ing o ces can be de ined as:
(1)
Fg
=𝜌
g
⋅g
(
h
p
⋅d⋅w
�)
Fig. 2 Schema ics o he human
body and ac ing o ces in lood-
ing s ai s acco ding o Li e al.
(2022)
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whe e μ is he e ec i e iscosi y, V is wa e eloci y, D is wa e dep h, ρ is he luid den-
si y, ρg is he human body densi y, CD is he d ag coe icien and CL is he li coe icien .
The c i ical condi ion o sliding ins abili y will be gi en by Eq. (6):
And he c i ical condi ion o oppling ins abili y will be gi en by Eq. (7):
2.1.2 Theo e ical s udies de ining sa e y c i e ia
Human ins abili y and e acua ion in unde g ound lood-p one a eas h ough s ai s
s a ed o be deeply s udied wo decades ago. Takedomi e al. (2001) p esen ed he i s
c i e ion o e alua e his. The au ho s p oposed he Momen um o Flow (MF) wi h Eq.
(8) as he c i ical alue o assess human e acua ion in looded s ai s.
whe e V (m/s) is wa e eloci y and D (m) is wa e dep h.
La e , in a guideline he Japanese Commi ee o Coun e measu es agains Inunda-
ion Disas e s in Unde g ound Spaces, (CCIDUS 2002) sugges ed ha 0.3m is he
c i ical wa e le el (D) a he op o s ai s o sa ely walk and e acua e. Besides, he
commi ee highligh ed ha unde g ound e acua ion ime is composed o i e in e als:
(a) he dange ecogni ion in e al, which is he equi ed ime o he lood o each
a wa e le el o 0.1m ei he in he uppe pa o he s ai s o he unde g ound space,
(b) he decision-making in e al, ha is he equi ed ime o he e acuee o decide
ha e acua ion needs o be done, (c) he unde g ound e acua ion in e al, ha is he
equi ed ime o mo e om he a hes loca ion in he unde g ound space un il each-
ing he a ea nex o he s ai s, (d) he s ai s en ance passing in e al, which is he
equi ed ime o pass he c owded (supposing ha se e al people e acua e a he same
ime) a ea be o e eaching he i s s ep, and (e) he e acua ion in e al on he s ai s,
ha is he equi ed ime o pass he s ai s. A subsequen s udy by Shao (2010) poin ed
ou ha , al hough he e acua ion p ocess could comp ise se e al s ages, he con olling
condi ion is he abili y o walk on s ai s.
(2)
Fb
=𝜌⋅g
(
h
⋅d⋅w
�)
(3)
F
D=
1
2
𝜌VCD(hp⋅w�
)
(4)
F
L=
1
2
𝜌VCL(D⋅w�
)
(5)
FR=𝜇FN=𝜇(Fg−Fb+FD
⋅
sin 𝜃−FL
⋅
cos 𝜃)
(6)
FR=FD
⋅
cos 𝜃+FL
⋅
sin 𝜃
(7)
(
Fg−Fb+FD⋅sin 𝜃−FL⋅cos 𝜃)⋅d=(FD⋅cos 𝜃+FL⋅sin 𝜃)⋅
1
2
h
(8)
(
M
F)
=V
2
⋅D=1.5 m
3
∕
s

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2.2 Expe imen al app oaches
2.2.1 Campaigns ins aigh ‑ un s ai s
T ying o p o ide expe imen al da a o complemen p e ious 2D nume ical and scaled
models on unde g ound lood beha iou (Ishigaki e al. 2003, 2004; Toda e al. 2004),
he i s eal-scale s udies on e acua ion in unde g ound looded spaces ound in he
li e a u e we e done by Ishigaki e al. (2005, 2006) a he Disas e P e en ion Resea ch
Ins i u e (DPRI) in Kyo o Uni e si y, Japan. The au ho s e alua ed di e en si ua ions
ha a pe son could ace e acua ing an unde g ound looded space: low o e s ai s, ela-
i e ime o e acua e looded s ai s, o ce ac ing on a leg due o he wa e d agging
e ec and he maximum wa e le el a which a pe son could open a doo .
The s ai s p o o ype consis ed o 20 s eps, wi h 0.3m ead, 0.15m ise , 3.0m
heigh , and 1.0m wide (Fig.3), he discha ge was up o 0.8 m3/s. 49 subjec s we e
es ed: 16 emales and 33 males. Fou low pa e ns be ween 0.1 and 0.4m wa e dep h
we e used. Resul s showed ha wa e dep hs be ween 0.3 and 0.4m made e acuees
equi e he use o a sa e y li eline and wi h 0.4m wa e dep h, he ela i e ime o
e acua ion inc eases up o 2.5 imes o emales and 1.6 imes o males compa ed o no
Fig. 3 Schema ics o he s ai s p o o ype (Ishigaki e al. 2008b)
Fig. 4 Rela i e e acua ion ime
o emales and males using
di e en wa e dep hs (Ishigaki
e al. 2005), T0 is he equi ed
ime wi hou wa e and TD is
he equi ed ime unde di e en
wa e dep hs
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wa e in he s ai case (Fig.4). The e o e, i was e idenced ha a wa e dep h o 0.3m
on he op g ound o he s ai s is c i ical o e acua ion.
The ac ing o ce on he leg was measu ed using a p o o ype using ou di e en shoe
ypes: ba e oo , sneake s, ouse s, and boo s was measu ed wi h a load scale ha egis-
e ed app oxima ely a maximum o 4, 6, and 8 kg when wa e dep h was espec i ely 0.2,
0.3, and 0.4m. The lowes equi ed o ce o gene a e sliding was wi h ba e oo and he
highes wi h ouse s. Besides, when he oo posi ion was close o he side o he s ai , he
egis e ed o ce was app oxima ely 30% highe when compa ed o he oo posi ioned in
he cen e o he s ai (Fig.5).
The c i ical limi o sa e e acua ion was e alua ed based on he Momen um o Flow as
Takedomi e al. (2001) p e iously p oposed (Eq.8). Ne e heless, a e he analysis o he
expe imen al campaign’s esul s (Fig.6). Ishigaki e al. (2005) sugges ed a mo e conse a-
i e alue o ma ch he expe imen al ou comes, being he c i ical limi o sa e e acua ion
based on he Momen um o Flow ede ined as i is p esen ed in equa ion (Eq. 9).
Con inuing wi h his expe imen al campaign, Onishi e  al. (2007), Ishigaki e al.
(2008a), and Ishigaki e al. (2009) inc eased he numbe o es ed subjec s o a o al
o 304: 47 emales and 257 males wi h an a e age age o 30 and 25yea s espec i ely.
Also, a new es condi ion was implemen ed conside ing a pa hway wi h an ini ial wa e
le el a he lowe pla o m be o e he s ai s. I was ound ha wi h a wa e dep h o
0.3m, 2% o he males and 34% o he emales needed o use hand ails and wi h a wa e
(9)
(
M
F)
=V
2
⋅D=1.2 m
3
∕
s
Fig. 5 Ac ing o ce on a leg o di e en oo wea cases (le ) and ac ing o ce on a leg o di e en loca-
ions o he oo ( igh ) (Ishigaki e al. 2005)
Fig. 6 Veloci y dis ibu ion (le ) and Momen um o Flow dis ibu ion along s ai s ( igh ) (Ishigaki e al.
2005). The ed dashed line is he e acua ion c i e ion o MF = 1.2
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dep h o 0.4m, 13% o he males and 78% o he emales needed i . Rega ding he p e i-
ously de ined c i e ia Momen um o Flow (MF), unde he new es condi ion, adequacy
was limi ed (Fig.7). The e o e, a new c i e ion was p oposed by Ishigaki e al. (2008b).
This c i e ion was called Speci ic Fo ce Pe Uni Wid h (SFPUW), Eq. (10).
whe e V is wa e eloci y, D wa e dep h and g is he g a i a ional accele a ion.
A e he expe imen al campaign Ishigaki e al. (2008b) ecommended a alue o
M0 = 0.125 m3/m as he sa e e acua ion limi and a alue o M0 = 0.25 m3/m as he c i i-
cal limi o e acua ion (Fig.8). A la e s udy done by Ma suo e al. (2011) s a ed his as
he mos conse a i e c i e ion compa ed o he Momen um o Flow.
A subsequen s udy done by Ishigaki e  al. (2010) de eloped an app oxima i e
me hod o y o assess he e acua ion o elde ly people (70yea s o mo e), he mos
ulne able popula ion al oge he wi h child en (14yea s o less). Elde ly we e ep e-
sen ed by adding o young adul s, de ices ha limi ed he eedom o mo emen in he
wais and knees and weigh s on ankles and w is s. I was ound ha elde people ha e
oughly 80% o a young adul capaci y. Consequen ly, new alues o sa e and c i ical
e acua ion limi s we e p esen ed based on age and sex (Table1). In his e iew, he use
o he e m “Sex” is based on he de ini ions p esen ed by he SAGER guidelines de el-
oped by Heida i e al. (2016). O iginal s udies may ha e used ano he e minology.
(10)
M
0
=V
2
D∕g+D
2
∕2;
(
m
3
∕m
)
Fig. 7 Dis ibu ion o (MF) along he s ai s in p e ious es condi ions (le ) and new es condi ion ( igh )
he s agna ion wa e le el is om 6 o 14m dis ance (Ishigaki e al. 2008b). The ed line is he MF = 1.2
e acua ion c i e ion
Fig. 8 Dis ibu ion o (SFPUW) along he e acua ion ou e in he s ai s es (le ) and he s ai s-co ido es
( igh ) The s agna ion wa e le el is om 6 o 14m dis ance (Ishigaki e al. 2008b). The ed dashed line is
he M0 = 0.125 and he ed line is he M0 = 0.25 e acua ion c i e ia
Na u al Haza ds
A s udy conduc ed by Baba e  al. (2017) buil on he p e ious esea ch wo ks
expanded he numbe o es ed subjec s, 100 mo e we e es ed including 11 child en
aged 8, and 3 child en aged 12. The expe imen al campaign was ca ied ou wi h di e -
en wa e dep hs a he op (0, 0.1, 0.2, 0.3, and 0.4m) and consis ed o measu ing he
equi ed ime o e acua e. I was obse ed ha in all child en, male, and emale cases,
he du a ion o e acua ion inc eases as he dep h condi ions become deepe . Besides,
e acua ion a es o child en a e subs an ially g ea e han hose o adul s (Fig. 9).
Howe e , he s udy i sel s a ed ha he limi ed sample implies a cons ain o u he
deduc ions.
Focused on he Ko ean unde g ound housing end, a s udy by Joo and Kim (2015)
e alua ed he equi ed e acua ion ime in looding s ai s. This expe imen app oached
wa e dep hs (D) based on an h opomo phic cha ac e is ics. The selec ed wa e le els
we e ela ed o human body pa s imme sed in he luid: one o he ankle (0.17m),
ano he o he shin (0.35m) and one mo e o he knee (0.45m). The s aigh - un s ai s
p o o ype consis ed o 20 s eps, wi h 0.3m ead, 0.15m ise , 3.0m heigh , 1.0m
wide and an uppe pla o m 2.0m wide. Wa e dep h and eloci y we e measu ed on he
lowe s ep. Fo D = 0.17m, he a e age wa e eloci y was 3.59m/s. Fo D = 0.35m he
a e age wa e eloci y was 5.41m/s, and o D = 0.45m he a e age wa e eloci y was
6,48m/s. The es measu ed e acua ion ime a hese h ee wa e dep hs while olun-
ee s wo e di e en shoes, wi h and wi hou using hand ails. The s udy did no speci y
how many people we e es ed, bu he au ho s highligh ed ha he sample numbe was
insu icien o s a is ical analysis.
Resul s showed ha while using hand ails ba e oo always egis e ed he as es
e acua ion ime, and slippe s we e he la es . When he hand ail was no used, e acu-
a ion ime signi ican ly inc eased wi h he inc emen in wa e dep h (Fig.10). Besides,
human eelings exe ed addi ional p essu e on es ed people and in luenced esul s. Fo
Table 1 Di e en ia ion by
sex o he SFPUW c i e ion
(Ishigaki e al. 2010)
Limi o sa e e acua ion Di icul
wi hou any
help
Male 0.125 0.250
Elde ly male 0.100 0.200
Female 0.100 0.200
Elde ly emale 0.080 0.160
Fig. 9 Compa ison o equi ed
ime o s ai s e acua ion (Baba
e al. 2017)
Na u al Haza ds
Using he so wa e FLOW-3D, Lee e  al. (2016) e alua ed slope e ec s using h ee
s ai s’ models (Table3). All o hem we e 2.88m in heigh and 1.2m wide, wi h 0.28m
ead, bu p esen ed changes in ise s ha changed he s eps’ numbe s. Fou di e en dis-
cha ges o 0.3, 0.5, 0.7, and 1.0 m3/s we e applied and human sa e e acua ion was e alu-
a ed based on he SFPUW c i e ia.
The s udy concluded ha he c i ical wa e dep h o he e acua ion o elde ly people is
a ound 0.2m and wi h wa e dep hs o 0.36m e en young males will ace oubles wi hou
any help. Also, i was e idenced ha slope is no as ele an as wa e dep h o human sa e
e acua ion o s ai s. Finally, he mos ele an inding o his s udy was ha he alues o
he s udied hyd aulic pa ame e s used o de e mine he SFPUW c i e ia a y e en inside
e e y s ep (Fig.23).
Hou e al. (2022) in es iga ed he slope e ec s h ough a 2D nume ical model (wi hou
conside ing wid h) o ou s ai s and wo escala o s (Table4). The chosen modelling ool
was FLUENT 17.0. The simula ion was alida ed wi h da a co esponding o he s ai s
(26.6° slope) used in he expe imen al campaigns ca ied ou a he DPRI o Kyo o Uni-
e si y in Japan. Th ee di e en discha ges (0.14, 0.28, and 0.6 m2/s) we e used o compa e
Fig. 22 Mean ai –wa e mix u e eloci y (a, b, and c) and (MF) c i e ia along he s epped chu es o h ee
ypes o s ai s (d, e, ). (Shao e al. 2015). The ed line ep esen s (MF) = 1.2; (a) & (d) C1: S aigh - un, (b)
& (e) C5: L-shape and (c) & ( ) C6: U-shape
Table 3 Speci ica ion o he s ai s’ models o e e y case (Lee e al. 2016)
Model Type S ep Heigh (m) To al Leng h (m) Numbe o
S eps (u)
Slope (°)
Case A Mild 0.12 6.72 21 23.2
Case B No mal 0.14 5.60 19 27.2
Case C S eep 0.18 4.48 17 32.7

Na u al Haza ds
eloci y and wa e dep h along he s eps. The analysis was di ided in o ou di e en pa s:
(a) slope e ec s o di e en s able wa e dep hs, (b) slope e ec s on di e en s able dis-
cha ges, (c) he in luence o a pe manen downs eam wa e dep h on e acua ion isks and
(d) unce ain y analysis o assess he eliabili y o he selec ed c i e ion MF = 1.2 m3/s2.
Pa (a) showed ha he eloci y inc eases g adually om he en ance o he exi , in
he uppe and middle segmen s o he s ai s and escala o s, whe eas i was ela i ely s able
in he lowe segmen . In pa (b) As a gene al in e ence, he s udy concluded ha unde
slopes anging om 26.6° and 28.2° a wa e le el o 0.3m a he en ance o a uni wid h
discha ge o 0.28 m2/s a sa e y e acua ion occu s. Bu wi h slopes beyond 28.2°, he sa e y
index is highe han he de ined c i ical alue. Pa (c) conside ed a wa e s agna ing con-
di ion in he co ido nex o he s ai s. Fo his, jus he s ai s wi h a slope o 26.6° we e
implemen ed. The ini ial downs eam wa e dep h was ixed a 0.3m, and he c i ical uni
wid h discha ge was 0.28 m2/s. I was ound ha some imes, in hese cases, discon inui-
ies like hyd aulic jumps occu ed and he Momen um o low (MF) a hese loca ions was
igge ed becoming highe han he sa e y e acua ion limi . This ein o ced p e ious ind-
ings abou he inadequacy o his c i e ion unde his condi ion. Finally, in pa (d) he
s udy included di e en s ai s o ms (see Fig.1) and i was concluded ha he c i e ion
(MF) = 1.2 m3/s2 p ope ly esponds in s aigh - un s ai s. Howe e , o s aigh - un s ai s
wi h a es pla o m, he alue o (MF) = 1.2 m3/s2 in he s eps downs eam needs o be
app op ia ely educed while o L-shape and U-shape s ai s, he e alua ion index alue o
he s eps downs eam could be inc eased.
Tellez Al a ez e  al. (2022) c ea ed a 3D nume ical model using he so wa e
FLOW-3D (Flow Science 2023) o analyse one o he access s ai s in he Pa al·lel s a-
ion o Ba celona’s me o sys em (Spain). The model se up consis ed o he 3D Reyn-
olds-a e aged, Na ie –S okes (RANS) equa ions conside ing ee su ace low wi h
Fig. 23 E alua ion o (M0) c i-
e ion along he s ai s’ cen eline
o a discha ge o 0.5 m3/s in
case B (Lee e al. 2016)
Table 4 S ai s and elec ic
escala o ypologies wi h
di e en slopes (Hou e al. 2022)
Typology Slope (°) S ep Heigh –
Rise (m)
S ep
Leng h—
T ead (m)
Type—A1 30° 0.15 0.260
Type—A2 29.1° 0.15 0.270
Type—A3 28.2° 0.15 0.280
Type—A4 26.6° 0.15 0.300
Type—A5 35° 0.24 0.345
Type—A6 30° 0.24 0.416
Na u al Haza ds
he Re-No maliza ion G oup (RNG) u bulence model, ai en ainmen , d i - lux, den-
si y e alua ion, and bubble and phase change. The s ai s cons uc ed wi h da a om
“T anspo s Me opoli ans de Ba celona” consis ed o 20 s eps wi h a 0.34m ead and
0.17m ise . A cons an low a e o 0.2 m3/s was used, and measu emen s we e done
as an a e age a he cen e line o each s ep. The s udy ocused on analysing a ia ions
in hyd aulic pa ame e s ( eloci y and dep h) due o he changes in cell sizes (0.01 and
0.02m). Resul s showed a maximum a ia ion in eloci ies o a ound 25% e idencing
he incidence on he mesh in he ou pu s.
Li e al. (2022) alida ed a se ies o nume ical La ge Eddy Simula ion (LES) models
coupled wi h he VOF me hod using expe imen al esul s om p e ious campaigns. The
s aigh - un s ai s and he s aigh - un s ai s wi h es pla o m implemen ed espec i ely
by Ishigaki e al. (2005) and Jiang e al. (2014) we e used o calib a ion and alida ion.
The las one was also employed o analyse how hyd aulic beha iou a ec s he s abili y o
human beings depending on hei loca ion o e s ai s. This selec ion lies in he e idence
s a ed by Jiang e al. (2014) and Shao e al. (2015) ha he es pla o m amids he s ai s
inc eases c i ical condi ions o people ying o e acua e. To ep esen he ae a ion phe-
nomenon in he s ai s, he heo e ical solu ion o ai concen a ion dis ibu ion p oposed
by Chanson (2001) was implemen ed. A g id sensi i i y analysis was unde aken wi h ou
di e en mesh sizes; 0.0050, 0.0075, 0.01, and 0.015m. The ma ginal e o was small in
all cases; he e o e, in he domain’s places whe e he human body was no loca ed a mesh
size o 0.025m was applied and a 0.01m mesh size was selec ed o encompassing he
human shape. The nume ical models we e 1:2 scale (same as he expe imen al campaign).
Fou nume ical models we e ca ied ou . Th ee o an adul human body on ep esen a-
i e loca ions o he s ai s: he uppe , he lowe pa , and he es pla o m and he las
one wi h a younge human (14yea s o less) in he lowe pa o he s ai s a e he es
pla o m. The haza d condi ions we e e alua ed based on he (MF) c i e ion compa ing
Ishigaki e al. (2005) and Takedomi e al. (2001) ecommended alues. The au ho s con-
cluded ha he human- luid in e ac ion e idenced changes in luid beha iou . The mechan-
ics-based analysis showed ha he dominan ins abili y ailu e cause was sliding and was
highe in he dummy ep esen ing he younge human. Also, he esul ing je low a e he
es pla o m was shown o be he mos haza dous zone o human e acua ion as p e ious
s udies poin ed ou (Fig.24).
Liang e al. (2023) in es iga ed he lood dynamics on s ai s wi h a junc ion in he es
pla o m (Fig.25). Using h ee scena ios (Table5), he au ho s e alua ed how sho e o
longe s eps and ise s in luence sa e y e acua ion. A 2D model based on Shallow Wa e
Equa ions (SWE) was used. The expe imen al campaign esul s by Ishigaki e al. (2005)
we e used o alida e he model. Fo he i s scena io, he s eps we e adjus ed om 0.3
o 0.5m wi h ise s anging om 0.15 o 0.25m, main aining a 1:2 a io. A e wa ds, in
he second scena io, he s eps main ained a leng h o 0.3m while he ise s anged om
0.15 o 0.21m, wi h slopes anging om 26.56˚ o 34.99˚. Finally, in he hi d scena io,
he s aigh - un s ai s wi h a junc ion in he es pla o m was modelled. In all cases, wa e
dep h a he op o he s ai s anged om 0.1 o 0.9m.
In he i s scena io, when main aining he p opo ion be ween s eps and ise s, wa e
dep h inc eases when he s ep’s leng h inc eases oo, while wa e eloci y dec eases. Fo
he second scena io, g ea e ise s co ela ed wi h highe wa e eloci y and low wa e
dep hs. Howe e , his co ela ion is almos in isible wi h wa e dep hs below 0.5m. The e-
o e, o lood- ela ed haza d e alua ion du ing human e acua ion, as men ioned be o e by
o he au ho s (Lee e al. 2016) slope e ec s ha e li le impac . Finally, in he hi d scena io,
esul s e idenced ha he wa e dep h and low eloci y on he b anch a e lowe compa ed
Na u al Haza ds
o hose alues in he main line o he s ai s (Fig.26). The e o e, his could be a good
op ion o a oid haza dous condi ions in he lowe pa o s aigh - un s ai s wi h a es
pla o m.
Fig. 24 T end o he (MF) c i e ion along he s ai s wi h es pla o m (Li e al. 2022)
Fig. 25 Schema ics o he
s aigh - un s ai s wi h junc ion
in he es pla o m (Liang e al.
2023)
Table 5 Summa y o design
scena ios (Liang e al. 2023)S ai s shape and scena io S ep leng h (m) S ep heigh (m)
S aigh s ai s (Valida ion) 0.3 0.15
S aigh s ai s (1s scena io) 0.3–0.5 0.15–0.25
S aigh s ai s (2nd scena io) 0.3 0.15–0.21
S ai s wi h junc ion in he es
pla o m (3 d scena io)
0.3 0.15
Na u al Haza ds
3 Compa ison o me hodological app oaches, u u e pe spec i es
andconclusions
3.1 Discussion
The p esen e iew showed he di e en “base s udies” and subsequen “complemen ing
s udies” p oposed o e alua e lood- ela ed haza d du ing he e acua ion o unde g ound
s ai s. They we e classi ied as expe imen al, heo e ical, o nume ical app oaches. The i e
“base s udies” (Table6) de ined sa e y c i e ia ei he elying on wa e dep h “D” alone o
in combina ion wi h wa e eloci y “V” unde sco ing he impo ance o hese wo hyd au-
lic pa ame e s o lood- ela ed haza d assessmen . La e , hese c i e ia we e used as a
benchma k by he “complemen ing s udies” (Table7) o modi y hem based on new ind-
ings o add in o ma ion abou o he ele an condi ione s ha in luence haza d indica o s,
like human age and sex, o s ai s’ slope and shape.
The s udies highligh ed abo e p o ided use ul in o ma ion al hough some limi a ions
could be discussed. In some cases, hese limi a ions we e o e come by pos e io s udies bu
o he s s ill need o be add essed. The majo limi a ion o he heo e ical s udies (Takedomi
e al. 2001; CCIDUS 2002) is he lack o expe imen al e idence o suppo hei p oposed
c i e ia. Fo ins ance, he Takedomi e al. (2001) c i e ion MF = 1.5 m3/s2 was la e educed
o 1.2 m3/s2 due o expe imen al campaign esul s ob ained by Ishigaki e al. (2005). The
CCIDUS (2002) guideline besides p oposing a wa e dep h o 0.3m in he uppe pa o
he s ai s as he c i ical limi o e acua ion, also sugges ed a se ies o in e als ha com-
posed he o al equi ed ime o e acua e. These pa ame e s we e a ely implemen ed o
assessed by o he s udies despi e hei po en ial impac on he sa e y e acua ion o people
and could be conside ed ha he main eason is i s dependence on si e-speci ic cons ain s.
The expe imen al campaigns could be di ided in o h ee g oups: he i s wo consis ed
o eal-scale p o o ypes, one ca ied ou in Japan (Ishigaki e al. 2005, 2008a, b, 2009,
2010; Onishi e al. 2007; Baba 2017) and he o he in Sou h Ko ea (Joo and Kim 2015;
Kim e al. 2018). The hi d was a 1:2 scaled model de eloped in China (Jiang e al. 2014).
The Japanese campaign s a ed by Ishigaki e al. (2005) has been widely e e enced (e.g.,
Go oh e al. 2006; Toda 2007; Yoneyama e al. 2009; Shao e al. 2015; Lee e al. 2016;
Ishigaki e al. 2016; Baba e al. 2017; Nakasaka e al. 2020; Hou e al. 2022; Nakasaka and
Ishigaki 2021; Wu e al. 2021; Lin e al. 2022). I su ged o p o ide eal da a o e i y p e-
ious nume ical models and as a esponse o hea y damages caused by u ban loods ha
Fig. 26 Wa e dep h and eloci y when D = 0.2m (le ) and D = 0.3m ( igh ) a he op o he s ai s (Liang
e al. 2023)
Na u al Haza ds
Table 6 Summa y o he base s udies/guidelines. The column “exposed elemen s/subjec s” e e s o people o objec s ha ha e been es ed du ing he expe imen s o nume i-
cal models on he looded s ai s
App oach & In ol ed
Pa ame e s
Au ho & Yea Inpu C i e ia Obse a ions Exposed Elemen s
/ Subjec s
Risk Managemen Coun-
e measu es
Theo e ical Wa e
eloci y (V)
Wa e dep h (D)
Takedomi e al.
(2001)
P oposed he i s c i-
e ion, Momen um
o Flow (MF)
(
MF
)
=V
2
⋅D=1.5 m
3
∕
s
De ined he i s c i i-
cal alue o human
e acua ion in s ai s
N/A N/A
Theo e ical Time ( )
Wa e dep h (D)
Japanese Commi ee
o Coun e meas-
u es agains Inun-
da ion Disas e s
in Unde g ound
Spaces (CCIDUS
2002)
S a ed ha he
e acua ion o
he unde g ound
spaces is composed
o se e al in e als
(5 in o al)
C i ical wa e dep h
(D) = 0.3 m
Di ided he e acua ion p o-
cess in o se e al in e als
C i ical dep h o
e acua ion is 0.3 m
on he op g ound o
he s ai
N/A Wa e le els a he s ai s’
en ances below 0.3
m will gua an ee sa e
e acua ion
Expe imen al
Wa e eloci y (V)
Wa e dep h (D)
Ishigaki e al. (2005) Fi s eal-scale
expe imen s
(i) E acua ion in
looded s ai s
(ii) Rela i e ime o
e acua e
(iii) o ce ac ing on
a leg due o he
wa e -d agging
e ec
C i ical wa e dep h
(D) = 0.3 m
(
MF
)
=V
2
⋅D=1.2 m
3
∕
s
The c i ical dep h
o e acua ion is
0.3 m on he op
g ound o s ai s. ·
16 emales and 33
males we e es ed.
· 0.4 m wa e dep h
inc eased e acua ion
ime by 2.5 imes
o emales and
1.6 imes o males
· The maximum
ac ing o ce on he
leg model o 4, 6,
and 8 kg when
wa e dep h was
espec i ely 0.2, 0.3,
and 0.4 m
Humans Wa e le els a he s ai s’
en ances below 0.3
m will gua an ee sa e
e acua ion
The de ini ion o e acu-
a ion plans and escue
sys ems o unde -
g ound spaces is u gen

Na u al Haza ds
Table 6 (con inued)
App oach & In ol ed
Pa ame e s
Au ho & Yea Inpu C i e ia Obse a ions Exposed Elemen s
/ Subjec s
Risk Managemen Coun-
e measu es
Expe imen al
Wa e eloci y (V)
Wa e dep h (D)
Ishigaki e al.
(2008b)
P oposed he (M0)
c i e ion -Speci ic
Fo ce Pe Uni
Wid h (SFPUW)
M
0=V
2
D
g
+D
2
2=0.125m3∕
m
M
0=V
2
D
g
+D
2
2=0.25m3∕
m
Found ha conside -
ing a s agna ion
wa e le el in he
lowe co ido
be o e he s ai s
he adequacy o
Momen um o low
is limi ed
· (M0) = 0.125 as he
sa e e acua ion limi
· (M0) = 0.25 as he
alue o he c i ical
e acua ion limi
Humans By using a haza d
c i e ion coupled
wi h a lood model
sel -e acua ion ou es
could be chosen and
a sa e e acua ion plan
de ined
Expe imen al
Wa e dep h (D)
based on an h opo-
mo phic cha ac e -
is ics
Joo and Kim (2015) Assessed e acua-
ion in looded
s ai s and he o ce
needed o open a
doo . Wa e le els
we e based on
an h opomo phic
cha ac e is ics
(ankle D = 0.17 m,
shin D = 0.35 m,
and knee D = 0.45
m)
C i ical wa e dep h (D) in he
las s ep
D = 0.35 m
High heels a e c i ical
oo wea o e acu-
a ion
Humans Legisla ion should
gua an ee he p esence
o hand ails in lood-
p one s ai s o imp o e
people’s e acua ion
esponse
Na u al Haza ds
Table 7 Summa y o he subsequen s udies ollowing he base s udies/guidelines
App oach &
in ol ed Va iables
Au ho & Yea Inpu C i e ia Obse a ions Exposed Elemen s /
Subjec s
Risk Managemen
Coun e measu es
Expe imen al Onishi e al. (2007),
Ishigaki e al.
(2008a, 2009)
Con inued wi h
Ishigaki e al. (2005)
expe imen al cam-
paign. The au ho s
inc eased he num-
be o es ed people
and also added a
new condi ion which
conside ed a wa e
le el s agna ion in
he lowe co ido
be o e he s ai s’
lowe pa
· 47 emales and 257
males we e es ed o
he classical s ai s
es
· 16 emales and 83
males we e es ed
conside ing he
ini ial wa e le el in
he lowe co ido
be o e he s ai s’
lowe pa . · When
D = 0.3 m, 2% o
males and 34% o
emales needed o
use hand ails and
wi h D = 0.4 m, 13%
o males and 78% o
emales needed i
Humans Wa e le els a he
s ai s’ en ances below
0.3 m will gua an ee
sa e e acua ion
Na u al Haza ds
Table 7 (con inued)
App oach &
in ol ed Va iables
Au ho & Yea Inpu C i e ia Obse a ions Exposed Elemen s /
Subjec s
Risk Managemen
Coun e measu es
Expe imen al
Wa e eloci y (V)
Wa e dep h (D)
& subjec di e -
en ia ion by sex
and age
Ishigaki e al. (2010) De eloped an app oxi-
ma i e me hod (by
using young adul s
and adding weigh o
hei bodies and lim-
i ing hei mobili y)
o assess e acua ion
o aged people (70
yea s o mo e) and
di e en ia ed he
SFPUW c i e ia by
sex and age
M
0=0.25 m
3
m
,M0=0.2 m
3
m,
M
0=0.16 m
3
m
,M0=0.125 m
3
m,
M
0=0.1 m
3
m
,M0=0.08 m
3
m
· Fo males M0 = 0.125
is he sa e e acua ion
limi and M0 = 0.25
is he c i ical e acu-
a ion limi . · Fo
emales and elde ly
males
M0 = 0.1 is he sa e
e acua ion limi and
M0 = 0.2 is he c i i-
cal e acua ion limi
· Fo elde ly emales
M0 = 0.08 is he sa e
e acua ion limi &
M0 = 0.16 is he c i i-
cal e acua ion limi
Humans Risk managemen coun-
e measu es should be
ocused on he mos
ulne able popula ion:
aged adul s, child en
and people wi h
handicaps
Nume ical
S ai s slope (°)
Wa e dep h (D)
Lee e al. (2016) E alua ed slope e ec s
using h ee di e en
s ai s models wi h
slopes o 23.3°,
27.2°, and 32.7°
· The au ho s con-
cluded ha s ai s
slope is no as el-
e an as wa e dep h
o lood- ela ed
haza d assessmen
du ing human e acu-
a ion o unde g ound
s ai s. · Wi h a wa e
dep h D = 0.36 m
e en young males
will ace oubles
wi hou any help
N/A Wa e dep h o e
unde g ound s ai s
should be kep below
0.2 m o people’s sa e
e acua ion
Na u al Haza ds
Table 7 (con inued)
App oach &
in ol ed Va iables
Au ho & Yea Inpu C i e ia Obse a ions Exposed Elemen s /
Subjec s
Risk Managemen
Coun e measu es
Expe imen al
Wa e dep h (D)
Baba e al. (2017) Expanded he numbe
o es ed subjec s
con inuing wi h
Ishigaki e al. (2005)
expe imen al cam-
paign and included
a new expe imen :
e acua ion om ca s
· 100 subjec s we e
es ed including 11
child en aged 8,
and 3 child en aged
12. · 44 males and
12 emales we e
es ed ying o open
a oom’s doo . ·
Concluded ha he
c i ical lood dep h
o emales and
males o e acua e
s ai s a e 0.3 m and
0.4 m espec i ely
Humans Risk managemen coun-
e measu es should be
ocused on he mos
ulne able popula ion:
aged adul s, child en
and people wi h
handicaps
Na u al Haza ds
is sa e. This di e s om o he u ban a eas in which hese alues could ep esen a haza d-
ous zone depending on he au ho s’ limi . Mo e han 0.25m o wa e dep h wi h eloci ies
highe han 2.0m/s in plain and mild slope a eas ep esen haza dous condi ions o all
limi s and his c i ical condi ion could be ob ained wi h less han 0.15m wa e dep h and
eloci ies o 4.5m/s. In con as , he haza d le el o hese wa e dep hs and eloci ies in
s ai s depends on he selec ed c i e ia.
In he case o looded s ai s, he haza dous condi ions appea ed wi h wa e dep hs om
0.36m onwa ds and eloci ies g ea e han 4.5m/s. The e o e, he limi s o sa e e acua-
ion conside ing all he s udied c i e ia in s ai s will be 0.36m o wa e dep h and 4.5m/s
o eloci y. The unce ain y zone allows highe wa e dep hs o be conside ed as possibly
sa e compa ed o he plain/mild slope a eas in u ban en i onmen s bu limi s eloci ies o
a maximum o 4.5m/s. To de e mine which o hese c i e ia ma ches he bes lood si ua-
ions in s ai s is necessa y o iden i y ins abili y zones along he s ai s unde speci ic dis-
cha ges. These zones will p o ide hyd aulic pa ame e s (wa e dep h and eloci y) o allo-
ca e haza d poin s in Fig.27 ( igh ) and con as he haza d limi s p esen ed by he au ho s
and e alua e hei accu acy.
3.2 Fu u e esea ch lines acco ding o his e iew
Al hough all hese s udies ha e been use ul and success ully applied o analyse di e en
si ua ions, he comp ehension o some challenges and de ails s ill needs o be add essed o
ensuing esea ch. Acco ding o he c i ical e iew o his a icle, he ollowing poin s could
be s udied in he u u e:
(1) All he expe imen al campaigns ha e been de eloped unde going he idealisa ion ha
e acua ion happens wi h jus one single pe son climbing he s ai s a a ime, bu as
concluded by se e al au ho s, du ing eme gency e en s, unde g ound spaces could be
c owded and se e al people will y o e acua e simul aneously (Jiang e al. 2014; A ci
and Ozbulu 2018; Okamo o e al. 2022). A deep unde s anding o how his human-
luid in e ac ion can al e sa e y condi ions es ablished in he a o emen ioned c i e ia is
o ele ance. This pa could be handled wi h expe imen al and nume ical campaigns
ha include wo o mo e people on he s ai s a he same ime.
Fig. 27 Rep esen a ion o haza d limi s in plane/mild-slope a eas (le ) and s ai s ( igh )

Na u al Haza ds
(2) Cha ac e isa ion o ins abili y zones is c ucial o e i y haza dous condi ions imple-
men ing haza d poin s and con as ing hem agains he ecommended sa e y c i e ia.
To do so, u u e expe imen al campaigns mus p o ide his in o ma ion.
(3) E alua e lood- ela ed haza d when humans ansi s ai s no only in unde g ound
spaces. Ci ies wi h hilly a eas usually ha e s ai s ha can also ace lood e en s. Fo
ins ance, his is he case o he s epped s ee s ai s in Is anbul, Tu key s udied by
Hala e al. (2021). Haza d assessmen based on p e iously men ioned c i e ia could
be implemen ed in such s ai s. Maybe some c i e ion could be gene alized o s ai s no
jus loca ed in unde g ound spaces bu also in open a eas and he en i e u ban clus e .
(4) The s udy ca ied ou by Kim e al. (2018) men ioned ha unde looding condi ions
in which he low is a ec ed only by a mosphe ic p essu e, lood- ela ed haza d du ing
he e acua ion o s ai s could be de ined using jus wa e dep h because each one has
a limi ed eloci y in he s ai s, s ep by s ep. Fu he analysis is equi ed o de e mine
how i is ela ed o he s ai ’s cha ac e is ics like shape and slope. This is wo h s udy-
ing in u he esea ch ei he by expe imen al s udies, by nume ical models o e en by
combined campaigns.
(5) The possibili y ha e acuees ha e o ace objec s anspo ed by he lux while climbing
he s ai s and how his could a ec hei sa e y o s abili y ha e no been s udied. The
only a ailable in o ma ion is he expe imen al campaign pe o med by Ribei o e al.
(2021) which p esen ed a me hodology o analyse 5 p isma ic solids in a low o e
scaled s ai s assessing ins abili y h ough semi-empi ical dimensionless o mulas. As
a pa icula i y, o cap u e pa o he low a d aining g id was added o ep esen he
“d aining s ai cases”, his allows he simul aneous use o he s ai s as wa e d ainage
and human locomo ion (Mangie i 2014). Two ela ed possible esea ch lines could
su ge: one o e alua e he possibili ies o e ed wi h he implemen a ion o d aining
s ai s in unde g ound spaces o educe he lux in s ai s and he e alua ion o he ea-
sible in e ac ion be ween human beings and loa ing objec s du ing he e acua ion o
unde g ound spaces.
(6) Al hough he impo ance o e ec i e communica ion has been men ioned because i
highly con ibu es o educing social ulne abili y (Ma anzoni e al. 2022), he de el-
opmen o some guidance o aising public awa eness and consequen ly imp o ing
he adap i e capaci y o subjec s o ace c i ical e en s such as unde g ound looding
is s ill needed. The c ea ion o clea ly unde s andable haza d maps and e acua ion
p ocedu es including signaliza ion ha could be easily in e p e ed by end-use s (mos
o hem non-expe s) should be p omo ed and be as simple as possible because i could
be a powe ul ool ha posi i ely in luences u ban esilience and gene al awa eness.
(7) I has been seen ha he calcula ion o he equi ed ime o e acua e unde g ound
looded spaces could be complex. An es ima ion o he a e age speed o people du -
ing he e acua ion o looded s ai s unde di e en wa e dep hs could be a use ul ool
o help simpli y he complexi y o his calcula ion. The assump ion ha he equi ed
ime can be seen as a sum o di e en in e als could be summa ized as (i) ecogni ion
and decision-making in e al, (ii) e acua ion o plane a eas, and (iii) e acua ion o
s ai s. Ha ing de ined he i s in e al, he dis ance o he a hes plane a ea, and he
o al dis ance o una oidable s ai s o be e acua ed. In he case o he second and hi d
in e als, mul iplying hem by he human a e age speed ( ela ed o a speci ic wa e
dep h) in each scena io could help o gi e an o e all e acua ion ime ha simpli ies
calcula ions. This could gi e policymake s, s akeholde s, and escue se ices cu ing-
edge knowledge abou e acua ion ime o an app op ia e esponse.
Na u al Haza ds
3.3 Conclusion
Due o he g owing in e es in esea ching his ield mainly because o he appea ance
o mo e ecu en ca as ophic e en s ha a ec unde g ound a eas. This e iew could
be o g ea in e es o ill some knowledge gaps ha need o be add essed o imp o e
esilience in u ban a eas and consequen ly human sa e y. Speci ically, in Eu ope, no
ela ed s udies we e ound ocusing on he sa e y e acua ion o unde g ound looded
s ai s. Wi h he occu ence o u ban loods ha a e ecu en ly a ec ing me o s a ions
in Eu opean ci ies, his knowledge and i s dissemina ion a e o g ea ele ance o he
p esen and u u e. I will help o gua an ee a p ope adap a ion o he unde g ound
in as uc u e ha in u n will help o ace lood scena ios amids clima e change con-
ex in a mo e esilien manne .
The goal o his e iew is o p o ide a consul ing e e ence o anyone in e es ed. The
main s udies aiming o e alua e lood- ela ed haza d du ing he human e acua ion o
s ai s and de ine sa e y c i e ia a e p esen ed based on hei app oaches. Also, he subse-
quen s udies ha complemen o help o de ail he p e ious main esea ch on his phe-
nomenon and how i a ec s people ha e been conside ed. The discussion session o e s
an o e iew o he limi a ions o hese s udies, compa isons wi h haza d limi s in o he
u ban a eas and u u e esea ch lines o be conside ed. This aims o con inue sp eading
he a ailable in o ma ion and esea ch. Thus, i is expec ed ha new con ibu ions in he
s udy o lood- ela ed haza d du ing unde g ound e acua ion h ough s ai s migh be
encou aged, p o iding aluable in o ma ion ha could be simply ansmi ed o s ake-
holde s and non-expe s.
As i was de ailed, al hough unde g ound s ai s a e encompassed in he u ban clus e
hei haza d limi s based on wa e dep h and eloci y di e om hose p esen ed o
plane and mild slope a eas, his di e en ia ion needs o be esea ched in de ail. Besides,
among he u u e esea ch lines, some equi e u gen a en ion. Fo ins ance, i is pa a-
moun o de elop esea ch based on he assump ion ha du ing eme gency e en s, se -
e al people will y o e acua e unde g ound s ai s simul aneously and iden i y he inci-
dence o he human- luid in e ac ion on sa e e acua ion. Also, i is u gen o iden i y he
ins abili y zones along he s ai s o know whe e a e he majo complica ions du ing an
e acua ion eme gency. This could help o de ail u u e eme gency e acua ion plans.
Au ho ’s con ibu ion Concep ualiza ion: CHAU, BR, JTÁ, and EM-G; Li e a u e sea ch: CHAU; da a
Analysis: CHAU; In es iga ion: CHAU; Me hodology: CHAU, BR, JTA, and EM-G; Supe ision: BR, JTÁ,
and EM-G Visualiza ion: CHAU; W i ing—o iginal d a : CHAU; W i ing— e iew & edi ing: CHAU, BR,
JTÁ, and EM-G.
Funding Open Access unding p o ided hanks o he CRUE-CSIC ag eemen wi h Sp inge Na u e. This
wo k was suppo ed by he Spanish na ional esea ch p ojec PID2019-110965RB-I00 “Analysis o lood
haza d conside ing ehicles and o he loa ing elemen s”.
Decla a ions
Con lic o in e es The au ho s decla e ha hey ha e no known compe ing inancial in e es s o pe sonal
ela ionships ha could ha e appea ed o in luence he wo k epo ed in his e iew.
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Re e ences
Apa icio U ibe CH, Bonilla B enes R, Hack J (2022) Po en ial o e o i ed u ban g een in as uc u e o
educe uno - a model implemen a ion wi h si e-speci ic cons ain s a neighbo hood scale. U ban
o U ban G een. h ps:// doi. o g/ 10. 1016/j. u ug. 2022. 127499
A ci O, Ozbulu O (2018) Th ea and ulne abili y isk assessmen o exis ing subway s a ions: a sim-
pli ied app oach. Case S ud T ansp Policy 6(4):663–673. h ps:// doi. o g/ 10. 1016/j. cs p. 2018. 08. 005
Baba Y, Ishigaki T, Toda K (2017) Expe imen al s udies on sa e y e acua ion om unde g ound spaces
unde inunda ed si ua ions. J Jpn Soc Ci il Eng 5(1):269–278. h ps:// doi. o g/ 10. 2208/ jou n alo j
sce.5. 1_ 269
BBC News (2021a) China loods: 12 dead in Zhengzhou ain and housands e acua ed in Henan. h ps://
www. bbc. com/ news/ wo ld- asia- china- 57861 067
BBC News (2021b) S o m Ida: Floodwa e pou s in o New Yo k Ci y subway s a ion. h ps:// www. bbc.
com/ news/ a / wo ld- us- canada- 58418 627
Be na dini G, Quaglia ini E, D’O azio M, B occhini M (2020) Towa ds he simula ion o lood e acu-
a ion in u ban scena ios: expe imen s o es ima e human mo ion speed in loodwa e s. Sa e y Sci.
h ps:// doi. o g/ 10. 1016/j. ssci. 2019. 104563
BUEDRI (Beijing U ban Enginee ing Design & Resea ch Ins i u e Co., L d.) (2005) Code o design o
me o (In Chinese)
CCIDUS (Commi ee o Coun e measu es agains Inunda ion Disas e s in Unde g ound Spaces). (2002).
Guideline o Measu es agains Inunda ion o Unde g ound Spaces. Minis y o Land, In as uc-
u e, T anspo and Tou ism (MLIT), Japan (in Japanese)
Chanson H (1993) S epped spillway lows and ai en ainmen . J Ci Eng 20(3):422–435
Chanson H (2001) Cha ac e is ics o skimming low o e s epped spillways. J Hyd aul Eng-Asce
126(11):860–873. h ps:// doi. o g/ 10. 1061/ (ASCE) 0733- 9429(2000) 126: 11(860)
Cox RJ, Shand TD, Blacka MJ (2010) Aus alian Rain all and Runo Re ision P ojec 10: App op ia e
Sa e y C i e ia o People, S age 1 epo P10/S1/006, p epa ed by he Wa e Resea ch Labo a o y,
Uni e si y o New Sou h Wales, Sydney
Cox RJ, Yee M, Ball J (2004) Sa e y o People in Flooded S ee s and Floodways. In: 8 h Na ional Con-
e ence on Hyd aulics in Wa e Enginee ing, Gold Coas . The Ins i u ion o Enginee s, Aus alia
CRED-UNDRR (2020) The human cos o disas e s: An o e iew o he las 20 yea s (2000–2019).
Cen e o Resea ch on he Epidemiology o Disas e s - UN O ice o Disas e Risk Reduc ion.
h ps:// www. und . o g/ media/ 48008/ downl oad? s a Downl oad= ue
Dias C, Rahman NA, Zai e A (2021) E acua ion unde looded condi ions: expe imen al in es iga ion
o he in luence o wa e dep h on walking beha io s. In J Disas e Risk Reduc . h ps:// doi. o g/ 10.
1016/j. ijd . 2021. 102192
El Mundo (2022a) Las peo es llu ias en 80 años en Co ea del Su dejan al menos 8 mue os. h ps://
www. elmun do. es/ in e nacio nal/ 2022/ 08/ 09/ 62 22 ca2 d dd b 92d8b 45ba. h ml
El Mundo (2022b) Pa ís, colapsada po las ue es llu ias y el ien o. h ps:// www. elmun do. es/ in e
nacio nal/ 2022/ 08/ 17/ 62 c9 08 e4 d4d84 8498b 45a3. h ml
Flow Science, Inc., San a Fe, NM, USA.FLOW-3D®Ve sion 2023R1 (2023)
Fo e o O iz E, Ma ínez Goma iz E (2020) Haza ds h ea ening unde g ound anspo sys ems. Na
Haza ds. h ps:// doi. o g/ 10. 1007/ s11069- 020- 03860-w
Fo e o-O iz E, Ma ínez-Goma iz E, Cañas Po cuna M (2020a) A e iew o lood impac assessmen
app oaches o unde g ound in as uc u es in u ban a eas: a ocus on anspo sys ems. Hyd ol Sci
J 65(11):1943–1955. h ps:// doi. o g/ 10. 1080/ 02626 667. 2020. 17844 24
Fo e o O iz E, Ma ínez Goma iz E, Po cuna MC, Loca elli L, Russo B (2020b) Flood isk assessmen
in an unde g ound ailway sys em unde he impac o clima e change-A case s udy o he Ba ce-
lona Me o. Sus ainabili y (Swi ze land). h ps:// doi. o g/ 10. 3390/ su121 35291
Fos e DN, Cox RJ (1973) S abili y o Child en on Roads Used as Floodways. Technical Repo
No.73/13, Wa e Resea ch Labo a o y o he Uni e si y o New Sou h Wales, Manly Vale, Aus alia
Na u al Haza ds
Goméz M (2008) Cu so de hid ología U bana (7ª Edición). Uni e i a Poli ècnica de Ca alunya, Ba ce-
lona, Flumen Resea ch Ins i u e
Go oh H, Ika i H, Sakai T, Tanioka H (2006) Compu a ion mechanics o a o ce on a human leg in low
o e an unde g ound s ai case in u ban lood. P oc Hyd aul Eng 50:865–870. h ps:// doi. o g/ 10.
2208/ p ohe. 50. 865
Goyal T, Kahali D, Ras ogi R (2020) Analysis o pedes ian mo emen s on s ai s a me o s a ions.
T ansp Res P oc 48:3786–3801. h ps:// doi. o g/ 10. 1016/j. p o. 2020. 08. 040
Hala OM, Ci i ci İ, Yucel G (2021) Modelling o u ban looding and wa e all e ec on s epped s ee s in
Is anbul, Tu key. Eskişehi Techn Uni J Sci Technol A Appl Sci Eng 22(2):148–159. h ps:// doi. o g/
10. 18038/ es ub da. 811503
Heida i S, Babo T, De Cas o P, To S, Cu no M (2016) Sex and gende equi y in esea ch: a ionale
o he SAGER guidelines and ecommended use. Res In eg i y Pee Re . h ps:// doi. o g/ 10. 1186/
s41073- 016- 0007-6
Hou J, Chen G, Zhang Y, Li B, Yang S, Tong Y, Zhang D, Fu D (2022) A simula ion s udy on isks o
pedes ian e acua ion om looded s ai cases o di e en slopes in he unde g ound space. Na Haz-
a ds 110(1):519–543. h ps:// doi. o g/ 10. 1007/ s11069- 021- 04956-7
Iagua Magazine (2021) Me o e inundaciones, una pelig osa combinación. h ps:// www. iagua. es/ no ic ias/
locken/ me o-e- inund acion es- pelig osa- combi nacion
ICC (In e na ional Code Council) (2011) In e na ional Building Code (IBC). (dis ibu ed by Cengage
Lea ning)
Ishigaki T, Toda K, Inoue K (2003) Hyd aulic model es s o inunda ion in u ban a ea wi h unde g ound
space. P oceedings o he IAHR wo ld Cong ess, Thessaloniki, G eece, 30:487–493
Ishigaki T, Nakagawa H, Baba Y (2004) Hyd aulic model es s and calcula ion o lood in u ban a ea wi h
unde g ound space. In: 4 h Cong ess o APD-IAHR, Hong Kong, 2:1411–1416
Ishigaki T, Baba Y, Toda K, Inoue K (2005) Expe imen al s udy on e acua ion om unde g ound space in
u ban lood. 31s IAHR Cong ess, pp 1116–1123
Ishigaki T, Toda K, Baba Y, Inoue K, Nakagawa H (2006) Expe imen al s udy on e acua ion om unde -
g ound space by using eal size models. P oc Hyd aul Eng 50:583–588. h ps:// doi. o g/ 10. 2208/ p ohe.
50. 583
Ishigaki T, Onishi Y, Asai Y, Toda K, Shimada H (2008a) E acua ion c i e ia du ing u ban looding in
unde g ound space. In: P oceedings o he 11 h In e na ional Con e ence on U ban D ainage Model-
ling, 7. Sco land, UK
Ishigaki T, Onishi Y, Baba Y, Toda K (2008b) C i e ion and i s applica ion o sa e y e acua ion du ing
unde g ound looding. P oc Hyd aul Eng 52:841–846. h ps:// doi. o g/ 10. 2208/ p ohe. 52. 841
Ishigaki T, Kawanaka R, Onishi Y, Shimada H, Toda K, Baba Y (2009) Assessmen o sa e y on e acua ing
ou e du ing unde g ound looding. ad ances in wa e esou ces and hyd aulic enginee ing. In: P o-
ceedings o 16 h IAHR-APD Cong ess and 3 d Symposium o IAHR-ISHS, pp 141–146. h ps:// doi.
o g/ 10. 1007/ 978-3- 540- 89465-0_ 27
Ishigaki T, Asai Y, Nakaha a Y, Shimada H, Baba Y, Toda K (2010) E acua ion o aged pe sons om inun-
da ed unde g ound space. Wa e Sci Technol. h ps:// doi. o g/ 10. 2166/ ws . 2010. 455
Ishigaki T, Kawanaka R, Ozaki T, Toda K (2016) Vulne abili y o unde g ound inunda ion and e acua ion
in densely u banized a ea. J Disas e Res 11(2):298–305. h ps:// doi. o g/ 10. 20965/ jd . 2016. p0298
Jiang LJ, Shao WY, Zhu DZ, Sun ZL (2014) Fo ces on su ace-pie cing e ical ci cula cylinde g oups on
looding s ai case. J Fluids S uc 46:17–28. h ps:// doi. o g/ 10. 1016/j. j lui ds u c s. 2013. 12. 011
Jonkman SN, Penning-Rowsell E (2008) Human ins abili y in lood lows. J Am Wa e Resou Assoc
44(5):1208–1218. h ps:// doi. o g/ 10. 1111/j. 1752- 1688. 2008. 00217.x
Joo J, Kim T-H (2015) An expe imen al s udy on e acua ion abili y du ing unde g ound space inunda ion. J
Ko ean Soc Haza d Mi ig 15(2):189–196. h ps:// doi. o g/ 10. 9798/ kosham. 2015. 15.2. 189
Ka onen T, Hepojoki A, Ko ola J, Hun a H-K (2000) The use o physical models in dam-b eak lood analy-
sis: escue ac ions based on dam-b eak lood analysis; Final Repo o Helsinki Uni e si y o Technol-
ogy; Helsinki Uni e si y o Technology: Helsinki, Finland
Kim M, Lee DH, Kim JS, Eom JH (2018) A s udy on e acua ion sa e y a inunda ed s ai s by using eal-
scale hyd aulic model expe imen . E3S Web o Con e ences. h ps:// doi. o g/ 10. 1051/ e3sco n / 20184
006016
K ame M, Chanson H (2018) T ansi ion low egime on s epped spillways: ai -wa e low cha ac e is ics
and s ep-ca i y luc ua ions. En i on J Fluid Mech 18(4):947–965
K očka D, Falcone RA, B ay M (2016) Flood haza d assessmen o ex eme lood e en s. Na Haza ds
84(3):1569–1599. h ps:// doi. o g/ 10. 1007/ s11069- 016- 2501-z
Na u al Haza ds
Leand o J, Bung DB, Ca alho R (2014) Measu ing oid ac ion and eloci y ields o a s epped spill-
way o skimming low using non-in usi e me hods. Exp Fluids 55(5):1732. h ps:// doi. o g/ 10. 1007/
s00348- 014- 1732-6
Lee DH, Kim M, Rhee DS (2016) E acua ion sa e y e alua ion o inunda ed s ai s using 3D nume ical
simula ion. In J Sma Home 10(3):149–158. h ps:// doi. o g/ 10. 14257/ ijsh. 2016. 10.3. 15
Lee HK, Hong WH, Lee YH (2019) Expe imen al s udy on he in luence o wa e dep h on he e acua ion
speed o elde ly people in lood condi ions. In J Disas e Risk Reduc . h ps:// doi. o g/ 10. 1016/j. ijd .
2019. 101198
Li Q, Xia J, Xie Z, Zhou M, Deng S (2022) Haza d and ulne abili y in u ban inunda ed unde g ound space:
Hyd odynamic analysis o human ins abili y o s ai way e acua ion. In J Disas e Risk Reduc . h ps://
doi. o g/ 10. 1016/j. ijd . 2021. 102754
Liang C, Guo K, Guan M (2023) In luence o s ai case design on lood cha ac e is ics in unde g ound spaces.
Tunnell Unde g Space Technol. h ps:// doi. o g/ 10. 1016/j. us . 2023. 105511
Lin Z, Hu S, Zhou T, Zhong Y, Zhu Y, Shi L, Lin H (2022) Nume ical simula ion o lood in usion p ocess
unde mal unc ion o lood e aining acili ies in complex subway s a ions. Buildings 12(6):853. h ps://
doi. o g/ 10. 3390/ build ings1 20608 53
Lind N, Ha o d D, Assa H (2004) hyd odynamic models o human s abili y in a lood. J Am Wa e Resou
Assoc 40(1):89–96. h ps:// doi. o g/ 10. 1111/j. 1752- 1688. 2004. b010 12.x
Lo e RJ, Ab SR, Wi le RJ, Taylo A (1989) Human s abili y in a high lood haza d zone. AWRA Wa e
Resou Bull 25(4):881–890. h ps:// doi. o g/ 10. 1111/j. 1752- 1688. 1989. b054 04.x
Lyu HM, Sun WJ, Shen SL, A ul ajah A (2018) Flood isk assessmen in me o sys ems o mega-ci ies using
a GIS-based modeling app oach. Sci To al En i on 626:1012–1025. h ps:// doi. o g/ 10. 1016/j. sci o en .
2018. 01. 138
Mangie i LSG (2014) A aliação dos sis emas de escada ias e ampas d enan es implan adas em assen amen-
os espon âneos na cidade do Sal ado - Bahia. Re is a Ele ônica De Ges ão E Tecnologias Ambien ais.
h ps:// doi. o g/ 10. 9771/ ges a. 2i1. 11977
Ma anzoni A, D’O ia M, Rizzo C (2022) Quan i a i e lood haza d assessmen me hods: a e iew. J Flood Risk
Manag. h ps:// doi. o g/ 10. 1111/ j 3. 12855
Ma ínez-Goma iz E, Gómez M, Russo B (2016) Expe imen al s udy o he s abili y o pedes ians exposed o
u ban plu ial looding. Na Haza ds 82(2):1259–1278. h ps:// doi. o g/ 10. 1007/ s11069- 016- 2242-z
Ma ínez-Goma iz E, Loca elli L, Gue e o M, Russo B, Ma ínez M (2019) Socio-economic po en ial impac s
due o u ban plu ial loods in Badalona (Spain) in a con ex o clima e change. Wa e (Swi ze land)
11(12):2658. h ps:// doi. o g/ 10. 3390/ W1112 2658
Ma suo K, Na ainia L, Yamada F (2011) Flood and e acua ion simula ions o u ban looding ela ed pape s
lood and e acua ion simula ions o u ban looding, pp 391–398
MOHURD (Minis y o Housing and U ban- u al De elopmen o he People’s epublic o China) (2013) Code
o design o ci il buildings. Chinese A chi ec u e and Building P ess (in Chinese)
Monjo R, Loca elli L, Milligan J, To es L, Velasco M, Gai án E, Pó oles J, Redola D, Russo B, Ribalaygua
J (2023) Es ima ion o u u e ex eme ain all in Ba celona (Spain) unde mono ac al hypo hesis. In J
Clima ol 43(9):4047–4068. h ps:// doi. o g/ 10. 1002/ joc. 8072
Musolino G, Ahmadian R, Falcone RA (2020) Compa ison o lood haza d assessmen c i e ia o pedes ians
wi h a e ined mechanics-based me hod. J Hyd ol X. h ps:// doi. o g/ 10. 1016/j. hyd oa. 2020. 100067
Nakasaka Y, Ishigaki T (2021) Vulne abili y o mega unde g ound inunda ion and e acua ion assuming de as-
a ing u ban lood. J Disas e Res 16(3):321–328. h ps:// doi. o g/ 10. 20965/ jd . 2021. p0321
Nakasaka Y, Ishigaki T, Kawanaka R (2020) A s udy on sa e e acua ion om inunda ed unde g ound mall by
a mul i-agen model. 22nd Cong ess o he In e na ional Associa ion o Hyd o-En i onmen Enginee ing
and Resea ch-Asia Paci ic Di ision, IAHR-APD 2020: C ea ing Resilience o Wa e -Rela ed Challenges.
Sappo o, Japan h ps:// www. iah . o g/ lib a y/ in o ? pid= 7627
Nanía LS (1999) Me odología numé ico expe imen al pa a el análisis del iesgo asociado a la esco en ía plu-
ial en una ed de calles. Technical Uni e si y o Ca alonia, Ba celona, Spain, PhD esis
Okamo o T, Wa anabe C, Oka S (2022) Expe imen s udy on alling down isk du ing e acua ion in unde -
g ound lood. J Jpn Soc Ci Eng Se . F2 (Unde g ound Space Resea ch), 78(1):1–8. h ps:// doi. o g/ 10.
2208/ jscej us . 78.1_1
Onishi Y, Ishigaki T, Baba Y, Toda K (2007) Di icul y o e acua ion du ing unde g ound inunda ion and opin-
ions o use s on u ban lood. P oc Hyd aul Eng 51:559–564. h ps:// doi. o g/ 10. 2208/ p ohe. 51. 559
Qu Y, Gao Z, Xiao Y, Li X (2014) Modeling he pedes ian’s mo emen and simula ing e acua ion dynamics on
s ai s. Sa Sci 70:189–201. h ps:// doi. o g/ 10. 1016/j. ssci. 2014. 05. 016
Ribei o HDB, Simões ALA, Kelly LDD, Mangie i LSG, Schulz HE, Schulz HE (2021) S abili y o solids in
s epped lume nappe lows: subsidies o human s abili y in lows. J Appl Fluid Mech 14(3):681–690.
h ps:// doi. o g/ 10. 47176/ ja m. 14. 03. 31815

Na u al Haza ds
Russo B (2009) Design o su ace d ainage sys ems acco ding o haza d c i e ia ela ed o looding o u ban
a eas. [Doc o al hesis, Technical Uni e si y o Ca alunya]. h ps:// dialn e . uni i oja. es/ se l e / esis? codigo=
258828
Russo B, Gómez M, Macchione F (2013) Pedes ian haza d c i e ia o looded u ban a eas. Na Haza ds
69(1):251–265. h ps:// doi. o g/ 10. 1007/ s11069- 013- 0702-2
Russo B, Velasco M, Loca elli L, Sunye D, Yube o D, Monjo R, Ma ínez-Goma iz E, Fo e o-O iz E,
Sánchez-Muñoz D, E ans B, Gómez AG (2020a) Assessmen o u ban lood esilience in Ba celona o
cu en and u u e scena ios. The RESCCUE P ojec . Sus ainabili y (Swi ze land) 12(14):5638. h ps://
doi. o g/ 10. 3390/ su121 45638
Russo B, Velasco M, Monjo R, Ma ínez-Goma iz E, Sánchez D, Domínguez JL, Gabàs A, Gonzalez A (2020b)
E aluación de la esiliencia de los se icios u banos en e a episodios de inundación en Ba celona. El
P oyec o RESCCUE. Ingenie ía Del Agua 24(2):101. h ps:// doi. o g/ 10. 4995/ ia. 2020. 12179
Shao WY (2010) C i ical ain all in ensi y o sa e e acua ion om unde g ound spaces wi h lood p e en ion
measu es. J Zhejiang Uni , Sci, A 11(9):668–676. h ps:// doi. o g/ 10. 1631/ jzus. A1000 137
Shand TD, Cox RJ, Smi h G, Blacka M (2010) App op ia e c i e ia o he sa e y and s abili y o people in
s o mwa e design. P oceedings S o mwa e 2010. Na ional Con e ence o he S o mwa e Indus y Asso-
cia ion, pp 1–12
Shao WY, Jiang LJ, Zhang YP, Zhu DZ, Sun ZL (2014) Hyd aulic ea u es o ai -wa e mix u e low on s ai -
case wi h es pla o ms. J Hyd aul Eng 140(6):04014016. h ps:// doi. o g/ 10. 1061/ (ASCE) HY. 1943- 7900.
00008 72
Shao WY, Jiang LJ, Fang L, Zhu DZ, Sun ZL (2015) Assessmen o he sa e e acua ion o people walking
h ough looding s ai cases based on nume ical simula ion. J Zhejiang Uni , Sci, A 16(2):117–130. h ps://
doi. o g/ 10. 1631/ jzus. A1400 154
Shi ani M, Kesse wani G, Richmond P (2020) Agen -based modelling o pedes ian esponses du ing lood
eme gency: mobili y beha iou al ules and implica ions o lood isk analysis. J Hyd oin 22(5):1078–
1092. h ps:// doi. o g/ 10. 2166/ hyd o. 2020. 031
Takahashi S, Endoh K, Mu o ZI (1992) Expe imen al s udy on people’s sa e y agains o e opping wa es on
b eakwa e s
Takedomi K, Tachi K, Mizukusa K, Yoshi ani J (2001) An expe imen al s udy on he dange o walke s caused
by inunda ion low o e s ai s in o unde g ound space. P oceedings 56 h Annual Con e ence on JSCE (in
Japanese), Pa 2, 244–245
Tellez Al a ez J, Gomez M, Russo B (2022) Nume ical simula ion o he hyd aulic beha io o s epped s ai s in
a me o s a ion. Ad ance in Hyd oin o ma ics. Sp inge Wa e . Singapo e, pp 1001–1009. h ps:// doi. o g/
10. 1007/ 978- 981- 19- 1600-7_ 62
Témez JR (1992) Con ol del desa ollo u bano en las zonas inundables. Monog . de Col. Ing. Caminos, Cana-
les y Pue os Nº 10. Mad id, Spain, pp 105–115
Toda K (2007) U ban looding and measu es. J Disas e Res 2(3):143–152. h ps:// doi. o g/ 10. 20965/ jd . 2007.
p0143
Toda K, Inoue K, Oyagi R, Nakai T, Takemu a N (2004) Hyd aulic model es o inunda ion wa e in usion
in o complica ed unde g ound space (Japanese). P oceedings 4 h Cong ess o APD-IAHR, pp 1403–1409
To es V, Olaizola B (2023) La llu ia p o oca co es en el Me o de Mad id, la M-30 y la M-40 y 337 salidas de
los bombe os: “No podemos i i ahí.” El Mundo. h ps:// elpais. com/ espana/ mad id/ 2023- 09- 15/ co es-
en- dos- lineas- de- me o-y- en- la-m- 30-a- causa- de- la- llu ia. h ml#
Uni edNa ions D. o E. and S. A. P. D (2018) The Wo ld’s Ci ies in 2018. Da a bookle (ST/ESA/ SER.A/417).
h ps:// www. un. o g/ en/ de el opmen / desa/ popul a ion/ publi ca io ns/ pd / u ban iza i on/ he_ wo lds_ ci ies_ in_
2018_ da a_ bookl e . pd ISBN / ISSN 9789211483062
Wu Q, Yao Y, Zhao Y, Zhang X, Xu H, Du Y, Du Z (2021) Nume ical assessmen o he wa e - low haza d o
wo ke s in he wa e disas e o unde g ound mine. J Hyd oin 23(6):1325–1342. h ps:// doi. o g/ 10. 2166/
HYDRO. 2021. 044
Xia J, Falcone RA, Xiao X, Wang Y (2014) New c i e ion o he s abili y o a human body in loodwa e s. J
Hyd aul Res 52(1):93–104. h ps:// doi. o g/ 10. 1080/ 00221 686. 2013. 875073
Yee M (2003) Human s abili y in loodways. Unde g adua e honou s hesis, Uni e si y o New Sou h Wales,
Aus alia
Yoneyama N, Toda K, Aiha a S, Yamamo o D (2009) Nume ical analysis o e acua ion possibili y om small
unde g ound space in u ban lood. In: Ad ances in Wa e Resou ces and Hyd aulic Enginee ing - P o-
ceedings o 16 h IAHR-APD Cong ess and 3 d Symposium o IAHR-ISHS, pp 107–112. h ps:// doi. o g/
10. 1007/ 978-3- 540- 89465-0_ 21
Yu H, Liang C, Li P, Niu K, Du F, Shao J, Liu Y (2019) E alua ion o wa e logging isk in an u ban subway s a-
ion. Ad Ci Eng. h ps:// doi. o g/ 10. 1155/ 2019/ 53931 71
Na u al Haza ds
Zheng Y, Li XG, Jia B, Jiang R (2019) Simula ion o pedes ians’ e acua ion dynamics wi h unde g ound lood
sp eading based on cellula au oma on. Simul Model P ac Theo y 94:149–161. h ps:// doi. o g/ 10. 1016/j.
simpa . 2019. 03. 001
Publishe ’s No e Sp inge Na u e emains neu al wi h ega d o ju isdic ional claims in published maps and
ins i u ional a ilia ions.