Cha ac e iza ion o he scou ca i y e olu ion a ound a complex
b idge pie
Ped o Xa ie Ramos1, Ana Ma ga ida Ben o1, Rod igo Maia1 e João Ped o
Pêgo1
1Ci il Enginee ing Depa men , Uni e si y o Po o – Facul y o Enginee ing, Po o,
Po ugal and CIIMAR - In e disciplina y Cen e o Ma ine and En i onmen al
Resea ch
E-mail: jppego@ e.up.p
Abs ac
A s udy on he ime de elopmen o local scou a ound a complex pie was
de eloped using a small-scale model embedded in a sedimen bed. A o al o 15
labo a o ial es s we e pe o med a he Hyd aulics Labo a o y o he Facul y o
Enginee ing o he Uni e si y o Po o. The du a ion o each expe imen was
p e iously es ablished o p og essi ely cha ac e ize he scou ca i y. A e each
expe imen , he lume was g adually emp ied o acili a e he applica ion o close-
ange pho og amme y. The scou dep h alues esul ing om he applica ion o
pho og amme y a he pile cap on ag ee well wi h he alues ob ained
expe imen ally. The empo al de elopmen o he scou ca i y is p esen ed and
discussed. Empi ical o mulas o he scou ca i y ime de elopmen and o he
ela ion o scou dep hs o scou ca i y olumes we e ob ained. The ob ained h ee-
dimensional models can also be used o calib a ion and alida ion o nume ical
models.
Keywo ds: Complex b idge pie ; Local scou ; Scou ca i y; Pho og amme y,
Sedimen anspo
In oduc ion
Local scou a ound pie s is he main cause o s uc u al collapse o b idges, due o
ailu e o piles ounda ions in i e beds. In he ecen decades, many esea che s ha e
in es iga ed he low and he scou pa e ns a ound b idge pie s.
A la ge numbe o s udies ocused essen ially in he p edic ion o he scou
dep h in he base o pie s (B euse s e al. 1977; B euse s and Raudki i 1991; Mel ille
and Coleman, 2000). These s udies we e mos ly done by expe imen al means, esul ing
in semi-empi ical equa ions o he e alua ion o he maximum scou dep h (Da gahi,
1990). Fo a be e unde s anding o he low ield a ound pie s, se e al esea che s
ha e s udied he low ield a ound cylinde s and pie s (Da gahi, 1989; G a and
Yulis iyan o, 1998; E ema e al. 2006; Dey and Rayka , 2007). Mos o he men ioned
s udies ha e only analysed he local scou a ound single pie s. Howe e , b idge design
commonly leads o he conside a ion o complex pie ounda ions, mos usually
in eg a ing a bo om pile on he op o a pile g oup, in which he di ec applica ion o
he esul s de i ed om single pie s is mos o en un eliable (Lande s and Muelle ,
1996). Resea che s as Coleman (2005), A aie-Ash iani e al. (2010) and Mo eno e al.
(2012) ha e ocused hei s udies on he p edic ion o he maximum scou dep h a ound
pile g oups and complex pie s.
The p edic ion o in si u scou a b idge pie s using empi ical o mulas should be
done wi h cau ion since hey we e de i ed mainly om small-scale labo a o y
expe imen s. This led o he de elopmen o ma hema ical models capable o simula ing
he scou ing p ocess a b idge pie s, known in he li e a u e as Compu a ional Fluid
Dynamics (CFD) ools. Olsen and Melaaen (1993) de eloped a 3D model o scou
a ound a ci cula single pie . A compa ison wi h expe imen ally measu ed scou
pa e ns e ealed good ag eemen . Tseng e al. (2000) pe o med 3D calcula ions o he
low a ound a e ical wall-moun ed cylinde using la ge-eddy simula ion (LES),
alida ing he esul s agains Da gahi’s (1989) expe imen al da a. Abdelaziz (2011)
simula ed he low and he sedimen anspo a ound a ci cula pie o compa e wi h he
eloci y ields and he opog aphic da a expe imen ally ob ained by Unge and Hage
(2006).
Fo a well-calib a ed nume ical model, good expe imen al da a is essen ial. To
he au ho s’ knowledge, he e a e no de ailed ime measu emen s o he scou ca i y
geome y de elopmen in he icini y o a complex pie (see Figu e 1).
The main goal o he p esen s udy is he h ee-dimensional cha ac e iza ion o
he scou e olu ion a ound a complex pie by close- ange pho og amme ic means. The
applica ion o pho og amme y in his ield is s ill in he beginning (Rapp and Ede ,
2012), bu i has p o ed o p o ide eliable insigh s in o he whole scou ca i y
geome y, leading o a deepe unde s anding o such phenomena. I has mos ly been
used o measu e he scou ca i y a ound single pie s (P lege e al. 2010; Ede e al.
2011, Rapp e al. 2012). The p oposed me hodology will lead o an o iginal
expe imen al da ase as well as a se o empi ical ela ions o he scou pa e ns o be
la e used as a use ul inpu o nume ical simula ions.
Expe imen al Se up
Expe imen al appa a us
The expe imen s we e pe o med in a 32.2 m long and 1 m wide eci cula ion lume,
loca ed in he Hyd aulics Labo a o y o he Facul y o Enginee ing o he Uni e si y o
Po o (FEUP). Figu e 2 illus a es a gene al longi udinal iew o he expe imen al se up.
The side-walls a e made o glass o enable he isualiza ion o he low. The wa e is
eci cula ed om a ese oi by means o a cen i ugal pump g oup. The in low
discha ge was manually egula ed and con olled by means o wo elec omagne ic
lowme e s a he channel en ance. In he ups eam each o he lume, some channel
bed mac o ugosi ies we e designed o ensu e a u bulen low de elopmen . The low
dep h was adjus ed by means o an elec ic ga e a he downs eam end o he lume.
The app oach low eloci y (u = 0.327 ms-1) was se o be 97% o he c i ical low
eloci y calcula ed by Neil’s o mula (Neil, 1967). The e o e, a low dep h o 0.18 m
and a low discha ge o 0.059 m3s-1 we e imposed, gua an eeing clea -wa e low
condi ions o he expe imen s pe o med. The lume bo om was buil upon he o iginal
conc e e lume bo om in o de o ob ain wo sedimen boxes: one, o c ea e a sand pi
whe e he complex pie was ins alled and, he o he one o c ea e a sand ap whe e he
e oded sedimen s we e e ained (bo h sedimen boxes 0.35 m deep and 3.40 m long).
The sand ma e ial was cha ac e ized by a median diame e , D50, o 0.86 mm, a
g ada ion coe icien o he sedimen size dis ibu ion, σd, o 1.4 and a densi y, ρ, o
2650 kgm-3.
The geome ic cha ac e is ics and he posi ion ela i e o he ini ial i e bed o
he complex pie used in he pe o med expe imen s is depic ed in Figu e 3. The model
was buil o his pu pose wi h he column and he pile cap made o ac ylic glass and he
ou ounda ion piles o Poly inyl chlo ide (PVC). The column and he pile cap ha e
ounded edges. The s udied pie was placed in he sand pi on he channel midplane and
posi ioned in o de o expose hal o he pile cap heigh (0.029 m) o he low cu en
( he posi i e x-axis indica es he di ec ion o he low). In ag eemen wi h Teixei a
(2013) he highes scou dep hs occu ed o his con igu a ion o he complex pie .
Acco ding o Mo eno e al. (2012), he con ac ion and wall e ec s we e negligible o
he scou ing p ocess, since a ios o B/Dpc ≥10 and B/h≥5 we e gua an eed (B being he
lume wid h, Dpc he pile cap diame e and h he low dep h).
Expe imen al p ocedu e
The expe imen al es s equi ed he ollowing p e ious s eps: (i) ins alla ion o he
complex pie ; (ii) illing o he box pi wi h sand un il he adjacen conc e e bed le el
was eached; (iii) co e age o he complex pie icini y ini ial bed le el a ea wi h hin
geo ex ile, coupled o a me allic g id, o p eclude undesi able scou a he beginning o
he expe imen ; (i ) g adual opening o he al es un il he desi ed wa e dep h and
in low discha ge was eached; and, ( ) emo al o he geo ex ile plaques wi h he aid o
wo la e al wi es. Hence, he expe imen was immedia ely ini ia ed. In o al, 15
expe imen s we e pe o med o cha ac e ize he scou ca i y e olu ion. Each es
co esponded o a p e iously designa ed ime du a ion, in acco dance o p e-de ined
ime s eps o he scou ing p ocess. Be o e each expe imen un, he sand bed was
adjus ed and le elled a 0.029 m abo e he pile cap bo om. In e e y expe imen , he
idimensional econs uc ion o he scou hole was pe o med a e he low was
s opped and he lume was slowly made emp y.
Expe imen al me hodology
The objec i es o his in es iga ion included he measu emen o he scou dep hs a
di e en posi ions and he cha ac e iza ion o he scou ca i y geome y. The o me
was pe o med by means o a limnime e , enabling o measu e he scou dep h a he
pile cap on (c oss in Figu e 4), and by eading o he scale a ached o each
indi idual ounda ion pile; he la e was possible by close- ange pho og amme ic
means, enabling he quan i ica ion o he spa ial dis ibu ion o scou a ound he
complex pie componen s.
Fo he applica ion o pho og amme y, he scou hole and he su ounding
a ec ed a ea we e pho og aphed wi h a single digi al came a (Canon Powe Sho SX
160 IS), successi ely posi ioned in di e en spo s o co e he whole a ea o in e es . To
enable he spa ial e e ence accomplishmen , a se o g ound con ol poin s (ci cles in
Figu e 4) was conside ed.

The came a cap u es we e aken om a ho izon al pla o m, ela i ely close o
he sedimen bed (a a dis ance o app oxima ely 0.60 m), a e each expe imen . Due o
he di e en du a ion o he expe imen s, he numbe o pho os and he loca ion o he
g ound con ol poin s we e adjus ed acco ding o he a eal ex en and dep h o he scou
hole. The g ound con ol poin s consis ed in speci ic (and symme ical) poin s on wo
la e al ule s (see Figu e 4). The pho og amme ic p ocessing so wa e, used in his
esea ch was Agiso Pho oScan P o essional, Ve sion 1.0.4 (Agiso 2014b).Unlike o
adi ional pho og amme y, his so wa e nei he equi es he idimensional loca ion
and o ien a ion o he came a a image cap u e, no he idimensional loca ion o he
con ol poin s p io o he scene econs uc ion. Howe e , he con ol poin coo dina es
a e s ill equi ed in pos -p ocessing o ans o m he model om ela i e o absolu e
coo dina es (Wes oby e al. 2012).
The digi al ele a ion models (DEMs) we e ex ac ed and impo ed in o Global
Mappe (Ve sion 15.0), a GIS Da a p ocessing so wa e. The Global Mappe so wa e
allowed o pe o m he calcula ion o he bed ele a ion and he measu emen o he
scou ca i y olume as well as o pe o m a compa ison wi h he scou dep hs di ec ly
ead in he labo a o y.
Resul s and Discussion
Figu e 5 illus a es he de elopmen o he bed le el con igu a ion p o iles along he
cen eline o he complex pie a e 60 min., 8 hou s, 24 hou s, 72 hou s, 8 days and 11
days., no malized by he low dep h (cons an , h=0.18 m). These p o iles we e ob ained
by pho og amme y; he c oss do s e e o he scou dep h measu ed by he limnime e
(a he pile cap on , o each o he expe imen s) and he ci cle do s deno e he scou
dep hs ob ained by means o eading he ule scales a he ounda ion piles (when
possible). Signi ican conclusions can be d awn om he analysis o he ups eam
s e ch o he bed p o ile ime e olu ion (Figu e 5) such as i s maximum slope o
compa e wi h he angle o epose o he sand bed. The maximum slope o he ups eam
s e ch eached a alue o 74%, co esponding o an angle o 36.5°. This angle is abou
20% highe han he ypical alue o 30° o we sand. Resea che s as Roulund e al.
(2005) also epo ed ha du ing he de elopmen o a scou ca i y, some a eas a he
ups eam side show highe local bed slopes han he angle o epose. Two main easons
we e iden i ied o explain his phenomenon: he backwa d low a he base o he pile
e oding he oo o he ups eam slope o he scou ca i y, and he con inuous sedimen
supply o sedimen s in o he scou ca i y.
Rega ding he ime du a ion equi ed o he se ies’ end expe imen , he c i e ion
o Mel ille and Chiew (1999) was used. I co esponds o he ime a which he a e o
inc ease o scou does no exceed 5% o he ounda ion pile leng h and he low dep h in
a 24 hou s pe iod (in he p esen case, 0.05 m and 0.18 m, espec i ely). In he p esen
case, he end scou s age was eached a e 264 hou s (11 days) wi h a maximum scou
dep h o 19.8 cm a he on o he i s ounda ion pile (Figu e 6). I should be e e ed
ha he ounda ion piles we e numbe ed om ups eam (pile 1) o downs eam (pile 4).
As s a ed be o e, only he scou measu emen s a he pile cap on could (and we e)
pe o med a he beginning o each expe imen . The scou measu emen s a he
ounda ion piles we e only egis e ed as soon as he p ocess o he scou ca i y
de elopmen eached he on o each o he piles, whe e a ule was glued. A educ ion
o he scou dep h a e a e app oxima ely 50 hou s (pile 1 in Figu e 6) may be
explained by a po en ial sliding o he ups eam slope o he scou ca i y. On he p esen
s udy, he scou dep hs measu ed a e ele en days we e: 19.48 cm along he pile cap
on alignmen , 19.8 cm a he i s ounda ion pile on , 13.1 cm
a he second and 7.5 cm and 6.2 cm a he hi d and ou h, espec i ely. This same
complex pie con igu a ion had been s udied by Teixei a (2013). This au ho compu ed
he alues sugges ed o his con igu a ion by wo scou dep h p edic ion me hods
e e enced in he li e a u e, Richa dson and Da is (2001) and FDT (2010). The o me
sugges s a maximum scou dep h o a ound 19.8 cm while he la e gi es a alue o
20.5 cm. These alues a e e y close o he expe imen al ones ob ained in his wo k.
Figu e 7 compa es he scou dep h empo al de elopmen o he end o he
se ies expe imen (du a ion = 11 days) wi h he scou dep h achie ed o each o he
o he (14) expe imen s ( e e ed o as “o he es s”), ob ained by limnime e
measu emen s and by means o pho og amme y a he pile cap on .
The g aph sugges s ha he in e up ion o he expe imen al es s and he
emp ying o he lume ( o he pho og amme y applica ion) do no in e e e wi h he
scou ing p ocess since i yielded a good ag eemen be ween he h ee se o poin s
ep esen ed in Figu e 7.
In o de o s udy he gene a ion and ime e olu ion o he scou ca i y, digi al
ele a ion models we e p oduced a e each expe imen al un and adequa ely ea ed.
The co esponding g aphs o he ins an s conside ed in Figu e 5 a e p esen ed in Figu e
8 as a unc ion o bed ele a ion- o- low dep h a io. The bed ele a ion wi h espec o
he x-y-plane appea s in a g ey-scale ange depending on he le el o each poin
(no malized wi h he low dep h – h=0.18 m).
Al hough many s udies we e dedica ed o in es iga e he empo al e olu ion o
he scou dep h in he icini y o a complex pie , e y ew s udies ha e add essed he
h ee-dimensional cha ac e iza ion o he scou ca i y. To achie e his goal, he digi al
ele a ion model esul s we e used o compu e he olume o he scou ca i y. Figu e 9
shows he ca i y’s scou a e olume empo al e olu ion wi h espec o he ime
du a ion o he end o he se ies expe imen ( e=11 days).
As expec ed, conside able anspo o sedimen s occu ed du ing he i s ime
s eps o he scou ing p ocess (wi h scou a es o 63.4 and 54.4 cm3min-1, o he i s
wo poin s on he a le in Figu e 9). Then, he scou a e dec eased asymp o ically o a
alue o 4 cm3min-1 a he inal scou s age. The ca i y’s olume scou a e (S) ime
de elopmen da a, ep esen ed in Figu e 9, could i wi h a high co ela ion coe icien
( 2=0.9668) o an exponen ial unc ion (Equa ion 1):
𝑆 =𝜆(𝑡
𝑡𝑒)−0.336 (1)
whe e λ assumes he alue o 3.43 in he p esen s udy. Figu e 10 shows he
ela ion o he scou ed ca i y olume, V, wi h he maximum scou ed dep h, ds, a any
scou ing s age. These a iables we e no malized wi h espec o he co esponding end
s age, Ve and dse. The cu e, exp essed by equa ion (2), con i ms ha he scou ed
olume is p opo ional o he powe o 3 o he scou dep h, as e i ied by many
expe imen s.
𝑉
𝑉𝑒=(𝑑𝑠
𝑑𝑠𝑒)3
(2)
F om Figu e 10, i is clea ha he maximum scou dep h app oaches much
as e he co esponding end s age han he ca i y olume. The same pa ame e s a e
plo ed in Figu e 11 wi h espec o he ime no malized wi h he du a ion o he inal
se ies expe imen ( / e); he co esponding g aphs enhance he p e ious
conclusion.Besides he scou ca i y olume conside a ions ano he impo an analysis
pe o med conce ns he geome ic cha ac e iza ion o he scou ca i y. By he end o
each expe imen , o he scou ca i y ob ained, h ee di e en leng h and wid h
measu emen s we e conduc ed: ou o hem in speci ic loca ions (l1, l2, w1 and w2)
and he o he wo a he loca ions whe e he maximum wid h and leng h occu ed (lmax
and wmax). These a iables a e schema ically ep esen ed in Figu e 12 in acco dance
Figu e 3: Geome ic cha ac e is ics and posi ion ela i e o he ini ial i e bed o he complex pie (dimensions in
me e s).
Figu e 4: Scheme o he expe imen al da a collec ion. Came a posi ions (squa e boxes), g ound con ol poin s
(ci cles) and limnime e measu ing poin (c oss).
0.029
0.050
0.475
0.506
0.120
0.058
0.080
column
pile cap
pile ounda ion
z
y
x
0.180
z
yx
0.354

Figu e 5: Bed p o ile con igu a ion ime e olu ion along he complex pie cen eline.
13
24 5 6
-0.2
0
0.2
-0.4 =60 min.
13
245 6
-0.2
0
0.2
-0.4 =8 hou s
-0.6
13
24 5 6
-0.2
0
0.2
-0.4
=24 hou s
-0.6
13
2456
-0.2
0
0.2
-0.4
=72 hou s
-0.6
-0.8
1 32 4 5 6
-0.2
0
0.2
-0.4
=8 days
-0.6
-0.8
-1.0
-1.2
13
24 5 6
-0.2
0
0.2
-0.4
=11 days
-0.6
-0.8
-1.0
-1.2
x/h
z/h
Figu e 6: End expe imen (11 days): Scou dep h e olu ion a he pile cap on and a he piles on .
Figu e 7: Compa ison o he expe imen al app oaches: scou dep hs a he pile cap.
0
5
10
15
20
25
0.01 0.1 1 10 100 1000
Scou dep h (cm)
Time (h)
pile cap pile 1 pile 2 pile 3 pile 4
0
5
10
15
20
25
0.01 0.1 1 10 100 1000
Scou dep h (cm)
Time (h)
se ies' end expe imen
o he se ies o es s, by means o limnime e measu emen s
o he se ies o es s, by means o pho og amme y
Figu e 8: Digi al ele a ion models.
Figu e 9: Ca i y’s olume scou a e ime e olu ion.
Figu e 10: Rela ion be ween he scou dep h and olume a es o each expe imen .
Figu e 11: Rela ion be ween maximum scou dep h and olume a es o he end expe imen .
Figu e 12: Scheme o he ypical scou ca i y and cha ac e is ic geome ic dimensions.
0
0.2
0.4
0.6
0.8
1
1.2
0.0001 0.001 0.01 0.1 1
/ e
ds/dse V/Ve
lmax
wmax
Dpc (12 cm)
w1 w2
l2
l1