Technical Note
Valley Crossings and Flood Management
for Ancient Roman Aqueduct Bridges
Wayne F. Lorenz, P.E., M.ASCE1; and Phillip Wolfram, S.M.ASCE2
Abstract: Calculation of stormwater flow passage underneath two ancient Roman bridges supporting an aqueduct in southern France
provides insight into the Roman engineers’ design of aqueduct bridges. The bridges are quite different although the watersheds they cross
have similar characteristics. At a height of 5.4 m (18 ft), the Simian Bridge has four arches while the Charmassone Bridge [height of 2 m
(7 ft)] has a culvert to pass stormwater flows. The Simian Bridge was designed to maintain the needed elevation across the valley by use
of arches, and it easily passes flood flows. In contrast, the Charmassone Bridge may have been designed to manage flood flows as evidenced
by the sizing of its culvert and use of buttressing to support upstream hydrostatic pressures due to stormwater retention behind the bridge.
DOI: 10.1061/(ASCE)IR.1943-4774.0000359. © 2011 American Society of Civil Engineers.
CE Database subject headings: Stormwater management; Water management; Aqueducts; Floods; Streamflow; Historic sites; Bridges;
France.
Author keywords: Aqueducts; Barbegal; Roman; Stormwater management; Water management; Bridges.
Introduction
Roman Engineering Approach
Roman engineers designed and built many aqueduct and bridge
structures subject to large stormwater runoff flows and floods.
Many of these structures have withstood storm events for millennia
and are still standing today. The stormwater runoff that occurred
in valleys of the Roman Empire was an obstacle to the aqueducts
bringing water to Roman cities. There are many well-known examples of ancient Roman aqueduct valley crossings with different solutions to this problem; among the most iconic are the Pont Du Gard
near Nîmes, France, the inverted siphon at Lyon, France, and the
Monumental Aqueduct of Segovia in Spain. There were also many
other small valley crossings, perhaps not as impressive as these
great monuments, but just as interesting to study from a stormwater
engineering standpoint.
For example, the Barbegal Aqueduct System located in southern
France included a number of aqueduct bridges that cross small valleys, some of which are still intact. Two of these bridges are quite
different in design even though the valleys they cross have some
similar characteristics. Calculations of stormwater flows and culvert hydraulics demonstrate that the height of the valley crossing
and the necessity to pass stormwater flows were clearly design considerations for these aqueduct bridges. Each of these design
considerations will be considered in turn.
On the basis of the archaeological record of Roman aqueducts, the
Romans appear to have used the height of a valley crossing as a
guideline for the type of aqueduct crossing to be used. It is known
from field evidence that Roman engineers used one of four approaches to preserve slope or, when the terrain dictated, the need
for a direct crossing:
1. Continuous solid stone and/or masonry bridge with a culvert to
pass stormwater flows,
2. Single-tiered load-bearing arch bridge,
3. Multitiered, load-bearing arch bridge, or
4. Inverted siphon.
For small valley crossings, a continuous solid bridge with a
culvert was favored by Roman engineers (Chanson 2002). On the
basis of our observations, culverts were used for crossing heights
up to 2 m (7 ft), and the height of the aqueduct crossing above the
stream or drainage bed may have been a Roman engineering guideline for selecting the approach for the type of bridge. Continuous
solid bridges with culverts were used in several small valley aqueduct bridge crossings in the Barbegal Aqueduct System.
For valley crossing heights between 2 m (7 ft) and approximately 20 m (66 ft), a single-tiered arch bridge was used. Multitiered arches were used for bridges up to approximately 50 m
(164 ft). For heights above 50 m (164 ft), Roman engineers used
inverted siphons for a valley crossing (Hodge 2002). There were
several single-tiered arch bridge crossings in the Barbegal Aqueduct System. Two small watershed crossings on the Barbegal
Aqueduct System employing the first two listed approaches will
be considered.
1
Director of Roman Aqueduct Studies, Wright Paleohydrological
Institute, 2490 W. 26th Avenue, Suite 100A, Denver, CO 80211 (corresponding author). E-mail: [email protected]
2
Research Associate, Wright Paleohydrological Institute, 2490 W. 26th
Avenue, Suite 100A, Denver, CO 80211; and Ph.D. Student, Environmental
Fluid Mechanics Laboratory, Stanford Univ., Y2E2, 473 Via Ortega, Office
M-17, Stanford, CA 94305. E-mail: [email protected]
Note. This manuscript was submitted on December 15, 2009; approved
on February 9, 2011; published online on February 11, 2011. Discussion
period open until May 1, 2012; separate discussions must be submitted for
individual papers. This technical note is part of the Journal of Irrigation
and Drainage Engineering, Vol. 137, No. 12, December 1, 2011. ©ASCE,
ISSN 0733-9437/2011/12-816–819/$25.00.
Barbegal Aqueduct System
Located in the Provence region of France is an ancient Roman
water system that includes aqueducts and the largest industrial facility known from antiquity: the Barbegal Mill. The mill contained
16 water wheels to grind grain to provide flour to the city of Arleate
(Lorenz 2005). The aqueduct that provided the water to turn the
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Table 2. Stormwater Flow Calculations
Stormwater flow
Location
Simian Bridge
Charmassone Bridge
Fig. 1. (Color) Schematic map of Barbegal Mill and Aqueduct
System—Southern France near Arles
L/s
cfs
2,900
2,100
103
76
For modern civil engineers, the stormwater flows presented in
Table 2 that need to pass under the bridges are relatively modest and
indicative of the small drainage basins. The Charmassone Bridge’s
calculated flows (2,100 L/s) are approximately 70% of the Simian
Bridge stormwater flows.
Simian Bridge
millstones also provided domestic water to the city. Two aqueducts’
branches provided water from springs located on the north and
south flanks of the Alpilles mountains. The location and layout
of the Barbegal Aqueduct System are shown in Fig. 1.
Two Watersheds
Two bridges on the Barbegal Aqueduct System, called the Simian
and Charmassone bridges, are located on the north aqueduct of the
Barbegal System, as shown in Fig. 1. These bridges were selected
for investigation because they are relatively intact and are located in
two similar watersheds (Table 1), but employ different designs. The
watersheds are relatively small and fairly uniform with agriculture
and open space as land uses. The vegetation in these watersheds
includes olive groves and native shrubs. The similar watershed
characteristics also produce similar stormwater flows.
Watershed slopes were computed by considering the elevation
drop along the thalweg, starting from the ridge to basin bottom
as measured from 1∶25;000 topographic mapping by the French
Institut Geographique National (IGN). The upstream catchment
area was computed by delineating the basin ridge while on foot
through a geographic positioning system (GPS) in August 2005.
Geographic information system (GIS) methods were employed
to compute the area enclosed by this polygon.
Stormwater Flows
Stormwater flows resulting from a large storm event in the Simian
and Charmassone areas were calculated using the rational method
because these are both small watershed areas (less than 0:65 km2 ).
A runoff coefficient of 0.35 was assumed consistent with very tight
limestone soil conditions, farmland, and relatively steep slopes
[ASCE and Water Pollution Control Federation (WPCF) 1982]. An
upper-bound estimate of the runoff coefficient is 0.6, consistent
with the use of higher values for larger storms. Average and
monthly precipitation and storm intensity data were gathered from
eight sites within the Barbegal region. The average annual precipitation ranges from 500–700 mm (20–28 in.) with large storms that
can have rainfall intensities of 200 mm/h (8 in./h) or greater. Estimated stormwater flows for watersheds upstream of the Simian and
Charmassone bridges are presented in Table 2.
The Simian Bridge is located on the northern Barbegal aqueduct
at a distance of approximately 4 km (2.5 mi) northwest of the
Barbegal Mill. The bridge ruins have been studied by Bellamy
and Ballais (2000) and are shown in the photograph in Fig. 2.
The Simian Bridge is the larger of the two bridges and is 48 m
(157 ft) in length and about 5.4 m (18 ft) in height. It is composed
of a single tier of four arches that span the small valley.
Charmassone Bridge
The Charmassone Bridge is also located on the northern Barbegal
aqueduct approximately 1.6 km (1 mi) upstream of the Barbegal
Mill site. The smaller bridge is shown in the photograph in Fig. 3
and is approximately 30 m (100 ft) in length. The height of the
Charmassone Bridge is approximately 2 m (7 ft) from the stream
thalweg to the aqueduct channel invert.
There are several unique aspects to the Charmassone Bridge.
First, the bridge has a limestone block-type culvert to pass stormwater under the bridge. The carved limestone block, shown in the
photograph in Fig. 4, shows a curved haunch that is mounted on
two limestone blocks that provide additional area for passing
stormwater flows. The cross-sectional area of this culvert opening
is much smaller than the area that is provided by the four arches at
the Simian Bridge.
Another unique aspect of the Charmassone Bridge is that there
are four buttresses that are on the downstream facing of the bridge.
These buttresses have dimensions of approximately 1.3 m (4.3 ft)
by 1.8 m (5.9 ft), as shown in Fig. 5. Each buttress is tapered from
the top to the bottom.
Table 1. Upstream Watershed Characteristics
Location
Simian Bridge
Charmassone Bridge
Catchment area (km2 )
Average slope
0.15
0.11
0.045
0.034
Fig. 2. (Color) Simian Bridge (image by Wayne Lorenz)
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Table 3. Major Bridge Differences
Bridge opening area
to pass stormwater
Bridge heighta
Location
m2
ft2
m
ft
Simian Bridge
Charmassone Bridge
16.5
1.1
178
12
5.4
2
18
7
a
Stream thalweg to aqueduct invert.
Discussion
Fig. 3. (Color) Charmassone Bridge with buttresses on downstream
side of structure (image by Wayne Lorenz)
Fig. 4. (Color) Culvert under Charmassone Bridge (image by Wayne
Lorenz)
The stormwater retention behind the bridges can be determined by
considering the mass conservation balance between stormwater
flows and the flows transmitted underneath the bridge through
the arches or culvert. Details are presented in the Appendix. For
simplicity, we consider the range of rainfall intensities that result
in full flow through the openings and overtopping the aqueduct
bridges in Tables 4 and 5, respectively.
The Simian Bridge was designed with more than enough area
within the arches to freely pass stormwater flows from a large precipitation event because the maximum recorded storm is an order of
magnitude smaller than the storm intensity required for floodwaters
to reach the top of the arches.
However, the Roman engineers did not use this approach with
the design of the Charmassone Bridge. The culvert under the Charmassone Bridge will act as an orifice during periods of high stormwater. Because the maximum recorded stormwater intensity is
200 mm=h, water would back up behind the Charmassone Bridge,
perhaps even to overtop the aqueduct during a larger flood that
most likely occurred in the 1,900-year history of the bridge. It
is unclear whether the Roman engineers explicitly accounted for
the quantity of stormwater flow in the sizing of the culvert. The
Charmassone Bridge has four buttresses on the downstream side
of the bridge. The buttresses appear to be of original construction
and are unique among known remnants on the Barbegal system.
Therefore, Roman engineers may have designed the Charmassone
Bridge to detain stormwater behind the bridge structure just as
modern stormwater engineers do to control flood flows. On the
basis of inspection, the buttresses were designed to easily withstand
the hydrostatic forces of stormwater detained upstream of the
bridge. In addition, buttresses of this type (e.g., on the downstream
side of the structure) are known to have been used by Roman
engineers for dam embankments to store water.
Table 4. Rainfall Intensities for Full Flow in Arches or Culvert
Rainfall intensity (mm=h)
Location
Simian Bridge
Charmassone Bridge
a
Minimuma
Maximumb
3,200
190
6,300
360
CB ¼ 0:6; CC ¼ 0:7.
C B ¼ 0:35; C C ¼ 0:8.
b
Fig. 5. Charmassone Bridge plan
Table 5. Rainfall Intensities for Overtopping of Aqueduct
Rainfall intensity (mm=h)
Methodology
Location
The Simian and Charmassone bridges are two very different structures that cross watersheds that have similar characteristics. The
area of bridge openings presented in Table 3 shows that the culvert
under the Charmassone Bridge has 7% of the area that is available
in the arches under the Simian Bridge.
Simian Bridge
Charmassone Bridge
a
Minimuma
Maximumb
7,800
260
9,300
520
CB ¼ 0:6; CC ¼ 0:7.
C B ¼ 0:35; C C ¼ 0:8.
b
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Conclusions
C B iAB ¼ C C
The Simian and Charmassone bridges have withstood stormwater
flows for nearly 2,000 years. That these bridges are still standing is
a testament to Roman structural and foundation engineering. The
Simian Bridge was designed with an arch bridge primarily because
of the large height it maintained of 5.4 m (18 ft). The arches’ large
area of opening easily allowed passage of maximum flood flows.
Flow passage was probably a secondary design objective because
this bridge is of the typical Roman arch design at this crossing
height.
At a height of 2 m (7 ft), the Charmassone Bridge was designed
with a culvert that has an inlet control for large flood flows. This
engineering aspect, combined with the buttresses on the downstream side of the bridge, is evidence that the Charmassone Bridge
may have been intended to detain large flood events in this small
watershed. The design is very similar to what would be used by
modern engineers to cross a small valley and manage flood flows.
It is unclear if the Charmassone Bridge was designed explicitly for
stormwater retention. Its design may simply have been to ensure the
required aqueduct grade across the valley. Regardless, detainment of
stormwater flows would require buttressing for structural integrity.
Thus, it is clear that Roman engineers understood the basics of stormwater engineering and were able to adequately design aqueduct
bridges to withstand stormwater flows through antiquity to today.
Appendix
The rational method estimates the stormwater flow through small
watershed basins as
Q ¼ C B iAB
ð1Þ
where Q = stormwater flow rate in the basin; C B = runoff coefficient; i = storm intensity; and AB = area of the basin. Eq. (1) provides for retention within the basin through C B and assumes that,
because of the small size of the basin, flows are quickly propagated
through the basin. Thus CB also accounts for time of concentration.
Because of this steady-state assumption, peak flows estimated with
Eq. (1) must be transmitted underneath bridges traversing the
stormwater catchment.
The arches or culvert can act as orifices where a simplified
Bernoulli’s equation provides for an estimated flow rate underneath
the bridges. The potential energy because of the water height retained upstream of the bridge provides a conservative estimate
for the hydraulic head forcing the flow. If the bridge is not overtopped and the upstream water elevation extends above the elevation of culvert or arch top invert, the velocity of water flowing
through the arch or culvert in the bridge governed by this total
available head is
pffiffiffiffiffiffiffiffi
v ¼ C C 2gh
ð2Þ
where v = velocity; C C = empirical coefficient related to frictional
losses and the hydraulic properties of the culvert; g = gravitational
constant; and h = depth of the water level upstream of the culvert
from the ground. Thus, the flow rate through the arch or culvert is
Q ¼ vðhÞAC ðhÞ
ð3Þ
assuming a uniform velocity through the arch or culvert with
AC = wetted area for a specific water depth h.
Combining Eqs. (1) and (3) through continuity of mass provides
an equation detailing the ability of the arch or culvert to pass stormwater flows,
pffiffiffiffiffiffiffiffi
2ghAC
ð4Þ
which, rearranged, yields the upstream water depth
1
h¼
2g
2
CB
A
i B
CC
AC
Eq. (4) is rearranged to yield
C C pffiffiffiffiffiffiffiffi AC
i¼
2gh
CB
AB
ð5Þ
ð6Þ
where the storm intensity i is calculated corresponding to overtopping depths and completely full culvert or arch flow conditions.
The range of possible values for the coefficient C C =C B yields
minimum and maximum estimates for i and h in Eqs. (5) and (6).
Estimates for the rational method coefficient C B have already been
presented. For the culvert loss coefficient C C , an anticipated value
of 0.7 corresponds to a projecting, square-edged entrance with
minor losses because of friction. However, this parameter may
range from roughly 0.5 to 0.8, depending on frictional losses in
the arches or culvert and basin (Lindeburg 2006, 19–28). These
values correspond to Froude (F) numbers ranging from 0.5 to
1.1 at the outlet for which flow is subcritical to just supercritical
(with the assumption that the upstream velocity is negligible).
Correspondingly, C C ¼ 0:7 yields F ¼ 1 and marks the transition
from the relatively quiescent upstream flow to a downstream jet
through the culvert or arches. Returning to the lumped coefficient,
C C =C B may range from 1.2 to 2.3, indicating the amount that
watershed heterogeneity and assumptions about stormwater flows
and hydraulic properties of the culvert and arches can affect flow
estimates.
Acknowledgments
The study of the Barbegal Mill and Aqueduct System has been possible through assistance from Wright Paleohydrological Institute
and Wright Water Engineers, Denver, Colorado.
The writers thank Ken Wright, P.E., for his review and support of
this study.
The writers gratefully acknowledge the Department of Defense
(DoD) through the National Defense Science & Engineering Graduate (NDSEG) Fellowship Program for Phillip Wolfram’s revision
of this manuscript while studying for a Ph.D. in the Environmental
Fluid Mechanics Laboratory at Stanford University with Professor
Oliver Fringer.
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