Valley Crossings and Flood Management for Ancient Roman Aqueduct Bridges

Home , Aqueduct (bridge), Aqueduct (water supply), Aqueduct of Segovia

Technical Note

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 On the basis of the archaeological record of Roman aqueducts, the structures subject to large stormwater runoff flows and floods. Romans appear to have used the height of a valley crossing as a Many of these structures have withstood storm events for millennia guideline for the type of aqueduct crossing to be used. It is known and are still standing today. The stormwater runoff that occurred from field evidence that Roman engineers used one of four ap- in valleys of the Roman Empire was an obstacle to the aqueducts proaches to preserve slope or, when the terrain dictated, the need for a direct crossing: bringing water to Roman cities. There are many well-known exam- 1. Continuous solid stone and/or masonry bridge with a culvert to ples of ancient Roman aqueduct valley crossings with different sol- pass stormwater flows, utions to this problem; among the most iconic are the Pont Du Gard 2. Single-tiered load-bearing arch bridge, near Nîmes, France, the inverted siphon at Lyon, France, and the 3. Multitiered, load-bearing arch bridge, or Monumental Aqueduct of Segovia in Spain. There were also many 4. Inverted siphon. other small valley crossings, perhaps not as impressive as these For small valley crossings, a continuous solid bridge with a great monuments, but just as interesting to study from a stormwater culvert was favored by Roman engineers (Chanson 2002). On the engineering standpoint. basis of our observations, culverts were used for crossing heights For example, the Barbegal Aqueduct System located in southern up to 2 m (7 ft), and the height of the aqueduct crossing above the France included a number of aqueduct bridges that cross small val- stream or drainage bed may have been a Roman engineering guide- leys, some of which are still intact. Two of these bridges are quite line for selecting the approach for the type of bridge. Continuous different in design even though the valleys they cross have some solid bridges with culverts were used in several small valley aque- similar characteristics. Calculations of stormwater flows and cul- duct bridge crossings in the Barbegal Aqueduct System. vert hydraulics demonstrate that the height of the valley crossing For valley crossing heights between 2 m (7 ft) and approxi- and the necessity to pass stormwater flows were clearly design con- mately 20 m (66 ft), a single-tiered arch bridge was used. Multi- siderations for these aqueduct bridges. Each of these design tiered arches were used for bridges up to approximately 50 m considerations will be considered in turn. (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 Aque- 1Director of Roman Aqueduct Studies, Wright Paleohydrological duct System. Two small watershed crossings on the Barbegal Institute, 2490 W. 26th Avenue, Suite 100A, Denver, CO 80211 (corre- Aqueduct System employing the first two listed approaches will sponding author). E-mail: [email protected] be considered. 2Research 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 Barbegal Aqueduct System 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 Located in the Provence region of France is an ancient Roman period open until May 1, 2012; separate discussions must be submitted for water system that includes aqueducts and the largest industrial fa- individual papers. This technical note is part of the Journal of Irrigation cility known from antiquity: the Barbegal Mill. The mill contained and Drainage Engineering, Vol. 137, No. 12, December 1, 2011. ©ASCE, 16 water wheels to grind grain to provide flour to the city of Arleate ISSN 0733-9437/2011/12-816–819/$25.00. (Lorenz 2005). The aqueduct that provided the water to turn the

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Downloaded 14 Jan 2012 to 128.12.204.138. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org Table 2. Stormwater Flow Calculations Stormwater flow Location L/s cfs Simian Bridge 2,900 103 Charmassone Bridge 2,100 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. Fig. 1. (Color) Schematic map of Barbegal Mill and Aqueduct System—Southern France near Arles Simian Bridge millstones also provided domestic water to the city. Two aqueducts’ The Simian Bridge is located on the northern Barbegal aqueduct branches provided water from springs located on the north and at a distance of approximately 4 km (2.5 mi) northwest of the south flanks of the Alpilles mountains. The location and layout Barbegal Mill. The bridge ruins have been studied by Bellamy of the Barbegal Aqueduct System are shown in Fig. 1. 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 Two Watersheds of a single tier of four arches that span the small valley. Two bridges on the Barbegal Aqueduct System, called the Simian and Charmassone bridges, are located on the north aqueduct of the Charmassone Bridge Barbegal System, as shown in Fig. 1. These bridges were selected for investigation because they are relatively intact and are located in The Charmassone Bridge is also located on the northern Barbegal two similar watersheds (Table 1), but employ different designs. The aqueduct approximately 1.6 km (1 mi) upstream of the Barbegal watersheds are relatively small and fairly uniform with agriculture Mill site. The smaller bridge is shown in the photograph in Fig. 3 and open space as land uses. The vegetation in these watersheds and is approximately 30 m (100 ft) in length. The height of the includes olive groves and native shrubs. The similar watershed Charmassone Bridge is approximately 2 m (7 ft) from the stream characteristics also produce similar stormwater flows. thalweg to the aqueduct channel invert. Watershed slopes were computed by considering the elevation There are several unique aspects to the Charmassone Bridge. drop along the thalweg, starting from the ridge to basin bottom First, the bridge has a limestone block-type culvert to pass storm- as measured from 1∶25;000 topographic mapping by the French water under the bridge. The carved limestone block, shown in the Institut Geographique National (IGN). The upstream catchment photograph in Fig. 4, shows a curved haunch that is mounted on area was computed by delineating the basin ridge while on foot two limestone blocks that provide additional area for passing through a geographic positioning system (GPS) in August 2005. stormwater flows. The cross-sectional area of this culvert opening Geographic information system (GIS) methods were employed is much smaller than the area that is provided by the four arches at to compute the area enclosed by this polygon. the Simian Bridge. Another unique aspect of the Charmassone Bridge is that there Stormwater Flows are four buttresses that are on the downstream facing of the bridge. Stormwater flows resulting from a large storm event in the Simian These buttresses have dimensions of approximately 1.3 m (4.3 ft) and Charmassone areas were calculated using the rational method by 1.8 m (5.9 ft), as shown in Fig. 5. Each buttress is tapered from because these are both small watershed areas (less than 0:65 km2). the top to the bottom. 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. Esti- mated stormwater flows for watersheds upstream of the Simian and Charmassone bridges are presented in Table 2.

Table 1. Upstream Watershed Characteristics Location Catchment area (km2) Average slope Simian Bridge 0.15 0.045 Charmassone Bridge 0.11 0.034 Fig. 2. (Color) Simian Bridge (image by Wayne Lorenz)

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Downloaded 14 Jan 2012 to 128.12.204.138. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org Table 3. Major Bridge Differences Bridge opening area to pass stormwater Bridge heighta Location m2 ft2 mft Simian Bridge 16.5 178 5.4 18 Charmassone Bridge 1.1 12 2 7 aStream thalweg to aqueduct invert.

Discussion

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 Fig. 3. (Color) Charmassone Bridge with buttresses on downstream simplicity, we consider the range of rainfall intensities that result side of structure (image by Wayne Lorenz) 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 Char- massone 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. Fig. 4. (Color) Culvert under Charmassone Bridge (image by Wayne Therefore, Roman engineers may have designed the Charmassone Lorenz) 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 Minimuma Maximumb Simian Bridge 3,200 6,300 Charmassone Bridge 190 360 a CB ¼ 0:6; CC ¼ 0:7. b CB ¼ 0:35; CC ¼ 0:8. Fig. 5. Charmassone Bridge plan

Table 5. Rainfall Intensities for Overtopping of Aqueduct Methodology Rainfall intensity (mm=h) Location Minimuma Maximumb The Simian and Charmassone bridges are two very different structures that cross watersheds that have similar characteristics. The Simian Bridge 7,800 9,300 area of bridge openings presented in Table 3 shows that the culvert Charmassone Bridge 260 520 under the Charmassone Bridge has 7% of the area that is available a CB ¼ 0:6; CC ¼ 0:7. b in the arches under the Simian Bridge. CB ¼ 0:35; CC ¼ 0:8.

Downloaded 14 Jan 2012 to 128.12.204.138. Redistribution subject to ASCE license or copyright. Visit http://www.ascelibrary.org pffiffiffiffiffiffiffiffi Conclusions CBiAB ¼ CC 2ghAC ð4Þ The Simian and Charmassone bridges have withstood stormwater which, rearranged, yields the upstream water depth flows for nearly 2,000 years. That these bridges are still standing is a testament to Roman structural and foundation engineering. The 2 ¼ 1 CB AB ð Þ Simian Bridge was designed with an arch bridge primarily because h i 5 2g CC AC 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. Eq. (4) is rearranged to yield Flow passage was probably a secondary design objective because this bridge is of the typical Roman arch design at this crossing pffiffiffiffiffiffiffiffi ¼ CC AC ð Þ height. i 2gh 6 CB AB 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 where the storm intensity i is calculated corresponding to overtop- engineering aspect, combined with the buttresses on the down- ping depths and completely full culvert or arch flow conditions. stream side of the bridge, is evidence that the Charmassone Bridge The range of possible values for the coefficient CC=CB yields may have been intended to detain large flood events in this small minimum and maximum estimates for i and h in Eqs. (5) and (6). watershed. The design is very similar to what would be used by Estimates for the rational method coefficient CB have already been modern engineers to cross a small valley and manage flood flows. presented. For the culvert loss coefficient CC, an anticipated value It is unclear if the Charmassone Bridgewas designed explicitly for of 0.7 corresponds to a projecting, square-edged entrance with stormwater retention. Its design may simply have been to ensure the minor losses because of friction. However, this parameter may required aqueduct grade across the valley. Regardless, detainment of range from roughly 0.5 to 0.8, depending on frictional losses in stormwater flows would require buttressing for structural integrity. the arches or culvert and basin (Lindeburg 2006,19–28). These Thus, it is clear that Roman engineers understood the basics of storm- values correspond to Froude (F) numbers ranging from 0.5 to water engineering and were able to adequately design aqueduct 1.1 at the outlet for which flow is subcritical to just supercritical bridges to withstand stormwater flows through antiquity to today. (with the assumption that the upstream velocity is negligible). Correspondingly, CC ¼ 0:7 yields F ¼ 1 and marks the transition from the relatively quiescent upstream flow to a downstream jet Appendix through the culvert or arches. Returning to the lumped coefficient, CC=CB may range from 1.2 to 2.3, indicating the amount that The rational method estimates the stormwater flow through small watershed heterogeneity and assumptions about stormwater flows watershed basins as and hydraulic properties of the culvert and arches can affect flow estimates. Q ¼ CBiAB ð1Þ where Q = stormwater flow rate in the basin; CB = runoff coefficient; i = storm intensity; and AB = area of the basin. Eq. (1) pro- Acknowledgments vides for retention within the basin through CB and assumes that, because of the small size of the basin, flows are quickly propagated The study of the Barbegal Mill and Aqueduct System has been pos- through the basin. Thus CB also accounts for time of concentration. sible through assistance from Wright Paleohydrological Institute Because of this steady-state assumption, peak flows estimated with and Wright Water Engineers, Denver, Colorado. Eq. (1) must be transmitted underneath bridges traversing the The writers thank Ken Wright, P.E., for his review and support of stormwater catchment. this study. The arches or culvert can act as orifices where a simplified The writers gratefully acknowledge the Department of Defense Bernoulli’s equation provides for an estimated flow rate underneath (DoD) through the National Defense Science & Engineering Grad- the bridges. The potential energy because of the water height re- uate (NDSEG) Fellowship Program for Phillip Wolfram’s revision tained upstream of the bridge provides a conservative estimate of this manuscript while studying for a Ph.D. in the Environmental for the hydraulic head forcing the flow. If the bridge is not over- Fluid Mechanics Laboratory at Stanford University with Professor topped and the upstream water elevation extends above the eleva- Oliver Fringer. tion 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 References pffiffiffiffiffiffiffiffi v ¼ C 2gh ð2Þ ASCE and Water Pollution Control Federation (WPCF) (Joint Committee). C (1982). “Design and construction of sanitary and storm sewers.” ASCE where v = velocity; C = empirical coefficient related to frictional manual on engineering practice No. 37 and WPCF manual of practice C No. 9, Reston, VA. losses and the hydraulic properties of the culvert; g = gravitational Bellamy, P., and Ballais, J.-L. (2000). “Le pont Simian à Fontvielle: Etude constant; and h = depth of the water level upstream of the culvert géo-archéologique d’un pont-aqueduc.” Travaux du Centre Camille from the ground. Thus, the flow rate through the arch or culvert is zJulian, 26, 25–38. “ ¼ ð Þ ð ÞðÞ Chanson, H. (2002). Hydraulics of large culvert beneath Roman aqueduct Q v h AC h 3 of Nimes.” J. Irrig. Drain Eng., 128(5), 326–330. Hodge, A. T. (2002). Roman aqueducts and water supply, Gerald assuming a uniform velocity through the arch or culvert with Duckworth & Co., London. AC = wetted area for a specific water depth h. Lindeburg, M. (2006). Civil engineering reference manual for the PE Combining Eqs. (1) and (3) through continuity of mass provides exam, 10th Ed., Professional Publications, Belmont, CA. an equation detailing the ability of the arch or culvert to pass storm- Lorenz, W. F. (2005). “Ancient roman water development in France.” Water water flows, Resources Impact, 7(3), 4–8.

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