Short Historical Dictionary on Urban Hydrology and Drainage
CAQUOT Albert Born in Vouziers, France in 1881 – Dead in Paris, France in 1976.
Figure 1 : Portrait of Albert Caquot.
1. SHORT BIOGRAPHY Third son of a farmer in Vouziers, a small city in the French Ardennes, Albert Caquot was born in 1881. He was a brilliant student (Kérisel, 2001) and entered in the French high engineering school Ecole Polytechnique in 1899 and later in the high engineering school ENPC - Ecole Nationale des Ponts et Chaussées where he got his civil engineer diploma in 1905. He worked in various engineering fields, especially in soil mechanics, concrete constructions and aeronautics. In all disciplines, he was curious, innovative, efficient and very productive. He started in the field of concrete and collaborated with Eugène Freyssinet (1879-1962). He then worked in aeronautics during both the first and second World Wars (Lissarague, 2001). From 1928 to 1933, he was appointed general technical director in the Ministry of Air. During this period, he created new institutes for fluid mechanics in France (Coët and Chanetz, 2001). Between 1949 and 1963, he was the first president of the scientific council of the ONERA (Office National d’Etudes et de Recherches Aéronautiques – National Office for Studies and Research in Aeronautics). Albert Caquot is famous as a civil engineer for his creation of novel techniques and structures which were frequently linked to great technical and economical challenges. He designed and built many innovative and great constructions (Buzaré, 2001; Hannois, 2001): bridges (La Caille in 1924-1928, Le Sautet in 1927-1928, La Fayette in Paris in 1927-1928, Donzère-Mondragon in 1951-1952), industrial buildings (aviation hall in Fréjus and in Lyon-Bron in 1932-1935), repair basins in harbours (Saint-Nazaire in
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Short Historical Dictionary on Urban Hydrology and Drainage
1935-1937), mole (Gironde in 1930-1934), dams and lock-gates (Le Sautet in 1930, La Girotte in 1946-1949). In 1967, he proposed to build a bridge over the channel between France and England. In 1972-1976, he suggested to build a tidal power plant across the Mont Saint-Michel bay (which, fortunately, was never built...). At international level, Caquot designed the concrete structure of the Redemptory Christ statue at the top of Corcovado peak in Rio de Janeiro, Brazil. He also proposed a very innovative hydraulic technique to move the whole Abu-Simbel temple in Egypt in 1963, but his proposal was not selected (Desroches-Noblecourt, 2001). Caquot has been elected member of the Institut (French Academy) in 1933, in recognition of his scientific achievements. He has been later elected member of the Académie des Sciences in 1936 and became president of this institution in 1952. Caquot is considered as the founder of the industrial standardisation in France. He was president of both AFNOR – Association Française de Normalisation (French Standards Association) and ISO – International Organisation for Standardization (1949-1952). Professor in many French high engineering schools, Caquot wrote not only numerous technical and scientific reports, notes and papers, but also some papers on economy and sociology. When he died in 1976, he was recognised, since half a century, as one of the “greatest living French engineers.” In 2001, the French post office published a stamp celebrating his 120th birthday (Figure 2). His name has been attributed to many streets, secondary schools, amphitheatres, professional associations, etc. A detailed biography of Albert Caquot, his life and his carrier, has been written by his son-in-law Jean Kérisel (2001).
Figure 2 : Stamp published in 2001 for the 120th birthday of Albert Caquot.
2. CAQUOT FORMULA FOR SEWER DESIGN Albert Caquot started to work in the field of urban hydrology and drainage in the city of Troyes, France, from 1905 to 1912, as engineer in the Ministry of Public Works. Applying the hygienist concepts and traditions, he designed and built the sewer system of Troyes in order to facilitate the drainage of the groundwater and to diminish the mortality due to typhoid fever, and also to solve the problem of leaking cesspools*. In an interview cited by Kérisel (2001, p. 31), Caquot said: “I had drawn one curve showing the groundwater level and another one showing the mortality. Both curves [...] were rather superimposed and this had convinced the inhabitants.” He asked to standardize sewer manholes and pipes : this was the premises of his activity in industrial © Jean-Luc Bertrand-Krajewski - 02/2006
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Short Historical Dictionary on Urban Hydrology and Drainage
standardisation, which was later continued e.g. with the standardisation of egg-shape sewer* cross sections after the Second World War (cf. paragraph 3).
Figure 3 : Front page of the paper written by Caquot (1941) on the calculation of runoff to be evacuated in modern urban agglomerations.
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Short Historical Dictionary on Urban Hydrology and Drainage
When he left Troyes in 1912, 80 km of pipes and trunk sewers were built. This new sewer system contributed to reduce the flood damages during the famous and terrible flood of the Seine river in January 1910 (Kérisel, 2001, p. 32). Based on his local work and experience, Caquot gave in 1911 two communications to the regional Société Académique de l'Aube: in March, on the geology and the water flow regime in Troyes, in April on the intensity of rainfall events and the flow of stormwater (Caquot, 1911a, 1911b). Thirty years later, in 1941, Albert Caquot published another paper 1 on urban drainage in the proceedings of the French Académie des Sciences (Figure 3) where he proposed a modified rational formula* to calculate the surface runoff to be evacuated in sewers accounting for the temporary storage of runoff within the sewer pipes (Caquot, 1941). Considering that no recent review had been devoted to this question since the sewerage manual written by the French engineer Pierre Koch* in 1937 (Koch, 1937), Caquot elaborated a method based on the main following assumptions: - the maximum rainfall intensity for strong storm events appears shortly after the beginning of the storm event; - assuming, like August Frühling* (Frühling, 1910) that strong storm events have a maximum intensity around a central point and that intensities are decreasing with increasing distances from this central point, the total volume of precipitation over a catchment is then less than proportional to its surface; - “Let's consider the sewer system at the moment when the maximum flow is reached, with a full system. The flow at this moment corresponds exactly to the rainfall volume precipitated during the unit of time, whereas the rainfall volume precipitated previously has been used for the flow, the filling of the sewer pipes and for the humidification of all catchments surfaces. [...] As rainfall intensity is maximum at the beginning of the event, the flow to be evacuated by the sewer system is established after the filling of both the sewer system capacity and the catchment capacity.” (Caquot, 1941, p. 510-511). Using the following notations: q maximum flow rate at the outlet of the sewer system (m3/s) T time at which q appears (minutes) H cumulated rainfall at time T (mm) A area of the catchment (ha) I mean slope of the sewer pipes (m/m) L length of streets over the catchment (hm) t1 time of concentration within the sewer pipes (minutes) time of concentration over the catchment surfaces (minutes) t2 α coefficient < 1 accounting for decreasing intensity around the central point (-) θ = (t1+t2)/β,
1
unfortunately, the original paper published in 1941 contains many typographic errors: exact equations may be found e.g. in Koch (1954), appendix I, pp. 319-324. © Jean-Luc Bertrand-Krajewski - 02/2006
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Short Historical Dictionary on Urban Hydrology and Drainage
Caquot based his calculations on the volume balance principle: “At the beginning of the storm event, the flow rate at the outlet of the sewer pipes is equal to zero, and then increases rapidly to reach the maximum flow rate q, in such a way that the mean flow rate during this period of time T is βq, β being a coefficient less than 1 and close to 0.85 for strong storm events. The volume of water [in m3] precipitated at the time T of the maximum flow rate q at the outlet of the planned catchment is equal to 10αHA; it is distributed on the one hand in the volume of water delayed, discharged and evaporated, this volume being represented by the fraction γ, and on the other hand in the volume stored in the system q(t1+t2), and lastly in the volume discharged by the sewer system βqT.” Expressed with homogeneous units, this volume balance is written (Figure 4): 1 αHA(1 − γ ) = q (t1 + t 2 ) + βqT 6
Eq. 1
Figure 4 : Volume balance equation (Caquot, 1941, p. 511, with a typographic error in the text: q (t1 + T2) shall be replaced by q (t1 + t2).
Based on hydrologic and hydraulic considerations, Caquot derived the following set of equations (including corrections in Eq. 2 given e.g. in Koch (1954, p. 322) to account for typographic errors in the original printed paper of Caquot): −4 11
1 t1 + t2 = I 11 A 30 q − 0.2 1.09
Eq. 2
α = A−ε with ε = -0.178
Eq. 3
−3 15 2 A 4 (1 − γ ) 14 = 0.56
Eq. 4
L
By choosing ε = -0.178 in Eq. 3, Caquot observed that the maximum flow rate was proportional to A3/4, as in the Bürkli-Ziegler* formula.
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Short Historical Dictionary on Urban Hydrology and Drainage
He also carried out a statistical analysis of the Parisian rainfall data given by Besson (1932) and found that the weekly frequency F of storm events corresponding to a value equal to or higher than H/(T+θ) was well represented by a Laplace-Gauss distribution: F=
1 π
z
∫e
−z2
dz with z = 1.32 + 1.8 log
−∞
H + 0.6 log θ T +θ
Eq. 5
which leads to −1
z
− 0.703 H = θ 3 101.8 T +θ
Eq. 6
Substituting Eq. 2, Eq. 3 and Eq. 6 into Eq. 1 gives Eq. 7 (including corrections given e.g. in Koch (1954, p. 323) to account for typographic errors in the original printed paper of Caquot): z 15 − 0.75 0.13 0.75 1 . 68 14 q = 0.170 × 10 I A (1 − γ )
Eq. 7
which shows that, like in the rational formula*, the maximum flow rate q depends on the catchment surface A, on the mean slope of the pipes I and on the runoff coefficient C = (1-γ) but with exponents which are not equal to 1. Additionally, q also depends on a variable z which itself depends on the rainfall return period P for which the sewer has to be designed. (e.g. z = 2.045 for P = 10 years). Substituting also Eq. 4 gives: z 3 − 0.75 0 . 13 0 . 75 q = 0.0566 × 101.68 I L = KλL4 (now with q in L/s)
Eq. 8
This is the initial Caquot formula, where the coefficients K and λ depend respectively on the mean slope of the pipes I in m/m and on the return period P in years (Figure 5). After some modifications and rewriting approved by Caquot himself, his formula was officially adopted and recommended to design sewer systems in the Instruction technique relative à l'assainissement des agglomérations CG 1333* (Technical guidelines for sewerage of cities) published in 1949 by the Ministry of Reconstruction and City Planning (CG 1333, 1949). After revision and regionalisation of some numerical values, the formula was still recommended in the new Instruction technique relative aux réseaux d'assainissement des agglomérations INT 77.284 (Technical guidelines for sewer systems in cities) published in 1977 by the Ministry of Interior to replace the CG 1333 (INT 77.284, 1977). (See CG 1333* for more details about these two French guidelines). In 2003, the application of the Caquot formula has been restricted to the pre-design of sewers in small catchments: it is now recommended to use more elaborated methods and simulation software (Certu, 2003). However, during more than 50 years, the formula established by Caquot and recommended by official
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Short Historical Dictionary on Urban Hydrology and Drainage
guidelines have been considered in France as “the Bible for all planners, private consulting companies, administrations... and all supervision services involved in sewer systems projects of any size.” (Garancher, 1966 cited by Koch, 1967, p. ix).
Figure 5 : Caquot formula and values of K and λ (Caquot, 1941, pp. 514-515).
3. CAQUOT STANDARD EGG-SHAPE SEWERS After the Second World War, Caquot conceived a series of homothetic egg-shape sewer* cross sections (Figure 6) rationally designed to ensure the minimum selfcleansing velocity* for a very wide range of flow rates (ratio from 1 to 40). The increasing sizes were calculated in such a way that two successive cross sections were proportional to the square of any linear dimension of the cross section (Koch, 1954, p. 104). After a large enquiry about the standardization of sewer cross sections, the French Standard Association AFNOR published in 1949 the standard NF P 16-401 (1949): the prescribed egg-shape cross sections resulted from a compromise between the rational design proposed by Caquot and practical considerations based on experience from existing sewers. The main modifications concerned the pipe wall thickness and the geometry of the invert in order to facilitate the walking of sewermen. These standard cross sections were recommended for sewer height between 1.0 and 2.0 m. The official French technical guidelines for sewerage of cities CG 1333*, also published in 1949, cited the standard NF P 106-401 (Figure 7) and its classification in three categories: man-entry ovoid sewers with height between 1.8 and 2.0 m, “semi man-entry” ovoid sewers with a 1.5 m height, and “exceptionally man-entry” ovoid sewers with heights ranging from 1.0 to 1.3 m (CG 1333, 1949, p. 16). Smaller pipes had to be circular. © Jean-Luc Bertrand-Krajewski - 02/2006
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Short Historical Dictionary on Urban Hydrology and Drainage
Figure 6 : "Rational" egg-shape sewer series by Caquot (in Koch, 1954, p. 104).
Figure 7 : Standard egg-shape sewers as prescribed in the French Standard AFNOR NF P 16-401 (in CG 1333, 1949, p. 49).
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Vouziers Paris
Troyes
References Besson L. (1932). Les averses dans la région parisienne. Annales des Services Techniques d'Hygiène de la Ville de Paris, XIII, 195-215. Buzaré J. (2001). Albert Caquot, Louis Armand et les ponts de la Caille. Le Curieux Vouzinois, 57, 25-29. ISSN 0991-2312. Caquot A. (1911a). Troyes : constitution géologique, régime d'écoulement des eaux. Troyes (France) : Société Académique de l'Aube, communication du 17 mars 1911. Caquot A. (1911b). L'intensité des chutes de pluie et l'écoulement des eaux pluviales. Troyes (France) : Société Académique de l'Aube, communication du 21 avril 1911. Caquot A. (1941). Sur la quantité des eaux pluviales à écouler dans les agglomérations urbaines modernes. Comptes Rendus des Séances de l'Académie des Sciences, Paris, 213(16), 509-515. Certu (2003). La ville et son assainissement - Principes, méthodes et outils pour une meilleure intégration dans le cycle de l'eau. Lyon (France) : Certu, CD-rom, juillet 2003 ISBN 2-11094083-2. CG 1333 (1949). Instruction technique relative à l'assainissement des agglomérations. Paris (France) : Ministère de la Reconstruction et de l'Urbanisme, circulaire CG 1333, 22 février 1949, 50 p. + annexes. Coët M.-C., Chanetz B. (2001). Albert Caquot et l'ONERA. Le Curieux Vouzinois, 27, 18-24. ISSN 0991-2312. Desroches-Noblecourt C. (2001). Albert Caquot et le sauvetage des temples d'Abou-Simbel. Le Curieux Vouzinois, 57, 43-46. ISSN 0991-2312. Hannois C. (2001). Albert Caquot, ingénieur et bâtisseur. Le Curieux Vouzinois, 57, 30-42. ISSN 0991-2312. INT 77.284 (1977). Instruction technique relative aux réseaux d'assainissement des agglomérations. Paris (France) : Ministère de l'Intérieur, instruction interministérielle n° 77.284/INT, 22 juin 1977, 62 p. + annexes. Kérisel J. (2001). Albert Caquot 1881-1976 : savant, soldat et bâtisseur. Paris (France) : Presses de l'Ecole Nationale des Ponts et Chaussées, 180 p. ISBN 2-85978-343-1. Koch P. (1937). L'assainissement des agglomérations - Tome 3 : calcul des projets, exécution des ouvrages et établissement des programmes d'assainissement urbain. Paris (France) : Léon Eyrolles éditeur, 292 p.
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Short Historical Dictionary on Urban Hydrology and Drainage
Koch P. (1954). Les réseaux d'égout. Paris (France) : Dunod, 1ère édition, 348 p. Koch P. (1967). Les réseaux d'égout. Paris (France) : Dunod, 3ème édition, 350 p. Lissarague P. (2001). Albert Caquot et l'aéronautique. Le Curieux Vouzinois, 57, 12-17. ISSN 0991-2312. NF P 16-401 (1949). Norme NF P 16-401 sur les sections intérieures des égouts ovoides. Paris (France) : AFNOR.
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