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FOURTH HUNTER ROUSE HYDRAULIC ENGINEERING LECTURE

Presented at the August 1983 Hydraulics Division Specialty Conference, held at Cambridge Massachusetts

August 9, 1983

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FIFTY YEARS OF SEDIMENTATION

By Vito A. Vanoni,1 Hon. M. ASCE

ABSTRACT: The development of sedimentation is traced from the 1930s through the 1970s, citing key contributions. Early in these five decades the main concern was with transport of bed load. This was followed closely with theoretical and experimental developments in transport of suspended sediment. Many total sediment discharge formulas then appeared. These were based mostly on fit-ting relations to field and laboratory data, a procedure facilitated by the elec-tronic computer. Laboratory and field studies of bed forms clarified their effect on flow resistance and several methods for predicting conditions under which these forms develop were presented. Much of the development in sedimen-tation occurred in response to the needs of the active programs of water re-sources development. This included studies of degradation below, dams, sed-iment yield and deposition in reservoirs, design of earth canals, hydraulic geometry and stream meandering. Studies of these and other factors in sedi-mentation contributed to their understanding but did not always yield com-pletely satisfactory solutions.

INTRODUCTION

The term sedimentation as used here includes the processes of ero-sion, entrainment, transportation, deposition, and compaction of sedi-ment. In this paper I will discuss what I believe are some of the key developments since 1930 in the general area of river sedimentation. The developments in this period have been substantial and it will not be possible to cover all of them. My selection of key contributions is bound to be influenced by my experience and may differ from those of others. This may result in some rebuttals which I am prepared to receive in the spirit of discussions of ASCE.

In 1930 river engineers and others working with sediment problems had limited technical information which would help in solving these problems. The successful ones depended on experience and judgment to a greater extent than is done even today. Irrigation engineers were basing design of earth channels on the classical permissible velocity data of Samuel Fortier and F. C. Scobey (1926), which was published in the 1926 Transactions of ASCE. The Kennedy (1895) relation for nonscouring and nonsilting canal velocities was not found satisfactory for American conditions.

The regime theory of Gerald Lacey (1930) apparently had not been adopted by American engineers. The Lacey method gave the nonsilting, nonscouring velocity, width and depth of a stream carrying sediment in terms of a silt factor which was related to the mean size of the bed sed-iment. In a subsequent paper, Lacey (1933) gave a relation between the Kutter friction factor and bed sediment size.

'Prof. Emeritus of Hydr . , California Inst, of Tech., Pasadena, Calif. 91125. Note.Discussion open until January 1, 1985. To extend the closing date one

month, a written request mus t be filed with the ASCE Manager of Technical and Professional Publications. The manuscript for this paper was submitted for re-view and possible publication on February 27, 1984. This paper is part of the Journal of Hydraulic Engineering, Vol. 110, No. 8, August , 1984. ASCE, ISSN 0733-9429/84/0008-1022/$01.00. Paper No. 19054.

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The need for design criteria for canals stimulated the development of the permissible velocity method. Experience had shown much about characteristics of earth canals and qualitative rules for design had been developed. As an example, newly built canals were known to be less erosion-resistant than seasoned ones. The result of this experience was a rule that the full design discharge should be put into a canal only after it has been seasoned by lower flows; the permissible velocity for deep canals was known to be higher than for shallow ones, etc.

The classical experimental work of Grove Carl Gilbert (1914) was avail-able. Gilbert produced a comprehensive set of experimental data on sed-iment transport and clear descriptions of the transport mechanism and bed forms. However, a transport relation was not developed so that the results of the work were not readily available to engineers. Gilbert ap-parently did not believe that a transport relation based on laboratory data could be safely extrapolated to river conditions. The lack of a trans-port relation does not detract from the importance of this work as will be discussed later.

The sediment transport formula of M. Du Boys (1879) was not in use by American engineers probably because the formula with the necessary coefficients was not readily available. Du Boys introduced the tractive force or bed shear stress which was an entirely new concept. He ex-pressed transport rate in terms of shear stress and the critical shear stress for initiation of sediment motion. The bed load formula of A. Schoklitsch (1926), which is essentially the same form as the Du Boys formula, was not in use by American engineers.

Hydraulic Laboratory Practice by John R. Freeman (1928) was published in English making available the European experience. Also at this time the Freeman Travel Fellowships were established under which a number of American engineers were able to study and observe European labo-ratory methods first hand. All of these activities set the stage for the rapid development of sedimentation in engineering and research in the United States in the decades ahead.

BED LOAD TRANSPORT RELATIONS

Much of the research in the early decades of this century dealt with the development of relations for transport of bed load by streams. This may be because the sediment in streams in western Europe, where much of the activity was centered, have rather coarse bed sediments which are carried mainly as bed load. The import formula of that era was the one developed by M. Du Boys (1879):

gs =

86 7 gs = S

15(q -qc) (2)

Vd7' in which gs = transport rate in pounds per second per foot of width; d" = bed sediment diameter in inches; S = stream slope; q = discharge in cubic feet per second per foot of width; and qc = critical value of q at which sediment motion is about to begin, given by the relation qc = 0.00532 d"/S4/3. The equation was verified and the coefficients deter-mined to a large extent by means of the data of Gilbert (1914).

The Schoklitsch relation, Eq. 2, gives values of gs for a sediment of uniform size, d. To calculate the sediment discharge for a stream with a graded sediment, the values of qc for each size fraction of the sediment is calculated. These quantities are then weighted according to the frac-tion by weight of each size, and then these weighted quantities are summed to give the total sediment discharge. This idea of calculating sediment discharge by size fractions has been used since by several other workers in developing transport relations.

In the early thirties one of the active groups in sedimentation was at the Swiss Federal Institute of Technology in Zurich, Switzerland, under the direction of Professor E. Meyer Peter. Meyer Peter and his co-work-ers, E. Favre and H. A. Einstein (1934), published their first bed load formula based on experiments with gravel in their large flume, 1.2 m wide by 50 m long. They also compared the predicted sediment dis-charges with data by Gilbert (1914) for fine gravel. In analyzing their data they used the sidewall correction method first developed by Hans Albert Einstein (1934) which has come into general use in sedimentation. This method corrects for friction on the sides of a channel and gives a flow depth that is equivalent to one in a channel without sides. Johnson (1942) modified the sidewall correction method to include the Darcy-Weisbach friction factor and thus the effect of temperature on flow re-sistance of sidewalls.

A most important and lasting work was that of A. Shields (1936), an American engineer doing research in Berlin. By applying the result of the emerging developments in fluid mechanics he determined that the critical shear stress, TC , could be expressed in terms of a dimensionless critical shear stress and the bed Reynolds number R * . These quantities are

T * = - and R* = hs~y)ds v

in which ys and y = specific weights of sediment and water, respec-tively; ds = the diameter of the sediment; M* = VTTP

= shear velocity; p = density of water; and v = kinematic viscosity of water. His chart of T* versus R* is shown in Fig. 1. Another American, Capt. Hans Kramer (1935), also worked in Berlin on investigation of properties of sediments pertinent to movable bed hydraulic models.

The original German paper by Shields was translated under the di-rection of Hunter Rouse by the staff of the laboratory of the Soil Con-servation Service at Caltech. Rouse, because of his keen understanding of fluid mechanics and fluency in German, was quick to recognize the fundamental value of Shields' work and to request its translation.

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1.0

0.6

0.4

02

! " T o Amber (Shields)

Carl Brown. The statistical ideas of Einstein have been extended by some of his former students, e.g., H. W. Shen and P. Todorovic (1971).

Kalinske (1947) based a bed load relation on a formulation involving the turbulent bed velocity fluctuations which were assumed to be nor-mally distributed. The resulting relation, like that of Einstein's (1942), gave a small but non-zero sediment discharge even when the bed shear stress was somewhat less than the so-called critical value.

DISTRIBUTION OF SUSPENDED SEDIMENT

Engineers and scientists had long been interested in the phenomenon of sediment suspension in streams. In the 1858 edition of a book, Dupuit (Rouse & Ince, 1957) surmised that the power of suspension depends on the velocity gradient of the flow. The developments in the mechanics of turbulent flow which occurred in the early decades of this century were brought to bear on the problem of sediment suspension in the late 1930s. The differential equation for suspension was apparently first pre-sented by Schmidt (1925) in studies of dust in the atmosphere:

dc wc + es = 0 (3)

dy

in which w = fall velocity of the particles; c = concentration of particles in the fluid; es = turbulent diffusion coefficient for sediment; and y = vertical coordinate. This equation was derived by Morough O'Brien (1933) in a general discussion of the relation of turbulent flow and sediment transport. Theodore von Karman (1934) also discussed this equation in connection with the paper by O'Brien (1933). von Karman pointed out that the diffusion coefficient for momentum was related to the velocity gradient, du/dy, and the shear stress, T, by the equations T = pe du/dy and, assuming es = e, Eq. 3 could be integrated to give

, c P*/ In - = -w (4)

, c (y du dy I n - = - p r o - ^ (5)

ca Ja dy T

in which c and ca = concentrations of sediment with fall velocity w at level y and a, respectively; u = velocity; T = shear stress at level y; and p = density of the fluid. As may be seen from Eq. 5 it is necessary to have a value of c in order to get the concentration c.

Hurst (1929) did experiments on suspension of sediment in a jar in which sediment was stirred into the water by a system of paddles ro-tating about a vertical axis. The analysis of his concentration data was similar to that of the kinetic theory of gases and resulted in an expo-nential distributionas does Eq. 4 with constant e s , and as did his mea-surements. While at Caltech with the Soil Conservation Service, Rouse (1938) made a series of careful experiments on sediment suspension in a jar in which turbulence was generated by an assembly of coarse mesh grids oscillating vertically. He used four well sorted sands for which he measured the fall velocity and varied the oscillation frequency of the grid

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and the amount of each sediment in the jar. His data confirmed the theory of suspension (Eq. 4) for constant es and showed that the si-multaneous distribution of different sizes of sediment followed the the-ory. There was some deviation from the theory of the data for coarse sediment and high frequency agitation suggesting that there may be some difference between mixing of fluid and sediment, i.e., that es may differ from e.

As one surveys the history of sedimentation it becomes clear that cer-tain developments stimulated others as in a chain reaction. One such key development was the theory of sediment suspension in turbulent flows in which a number of workers, among whom was Hunter Rouse, played important roles.

The classical paper by Rouse (1937) on mechanics of fluid turbulence must have stimulated him to write at length about the effect of turbu-lence on sediment transportation. During this era he employed his writ-ing ability in preparing several papers among which were two, 1939 and 1939a.

In the closing discussion of his classical paper referred to earlier, Rouse published his well known "Rouse Equation" for the distribution of sus-pended sediment in turbulent flow. This resulted from integration of Eq. 5 with the velocity gradient determined from the Karman-Prandtl log-arithmic velocity law. The resulting equation is

(d-y) a V -T, : (6)

. y (d- a)_ in which the exponent z = w/ku *; d = flow depth; k = the von Karman constant; and the other symbols are as defined previously. Eq. 6 (plotted in Fig. 2) is seen to give unrealistic concentrations of zero at the surface, y = d, and infinite at the bed, i.e, y = 0. Despite these deficiencies, the Rouse equation has come into general use and has not been replaced by later ones. Among these later equations are those by Hunt (1954) and Ippen (1971).

The work of Ippen (1971) needs special mention. It was started in 1934 (Ippen, 1971) when both Ippen and Rouse were at Caltech. The Ippen relation for distribution of concentration differs from that of Rouse only in that the Krey (1927) equation for the velocity profile was used in place of that of Karman-Prandtl. The Ippen equation gives finite concentration at the bed and zero concentration at the surface.

The theoretical equations for...