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Measurements of critical shear stress in sewers
PII: S0043-1354(97)00447-8
Wat. Res. Vol. 32, No. 7, pp. 2035±2040, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0043-1354/98 $19.00 + 0.00
MEASUREMENTS OF CRITICAL SHEAR STRESS IN SEWERS V. HRISSANTHOU* and S. HARTMANN Institute of Hydrosciences, Federal Armed Forces University Munich, 85577 Neubiberg, Germany (First received April 1997; accepted in revised form October 1997) AbstractÐCritical shear stress of sediment located in a grit chamber and in a sewer was determined in full-scale by a measuring device constructed in the laboratory of the Institute of Hydrosciences at the Federal Armed Forces University, Munich. The estimation of critical shear stress is actually based on the measurement of the corresponding critical water discharge. Incipient motion was recorded by a video camera and the recorded pictures were treated by an automatic image processing system. The measurement results were compared with data taken from the literature. A good agreement between measurements and literature data was obtained. The automatic image processing contributes to a more objective quanti®cation of the sediment transport initiation. # 1998 Elsevier Science Ltd. All rights reserved Key wordsÐcritical shear stress, critical erosion velocity, grit chamber, sewer, measurements, automatic image processing system
NOMENCLATURE 1, 2, 3= position numbers of deposits A, B, C= computing methods of the mean critical shear stress dch= characteristic grain diameter (m) median grain diameter (m) d50= grain diameter for which 90% of the material is ®ner (m) d90= d95, d30= corresponding de®nitions as for d90 (m) Fr*= sediment Froude number g= gravity acceleration (m sÿ2) + dimensionless transport rate in the UnsoÈld diagram qs = critical discharge (m3 sÿ1) Qcr= Re*= sediment Reynolds number mean critical erosion velocity (m sÿ1) vmcr= vo*= shear velocity (m sÿ1) w= water content (%); water percentage by weight related to the soil dried at 1058C xS = mean standard deviation of the grey values for all the columns of a digitized picture xZ = mean standard deviation of the grey values for all the lines of a digitized picture xQ = ratio xS =xZ n= kinematic viscosity of the water (m2 sÿ1) rF = sediment density (kg mÿ3) water density (kg mÿ3) rW= t o= average shear stress (N mÿ2) tcr= mean critical shear stress (N mÿ2)
INTRODUCTION
The knowledge of critical erosion velocity or critical shear stress in a river or a sewer is important for the calculation of the sediment transport. The knowledge of incipient motion is also of interest *Author to whom all correspondence should be addressed. [Present address: Section of Hydraulic Works, Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece; Tel: +30541-79608; Fax: +30-541-20371; E-mail: [email protected]].
under ecological aspects because the sediments in rivers or sewers usually contain pollutants, e.g. heavy metals (Westrich, 1985). The in situ estimation of the critical shear stress provides an important basis for a realistic calculation of the transported sediments and for the consideration of the sedimentological peculiarities of a river or a sewer. A signi®cant problem appearing during sediment transport experiments is the de®nition of the incipient motion that cannot be exactly quanti®ed. Thus, the researcher has to determine this critical situation subjectively for a set of experiments. Other authors (Kramer, 1935; Shields, 1936; Vanoni, 1964) found that the boundary between immobility and motion cannot be determined de®nitely. Therefore, it is appropriate to describe the initiation of motion not with an individual arithmetic value but by means of a range of values where the incipient conditions are given (Bechteler et al., 1996). The diagram of Shields (1936) is until now the basis for investigations concerning incipient motion of noncohesive materials. In the meantime, several modi®cations of the Shields results were done (Mantz, 1977; Yalin and Karahan, 1979; UnsoÈld, 1984, etc.). Generally it can be concluded that the experimental results of dierent authors for noncohesive, uniformly graded sediment do not deviate signi®cantly from each other. However, the de®nitions they used for the incipient motion were dierent. As far as cohesive material is concerned, considerable dierences exist not only in the de®nition
2035
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V. Hrissanthou and S. Hartmann
of incipient motion but also in the preparation of soils, the experimental conditions, the erosion load, the duration of the experiments, the measured soil parameters and the measurement of the erosion rates. Therefore, the comparison between dierent experimental results is not easy (Krier, 1987). In spite of the dierences mentioned above, two characteristic stages of cohesive soil erosion may be identi®ed in the literature: the surface erosion and the mass erosion. Correspondingly, two critical situations may also be distinguished: the initiation of surface erosion and the initiation of mass erosion.
MEASURING DEVICE
The measuring device consists mainly of a prismatic channel 0.77 m long, with a rectangular cross-section 0.104 m wide and 0.052 m high. The side walls of the channel are made of PVC, the cover of plexiglass and the bottom of sheet metal. A rectangular opening of the bottom, 0.263 m long and 0.08 m wide, is situated on the particular sediment area considered. The water ¯ows into the channel through a diuser which enables the transition from the circular to the rectangular cross-section. Turbulence damping screens are disposed in the inlet of the measuring channel while small tubes, shaped like honeycombs following the screens, favour a rectilinear ¯ow. An outlet nozzle is linked to the main part of the channel (Fig. 1). A metal frame mounted on the measuring channel can be pushed into the sediment area
and, consequently, can be ®xed against lateral movement. An underwater video camera is mounted horizontally on the plexiglass cover of the channel over the bottom opening to record the incipient motion of the tested sediment. This camera is provided with two lamps that illuminate the sediment area, and it can take a snapshot of 0.08 0.11 m of the sediment area through a mirror. The video pictures can be assessed subjectively as well as evaluated objectively by means of an automatic image processing system. A washing device serves to remove the air bubbles from the underside of the plexiglass cover (Fig. 1). A ®re plug can be used for loading the instrument with water by means of a ®re hose. The water discharge is determined by an inductive measuring unit. Figure 1 illustrates the concept of the measuring device. Automatic image processing Quanti®cation of the critical stage for the sediment transport was obtained by automatic image processing. Hereby an analogue picture is digitized into 512 512 pixels, i.e. picture elements, and is resolved into 256 dierent grey values. Consequently, it may be assumed that a digitized picture consists of 512 lines and 512 columns. The evaluation method is based on the idea that every soil particle in motion passes a certain column of the recorded picture. The passing of the particle causes a grey value alteration on the column that is perpendicular to the ¯ow direction. If the column is
Fig. 1. Scheme of the measuring device.
Critical shear stress in sewers
stored 512 times in a second image in time intervals of 0.12 s, a line of this image represents the temporal alteration of the grey value of a pixel in time intervals of 0.12 s. The changes of the grey values on a line of the second image are caused mainly by particle transport and can be expressed by the standard deviation of the grey values. The mean value x Z of the standard deviations for all the lines is an index for the motion of soil particles. The value of x Z increases with increasing transport. The changes of the grey values on a column are due mainly to the properties of the material. Thus, the mean value x S of the standard deviations for all the columns is an index for the material composition. The value of x S varies slightly during the measurement. The ratio of the two indices, x Q x S =x Z , characterizes both the material transport and the material composition. On the basis of several measurements it was concluded that the incipient motion occurs if x Q is less than 3.0. DESCRIPTION OF THE DEPOSITS
The measurements were conducted in a grit chamber at the university campus as well as in a sewer of the city of Braunschweig under ¯ow conditions during drying time. The grit chamber was loaded with storm water collected on campus; the water in the grit chamber was pumped out before installing the measuring instrument. Two sorts of solid materials were deposited in the grit chamber: coarse material, i.e. grit, in the inlet and ®ne material, i.e. mud, in the middle and outlet of the chamber. Two layers were distinguished in the middle of the grit chamber: a sand/silt mixture on the bottom and a cover material of mud with grass, roots, leaves etc. The sewer deposits in Braunschweig were very inhomogeneous. Mirtskhoulava (1991) de®nes the inhomogeneity coecient as the ratio d50/d95. The values of this ratio vary between 0 and 1. The lower the coecient value, the more inhomogeneous the soil. The inhomogeneity coecient of the investigated soils was as follows: . Grit chamber inlet 0.29, . Sewer 0.05. The equivalent sand roughness of the deposits in the grit chamber and in the sewer is represented by the diameter d90. Table 1 shows some physical properties of the deposits in the grit chamber and in the sewer.
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Although the d50 value of the sewer deposits is lower than that of the deposits in the grit chamber inlet, the sewer deposits have a higher roughness, d90=0.0075 m compared with d90=0.0048 m for the grit chamber, due to higher inhomogeneity. DESCRIPTION OF THE CRITICAL STAGES
The coarse material in the inlet of the grit chamber and the sewer deposits are not uniformly graded. In this case the ®ner bed grains start to move at relatively low ¯ow velocities. Based on this fact it would be possible to determine the grain diameter, e.g. d10 or d20 or d30, as a characteristic diameter for the initiation of motion of the ®ner grains. Consequently, the diameter d50 does not characterize the prime sporadic motion of the relatively ®ne grains but that of the coarser grains. As far as the deposits in the middle of the grit chamber are concerned, the following motion stages were observed: For low ¯ow velocities, e.g. 0.12 m sÿ1, a sporadic, discontinuous motion of individual aggregates of the cover material takes place. For increased ¯ow velocities, e.g. 0.15 m sÿ1, a more intensive motion of the cover material and, at the same time, a motion of individual bottom grains take place. This stage was de®ned as initial surface erosion. For further increased ¯ow velocities, e.g. 0.19 m sÿ1, a more intensive motion of both cover material and bottom can be seen. This situation was de®ned as initial mass erosion. The identi®cation of the latter stage is dicult because the beginning of the mass erosion is not as pronounced as for purely cohesive soils. A further phenomenon observed during the measurements is the additional transverse eddy motion of grains and aggregates. This kind of motion results from secondary ¯ows due to bed deepening and irregularities or to the dierent roughness of the depositions. Generally it may be noted that the transport of sediments consisting not only of sand, under constant water discharge, decreases with time and is characterized by a discontinuity. Application of the automatic image processing By applying the evaluation process mentioned above to the sewer deposits, the following results were obtained: Fig. 2 represents the ratio x Q as a function of the mean ¯ow velocity. Each curve represents a single measurement. Generally, ignoring
Table 1. Properties of the deposits No. 1 2 3
Position grit chamber, inlet grit chamber, middle sewer
d50 (m) 0.00175 0.00015 0.00064
rF (kg mÿ3)
Organic material (%)
w (%)
2670 2440 2600
2.5 15.4 5.7
23 278 41
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V. Hrissanthou and S. Hartmann
Fig. 2. Statistical variation of the sewer deposits with the ¯ow velocity.
the incipient part of a certain curve which is in¯uenced by non-transport phenomena, a decreasing tendency of the ratio x Q with increasing ¯ow velocity can be observed. The threshold value x Q 3:0 is also marked in Fig. 2. The curves intersect this straight line at points which correspond to ¯ow velocities of 0.13±0.17 m sÿ1. The critical erosion velocity of the ®ner material part of the sewer sediments was determined to be 0.15 m sÿ1 by optical estimate. It is clear from the above example that automatic image processing by itself is not sucient for the quanti®cation of the critical stage. However, it has to be combined with the optical estimate on the monitor or directly on the tested area under consideration of the transport mechanics and the material composition. HYDRAULIC EVALUATION OF THE MEASUREMENTS
On the basis of the critical water discharge measured by the inductive measuring unit, the corresponding ¯ow velocity was calculated since the
cross-section area of the prismatic channel is known. From the critical ¯ow or erosion velocity the corresponding critical shear stress was calculated by three dierent methods: A, B and C. Before applying these methods the channel crosssection was divided into a bottom zone, a cover zone and a wall zone due to the dierent heights of roughness. The hydraulic radius of the bottom zone as well as the corresponding friction factor were calculated iteratively from the Colebrook±White equation (Krier, 1987). Method A is based on the Darcy±Weisbach equation for energy losses while method B on the Gauckler±Manning±Strickler formula (GMS formula) for the mean ¯ow velocity (Naudascher, 1987). Both relationships are applied to the crosssection part in¯uencing the bed for the calculation of the energy line slope. From the energy line slope the average critical shear stress is computed by the well known relationship for bottom shear stress. The application of the GMS formula, mostly used for uniform and steady ¯ow in open channels, seems to be permissible under the hydraulic and
Table 2. Critical discharges, erosion velocities and shear stresses a
Position number 1 1 2 2 3 3 a
See Table 1.
3 ÿ1
Qcr (m s ) 0.0012 0.0016 0.00082 0.00102 0.00081 0.00108
vm
cr
(m sÿ1)
0.24 0.32 0.151 0.188 0.15 0.20
tcr (N mÿ2) method A 0.50 0.88 0.12 0.18 0.23 0.41
tcr (N mÿ2) method B 0.41 0.91 0.11 0.17 0.21 0.37
tcr (N mÿ2) method C 0.50 0.89 0.10 0.15 0.23 0.41
Fig. 3. Comparison of measurements with the UnsoÈld diagram.
Critical shear stress in sewers 2039
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V. Hrissanthou and S. Hartmann
roughness conditions of the measurements presented in this paper (Naudascher, 1987). According to method C the Karman±Prandtl logarithmic wall law (Zanke, 1982) is applied to the midpoint of the ¯ow cross-section for calculating the critical shear velocity. Table 2 contains the measured critical discharges Qcr and the calculated mean critical erosion velocities vmcr and mean critical shear stresses tcr according to the computing methods A, B and C for the deposits presented in Table 1. The ®rst values for position numbers 1 and 3 concern the initial motion of a ®ner grain fragment with the characteristic diameter d30. This diameter equals 0.00092 m for the chamber inlet and 0.0004 m for the sewer. The second values for position numbers 1 and 3 characterize the initial motion of a coarser grain fragment with the characteristic diameter d50. The distinction of two grain fragments for the initiation of motion results from the deposits' inhomogeneity. The ®rst value for position number 2 designates the initial surface erosion while the second value for the same position number designates the initial mass erosion. The computed values of the critical shear stress for position numbers 1, 2, 3 and for all test cases, i.e. ®ne or coarse grain fragment, beginning of surface or mass erosion, were compared with the UnsoÈld diagram (Fig. 3). This diagram shows the dependence of the sediment Froude number Fr* on the sediment Reynolds number Re*. The incipient motion is represented by dierent parallel curves corresponding to dierent dimensionless transport rates q+ s (UnsoÈld, 1984). The computational results for the soil of position number 2, which is subjected to cohesion in¯uence and contains organic material, were intentionally compared with the UnsoÈld diagram. It is apparent from Fig. 3 that the computational results according to methods A and C are identical and deviate slightly from the results according to method B. Regarding this, it is added that the ¯ow over the soils of position numbers 1 and 3 is hydraulically rough, and the GMS formula on which method B is based is mainly valid for hydraulically rough ¯ows. CONCLUSIONS
By full-scale determination of the critical shear stress, the real conditions which cannot be simulated in the laboratory were taken into account. These conditions include secondary ¯ows, nonuniform bed roughness and bed irregularities. The Shields diagram or its modi®cations yield a ®rst rough indication for estimating the incipient motion of sediments consisting of both mineral and organic materials. Mineral sediments contain cohesive and/or noncohesive materials. The deviations of the subjective estimates from the Shields curve are due to:
. the dierent de®nition of the critical stage, . the method used to calculate the critical shear stress, . the particularities of the natural depositions, e.g. composition, inhomogeneity, organic content, cohesion in¯uence etc. The critical conditions, i.e. beginning of surface and/or mass erosion, for soils consisting of both cohesive and noncohesive materials are not distinct. Cohesive soils have a typical behaviour during the initiation of motion described in the literature (Krier, 1987). Automatic image processing is a useful tool for the quanti®cation of the changes of a sediment area due to transport by water. By using this method the subjectivity of the optical estimate of the critical stage may be reduced.
REFERENCES
Bechteler, W., Hrissanthou, V. and Hartmann, S. (1996) Messung der kritischen Sohlschubspannung von Ablagerungen (Measurement of critical shear stress of deposits). In Stoaustrag aus Kanalisationen Ð Hydrologie bebauter Gebiete, Chapter 3, pp. 43±58. DFG, VCH Verlagsgesellschaft, Weinheim. Kramer H. (1935) Sand mixtures and sand movement in ¯uvial models. Trans. ASCE 100, 798±878. Krier, H. (1987) Zum Langzeit-Erosionsverhalten kohaÈsiver FlieûgewaÈssersohlen (On longterm erosion behaviour of cohesive stream beds). Wasserbau Mitteilungen, No. 27, Institut fuÈr Wasserbau, TH Darmstadt. Mantz P. A. (1977) Incipient transport of ®ne grains and ¯akes by ¯uids Ð Extended Shields diagram. J. Hydr. Div. ASCE 103(6), 601±615. Mirtskhoulava T. E. (1991) Scouring by ¯owing water of cohesive and noncohesive beds. J. Hydr. Res. 29(3), 341±354. Naudascher, E. (1987) Hydraulik der Gerinne und Gerinnebauwerke (Hydraulics of open channel structures). Springer-Verlag, Wien, New York. Shields, A. (1936) Anwendung der AÈhnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung (Application of similarity mechanics and turbulence investigation to bed load motion). Vol. 26, Mitteilungen der preussischen Versuchsanstalt fuÈr Wasser- und Schibau, Berlin. UnsoÈld, G. (1984) Der Transportbeginn feinstkoÈrnigen rolligen Sohlmaterials in gleichfoÈrmigen turbulenten StroÈmungen: Eine experimentelle UÈberpruÈfung und Erweiterung der Shields-Funktion (An experimental examination and extension of Shields function). Report No. 70, SFB 95, UniversitaÈt Kiel. Vanoni, V. A. (1964) Measurements of critical shear stress for entraining ®ne sediments in a boundary layer. California Institute of Technology, Report No. KH-R7, Pasadena, California, U.S.A. Westrich, B. (1985) Hydromechanische Ein¯uûfaktoren auf das Transportverhalten kontaminierter Schwebstoe in FluÈssen (Hydromechanical in¯uencing factors of transport behaviour of polluted suspended load in rivers). DVWK Mitteilungen, Heft 9. Yalin M. S. and Karahan E. (1979) Inception of sediment transport. J. Hydr. Div. ASCE 105(11), 1433±1443. Zanke, U. (1982) Grundlagen der Sedimentbewegung (Fundamentals of sediment motion). Springer, Berlin.
Wat. Res. Vol. 32, No. 7, pp. 2035±2040, 1998 # 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 0043-1354/98 $19.00 + 0.00
MEASUREMENTS OF CRITICAL SHEAR STRESS IN SEWERS V. HRISSANTHOU* and S. HARTMANN Institute of Hydrosciences, Federal Armed Forces University Munich, 85577 Neubiberg, Germany (First received April 1997; accepted in revised form October 1997) AbstractÐCritical shear stress of sediment located in a grit chamber and in a sewer was determined in full-scale by a measuring device constructed in the laboratory of the Institute of Hydrosciences at the Federal Armed Forces University, Munich. The estimation of critical shear stress is actually based on the measurement of the corresponding critical water discharge. Incipient motion was recorded by a video camera and the recorded pictures were treated by an automatic image processing system. The measurement results were compared with data taken from the literature. A good agreement between measurements and literature data was obtained. The automatic image processing contributes to a more objective quanti®cation of the sediment transport initiation. # 1998 Elsevier Science Ltd. All rights reserved Key wordsÐcritical shear stress, critical erosion velocity, grit chamber, sewer, measurements, automatic image processing system
NOMENCLATURE 1, 2, 3= position numbers of deposits A, B, C= computing methods of the mean critical shear stress dch= characteristic grain diameter (m) median grain diameter (m) d50= grain diameter for which 90% of the material is ®ner (m) d90= d95, d30= corresponding de®nitions as for d90 (m) Fr*= sediment Froude number g= gravity acceleration (m sÿ2) + dimensionless transport rate in the UnsoÈld diagram qs = critical discharge (m3 sÿ1) Qcr= Re*= sediment Reynolds number mean critical erosion velocity (m sÿ1) vmcr= vo*= shear velocity (m sÿ1) w= water content (%); water percentage by weight related to the soil dried at 1058C xS = mean standard deviation of the grey values for all the columns of a digitized picture xZ = mean standard deviation of the grey values for all the lines of a digitized picture xQ = ratio xS =xZ n= kinematic viscosity of the water (m2 sÿ1) rF = sediment density (kg mÿ3) water density (kg mÿ3) rW= t o= average shear stress (N mÿ2) tcr= mean critical shear stress (N mÿ2)
INTRODUCTION
The knowledge of critical erosion velocity or critical shear stress in a river or a sewer is important for the calculation of the sediment transport. The knowledge of incipient motion is also of interest *Author to whom all correspondence should be addressed. [Present address: Section of Hydraulic Works, Department of Civil Engineering, Democritus University of Thrace, 67100 Xanthi, Greece; Tel: +30541-79608; Fax: +30-541-20371; E-mail: [email protected]].
under ecological aspects because the sediments in rivers or sewers usually contain pollutants, e.g. heavy metals (Westrich, 1985). The in situ estimation of the critical shear stress provides an important basis for a realistic calculation of the transported sediments and for the consideration of the sedimentological peculiarities of a river or a sewer. A signi®cant problem appearing during sediment transport experiments is the de®nition of the incipient motion that cannot be exactly quanti®ed. Thus, the researcher has to determine this critical situation subjectively for a set of experiments. Other authors (Kramer, 1935; Shields, 1936; Vanoni, 1964) found that the boundary between immobility and motion cannot be determined de®nitely. Therefore, it is appropriate to describe the initiation of motion not with an individual arithmetic value but by means of a range of values where the incipient conditions are given (Bechteler et al., 1996). The diagram of Shields (1936) is until now the basis for investigations concerning incipient motion of noncohesive materials. In the meantime, several modi®cations of the Shields results were done (Mantz, 1977; Yalin and Karahan, 1979; UnsoÈld, 1984, etc.). Generally it can be concluded that the experimental results of dierent authors for noncohesive, uniformly graded sediment do not deviate signi®cantly from each other. However, the de®nitions they used for the incipient motion were dierent. As far as cohesive material is concerned, considerable dierences exist not only in the de®nition
2035
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V. Hrissanthou and S. Hartmann
of incipient motion but also in the preparation of soils, the experimental conditions, the erosion load, the duration of the experiments, the measured soil parameters and the measurement of the erosion rates. Therefore, the comparison between dierent experimental results is not easy (Krier, 1987). In spite of the dierences mentioned above, two characteristic stages of cohesive soil erosion may be identi®ed in the literature: the surface erosion and the mass erosion. Correspondingly, two critical situations may also be distinguished: the initiation of surface erosion and the initiation of mass erosion.
MEASURING DEVICE
The measuring device consists mainly of a prismatic channel 0.77 m long, with a rectangular cross-section 0.104 m wide and 0.052 m high. The side walls of the channel are made of PVC, the cover of plexiglass and the bottom of sheet metal. A rectangular opening of the bottom, 0.263 m long and 0.08 m wide, is situated on the particular sediment area considered. The water ¯ows into the channel through a diuser which enables the transition from the circular to the rectangular cross-section. Turbulence damping screens are disposed in the inlet of the measuring channel while small tubes, shaped like honeycombs following the screens, favour a rectilinear ¯ow. An outlet nozzle is linked to the main part of the channel (Fig. 1). A metal frame mounted on the measuring channel can be pushed into the sediment area
and, consequently, can be ®xed against lateral movement. An underwater video camera is mounted horizontally on the plexiglass cover of the channel over the bottom opening to record the incipient motion of the tested sediment. This camera is provided with two lamps that illuminate the sediment area, and it can take a snapshot of 0.08 0.11 m of the sediment area through a mirror. The video pictures can be assessed subjectively as well as evaluated objectively by means of an automatic image processing system. A washing device serves to remove the air bubbles from the underside of the plexiglass cover (Fig. 1). A ®re plug can be used for loading the instrument with water by means of a ®re hose. The water discharge is determined by an inductive measuring unit. Figure 1 illustrates the concept of the measuring device. Automatic image processing Quanti®cation of the critical stage for the sediment transport was obtained by automatic image processing. Hereby an analogue picture is digitized into 512 512 pixels, i.e. picture elements, and is resolved into 256 dierent grey values. Consequently, it may be assumed that a digitized picture consists of 512 lines and 512 columns. The evaluation method is based on the idea that every soil particle in motion passes a certain column of the recorded picture. The passing of the particle causes a grey value alteration on the column that is perpendicular to the ¯ow direction. If the column is
Fig. 1. Scheme of the measuring device.
Critical shear stress in sewers
stored 512 times in a second image in time intervals of 0.12 s, a line of this image represents the temporal alteration of the grey value of a pixel in time intervals of 0.12 s. The changes of the grey values on a line of the second image are caused mainly by particle transport and can be expressed by the standard deviation of the grey values. The mean value x Z of the standard deviations for all the lines is an index for the motion of soil particles. The value of x Z increases with increasing transport. The changes of the grey values on a column are due mainly to the properties of the material. Thus, the mean value x S of the standard deviations for all the columns is an index for the material composition. The value of x S varies slightly during the measurement. The ratio of the two indices, x Q x S =x Z , characterizes both the material transport and the material composition. On the basis of several measurements it was concluded that the incipient motion occurs if x Q is less than 3.0. DESCRIPTION OF THE DEPOSITS
The measurements were conducted in a grit chamber at the university campus as well as in a sewer of the city of Braunschweig under ¯ow conditions during drying time. The grit chamber was loaded with storm water collected on campus; the water in the grit chamber was pumped out before installing the measuring instrument. Two sorts of solid materials were deposited in the grit chamber: coarse material, i.e. grit, in the inlet and ®ne material, i.e. mud, in the middle and outlet of the chamber. Two layers were distinguished in the middle of the grit chamber: a sand/silt mixture on the bottom and a cover material of mud with grass, roots, leaves etc. The sewer deposits in Braunschweig were very inhomogeneous. Mirtskhoulava (1991) de®nes the inhomogeneity coecient as the ratio d50/d95. The values of this ratio vary between 0 and 1. The lower the coecient value, the more inhomogeneous the soil. The inhomogeneity coecient of the investigated soils was as follows: . Grit chamber inlet 0.29, . Sewer 0.05. The equivalent sand roughness of the deposits in the grit chamber and in the sewer is represented by the diameter d90. Table 1 shows some physical properties of the deposits in the grit chamber and in the sewer.
2037
Although the d50 value of the sewer deposits is lower than that of the deposits in the grit chamber inlet, the sewer deposits have a higher roughness, d90=0.0075 m compared with d90=0.0048 m for the grit chamber, due to higher inhomogeneity. DESCRIPTION OF THE CRITICAL STAGES
The coarse material in the inlet of the grit chamber and the sewer deposits are not uniformly graded. In this case the ®ner bed grains start to move at relatively low ¯ow velocities. Based on this fact it would be possible to determine the grain diameter, e.g. d10 or d20 or d30, as a characteristic diameter for the initiation of motion of the ®ner grains. Consequently, the diameter d50 does not characterize the prime sporadic motion of the relatively ®ne grains but that of the coarser grains. As far as the deposits in the middle of the grit chamber are concerned, the following motion stages were observed: For low ¯ow velocities, e.g. 0.12 m sÿ1, a sporadic, discontinuous motion of individual aggregates of the cover material takes place. For increased ¯ow velocities, e.g. 0.15 m sÿ1, a more intensive motion of the cover material and, at the same time, a motion of individual bottom grains take place. This stage was de®ned as initial surface erosion. For further increased ¯ow velocities, e.g. 0.19 m sÿ1, a more intensive motion of both cover material and bottom can be seen. This situation was de®ned as initial mass erosion. The identi®cation of the latter stage is dicult because the beginning of the mass erosion is not as pronounced as for purely cohesive soils. A further phenomenon observed during the measurements is the additional transverse eddy motion of grains and aggregates. This kind of motion results from secondary ¯ows due to bed deepening and irregularities or to the dierent roughness of the depositions. Generally it may be noted that the transport of sediments consisting not only of sand, under constant water discharge, decreases with time and is characterized by a discontinuity. Application of the automatic image processing By applying the evaluation process mentioned above to the sewer deposits, the following results were obtained: Fig. 2 represents the ratio x Q as a function of the mean ¯ow velocity. Each curve represents a single measurement. Generally, ignoring
Table 1. Properties of the deposits No. 1 2 3
Position grit chamber, inlet grit chamber, middle sewer
d50 (m) 0.00175 0.00015 0.00064
rF (kg mÿ3)
Organic material (%)
w (%)
2670 2440 2600
2.5 15.4 5.7
23 278 41
2038
V. Hrissanthou and S. Hartmann
Fig. 2. Statistical variation of the sewer deposits with the ¯ow velocity.
the incipient part of a certain curve which is in¯uenced by non-transport phenomena, a decreasing tendency of the ratio x Q with increasing ¯ow velocity can be observed. The threshold value x Q 3:0 is also marked in Fig. 2. The curves intersect this straight line at points which correspond to ¯ow velocities of 0.13±0.17 m sÿ1. The critical erosion velocity of the ®ner material part of the sewer sediments was determined to be 0.15 m sÿ1 by optical estimate. It is clear from the above example that automatic image processing by itself is not sucient for the quanti®cation of the critical stage. However, it has to be combined with the optical estimate on the monitor or directly on the tested area under consideration of the transport mechanics and the material composition. HYDRAULIC EVALUATION OF THE MEASUREMENTS
On the basis of the critical water discharge measured by the inductive measuring unit, the corresponding ¯ow velocity was calculated since the
cross-section area of the prismatic channel is known. From the critical ¯ow or erosion velocity the corresponding critical shear stress was calculated by three dierent methods: A, B and C. Before applying these methods the channel crosssection was divided into a bottom zone, a cover zone and a wall zone due to the dierent heights of roughness. The hydraulic radius of the bottom zone as well as the corresponding friction factor were calculated iteratively from the Colebrook±White equation (Krier, 1987). Method A is based on the Darcy±Weisbach equation for energy losses while method B on the Gauckler±Manning±Strickler formula (GMS formula) for the mean ¯ow velocity (Naudascher, 1987). Both relationships are applied to the crosssection part in¯uencing the bed for the calculation of the energy line slope. From the energy line slope the average critical shear stress is computed by the well known relationship for bottom shear stress. The application of the GMS formula, mostly used for uniform and steady ¯ow in open channels, seems to be permissible under the hydraulic and
Table 2. Critical discharges, erosion velocities and shear stresses a
Position number 1 1 2 2 3 3 a
See Table 1.
3 ÿ1
Qcr (m s ) 0.0012 0.0016 0.00082 0.00102 0.00081 0.00108
vm
cr
(m sÿ1)
0.24 0.32 0.151 0.188 0.15 0.20
tcr (N mÿ2) method A 0.50 0.88 0.12 0.18 0.23 0.41
tcr (N mÿ2) method B 0.41 0.91 0.11 0.17 0.21 0.37
tcr (N mÿ2) method C 0.50 0.89 0.10 0.15 0.23 0.41
Fig. 3. Comparison of measurements with the UnsoÈld diagram.
Critical shear stress in sewers 2039
2040
V. Hrissanthou and S. Hartmann
roughness conditions of the measurements presented in this paper (Naudascher, 1987). According to method C the Karman±Prandtl logarithmic wall law (Zanke, 1982) is applied to the midpoint of the ¯ow cross-section for calculating the critical shear velocity. Table 2 contains the measured critical discharges Qcr and the calculated mean critical erosion velocities vmcr and mean critical shear stresses tcr according to the computing methods A, B and C for the deposits presented in Table 1. The ®rst values for position numbers 1 and 3 concern the initial motion of a ®ner grain fragment with the characteristic diameter d30. This diameter equals 0.00092 m for the chamber inlet and 0.0004 m for the sewer. The second values for position numbers 1 and 3 characterize the initial motion of a coarser grain fragment with the characteristic diameter d50. The distinction of two grain fragments for the initiation of motion results from the deposits' inhomogeneity. The ®rst value for position number 2 designates the initial surface erosion while the second value for the same position number designates the initial mass erosion. The computed values of the critical shear stress for position numbers 1, 2, 3 and for all test cases, i.e. ®ne or coarse grain fragment, beginning of surface or mass erosion, were compared with the UnsoÈld diagram (Fig. 3). This diagram shows the dependence of the sediment Froude number Fr* on the sediment Reynolds number Re*. The incipient motion is represented by dierent parallel curves corresponding to dierent dimensionless transport rates q+ s (UnsoÈld, 1984). The computational results for the soil of position number 2, which is subjected to cohesion in¯uence and contains organic material, were intentionally compared with the UnsoÈld diagram. It is apparent from Fig. 3 that the computational results according to methods A and C are identical and deviate slightly from the results according to method B. Regarding this, it is added that the ¯ow over the soils of position numbers 1 and 3 is hydraulically rough, and the GMS formula on which method B is based is mainly valid for hydraulically rough ¯ows. CONCLUSIONS
By full-scale determination of the critical shear stress, the real conditions which cannot be simulated in the laboratory were taken into account. These conditions include secondary ¯ows, nonuniform bed roughness and bed irregularities. The Shields diagram or its modi®cations yield a ®rst rough indication for estimating the incipient motion of sediments consisting of both mineral and organic materials. Mineral sediments contain cohesive and/or noncohesive materials. The deviations of the subjective estimates from the Shields curve are due to:
. the dierent de®nition of the critical stage, . the method used to calculate the critical shear stress, . the particularities of the natural depositions, e.g. composition, inhomogeneity, organic content, cohesion in¯uence etc. The critical conditions, i.e. beginning of surface and/or mass erosion, for soils consisting of both cohesive and noncohesive materials are not distinct. Cohesive soils have a typical behaviour during the initiation of motion described in the literature (Krier, 1987). Automatic image processing is a useful tool for the quanti®cation of the changes of a sediment area due to transport by water. By using this method the subjectivity of the optical estimate of the critical stage may be reduced.
REFERENCES
Bechteler, W., Hrissanthou, V. and Hartmann, S. (1996) Messung der kritischen Sohlschubspannung von Ablagerungen (Measurement of critical shear stress of deposits). In Stoaustrag aus Kanalisationen Ð Hydrologie bebauter Gebiete, Chapter 3, pp. 43±58. DFG, VCH Verlagsgesellschaft, Weinheim. Kramer H. (1935) Sand mixtures and sand movement in ¯uvial models. Trans. ASCE 100, 798±878. Krier, H. (1987) Zum Langzeit-Erosionsverhalten kohaÈsiver FlieûgewaÈssersohlen (On longterm erosion behaviour of cohesive stream beds). Wasserbau Mitteilungen, No. 27, Institut fuÈr Wasserbau, TH Darmstadt. Mantz P. A. (1977) Incipient transport of ®ne grains and ¯akes by ¯uids Ð Extended Shields diagram. J. Hydr. Div. ASCE 103(6), 601±615. Mirtskhoulava T. E. (1991) Scouring by ¯owing water of cohesive and noncohesive beds. J. Hydr. Res. 29(3), 341±354. Naudascher, E. (1987) Hydraulik der Gerinne und Gerinnebauwerke (Hydraulics of open channel structures). Springer-Verlag, Wien, New York. Shields, A. (1936) Anwendung der AÈhnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebebewegung (Application of similarity mechanics and turbulence investigation to bed load motion). Vol. 26, Mitteilungen der preussischen Versuchsanstalt fuÈr Wasser- und Schibau, Berlin. UnsoÈld, G. (1984) Der Transportbeginn feinstkoÈrnigen rolligen Sohlmaterials in gleichfoÈrmigen turbulenten StroÈmungen: Eine experimentelle UÈberpruÈfung und Erweiterung der Shields-Funktion (An experimental examination and extension of Shields function). Report No. 70, SFB 95, UniversitaÈt Kiel. Vanoni, V. A. (1964) Measurements of critical shear stress for entraining ®ne sediments in a boundary layer. California Institute of Technology, Report No. KH-R7, Pasadena, California, U.S.A. Westrich, B. (1985) Hydromechanische Ein¯uûfaktoren auf das Transportverhalten kontaminierter Schwebstoe in FluÈssen (Hydromechanical in¯uencing factors of transport behaviour of polluted suspended load in rivers). DVWK Mitteilungen, Heft 9. Yalin M. S. and Karahan E. (1979) Inception of sediment transport. J. Hydr. Div. ASCE 105(11), 1433±1443. Zanke, U. (1982) Grundlagen der Sedimentbewegung (Fundamentals of sediment motion). Springer, Berlin.