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Effects of bed material properties on cohesive sediment erosion
Marine Geology 207 (2004) 83 – 93 www.elsevier.com/locate/margeo
Effects of bed material properties on cohesive sediment erosion Jochen Aberle a,*, Vladimir Nikora b, Roy Walters b a
Leichtweiss-Institut fu¨r Wasserbau, Technische Universita¨t Braunschweig, Beethovenstr. 51a, 38108 Braunschweig, Germany b National Institute of Water and Atmospheric Research (NIWA), P.O. Box 8602, Christchurch, New Zealand Received 21 October 2002; received in revised form 18 August 2003; accepted 18 March 2004
Abstract A straight benthic in situ flume was used to measure the erosion rate of cohesive sediments in freshwater and saltwater environments in New Zealand. The data show an exponential decay of erosion rate with time, which is indicative of depthlimited erosion. Two approaches for the calibration of an erosion formula are used, both leading to similar results. The data show the dependency of erosion rate on bed material properties, such as dry bulk density, water content, organic content and sand content. Both methodologies also highlight differences between data from freshwater and saltwater environments. Also shown is a requirement for direct measurements of bed density profiles and bed load transport during in situ investigations. D 2004 Elsevier B.V. All rights reserved. Keywords: cohesive sediment; erosion rate; fine sediment transport; critical bed shear stress; mud
1. Introduction Although cohesive sediment dynamics is important for many engineering and ecological applications, its general theory is still unavailable (Black et al., 2002). Studying cohesive sediment erosion directly in the field, without disturbing natural cohesive beds, is probably one of the most promising directions in advancing this topic. Various in situ sediment flumes have been developed for such studies. In their deployments, researchers often follow an experimental procedure in which increasing values of bed shear * Corresponding author. Tel.: +49-531-391-3973; fax: +49-531391-8184. E-mail addresses: [email protected] (J. Aberle), [email protected] (V. Nikora), [email protected] (R. Walters). 0025-3227/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.margeo.2004.03.012
stress are applied step-wise over fixed time intervals (usually 5 –20 min; Amos et al., 1992, 1997, 1998; Maa et al., 1998; Ravens and Gschwend, 1999; Houwing, 1999; Aberle et al., 2003a). Two erosion mechanisms have emerged from these investigations that are directly associated with the bed structure. Depth-limited or type I erosion occurs once the threshold for motion due to hydrodynamic forces is exceeded and particles are eroded from the surface (Mehta and Partheniades, 1982; Parchure and Mehta, 1985). Erosion ceases when the applied bed shear stress sb reaches the bed shear strength ss at a certain eroded depth. Such erosion behaviour can be explained by increasing bed shear strength with depth. On the other hand, steady-state or type II erosion is characteristic of uniform beds where the bed shear strength does not change with depth (Parchure and Mehta, 1985; Zreik et al., 1998). In
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this case, the erosion rate is constant (Amos et al., 1992; Paterson and Black, 1999). In practice, the erosion rate does not necessarily cease during an experimental interval and there is no clear distinction between depth-limited and steadystate erosion (Amos et al., 1992, 1997). Such erosion behaviour is defined as transitional erosion or type I/II erosion (Amos et al., 1997; Andersen et al., 2002). If the time duration of the experimental interval is insufficient for the condition sb = ss to be attained, erosion will not cease and could be classified as type I/II erosion or type II erosion, although in reality it may be type I erosion (Parchure and Mehta, 1985; Piedra-Cueva and Mory, 2001). In this paper, we first discuss the time dependency of erosion rates on the basis of time series of erosion rate measured by the NIWA in situ flume (Aberle et al., 2003a). The data are used to estimate the erosion parameters within Sanford and Maa’s (2001) erosion formulation. Then, effects of flow and bed material variations on the erosion parameters are studied. Finally, limitations and needs for further developments are discussed.
2. Methods Data were collected with the NIWA in situ flume (Fig. 1) in several aquatic environments near Christchurch and Hamilton, New Zealand. The flume was designed as a straight benthic flow-through flume with a rectangular cross-section (0.10 m high and 0.20 m
wide). It consists of a bottomless 0.30-m-long entrance section, a bottomless, straight 0.90-m-long erosion section, and a section with a solid bottom. Water is sucked through the flume with a propeller, driven by an electrical motor. Water turbidity is monitored with two optical back-scatter (D & A OBS-3) sensors, one in the solid bottom section and the other at the flume entrance. OBS-3 readings are sampled each second and then logged by a Campbell data logger as average values over 30 s intervals. Turbidity readings are calibrated against suspended sediment concentration (SSC) for each in situ experiment, where SSC is determined from in situ water samples taken with a small pump near the downstream OBS-3 sensor. For each deployment, SSC- values for six water samples are plotted against turbidity readings averaged over the time intervals for corresponding water samples. Calibration coefficients are obtained from these data using linear regression. Flow velocities are measured in the centre of the flume over the fixed bedfixed-bed section using an Ott C2 current meter, and are recorded continuously with an averaging time interval of 30 s. The centreline velocity is empirically related to the bed shear stress using acoustic Doppler velocimeter (ADV) measurements of near-bed Reynolds stresses for two different types of roughness (smooth wood and sandpaper with particle diameter d c 0.4 mm, Aberle et al., 2003a). The SSC and velocity data were used to calculate the erosion rates using the input and output fluxes of sediment and the continuity equation for the solid phase. More details on the flume and its performance may be found in Aberle et al. (2003a).
Fig. 1. The NIWA in situ flume. The flume has been designed as a straight benthic flow-through flume and is equipped with OBS-3 sensors, photodetectors, an Ott current meter, and a water sampling system. Special ADV-hatches allow for ADV measurements inside of the flume. Note that the wheels are uplifted during operation. Handles and frames attached to the flume are removable.
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In our field experiments, the flume was floated into the water and carefully deployed without disturbing the bed at the deployment site. The most suitable range of water depths for deployments is from ca. 0.40 to ca. 1.10 m. After both OBS-sensors showed constant (ambient) readings, the velocity in the flume was step-wise increased at intervals of 10– 15 min with a ramping period of 5 –10 s at the beginning of each interval. The experiments were terminated after a scour developed at the entrance section of the flume or at the transition between open and fixed bed or when the maximum flow velocity in the flume (approximately 1.10 m s 1) was reached. The appearance of the scour could be detected visually and/or by anomalous change in OBS readings. Information on bed material properties, such as bulk density, water content and loss on ignition (LOI) were obtained from averaged values of five bulk bed material samples taken in the vicinity of the flume. The samples were taken with a specially designed, sharp edged bed material sampler with the dimensions 15 15 3 cm (length width height). The relatively large sample volume of 675 cm3 ensures that the effect of potential sediment disturbances due to the sampling procedure is minimised. The grain size distributions for mixtures of these five samples were determined using a Malvern-S
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particle size analyser. In Table 1, we present bed material characteristics and information on grain size distribution for 11 deployments. Eight of these deployments were in freshwater and three in saltwater. Half of freshwater deployments were in non-tidal rivers (Halswell River, Avon River 1, 2 and LII), one measurement site was influenced by tidal backwater (Styx River), and the other three freshwater deployments were carried out in a wetland environment (Travis Wetlands 1, 2 and 3). The saltwater deployments were in tidal estuarine environments. Unfortunately, sedimentation history at the measurement sites is not available. Geographically, the sites were distributed in close proximity to Christchurch and Hamilton, New Zealand, and therefore their detailed location maps are not shown here.
3. Data analysis Fig. 2 shows a typical plot of velocity and OBS-3 data (converted to SSC) obtained during our investigations at the Styx River near Christchurch, New Zealand. A typical feature of this plot is that the erosion rates were initially high at the onsets of bed shear stress increases, once erosion threshold was exceeded. The
Table 1 Sediment characteristics at the deployment sites Site
d50 (Am)
Claya (%)
Siltb (%)
Sandc (%)
Wet bulk density (kg m 3)
Dry bulk density (kg m 3)
Waterd content (%)
LOIe (%)
Halswell Riverf Travis Wetlands 1f Travis Wetlands 2f Travis Wetlands 3f Avon River 1f Avon River 2f Styx Riverf Allendaleg Avon Estuaryg LIIf Raglan Harbourg
34 23 10 18 70 48 108 6 13 26 21
10 13 16 14 5 6 10 23 15 12 14
54 62 66 67 43 52 36 74 68 63 65
36 25 17 19 52 42 54 2 17 25 21
1305 1497 1293 1473 1235 1130 1420 1431 1581 1137 1753
529 813 492 868 339 280 642 697 949 216 1153
61.2 44.6 65.1 41.6 73.1 75.3 56.1 51.5 40.2 81.0 31.2
9.1 3.9 12.2 4.9 18.4 15.4 12.2 4.5 3.5 12.0 3.6
a
d V 2 Am. 2 Am < d V 64 Am. c d > 64 Am. d Samples dried at 105 jC. e Samples ashed at 500 jC for a period of 24 h. f Freshwater environment. g Marine environment. b
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Fig. 2. The time series of the centreline velocity UOtt (triangles) and the SSC from OBS-3 sensors: upstream (at flume entrance, diamonds) and downstream (in fixed-bed section, squares), field deployment in the Styx River near Christchurch, New Zealand. Once the critical threshold for erosion is exceeded, erosion increases sharply at the onset of each velocity level and then ceases.
high initial erosion rate decreased exponentially within each time interval of constant velocity (for t>3000 s). One may also note that erosion did not always cease before the next increase in flow velocity (e.g., t>5000 s). In general, surficial sediments are often characterised by large vertical gradients in bed shear strength (Amos et al., 1992; Maa et al., 1998; Zreik et al., 1998; Ravens and Gschwend, 1999; Sanford and Maa, 2001) and, therefore, erosion depths in field deployments may be restricted to the top few millimetres. In relation to our field experiments, we infer that the time duration of 10 min for each velocity step was insufficient for the condition sb = ss to be attained. Overall, the data suggest that we deal with the depth-limited erosion (type I; due to the vertical heterogeneity in bed structure) or a combination of depth-limited erosion and steady-state erosion (type II). This assumption is supported by the results of Aberle et al. (2002, submitted for publication 2003b) showing that potential hydrodynamic effects that could enhance erosion during the ramping periods are insignificant for our flume. Many existing formulations for erosion types I and II are based on the concept of critical bed shear stress, that is, erosion occurs as long as the applied bed shear stress is larger than the critical bed shear stress for erosion. In a reasonably general form, the existing formulations may be summarised as a power relationship: E ¼ M ðzÞðsb sc ðzÞÞn
ð1Þ
where E is the erosion rate (kg m 2 s 1), M(z) is an empirical erosion coefficient with its dimension depending on an exponent n (for n = 1: kg m 2 s 1 Pa 1), sb is the bed shear stress (Pa), sc(z) is the critical bed shear stress for erosion (Pa) that may vary with z (Maa et al., 1998; Ravens and Gschwend, 1999; Mehta and Parchure, 2000). Eq. (1) may be also presented in a dimensionless form (e.g., by normalising on sc), but this does not provide significant improvements or simplification. Use of Eq. (1) in determining the erosion parameters from in situ measurements is not straightforward because both parameters M and sc, and a variety of physical, chemical and biological factors influencing them, are unknown functions of sediment depth. Indeed, there is a lack of consistency in the way the various parameters from field deployments are interpreted. For example, in some investigations, E is defined as the initial erosion rate after application of a new bed shear stress (peak erosion rate, Amos et al., 1992; Maa et al., 1998; Houwing, 1999). Ravens and Gschwend (1999) determine the erosion rate as the rate of sediment resuspension after some initial response has passed, while Amos et al. (1998) and Andersen et al. (2002) averaged erosion rates over each velocity step. Different approaches provide different values for the erosion rates and, thus, for the parameters of Eq. (1), or other erosion formulations. As a result of these difficulties, we have adopted an approach where we use simple time-dependent
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expressions for E that can be evaluated with field experiments. The approach follows from recent results of Sanford and Maa (2001). The basic idea is to differentiate Eq. (1) with respect to time to describe the transient behaviour of E, then solve this differential equation for simple initial conditions such as a step-wise increase of bed shear stress. For suitable assumptions that neglect time dependence of M and sc, and setting n = 1, Sanford and Maa (2001) derived:
dure to account for potential offsets and errors in the data, and therefore to improve estimates of b2. On the other hand, b3 is usually much lower than b1 so the estimates of M are not greatly affected. For the ‘bulk’ approach, we use the depth-averaged value of dry bulk density as directly measured by our 3 cm deep bulk bed material samples and consider erosion rates E0 at t = t0 only. In this case, Eq. (2) reduces to E0 = Udh(sbsc0). Taking n velocity steps into account and summing E0 for each velocity step (to reduce random errors) yields,
E ¼ qd ðzÞbðsb sc 0 Þecbðtt0 Þ
n X
ð2Þ
i¼1
where qd (z) is dry bulk density at sediment depth z, b is a local parameter, sc0 is critical bed shear stress when sb is first applied at t = t0, t is time, and c = dsc/ dz is the vertical gradient of the critical bed shear stress (or bed shear strength). Eq. (2) is based on an assumption of a locally constant vertical gradient of bed shear strength sc, and a direct proportionality between the erosion constant M and sediment concentration at the water – sediment interface M = qd(z)b. For a uniform bed, c = 0 and Eq. (2) reduces to the linear erosion formulation E = M(sb sc). For a stratified bed, c p 0 and Eq. (2) describes an exponential decay of erosion rate with time, as shown in Maa and Lee (1997) and Piedra-Cueva and Mory (2001). Proper evaluation of parameters in Eq. (2) requires information on vertical profiles of the bulk density and water content with a high spatial resolution. Such information is not available for our experiments, as bulk densities were estimated from 3-cm-deep sampling volumes. Therefore, we developed two methods, ‘bulk’ and ‘last step’ methods, for evaluating b, a key parameter in Eq. (2). Both methods were suggested as an attempt to extract maximum information from our data, and are described in detail in Aberle et al. (2003b submitted for publication). In brief, time series of erosion rates for each velocity step during an experiment were fitted to the function E ¼ b1 eb2 ðtt0 Þ þ b3 using a least-squares algorithm, where b1, b2 and b3 are fitted parameters. As an example in Fig. 2, step intervals of constant velocity of 2400 – 3000, 3000 – 3600, 3600 – 4200, 4200 – 4800, 4800 – 5400 and 5400 – 6000 s were fitted. Factor b3 is introduced into the fitting proce-
E0;i ¼
n X ðb1;i þ b3;i Þ ¼ M ðsb;n sc 0;1 Þ
ð3Þ
i¼1
with M = qdb. Thus, plotting the cumulative sum of (b1,i + b3,i) against the bed shear stress yields information on M. Under the simplified assumption of a constant dry bulk density, which should be equal to the measured depth-averaged bulk density, b can then be calculated. Examples of plots Rn ðb1;i þ b3;i Þ ¼ f ðsb;n Þ are shown in Fig. 3 for the data sets from Avon River 1, Styx River, L II River and Raglan Harbour, with the depth-averaged dry bulk densities given in Table 1. According to Eq. (3), data points that can be approximated by a straight line indicate a constant value of M, and hence reflect no significant changes of the product qd b during the experiment (e.g., Styx River and LII River sites in Fig. 3). Convexity of the curve Rn ðb1;i þ b3;i Þ ¼ f ðsb;n Þ indicates a decrease in qdb with increasing depth (e.g., Avon River 1 and Raglan Harbour sites in Fig. 3), while concavity of the data points indicates an increase of qdb with depth. If b changes with depth, the theoretical framework of Eqs. (2) and (3) should be extended and would result in a formulation that would deviate from simple exponential behaviour. However, if values of b do not change significantly during a single erosion event, Eq. (2) remains a locally valid approximation (Sanford and Maa, 2001). In our analysis, we used estimates of M and hence b only if the data points could be fitted with a straight line with a squared correlation coefficient R2>0.90. Otherwise, we used only the first few data points, which could be reasonably approximated by a straight line (e.g., only the first three data points for Avon River 1 and Raglan Harbour in Fig. 3). Table 2 shows the number of subsequent steps included in the analysis, the
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Fig. 3. Cumulative plot of (b1 + b3) against the bed shear stress, used for estimation of M (and b) by the bulk method for the experiments in Avon River 1, Styx River, Raglan Harbour, and L II-River.
estimated value of b, and the R2 value for the linear fit in estimating b for each deployment. The ‘last step’ method is based on an assumption that the 3 cm depth-averaged bed characteristics are mainly determined by the bed material properties at the last experimental step before the experiment was terminated (e.g., velocity step at t > 5500 s in Fig. 2). The thin surface sediment layer with increasing bed density is eroded during the precedent experimental steps, and thus the measured depth-averaged values,
biased by deeper sediments, should provide a good estimate for the dry bulk density for the layer eroded during the last experimental step. Bearing this in mind, the value of M for the last erosion step can be estimated from Eq. (2) and then the corresponding value of b can be calculated. Assuming that b does not change with depth, one may calculate dry bulk densities for the sediment layers eroded before the last experimental step. In our analysis, we excluded the end steps when the calculated bulk densities for the
Table 2 Estimates of b from the ‘bulk’ and ‘last step’ methods Experiment
Halswell Rivera Travis Wetlands 1a Travis Wetlands 2a Travis Wetlands 3a Avon River 1a Avon River 2a Styx Rivera Allendalec Avon Estuaryc LIIa Raglan Harbourc a
Bulk approach No. of steps
b bulk (m s 1 Pa 1)
R bulk method
No. of steps
b last step (m s 1 Pa 1)
Maximum density (kg m 3)
3 3 3 3 3 5 6 6 5 4 3
3.51 10 4 2.01 10 4 9.29 10 4 7.36 10 5 3.57 10 4 1.47 10 4 1.96 10 5 5.69 10 4 1.54 10 4 9.22 10 4 3.08 10 5
0.99 0.97 0.99 0.99 0.94 0.98 0.99 0.91 0.98 0.99 0.99
3 5 3 2 –b 4 6 5 4 4 3
3.42 10 4 5.24 10 4 9.73 10 4 8.08 10 5 –b 1.76 10 4 2.55 10 5 7.58 10 4 2.25 10 4 7.84 10 4 3.09 10 5
560 813 492 889 –b 310 642 697 972 294 1335
Freshwater environment. Not applicable. c Marine environment. b
Last step approach 2
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previously eroded layers were unrealistically large. For example, the method was not applicable to analyse data from the Avon River 1 site where estimates of the bulk densities calculated from this method exceeded values of 3500 kg/m3. The possible reasons for this increased uncertainty could be anomalous distribution of bed material properties and effects of organic inclusions (see also Sections 4 and 5). Table 2 provides information on the total numbers of steps included into the analysis for this method, estimated values of b, and the estimated maximum bulk density for each site. A comparison between the estimates of b (Table 2) indicates that both methods yield similar results. The largest difference is observed for the site Travis Wetlands 1 that can be explained by the experimental setup. During the deployment, an operator carefully approached the flume from behind after three velocity steps. Walking close to the flume resulted in an artificially introduced erosion event in the flume (see also Aberle et al., 2003a), although the applied bed shear stress was constant. Such artificially introduced erosion events (two erosion peaks within the same velocity step) make it difficult or impossible to apply these methods and introduce additional uncertainty in the analysis.
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4. Results Fig. 4 shows estimates of b from both methods as a function of the dry bulk density. The bulk density used in Fig. 4 represents mean values of five 3 cm deep samples taken in the vicinity of the flume. As one can see in Fig. 4, the parameter b decreases with increasing dry bulk density or, in other words, b increases with increasing water content due to a direct relationship between dry bulk density and water content (Flemming and Delafontaine, 2000). However, three data points can be identified in Fig. 4 that deviate from this behaviour (Halswell, Avon River 1, and Avon River 2). All three sites are within freshwater lowland streams with a river-bed filled with fibrous organic material such as decomposing leaves, root systems, etc. We found that such organic layers, if specially structured, show an immense resistance to erosion. In our experiments, we could not erode these structured organic layers, which sheltered sediment layers below. As a consequence, erosion stopped after some velocity steps and further velocity increases did not lead to erosion events. Hence, low values of b were obtained for these sites where the amount of organics, indicated by LOI in Table 1, was large. However, LOI alone cannot characterise the structural
1.2x10-3
β (ms -1 Pa -1 )
1.0x10-3
Bulk method Last step method
8.0x10-4 6.0x10-4
Fibrous organic layers
4.0x10-4 2.0x10-4 S 0 0
200
400
600
800
1000
1200
1400
Dry bulk density (kgm -3) Fig. 4. The parameter b vs. the dry bulk density. The three marked data points correspond to the sites within Halswell River, Avon River 1, and Avon River 2, which were characterised by the presence of structured layers of fibrous organics. S identifies data from the Styx River (see text for discussion).
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Fig. 5. The parameter b vs. the sand content. The data can be subdivided into two groups: freshwater and saltwater data. The solid lines indicate best-fit relationships based on the last step method.
arrangement of the organic fibrous components and, therefore, cannot be used unambiguously for quantifying resistance to erosion. Fig. 4 also contains a fourth point that deviates from the general trend (Styx River site). In addition to large organic content, the bed material for this particular experiment had a large sand fraction (54%). A possible dependency of M and thus b on bed material composition was indicated by Sanford and Maa (2001). In order to explore this effect, the parameter b is plotted against the sand content in Fig. 5. This figure indicates that an increase in sand content results
in a decrease in b. A potential explanation for such behaviour is the presence of bed load (see also Section 5 below). Another interesting observation from Fig. 5 is that the data are grouped separately for freshwater and saltwater environments. However, note that one freshwater data point (Travis Wetlands 3) lies within the saltwater data group. This particular site was located in a small pond where the bed was disturbed a year or so before the experiment by some construction work. This site had a relatively high, for freshwater, water conductivity of 820 AS/cm 1. These conditions distinguish this particular freshwater site
Fig. 6. The exponent b2 as a function of the applied bed shear stress for all data under investigation.
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from other freshwater sites and may explain why this point grouped together with the saltwater data. Fig. 5 does not reveal strong effects of organic layers as in Fig. 4. This may be explained by a large sand content in the lowland streams in addition to the observed vegetative layers. Based on Fig. 5 and the data for the ‘last step’ method, the following empirical relationships can be derived for b (with the dimensions m s 1 Pa 1) as a function of the sand content, b = 3.0 10 3 exp( 0.063 SC) for the freshwater sites, and b = 9.8 10 4 exp( 0.113 SC) for the saltwater sites, where SC is the sand content in [%] percent (%) and the R2 values are 0.93 and 0.97, respectively. Similar relationships may be obtained for b from the bulk method. We chose an exponential fit because an exponential function does not yield negative values for b for larger sand contents and yields a slightly better fit compared to a power function. Fig. 6 shows estimates of the exponent b2 in E ¼ b1 eb2 ðtt0 Þ þ b3 as a function of the applied bed shear stress. Fig. 6 indicates a general decaying behaviour of the exponent b2 approaching a constant with increasing bed shear stress. Such behaviour can be expected since b2 ¼ cb ¼ bdsc =dz. For assumed constant values of b, the gradient in bed shear strength reduces or is nearly constant as the bed is eroded. Larger deviations from this behaviour can be explained by sediment layers which are harder to erode and thus by a non-homogeneous sediment structure with depth.
5. Discussion The importance of the bulk density and water content in the erosion process, as shown in Fig. 4, has been highlighted in several studies. Fukuda and Lick (1980) reported an effect of decreasing erosion rate with decreasing water content, which is equivalent to the effect of increasing bulk density. Jepsen et al. (1997) and Roberts et al. (1998) also found that erosion rates for homogeneous beds decrease with increasing bulk density. Lower values of the erosion rate in beds with larger bulk densities can be explained by a larger resistance against erosion for such beds, as observed by Amos et al. (1997) and Torfs (1997).
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However, the dry bulk density does not explicitly include the bed material composition. Kamphuis and Hall (1983) reported that the capability of a cohesive soil to resist erosion increases with clay content and plasticity index. For beds composed of larger particles, erosion rate is independent of bulk density and is a function of grain size only (Roberts et al., 1998). Mitchener and Torfs (1996) found that when the bed is composed with sand content greater than 70%, critical bed shear stresses for erosion depend on both grain size of the sand and the cohesive properties of the mud. Thus, for beds composed of mud/sand mixtures, the composition of the bed material plays an important role in addition to the bulk density (Mitchener and Torfs, 1996; Houwing, 1999). Our results, summarised in Fig. 5, are consistent with previous studies and show how b decrease with increasing sand content. This behaviour is equivalent to reduction in the erosion rate with sand content increase. It also worth mentioning that Roberts et al. (1998) found, in experiments with fixed dry bulk densities and varying grain sizes, that erosion rate E increased rapidly for the smaller particles, reached a maximum, and then decreased rapidly for the larger particles. We attribute the separation of freshwater and saltwater data in Fig. 5 to the effects of salinity and antecedent conditions. According to Parchure and Mehta (1985), salinity has a major influence on resistance to erosion and for higher salinity, a higher resistance to erosion can be expected. Mehta and Parchure (2000) found that the influence of salt concentration on the erosion rate and bed stability also depends on the composition of the sediment. These findings agree well with our results shown in Fig. 5, where erosion rates at saltwater sites were reduced up to five times compared to the freshwater sites. As for the effect of vegetation debris on erosion resistance, we can only speculate on this issue since the fibrous materials or root systems cannot be properly quantified in this study. Our data in Fig. 4 suggest that resistance to erosion for such beds should increase. However, this effect is not evident in Fig. 5. This issue is still unclear, as in Houwing (1999), and needs to be specially addressed. Our results shown in Fig. 6 for the exponent b2 are in agreement with findings of Maa et al. (1998) and
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Sanford and Maa (2001), who reported similar behaviour for b2 with increasing bed shear stress. They reported the range of values for b2 from 0.002 to 0.1. However, the potential dependency of b2 on the fitting procedure (Aberle et al., submitted for publication 2003b) prevents a direct and rigorous comparison of our data on b2 with other published data. Our estimates of the bed shear strength gradients c in the nearsurface sediment layer range from 4 to 500 Pa/ m 1. Large gradients may be questionable since b and b2 have been determined from SSC-data only and bed load is not considered in the estimates of the erosion rate. Experiments of Mitchener and Torfs (1996), in which both the SSC and bed load were measured, indicate that bed load transport may have a significant effect on the estimates of the total erosion. Mitchener and Torfs (1996) and Torfs (1997) suggest that the bed structure of sand/mud mixtures may consist of distinct layers of mud and sand. Muddy layers are predominantly eroded directly into suspension, whereas sand layers are mainly eroded into bed load. Furthermore, for purely consolidated cohesive beds large aggregates or lumps of material are being transported mostly as bed load (Mitchener and Torfs, 1996). It is unlikely that the length of the flowthrough flumes is sufficient for these aggregates to be completely destroyed. In field deployments, they are most probably washed out of the flume without being measured. Thus, erosion rates as well as erosion depths will generally be underestimated if bed load transport occurs, because the suspended sediment sensors (e.g., OBS-3) do not record bed load. In some additional tests over sand beds, we visually observed sediment being transported out of the flume but did not obtain any response of our OBS-3 sensors. Such an underestimation of the erosion rate due to bed load may influence the results presented in Fig. 5. Finally, uncertainties in estimating the bed shear stresses in field experiments should be further addressed. For most in situ flumes, estimates for the bed shear stress are obtained using a calibration curve derived under controlled experimental conditions. However, the roughness of cohesive beds may deviate from that corresponding to calibration, and may also change significantly during the experiment (Maa et al., 1993; Berlamont et al., 1993). For instance, for
our in situ flume, we found, using laboratory tests and numerical simulations (the model is described in Walters, 2001), an uncertainty factor of 2.
6. Conclusions This paper describes a method for interpretation of in situ cohesive sediment data based on the erosion formulation proposed by Sanford and Maa (2001). This formulation is appealing since as it is relatively simple and can be used to describe both depth-limited erosion (type I) and/or steady-state erosion (type II). We applied this approach to analyse the data collected with the NIWA in situ flume in several different aquatic environments in New Zealand. Two methods are suggested and applied for evaluating the parameters in Sanford and Maa’s (2001) relationship (2). Both approaches yield similar results and support a linear dependence of the erosion constant M on the dry bulk density and/or porosity. Sanford and Maa (2001) indicated the possibility of variability of the parameter b with increasing critical bed shear stress. Some of our data support this suggestion. We found a dependency of b on sand content and water salinity. Our data collapsed into two distinct groups, for freshwater and saltwater, and we suggested a relationship for b for each of these groups. However, the dependency of the erosion process on the sediment composition needs to be examined further, including the effects of bedload. Future in situ investigations should include detailed measurements of bed material density profiles and bed elevations. To address this issue, we are currently developing a new generation of in situ flume, which will be equipped with a SeaTek 5 MHz Ultrasonic Ranging System (URS) allowing non-invasive monitoring of bed elevations inside the flume. Currently, the erosion rate and erosion depth can only be calculated from the sediment continuity equation. With the use of the ranging system, we will be able to measure the erosion rates and erosion depth in the flume directly with reduced uncertainty and independently of the OBS-3 readings. Such data should give us further insight into the erosion processes of cohesive beds.
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Acknowledgements The research was conducted under contract CO1X0215 (Sustainability of Aquatic Ecosystems and Water Resources, Sediment Processes and Dynamics) from the Foundation for Research Science and Technology (New Zealand). R. Pridmore provided helpful advice and generous support to this project. C. Grace, D. Gunn, J. Heilig, F. Munro, and C. Mason assisted during field measurements. NIWA Instrument Systems helped with flume instrumentation and maintenance. References Aberle, J., Nikora, V., Walters, R., 2002. In situ measurement of cohesive sediment dynamics using a straight benthic flume. Hydraulic Measurements and Experimental Methods Conference, Estes Park, Colorado. Papers on CD-RomROM. Aberle, J., Nikora, V., McLean, S., Doscher, C., McEwan, I., Green, M., Goring, D., Walsh, J., 2003a. A straight benthic flowthrough flume for in situ measurement of cohesive sediment dynamics. J. Hydraul. Eng. 129 (1), 63 – 67. Aberle, J., Nikora, V., Walters, R., 2003b. Data interpretation for in situ measurements of cohesive sediments. J. Hydraul. Eng. (submitted for publication). Amos, C.L., Daborn, G.R., Christian, H.A., Atkinson, A., Robertson, A., 1992. In situ erosion measurements on fine-grained sediments from the Bay of Fundy. Mar. Geol. 108, 175 – 196. Amos, C.L., Feeney, T., Sutherland, T.F., Luternauer, J.L., 1997. The stability of fine-grained sediments from the Fraser river delta. Estuar. Coast. Shelf Sci. 45, 507 – 524. Amos, C.L., Brylinsky, M., Sutherland, T.F., O’Brien, D., Lee, S., Cramp, A., 1998. The stability of a mudflat in the Humber estuary, South Yorkshire, UK. In: Black, K.S., Paterson, D.M., Cramp, A. (Eds.), Sedimentary Processes in the Intertidal Zone. Special Publications, vol. 139. Geological Society, London, pp. 25 – 43. Andersen, T.J., Houwing, E.J., Pejrup, M., 2002. On the erodibility of fine-grained sediments in an infilling freswater system. In: Winterwerp, J.C., Kranenburg, J. (Eds.), Fine Sediment Dynamics in the Marine Environment. Elsevier, Amsterdam, pp. 671 – 685. Berlamont, J.E., Ockenden, M.C., Toorman, E.A., Winterwerp, J.C., 1993. The characterisation of cohesive sediment properties. Coast. Eng. 21, 105 – 128. Black, K.S., Tolhurst, T.J., Paterson, D.M., Hagerthey, S.E., 2002. Working with natural cohesive sediments. J. Hydraul. Eng. 128 (1), 2 – 8. Flemming, B.W., Delafontaine, M.T., 2000. Mass physical properties of muddy intertidal sediments: some applications, mis-
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applications and non-applications. Cont. Shelf Res. 20, 1179 – 1197. Fukuda, M.K., Lick, W., 1980. The entrainment of cohesive sediments in freshwater. J. Geophys. Res. 85 (C5), 2813 – 2824. Houwing, E.-J., 1999. Determination of the critical erosion threshold of cohesive sediments on intertidal mudflats along the Dutch Wadden Sea coast. Estuar. Coast. Shelf Sci. 49, 545 – 555. Jepsen, R., Roberts, J., Lick, W., 1997. Effects of sediment bulk density on sediment erosion rates. Water Air Soil Pollut. 99, 21 – 37. Kamphuis, J.W., Hall, K.R., 1983. Cohesive material erosion by unidirectional current. J. Hydraul. Eng. 109 (1), 49 – 61. Maa, J.P.-Y., Lee, C.-H., 1997. Variation of the resuspension coefficients in the lower Chesapeake Bay. J. Coast. Res. SI 25, 63 – 74. Maa, J.P.-Y., Wright, L.D., Lee, C.-H., Shannon, T.W., 1993. VIMS Sea Carousel: a field instrument for studying sediment transport. Mar. Geol. 115, 271 – 287. Maa, J.P.-Y., Sanford, L., Halka, J.P., 1998. Sediment resuspension characteristics in Baltimore Harbor, Maryland. Mar. Geol. 146, 137 – 145. Mehta, A.J., Partheniades, E., 1982. Resuspension of Deposited Cohesive Sediment Beds. Coastal Engineering, Cape Town, South Africa. ASCE, Reston, VA, pp. 1569 – 1588. Mehta, A.J., Parchure, T.M., 2000. Surface erosion of fine-grained sediment revisited. In: Flemming, B.W., Delafontaine, M.T., Liebezeit, G. (Eds.), Muddy Coast Dynamics and Resource Management. Elsevier, Amsterdam, pp. 55 – 74. Mitchener, H.J., Torfs, H., 1996. Erosion of mud/sand mixtures. Coast. Eng. 29, 1 – 25. Parchure, T.M., Mehta, A.J., 1985. Erosion of soft cohesive sediment deposits. J. Hydraul. Eng. 111 (10), 1308 – 1326. Paterson, D.M., Black, K.S., 1999. Water flow, sediment dynamics and benthic biology. Adv. Ecol. Res. 29, 155 – 193. Piedra-Cueva, I., Mory, M., 2001. Erosion of a deposited layer of cohesive sediment. In: McAnally, W.H., Mehta, A.J. (Eds.), Coastal and Estuarine Fine Sediment Processes. Elsevier, Amsterdam, pp. 41 – 51. Ravens, T.M., Gschwend, P.M., 1999. Flume measurements of sediment erodibility in Boston Harbor. J. Hydraul. Eng. 125 (10), 998 – 1005. Roberts, J., Jepsen, R., Gotthard, D., Lick, W., 1998. Effects of particle size and bulk density on erosion of quartz materials. J. Hydraul. Eng. 124 (12), 1261 – 1267. Sanford, L., Maa, J.P.-Y., 2001. A unified erosion formulation for fine sediments. Mar. Geol. 179, 9 – 23. Torfs, H., 1997. Erosion of mixed cohesive/non-cohesive sediments in uniform flow. In: Burt, N., Parker, R., Watts, J. (Eds.), Cohesive Sediments. Wiley, Chichester, pp. 245 – 252. Walters, R., 2001. From river to ocean: a unified modelling approach. Proc. of 7th International Conference on Estuarine and Coastal Modelling. St Pete Beach, Florida, pp. 683 – 694. Zreik, D.A., Krishnappan, B.G., Germaine, J.T., Madsen, O.S., Ladd, C.C., 1998. Erosional and mechanical strengths of deposited cohesive sediments. J. Hydraul. Eng. 124 (11), 1076 – 1085.
Effects of bed material properties on cohesive sediment erosion Jochen Aberle a,*, Vladimir Nikora b, Roy Walters b a
Leichtweiss-Institut fu¨r Wasserbau, Technische Universita¨t Braunschweig, Beethovenstr. 51a, 38108 Braunschweig, Germany b National Institute of Water and Atmospheric Research (NIWA), P.O. Box 8602, Christchurch, New Zealand Received 21 October 2002; received in revised form 18 August 2003; accepted 18 March 2004
Abstract A straight benthic in situ flume was used to measure the erosion rate of cohesive sediments in freshwater and saltwater environments in New Zealand. The data show an exponential decay of erosion rate with time, which is indicative of depthlimited erosion. Two approaches for the calibration of an erosion formula are used, both leading to similar results. The data show the dependency of erosion rate on bed material properties, such as dry bulk density, water content, organic content and sand content. Both methodologies also highlight differences between data from freshwater and saltwater environments. Also shown is a requirement for direct measurements of bed density profiles and bed load transport during in situ investigations. D 2004 Elsevier B.V. All rights reserved. Keywords: cohesive sediment; erosion rate; fine sediment transport; critical bed shear stress; mud
1. Introduction Although cohesive sediment dynamics is important for many engineering and ecological applications, its general theory is still unavailable (Black et al., 2002). Studying cohesive sediment erosion directly in the field, without disturbing natural cohesive beds, is probably one of the most promising directions in advancing this topic. Various in situ sediment flumes have been developed for such studies. In their deployments, researchers often follow an experimental procedure in which increasing values of bed shear * Corresponding author. Tel.: +49-531-391-3973; fax: +49-531391-8184. E-mail addresses: [email protected] (J. Aberle), [email protected] (V. Nikora), [email protected] (R. Walters). 0025-3227/$ - see front matter D 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.margeo.2004.03.012
stress are applied step-wise over fixed time intervals (usually 5 –20 min; Amos et al., 1992, 1997, 1998; Maa et al., 1998; Ravens and Gschwend, 1999; Houwing, 1999; Aberle et al., 2003a). Two erosion mechanisms have emerged from these investigations that are directly associated with the bed structure. Depth-limited or type I erosion occurs once the threshold for motion due to hydrodynamic forces is exceeded and particles are eroded from the surface (Mehta and Partheniades, 1982; Parchure and Mehta, 1985). Erosion ceases when the applied bed shear stress sb reaches the bed shear strength ss at a certain eroded depth. Such erosion behaviour can be explained by increasing bed shear strength with depth. On the other hand, steady-state or type II erosion is characteristic of uniform beds where the bed shear strength does not change with depth (Parchure and Mehta, 1985; Zreik et al., 1998). In
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this case, the erosion rate is constant (Amos et al., 1992; Paterson and Black, 1999). In practice, the erosion rate does not necessarily cease during an experimental interval and there is no clear distinction between depth-limited and steadystate erosion (Amos et al., 1992, 1997). Such erosion behaviour is defined as transitional erosion or type I/II erosion (Amos et al., 1997; Andersen et al., 2002). If the time duration of the experimental interval is insufficient for the condition sb = ss to be attained, erosion will not cease and could be classified as type I/II erosion or type II erosion, although in reality it may be type I erosion (Parchure and Mehta, 1985; Piedra-Cueva and Mory, 2001). In this paper, we first discuss the time dependency of erosion rates on the basis of time series of erosion rate measured by the NIWA in situ flume (Aberle et al., 2003a). The data are used to estimate the erosion parameters within Sanford and Maa’s (2001) erosion formulation. Then, effects of flow and bed material variations on the erosion parameters are studied. Finally, limitations and needs for further developments are discussed.
2. Methods Data were collected with the NIWA in situ flume (Fig. 1) in several aquatic environments near Christchurch and Hamilton, New Zealand. The flume was designed as a straight benthic flow-through flume with a rectangular cross-section (0.10 m high and 0.20 m
wide). It consists of a bottomless 0.30-m-long entrance section, a bottomless, straight 0.90-m-long erosion section, and a section with a solid bottom. Water is sucked through the flume with a propeller, driven by an electrical motor. Water turbidity is monitored with two optical back-scatter (D & A OBS-3) sensors, one in the solid bottom section and the other at the flume entrance. OBS-3 readings are sampled each second and then logged by a Campbell data logger as average values over 30 s intervals. Turbidity readings are calibrated against suspended sediment concentration (SSC) for each in situ experiment, where SSC is determined from in situ water samples taken with a small pump near the downstream OBS-3 sensor. For each deployment, SSC- values for six water samples are plotted against turbidity readings averaged over the time intervals for corresponding water samples. Calibration coefficients are obtained from these data using linear regression. Flow velocities are measured in the centre of the flume over the fixed bedfixed-bed section using an Ott C2 current meter, and are recorded continuously with an averaging time interval of 30 s. The centreline velocity is empirically related to the bed shear stress using acoustic Doppler velocimeter (ADV) measurements of near-bed Reynolds stresses for two different types of roughness (smooth wood and sandpaper with particle diameter d c 0.4 mm, Aberle et al., 2003a). The SSC and velocity data were used to calculate the erosion rates using the input and output fluxes of sediment and the continuity equation for the solid phase. More details on the flume and its performance may be found in Aberle et al. (2003a).
Fig. 1. The NIWA in situ flume. The flume has been designed as a straight benthic flow-through flume and is equipped with OBS-3 sensors, photodetectors, an Ott current meter, and a water sampling system. Special ADV-hatches allow for ADV measurements inside of the flume. Note that the wheels are uplifted during operation. Handles and frames attached to the flume are removable.
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In our field experiments, the flume was floated into the water and carefully deployed without disturbing the bed at the deployment site. The most suitable range of water depths for deployments is from ca. 0.40 to ca. 1.10 m. After both OBS-sensors showed constant (ambient) readings, the velocity in the flume was step-wise increased at intervals of 10– 15 min with a ramping period of 5 –10 s at the beginning of each interval. The experiments were terminated after a scour developed at the entrance section of the flume or at the transition between open and fixed bed or when the maximum flow velocity in the flume (approximately 1.10 m s 1) was reached. The appearance of the scour could be detected visually and/or by anomalous change in OBS readings. Information on bed material properties, such as bulk density, water content and loss on ignition (LOI) were obtained from averaged values of five bulk bed material samples taken in the vicinity of the flume. The samples were taken with a specially designed, sharp edged bed material sampler with the dimensions 15 15 3 cm (length width height). The relatively large sample volume of 675 cm3 ensures that the effect of potential sediment disturbances due to the sampling procedure is minimised. The grain size distributions for mixtures of these five samples were determined using a Malvern-S
85
particle size analyser. In Table 1, we present bed material characteristics and information on grain size distribution for 11 deployments. Eight of these deployments were in freshwater and three in saltwater. Half of freshwater deployments were in non-tidal rivers (Halswell River, Avon River 1, 2 and LII), one measurement site was influenced by tidal backwater (Styx River), and the other three freshwater deployments were carried out in a wetland environment (Travis Wetlands 1, 2 and 3). The saltwater deployments were in tidal estuarine environments. Unfortunately, sedimentation history at the measurement sites is not available. Geographically, the sites were distributed in close proximity to Christchurch and Hamilton, New Zealand, and therefore their detailed location maps are not shown here.
3. Data analysis Fig. 2 shows a typical plot of velocity and OBS-3 data (converted to SSC) obtained during our investigations at the Styx River near Christchurch, New Zealand. A typical feature of this plot is that the erosion rates were initially high at the onsets of bed shear stress increases, once erosion threshold was exceeded. The
Table 1 Sediment characteristics at the deployment sites Site
d50 (Am)
Claya (%)
Siltb (%)
Sandc (%)
Wet bulk density (kg m 3)
Dry bulk density (kg m 3)
Waterd content (%)
LOIe (%)
Halswell Riverf Travis Wetlands 1f Travis Wetlands 2f Travis Wetlands 3f Avon River 1f Avon River 2f Styx Riverf Allendaleg Avon Estuaryg LIIf Raglan Harbourg
34 23 10 18 70 48 108 6 13 26 21
10 13 16 14 5 6 10 23 15 12 14
54 62 66 67 43 52 36 74 68 63 65
36 25 17 19 52 42 54 2 17 25 21
1305 1497 1293 1473 1235 1130 1420 1431 1581 1137 1753
529 813 492 868 339 280 642 697 949 216 1153
61.2 44.6 65.1 41.6 73.1 75.3 56.1 51.5 40.2 81.0 31.2
9.1 3.9 12.2 4.9 18.4 15.4 12.2 4.5 3.5 12.0 3.6
a
d V 2 Am. 2 Am < d V 64 Am. c d > 64 Am. d Samples dried at 105 jC. e Samples ashed at 500 jC for a period of 24 h. f Freshwater environment. g Marine environment. b
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Fig. 2. The time series of the centreline velocity UOtt (triangles) and the SSC from OBS-3 sensors: upstream (at flume entrance, diamonds) and downstream (in fixed-bed section, squares), field deployment in the Styx River near Christchurch, New Zealand. Once the critical threshold for erosion is exceeded, erosion increases sharply at the onset of each velocity level and then ceases.
high initial erosion rate decreased exponentially within each time interval of constant velocity (for t>3000 s). One may also note that erosion did not always cease before the next increase in flow velocity (e.g., t>5000 s). In general, surficial sediments are often characterised by large vertical gradients in bed shear strength (Amos et al., 1992; Maa et al., 1998; Zreik et al., 1998; Ravens and Gschwend, 1999; Sanford and Maa, 2001) and, therefore, erosion depths in field deployments may be restricted to the top few millimetres. In relation to our field experiments, we infer that the time duration of 10 min for each velocity step was insufficient for the condition sb = ss to be attained. Overall, the data suggest that we deal with the depth-limited erosion (type I; due to the vertical heterogeneity in bed structure) or a combination of depth-limited erosion and steady-state erosion (type II). This assumption is supported by the results of Aberle et al. (2002, submitted for publication 2003b) showing that potential hydrodynamic effects that could enhance erosion during the ramping periods are insignificant for our flume. Many existing formulations for erosion types I and II are based on the concept of critical bed shear stress, that is, erosion occurs as long as the applied bed shear stress is larger than the critical bed shear stress for erosion. In a reasonably general form, the existing formulations may be summarised as a power relationship: E ¼ M ðzÞðsb sc ðzÞÞn
ð1Þ
where E is the erosion rate (kg m 2 s 1), M(z) is an empirical erosion coefficient with its dimension depending on an exponent n (for n = 1: kg m 2 s 1 Pa 1), sb is the bed shear stress (Pa), sc(z) is the critical bed shear stress for erosion (Pa) that may vary with z (Maa et al., 1998; Ravens and Gschwend, 1999; Mehta and Parchure, 2000). Eq. (1) may be also presented in a dimensionless form (e.g., by normalising on sc), but this does not provide significant improvements or simplification. Use of Eq. (1) in determining the erosion parameters from in situ measurements is not straightforward because both parameters M and sc, and a variety of physical, chemical and biological factors influencing them, are unknown functions of sediment depth. Indeed, there is a lack of consistency in the way the various parameters from field deployments are interpreted. For example, in some investigations, E is defined as the initial erosion rate after application of a new bed shear stress (peak erosion rate, Amos et al., 1992; Maa et al., 1998; Houwing, 1999). Ravens and Gschwend (1999) determine the erosion rate as the rate of sediment resuspension after some initial response has passed, while Amos et al. (1998) and Andersen et al. (2002) averaged erosion rates over each velocity step. Different approaches provide different values for the erosion rates and, thus, for the parameters of Eq. (1), or other erosion formulations. As a result of these difficulties, we have adopted an approach where we use simple time-dependent
J. Aberle et al. / Marine Geology 207 (2004) 83–93
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expressions for E that can be evaluated with field experiments. The approach follows from recent results of Sanford and Maa (2001). The basic idea is to differentiate Eq. (1) with respect to time to describe the transient behaviour of E, then solve this differential equation for simple initial conditions such as a step-wise increase of bed shear stress. For suitable assumptions that neglect time dependence of M and sc, and setting n = 1, Sanford and Maa (2001) derived:
dure to account for potential offsets and errors in the data, and therefore to improve estimates of b2. On the other hand, b3 is usually much lower than b1 so the estimates of M are not greatly affected. For the ‘bulk’ approach, we use the depth-averaged value of dry bulk density as directly measured by our 3 cm deep bulk bed material samples and consider erosion rates E0 at t = t0 only. In this case, Eq. (2) reduces to E0 = Udh(sbsc0). Taking n velocity steps into account and summing E0 for each velocity step (to reduce random errors) yields,
E ¼ qd ðzÞbðsb sc 0 Þecbðtt0 Þ
n X
ð2Þ
i¼1
where qd (z) is dry bulk density at sediment depth z, b is a local parameter, sc0 is critical bed shear stress when sb is first applied at t = t0, t is time, and c = dsc/ dz is the vertical gradient of the critical bed shear stress (or bed shear strength). Eq. (2) is based on an assumption of a locally constant vertical gradient of bed shear strength sc, and a direct proportionality between the erosion constant M and sediment concentration at the water – sediment interface M = qd(z)b. For a uniform bed, c = 0 and Eq. (2) reduces to the linear erosion formulation E = M(sb sc). For a stratified bed, c p 0 and Eq. (2) describes an exponential decay of erosion rate with time, as shown in Maa and Lee (1997) and Piedra-Cueva and Mory (2001). Proper evaluation of parameters in Eq. (2) requires information on vertical profiles of the bulk density and water content with a high spatial resolution. Such information is not available for our experiments, as bulk densities were estimated from 3-cm-deep sampling volumes. Therefore, we developed two methods, ‘bulk’ and ‘last step’ methods, for evaluating b, a key parameter in Eq. (2). Both methods were suggested as an attempt to extract maximum information from our data, and are described in detail in Aberle et al. (2003b submitted for publication). In brief, time series of erosion rates for each velocity step during an experiment were fitted to the function E ¼ b1 eb2 ðtt0 Þ þ b3 using a least-squares algorithm, where b1, b2 and b3 are fitted parameters. As an example in Fig. 2, step intervals of constant velocity of 2400 – 3000, 3000 – 3600, 3600 – 4200, 4200 – 4800, 4800 – 5400 and 5400 – 6000 s were fitted. Factor b3 is introduced into the fitting proce-
E0;i ¼
n X ðb1;i þ b3;i Þ ¼ M ðsb;n sc 0;1 Þ
ð3Þ
i¼1
with M = qdb. Thus, plotting the cumulative sum of (b1,i + b3,i) against the bed shear stress yields information on M. Under the simplified assumption of a constant dry bulk density, which should be equal to the measured depth-averaged bulk density, b can then be calculated. Examples of plots Rn ðb1;i þ b3;i Þ ¼ f ðsb;n Þ are shown in Fig. 3 for the data sets from Avon River 1, Styx River, L II River and Raglan Harbour, with the depth-averaged dry bulk densities given in Table 1. According to Eq. (3), data points that can be approximated by a straight line indicate a constant value of M, and hence reflect no significant changes of the product qd b during the experiment (e.g., Styx River and LII River sites in Fig. 3). Convexity of the curve Rn ðb1;i þ b3;i Þ ¼ f ðsb;n Þ indicates a decrease in qdb with increasing depth (e.g., Avon River 1 and Raglan Harbour sites in Fig. 3), while concavity of the data points indicates an increase of qdb with depth. If b changes with depth, the theoretical framework of Eqs. (2) and (3) should be extended and would result in a formulation that would deviate from simple exponential behaviour. However, if values of b do not change significantly during a single erosion event, Eq. (2) remains a locally valid approximation (Sanford and Maa, 2001). In our analysis, we used estimates of M and hence b only if the data points could be fitted with a straight line with a squared correlation coefficient R2>0.90. Otherwise, we used only the first few data points, which could be reasonably approximated by a straight line (e.g., only the first three data points for Avon River 1 and Raglan Harbour in Fig. 3). Table 2 shows the number of subsequent steps included in the analysis, the
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Fig. 3. Cumulative plot of (b1 + b3) against the bed shear stress, used for estimation of M (and b) by the bulk method for the experiments in Avon River 1, Styx River, Raglan Harbour, and L II-River.
estimated value of b, and the R2 value for the linear fit in estimating b for each deployment. The ‘last step’ method is based on an assumption that the 3 cm depth-averaged bed characteristics are mainly determined by the bed material properties at the last experimental step before the experiment was terminated (e.g., velocity step at t > 5500 s in Fig. 2). The thin surface sediment layer with increasing bed density is eroded during the precedent experimental steps, and thus the measured depth-averaged values,
biased by deeper sediments, should provide a good estimate for the dry bulk density for the layer eroded during the last experimental step. Bearing this in mind, the value of M for the last erosion step can be estimated from Eq. (2) and then the corresponding value of b can be calculated. Assuming that b does not change with depth, one may calculate dry bulk densities for the sediment layers eroded before the last experimental step. In our analysis, we excluded the end steps when the calculated bulk densities for the
Table 2 Estimates of b from the ‘bulk’ and ‘last step’ methods Experiment
Halswell Rivera Travis Wetlands 1a Travis Wetlands 2a Travis Wetlands 3a Avon River 1a Avon River 2a Styx Rivera Allendalec Avon Estuaryc LIIa Raglan Harbourc a
Bulk approach No. of steps
b bulk (m s 1 Pa 1)
R bulk method
No. of steps
b last step (m s 1 Pa 1)
Maximum density (kg m 3)
3 3 3 3 3 5 6 6 5 4 3
3.51 10 4 2.01 10 4 9.29 10 4 7.36 10 5 3.57 10 4 1.47 10 4 1.96 10 5 5.69 10 4 1.54 10 4 9.22 10 4 3.08 10 5
0.99 0.97 0.99 0.99 0.94 0.98 0.99 0.91 0.98 0.99 0.99
3 5 3 2 –b 4 6 5 4 4 3
3.42 10 4 5.24 10 4 9.73 10 4 8.08 10 5 –b 1.76 10 4 2.55 10 5 7.58 10 4 2.25 10 4 7.84 10 4 3.09 10 5
560 813 492 889 –b 310 642 697 972 294 1335
Freshwater environment. Not applicable. c Marine environment. b
Last step approach 2
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previously eroded layers were unrealistically large. For example, the method was not applicable to analyse data from the Avon River 1 site where estimates of the bulk densities calculated from this method exceeded values of 3500 kg/m3. The possible reasons for this increased uncertainty could be anomalous distribution of bed material properties and effects of organic inclusions (see also Sections 4 and 5). Table 2 provides information on the total numbers of steps included into the analysis for this method, estimated values of b, and the estimated maximum bulk density for each site. A comparison between the estimates of b (Table 2) indicates that both methods yield similar results. The largest difference is observed for the site Travis Wetlands 1 that can be explained by the experimental setup. During the deployment, an operator carefully approached the flume from behind after three velocity steps. Walking close to the flume resulted in an artificially introduced erosion event in the flume (see also Aberle et al., 2003a), although the applied bed shear stress was constant. Such artificially introduced erosion events (two erosion peaks within the same velocity step) make it difficult or impossible to apply these methods and introduce additional uncertainty in the analysis.
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4. Results Fig. 4 shows estimates of b from both methods as a function of the dry bulk density. The bulk density used in Fig. 4 represents mean values of five 3 cm deep samples taken in the vicinity of the flume. As one can see in Fig. 4, the parameter b decreases with increasing dry bulk density or, in other words, b increases with increasing water content due to a direct relationship between dry bulk density and water content (Flemming and Delafontaine, 2000). However, three data points can be identified in Fig. 4 that deviate from this behaviour (Halswell, Avon River 1, and Avon River 2). All three sites are within freshwater lowland streams with a river-bed filled with fibrous organic material such as decomposing leaves, root systems, etc. We found that such organic layers, if specially structured, show an immense resistance to erosion. In our experiments, we could not erode these structured organic layers, which sheltered sediment layers below. As a consequence, erosion stopped after some velocity steps and further velocity increases did not lead to erosion events. Hence, low values of b were obtained for these sites where the amount of organics, indicated by LOI in Table 1, was large. However, LOI alone cannot characterise the structural
1.2x10-3
β (ms -1 Pa -1 )
1.0x10-3
Bulk method Last step method
8.0x10-4 6.0x10-4
Fibrous organic layers
4.0x10-4 2.0x10-4 S 0 0
200
400
600
800
1000
1200
1400
Dry bulk density (kgm -3) Fig. 4. The parameter b vs. the dry bulk density. The three marked data points correspond to the sites within Halswell River, Avon River 1, and Avon River 2, which were characterised by the presence of structured layers of fibrous organics. S identifies data from the Styx River (see text for discussion).
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Fig. 5. The parameter b vs. the sand content. The data can be subdivided into two groups: freshwater and saltwater data. The solid lines indicate best-fit relationships based on the last step method.
arrangement of the organic fibrous components and, therefore, cannot be used unambiguously for quantifying resistance to erosion. Fig. 4 also contains a fourth point that deviates from the general trend (Styx River site). In addition to large organic content, the bed material for this particular experiment had a large sand fraction (54%). A possible dependency of M and thus b on bed material composition was indicated by Sanford and Maa (2001). In order to explore this effect, the parameter b is plotted against the sand content in Fig. 5. This figure indicates that an increase in sand content results
in a decrease in b. A potential explanation for such behaviour is the presence of bed load (see also Section 5 below). Another interesting observation from Fig. 5 is that the data are grouped separately for freshwater and saltwater environments. However, note that one freshwater data point (Travis Wetlands 3) lies within the saltwater data group. This particular site was located in a small pond where the bed was disturbed a year or so before the experiment by some construction work. This site had a relatively high, for freshwater, water conductivity of 820 AS/cm 1. These conditions distinguish this particular freshwater site
Fig. 6. The exponent b2 as a function of the applied bed shear stress for all data under investigation.
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from other freshwater sites and may explain why this point grouped together with the saltwater data. Fig. 5 does not reveal strong effects of organic layers as in Fig. 4. This may be explained by a large sand content in the lowland streams in addition to the observed vegetative layers. Based on Fig. 5 and the data for the ‘last step’ method, the following empirical relationships can be derived for b (with the dimensions m s 1 Pa 1) as a function of the sand content, b = 3.0 10 3 exp( 0.063 SC) for the freshwater sites, and b = 9.8 10 4 exp( 0.113 SC) for the saltwater sites, where SC is the sand content in [%] percent (%) and the R2 values are 0.93 and 0.97, respectively. Similar relationships may be obtained for b from the bulk method. We chose an exponential fit because an exponential function does not yield negative values for b for larger sand contents and yields a slightly better fit compared to a power function. Fig. 6 shows estimates of the exponent b2 in E ¼ b1 eb2 ðtt0 Þ þ b3 as a function of the applied bed shear stress. Fig. 6 indicates a general decaying behaviour of the exponent b2 approaching a constant with increasing bed shear stress. Such behaviour can be expected since b2 ¼ cb ¼ bdsc =dz. For assumed constant values of b, the gradient in bed shear strength reduces or is nearly constant as the bed is eroded. Larger deviations from this behaviour can be explained by sediment layers which are harder to erode and thus by a non-homogeneous sediment structure with depth.
5. Discussion The importance of the bulk density and water content in the erosion process, as shown in Fig. 4, has been highlighted in several studies. Fukuda and Lick (1980) reported an effect of decreasing erosion rate with decreasing water content, which is equivalent to the effect of increasing bulk density. Jepsen et al. (1997) and Roberts et al. (1998) also found that erosion rates for homogeneous beds decrease with increasing bulk density. Lower values of the erosion rate in beds with larger bulk densities can be explained by a larger resistance against erosion for such beds, as observed by Amos et al. (1997) and Torfs (1997).
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However, the dry bulk density does not explicitly include the bed material composition. Kamphuis and Hall (1983) reported that the capability of a cohesive soil to resist erosion increases with clay content and plasticity index. For beds composed of larger particles, erosion rate is independent of bulk density and is a function of grain size only (Roberts et al., 1998). Mitchener and Torfs (1996) found that when the bed is composed with sand content greater than 70%, critical bed shear stresses for erosion depend on both grain size of the sand and the cohesive properties of the mud. Thus, for beds composed of mud/sand mixtures, the composition of the bed material plays an important role in addition to the bulk density (Mitchener and Torfs, 1996; Houwing, 1999). Our results, summarised in Fig. 5, are consistent with previous studies and show how b decrease with increasing sand content. This behaviour is equivalent to reduction in the erosion rate with sand content increase. It also worth mentioning that Roberts et al. (1998) found, in experiments with fixed dry bulk densities and varying grain sizes, that erosion rate E increased rapidly for the smaller particles, reached a maximum, and then decreased rapidly for the larger particles. We attribute the separation of freshwater and saltwater data in Fig. 5 to the effects of salinity and antecedent conditions. According to Parchure and Mehta (1985), salinity has a major influence on resistance to erosion and for higher salinity, a higher resistance to erosion can be expected. Mehta and Parchure (2000) found that the influence of salt concentration on the erosion rate and bed stability also depends on the composition of the sediment. These findings agree well with our results shown in Fig. 5, where erosion rates at saltwater sites were reduced up to five times compared to the freshwater sites. As for the effect of vegetation debris on erosion resistance, we can only speculate on this issue since the fibrous materials or root systems cannot be properly quantified in this study. Our data in Fig. 4 suggest that resistance to erosion for such beds should increase. However, this effect is not evident in Fig. 5. This issue is still unclear, as in Houwing (1999), and needs to be specially addressed. Our results shown in Fig. 6 for the exponent b2 are in agreement with findings of Maa et al. (1998) and
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Sanford and Maa (2001), who reported similar behaviour for b2 with increasing bed shear stress. They reported the range of values for b2 from 0.002 to 0.1. However, the potential dependency of b2 on the fitting procedure (Aberle et al., submitted for publication 2003b) prevents a direct and rigorous comparison of our data on b2 with other published data. Our estimates of the bed shear strength gradients c in the nearsurface sediment layer range from 4 to 500 Pa/ m 1. Large gradients may be questionable since b and b2 have been determined from SSC-data only and bed load is not considered in the estimates of the erosion rate. Experiments of Mitchener and Torfs (1996), in which both the SSC and bed load were measured, indicate that bed load transport may have a significant effect on the estimates of the total erosion. Mitchener and Torfs (1996) and Torfs (1997) suggest that the bed structure of sand/mud mixtures may consist of distinct layers of mud and sand. Muddy layers are predominantly eroded directly into suspension, whereas sand layers are mainly eroded into bed load. Furthermore, for purely consolidated cohesive beds large aggregates or lumps of material are being transported mostly as bed load (Mitchener and Torfs, 1996). It is unlikely that the length of the flowthrough flumes is sufficient for these aggregates to be completely destroyed. In field deployments, they are most probably washed out of the flume without being measured. Thus, erosion rates as well as erosion depths will generally be underestimated if bed load transport occurs, because the suspended sediment sensors (e.g., OBS-3) do not record bed load. In some additional tests over sand beds, we visually observed sediment being transported out of the flume but did not obtain any response of our OBS-3 sensors. Such an underestimation of the erosion rate due to bed load may influence the results presented in Fig. 5. Finally, uncertainties in estimating the bed shear stresses in field experiments should be further addressed. For most in situ flumes, estimates for the bed shear stress are obtained using a calibration curve derived under controlled experimental conditions. However, the roughness of cohesive beds may deviate from that corresponding to calibration, and may also change significantly during the experiment (Maa et al., 1993; Berlamont et al., 1993). For instance, for
our in situ flume, we found, using laboratory tests and numerical simulations (the model is described in Walters, 2001), an uncertainty factor of 2.
6. Conclusions This paper describes a method for interpretation of in situ cohesive sediment data based on the erosion formulation proposed by Sanford and Maa (2001). This formulation is appealing since as it is relatively simple and can be used to describe both depth-limited erosion (type I) and/or steady-state erosion (type II). We applied this approach to analyse the data collected with the NIWA in situ flume in several different aquatic environments in New Zealand. Two methods are suggested and applied for evaluating the parameters in Sanford and Maa’s (2001) relationship (2). Both approaches yield similar results and support a linear dependence of the erosion constant M on the dry bulk density and/or porosity. Sanford and Maa (2001) indicated the possibility of variability of the parameter b with increasing critical bed shear stress. Some of our data support this suggestion. We found a dependency of b on sand content and water salinity. Our data collapsed into two distinct groups, for freshwater and saltwater, and we suggested a relationship for b for each of these groups. However, the dependency of the erosion process on the sediment composition needs to be examined further, including the effects of bedload. Future in situ investigations should include detailed measurements of bed material density profiles and bed elevations. To address this issue, we are currently developing a new generation of in situ flume, which will be equipped with a SeaTek 5 MHz Ultrasonic Ranging System (URS) allowing non-invasive monitoring of bed elevations inside the flume. Currently, the erosion rate and erosion depth can only be calculated from the sediment continuity equation. With the use of the ranging system, we will be able to measure the erosion rates and erosion depth in the flume directly with reduced uncertainty and independently of the OBS-3 readings. Such data should give us further insight into the erosion processes of cohesive beds.
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Acknowledgements The research was conducted under contract CO1X0215 (Sustainability of Aquatic Ecosystems and Water Resources, Sediment Processes and Dynamics) from the Foundation for Research Science and Technology (New Zealand). R. Pridmore provided helpful advice and generous support to this project. C. Grace, D. Gunn, J. Heilig, F. Munro, and C. Mason assisted during field measurements. NIWA Instrument Systems helped with flume instrumentation and maintenance. References Aberle, J., Nikora, V., Walters, R., 2002. In situ measurement of cohesive sediment dynamics using a straight benthic flume. Hydraulic Measurements and Experimental Methods Conference, Estes Park, Colorado. Papers on CD-RomROM. Aberle, J., Nikora, V., McLean, S., Doscher, C., McEwan, I., Green, M., Goring, D., Walsh, J., 2003a. A straight benthic flowthrough flume for in situ measurement of cohesive sediment dynamics. J. Hydraul. Eng. 129 (1), 63 – 67. Aberle, J., Nikora, V., Walters, R., 2003b. Data interpretation for in situ measurements of cohesive sediments. J. Hydraul. Eng. (submitted for publication). Amos, C.L., Daborn, G.R., Christian, H.A., Atkinson, A., Robertson, A., 1992. In situ erosion measurements on fine-grained sediments from the Bay of Fundy. Mar. Geol. 108, 175 – 196. Amos, C.L., Feeney, T., Sutherland, T.F., Luternauer, J.L., 1997. The stability of fine-grained sediments from the Fraser river delta. Estuar. Coast. Shelf Sci. 45, 507 – 524. Amos, C.L., Brylinsky, M., Sutherland, T.F., O’Brien, D., Lee, S., Cramp, A., 1998. The stability of a mudflat in the Humber estuary, South Yorkshire, UK. In: Black, K.S., Paterson, D.M., Cramp, A. (Eds.), Sedimentary Processes in the Intertidal Zone. Special Publications, vol. 139. Geological Society, London, pp. 25 – 43. Andersen, T.J., Houwing, E.J., Pejrup, M., 2002. On the erodibility of fine-grained sediments in an infilling freswater system. In: Winterwerp, J.C., Kranenburg, J. (Eds.), Fine Sediment Dynamics in the Marine Environment. Elsevier, Amsterdam, pp. 671 – 685. Berlamont, J.E., Ockenden, M.C., Toorman, E.A., Winterwerp, J.C., 1993. The characterisation of cohesive sediment properties. Coast. Eng. 21, 105 – 128. Black, K.S., Tolhurst, T.J., Paterson, D.M., Hagerthey, S.E., 2002. Working with natural cohesive sediments. J. Hydraul. Eng. 128 (1), 2 – 8. Flemming, B.W., Delafontaine, M.T., 2000. Mass physical properties of muddy intertidal sediments: some applications, mis-
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