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Deriving erosion thresholds of freshly deposited cohesive sediments from the port of Hamburg using a closed microcosm system

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The quantification of the erodibility of cohesive sediments is fundamental for an advanced understanding of estuarine sediment transport processes. In this study, the surface erosion threshold τc for cohesive sediments collected from two sites in the area of the Port of Hamburg in the River Elbe is investigated in laboratory experiments. An improved closed microcosm system (C-GEMS) is used for the erosion experiments, which allows the accumulation of suspended sediment concentration (SSC) over an experimental run. A total of 34 erosion experiments has been conducted with homogenized samples and bulk densities between 1050 kg/m³ and 1250 kg/m³. The covered range of bulk densities is seen to represent the values commonly exhibited by freshly deposited cohesive sediments. Two approaches to derive τc based on the erosion rate (ε-method) and the SSC (SSC-method) were elaborated and compared. For both approaches, only one parameter has to be set in order to facilitate transferability to other devices. The results show a better performance of the SSC-method in terms of lower uncertainties, especially at the upper application limits of the utilized C-GEMS. The application of the SSC method yields values for τc between 0.037 N/m² and 0.305 N/m², continuously increasing with bulk density. Repetition tests proved the repeatability of the experimental procedure and utilized methods to derive τc . The derived data for τc is used to fit two mathematical models: i) a highly empirical model relating τc to dry bulk density and ii) a recently proposed model relating τc to the physical properties of the sediment-mixture. While the derived parameters for the first model vary widely for the two sampling sites, the fit-parameter for the latter model is virtually independent of the investigated site, suggesting the superiority of this approach.
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Deriving erosion thresholds of
freshly deposited cohesive
sediments from the port of
Hamburg using a closed
microcosm system
M. Witt
1
*,J.Patzke
1
,E.Nehlsen
2
and P. Fröhle
1
1
Institute of River and Coastal Engineering, Hamburg University of Technology, Hamburg, Germany,
2
Department of Architecture and Civil Engineering, Technical University of Applied Sciences Lübeck,
Lübeck, Germany
The quantication of the erodibility of cohesive sediments is fundamental for an
advanced understanding of estuarine sediment transport processes. In this study,
the surface erosion threshold t
c
for cohesive sediments collected from two sites
in the area of the Port of Hamburg in the River Elbe is investigated in laboratory
experiments. An improved closed microcosm system (C-GEMS) is used for the
erosion experiments, which allows the accumulation of suspended sediment
concentration (SSC) over an experimental run. A total of 34 erosion experiments
has been conducted with homogenized samples and bulk densities between
1050 kg/m³ and 1250 kg/m³. The covered range of bulk densities is seen to
represent the values commonly exhibited by freshly deposited cohesive
sediments. Two approaches to derive t
c
based on the erosion rate (e-method)
and the SSC (SSC-method) were elaborated and compared. For both
approaches, only one parameter has to be set in order to facilitate
transferability to other devices. The results show a better performance of the
SSC-method in terms of lower uncertainties, especially at the upper application
limits of the utilized C-GEMS. The application of the SSC method yields values for
t
c
between 0.037 N/m² and 0.305 N/m², continuously increasing with bulk
density. Repetition tests proved the repeatability of the experimental
procedure and utilized methods to derive t
c
. The derived data for t
c
is used to
t two mathematical models: i) a highly empirical model relating t
c
to dry bulk
density and ii) a recently proposed model relating t
c
to the physical properties of
the sediment-mixture. While the derived parameters for the rst model vary
widely for the two sampling sites, the t-parameter for the latter model is virtually
independent of the investigated site, suggesting the superiority of this approach.
KEYWORDS
cohesive sediment, erosion threshold, erodibility, port of Hamburg, Elbe, microcosm,
C-GEMS
Frontiers in Marine Science frontiersin.org01
OPEN ACCESS
EDITED BY
Bram Van Prooijen,
Delft University of Technology, Netherlands
REVIEWED BY
Carl Friedrichs,
College of William & Mary, United States
SunMin Choi,
Inha University, Republic of Korea
Wenping Gong,
Sun Yat-sen University, China
*CORRESPONDENCE
M. Witt
markus.witt@tuhh.de
RECEIVED 14 February 2024
ACCEPTED 03 April 2024
PUBLISHED 06 May 2024
CITATION
Witt M, Patzke J, Nehlsen E and Fröhle P
(2024) Deriving erosion thresholds of
freshly deposited cohesive sediments
from the port of Hamburg using a
closed microcosm system.
Front. Mar. Sci. 11:1386081.
doi: 10.3389/fmars.2024.1386081
COPYRIGHT
© 2024 Witt, Patzke, Nehlsen and Fröhle. This
is an open-access article distributed under the
terms of the Creative Commons Attribution
License (CC BY). The use, distribution or
reproduction in other forums is permitted,
provided the original author(s) and the
copyright owner(s) are credited and that the
original publication in this journal is cited, in
accordance with accepted academic
practice. No use, distribution or reproduction
is permitted which does not comply with
these terms.
TYPE Original Research
PUBLISHED 06 May 2024
DOI 10.3389/fmars.2024.1386081
1 Introduction
Estuarine cohesive sediments consist of minerals of different
sizes (predominantly clay and silt), water and organic matter. This
mixture is often referred to as mud. While the erosion
mechanisms of non-cohesive sediments can be reasonably well
described based on their physical properties such as the grain
size, predicting the erodibility of cohesive sediments/mud is still
difcult due to the large amount of inuencing physical,
geochemical and biological parameters (Berlamont et al., 1993;
Grabowski et al., 2011). The existing mathematical models to
describe the erodibility of cohesive sediments are empirical to
varying degrees and need to be adjusted to the local conditions
based on eld or laboratory experiments, rising the need for
reproducible, comparable experimental procedures.
For the lower and outer Elbe River, which is one of the largest
estuaries in Europe and provides access to the Port of Hamburg, the
third-largest European container port, no sufcient experimental
data on the erodibility of cohesive sediments exists. Between 2013
and 2018 several hydrological and morphological changes have
been observed in the tidal Elbe, particularly an unusually high
increase in tidal range, turbidity and sedimentation rates (Weilbeer
et al., 2021). The latter has been countered by increased
maintenance dredging, which is an economic and ecological
burden. Additionally, the navigation channel of the lower and
outer Elbe was deepened until 2022 to allow a tide-independent
maximum draught of 13.5 m. In order to improve the ability of
numerical models to reproduce the complex sediment transport
processes leading to or triggered by changes in the system, data on
the erodibility of the site-specic cohesive sediments is required,
among a multitude of others.
Erosion experiments on the transport behavior of cohesive
sediments are conducted either with natural, (density-)stratied
samples (in-situ or in lab) or with remolded homogenized samples,
also referred to as placed beds(Winterwerp et al., 2021). Both
approaches have their own advantages and disadvantages. While
more or less undisturbed stratied samples are generally seen to
exhibit erosion characteristics closer to nature (e.g Whitehouse et al.
(2000)), it is more difcult to derive generalized statements from
these kinds of experiments, since often only the top-most layer is
eroded in the experiments and the samples vary over depth in
properties like density and composition. Working with remolded
samples in the laboratory, assuming homogeneous sediment
properties over the depth of the sample, allows the variation of
specic parameters and therefore the investigation of their inuence
on the erosion behavior of the sediment. Density proles of freshly
deposited cohesive sediments measured in the Weser estuary
(Patzke et al., 2022) additionally show that natural samples may
have homogeneous density proles over several tens of centimeters
depth, presumably due to the rapid formation of these layers
compared to consolidation rates.
The parameters describing the erodibility of the sediment,
which determination is the aim of the erosion experiments, are i)
the critical erosion threshold t
c
, generally dened as the bed shear
stress at which the sediment motion sets in (e.g. van Rijn (1993))
and ii) the erosion rates ein relation to the applied bed shear stress
as mass per time and area. Since for homogenized samples the
critical erosion threshold t
c
does not change with depth, the
samples theoretically exhibit continuous erosion at constant
erosion rates when t
c
is exceeded and the applied bed shear stress
is kept constant as well. This behavior is referred to as unlimited
erosion or Type II erosion in literature, in contrast to depth limited
or Type I erosion, which is usually studied on stratied beds
(Sanford and Maa, 2001;Winterwerp et al., 2012).
Unfortunately, the denition of t
c
from laboratory experiments
is not trivial and previous studies have shown a large inuence of
the erosion device and experimental procedure on the derived
values, illustrating the need for reproducible standardized
approaches (Tolhurst et al., 2000;Widdows et al., 2007;Zhu
et al., 2008). In fact, even the denition of t
c
itself is not uniform,
which is also due to the different erosion modi of cohesive
sediments (particle-, surface- and masserosion) (c.f. Debnath and
Chaudhuri (2010)). In past studies, the beginning of erosion was
often dened visually by evaluating either the incipient motion of
particles on the sediment surface itself (e.g. Young and Southard
(1978)), visually identifying a sharp increase in the measured
suspended sediment time series (e.g. Tolhurst et al. (2000))orat
the load step at which the SSC or erosion rates rst reached a
specic magnitude (e.g. Patzke et al. (2022)).
Amos et al. (2003) compared three methods for determining t
c
from in-situ erosion experiments using a closed Sea Carousel
system, two of which were found to be practical: i) extrapolation of
measured erosion rates to a threshold value by a log-log regression
and ii) extrapolation of measured SSC to ambient conditions by a
log-log regression. The applied bed shear stress reached up to
around 5 N/m² and the experiments were conducted with
naturally stratied samples. For both techniques, it had to be
determined at which load step erosion started to exclude the data
from prior load steps from regression. The two methods yielded
comparable values for t
c
, but the authors concluded that the SSC
method was best suited due to high correlation coefcients and an
unambiguous denition of the ambient SSC. The higher correlation
coefcients for the SSC method compared to the erosion rate
method are presumably caused by the fact that the SSC parameter
accumulates over the experimental duration in contrast to the
erosion rate, leading to lower scatter. Ha and Ha (2021) carried
out comparable investigations with naturally stratied samples in
an open microcosm system. Three methods were compared based
on a linear regression of i) SSC, ii) erosion rate and iii) eroded mass.
The surface erosion threshold was dened as the x-intercept of the
regression line resp. background level of eor SSC. For the linear
regression used for determination of t
c
only load steps showing type
1b erosion (see Amos et al. (1992)) were included. This procedure
implies the need for the denition of an upper and a lower
boundary for this erosion type and leads to a relatively low
amount of data points to t the regression line. The authors
concluded that the eroded mass method, which again represents
the accumulating parameter (SSC not accumulation in an open
system), was best suited for the application case.
Many different models have been proposed to describe the
measured erosion thresholds of cohesive sediments mathematically.
An overview of different models can be found in Zhu et al. (2008)
Witt et al. 10.3389/fmars.2024.1386081
Frontiers in Marine Science frontiersin.org02
and Le Hir et al. (2008). Most traditional models are highly
empirical and relate the erosion threshold directly to the bulk
density r
b
,drybulkdensityr
db
(sediment concentration),
plasticity index or other properties of the sediment. One
commonly used formulation is a power-law relation between t
c
and r
db
(e.g. van Rijn (1993),Whitehouse et al. (2000)):
tc=mrn
db (1)
with mand nas empirical coefcients that need to be tted
based on site specic erosion experiments. The dry bulk density r
db
can be calculated from the (wet) bulk density r
b
of the suspension,
the water density r
w
and the density of the sediment particles r
s
as:
rdb= rbrw
rsrw

rs(2)
Recent studies aim at nding unied formulas to describe the
erosion threshold of sand, sand-mud-mixtures and pure mud and
relate it to more physically based parameters (van Ledden, 2003;
Chen et al., 2018,2021). The term pure mud describes a sediment
mixture consisting of a mud-fraction (clay and silt) only and
therefore the absence of a sand fraction. In Chen et al. (2021) the
following formulation for t
c
for sediment mixtures with a mud-
fraction P
m
above a critical fraction of 5-15% is proposed:
tc=A1
dm
rdm
rpm

2
3rdm
rpm

1
3
1
"#
2
e2:4rdm
rpm (3)
with r
dm
as dry bulk density of the mud-fraction and d
m
respectively r
pm
as the diameter and density of the particles of
the mud-fraction. The model incorporates only a single t-
parameter (A[J/m²]), that is supposed to be dependent on
cohesion strength of the cohesive part of the sediment and the
roughness of the bed surface. The equation implies that the dry bulk
density of the mud-fraction of the sediment mixture is the key
parameter to describe the variation of the erosion threshold. The
dry bulk density of the mud-fraction itself can be calculated as:
rdm =rdbPm
1rdbPs
rps
(4)
with P
s
as sand content in percent and r
ps
as density of sand
particles (Equation 4).
The present study aims to:
develop an adapted method to derive t
c
from erosion
experiments with a closed microcosm system (C-GEMS)
with as few parameters to set as possible,
prove the reproducibility of the method and
t the above-mentioned models to the derived dataset of
erosion thresholds for cohesive sediments with varying bulk
densities from the Port of Hamburg.
The utilized methods, results and their discussion are described
in the following sections.
2 Materials and methods
2.1 Location and sampling
The sediment samples used for the erosion experiments were
collected from two sites of the Elbe in the area of the Port of
Hamburg. Upstream of the port area, the Elbe divides into two
parts, the Norderelbe (NE) and the Suederelbe (SE), which
subsequently reunite in the center of the port and surround the
island of Wilhelmsburg (see Figure 1). The sediment samples were
collected during two measurement campaigns, one each on the NE
and SE, at known sedimentation hotspots of cohesive sediments.
The SE-campaign was conducted in June 2023 and located in a ship
turning point. As the ship turning point provides a widening of the
FIGURE 1
Sampling locations in the Norderelbe(NE) and Suederelbe(SE).
Witt et al. 10.3389/fmars.2024.1386081
Frontiers in Marine Science frontiersin.org03
cross-section, sediments accumulate due to relatively low ow
velocities and evolving ow shadows. The sediment samples at
this site were collected during ood slack water. The NE-campaign
was carried out in November 2023 in the harbor entrance to
Baakenhafen. Reduced ow velocities lead to ne-sediment
accumulation in this area as well, whereas at this location the
extension of the accumulation tends to reach further into the main
ow area. The NE-samples used for the experiments in this paper
were collected during ebb slack water.
The sampling device used was a sediment corer developed at the
Institute of River and Coastal Engineering (Patzke et al., 2019,
2022). The corer penetrates the upper sediment layers by its own
weight and extracts cores with a diameter of 20 cm and a maximum
height of 1.20 m. The penetration depth of the corer varies
depending on the attached extra weights and the present bed
densities. In both campaigns, the corer penetrated about one
meter into the bed. In Witt et al. (2023) it was shown that the
device is capable of collecting naturally stratied bed samples, thus
the properties (grain size distribution, loss on ignition) of the
sediment used in this study can be seen as an average of the top
one-meter layer of the bed.
2.2 Sediment characteristics
The sediment samples from the two sampling areas exhibit a
comparable grain size distribution (GSD) (see Table 1). The GSD
was derived by a combined sieve and hydrometer analysis according
to DIN EN ISO 17982-4. The clay content (d < 2 mm) of both
samples with around 24% is way above the threshold of 5-15%
found in literature for dominant cohesive behavior of the sediment
(e.g. van Rijn (1993), clay dened as d < 4 mm). In terms of silt
(2 63 mm) and sand (> 63 mm) content the samples vary slightly
with a three percent difference in each case, with the sample from SE
showing a higher silt and correspondingly a lower sand content. For
both samples, the sand fraction is in the range of ne sand (< 200
mm) only. Consequently, the values for the median diameter D
50
and D
50, mud
, which is dened as the median diameter of the mud-
fraction (clay and silt), are comparable. The loss on ignition is
higher for sampling site SE (11.5%) than for site NE (8.4%)
indicating a higher organic content.
2.3 Erosion experiments
2.3.1 Adapted microcosm system C-GEMS
An adapted Gust-Erosion-Microchamber-System (GEMS) was
utilized for the erosion experiments. The GEMS was presented in
(Gust, 1989) in its original version as an apparatus for generating
precisely dened wall shear stresses. To generate wall shear stresses,
a disk (with or without a skirt) rotates at a known speed and
distance to the sediment surface in a cylinder, which upper part is
lled with water. Simultaneously water is pumped out through the
center of the disk at a specied rate and eccentrically pumped back
into the chamber through the chambers lid. Both the attached skirt
and the pumping of the water are supposed to further homogenize
the bed shear stress distribution on the sediment surface (Gust,
1989;Gust and Müller, 1997). The GEMS is usually employed as an
open system(Work and Schoellhamer, 2018;Seo et al., 2020),
meaning the water from the erosion chamber is pumped to a
turbidity meter and collected as water samples, which are ltrated
afterwards to calibrate the turbidity measurements and derive the
SSC evolution in the erosion chamber over time. The water, which
is pumped out of the erosion chamber, is constantly replaced with
new water from a tank with tap or site-specicwater.This
procedure entails that the SSC in the erosion chamber does not
accumulate over the duration of the experiment, but is directly
related to the rising and falling of the erosion rate. The main
disadvantages of this setup are the high consumption of
experimental water and the effort to derive the SSC evolution
from turbidity data, since the utilized turbidity probes are usually
calibrated based on the determination of the SSC of water samples
taken during the experiment. Both of these factors can result in a
relatively small number of applied load steps in practice.
The Closed-GEMS (C-GEMS) introduced in Patzke et al. (2022)
aims to overcome these restrictions and additionally provides near-
natural conditions by allowing the accumulation of suspended
sediment over the experimental procedure. In this setup, the
water, which is pumped from the erosion chamber, is led to a
second chamber, the measuring chamber, where the evolution of
the SSC is measured. From the measuring chamber, the suspension
is returned to the erosion chamber at the same ow rate, leading to
constant volumes in both chambers. In the measuring chamber, an
additional pump cycle ensures continuous homogenization of the
suspension and prevents the accumulation of sediment particles at
the bottom of the chamber. In this study, major optimizations of the
C-GEMS are introduced in terms of reduced measurement chamber
dimensions and improved SSC-measurements by using a wide-
range turbidity sensor.
An outline of the system employed for this study is shown in
Figure 2. The erosion chamber has a diameter of 20 cm and the
rotating disk is adjusted to a distance of 7 cm to the lutocline. The
total volume of water in the system is ~9.2 liter, of which ~2/3 are
contained in the measuring chamber and ~1/3 in the erosion
chamber. A larger inner volume of the system would lead to a
higher total capacity for suspended sediments until the maximum
practicable concentration is reached and therefore might allow longer
experimental runs, but would also lead to a rising time lag in
TABLE 1 Sediment characteristics of the samples used for erosion experiments.
Location [-] Sample [-] Clay [%] Silt [%] Sand [%] D
50
[mm] D
50, mud
[mm] LOI [%]
SE SE1-2 24.4 62.3 13.2 20.22 14.0 11.5
NE NE1-2/3 24.6 59.3 16.1 23.46 14.1 8.4
Witt et al. 10.3389/fmars.2024.1386081
Frontiers in Marine Science frontiersin.org04
recording the change in SSC due to the volumes buffer effect. The
chosen volume has proven tooffer a reasonable compromise between
these opposing attributes. For the SSC-measurement in the
measuring chamber a precalibrated Hach®Solitax hs-line sc probe,
working on a combined infrared absorption scattered light technique,
is utilized with a nominal measuring range from 0 150 g/l. During
the experiments, the density in the measuring chamber is measured
with an Anton Paar DMA 35 density meter at least once per load step
to check and if necessary, adjust the calibration of the SSC probe.
For the experiments two C-GEMS of similar construction and
dimensions, but slightly different pump rates were used. The usage
of two different pump rate setups was due to the availability of these
devices and had no further cause in the experimental design. The
applied shear stress velocity and pump rate for the low pumping
setup (setup 1) are related to the stirring disk evolutions as follows:
(Equations 5,6)
u=2:07105n2+1:57102n+0:10527 (5)
Q=0:0318n2+5:5n+20 (6)
with u
*
as shear stress velocity [cm/s], stirrer revolutions n[1/
min] and pump rate Q[ml/min]. The applied bed shear stress t
b
is
calculated as tb=u2
*rw. For the calculation of t
b
, the increase of
the density of the suspension above the sediment surface over the
experimental duration due to the increasing SSC is neglected, since
the inuence is sufciently small (mostly < 1%). Setup 2 worked on
higher pumprates (factor 1.5) resulting in higher shear stresses
(factor 1.22).
2.3.2 Sample preparation and
experimental procedure
In total 34 erosion experiments with homogenized samples and bulk
densities from 1050 1250 kg/m³ have been conducted. For sediment
from sampling location SE densities from 1050 1200 kg/m³ were
tested, whereas for NE-sediment the range from 1100 to 1250 kg/m³ was
covered. For both locations steps of 25 kg/m³ were applied (see Table 2).
The structural density, which is dened as the density at the gelling
point, where an interconnected matrix of solids has formed (see
Winterwerp et al. (2021)), for sediment from location SE was
determined as ~1080 kg/m³ from previous settling column
experiments, thus densities 1050 kg/m³ and 1075 kg/m³ are slightly
below the structural density. The full range of tested densities covers the
in-situ measured densities of the top 50 cm layer of the sediment bed at
location SE (Witt et al., 2023).
The raw sediment samples were thoroughly homogenized before
being partially lled into the erosion chamber. In the chamber, the
samples were diluted with site-specicwater(r
w
=998 kg/m³) to the
desired density and homogenized again. The desired density was set
with an accuracy of ±1 g/l and was repeatedly checked with an Anton
Paar DMA 35 density meter. The nal sediment layers had a height of
612 cm depending on the density of the diluted sample (lower
height for high densities due to lower expected erodibility). Then,
site-specic water was added on top of the sediment-mixture to the
chamber. This process had to be carried out very carefully and slowly
(~15 minutes for 3 l of water) to minimize the disturbance of the
sediment surface. The top-part of the C-GEMS (consisting of lid,
stirring plate and a height adjustment system) was attached and the
stirring plate was adjusted to the correct height in relation to the
sediment surface. The last step was to ll the measuring chamber with
site-specic water and start the pump cycles. One hour after the last
homogenization of the samples the erosion experiments were started
(except experiments with densities 1050 kg/m³ and 1075 kg/m³ with
only 0.5 hours in between to reduce settling effects due to density
below the structural density).
During the experiments, a maximum of 13 load steps of 0.028 -
0.33 N/m² (setup 1) respectively 0.034 0.40 N/m² (setup 2) were
applied with a load step duration of 15 minutes. At the beginning of
each load step, the distance between the sediment surface and the
stirring plate was checked and adjusted if necessary. When an SSC
of approximately 15 g/l was reached during the experiment, the
experiment was terminated because of the increasing non-
Newtonian ow behavior of the uid.
TABLE 2 Overview of conducted experiments and tested wet bulk densities for the two sampling sites, numbers indicate amount of repetitions.
Bulk density [kg/m³]
Sample 1050 1075 1100 1125 1150 1175 1200 1225 1250
SE 2222222
NE 3272223
FIGURE 2
Schematic outline of the utilized adapted Closed Gust Erosion
Microcosm System (C-GEMS).
Witt et al. 10.3389/fmars.2024.1386081
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2.3.3 Data processing
The SSC in the measuring chamber was recorded with the
Hach®Solitax sc at 5-second intervals. The measured SSC values
were corrected by the background SSC measured at the beginning of
the experiment, typically lying in the range of 10 30 mg/l.
Therefore, the further used SSC values describe the rise in SSC in
relation to the initial concentration. To reduce scatter in the data, a
moving average of 60 s was calculated for further processing of the
data. For one experiment with sediment from site NE, setup 2 and
r=1250 kg/m³ the data of six load steps had to be excluded due to
problems with the pump, which circulates the suspension in the
measuring chamber.
Erosion rates ewere derived from the processed SSC data by
relating the change in measured SSC at two consecutive time steps
to the time interval Dt, the total uid volume V
f
and the area of the
sediment surface A
s
(Equation 7):
e=(SSCtSSCt+Dt) Vf
DtAs
(7)
2.3.4 Methods to determine t
c
Two methods to determine the erosion threshold t
c
have been
utilized and compared. In both cases t
c
is dened as the surface
erosion threshold, implying that small erosion rates might also
occur at shear stresses below t
c
due to erosion of single ocs (c.f.
Winterwerp et al. (2021)). The two methods are:
Log-log regression of mean erosion rates per load step vs.
applied bed shear stress t
b
. The erosion threshold t
c
is
determined as the interpolated shear stress at the intercept
of the regression with e
f
=1 x 10
-5
kg/(m²s), as an
extrapolation to zero erosion is not possible. The oc
erosion rate e
f
is dened as the value of eat t
b
t
c
=0,
meaning at zero excessive shear (background erosion rate)
(Parchure and Mehta, 1985). Parchure and Mehta (1985)
evaluated e
f
for different mud samples and despite some
variation in the derived magnitudes, the utilized value of
e
f
=1 x 10
-5
kg/(m²s) in Amos et al. (2003) is seen as a
practical choice.
Log-log regression of mean SSC per load step vs. applied
bed shear stress t
b
. The value of t
c
is determined as the
interpolated shear stress of the regression with SSC
T
=40
mg/l. The threshold describes the accumulated eroded mass
over all prior load steps and was set to this value based on an
analysis showing a good correspondence with the value of e
f
used for method one. An extrapolation to zero SSC is again
not possible, due to log space. Solving for background SSC,
without prior correction of the measured SSC by this value,
would be possible, but would lead to very low derived t
c
values because the highly sensitive SSC-probes detect an
increase in SSC usually even during the rst load step
(background- or oc erosion). The value of SSC
T
=40 mg/l
can be generalized and adapted to devices with other
dimensions by relating it to the uid-volume and
sediment-surface area of the GEMS system, leading to a
total eroded mass of 0.37 g and ~13 g/m² respectively.
Though the chosen SSC-threshold is seen to be dependent
on the load-step duration and might need calibration for
varying values.
For both methods, all data points were used for the respective
regression. No further distinction between erosion modes and the
point of transition between them was applied to limit the
parameters to be set.
3 Results
3.1 Evolutions of suspended sediment
concentration and erosion rate
For all conducted experiments the SSC evolution in the
measuring chamber was captured and the corresponding erosion
rates were derived (see sections 2.3.2 and 2.3.3). In Figure 3 the
results for both the SSC and the erosion rates for three different
exemplary bulk densities (1100, 1150 and 1200 kg/m³) for the two
sampling sites SE and NE are shown. The chosen densities represent
the range of tested densities for which data from both sampling
locations is available and illustrate the observed trends and
relationships. The gure gives an impression of the generally high
repeatability of the SSC measurements and erosion rate
calculations, especially when considering the rapid change of
erodibility with increasing bulk densities of the sediment mixture.
Focusing on the SSC plots against experimental time (panel
(A)-(C) for SE and (D)-(F) for NE) the strong relationship between
r
b
of the samples and the observed SSC evolution becomes evident.
For sediment from SE at r
b
=1100 kg/m³ the rst increase in SSC on
the applied linear scale becomes visible at around minute 50 and the
curve rises quickly over the following load steps to reach values of
20 g/l after 120 minutes duration. The SSC evolutions for r
b
=1150
kg/m³ and r
b
=1200 kg/m³ exhibit a consistent shift to the right,
meaning a longer experimental duration and thus higher applied
bed shear stresses are needed to cause a similar SSC-increase. For
r
b
=1200 kg/m³ the SSC reaches values of < 1 g/l after the maximum
duration of 3.25 h. The decreasing erodibility with rising bulk
densities of the slurry is caused by an increased amount of
cohesive particles per volume element and therefore more and
stronger bonds between the single particles. Since the samples tested
are homogenized and have uniform erosion characteristics over the
depth of the sample, the gradient of the SSC curves is theoretically
constant for each load step and increases with the applied bed shear
stress. This relationship is generally well represented in the
measured data, especially for higher applied bed shear stresses.
For load-steps of lower bed shear stresses most of the SSC curves
approach a plateau asymptotically. This observation is conrmed by
the corresponding plots of e, which are shown under the SSC-plots
(panel (G)-(I) for SE and (J)-(L) for NE). For low t
b
the erosion rates
tend to peak at the beginning of each load-step and decrease over the
remaining load step duration. This trend in e-evolution is commonly
observed in experiments with density-stratied samples and
increasing erosion resistance over the depth of the sample (type I
erosion, see section 1). The reason why the described trend is also
Witt et al. 10.3389/fmars.2024.1386081
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apparent in the presented experiments, despite working with
homogeneous samples, is seen in the fact that during the rst load
steps only the topmost part of the sample (< 1 mm depth) is eroded.
In this top-layer particles are incorporated into the grain structure to
varying degrees and therefore exhibit a differing erosion resistance,
meaning that the erosion resistance (as also the applied load) follows
a probability distribution (Winterwerp et al., 2012). This leads to
decreasing erosion rates over the load-step duration, since the
BC
DEF
GHI
JKL
A
FIGURE 3
Exemplary evolution of SSC and efor experiments with bulk densities of 1100, 1150 and 1200 kg/m³. (AC) show the SSC evolution for SE-
experiments, (DF) show SSC for NE-experiments. (GL) show the e-evolution for SE resp. NE. Only highlighted regimes (initial runs v
1
and v
2
) are
shown in e-plots for better readability. Additional runs (v
i
) shown in low opacity. Color indicates C-GEMS setup 1 (blue) and setup 2 (red). Revolutions
per minute (RPM) are displayed on secondary y-axes instead of t
b
because the two C-GEMS setups worked on identical RPM regimes, but slightly
different t
b
steps (see end of section 2.3.1).
Witt et al. 10.3389/fmars.2024.1386081
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number of particles that might get eroded declines. With increasing
load and erosion depth, the erosion rates become more and more
constant over each load-step and reach values of up to 5 x 10
-3
kg/(m²s).
The setup 2 of the utilized C-GEMS generally records an earlier
increase in SSC and ecompared to setup 1, as expected due to the
slightly higher t
b
applied. Comparing the results of the two
sampling sites SE and NE, the evolution of SSC- and eindicates a
higher erodibility for material from site NE. For example, for
r
b
=1200 kg/m³ the measured nal SSC for site SE is < 1 g/l,
whereas values of ~4-5 g/l are measured for site NE. For the
other densities, this relationship is reected by faster increasing
SSC and erosion rates as well.
3.2 Derivation of erosion thresholds
From the SSC and e-evolutions, the mean values of the
parameters per load-step have been calculated (see section 2.3.4)
and are shown in Figure 4 (SE) and Figure 5 (NE) against the
applied bed shear stress. Focusing on the exemplary bulk densities
for sampling site SE (Figure 4), the diagrams illustrate that for both
methods to derive t
c
, the erosion threshold increases together with
the bulk density. Additionally, the gradient of the regression lines
consistently decreases with increasing bulk density. These
fundamental relationships are in line with the observations
described in section 3.2 and theory and indicate a lower
erodibility for higher bulk densities. For the illustrated densities
the erosion rate method leads to values for t
c
of 0.053 0.430 N/m².
While for bulk densities of 1100 kg/m³ and 1150 kg/m³, this method
yields a small semi-range (SR) for calculated t
c
in repetition tests of
< 0.005 N/m², the spread of the derived values rises drastically for
r
b
=1200 kg/m³ (SR=0.086 N/m²). Also, the calculated coefcients of
determination (R²; calculated based on log-transformed data)
indicate a strong linear relation between the applied bed shear
stress and efor bulk densities 1100 kg/m³ and 1150 kg/m³ (R²
0.94), but drops for r
b
=1200 kg/m³. The SSC-method yields values
for t
c
in the range of 0.060 0.159 N/m² and results in small semi-
ranges of t
c
in repetition tests (SR < 0.008 N/m²) and high values
(R² 0.91) for all three shown bulk densities. Compared to the e-
method the SSC-method leads to slightly higher t
c
values for
r
b
=1100 kg/m³ and r
b
=1150 kg/m³, but signicantly lower values
for r
b
=1200 kg/m³. The reason for the inconsistent results of the e-
method for r
b
=1200 kg/m³ is seen in the fact that this bulk density
is close to the application limit of the utilized C-GEMS devices for
sediment from this specic site. Only a small amount of sediment is
BC
DEF
A
FIGURE 4
Log-log-regression of e/SSC against t
b
and derived values for t
c
for sampling location SE (exemplary bulk densities 1100, 1150, 1200 kg/m
3
). (A-C)
show results for e-method, (D-F) show results for SSC-method. For the initial two experiments (v
1
,v
2
) the regression lines and calculated values for
t
c
are highlighted and the data from additional runs (v
i
, if conducted) is shown in low opacity and without regression lines for better readability.
Witt et al. 10.3389/fmars.2024.1386081
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eroded over the experimental duration, leading to low erosion rates
and large scatter in the erosion rate data (see Figures 3,4). The large
scatter in erosion rate data in turn yields low values and a large
spread in derived erosion thresholds. Since, in contrast to e, the SSC
is accumulating over time, the SSC data exhibits much less scatter
and allows a more reliable determination of t
c
even at the
application boundary. In the upper part of Table 3, the results for
all experiments conducted with material from sampling site SE are
summarized. The data derived in the additional experiments
underlines that both applied approaches yield comparable values
for t
c
, SR and R², except at the upper application limit where the
SSC-method is superior to the e-method.
The described trends and relationships are also valid for the
experiments conducted with sediment from site NE. The results for
the three exemplary bulk densities are illustrated in Figure 5 and the
data for all experiments is summarized in the lower part of Table 3.As
expected from the data shown in Figure 3, the erosion thresholds
derived for site NE are generally lower than for site SE. The higher
erodibility of the NE-sediment also leads to a shift of the application
limit of the GEMS device to higher bulk densities. While for SE
sediment for r
b
=1200 kg/m³, only the SSC-method yielded reasonable
results, for sediment from site NE the e-method was still applicable for
this bulk density as well. The application limit was reached at r
b
=1250
kg/m³ for site NE, where the e-method again led to unreasonably high
values for t
c
, a high spread of the derived values and low R².
For NE-sediment with r
b
=1100 kg/m³, r
b
=1150 kg/m³ and
r
b
=1250 kg/m³ additional experiments have been conducted to check
and quantify the repeatability of the experimental setup and approaches
to derive t
c
. The additional repetitions were conducted around one
month after the initial experiments, which were carried out in the rst
two weeks after the measurement campaign. In the additional
experiments, slightly lower values for t
c
were derived. While the
SSC-method for r
b
=1150kg/m³intheinitialexperimentsyieldeda
mean t
c
of 0.081 N/m² (SR=0.008 N/m², n=2), for the additional
repetitions a mean of 0.075 N/m² (SD=0.005 N/m², n=5) was derived,
leading to an overall value of 0.077 N/m² (SD=0.007 N/m², n=7) (see
Table 3).Themeasuredchangemightbecausedbyachangein
sediment properties evoked by biological activity. However, due to the
relatively small database and small measured changes in t
c
,thisisonly
an assumption yet and needs further investigation.
The two methods used to derive t
c
delivered comparable results
for most of the bulk densities tested, with a small spread in derived
values in repetition tests and strong linear correlation (in log-space)
between applied bed shear stress and measured SSC/e(slightly higher
for SSC-method). Especially because of the better performance of the
SSC-method at the upper limits of application, this method should be
BC
DE F
A
FIGURE 5
Log-log-regression of e/SSC against t
b
and derived values for t
c
for sampling location NE (exemplary bulk densities 1100, 1150, 1200 kg/m³). (A-C)
show results for e-method, (D-F) show results for SSC-method. For the initial two experiments (v
1
,v
2
) the regression lines and calculated values for
t
c
are highlighted and the data from additional runs (v
i
, if conducted) is shown in low opacity and without regression lines for better readability.
Witt et al. 10.3389/fmars.2024.1386081
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preferred though and the data derived by this method is used to t
models for t
c
in section 3.3. To investigate the inuence of the applied
values of the thresholds for SSC (SSC
T
)ande(e
T
) on the derived
values for t
c
, a sensitivity analysis was conducted using the example of
site SE (Figures 6A,B). The chosen thresholds were varied by ±50%.
As expected from the decreasing slope of the regression lines with
increasing bulk density (Figure 4), the total variation of the derived t
c
also increases with r
b
. Especially for the lower and middle values of
the tested density range, the variation is relatively small, e.g. for SSC-
method and r
b
=1150 kg/m³ the variation of SSC
T
of ±50% leads to a
change in the derived t
c
of +10.6% and -15,7%, respectively.
Figure 6C additionally shows an analysis of the inuence of
different time periods (t
av
) over which the average value of eis
calculated for each load step when using the e-method. A value of
t
av
=5 min means only the rst ve minutes of each load step were
used for averaging. This analysis can be interpreted as the expected
sensitivity of the calculated t
c
with respect to a corresponding change
in load step duration. Since the magnitude of edecreases signicantly
over the applied load step duration for load steps of lower t
b
(see
Figure 3), a shortening of t
av
leads to higher calculated averages of e
and consequently to a decrease of the derived values of t
c
. For the
SSC-method, a similar analysis is not feasible based on the dataset,
since this parameter accumulates over the duration of the experiment
und thus the actually applied load step duration directly inuences
the SSC in subsequent load steps.
Summaries of t
c
derived from eld and laboratory experiments in
other studies can be found in Debnath and Chaudhuri (2010) and
Houwing (1999). As stated in section 1, the derived values are strongly
inuenced by the erosion device used, the specic sediment properties
and the applied denition of the erosion threshold. There is only a
limited amount of data available for bulk densities in the range that was
tested in this study. However, the studies from Righetti and Lucarelli
(2007), who tested benthic lake sediments with bulk densities from
1025 1175 kg/m³ in a Sedume and derived values for t
c
in the range
of 0.01 0.23 N/m², and Amos et al. (1997), who worked with mud at
sediments with r
b
from 787 1273 kg/m³ in a Sea Carousel and
derived values for t
c
of 0.15 0.5 N/m², show that the ndings in the
present study are well covered by the observations in previous studies.
3.3 Model application
The data on t
c
derived by SSC-method in section 3.2 is used to t
two mathematical models. The rst model is a power-law relation
TABLE 3 Summary of derived mean erosion thresholds for all tested densities for both sampling locations with e- and SSC-Method.
Method 1
Erosion rate
Method 2
SSC
Sampling
site
Bulk
density
Dry
bulk
density
Reps. Mean
erosion
threshold
semi-
range/SD (*)
Mean
Mean
erosion
threshold
semi-
range/SD (*)
Mean
r
b
r
db
nt
c
t
c
kg/m³ kg/m³ [N/m²] [N/m²] [N/m²] [N/m²]
SE
1050 85 2 0.032 0.005 0.85 0.037 0.001 0.96
1075 126 2 0.033 0.002 0.93 0.040 0.001 0.99
1100 166 2 0.057 0.004 0.98 0.065 0.005 0.99
1125 207 2 0.086 0.008 0.94 0.087 0.005 0.97
1150 248 2 0.088 0.001 0.95 0.097 0.001 0.98
1175 289 2 0.111 0.010 0.91 0.106 0.010 0.95
1200 329 2 0.344 0.086 0.49 0.151 0.008 0.95
NE
1100 166
2 (init.) 0.056 0.000 0.94 0.063 0.000 0.97
3 (all) 0.053 0.005* 0.94 0.060 0.005* 0.97
1125 207 2 0.068 0.006 0.95 0.078 0.008 0.97
1150 248
2 (init.) 0.076 0.007 0.97 0.081 0.008 0.98
7 (all) 0.071 0.007* 0.94 0.077 0.007* 0.97
1175 288 2 0.099 0.007 0.97 0.097 0.001 0.95
1200 329 2 0.100 0.003 0.84 0.100 0.003 0.97
1225 370 2 0.142 0.001 0.82 0.157 0.012 0.98
1250 411
1 (init.) 7.196 0.24 0.305 1.00
3 (all) 5.953 4.441* 0.16 0.289 0.022* 0.98
Standard deviation (SD) calculated for n > 2, semi-range for n=2.
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between r
db
and t
c
(Equation 1) and the second model is a more
complex and physically based model shown in Equation 3, proposed
in Chen et al. (2021). The application of both models requires the
calculation of r
db
as shown in Equation 2. From the assumed density
of the particles of the mud-fraction r
pm
=2575 kg/m² (cf. Malcherek
(2010)) and sand particles (r
pps
=2650 kg/m³) the weighted particle
density for the sediment mixture is calculated as r
s
=r
ps
+r
pm
P
m
.
The derived values for r
db
are shown in Table 3.InFigure 7 the tted
models are illustrated. Both models have been tted to the data
obtained from the two sampling sites separately and additionally to
the whole dataset using least-squares method. For site NE only the
derived data from the initial two experiments (one in case of
r
b
=1250 kg/m³) was used, even if more repetitions have been
carried out, due to the unclear effect of the time span between the
experiments (see section 3.2). The obtained t parameters and the
resulting root mean squared errors (RMSE) are summarized
in Table 4.
The power law-t for site SE suggests an almost linear increase
of t
c
over the considered range of bulk densities (exponent n=1.15)
while for site NE the power-law relation is more distinct. However,
the derived model for NE underpredicts the erosion thresholds in
the lower range of r
b
=1100 1150 kg/m². Fitting the model on the
whole dataset (SE+NE) yields a reasonable model for the whole
considered range of densities and both sampling sites. The derived
t-parameters for this model are m=1.83 x 10
-6
and n=1.96. Earlier
investigations, which were carried out by Owen (1975) and Thorn
and Parsons (1980) (see see Zhu et al. (2008)) with remolded
sediment samples from four different estuaries, led to values for
mof 6.85 x 10
-6
resp. 5.42 x 10
-6
and values for nof 2.44 resp. 2.28.
An extensive overview of derived t-parameters from other studies
carried out with different muds and erosions devices can also be
found in Schweim (2005), with mranging between 2.5 x 10
-8
1.5 x
10
-2
and nbetween 0.73 2.44. Although the t-parameters derived
in this study are comparable to earlier studies, their values vary
signicantly with the underlying dataset both for this study and
earlier works.
The model proposed in Chen et al. (2021) includes only a single
t-parameter, denoted as A(units J/m²). Additional sediment
properties used to t the model are shown in Table 1. The mud-
fraction is calculated as the sum of clay and silt fractions and for
parameters r
ps
and r
pm
the same assumptions are made as described
for the power-law model. The derived values for the t parameter A
are 8.56 x 10
-6
J/m² based on SE-data and 8.38 x 10
-6
J/m² based on
NE-data. The t on the whole dataset yielded A=8.43 x 10
-6
J/m². It
stands out that the t-parameters show only a marginal spread. In
Chen et al. (2021) the authors applied the model to multiple natural
muds from different locations and concluded that the value of Ais
generally in the order of 10
-6
or 10
-5
J/m² and specically for natural
mud and sand-mud mixtures in the range of 2.86 x 10
-6
1.04 x 10
-5
J/m² (if no eld data is available the authors propose a general value
of A=3.97 x 10
-6
J/m²). The values for Aderived in this study are
covered well by the ndings of the authors, lying close to the mean of
A-values determined by them. The small spread in Asuggests that
the consideration of the physical parameters describing the mud-
fraction of the sediment leads to a more profound model than the
power-law model also applied, relating the evolution of t
c
to the
actual sediment properties and leaving a lower degree of freedom for
the empirical t. Figure 7B additionally shows that the slightly lower
erosion thresholds for NE-sediment might be at least partly caused
by the (also slightly) different grain size distribution, since the same
t-parameter (solid lines) leads to lower t
c
values. The lower spread
of Ais also reected in the calculated RMSE. While for the power-
law t the RMSE rise considerably for both individual sites when the
model is tted on the whole dataset and not on the site-associated
data only, for this model, the RMSE is almost independent of the
chosen database for the model t (see Table 4). A comparison of the
RMSE of the two different models tted on the whole dataset
additionally reveals a slightly better adaption of the Chen-model
to the measured erosion threshold data overall. A sensitivity analysis
conducted for the value of the t-parameter Awith respect to the
applied values of SSC
T
and e
T
, using the example of site SE (tting
lines shown in Figures 6A,B), shows that a variation of the values of
±50% leads to a range of Aof 7.30 x 10
-6
1.0 x 10
-5
J/m² for e-
B
C
A
FIGURE 6
Sensitivity analysis of the calculated values for t
c
and parameter A of
the Chen-model with respect to the thresholds for SSC (SSC
T
) and e
(e
T
) and the time periods over which the average value of eis
calculated for each load step (t
av
), using the example of site SE. (A)
shows the results for varying SSC
T
using the SSC-method, (B) for
varying e
T
using the e-method and (C) for varying t
av
using the e-
method. For e-method r
b
=1200 kg/m³ is excluded.
Witt et al. 10.3389/fmars.2024.1386081
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method and 6.54 x 10
-6
1.01 x 10
-5
J/m² for SSC-method. The
analysis of different time periods t
av
used for averaging efor each
load step when using the e-method (Figure 6C) shows that the
applied reduction of t
av
from 15 to 5 min leads to a range of Aof 6.55
x10
-6
8.91 x 10
-6
J/m². Despite the applied variation of SSC
T
,e
T
and t
av
the derived values for Aare well covered by the expected
range of A, accordingly.
4 Discussion and summary
4.1 Discussion
Some additional considerations regarding the results obtained
and the experimental procedure are discussed in this section. Since
the C-GEMS is a closed system and the eroded sediment
accumulates throughout the duration of the experiment, the
question arises, as with all closed erosion devices, whether
deposition occurs simultaneously with erosion. In general, two
concepts to describe the onset of deposition of cohesive sediment
exist: i) the existence of a critical shear stress for deposition t
d
, which
is lower than t
c
, meaning deposition and erosion are mutually
exclusive (Krone, 1962;seeWhitehouse et al. (2000))andii)the
assumption that deposition occurs continuously also at higher shear
stresses (see e.g. Winterwerp et al. (2021)). While modeling of in-situ
data may yield better results under the assumption of continuous
deposition, many laboratory studies have demonstrated the existence
of a critical shear stress, below which deposition does not occur (see
Sanford and Halka (1993)). This discrepancy may be due to
differences in scale and turbulence conditions and the absence of
still water/occulation periods in laboratory experiments. In the C-
GEMS, the turbulent mixing in the erosion chamber is supported by
the constant suction and feeding of the suspension and occulation
of eroded particles is hardly possible because the particles are
exposed to high shear rates in the different pumping cycles,
resulting in very small oc sizes and (theoretical) settling rates.
Both of these factors would signicantly harm deposition. Even if
these ocs/particles briey were to come into brief contact with the
sediment surface it is not unlikely that they would be able to
withstand the applied bed shear stress, so they would be
immediately eroded again. Nevertheless, we cannot completely rule
out the presence of deposition during the experiments, so the derived
erosion rates can be interpreted as net erosion ux.
In section 3.3 it was shown that the Chen-model can explain the
observed higher erodibility of sediments from site NE at least partly
with the sediment composition (cf. Figure 7B), slightly lower
TABLE 4 Derived t-parameters for the applied mathematical models.
Power-law t(tc=mrn
db)Chen et al. (2021)
Database m [-] n [-] RMSE [N/m²] A [J/m²] RMSE [N/m²]
SE 1.74*10
-4
1.15 0.008 8.56*10
-6
0.020
NE 1.98*10
-8
2.73 0.035 8.38*10
-6
0.034
SE+NE 1.83*10
-6
1.96
SE: 0.019
NE: 0.038
SE+NE: 0.030
8.43*10
-6
SE: 0.020
NE: 0.034
SE+NE: 0.028
BA
FIGURE 7
(A) Power-law toft
c
,(B) Fit of Chen-approach for t
c
(both shown against bulk density). Dashed lines indicate ts of SE/NE data based on
respective datapoints only. Solid lines indicate t of SE/NE data based on t parameters derived from whole dataset (in (B) the dashed lines are fully
covered by the solid lines).
Witt et al. 10.3389/fmars.2024.1386081
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predicted t
c
for NE-sediment for the same value of A). To make a
statement whether this is the only reason for the noticed difference
in erodibility or if other reasons e.g., a difference in the kind of
organic matter, inuence the erosion behavior, further investigation
is needed. Focusing on the t-parameter A,inChen et al. (2021) it is
stated that the value of Ais supposed to be site-specic because it
describes the bed surface roughness and the cohesion strength,
which is, among others, inuenced by the mineral composition of
the sediment and the pore water environment. Since the sampling
sites investigated in this study are only a few kilometers apart and
comparable in characteristics, it seems plausible to assume a broad
agreement in characteristics. This assumption in turn leads to the
expectation, that the derived parameters for Aare in the same range
for both sites, as demonstrated in this study.
Another noteworthy point is that the lowest bulk densities
tested for site SE (r
b
=1050 kg/m³ and 1075 kg/m³) are below the
structural density (as stated in section 2.3.2). Despite the adjusted,
shortened time between sample preparation and the beginning of
the erosion experiment for these densities, the onset of the settling
process presumably led to higher densities below the lutocline than
initially set. The increased densities might have led to an
overestimation of the erosion threshold from the conducted
measurements and explain the underprediction of t
c
for these
bulk densities by the models.
Looking at the applied techniques to derive t
c
, erosion rate and
SSC method, the chosen values for the thresholds of eand SSC are
obviously debatable. However, no other method to derive t
c
is
available that does not include either dened threshold values, the
differentiation of erosion-modi or the denition of erosion/no-
erosion states. Indeed, the implementation of a kind of threshold
(that is always arguable) is imperative, since with highly sensitive
sensors even at very low applied bed shear stresses measurable
erosion rates can be detected (as shown in this study), which rather
result from particle/background erosion than from surface erosion.
This observation rises the question if a single value for t
c
is a
reasonable concept to describe the initiation of motion of cohesive
sediment. However, since most the erosion models in use depend
on this type of data, the practical benets are beyond doubt. Some
models (e.g. Parchure and Mehta (1985)) also incorporate the
unsharp initiation of motion. The benet of the tested methods in
this work in deriving these data is, that only one single SSC-/e-
threshold is used and that the thresholds are transferable to other
devices straightforward, which is hoped to contribute to better
comparability of derived erosion thresholds of future investigations.
4.2 Summary
In this work, an improved version of a closed microcosm system
(C-GEMS) proposed in Patzke et al. (2022) is presented. The device is
used to perform erosion experiments with freshly deposited cohesive
sediments collected from two sites on the River Elbe in the area of the
Port of Hamburg. For the erosion experiments, the sediments were
homogenized and diluted to bulk densities from 1050 1250 kg/m³,
which is the observed range of bulk densities in earlier investigations
over the top layer of the sediment bed (multiple ten-centimeters to
about one meter). During the experiments a maximum of 13 load
steps were applied with increasing bed shear stresses from 0.028 to
0.33 N/m² (setup 1) resp. 0.034 0.40 N/m² (setup 2). The evolution
of SSC in the measuring chamber of the C-GEMS was recorded using
aHach
®Solitax sc probe and the corresponding erosion rates were
calculated from the change in SSC over time. The results of the SSC-
and e-evolutions indicate a distinct relationship between the bulk
density of the cohesive sediment-mixture and the erodibility and
exhibit good repeatability. The further investigations focused on the
derivation and quantication of the surface erosion thresholds. Two
methods were applied for this purpose: i) interpolation of the log-log-
regression of mean erosion rates to the threshold value of e=1 x 10
-5
kg/(m²s) and ii) interpolation of the log-log-regression of mean SSC
to the threshold value of 40 mg/l. The derived values for t
c
for both
methods showed a good agreement for the considered range of bulk
densities except at the upper application limits of the utilized C-
GEMS device, where only the SSC-method yielded reasonable results
due to signicantly lower scatter in the SSC-data compared to e-data.
The reason for the lower scatter of the SSC-data is seen in the
accumulating nature of this parameter, as the C-GEMS is a closed
system. Comparable studies with other erosion devices support the
conclusion that deriving erosion thresholds based on an
accumulating parameter leads to more robust results (Amos et al.,
2003;Ha and Ha, 2021). Because of the better performance at the
application limits its suggested that the SSC-method should be
preferred over the e-method when working at the application
limits of the device. The derived mean t
c
for location SE (r
b
=1050
1200 kg/m²) with SSC-method are in the range of 0.037 0.151 N/
and for location NE (r
b
=1100 1250 kg/m²) in the range of0.063
0.305 N/m². For NE-site with r
b
=1150 kg/m³, a total of seven
repetitions has been carried out yielding a mean t
c
of 0.077 N/m²
with a standard deviation of 0.007 N/m², underlining the
reproducibility of the utilized experimental procedure. In a last
step the derived t
c
-data was used to t two mathematical models, a
power-law relationship between dry bulk density and t
c
and a model
proposed in Chen et al. (2021).Thetting of the power-law model
showed a strong dependency of the derived t-parameters on the
respective data used for the t (SE, NE or SE+NE), while the tting of
the Chen-model yielded practically the same value for the t-
parameter Aindependent of the chosen database. Using the whole
dataset to t the models, the power-law t yielded values of the
prefactor m=1.83 x 10
-6
and the exponent n=1.96. The tting of the
Chen-model on the whole database led to A=8.43 x 10
-6
. All derived
t-parameter are well-covered by the range of values reported in
previous studies. Since the Chen-model relates the change in t
c
to the
physical properties of the sediment mixture, shows a better adaption
to the measured data and the value of the t-parameter is stable
independently of the underlying data subset, its concluded that the
model is more profound and should be preferred over the highly
empirical power-law model.
4.3 Outlook
In further investigations, different models for the erosion rate
will be applied to the collected data. Taking the derived relationship
Witt et al. 10.3389/fmars.2024.1386081
Frontiers in Marine Science frontiersin.org13
between r
b
and efor the examined samples into account, the often
used linear model based on the work of Partheniades (1965) (see
McAnally and Mehta (2000)) reading e=m(t
b
-t
c
) for t
b
>t
c
, with
mas erosion constant, presumably allows only an unsatisfactory
adaption to the collected data. In combination with in-situ
measured density proles the derived relations of t
c
and eenable
the generation of depth proles of the regarding values for the upper
layers of the sediment bed. Additionally, it is planned to utilize the
presented C-GEMS device for erosion experiments with (almost)
undisturbed naturally stratied sediment samples as well. These
experiments will be conducted i) with sediment cores extracted
from the navigation channel of the Elbe right after withdrawal
directly on the vessel and ii) by applying the C-GEMS in-situ in the
tidal ats of the Elbe by mounting the system on a piercing cylinder.
Data availability statement
The raw data supporting the conclusions of this article will be
made available by the authors, without undue reservation.
Author contributions
MW: Writing original draft. JP: Writing review & editing.
EN: Writing review & editing. PF: Writing review & editing.
Funding
The author(s) declare nancial support was received for the
research, authorship, and/or publication of this article. This study
was conducted as part of the research project ELMOD - Simulation
and analysis of the hydrological and morphological development of
the Tidal Elbe for the period from 2013 to 2018. The project on
which this report is based was funded by the German Federal
Ministry of Education and Research (BMBF) under the funding
code 03F0928A. The responsibility for the content of this
publication lies with the authors.
Acknowledgments
The authors would like to thank the Hamburg Port Authority
(HPA) for providing ship capacities and employees for the
conducted measurement campaigns. Special thanks are also
addressed directly to all involved employees of the HPA, Federal
Waterways Engineering and Research Institute (BAW) and TUHH
for their great support during the campaigns. Publishing fees
supported by Funding Program Open Access Publishing of
Hamburg University of Technology (TUHH).
Conict of interest
The authors declare that the research was conducted in the
absence of any commercial or nancial relationships that could be
construed as a potential conict of interest.
Publishers note
All claims expressed in this article are solely those of the authors
and do not necessarily represent those of their afliated
organizations, or those of the publisher, the editors and the
reviewers. Any product that may be evaluated in this article, or
claim that may be made by its manufacturer, is not guaranteed or
endorsed by the publisher.
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