Clast imbrication is
one of the most conspicuous sedimentary structures in coarse-grained clastic
deposits of modern rivers but also in the stratigraphic record. In this
paper, we test whether the formation of this fabric can be related to the
occurrence of upper flow regime conditions in streams. To this end, we
calculated the Froude number at the incipient motion of coarse-grained
bedload for various values of relative bed roughness and stream gradient as
these are the first-order variables that can practically be extracted from
preserved deposits. We found that a steeper energy gradient, or slope, and a
larger bed roughness tend to favor the occurrence of supercritical flows. We
also found that, at the onset of grain motion, the ratio
Conglomerates, representing the coarse-grained spectrum of clastic sediments, bear key information about the provenance of the material (Matter, 1964), the sedimentary environments (Rust, 1978; Middleton and Trujillo, 1984), and the hydro-climatic conditions upon transport and deposition (Duller et al., 2012; D'Arcy et al., 2017). Conglomerates display the entire range of sedimentary structures, including a massive-bedded fabric, cross beds and horizontal stratifications. However, the most striking feature is clast imbrication (Fig. 1a), which refers to a depositional fabric where sediment particles of similar sizes overlap each other, similar to a run of toppled dominoes (e.g., Pettijohn, 1957; Yagishita, 1997; Rust, 1984; Potsma and Roep, 1985; Todd, 1996). Imbrication may lead to armor development and the interlocking of clasts. As a consequence the search for possible controls on this fabric has received major attention in the literature (e.g., Bray and Church, 1980; Carling, 1981; Aberle and Nikora, 2006).
In the past decades, clast imbrication in streams has been considered to
record high-stage flows (Rust, 1978; Miall, 1978; Sinclair and Jaffey, 2001).
This could occur in the upper flow regime, where the flow velocity of a
stream
Significant sediment accumulation may occur underneath the hydraulic jump upon deceleration of the flow's velocity (Slootman et al., 2018). Contrariwise, a downstream change from a lower to an upper flow regime has no distinct surface expression, neither in terms of flow depth nor flow surface texture. While these mechanisms have been well explored and reported both from modern environments (e.g., Fig. 1) and fine-grained stratigraphic records (Alexander et al., 2001; Schlunegger et al., 2017; Slootman et al., 2018) and illustrated on photos from the field (Spreafacio et al., 2001), less evidence for a supercritical flow has been documented from conglomerates. This even led Grant (1997) to note that supercritical flows in fluvial channels are rare and that the use of the Froude number lacks justification from sedimentary records. In addition, Jarrett (1984) and Trieste (1992, 1994) considered that reports of inferred upper flow regimes might be biased by underestimations of the bed roughness in mountain streams. Nevertheless, the surface texture of the flow illustrated in Fig. 1a is characteristic for many streams (Spreafico et al., 2001), where hydraulic jumps are observed on the stoss side of large imbricated clasts. Furthermore, because the shift in large clasts such as cobbles and boulders does involve large shear stresses and thus high-discharge flows (Rust, 1978; Miall, 1978; Sinclair and Jaffey, 2001), the deposition of these particles, and particularly the formation of an imbricated fabric, is likely to occur during supercritical flows. Here, we explore the validity of this hypothesis for modern coarse-grained streams and stratigraphic records, and we calculate the related hydrological conditions. Similar to Grant (1997), we determine the Froude number at the incipient motion of coarse-grained bedload for various bed roughness and stream gradient values. We compare these results with data from modern streams in the Swiss Alps, stratigraphic records and published laboratory experiments.
Channel depth and grain size are the simplest variables that can be extracted from stratigraphic records (Duller et al., 2012). These variables can additionally be used to calculate paleoslope and roughness values of streams for the geologic past (Paola and Mohring, 1996; Duller et al., 2012; Schlunegger and Norton, 2015; Garefalakis and Schlunegger; 2018), and they form the basis to related channel depth and grain size to flow strength and sediment transport. We therefore decided to focus on the simplest expressions that can also be applied to geological records. We are aware that this requires large generalizations and simplifications, which will not consider the entire range of hydrological complexities.
In the following, we consider the hydrological situation at the incipient
motion of coarse-grained bedload. For these conditions, the dimensionless
Shields parameter
The relationships denoted in Eq. (1a) differ for channel-forming floods,
where channel-forming Shields
stresses
A Shields variable of
Bed shear stress is calculated using an approximation for a steady, uniform
flow down an inclined plane, where channel width is more than 20 times larger
than water depth (e.g., Tucker and Slingerland, 1997):
Sites where modern gravel bars in streams were inspected for the
occurrence of clast imbrication (blue dots). The figure also shows the
locations of the stratigraphic sections where conglomerates were analyzed for
their sedimentary structures.
Alternatively, bed shear stress can also be computed as a function of the
kinetic energy represented by the flow velocity
As outlined in the introduction, the Froude number
We used observations about clast arrangements in gravelly streams in
Switzerland. We paid special attention to the occurrence of clast
imbrication, as we hypothesize that this fabric may document the occurrence
of an upper flow regime (Fig. 1) upon sedimentation and gravel bar migration.
We explored multiple gravel bars for the occurrence or absence of clast
imbrication over a reach of several hundreds of meters where Litty and
Schlunegger (2017) reported grain size data (Table 1). We then determined a
mean energy gradient over a ca. 500 m long reach, which we calculated from
topographic maps at scales
Grain size and observational data and that have been collected in the field. See text for further explanations.
The selected streams are all situated around the Central Alps (Fig. 2), have
different source rock lithologies (Spicher, 1980) and have
different grain size distributions. At sites where grain size data have been collected, the ratio
between the clasts' medium
The Swiss Federal Office for the Environment (FOEN) estimated the Froude
numbers for various flood magnitudes of streams on the northern side of the
Swiss Alps (Spreafico et al., 2001; see Fig. 2 for location of sites). These
estimates are based on flow velocities, flow depths and cross-sectional
geometries of channels. The authors of this study also determined the
corresponding channel gradient over a reach of several hundred meters. We
will thus use the Spreafico et al. (2001) dataset to constrain the range of
possible
We finally identified relationships between channel gradient, bed roughness and clast imbrication from stratigraphic records. We focused on the late Oligocene suite of alluvial megafan conglomerates (Rigi and Thun sections, Fig. 2) deposited at the proximal border of the Swiss Molasse basin. For these conglomerates, Garefalakis and Schlunegger (2018) and Schlunegger and Norton (2015) collected data about the depth and gradient of paleochannels, as well as information about the grain size distribution along ca. 3000 to 3600 m thick sections (Table 1). We returned to these sections and examined ca. 50 sites for the occurrence of clast imbrication within the conglomerate suites.
Relationships between
We calculated the Froude numbers
The Froude number pattern is quite similar for increasing bed roughness
(Fig. 3b). For
This figure relates the occurrence of imbrication (blue bars) or no
imbrication (red bars) to
We also calculated the Froude numbers for
In summary, the calculations predict that water flow may shift to an upper
flow regime for slopes steeper than relative bed roughness values greater than
Spreafico et al. (2001) estimated the Froude numbers for various streams
situated on the northern side of the Swiss Alps. The
The Froude number estimates by Spreafico et al. (2001) disclose a large
scatter in the relationship to channel gradient (Fig. 3a, vertical bars).
This can partially be explained by site-specific differences in bed roughness
due to anthropogenic corrections and constructions (Spreafico et al., 2001).
Nevertheless, the comparison between these data and the results of our
calculations reveal that the entire range of
Here, we present evidence for imbrication and non-imbrication from modern rivers situated both in the core of the Swiss Alps and the foreland, which we relate to channel slope (Fig. 4a) and bed roughness (Fig. 4b). The bedrock geology of the headwaters includes the entire range of lithologies from sedimentary units to schists, gneisses and granites. In addition, the streams cover the full range of water sources including glaciers and surface runoff. Except for the Maggia river between the sites Bignasco and Losone (Fig. 2), all streams are channelized by artificial riverbanks. These are either made up of concrete walls or outsized boulders. Information about the hydrographs, grain size and the results of the shear stress calculations considers the time after these constructions have been made.
The thalweg of the streams meanders between the artificial walls within a 20
to 50 m wide belt. Flat-topped longitudinal bars that are several tens of
meters long and that emerge up to 1.5 m above the thalweg are situated
adjacent to the artificial riverbanks on the slip-off slope of these
meanders. They evolve into subaquatic transverse bars, or riffles, farther
downstream where the thalweg shifts to the opposite channel margin. Channels
are deepest and flattest along the outer cutbank side of the meanders and in
pools downstream of riffles, respectively. The thalweg then steepens where it
crosses the transverse bars and riffles. This is also the location where some
streams show evidence for standing waves with wavelengths
> 5 m (e.g., at Reuss, Fig. 5). Standing waves have also been
encountered in the Waldemme river at Littau (Fig. 6b; see supplement) when
water runoff at that particular site was ca. 100 m
Inspections of gravel bars have shown clear evidence for imbrication in the
Glenner, the Landquart, the Verzasca and the Waldemme rivers (Table 1). In
these streams, channel gradients range between 0.6
At Maggia, Reuss and Waldemme Littau, the largest clasts are arranged as
triplets or quadruplets of imbricated constituents within generally
flat-lying to randomly oriented finer-grained sediment particles. The density of
these arrangements ranges between 5 groups per 10 m
Photos from the field.
At all sites mentioned above, clasts on subaquatic and subaerial gravel bars
are generally arranged as well-sorted and densely packed clusters, possibly
representing incipient bedforms (e.g., Fig. 6d). In most cases, grains
imbricate behind an outsized clast, which usually delineates the front of
imbricated grains. In addition, the lowermost 10 % to 20 % part of most of
the large clasts is embedded, and thus buried, in a fine-grained matrix,
which was most likely deposited during the waning stage of a flood. Isolated,
unburied clasts that are flat lying on their
Gravel bars within the Emme stream are made up of generally flat-lying
gravels and cobbles. A small tilt (< 10
The Sense river differs from the Emme stream in the sense that bedrock
reaches alternate with alluvial segments over 100–200 m and more. Alluvial
segments are flat (ca. 0.3
Here, we calculated patterns of bed roughness and related channel gradients
from stratigraphic records and explored ca. 50 conglomerate sites for clast
imbrication. We used published data about channel depth
The Rigi deposits are ca. 3600 m thick and made up of an alternation of
conglomerates and mudstones (Stürm, 1973) that were deposited between 30
and 25 Ma according to magneto-polarity chronologies and mammal
biostratigraphic data (Engesser and Kälin, 2017). Garefalakis and
Schlunegger (2018) subdivided the Rigi section into four segments labeled as
The top of the Rigi section, referred to as segments
The ages of the up to 3000 m thick Thun conglomerates are younger and span
the time interval between ca. 26 and 24 Ma according to magneto-polarity
chronologies (Schlunegger et al., 1996). Similar to the Rigi section, the
Thun conglomerates start with an alternation of conglomerates, mudstones and
sandstones (unit A). This suite is overlain by an up to 2000 m thick
amalgamated stack of conglomerate beds (unit B). Channel depths within unit A
range between 3 and 5 m, and streams were between 0.1
Similar to the modern examples, imbricated clasts form a well-sorted cluster and commonly include the largest constituents of a gravel bar. In most cases, clasts imbricate behind an outsized constituent, which usually delineates the front of imbricated grains (Fig. 7b).
Our calculations reveal that the results are strongly dependent on the following:
The selection of values for the Shields variable The
way in which we consider variations in slope The consideration of flood magnitudes which either result in the motion
of individual sediment particles or the change in an entire channel (channel-forming floods).
This section is devoted to justify the selection of our
preferred boundary conditions.
We constrained our calculations on the incipient motion of individual clasts
and used Eq. (1a) for all other considerations. This might contrast to the
hydrological conditions during channel-forming floods where thresholds for
the evacuation of sediment are up to 1.2 times larger, as theoretical and
field-based analyses and have shown (Parker, 1978; Philips and Jerolmack,
2016; Pfeiffer et al., 2017). However, a 1.2-times larger threshold will
increase the
Larger bed surface grains, as is the case for most of the imbricated clasts,
may exert lower mobility thresholds because of a greater protrusion and a
smaller intergranular friction angle, as noted by Buffington and
Montgomery (1997) in their review. This has been explored through experiments
and field-based investigations (e.g., Buffington et al., 1992; Johnston et
al., 1998). These studies resulted in the notion that the entrainment of the
largest clasts (e.g., the
However, we consider it unlikely that the formation of most of the
imbrication, as we encountered in the analyzed Alpine streams and in the
stratigraphic record, was associated with thresholds as low as those proposed
by e.g., Lenzi et al. (2006) and Van den Berg and Schlunegger (2012). We base
our inference on the observation that the large clasts are generally well
sorted and densely packed, both on subaerial (during low-water stages) and
subaquatic bars. This results in a high interlocking degree within the bars
we have encountered in the field. In addition, field inspections showed that
the base of most of the large clasts, particularly those in subaquatic bars,
are embedded and thus buried in finer-grained material, and only very few
clasts are lying isolated and flat on their
Figure 3 shows that the results largely hinge on the values of
We have found an expression where the Froude number
The tendency towards lower Froude numbers for a channel gradient >1
Interpretations of the possible linkages between hydrological conditions upon
material transport and the formation of imbrication are hampered because
experiments have not been designed to explicitly explore these relationships.
In addition, as noted by Carling et al. (1992), natural systems differ from
experiments because of the contrasts in scales. Nevertheless, many
experiments have reproduced clast imbrication in subcritical flumes (Carling
et al., 1992) or even in stationary flows (Aberle and Nikora, 2006). For
instance, imbrication was reproduced at low Froude numbers between ca. 0.55
and 0.9 (Powell et al., 2016; Bertin and Friedrich, 2018), or at least during
some non-specified subcritical flow (Johansson, 1963). Note that we inferred
the Froude numbers from the experimental setup of these authors. Also in
experiments, material transport occurred at
However, inspections of photos illustrating the experimental setup reveal
that the surface grains are either flat lying on finer-grained sediments
before their entrainment (Fig. 3 in Powell et al., 2016), occur isolated on
the ground (Fig. 2.1b in Carling et al., 1992), or have a low degree of
interlocking (Fig. 3a in Lamb et al., 2017). Interestingly, the experiment by
Buffington et al. (1992) followed a different strategy, where a natural bed
surface of a stream was peeled off with epoxy. They subsequently used this
peel in the laboratory to approximate a natural channel bed surface (see
their Fig. 4), on top of which they randomly placed grains with a known size
distribution. Buffington and co-authors then measured the friction angle of
the overlying grains, based on which they calculated the critical boundary
shear stress values
Here, we provide evidence for linking clast imbrication with supercritical flows provided that gravels are well sorted and densely packed and form a clast-supported fabric. We sustain our inferences with (i) published examples from natural environments, (ii) our observations from Swiss streams and (iii) the results of our calculations.
For the North Saskatchewan River in Canada, Shaw and Kellerhals (1977) reported gravel mounds on a lateral gravel bar with a spacing between 2 and 3 meters and a relatively flat top. Shaw and Kellerhals considered these bedforms as antidunes, which might have formed in the upper flow regime. In the same sense, transverse ribs were considered as evidence for the deposition either under upper flow regime conditions or in response to upstream-migrating hydraulic jumps (e.g., Koster, 1978; Rust and Gostin, 1981). These features have been described from modern streams as a series of narrow, current-normally orientated accumulations of large clasts. Koster (1978) additionally reported that transverse ribs are associated with clast imbrication (Fig. 2 in Koster, 1978). Alexander and Fielding (1997) found modern gravel antidunes with well-developed clast imbrication in the Burdekin River, Australia. Finally, Taki and Parker (2005) reported cyclic steps of channel floor bedforms with wave-lengths 100–500 times larger than the flow thickness. These bedforms most likely represent chute-and-pool configurations (Taki and Parker, 2005), which could have formed in response to alternations of upper and lower flow regime conditions, as outlined by Grant (1997). In such a situation, the upstream flow on the stoss side of the bedform experiences a reduction of the flow velocity, with the effect that the flow may shift to subcritical conditions. This would be associated with a hydraulic jump and a flow velocity reduction and thus with a drop of shear stresses (Fig. 1a), which could result in the deposition of clasts. In such a scenario, the site of sediment accumulation most likely migrates upstream (Fig. 8).
Conceptual sketch illustrating the formation of an ensemble of
imbricated clasts as time proceeds (
Our inspections of modern gravel bars and stratigraphic records (Fig. 4)
reveal the occurrence of imbrication where channel slopes are steeper than
0.4
The proposed threshold slope is consistent with the results of previous work,
where upper flow regime bedforms such as transverse ribs have been described
for the Peyto outwash (slope ca. 1.09
We started with the hypothesis that the transport and deposition of
coarse-grained particles, and particularly the formation of an imbricated
fabric, may be related to changes in flow regimes. We then calculated the
Froude number
Despite our simplifications, we find evidence for proposing that the
formation of imbrication likely occurs at supercritical conditions provided
that (i) channels are steeper than ca. 0.5
All data that have been used in this paper are listed in Table 1.
FS designed the study and carried out the calculations, PG and FS collected the data, FS wrote the text with contributions by PG, and both authors contributed to the analyses and discussion of the results.
The authors declare that they have no conflict of interest.
This research was supported by grant no. 154198 awarded to Schlunegger by the Swiss National Science Foundation. Edited by: Sebastien Castelltort Reviewed by: Stuart McLelland, Rebecca Hodge, and Andrew Wickert