The effect of permeability on the erosion threshold of fine-grained sediments

Highlights

• The effect of soil properties on the erosion behaviour of marine sediments.

• Unique relationship between permeability and erosion threshold discovered.

• Novel empirical relationship proposed to predict threshold shear stress for fine-grained sediments.

• New model predicting threshold conditions agrees well with existing data from literature.

Abstract

The erosion of marine sediments, although difficult to predict, can lead to important implications in offshore engineering, sedimentology and coastal management. Continued research is, therefore, warranted to compile high-quality erosion data from which to develop models to better predict the erosion resistance of different types of marine sediments. In this paper, dimensional analysis is performed to express the threshold shear stress as a function of a selection of soil properties that are commonly linked to the erosion process of sediments. To identify the dominant dimensionless group, an experimental investigation on the erosion threshold was carried out using fine-grained sediments that were systematically prepared to ensure variations in (i) particle size distribution (i.e. fines content), (ii) bulk density, and (iii) hydraulic permeability. The samples included silica, carbonate and marine sediments, each of which are expected to have limited or no clay-mineral content.

The measurements were analysed and compared with existing literature and predictive models. It was found that marine sediment samples with limited fines content showed good agreement with the empirical Shields curve, irrespective of particle size distribution, bulk density and permeability. In contrast, for finer marine sediment it was found that variations in these soil properties modify the threshold shear stress away from the Shields curve. Across each of these parameters only permeability appeared to independently correlate with the observed range of threshold measurements. Motivated by this finding, a model is introduced to predict the threshold shear stress as a function of permeability and the reference erosion rate that is used to define when the threshold is reached. The resulting expression is shown to quantitatively explain the experimental data and is found to also agree with existing data from the literature for quartz sediments with a wide range in fines content. An apparent advantage of the new model is that it is consistent with existing studies that identify variations in threshold shear stress due to changes in bulk soil parameters – including fines content and bulk density – since each of these parameters also affect permeability.

Introduction

In coastal and offshore engineering, the prediction of sediment erosion is fundamental to the design of offshore structures, such as foundations and pipelines that are placed on the seabed. This is because ocean currents, tidal currents and waves can initiate sediment transport around the structure, leading to scour and significant changes in the local bathymetry. In turn, these changes can alter the hydrodynamic loading and geotechnical resistance; affecting the stability of the structures. Outside of offshore engineering, the prediction of sediment erosion is also important, for example, in the fields of environmental engineering, sedimentology and coastal management.

Motivated by the importance of predicting sediment erosion, numerous previous studies have focused on predicting the threshold shear stress of different sediments. The majority of this work has focused on sediments with individual grains that are well-rounded and uniformly graded, for which the well-known Shields curve typically gives a reasonable prediction of the threshold of erosion described by the dimensionless threshold Shields parameter (Shields 1936; Miller et al., 1977; Soulsby and Whitehouse 1997; Vanoni 2006). In comparison with these commonly studied sediments, natural marine sediments can be comprised of irregular shaped grains and may be widely graded, being composed of a range of particle sizes (Mehta 2013). Fine-grained sediments have also been found to exhibit very different threshold shear stress to that predicted using the Shields curve (see, for example, Whitehouse et al., 2000; Winterwerp and van Kesteren 2004; Torfs 1995; Grabowski et al., 2011). In particular, Mohr et al. (2013) showed significant differences in threshold shear stress compared with Shields curve predictions for silty sand and sandy silt recovered from the North West Shelf of Australia.

For sediments exhibiting higher threshold shear stress than predicted by the Shields curve, the increase in threshold shear stress has been traditionally attributed to the bulk properties of the sediment if it has significant fines content (i.e. more than $~$10% by mass of sediment finer than 63 μm; Whitehouse et al., 2000). For example in the case of sediments with significant fines content including particles much smaller than 63 μm, it has been shown experimentally that the threshold shear stress is dependent on bulk density (which is linked to the state of consolidation) and the particle size distribution or fines content (see, for example, Paphitis 2001; Lick and McNeil 2001; Torfs 1995; Panagiotopoulos et al., 1997). These finer sediments are also often sticky to the touch and cling together when moist. For this reason they are commonly referred to in the literature as ‘cohesive’ sediments (Whitehouse et al., 2000; Winterwerp and van Kesteren 2004) which suggests that cohesive bonds between particles are also a contributing factor. However, it should be noted that particles in sediments with low permeability may cling together when moist or saturated because of negative pore pressure, irrespective of cohesive bonds. Additionally, many sediments, including marine sediments, may have predominantly fine non-clay mineral particles; Mehta (2013) notes that due to their low specific area fine non-clay mineral particles do not display significant cohesion.

More recently, Winterwerp (2012) suggested that turbulent stresses on a particle may induce local negative pore pressure (i.e. suction) which is dependent on the rate of deformation (i.e. erosion rate) and the seepage flow within the bed (i.e. permeability). In line with this suggestion, Mohr et al. (2018) presented a set of experimental results on the erosion behaviour of fine-grained reconstituted marine sediments showing that permeability is the only soil parameter that showed a consistent correlation with observed erosion trends produced by variations in the bulk properties of the sediments.

Based on the literature above, the measured shear stress (denoted as ${\tau }_{\text{cr}}^{\text{'}}$ in this paper) may be related to the following set of variables if cohesive bonding is neglected (e.g. for sediment with no or limited clay-mineral content and no biological bonding)

$${\tau }_{\text{cr}}^{\text{'}}=f\left(\rho ,\nu ,d_{50},\left({\rho }_s-\rho \right)\text{g},{\rho }_{\text{bulk}},\text{Fines},k,{\eta }_{\text{cr}}^{\text{'}}\right).$$

The first four parameters on the right hand side of Eq. (1) are commonly used for non-cohesive sediments and include the fluid density ρ, the fluid kinematic viscosity ν, the median grain diameter $d_{50}$, and the submerged specific weight given in terms of the density of the sediment ${\rho }_s$, the fluid density ρ and acceleration due to gravity g. The next three parameters in Eq. (1) represent the bulk properties of the sediment, with ${\rho }_{\text{bulk}}$ defining the bulk density, $\text{Fines}$ the fines content and k the hydraulic conductivity. The last parameter in Eq. (1) is the reference erosion rate of the sediment at threshold (${\eta }_{\text{cr}}^{\text{'}}$) and is equal to the volume of sediment per unit area and time being removed at threshold from the sample (i.e. the flux of sediment being removed at threshold). Typically this rate will not be equal to zero, since most studies (e.g. Vanoni 1964; Miller et al., 1977; Buffington and Montgomery 1997; Roberts et al., 1998; Paphitis 2001) define threshold to occur when the erosion rate or transport rate exceeds some small measurable value (as discussed later, in this study threshold is defined to occur when the erosion rate first exceeds ${10}^{-7}$ m/s; e.g. ${\eta }_{\text{cr}}^{\text{'}}={10}^{-7}$ m/s). Equation (1) does not explicitly include the shape of the particles, or the fabric of the sediment, but the effect of these properties on tortuosity is encapsulated through k. The sediments tested and compared in this paper consider a wide range of particle shape (from angular marine sediment to rounded quartz), but it will be shown that this does not appear to effect the ability of the parameters in (1) to explain the measured threshold shrear stress.

Noting that there are three primary dimensions, Eq. (1) can be re-written as

$$\frac{{\tau }_{\text{cr}}^{\text{'}}}{\left({\rho }_s-\rho \right)g{d}_{50}}={\theta }_{\text{cr},\text{s}}^{\text{'}}=f\left({\text{Re}}_{{\text{d}}_{50}}=\frac{u_{\text{*},\text{cr}}{d}_{50}}{\nu },\frac{{\rho }_{\text{bulk}}}{\rho },\text{Fines},{\text{Re}}_{\text{k}}=\frac{u_{\text{*},\text{cr}}\sqrt{k}}{\sqrt{\nu \text{g}}},\frac{{\eta }_{\text{cr}}^{\text{'}}}{k}\right),$$

where ${\theta }_{\mathrm{cr}}^{\text{'}}$ is the non-dimensional threshold shear stress and $u_{\text{*},\text{cr}}=\sqrt{{\tau }_{\text{cr}}^{\text{'}}/\rho }$ is the critical friction velocity. The four parameters on the right hand side of Eq. (2) represent the grain Reynolds number (${\text{Re}}_{{\text{d}}_{50}}$), a non-dimensional bulk density, the (already) dimensionless fines content, the permeability Reynolds number (${\text{Re}}_{\text{k}}$) and a relative erosion rate (akin to the ratio of deformation to seepage flow within the sediment).

The aim of this paper is to explore the functional relationship in Eq. (2). For fine sediments (and for all those tested herein) the permeability Reynolds number is often significantly less than unity, implying that the flow is laminar within the sediment itself (Voermans et al., 2017); hence variations in this parameter are not expected to alter the flow regime within the soil matrix. This paper therefore presents a set of experiments on artificial and marine sediments that explore in detail how the remaining four dimensionless groups in Eq. (2) correlate with threshold shear stress. The experimental results are also compared with existing empirical models (including the Shields curve) and existing findings in the literature. Based on these comparisons, the underlying experimental results and dimensional analysis, a novel predictive model is introduced that considers erosion as a rate dependent process, accounting for hydraulic permeability. This model suggests that a suction force (defined in terms of the erosion rate and soil permeability) should be considered in the force balance on a given particle. Due to the addition of this suction force, the dimensionless expression predicts that the measured threshold shear stress for fine sediments may be higher than the empirical Shields curve by an amount that depends on the hydraulic permeability of the sediment and the reference erosion rate that is used to define threshold shear stress. Both parameters appear to control the trends in the experimental results. The proposed model has been calibrated based on data from this study and is subsequently compared to independent experimental data from the wider literature.

As noted later in the paper, threshold shear stress and the erosion rate close to threshold may be interpreted in terms of a probability of erosion (see e.g. Mehta 2013 and the references cited therein). This idea is not pursued further in this paper, but would be a useful area of further work to expand on the results herein. In this paper a focus is placed on correlating mean shear stress with bulk soil properties.