The settling dynamics of flocculating mud-sand mixtures: Part 1—Empirical algorithm development

Abstract

European estuaries tend to be regarded as being either predominantly muddy or sandy. In some estuaries, the cohesive and non-cohesive fractions can become segregated. However, recent laboratory tests have revealed that mud and sand from many coastal locations can exhibit some degree of flocculation. A clear understanding of the dynamic behaviour of sediments in the nearshore region is of particular importance for estuarine management groups who want to be able to accurately predict the transportation routes and fate of the suspended sediments. To achieve this goal, numerical computer simulations are usually the chosen tools. In order to use these models with any degree of confidence, the user must be able to provide the model with a reasonable mathematical description of spatial and temporal mass settling fluxes. However, the majority of flocculation models represent purely muddy suspensions. This paper assesses the settling characteristics of flocculating mixed-sediment suspensions through the synthesis of data, which was presented as a series of algorithms. Collectively, the algorithms were referred to as the mixed-sediment settling velocity (MSSV) empirical model and could estimate the mass settling flux of mixed suspensions. The MSSV was based entirely on the settling and mass distribution patterns demonstrated by experimental observations, as opposed to pure physical theory. The selection of the algorithm structure was based on the concept of macroflocs—the larger aggregate structures—and smaller microflocs, representing constituent particles of the macroflocs. The floc data was generated using annular flume simulations and the floc properties measured using the video-based LabSFLOC instrumentation. The derived algorithms are valid for suspended sediment concentrations and turbulent shear stress values ranging between 0.2–5 g l⁻¹ and 0.06–0.9 Pa, respectively. However, the MSSV algorithms were principally derived using manufactured mixtures of Tamar Estuary mud and a fine silica sand, which means that the algorithms presented are site-specific in nature, and not fully universal in application. In terms of mass settling flux (MSF) accuracy: at the lower flux range (195–777 mg m⁻² s⁻¹) most MSSV predictions were within a few percent of the observations, whilst for the largest observed MSFs (1.3–21 g m⁻² s⁻¹), the MSSV demonstrated a close fit with the data. Even for the highest observed MSF of 33 g m⁻² s⁻¹ (produced by a 75M:25S mixed suspension), the MSSV only under-estimated the flux by 18%. The MSSV algorithms indicated a trend whereby a rise in sand content, and a subsequent decrease in mud, favours the microflocs as the dominant flux contributor. Parameter comparison testing indicated that by applying a single-sediment assumption to a mixed-sediment environment, pure mud algorithms under-predicted at each concentration by as much as 25% and did not handle sandy mud sediments particularly well. Slow constant settling velocity (0.5 and 1 mm s⁻¹) parameters severely under-predicted MSF (at times down to only 13% of the observed flux), whilst the fastest constant fall rate (5 mm s⁻¹) parameter over-predicted by as much as 246%. Fixed settling velocity parameters produced quite large mean errors in MSF estimation. A concentration Power Law and van Leussen (1994) approaches generally under-predicted by 25–37%, with extremely high mean errors and standard deviations. By assuming every suspension scenario was pure sand, over-estimated the mass settling flux by over 400% at dilute suspensions, reducing to about 100% at a concentration of 5 g l⁻¹. One would assume that if we knew what percentage of mud and sand were in suspension at any one point in time and space, we should be able to predict the MSF with greater accuracy. However, the modification of one of a purely cohesive parameterisation with the addition of a pure sand fall velocity to account for the sand fraction, tended to create even greater MSF predictive errors, and in most cases produced excessive over-estimations in MSF. The reason for these predictive errors was that this hybrid approach still treated mud and sand separately. This is potentially reasonable if the sediments are segregated and non-interactive, but appears to be unacceptable when the mud and sand are flocculating via an interactive matrix. The MSSV empirical model may be regarded as a ‘first stage’ approximation for scientists and engineers either wishing to investigate mixed-sediment flocculation and its depositional characteristics in a quantifiable framework, or simulate mixed-sediment settling in a numerical sediment transport model where flocculation is occurring. The preliminary assessment concluded that in general when all the SPM and shear stress range data were combined, the net result indicated that the new mixed-sediment settling velocity empirical model was only in error by −3 to −6.7% across the experimental mud:sand mixture ratios. Tuning of the algorithm coefficients is required for the accurate prediction of depositional rates in a specific estuary, as was demonstrated by the algorithm calibration using data from Portsmouth Harbour. The development of a more physics-based model, which captures the essential features of the empirical MSSV model, would be more universally applicable.

Appendix 1

Table 9 Summary of laboratory flume floc properties for suspensions with a ratio of 75% mud and 25% sand

Table 10 Summary of laboratory flume floc properties for suspensions with a ratio of 50% mud and 50% sand

Table 11 Summary of laboratory flume floc properties for suspensions with a ratio of 25% mud and 75% sand