**4. Source Term Definition**

Efficient managemen<sup>t</sup> of sediment handling operations requires sufficient knowledge of dredging and disposal methods and of main mechanisms of release that can affect the SSC transport processes for different excavation and disposal techniques. The selection of spill scenarios is a key factor for environmental assessment and approval of the work plans. Indeed, it influences the source term needed as input to far field models.

In particular, the temporal and spatial characterization of the source term is important for the comparison, on different spatial and temporal scales, of scenarios with the least probabilities of detrimental impacts on water quality and to define whether (and when) mitigation measures should be taken on future work plans (e.g., [30]). This paper is aimed at estimating the contribution to source terms of phenomena directly related to marine sediment handling activities. However, sedimentation processes and the related re-suspension of the sediment due to hydrodynamic agitation (waves and currents) can have a significant influence on the magnitude of the source terms and therefore on the sediment transport modeling (see Section 6). Some mathematical models do not explicitly include the modeling of sedimentation and re-suspension related to hydrodynamic agitation. Nevertheless, their knowledge (or monitoring) may be crucial when the choice of the type and mode of implementation of the models is concerned. Moreover, also the definition of the background (baseline) conditions for the parameters of interest (e.g., SSC and turbidity), needed to identify the related single or multiple site-specifics reference levels, can be related to the sedimentation and re-suspension related to hydrodynamic agitation.

Basically, two main approaches may be used to model the flux of fine sediments available to the far field dispersion. Computational fluid dynamics (CFD) framework may be used for detailing near-field regimes and then to ge<sup>t</sup> a reliable estimate of the mechanisms that govern the dynamic of the sediment fraction leaving the re-suspension/release area as a passive (dispersive) plume. Such an approach has large computational costs and the results may be hardly generalized. On the other hand, a second approach may be used within the frame of macro-scale modeling (i.e., conceptual or empirical models). A series of empirical and numerical near-field models to estimate the suspended sediment flux leaving the intervention area have been developed so far (e.g., [6,8,31–35]).

A few conceptual models to predict the resuspended sediment mass rate at the resuspension point, and thus its source strength and geometry, have been proposed for dredging actitivies (e.g., [6,31,33,34], see Lisi et al. [13] for a comprehensive review). They give an estimate of source term as a function of the site (i.e., sediment properties, water depth, currents) and operational (i.e., dredge type, dredge-head dimension) parameters.

As suggested by John et al. [30] and recalled by Becker et al. [8], the source term may be estimated either (i) by looking at the sediment concentration increase at the re-suspension area (e.g., [6]), or (ii) by providing the sediment release rate at the re-suspension area (e.g., [6]), or (iii) by taking advantage of the definition of the S-factor (e.g., [31,34]) that gives the estimate of the released sediments as a fraction of the total mass of handled sediments, or (iv) by providing the sediment flux across the area bounding the re-suspension zone (e.g., [6]). All these approaches are hard to be used in a generalized way as they are site- and operation-dependent. Indeed, the available conceptual methods for estimating the source term induced by different re-suspension sources are based on the use of tabular data, e.g., the turbidity generation unit (TGU) approach proposed by Nakai [31] and the re-suspension factor proposed by Hayes et al. [34]. On the other hand, the use of empirical formulations involve sets of dimensionless parameters related to operating and site characteristics (e.g., [6,33,36]).

As for dredging activities, a few conceptual models exist also for other sediment handling works (e.g., either open water disposal [4,35] or beach nourishments [37]).

In order to overcome the lack of engineering tools, Becker et al. [8] proposed a general approach able to provide the estimation of source term. Basically, they sugges<sup>t</sup> to estimate the amount of fine-graded sediments and to distribute the release into the water column after an in-depth analysis of possible plume sources. Hence, for each phase (excavation, loading/transport and disposal) of the considered handling work, it is possible to estimate a specific source term fraction to be used as input for the far-field model if it is properly applied on the computational grid. It can be observed that this approach perfectly suits the approach proposed herein.

The results of specific in-situ analyses on the sediments to be handled allows estimating the quantity of fine-graded fraction available to the far field. The fraction expressed by either *R*74 (the fraction of sediments with grain diameter lower than 74 μm as per the fine-sediments definition of the unified soil classification system, e.g., [6]) or *R*63 (the fraction of sediments with grain diameter lower than 63 μm as per the Wentworth scale, e.g., [8]) may be used to estimate the fine sediments mass ( *mf*) available to the far field (e.g., [8]):

$$m\_f = \rho\_d V\_t \mathbf{R}\_f \tag{1}$$

where *ρd* is the dry density of the in situ material, *Vt* is the handled volume of sediments and *Rf* is the considered fine fraction (either *R*74 or *R*63). The dry mass of fine sediment released into the water column ( *mr*) can be then easily estimated by using a series of empirical parameters ( *σ*):

$$m\_{\mathbb{T}} = \sigma m\_f.\tag{2}$$

Becker et al. [8] (see their Table 1) provide reasonable values of the empirical source term fraction (i.e., *σ*) for drag-head induced re-suspension ( *σ* = 0.00–0.03), overflow induced re-suspension (*σ* = 0.00–0.20), cutter-head induced re-suspension ( *σ* = 0.00–0.04), spill from mechanical dredging (*σ* = 0.00–0.04), disposal by bottom door either mechanical ( *σ* = 0.00–0.10) or hydraulic ( *σ* = 0.00–0.05). It has to be stressed that the definition of the empirical source term fractions may take advantage of either monitoring activities or empirical formulations. Just as an example, Hayes et al. [33] proposed

an empirical formulation aimed at estimating the rate of sediment (*r*) re-suspended by cutterhead dredge as a fraction of sediment mass dredged:

$$\tau = \frac{(L\_{\rm cf} d\_{\rm c})^{1.966} \left| V\_{\rm s} \pm \pi d\_{\rm c} a \right|^{1.966} \left( V\_{\rm s} A\_{\rm E} \right)^{1.804}}{1.099 Q^{3.770}},\tag{3}$$

where *r* (%) is the fraction of sediment mass dredged expressed as a percentage (hence intimately related to the source term fraction *σc* = *r*/100), *Lc* (m) is the length of the cutterhead, *dc* (m) is the cutter diameter, *Vs* (m/s) is the swing velocity, *α* (rounds per second) is the rotational speed of the cutter, *AE* (m2) is the total surface area exposed to washing, *Q* (m3/s) is the volumetric flow rate into the dredge pipe. If overcutting is considered (i.e., the positive sign is used in the numerator of Equation (3)), Figure 3 shows the estimate of the empirical source term fraction *σc* for varying swing velocity (*Vs*) and varying rotation speed of the cutter (*α*) for a typical 16-in. (0.41 m) dredge (e.g., [33], *dc* = 1.07 m, *Lc* = 0.91 m, *AE* 1.3 m2). It could be observed that the empirical source term fraction proposed by Becker et al. [8] (dashed areas in Figure 3) is of the same order of magnitude given by the more detailed empirical formulation by Hayes et al. [33].

**Figure 3.** Empirical source term fraction (*<sup>σ</sup>c*) for cutter-head induced re-suspension as a function of the swing speed (*Vs*, upper panel) and of the rotational speed of the cutter (*<sup>α</sup>*, lower panel) as estimated on the basis of the model proposed by Hayes et al. [33]. Shaded areas highlight the range suggested by Becker et al. [8].

It has to be noticed that Equation (2) gives the mass of fine sediments available to the far field. In order to ge<sup>t</sup> the correct estimate of the source term, a sediment flux should be provided. Then, Becker et al. [8] sugges<sup>t</sup> to simply divide the mass *mr* by the time duration of the considered phase (i.e., either excavation, transport, or disposal). This highlights the importance of the analysis of the work phases. This is equally crucial when dealing with the timing and the location of the source term within the computational domain (see Section 5, Figures 4 and 5). Indeed, depending on the operational parameters of the handling works, the source term can be described by either a time-varying or constant intensity and by either a time-varying or fixed location. On the other hand, depending on the spatial resolution of the study, the source term can be described by either a punctual or a finite extent re-suspension source.

Figure 4 aims at synthesizing the main features of the source term estimation and how it can be applied to the computational domain.

**Figure 4.** Main steps of the source term module for both the estimation and the application of the source term in the computational domain.

**Figure 5.** Analytical solution obtained by using the model proposed by Di Risio et al. [39]. Typical examples for hydraulic dredging (**left**) and mechanical dredging (**right**) are shown. Constant velocity along x-direction is considered. Dashed lines depict the dredge-head path during the works execution, square markers indicate the instantaneous location of the dredge-head. Color scale refers to the suspended sediment concentration (SSC) (g/m3).
