River, Coastal and Estuarine Morphodynamics: RCEM2011 © 2011 Floodplain heterogeneity and meander migration MOTTA Davide Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign, Urbana, Illinois, USA E-mail: [email protected] ABAD Jorge D. Department of Civil and Environmental Engineering University of Pittsburgh, Pittsburgh, Pennsylvania, USA E-mail: [email protected] LANGENDOEN Eddy J. US Department of Agriculture, Agricultural Research Service National Sedimentation Laboratory, Oxford, Mississippi, USA E-mail: [email protected] GARCIA Marcelo H. Department of Civil and Environmental Engineering University of Illinois at Urbana-Champaign, Urbana, Illinois, USA E-mail: [email protected] ABSTRACT: The impact of horizontal heterogeneity of floodplain soils on rates and patterns of meander migration is analyzed with a Ikeda et al. (1981)-type model for hydrodynamics and bed morphodynamics, coupled with a physically-based bank erosion model according to the approach developed by Motta et al. (2011). We assume that rates of migration are determined by the resistance to hydraulic erosion of the soils, which is described by an excess shear stress relation. This relation uses two parameters characterizing the resistance to erosion: critical shear stress and erodibility coefficient. The spatial distribution of critical shear stress in the floodplain is generated on a regular grid with varying degree of randomness to mimic natural settings and the corresponding erodibility coefficient is computed with a relation derived from field-measured pairs of critical shear stress and erodibility. Centerline migration and associated statistics for randomly-disturbed distribution based on the distance from the valley axis are compared for sine-generated centerline using the Monte Carlo method. Two relevant parameters are identified: (i) the standard deviation of the critical shear stress distribution, which is an indicator of the local soil heterogeneity, determines centerline skewness and its variability, and can lead to development of downstream skewness and complex planform features, while not significantly affecting lateral migration; (ii) the cross-valley increase in soil resistance, which mainly constrains rates of lateral migration also affecting skewness. The Monte Carlo approach, applied this time to the case of a natural river alignment and purely random floodplain-soil distribution, shows that migrated centerlines present larger variability the coarser is the scale of the floodplain heterogeneity (third key parameter for describing the effect of floodplain heterogeneity on migration) and the increase in variability with the heterogeneity scale is less then linear. Finally, when the approach for meander migration based on hydraulic erosion is compared to the “classic” approach based on excess velocity at the outer bank, the former approach produces more variability and shape complexity for equal stochastic variability of the corresponding governing parameters, because of the presence of a threshold for bank erosion missing in the case of classic approach for migration. 1 INTRODUCTION A great quantity of two-dimensional (2D) depth-averaged analytical models have focused on the impact of hydrodynamics and bed morphodynamics on the migration of meandering rivers (Ikeda et al., 1981; Blondeaux and Seminara, 1985; Johannesson and Parker, 1989; Sun et al., 2001a; Zolezzi and Seminara, 2001) and on the degree of planform-shape complexity that can be obtained (Seminara et al., 2001; Frascati and Lanzoni, 2009). Less attention has been given to the complexity resulting from the heterogeneity of the floodplain soils, the quantification of its importance, and the identification of the important parameters. Past studies have been all based on the concept of rate of bank erosion linearly proportional, through a migration coefficient, to near-bank excess velocity (Howard, 1992, 1996; Sun et al., 1996, 2001b; Posner and Duan, 2011), according to the method independently introduced by Hasegawa (1977) and Ikeda et al. (1981). Howard (1992), Howard (1996), and Sun et al. (1996) studied the development of heterogeneities in the floodplain caused by river migration and their influence on the future development of the channel. In particular, Sun et al. (1996) focused on the change in erodibility associated to different sedimentary environments such as point bar deposits, floodplain deposits, and oxbow lake deposits, and were able to reproduce the formation of meander belts for long-term simulations. Sun et al. (2001b) went a step further and simulated the development of size distribution as channel migrates. Posner and Duan (2011) compared a deterministic model, adopting a constant migration coefficient, with a stochastic model, where the instantaneous migration coefficient at each bank location is a random variable satisfying either uniform or normal distribution, and compared the two approaches against experimental data, finding that the stochastic approach yields more realistic predictions of meandering-planform evolution. In terms of planform shapes, Sun et al. (1996) claimed that the typical meander wavelength is determined mainly by hydraulic factors (flow in the channel and inclination of the underlying floodplain) and is independent of the difference in the erodibilities of sedimentary deposits. Perucca et al. (2007), who focused on the role played by vegetation on meandering river morphodynamics and the feedback between riparian vegetation dynamics and meandering dynamics, showed the possible occurrence of peculiar meander shapes that do not show the usual marked upstream skewness, when the bank erodibility is linked to the biomass density. In this paper we discuss how soil floodplain distribution modulates planform shapes and rates of migration. The model by Motta et al. (2011) is used, which allows for focusing on the horizontal heterogeneity of the physical parameters for hydraulic erosion, which are erodibility and critical shear stress. Motta et al. (2011)'s model quantifies the migration of meandering streams through a physically- and process-based method that relates channel migration to the streambank erosion processes of hydraulic erosion and mass failure. Hence, channel migration depends on measurable soil properties, natural bank geometry, and both vertical and horizontal heterogeneity of floodplain soils. In general, the processes responsible for bank retreat are classified as follows: hydraulic (fluvial) erosion, and cantilever, planar, rotational, and piping streambank failure (Pizzuto and ASCE Task Committee on Hydraulics, Bank Mechanics, and Modeling of River Adjustment, 2008). As shown by Constantine et al. (2009), using field measurements, and by Motta et al. (2011), through modeling, mass failure mechanisms like planar failures, although important, can be indirectly represented by modifying the parameters for hydraulic erosion to quantify rates of migration, at least for the case of vertical homogeneity of the bank material. Hydraulic erosion requires that the local boundary shear stress exceeds the critical value to initiate motion of the soil particles. From a modeling perspective, the rate of lateral hydraulic erosion E* (with dimensions of length over time) for each bank-material layer is modeled using an excess shear stress relation, typically used for fine-grained materials (but also applicable to non-cohesive materials) ******* EM=(ττcc−1) = k( τ− τ) (1) * * where M is the erosion-rate coefficient (with dimensions of length over time), τ c is the critical shear * * * * * stress, k is the erodibility, and τ is the shear stress acting on the bank. M , τ c, and k are all site-specific. The critical erosional strength denotes the cohesion strength provided by interparticle forces of attraction or repulsion acting at the microscopic level, including electrostatic forces, Van der Waals forces, 2 hydration forces, and biological forces (Papanicolaou et al., 2007). Although Eq. 1 appears simple, in practice it is necessary to define the erodibility parameters and the boundary shear stress τ*. These are all highly variable, which explains why observed rates of fluvial erosion range over several orders of magnitude (Darby et al., 2007). * * * Besides the complexity related to the experimental quantification of the parameters τ c and k (or M ), there is that of their spatial distribution in the floodplain, which depends on the soil distribution that is the result of the development of the fluvial system in time, through processes of channel deposition because of lateral migration and overbank deposition formed by vertical accretion. Anomalies in the modern floodplain can be the remnant of the evolution over geologic time scales. Therefore, depending on when the computer modeling of meander migration begins, the spatial distribution of soil erodibility may vary. However, a general characterization of a typical modern floodplain can be made, with a general decrease of sediment size and consequent decrease in erodibility away from the channel. It is also recognized that cutoff deposits generated by a meandering river tend to confine it to a strip in the flood basin, known as meander belt (Allen, 1965; Sun et al., 1996). As regards the shear stress acting on the river bank, it is the sum of the stress resulting from drag on bedforms and the stress acting on the actual boundary (Constantine et al., 2009). Therefore, in Eq. 1, τ* has to be interpreted as effective shear stress. The