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Sediment transport and deposition                                     233

                   biofilms . Flocs may be formed when particles collide; the frequency of collisions between
                   particles increases with increasing turbulence, but the shear stress es induced by turbulence
                   around the flocs themselves can break up large flocs. Given a constant shear stress, the
                   particle size distribution in the water column will achieve a steady state , in which the creation
                   and destruction of flocs are in equilibrium. Increasing the shear stress increases the rate of
                   flocculation and shortens the time to steady state, but decreases the median floc size. As flocs
                   are very porous, they are considerably less dense than the individual particles. Nevertheless,
                   the effect of the larger particle size prevails and the settling velocity of the flocs is generally
                   faster than the settling velocity of the individual particles. Hence, flocculation results in an
                   enhanced sedimentation  .


                   12.5  SEDIMENT EROSION

                   If the bottom shear stress  at the soil–water interface exceeds the critical shear stress  for
                   erosion , a net sediment  flux from the soil or bed sediment to the water column occurs. Like
                   the deposition flux, the erosion flux can be formulated as a function of the shear stress:

                    J e    M  b  1                                                    (12.21)
                            b ,e
                                                -1
                                             -2
                   where J  = the erosion  flux [M L  T ], and M = the erosion flux when τ  = 2τ . Just as in
                         e                                                   b    b,e
                   the case of sedimentation , the erosion flux can be modelled as a linear function of the flow
                   velocity instead of the bottom shear stress . The critical bottom shear stress  for erosion τ
                                                                                          b,e
                   increases with the degree of consolidation of the sediment  (which is inversely related to the
                   water content of the sediment), the organic matter content , the clay content, and the activity
                                                                       -2
                   of soil organisms. The value for τ  is in the order of 0.05–0.5 N m  (Van Rijn, 1989).
                                             b,e
                      Equation (12.21) is only valid for consolidated sediments in which the critical shear

                   stress  for erosion τ  is constant over the sediment profile (Mehta et al., 1989). However,
                                  b,e
                   in surface waters an unconsolidated sediment  layer with a high water content (> 50 %) is
                   usually present between the consolidated sediment and the water column. Parchure and
                   Mehta (1985) described the erosion or resuspension  rate for these soft cohesive sediment
                   layers using the following empirical expression:
                    J     e   b  b  e ,                                               (12.22)
                     e   f
                                                                                        -0.5
                                                     -2
                                                                                  0.5
                                                        -1
                   where ε  = resuspension  flux constant [M L  T ], and β = empirical constant [L  T M ].
                         f
                   The critical shear stress  for erosion  usually increases with depth and if τ  becomes larger, the
                                                                           b,e
                   resuspension process can be described using Equation (12.21). Mehta et al. (1989) reported
                                 -0.5
                                               -0.5
                   values of 8.3 m N  and 13.6 m N  for β for lake sediments. The accompanying values for
                                                           -2 -1
                                    -5
                                                     -5
                                         -2 -1
                   ε  range from 0.07⋅10  kg m  s  to 0.53⋅10  kg m  s , respectively.
                    f
                      On slopes, erosion  also occurs due to the impact of falling raindrops; this is also referred
                   to as  splash detachment . The erosion flux as a result of splash detachment is a function
                   of the kinetic energy of the rainfall, the depth of the surface water layer, and the stability
                   of soil aggregates present at the soil surface. The kinetic energy can arise from both direct
                   rainfall and drainage from leaves (throughfall ). The LISEM  model (LImburg Soil Erosion
                   Model) (De Roo et al., 1996; Jetten, 2013) uses the following equation to estimate splash
                   detachment (Jetten, 2013):
                             . 2  82  . 1  48 H
                   E            K  e      . 96  P                                     (12.23)
                                          2
                     s           e
                            A s
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