Balance of forces and thresholds of motion

As flow goes over sand

Above sand the streamlines are deflected and get closer together, past the sand creates separation zone(increase turbulence and decrease velocity) the creation in the low pressure field and friction wants the movements of the grain creating DRAG,

Vertical component of LIFT tries to bring grain upwards

Resultant fluid force brings it dsowntreamds and up but depends on balance of these vs weight and gravity. If drag can exceed gravity and lift then it will move downstream

Fl lift force

P(fluid)C(drag of liq)d²u²

F(D) drag force

½ p(fluid den) C(drag)A(area impacted)u²

F(g) gravity force

Pg(s(ratio of sediment to fluid den ps/p)-1)V

Caveats /constraints

Bed is flat and level, grain is spherical , congestion less and alone

The applied flow is unidirectional and steady

Shields curve

He used diff density sediment grains in recirculating flume

He used a graph to use non dimensional parameters on both axis therefore less dependency on water depth etc.

the x axis is the grain Reynolds number , can replace w dimensionless grain size D*

Y axis is non dimensional shields parameter , balance of shear stress and stabilising forces on the grain

• anything that falls above the line shopuld be in motion and below should be stationary

Threshold current speed

Tho is is dependent on fa Crosby which as water depth

The depth av velocity threshold gets higher as they equates gets deeper

Empirical equations - thresholds of motion

(Shields curve|) Θ cr= 0.3/1+1.2D + 0.055[ 1- exp(-0.020D)]

Van rijn (1084)- for sediment where median is between 100-500um

Ur= 0.19(d50)^0.1 x log10(4H/d90 )

Soulsby (1997) for sediment D*>0.1

Ucr=

Caveats / complications

Unidirectional, steady flow

Non-cohesive sediment

That you can accurately mesasdure the start if the motion

In rl- you can see gravely is moving but not all of it so how do you define threshold , how much is enough

Cohesive sediments

Cannot be individual sand

Though they are smaller can be higher thresholds than sands, the force of cohesion can be considered to our balance of forces

Instead consider omnset erosion of the bed, can be premiered on shear strength of the bed

This will change vertically as the bed is more consolidated with depth it becomes harder to erode.

SEdiment mixtures

Not all sediment is pure sand or mud

The non-cohesive will be filled around with congestive grains

At the start the large grain is sitting on non-co , the angle of repose or friction angle means the threshold for motion is higher

Second stage - co material starts to fill gaps between non-co which buries the grain therefore increase angle of repose therefore more diff to erode , threshold higher than pure sand

Last stage- lots of co material that non-co are held in matrix therefore sediment axctsz as though co matrix itself and v hard to erode.