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H24HSE-E1

The University of Nottingham

DEPARTMENT OF CIVIL ENGINEERING

A LEVEL 4 MODULE, AUTUMN 2013-2014

SEDIMENTATION AND EROSION ENGINEERING

Time allowed TWO Hours

Candidates must NOT start writing their answers until told to do so.

Answer ALL questions

Only silent, self-contained calculators with a Single-line Display or Dual-line Display arepermitted in this examination.

Dictionaries are not allowed with one exception. Those whose first language is not Englishmay use a standard translation dictionary to translate between that language and English

provided that neither language is the subject of this examination. Subject specific translation

dictionaries are not permitted.

No electronic devices capable of storing and retrieving text, including electronic dictionaries,may be used.

Do NOT turn examination paper over until instructed to do so.

ADDITIONAL MATERIAL:   Formula Sheet (3 sides)

INFORMATION FOR INVIGILATORS:   None

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1   (a) Explain with the aid of a diagram the difference between suspended load sediment transportand sheet flow sediment transport. [3]

(b) What is meant by the settling velocity of a sediment grain? [2]

(c) Explain what a well-sorted sediment mixture is and how that property is determined. [3](d) Calculate the settling velocity of a grain of sand of diameter 0.15mm in fresh water at

10◦C. [4]

(e) Explain what is meant by the term “settling lag”. [4]

(f) Give an example of when median grain size (D 50) might not be a good representation of asediment mixture. Explain why it might not be. [4]

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2   (a) A wide open channel of uniform depth 3.5m and a bed slope 0.00002 has a bed composedof erodible sediment of grain diameter 0.1mm.

Use the Shields relation to determine whether the sediment will be mobilised by the flow. [7]

(b) A wide open channel has a bed slope 0.00001, and grain diameter of erodible bed materialof 0.5mm.

Use the Shields relation to determine maximum discharge per unit width in the channel if sediment mobilisation is to be avoided. [8]

(c) In a coastal region a tidal, depth-averaged velocity is measured as 1.1 m/s, and depth of water as 3.9m.

If the bed grain diameter there is 1.5mm, use the Shields relations to determine whetherthe sediment is mobilised and, if so, how it is transported. [10]

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3   (a) You are asked to design a wide open channel of trapezoidal cross-section. It is determinedthat the channel will have side slopes of 1:2, a water depth of 4m, and a longitudinalgradient of 0.00003.

Determine a minimum sediment grain size that can line the channel so that we can be surethat there will be no sediment mobilisation, making sure to account for slope effects. [12]

(b) A uniform open channel of width 50m, discharge 130 m3/s , and depth 3.4m, and gradient2.358× 10−5, is spanned by a bridge, the abutments of which form a contraction of thechannel such that it narrows to 30m at that location. The median sediment grain size inthe channel is 0.25mm.

Estimate the contraction scour at the bridge. [13]

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4   (a) A navigation channel of width 90m and total water depth 12m, is subject to infilling bytidal currents that run perpendicular to the channel. The flood current (on the un-dredgedsea bed) persists for 2.5 hours at a mean, depth-averaged velocity of 1.5 m/s; and the ebbpersists for 3 hours at 0.75 m/s. The tides are semi-diurnal. Sediment transport is by bedload only. The surrounding (un-dredged) water depth is 6m, and the sand grain size in thearea is 0.6mm.

Determine at what rate (mm per day) the channel will infill, assuming that sediment isdeposited uniformly across the channel bed, and ignoring any effect of the channel sideslopes. [15]

(b) A narrow reservoir (see Figure Q.4) receives inflow of constant discharge (Q ) of 60  m3/s 

from a river (width 30m) at  x   =  x 1. The river carries suspended sediment only, of grainsize 0.05mm. At  x  =  x 1, the concentration is measured as 0.005. No entrainment or bedload transport takes place in the reservoir.

Using the Exner and concentration equations, ignoring any lateral expansion in the reservoir,and assuming that the concentration is depth uniform, calculate the rate per day at whichthe bed level is increasing halfway along the reservoir.

(h1  = 2m;  h2  = 20m;  L  = 200m). [15]

x  =

 x 1   x  =

 x 2

h1Q 

Q 

h2

L

Figure Q.4

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τ 0,crit ,tanβ  = k L/T 

tanβ 

τ 0,crit  ,

 

tanβ   

  L  

  T 

k Ltanβ  = sin(φs − β )

sinφs 

k 

L

tanβ  =

 sin(φs  +  β )

sinφs 

k T 

tanβ  = cos β 

1−

  tan2 β 

tan2 φs 

1/2

.

τ 0,crit ,tanβ  ≈ k Ltanβ Lk T 

tanβ T τ 0,crit  ,

 

tan β L 

  tan β T 

 

τ 0

τ 0,tan β   

 

τ 0,tan β 

 

0.75τ 0

 

0.85τ 0

 

0.90τ 0

 

0.95τ 0

≤     τ 0

θcrit ,s  =  τ 0,crit ,s 

(ρs  − ρ)gD   =

  0.16w 2s 

(s − 1)gD  ,

 

τ 0,crit ,s 

 

 q b 

 

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q b  = Φg (s − 1)D 3

1/2,

 

Φ = 8 (θ − θcrit )3/2 .

 

(1− n)∂ b 

∂ t   +

 ∂ q b ∂ x 

  = w s c − E  ,

 

b 

  c   

  E 

∂ (hc )

∂ t   +

 ∂ (huc )

∂ x   = −w s c  +  E