BED, BANK & SHORE BED, BANK & SHORE PROTECTION - CHAPTER 3 pps

• focus on stability of loose non-cohesive grains • rock: important material for protection • grains may vary in size from μc sand to m rock... occasional movement at some locations 2..

Chapter 3

Flow - stability

• focus on stability of loose non-cohesive grains

• rock: important material for protection

• grains may vary in size from μc (sand) to m (rock)

Uniform flow – Horizontal bed

Forces on a grain in flow

1 2 1 2 1 2

Balance equations

d g K

= u d

g

= d g

-

w

w s

d g )

(

-d u

d O W

= d O F

: 0

=

M

W

= F

: 0

= V

F W

x f

= F

: 0

= H

3 w

s

2 2 c w

S D, L

F S

D,

ρ ρ

Σ

= Σ

) ( )

(

Relation between load and strength

Isbash (1930)

g 2

u 0.7

= d

or

1.7

= d g

u

or

d g 2

1.2

=

u

2 c c

Δ Δ

used for first approximation when:

• relation between velocity and waterdepth not clear

(e.g a jet entering a body of water)

( ) ( )

2

* Re

Critical shear stress

Shields Van Rijn

=

υ ρ

ρ

τ

d g

u d

g

c c

w s

c c

*

* 2

1500 10

33 1

002 0

u gd

u

c c

63 10

33 1

002

0 042

s m gd

u*c = ψ cΔ = 0 04 × 1 65 × 9 81 × 0 002 = 0 036 /

Guess: u*c = 1 m/s

Shields

Example (cont.)

42 )

10 33

1 (

81 9 65 1 002

.

0 3

2 6

u*c = ψ cΔ = 0 04 × 1 65 × 9 81 × 0 002 = 0 036 /

Van Rijn

Relative protrusion

Load and strength distribution

0 no movement at all

1 occasional movement at some locations

2 frequent movement at some locations

3 frequent movement at several locations

4 frequent movement at many locations

5 frequent movement at all locations

6 continuous movement at all locations

7 general transport of the grains

Shields

Videos on stability of rock on a bed

with current only

n

d

C u

ψ

= Δ

1.7

ic

u

gd = Δ

Isbash: 18log12

r

R C

Influence waterdepth on critical

velocity

Roughness and threshold of motion

Angles of repose for non-cohesive

Influence of slope on stability

Case b: slope parallel to flow Case c: slope perpendicular to flow

φ = 40 ο

Slope parallel to current

φ

α φ

W

= F(0)

)

F(

= )

K(

tan

sin tan

cos //

//

φ

α

φ φ

α φ

α φ

=

sin

sin sin

sin cos

cos

2

2 2

2

=

-

= F(0)

α α

sin

sin tan

tan cos

=

1

-=

Stability on top of sill

use velocity on top of the sill

Experiments: first damage at downstream crest

Stability and head difference

Shields is useless here because Shields contains waterdepth

waterlevel downstream is below the top of the dam

Shields for flow over sill

) h - (h g 2

) d

h 0.04 +

(0.5

= ) h - (h g 2

=

n

d d

Vertical constriction Stability with flow under weir

Shields in horizontal constriction

sin

2 4

Stability on head of dam

cs

cu c

c v

u

u structure

with u

structure without

u

ucu: vertically averaged critical velocity in uniform flow

ucs: velocity in case with a structure

Effect of flow field

Relation between K v and turbulence

cs

cs cu

ucu : vertically averaged critical velocity in uniform flow

ucs : velocity in case with a structure

rcu : turbulence intensity in uniform flow

rcs : vertically averaged turbulence intensity

Stability downstream of a sill

high dam

no dam

D h

h K

u D h

h u

h u D

2

2 1

2 2 2

K v in vertical constriction

Damage after some time

Stone stability downstream of a

hydraulic jump

Peak velocities and incipient motion

damage after constriction

Kv - factors for various structures

Structure Shape K v0 K vG K vM

angular

Rect-b 0 *K vG /b G 1.3 - 1.7 1.1 - 1.2 Groyne

zoidal

Trape-b 0 *K v b G 1.2 1

Angular

Rect-b 0 *K v /b G 1.3 - 1.7 1.2

Round b 0 *K v /b G 1.2 - 1.3 1.2 Abutm ent

Stream Lined

b 0 *K v /b G 1 - 1.1 1 - 1.1

Round b 0 *K v /b G ⊗

2*K v

1.2 - 1.4 ⊗ 1 - 1.1 Pier

Angular

Rect-b 0 *K v /b G ⊗

2*K v

1.4 - 1.6 ⊗ 1.2 - 1.3

Abruptly 1 Outflow

Stream Lined

Top Section

3.6.1

Section 3.6.1

Section 3.6.1 Sill

Down Stream

Fig 3.13 Fig 3.13 Fig 3.13

⊗ For many piers in a river the first expression for K v is appropriate The second

is valid for a detached pier in an infinitely wide flow, where K G is not defined.

Definition of velocities

groyne vertical pole

Combined equation

C K

u

*

K

=

d

2 c

s

c

2 2

v

Δ

ψ

Kv : reduction for constriction, etc.

Ks : reduction for slope (parallel, perpendicular))

ρ

ρ ρ

Gabions

Clay soils

Vegetation

Placed blocks

Mats