Interface stability of granular filter structures under …...Interface stability of granular filter...
Transcript of Interface stability of granular filter structures under …...Interface stability of granular filter...
Interface stability of granular filter
structures under currents
Henk Verheij (Deltares)
Co-authors: Gijs Hoffmans, Kees Dorst, Stefan Vandesande
August, 2012
ICSE-6 Paris 2012
Granular filters
ICSE-6 Paris 2012
df15/ db85 < 4
(Terzaghi/Peck 1948)
• Geometrically closed (sand-tight) filters
• Stable Geometrically-open (sand-tight) filters
85
15 85
0.161
f f fF
f f b b
n dD
d n d
Wörman
Geometrically closed filter structure
Stable geometrically open filter structure
Unstable geometrically open filter structure
1989
1989 Klein-Breteler
1994 Bakker-Konter
mechanisms
ICSE-6 Paris 2012
Shear failure Winnowing Edge failure
Shields (1936) Simultaneous
movement
Filter material
moves first
Base material
moves first
50 50f bd d
15
ff
Dd
Principle idea behind the new formula
New formula
ICSE-6 Paris 2012
50 ,
15 50 ,
1ln
1
f f c f fFd
f b b c b b
d VD
d d V
expf
b d
k z z
k L
Hoffmans (2012)
(Klar, 2005)
50
15 50
lnf f
d
f b
D d
d d
Laboratory experiments
ICSE-6 Paris 2012
Test
db50
base
[m]
df50 filter
[mm]
df50 / db50
[-]
DF / df15
[-]
Thickness
DF [mm]
remark
T-01 309 7.1 23.0 3.29 20
T-02 309 21.3 68.9 1.44 27
T-03 309 21.3 68.9 3.29 61.5
T-04 633 21.3 33.6 1.44 27
T-05 309 15.1 49.0 0.57 8
T-06a 309 15.1 49.0 3.01 40
T-06b 309 15.1 49.0 3.01 40 High
turbulence due
to sill
T-06c 309 15.1 49.0 3.01 40 High
turbulence due
to piers
T-07 309 15.1 49.0 4.13 57
results
ICSE-6 Paris 2012
0 50 100 150 200 250 300 350 400 4500
2
4
6
8
10
12
1
2
3
4
5
6
7
Geometrically closed filters
d =1.2 (value proposed by Hoffmans)
d =0.86 (upper limit)
d =0.7 (90% lower)
d =0.28(lower limit)
df50
/db50
[-]
Df/d
f50 [
-]
van de Sande [2012], filter material eroded before base material (with test number)
van de Sande [2012], simultanious erosion (with test number)
van de Sande [2012], base material eroded before filter material (with test number)
Wörman [1989]
Dixen et al. [2008]
Other tests, filter material eroded before base material
Other tests, simultaneous erosion
Other tests, base material eroded before filter material
conclusions
ICSE-6 Paris 2012
1. The relative layer thickness fits better with df50
than with df15
2. Simplified design equation:
3. The alpha value proposed by Hoffmans [2012] is
too high (αd = 1.5)
• Deterministic approach;
• αd = 0.82 (safe upper limit)
• αd = 0.69 (90% confidence bound)
• Probabilistic approach;
• µ(αd )= 0.47
• σ(αd )= 0.04
50
15 50
lnf f
d
f b
D d
d d
recommendations
ICSE-6 Paris 2012
Extra tests:
• Damping in the filter
• Infuence of Turbulence on the αd value
Large stones – no extra turbulence Large stones – with extra turbulence
Granular filters
Relevant equations for designing geometrical open filters
1) Relative strength
2) Relative load
3) Damping length
4) Critical phase
If
and combining Eq’s 1, 2, 3 and 4 then
and c Fz D , ,50
50 ,
c bf c bb bc
c f f c f
gd
gd
exp
f
b d
k z z
k L
15 with 1.5d d f dL d
and c Fz D
, , 50 15, and / 1.2f b c f c b f fd d
50
50 50
1.2lnfF
f b
dD
d d