interface stability of granular filter structures under …...interface stability of granular filter...
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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