8 - waves, erosion and stability - tu delft ocw · 8 - waves, erosion and stability ct4310 ... june...
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Vermelding onderdeel organisatie
June 3, 2012
1
8 - Waves, erosion and stability ct4310 – Bed, Bank and Shoreline Protection
H.J. Verhagen
Faculty of Civil Engineering and Geosciences Section Hydraulic Engineering
June 3, 2012 2
Introduction
• there is a relation between the slope angle and the grain size
• for sand, standard profile can be used
• For stability the value H/d is important
• H/d < 1 caissons or seawalls
• H/d = 1...4 stable breakwaters
• H/d = 3...6 S-shaped and berm breakwaters
• H/d = 6...20 rock slopes
• H/d = 15...500 gravel beaches
• H/d > 500 sand beaches (during storm surge)
June 3, 2012 3
erosion of slope by waves
June 3, 2012 4
The Vellinga Profile
0.44 0.78 0.780.39z w x p x
1.28 1.28
e sL p H
0.51.28 0.56
0 0
7.6 7.60.4714 18 2.00
0.0268s s
wy x
H H
June 3, 2012 6
three main types of protection against waves
June 3, 2012 7
definition of leakage length
T F F T
T F F T
d k d d
k k d k
June 3, 2012 8
leakage length
T F F T
T F F T
d k d d
k k d k
Parameter "Rock" "Blocks" "Asphalt"
dT (m) 0.5 0.25 0.25
dF (m) 0.25 0.2 2
kT (m/s) 0.5 0.001 "0"
KF (m/s) 0.1 0.05 0.0001
(m) 0.15 1.5 ""
L (m) 1-2 1-2 1-2
June 3, 2012 9
influence of leakage length
T F F T
T F F T
d k d d
k k d k
June 3, 2012 10
Erosion at the toe
June 3, 2012 11
modified Shields diagram for waves and stability in non-breaking waves
June 3, 2012 12
direct equation for bed stability
2.5
50 1.52
50
ˆ0.025 2.15b b b
n
a a ud
T g d T g
ab orbital stroke at the bottom
ûb maximum orbital velocity
dn50 assumed equal to 0.85 d50
T wave period
June 3, 2012 13
Erosion at the toe
Research by Ha
June 3, 2012 14
stability on a slope
2 3 tan cos sin
"drag" force resisting force slope correction
w s wg H d g d
3
33 tan cos sin
s HM
MH
K
H
dKs sc
D
scD
3
33
cotcot ) (or:
Iribarren
Hudson
June 3, 2012 15
limitations of Hudson
Not included in the equation:
• wave period
• permeability
• storm duration
• damage level
June 3, 2012 16
Van der Meer
0.2
0.18 0.5
50
0.2
0.13
50
6.2 (plunging breakers)
1.0 cot (surging breakers)
sc
n
Psc
n
H SP
d N
H SP
d N
1
0.31 0.5transition 6.2 tan PP
> transition surging breakers
< transition plunging breakers
Video: Rock slopes on gravel beaches wbk 049 - 14 min
June 3, 2012 17
reference case
sign. wave height Hs 2 m
slope of revetment cot 3
“Permeability” P 0.5
mean period Tm 6 s
number of waves N 3000
rock size dn50 0.6 m (300-1000 kg)
relative density 1.65
damage level S 2
Hudson coefficient KD 2
June 3, 2012 18
Wave period
June 3, 2012 19
permeability
P = notional permeability factor notional:
belonging to the realm of ideas,
not of experience; existing only in
the mind
June 3, 2012 20
number of waves
maximum number of waves: 7500
3000 waves of 6 s is 5 hours
June 3, 2012 21
damage level
June 3, 2012 22
slope angle
June 3, 2012 23
damage development
June 3, 2012 24
mild slopes
June 3, 2012 25
low crested dams (1)
50
0
1Reduction
1.25 4.82
n
pc
s
dsR
H
3
50
17 ln
2.1 0.1
s cp
n
H hs
d S h
Rc crest height with respect to SWL
s0p (deep water) wave steepness (from Tp)
h waterdepth
hc height of dam
crest above water level
crest below water level
June 3, 2012 26
low crested dams (2)
June 3, 2012 27
stability of toes
1.4
50
8.7s t
n m
H h
d h
50 50
1.1 0.24 1.6s t
n n
H h
d d
a: deep toes with small damage b: shallow toes
June 3, 2012 28
block types and filters in revetments
June 3, 2012 29
Two failure mechanisms for blocks
• The piston type failure
• The beam type failure
June 3, 2012 30
load and strength of block revetments
June 3, 2012 31
flow through block revetment and leakage length
d
d
FF Fv k
x
F T
T T
T
v kd
2 22
2 2 2
d d
d d
T F T F TF FF T
F T F
k
x k d d x
flow in filter:
flow through top layer:
Using continuity this leads to:
T and F are piezometric heads ( = p/g+z) on top layer and in filter layer
June 3, 2012 32
head difference over block for large and small leakage length
June 3, 2012 33
Measured head differences
Revetments and Numerical Simulation
(8 min) (SteenZet.mpg
June 3, 2012 34
Conclusion regarding leakage length
• small leakage length is best
• this means that top layer has to be more permeable than filter layer
• extreme case: make filter layer nearly impermeable
• practical example: blocks on clay
• However …………..??
• execution problem
• creation of gullies
June 3, 2012 35
Two failure mechanisms for blocks
• The piston type failure
• The beam type failure
June 3, 2012 36
Pulling tests
Type of block Averageweight
(kg)
Pullingforce(kgf)
Stand.dev. ofPulling force
(kgf)
Basalt 1Basalt 2Basalt 3Basalt 4HaringmanVilvoordse
1732355018016
17632178152888743764668
12821248103733242194369
June 3, 2012 37
Pulling force vs. position
Pulling tests Zeeland (Verhagen, 1984)
0
10
20
30
40
50
60
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0
distance below top (m)
pu
llin
g f
orc
e (
kN
)
June 3, 2012 38
stability of block revetment
cos( ) cos 0.33 0 3s
m w w s
Hgd g H
d
first guess
June 3, 2012 39
test results for placed blocks
June 3, 2012 40
the Pilarczyk formula
cossu b
m p
H
D
u system defined (stability) upgrading factor
{for riprap by definition u = 1}
stability factor
Hs significant wave height
Tp peak period of the waves
p Iribarren-number for peak period
D specific size of protection unit
slope angle
m relative density of the system unit
b exponent 0.5 < b < 1
for riprap b=0.5, for smooth blocks b=1
on average b 2/3
June 3, 2012 41
the Pilarczyk formula (2)
= 2.0 for incipient motion of stones
= 2.25 average value for incipient motion
= 3.0 as a first approximation for max. tolerable damage
0.12
0.186.2 3,S
P for breaking wavesN
u 1.0 riprap (by definition)
1.0 poor quality pitched stone
1.5 high quality pitched stone
1.5 loose closed blocks
2.0 high quality blocks (Basalton, Hydroblock)
1.5 Pattern grouting
2.0 Fixstone
2.5 gabions
2.5 Armorflex (cable system)
June 3, 2012 42
time effect
June 3, 2012 43
Asphalt
Technisch Rapport Asfalt voor Waterkeren TAW 2002 (www.enwinfo.nl) (not yet translated in English)
June 3, 2012 44
Types of asphalt revetments closed revetments open revetments
dike type zone asphalt
concrete
asphalt
mastic
penetrated
riprap
partly
penetrated
riprap
open
stone
asphalt
open
stone
asphalt
mat
sand
asphalt
riverdike I
II
III
IV
-
-
+
o
+
-
-
-
+
+
o
o
o
o
o
o
-
+
+
o
+
+
o
o
o
o
o
o
lake dike I
III
IV
-
+
o
+
-
-
+
o
o
+
+
+
-
+
+
o o
o
o
seadike I
II
III
IV
-
-
+
+
+
-
-
-
+
+
+
o
+
+
+
o
-
+
+
+
+
+
+
o
o
o
o
o
Dike zones: I always below water II between low water and high water III between high water and design level IV run-up zone
June 3, 2012 45
impervious layers in waves
1
22cosh
m w w
Hg d g
hL
June 3, 2012 46
static pressure on impervious layers
0.21 ( ) wn w
a w
d Q a v R
Qn – reduction for slope Rw – reduction for relative position of outer water level a – depth of revetment under water v – groundwater level above outer water level
v
a
June 3, 2012 47
wave impact on slope and influence material properties
max wp gqH
max wp gqH q - impulse factor (=3.4) c - soil stiffness E - soil elasticity
stiffness ratio
June 3, 2012 48
Loads on asphalt and influence filter
max
3 2
4 3
31 exp cos sin
2 2 2
2.65in which :
p H H H
Hd
Edc
June 3, 2012 49
But every wave is different….
Führböter [1988] has derived a probability function for the impact factor q for a slope 1:4
2
2
1Pr( ) exp
22q
q qq
q
June 3, 2012 50
Relation impact factor and slope
For other slopes a linear interpolation with slope is made:
tan
1/ 4rq q
June 3, 2012 51
Fatigue
The number of loads that leads to failure is:
fa
f fN k
kf and af are fatigue parameters of the asphalt, to be determined by the producer or from test samples of the placed asphalt
is the tension stress at the underside of the asphalt (in MPa)
Note: This formula is NOT dimensionless
So, with this formula I can determine for each given tension stress, the allowed number of load repetitions
June 3, 2012 52
Determination of the fatigue parameters
• Plot measured values
• calculate average and reliability limits
• linearize lower reliability limit
• a= slope of best fit
• log(k)= intercept
June 3, 2012 53
The Miner sum
Rule of Miner:
The cover layer will not fail as long as the following condition is true:
in which:
ni - number of load repetitions i
Nf,I - number of load repetitions i, leading to failure
,
1i
f i
n
N
June 3, 2012 54
Example
• I have three loads, one of 1 MPa, 1.5 MPa and 2 Mpa
N1MPa =103.02 1-3.77 =1000
N1.5MPa =103.02 1.5-3.77 = 217
N2MPa =103.02 2-3.77 = 73
• Load 1 occurs 500 times, load 2 occurs 50 times and load 3 occurs 20 times.
• Minersum:
• Conclusion: This type of load is exactly the limit
500 50 200.5 0.23 0.27 1
1000 217 73
June 3, 2012 55
Practical calculation
• Determine the different load levels during a storm (i.e. select a number of H/T classes)
• Calculate for each level of the revetment the number of loads for each load level
• Calculate for each combination the partial Miner-sum
• Add up all Miner sums and verify that this sum is <1.
• This can be done with the computer program Golfklap (only in Dutch, but downloadable from Blackboard)
June 3, 2012 56
necessary thickness of asphalt concrete on sand or clay
June 3, 2012 57
Asphalt penetration
June 3, 2012 58
Very open plate structures
• Open stone asphalt
• Is able to follow subsoil settlements
• Sensitive to fatigue
• Sensitive to damage by abrasion
• Colloidal concrete
• Very stiff and not very elastic
• Very strong and not sensitive to abrasion in case of very good execution
• Stones glued with polymers
• Not sensitive to fatigue
• Very resistant against abrasion
• Very elastic, but is maybe not able to cope with large deformations
June 3, 2012 59
Open stone asphalt
June 3, 2012 60
Glued revetments
• It is possible to glue small stones
• Elastocoast from BASF (using Polyurethane glue)
• InfraElast from Rotim (using Epoxy)
June 3, 2012 61
What is Elastocoast ?
• Revetment structure of small stones glued together with polyurethane glue with a very strong bonding
• Details will be discussed by Bijlsma on Thursday afternoon (session C7)
June 3, 2012 62
Small scale tests are complicated
• Nearly full scale tests were executed in the GWK-facility in Hannover
• Fully instrumented with nearly 100 sensors (waterpressure, displacement, wave)
June 3, 2012 63
Two layouts of the construction
• 15 cm Elastocoast on geotextile, directly on sand
• Same, plus additional 10 cm filter layer (consisting of same material, but without polyurethane)
June 3, 2012 64
Failure of the thin model
15 cm Elastocoast 15 cm Elastocoast 10 cm filter geotextile geotextile sand sand
Regular waves H = 1.3 m T = 5 sec
Test GWK, Oumeraci et.al, 2009
June 3, 2012 65
Failure because of exceeding strength of stone
Test GWK, Oumeraci et.al, 2009
June 3, 2012 66
Displacement of the Elastocoast
Test GWK, Oumeraci et.al, 2009
June 3, 2012 67
Origin of the failure
Test GWK, Oumeraci et.al, 2009
June 3, 2012 68
Stability relation for Elastocoast
• Elastocoast is much more stable than gabions
• Elastocoast seems to be more stable than concrete blocks
June 3, 2012 69
Preliminary conclusions
• Elastocoast seems to be more stable than concrete blocks
• Thin Elastocoast directly on sand may lead to liquefaction problems
• Breakage is caused by breakage of stones, and not of the bonding with the polyurethane