330( VL Ship waves and the stability of armour layers protecting slopes delft hydraulics

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P I: 330( VL
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number 428
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Ship waves and the stability of
armour layers protecting slopes
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H.J. Verhey and M.P. Bogaerts
November 1989
Rijkswaterstaat
Dienst Verkeerskunde
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publication no. 428
Ship waves and the stability of
armour layers protecting slopes
Paper presented at the 9th International Harbour Congr
Antwerp, Belgium, 20-24 June 1989
H.J. Verhey and M.P. Bogaerts
November 1989
delft hydraulics
SHIP WAVES AND THE STABILITY OF ARMOUR LAYERS PROTECTING SLOPES
by
H.J. VERHEY, Senior Project Engineer, Rivers, Navigation'and Structures
Division, Delft Hydraulics, Delft, the Netherlands, and
M.P. BOGAERTS, Head Navigation Fairways, Transportation and Traffic
Engineering Division, Rijkswaterstaat, Dordrecht, the Netherlands
ABSTRACT
Equations are presented for predicting the height and length of ship waves, which take into account
the influence of ship speed, distance to the sailing line and shape of the ship's bow. The
equations are based upon small-scale physical experiments and full-scale measurements. Stability
criteria are given for riprap bank protection and block revetments attacked by ship waves. The in
fluence of the wave length and the oblique angle of incidence relative to the normal of the slope
are taken into account. A reliability function is presented for riprap bank protection to enable
probabilistic calculations to determine the probabilities of occurrence for a particular number of
stones transported. Finally, equations are given for determining the extent of the area attacked by
ship waves. All equations related to the stability of the armour layers are based upon extensive
tests. An important conclusion, concerning these equations, is that ship waves are very similar to
wind waves despite the different origin.
INTRODUCTION
Ships sailing in canals, entrance channels and harbour basins, induce a water motion which exerts
loads on the banks. Secondary ship waves are one of the components of this induced water motion,
others being, for example screw race, return current and water level depression. The height of
these waves depends mainly on the ship speed, but also on the distance from the sailing line and
the ship's shape. Ships sailing at high speeds can produce high waves. Tugs, and patrol and pilot
boats, for instance,can cause wave heights of about 0.50 m and even 0.75 m on occasions.Container
ships and ferries sailing in almost unconstrained waters may even generate wave heights up to 1.0
m. Obviously, these waves should be taken into account when designing armour layers for banks along
navigation fairways or harbour basins.
Scarcely any general equations are available for predicting wave height and wave length of
secondary ship waves at a particular distance of the ship with parameters related to ship and canal
characteristics. The equations presented in literature are usually valid for the wave height near
the ship or for a particular ship type only ( see [2][3][4][5][10]), although the basic theory was
published in 1887 by Lord Kelvin [17]. Besides, measured wave height data have often been used in
connection with resistance and propulsion problems. Research carried out by Delft Hydraulics using
small-scale physical models and wave height data presented in literature, has resulted in general
equations which make it possible to predict the characteristics of secondary ship waves. These
equations are presented in this paper, together with the results of full -scale investigations
carried out by Rijkswaterstaat and Delft Hydraulics.
Secondary ship waves primarily attack the surface layer of bank protection at about the water
level. These surface layers can, for instance, consist of loosely packed coarse material or block
revetments. The stability of surface layers against wave attack is usually checked against
stability criteria such as the well-known Hudson or Iribarren equations or their derivatives. These
criteria, however, have been developed for a large number of wind waves propagating in a direction
normal to the bank. In contrast to wind waves the number of secondary ship waves is limited and the
direction of propagation is at an angle to the bank. Taking into account these particular
conditions a modified Hudson equation has been developed for checking the stability of cover layers
attacked by secondary ship waves. In addition, an equation has been developed which enables the
number of stones displaced by secondary ship waves to be computed. This transport equation is one
of the transfer functions needed for probabilistic calculations which aim at computing the damage
to a structure on, for instance, a yearly base. Equations are presented in this paper which enable
the upper and lower level of the protection zone against secondary ship waves to be determined
with respect to the undisturbed water level.
EQUATIONS FOR SHIP WAVE CHARACTERISTICS
General theory and test set-up
Secondary ship waves manifest themselves as transverse waves and interference peaks, see Figure 1.
These peaks, referred to here briefly as "ship waves", are the result of interference between
transverse and diverging waves, which are generated by the dynamic pressure distribution on the
hull of a ship under way. Ship waves,or interference peaks, are of special interest in relation to
bank attack. Transverse waves are relatively less important than ship waves in this context.
Attention is, therefore, focussed on ship waves.
//////////////// diverging waves
bank
19.5"
angle ol direction ol propagation *r—^."*\t
incidence i54.7* ol ship waves
/pressure
\ line ol loca tion
point
\ ol snip woc ves
interlerence peaks
( or ship waves)
soiling line
Kelvin wave pattern lor a moving point pressure disturbance
Figure 1 Ship wave characteristics
Lord Kelvin deduced the theory of ship waves using a surface point pressure disturbance moving on
deep water[17]. The pressure point generates a system of diverging and transverse waves known as
the Kelvin wave pattern (see Figure 1). As already mentioned these waves meet to form interference
peaks or ship waves located along lines which makes an angle of 19.5 degrees to the sailing line.
Ship waves, being the dominant phenomenon, have to be considered as a stationary wave pattern with
regard to the moving pressure point. This is only possible if the propagation angle of these waves
makes an angle of 35.3 degrees with the sailing line.
Havelock developed a relationship for the relative wave height of ship waves in deep water
conditions using Lord Kelvin's theory[6J. The relationship can be transformed into the equation :
^ -0.3 3 t o (1)
n s
with
F - v /(gh)°«5 (2)
s s
in which % » height of ship wavefm], h = water depthfm], s = distance between ship's side and
bank[m], v =ship speed[m/s], g=acceleration due to gravity [m/s2] and F=Froude number based on
g
ship speed and water depth [-]. The exponent 0.33 corresponds to the angle of 19.5 degrees
mentioned above and has been confirmed by the test results of, for instance, Sorensen[16]. The
coefficient <x\ and the exponent 03 have to be determined by carrying out small-scale physical tests
and also using results of full-scale tests and results presented in literature.
The same theory and the theory about deep water waves result in the following equation for the wave
length L :
L = 2ir cos2 (35.3*) v2/g 0.67 . 2tt vVg (3)
wi s
The wave period can easily be calculated using the equation L = g • T|/2ir.
wi
Experiments to confirm Equations (1) and (3) were
carried out in a towing tank with different ship
types representing tugs,inland motor vessels and
European barges (see Figure 2). The model ships
used their own propulsion systems together with an
additional towing fovrce to compensate for scale
effects. The length scale varied between 10.5 and
25. Wave heights and wave lengths were measured at
regular intervals from close to the sailing line
up to a distance equivalent to 100 m. Ship speed
and water depth were varied.
Figure 2 Ship waves produced by a tug
Calculation formulas for wave height and wave length
The results of the tests suggested a value of 4.0 for the exponent a, in Equation (1). A re-
analysis of full-scale measurements (see [14]), together with an analysis of test results of
Brebner et al[2],Dand[3], Hay[7] and Sorensen[16] confirmed the value of a, = 4.0.
The coefficient ct^ was then determined to be:
= 1.0 for tugs,patrol boats and loaded conventional inland motor vessels
= 0.5 for empty European, barges (wave heights produced by loaded barges are relatively small and
can be neglected)
= 0.35for empty conventional motor vessels.
A comparison between measured and calculated wave heights is presented in Figure 3; the figure also
includes results of full-scale tests.
It should be noted that a similar equation,
presented by Delft Hydraulics for the wave height,
line of perfect agreement gave ai = 0.35 and 0.3 = 2.67 in the case of
with Equation (1 ) j
tugs[l]. This equation is still correct, but, the
equations presented in the present paper are based
/
on many more test results and are therefore
\ . / /• recommended.
(lcinoee fofit cipeenrt fecOti aing rEeeqmuaetnito n (1) | % / '
multiplied by 1.2 ) [ * An attempt has been made to incorporate the ship's
' -j
shape in the coefficient o , in particular the
/
ship's bow as the origin of ship waves. An
/ A analysis of the results given in literature
clearly indicated the importance of the ratio ship
BB ff mm draught to entrance length (T = ship draught [m],
L = entrance length or distance from the ship's
g
A/ bow to the beginning of the parallel midship sec
tion [m]). Consequently, is given by:
——
--
i a l " a2 T/L (4)
t H,)CQ|C
x tug ( small-scale tests)
• empty conventional motor vessel (small-scale tests}
o loaded conventional motor vessel { lull-scale tests)
• tug (full-scale tests)
V empty European Darges ( full-scale tests)
Figure 3 Comparison between measured and calculated
wave heights, equation (1)
The value of was determined for the different ship types for which information was available,
for example passenger ships, freighters, tankers, supply boats, ferries and container ships. In'
many cases the value of L had to be estimated which led to variations in the result, a lying
fi
between 1.5 and 4.0. 2
Calculated and measured wave heights are presented in Figure 4 for all available test results.
2 8 Investigations carried out at both
• full-scale and at a reduced scale have
2.6
confirmed that wave heights on banks
lin of p« rfect jgrBcn lent with slopes in the range 1:2 to 1:4 can
2 4 wil h Equc tionst r and (4)
be predicted by Equations 1 and 4.
2.2 / Investigations have also confirmed
Equation 3 for wave lengths (see
/
2.0 Figure 5).
/
/
• a /
/ g
/ .
•
/)
/. ms
• • °
/• 30
S
/ / ' o~~ y 33 V. .• cluogn vantionoi motor «*»«!
•/ •
y • 44**00
^ •
'*/
•
-4
» f
A
AX
K •
0.2 0.4 0.6 OB W 1.6 1.8 2.0 2.
t Hj) calculated (m)
•
test results Delft Hydraulics
:}t est results mentioned in literature o q IO \ -A ij k6 t K 1 K> 4 TO 450
note: the wave height (Hj )ca|culated hos ba<Ir calculated using the
value of 0-2 determined for the particular ship type
Figure 4 Comparison of the wave height equations, Figure 5 Comfirmation of the wave length
equation (1) and (4) using available data equation, equation (3) using
test results
The equations presented here can be used for predicting of height and length of ship waves.
Generally,ship types such as tugs and patrol boats will produce the highest waves because of their
higher speeds. The most accurate values will be obtained by using = 1.0, but for a safe upper
limit a value of a. = 1.2 should be used. In the case of waves produced by other ship types a con
servative prediction should be made by using = 4.0, and an accurate value will be obtained by
using the different values of a, belonging to the particular ship types.
The applicability of the equations is restricted to conditions corresponding with deep water, that
is conditions fulfilled in practice if the Froude number F is less than 0.7.
g
The second restriction is imposed by the water depth criterion that waves should not break,thus
H./h should be less than 0.6.
STABILITY CRITERIA FOR BANK PROTECTION
Experimental set-up
Investigations have been carried out to determine the stability of a bank protection of riprap and
loose concrete blocks. Test sections
were constructed with graded gravel
(DCQ = 5.5 mm and D^Q = 10.9 mm, p =
2650 kg/m3) and blocks simulating loose
block revetments (30x30x15 mm , p =
1380 kg/m3) on different subsoils? The
gravel was coloured and placed in
patterns so that the number of
stones displaced could be determined
(see Figure 6). The length scale of the
experiments was 1 to 10.5. The results
of full-scale measurements will be
obtained by using the different values
of belonging to the particular ship
types have also been used in the
investigations [14].
Figure 6 Test section used to determine scour
Design formula for riprap surface layers
An armour layer of riprap should be able to resist, amongst other things, the hydraulic attack of
ship waves. The design criterion used here will be little or no movement of individual stones of a
riprap surface layer ("initiation of motion"). Relevant parameters 'flbr ship wave attack are: wave
height U, wave length L angle of incidence to the normal 8, characteristic riprap diameter D^Q
i WI>
or Dn50' relative density A = (p - P )/p and slope angle a. Many researchers have presented
g w w
equations for checking the stability of loosely packed coarse material for angles of incidence 6 =
0 degrees (that is: the propagation angle of waves normal to the bank), for instance, Iribarren. In
this context use has been made of the Hudson formula [8]:
A D cotct Sf)°-33 (5)
50
in which K = stability factor [-] and S = shape factor [-]. Hudson recommended a value of 2.2
RR f
for K in circumstances with breaking waves with heights less than 1.5 m . An average value of S
f
= 0.65 can be used for riprap. Equation (5) cannot be used directly, however, because the
propagation angle of ship waves makes an angle of 35.3 degrees with the sailing line and therefore
the angle of incidence to the normal of the slope equals 54.7 degrees. According to Van Hijum [9]
this can be taken into account by reducing the wave height by a factor (cosg)0-5. Equation (5) then
becomes:
H . (cose)0-5
A D (KRF cota Sf)0.33 (6)
50
Small-scale test results for a slope 1:4 are presented in Figure 7. It can be deduced that little
or no movement of stones occurs for values of:
H . (cosg)0-5
t
< 1.8 to 2.3 (7)
A D
50
symbol material 1
•
gravel D50 = 5.5 mm •
gravel DJO:l0.9 mm *
•
a
a
a
1 a
• a
2E a
a
C 40 a .
a
• •
a
•
Wr* : T->
3 4 5 wave height parameter Hj/aDjo
wave height parameter Hj/AD 50
Figure 7 Small-scale test results: number of Figure 8 Full-scale test results:
stones displaced number of stones displaced
(tug)
in which the value of 1.8, corresponding to the value of K recommended by Hudson,proved to be too
RR
conservative.
Similar results were obtained for slopes 1:2 and 1:3 and with full-scale measurements, see Figure
8. The influence of the subsoil and the surface roughness of the riprap on the stability could not
be determined.
The equations presented do not take into account the wave length, despite the fact that its
influence on the stability has been established by various researchers. The wave length can be
incorporated in Equation (6) by using the surf similarity parameter £ [15]:
.0.5
Hj . (cosg) -0.50 ,o\
— i- < 2.25 (cosa + sina) . £ * (8)
n50
with <• = tana • (Hj/L^)-0 •5 (9)
in which D = (W /p )°•33, W = 50% value of mass distribution curve [kg]
n50 50 s 5Q
The relationship between D^Q and is:
n = D . CS 1°.33 (10)
Un50 u50 K*f'
J •v
Equation (8) is valid for values
of £ less than (0.05 . cota)-0*5, which
generally will be the case. For greater
"\ »90
825 values of 5 the righthand term of
Equation (8) changes.
i •ties
Test results for a slope 1:4 are
presented in Figure 9 and confirm
\
Equation (8). However, for a slope 1:3
0000000000000 \ incre asmg
^trans port the equation seems too optimistic.
Nevertheless, when dimensioning riprap
\
\
Equation (8) should be preferred to
Equation (7) because of the possibility
ppppppppppppp to take into account the influence of
the wave length in the latter.
22 M, (CO
/
*> *
0000000000000
Hudson equation with Krr = 2 2 /
aaaaaaaaaaaaa
6666666666666
symbol mater Ol
^^»» ggrraavveell DDssoo :: 55..55 mmmm
AA
ggrraavveell DD4400 ==1100..99 mmmm
figure* rapraiunt the number
of stones displaced
.............0000000000000 i 07 i qsi Q9i lfl U \* V V1 *°
.surl similarity paromaur 5
Figure 9 Riprap stability test results for a slope of
1:4 with the influence of the wave length
Design formulas for block revetments
The design criterion for block revetments is that the lifting of individual blocks by pressure
forces perpendicular to the slope is unacceptable. A bank protection consisting of a block
revetment derives its strength from the mass of each individual block. Friction between individual
blocks increases the strength of the protection in the same way as cables connecting the blocks
together or interlocking blocks. Impermeable sublayers also contribute to the strength of a slope
revetment, because the pressure underneath the blocks cannot be built-up as easily as in the case
of permeable sublayers. However, it is stressed that care has to be exercised when considering
these additional strength forces, because the lifting of one individual block may introduce pro
gressive scour.
A black-box equation has been determined on the basis of full-scale and reduced scale
investigation, by Pilarczyk [13]. Modified for ship waves, this reads:
H . (cosB)0-5
l -0.5 (11)
< cco set
in which D = block thickness [m] and c = coefficient [-]. Equation (11) can be transformed for
slopes not steeper than 1:2 and 5 < 3, into:
U . (cosB)0-5
i r-O.S (12)
< c
It should be noted that the factors
which increase strength mentioned above,
ator eas hips uwbjaevcetse d are taken into account implicitly in the
k H coefficient c in Equations (11) and
(12). Average values for c are: c = 3,
loose blocks; c = 4, cable-connected
blocks and blocks interlocked by
friction [13] (see also Figure 10).
Figure 10 Stability test results for block revetments
shown schematically
The stability tests with ship waves resulted in one block being lifted out of the revetment. In
this particular case the stability criterion, according to Equation (12), was exceeded. With the
loads exerted on the blocks during the other test runs, however, the stability criterion was also
exceeded many times. Apparently, the blocks not being lifted out during these test runs could
mobilize the mass of the block to withstand the wave loads and, in addition, also friction factors.
The results of full-scale investigations did not add any new information (see [1] and [14]).
The limited results of the experiments do not allow final conclusions to be drawn about Equation
(12). Nevertheless, this stability equation is recommended because of the similarities between wind
waves and ship waves and because stability equations for riprap bank protection attacked by wind
waves have also proved to be valid for ship waves.
PROBABILISTIC DESIGN CRITERIA
Design technique
If the strength of a surface layer is higher than the load, there will be little or no transport of
material. However, if the load is greater than the strength, surface material will be displaced,
although this displacement may be acceptable. The probabilistic design approach makes it possible
to take into account these material displacements by calculating the probability of failure of a
structure using a failure mechanism based upon bank protection material displacement. A transport
equation was, therefore, determined. The probabilistic approach also gives a clear view of the weak
points of a structure and the various ways in which it can be optimized and also takes into account
the stochastic character of input variables.
Transport equation for riprap surface layers
A great number of stones can be transported by ship waves as can be seen from Figures 7,8 and 9.
The results of small-scale and full-scale experiments are presented in Figure 11 and on the basis
of these results, the following equation was determined: