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The quantification of breakwater armour profiles for design purposes
Coastal Engineering, 10 (1986) 253--273 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands
253
THE QUANTIFICATION OF BREAKWATER ARMOUR PROFILES FOR DESIGN PURPOSES
J.P. LATHAM and A.B. POOLE
Centre for Applied Earth Science Research, Queen Mary College, London E1 4NS, U.K. (Received October 8, 1985; revised and accepted February 25, 1986)
ABSTRACT Latham, J.P. and Poole, A.B., 1986. The quantification of breakwater armour profiles for design purposes. Coastal Eng., 10: 253--273. A new approach for the evaluation of block shape effects in both artificial and rock armour layers is proposed. Topographic profiles based on high-resolution sampling frequencies of between 10 and 20 heights per nominal armour block width are considered. Model surfaces of (a) glass spheres and (b) rock aggregate, were prepared and examined by topographic profile sampling. A preliminary set of 15 statistical parameters or roughness descriptors were evaluated for each of 10 sets of profile height data. A statistical comparison between the surfaces of models (a) and (b) indicates the potential of roughness descriptors such as mean peak curvature and peak density to discriminate between surfaces generated from blocks of different shapes. Filtering of height data for discrimination enhancement is also illustrated. Nomenclature is introduced to distinguish the planar orientations of the principal profiles of the breakwater: the AC plane cross-cuts the long axis and is the plane observed in the well known studies of S-shaped profiles; the BC and BD planes parallel the axis and are the planes proposed for analysis. It is argued that the new monitoring method of topographic profile sampling and roughness descriptor analysis provides a promising additional means of assessing the relationship between block shape and hydraulic stability for model and prototype armour layers. The importance of further development and testing of these techniques for the quantitative evaluation of surface geometry is stressed in view of the many possible future applications of these methods.
INTRODUCTION
The success o f a rubble m o u n d breakwater will depend on the efficiency o f that structure to convert the energy o f incident waves into a harmless form, t h r o u g h o u t its design life. In general terms, the funct i on of the artificial or natural rock a r m o u r unit layer is to p r o m o t e dissipation of wave energy b y generating turbulence between the blocks whilst protecting the relatively weak core of the structure. In order t h a t the arm our blocks
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254 perform this function, they must remain hydraulically and structurally stable to the extent that they continue to serve as protection against the predicted storm and wave climate characteristics of the breakwater site, by virtue of their b o d y weight and interlocking properties. In simplistic terms, the design engineer therefore seeks a relationship between the size of armour blocks, the slope of the seaward face of the structure, the wave climate characteristics and the amount of damage that will occur. There may also be a range of possible block shapes and materials for the designer to consider. These will introduce additional important variables into the already complex relationship. The block shape or material property dependent bulk parameters of the armour layer such as macroporosity, interlock, skin friction, abrasion resistance for example, may take corresponding ranges of values, each with a different functional relationship to stability. The hydraulic importance of the macro-roughness and permeability of the armour layer has received somewhat greater study in relation to runup and run-down than to stability itself. Losada and Gimenez-Curto (1979} and Giinbak (1979) have used various sources of experimental data on runup (for example Ahrens, 1975 and Giinbak, 1976) to fit nonlinear relationships between run-up and the Iribarren (or surf similarity) coefficient, ~. These relationships involve two constants A and B which are different for each type of armour unit; an obvious influence from these studies being that A and B depend fundamentally upon the geometric form of the roughness and the permeability created by the armour units. Losada and Gimenez-Curto (1979) performed a similar (exponential) curve-fitting procedure on several sets of data for armour stability. They obtained another two constants, again different for each type of unit, which give the relationship between a stability coefficient, the seaward slope and the surf similarity coefficient. Roughness, interlock and permeability are generally recognised to be the most important factors excluded from such relationships and these omissions are probably because of the lack of appropriate parameters. However, some roughness parameters have been used in relation to rubble m o u n d materials. One empirical roughness parameter is the "run-up reduction relative to smooth slopes" (PIANC, 1976) which exhibits sensitivity to the type of breaker (i.e. G-value) and this obscures the independent role of the geometric roughness. Bruun and Johannesson (1976) implicitly recognising the importance of roughness and interlock used the angle of repose to evaluate interlayer friction between different sizes of crushed quartzite. They attempted with partial success to relate the significance of these static conditions to failure conditions in the wave flume. The angle of internal friction used in geotechnical analyses of slip surfaces (e.g. Barends et al., 1983) includes yet another empirical parameter for the influence o f porosity, smoothness, roundness and rock type. A highly damaging and unstable resonance condition was identified by
255 Bruun and Giinbak (1976). Sawaragi et al. (1983) have further investigated this condition which occurs when wave period and r u n - u p / r u n - d o w n period are repeatedly synchronized. They proposed limiting conditions for a "dimensionless roughness height" and a "void ratio of the surface" which when combined with the resonance condition for smoother slopes (2 ~ 3) would give the most dangerous conditions for permeable rough slopes. All these indications from the research c o m m u n i t y point towards an important role for such geometric parameters in future hydrodynamic investigations of breakwater stability. Seeking to simplify the complexity of the real situation, designers have often applied the well known Hudson equation (Hudson, 1959) and have used the stability coefficient K D which is primarily intended to account for block shape effects determined from physical model experiments. The interpretation o f such KD results without making corrections for the important influence of wave period and breaker type is now recognised to have severe shortcomings. K D values of 3.2 for natural stone and 9.5 for tetrapods were reported in Hudson's original study for conditions of no damage and no overtopping. The experimental determination of these K D values and other similar stability coefficients yields little information about the physical processes that lead to enhanced stability. The relative importance of void ratio and interlock in controlling the stability of dolosse or tetrapod armour layers for example, has not been evaluated. Not until it is possible to relate hydraulically and structurally sensitive geometric parameters of the armour layer pack of blocks to the fine and gross scale shapes of individual blocks will it become possible to select or design individual block shapes on all but the most generalized systematic lines. A preliminary search for just such sensitive parameters is the subject of this paper where we introduce the concept of profile roughness descriptors. The complementary study of shape descriptors is the subject of ongoing research. In contrast to the situation with artificial unit armour layers, the relative importance of the influence of block shape on the stability of natural rock armour layers is by no means clear. From an extensive series of model tests using random wave attack, van der Meer and Pilarczyk (1984) have set o u t new empirically derived practical design formulae. However, rubble shape was n o t a test variable and an assumption implicit in these design formulae is that typical shape variations from different sources of rip-rap have an insignificant effect upon stability. Wave period, number of waves and permeability of the core were found to be highly significant whereas armour grading, spectrum shape and groupiness of waves were not. Bergh (1984) has investigated rip-rap block shape in flume tests using roughly cubic blocks of granite and slate, flat slabs of slate and rounded glacier boulders but using an impermeable core in his models. Bergh's tests also confirmed a lack of sensitivity to grading of armour blocks. However, his result that flat slates gave zero damage wave heights of 20% less and rounded boulders 40% less than for cubic slates was significant. This would imply a 100%
256 increase in the required weight for the flatter slate and that in-service rounding of rocks, if rapid, could result in a serious reduction in stability. Anticipating the potential importance of in-service block degradation and shape modification regardless of the importance of the initial block shape, preliminary methods for the assessment of armour block shapes and statistical properties of the armour layer surface were investigated by Allsop et al. {1985). They suggest a set of damage assessment criteria on the basis of field data collected from breakwaters of known ages. The required data uses subjectively assessed quantities such as the number of sub-sized, unstable, fractured and missing blocks. Geometric properties such as block size, roundness, interlock and void ratio were also measured and their results have improved our understanding of the ageing process. Unfortunately, these measurements all require a very large investment of human energy in proportion to the a m o u n t of useful field data yielded. The data retrieved by photography was relatively unsystematic. This approach for the acquisition and assessment of shape data is therefore in need of review. TOPOGRAPHIC PROFILES FROM BREAKWATERS The term surface has a sufficiently obvious meaning for the present purpose although the particulate form of the armour layer requires that a precise definition be introduced when considering profiles. We now propose the following working hypothesis. The spatial form of the surface (i.e. its overall roughness characteristics) is largely a function of {a) the initial shape and statistical distribution of shapes and sizes of blocks prior to construction and (b) the history of their m o t i o n and deformation in response to forces applied from the time of construction to the time of observation. The information residing in this surface and how it responds to wave action is of course the source of all breakwater performance or damage assessment criteria. One obvious m e t h o d of extracting from this surface a set of meaningful quantitative parameters for use in design equations is the use of photographic techniques. However, because blocks overlap and obscure each other in photographs, objective quantitative data is difficult to obtain so that the derivation of bulk statistical parameters from imaging of individual blocks is fraught with difficulties, particularly from field surveys. However, we can define a set of data which can be directly measured mechanically and possibly by remote techniques such as photogrammetry or sonar devices. Within a chosen reference plane the breakwater's topographic profile is the profile obtained by plotting the coordinate positions of the highest solid/fiuid interface. Embayments or reentrants caused by overhangs are represented by 90 ° or high-angle slopes relative to a horizontal reference direction. Over the straight part of a breakwater the four reference directions
257 are: A width; B length; C vertical; D normal to mean seaward slope. The most useful reference planes for inspection are then the AC, BC and BD planes. The spatial configuration is shown in Fig. 1. The AC plane has of course been chosen for topographic profile examination by many researchers interested in the natural development and design of S-shap~:J profiles (see references cited by Bruun, 1985 and the work of Naheer and Buslov, 1983). In these studies, mapped profiles of both models and prototypes formed smoothed outlines due to sparsely sampled or imprecise height determinations. Van der Meer and Pilarczyk (1984), sampling 9 sections parallel to the AC plane for each model have recorded the heights of blocks at a sampling interval roughly equal to the nominal diameter of individual blocks. The smoothed S-shaped profiles obtained after cumulative wave attack were used to compute a statistically averaged measure of damage by considering certain 'areas' of material removed. This paper is concerned with detailed statistical techniques applied to highly resolved height data from any chosen reference plane.
~
~
~f'~
/
i
..s~-... Ac
Fig. 1. Topographic profile configuration of a breakwater. In the fields of research concerned with the mechanical properties of sliding contacting surfaces, known as tribology, the statistical description of machined (metal) surfaces has become highly sophisticated. See for example the b o o k 'Rough Surfaces' edited by Thomas (1982) The roughness can be described by a large number of statistical parameters which are loosely termed roughness descriptors. Given a sufficient data set of (x, y) co-ordinates of the profiles sampled, a set of descriptors may be c o m p u t e d which can distinguish between surfaces prepared by different machines, the degree to which they have been worn and their likely performance as bearing surfaces. Naturally, the amplitudes of roughness and the slopes of the asperities on both the model and p r o t o t y p e breakwater, are vastly different from those on machined metal surfaces. However, the same kind of statistical approach can be used to investigate hydraulic and
258
structural properties of the breakwater armour layers using roughness descriptors from the BC or BD and AC planes. In addition to the use of roughness descriptors in refining the initial breakwater design equations -- a long-term objective -- there is general agreement on the need for monitoring and assessment of long-term changes (e.g. over several years} and immediate storm-induced changes in the spatial distribution of armour blocks and in the block shapes themselves. Damage assessment obtained from sampling of topographic profiles would n o t necessarily require exact relocation surveying of the profile, merely a statistically valid sampling procedure which can be determined using laboratory models. Compaction of newly placed blocks will presumably correlate well with descriptors relating to roughness amplitudes or peak to valley height. Some national roughness standards also recognise a void coefficient and a similar type of coefficient to this might prove useful as a descriptor for monitoring specific hydraulic properties. Changes in shape of armourstone blocks occur in response to abrasion, dissolution and spalling, and crack propagation {Poole et al., 1984). The gradual removal of material from the armour layer, particularly in the intertidal zones, leaves behind armourstone which is progressively rounded with age. The rounding process will be particularly well monitored by descriptors such as peak curvature. By sampling topographic profiles across model particle packs (i.e. aggregates) of known average shape descriptors, roughness descriptors (e.g. peak density or average peak curvature) could be calibrated as measures of average roundness and therefore yield information on weight loss and loss rates. Block size is another important design parameter which, with the help of laboratory model work, could be described by an appropriate profile descriptor such as an average wavelength, or a correlation function. Points (a) and (b) from the above hypothesis immediately suggest several related research objectives which could provide an evaluation of presently speculative but promising new profiling t~chniques. METHOD E V A L U A T I O N USING MODELS
Before turning to wave flumes and models in search of descriptors that are sensitive to hydraulic stability, it is necessary to establish some familiarity with the suite of statistical parameters and their sensitivity to predetermined differences in surface topography. For this purpose, a glass ball model and an aggregate model were constructed. If the sampled value of a particular roughness descriptor can be just as easily assigned to the glass ball surface as to the aggregate surface, then that descriptor is unlikely to be of further practical value. In other words, the preliminary studies outlined here are required to establish the sensitivity of the various descriptors to changes in profile shape while accommodating the inevitable statistical variation associated with the profile.
259
Construction o f the laboratory models Glass balls A large quantity (1000) of spherical glass balls with equal diameters of 1 7 . 8 m m was used in the construction of the model. To provide an adhesive solution of relatively low viscosity, 1 part Butvar B98 powder (polyvinyl butyral) was dissolved in 3 parts methylated spirit (by bulk volume). A trough measuring about 500 x 150 x 1 0 0 m m was prepared using a malleable wire mesh. The glass balls were thoroughly coated with a thin film of the adhesive solution and poured into the trough. The trough was suspended to allow the adhesive solution to drain freely through the base of the model and to encourage rapid setting. No attempt was made to even o u t or 'flatten' the uppermost 'surface' of the balls and the well known regular packing geometries were deliberately inhibited from developing by the initial geometry imposed by the wire mesh at the base of the model. After 24 hours the entire model could be handled as a single rigid block until such time after analysis, when the model was broken up and the glass balls cleaned and recycled for further use. Aggregate The same procedure was used to make the aggregate model. However, it should be mentioned that the particle sizes of the aggregate were not sorted or measured for these preliminary experiments. Typically, the larger particles were of maximum and minimum dimensions of 40 and 15 mm, respectively, the great majority of particles having maximum and minimum dimensions between 30 and 10 mm. Very small grit particles were also present (unintentionally) on the model's surface. Data acquisition In these preliminary studies three precision carpenters profiling gauges were joined together to produce a linear profile gauge (length 4 6 0 m m ) of approximately 560 pins and pin diameter 0.8 mm. The gauge was clamped close to the model's surface with its axis approximately horizontal and its plane of pins vertical. Sampling of the profile topography required delicate manual contacting of each pin with the solid surface and the bonding of the particles of the model ensured that no particle movement occurred. Sampling of each model's surface was limited to 5 successive parallel profiles taken at 25-mm intervals. Photographs were taken of the pin positions corresponding to each profile and these were printed at considerable enlargement to give an image of true scale. Each full scale print of the profile gauge was digitized using a microphone array digitizer. The sparker source was placed over the photograph and located (to within 0.5 mm) successively at the end of each pin. The X and Y coordinates were automatically recorded (to an accuracy of better than
260 0.2 mm) and input to a computer data file. Each photograph too about 25 minutes to digitize.
Computer data analysis The data files containing approximately 560 pairs of X and Y coordinates for each profile are reformatted so that Y coordinates (the ordinates or heights) are held as integers and a regular X-interval is assumed. The data analysis is based on the program TPROFK, written by Dr. R.S. Sayles (1976) which has provided the vehicle for numerous research programmes and industrial applications in the field of tribology. In this study, the analysis of rough surface geometry, normally concerned with machined metal or fractured surfaces with irregularity amplitudes of several microns, has been applied to millimetre scale features with much steeper slopes. The full scope afforded by the range of analyses contained in TPROFK has yet to be explored. Some of the most important profile parameters have been chosen for investigation in this study and are described below. PROFILE
ANALYSIS
Profile analysis terms Roughness A straight mean-line is fitted by least-squares regression to the ordinates (z-values). This has the result that the areas enclosed above and below the mean line are equal. If the mean line is subtracted from z, the residual, y, is the mean line referred ordinate (see Fig. 2). It is this latter value y, which is used in the analyses of the profile. The centre line average (CLA) roughness, Ra, is given by the equation: L
1 r Ra = - - |dl y l d x L 0
and the root mean square (RMS) roughness, o, by: L
o =
L
y2 dx 0
t
In terms of the surface height distribution p(y), the RMS roughness is the standard deviation or, the square root of the variance or second m o m e n t of p(y). For a surface with a normal (Gaussian) distribution of ordinates, a --~ 1.25Ra. Although the RMS roughness is probably the most fundamental profile
261
0
Fig. 2. The profile coordinates, mean-line and sampling length. parameter, it is clearly possible to have two profiles from entirely different surfaces, with identical values of a.
Feature density, peaks and valleys The zero-crossing density, Do, is the number of times the profile crosses the mean-line per unit length. The profile peak density, Dp, is the number of peaks per unit length. Peaks and valleys are defined by examining three consecutive ordinates. Peaks are defined as points higher than their two respective neighbours. Valleys are similarly defined as a minimum. Curvature The curvature, C, of a valley or peak is defined using three consecutive ordinates as the negative of: y(i + 1) -- 2y(i) + y(i -- 1) (Ax) 2
(where ~ x is the sampling interval ~ 0.8 mm in this study), so that C > 0 for peaks and C < 0 for valleys.
8lope The slope, tan 0, is defined for any two consecutive ordinates as: tan0 =
y(i + 1) - - y ( i ) Ax
from which the mean absolute slope 0 in degrees can be computed.
Distribu tions From each profile, the distributions that are likely to contain important coded information and which have the simplest relationships to the surface geometry are the following: ordinates (y) peak curvature (Cp) peak ordinates (yp) valley curvature (Cv) valley ordinates (Yv) profile curvature (C) profile slope (tan0) For each profile sampled, any of the above distributions may be calculated
262
yielding four statistical parameters: the mean, standard deviation, skewness and kurtosis of the distribution.
Analytical results For the purposes of this exploratory study ten profiles were investigated, five from the glass bail model and five from the angular aggregate model. Typical profiles of each model are illustrated in Figs. 3 and 4. Tables 1 and 2 show a selection of fifteen statistically derived profile parameters (the profile descriptors of this study). The values of the descriptors vary considerably from one profile to the next for certain descriptors, see for example the mean peak height Yp~ in either of the models. Other descriptors such as profile peak density Dp are apparently more consistent. Bearing in mind the limitations of deriving statistics from five samples, for each descriptor, the mean and standard deviation of the mean has also been tabulated. It seemed reasonable to require that the mean value of any descriptor obtained from the glass ball model should be significantly different from that of the aggregate model, if there is to be any scope for that parameter as a profile descriptor. The simplest way to gain a measure of the significance in the difference in means of any one descriptor is to calculate the standard deviation of the difference of the means, and then to use a test such as Student's t test to obtain confidence limits. This procedure can be criticised
,,
i' ,~ ,,~
. 'i
"
!/!
~,
:
i,
=
/tJ'
t
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,,! i:
I
"4
q:
LO
! HOpIZONrA~
[),~,T~1,%'C~
f IO'C
b,%,T ~)
~o'M'~
J
Fig. 3. Unfiltered and 18ram filtered data from profile RGB1P5 of the glass sphere model. Top: unfiltered profile with the gross smoothing effect of the 18ram low pass filtering shown superimposed. Bottom: effect of 18 mm high pass filtering giving a broad leveling of the profile.
263 zD 1
o
120
Z40
HORIZONTAL
D/STANCE
~60
(/~0
4e0
UIVIT5
=
80,'WM)
Fig. 4. Unfiltered and 18 mm filtered data from profile RAG1P1 of the aggregate model. See Fig. 3 caption.
on a number of grounds when it is applied to the sampling in this study. For example, it is n o t known whether for each descriptor, the five profiles give five values each of which has been taken from a normally distributed population -- a requirement of the t test's applicability. In Table 3, the t statistic is given for each of the descriptors. The confidence limits are calculated for eight degrees of freedom and the two-tail test is assumed to apply (which will give conservative confidence limits in most cases). A null hypothesis stating that there is no difference between the mean values of a descriptor for the glass ball surface and the aggregate surface can be rejected at different levels of confidence depending upon t. Thus t is a standardized measure of the difference in the sample means. Consider for example, peak density Dp (see Table 3). The difference in means that were sampled is 86.9. This a m o u n t of deviation is 9.4 times the expected deviation of 9.25, had there in fact been no difference in the means of the peak density. A table showing critical values of t for the Student's t distribution, at a significance level of 5% gives t = 2.31. It may be expected t h a t the difference in means will be up to but not exceeding 2.31 times its standard deviation in 95% of cases. In Table 3, 11 of the 15 descriptors have differences which do exceed 2.31 times their standard deviation and rejection of the null hypothesis at 95% confidence may be applied to all 11 of these descriptors. Rejection is at 98% confidence for t = 2.90 and 99.8% confidence for t = 4.50. The descriptors in Table 3 have been ranked according to their t value as well as grouped into confidence intervals. The mean peak curvature and peak density are predictably the most powerful of all the descriptors.
o Ra Dp
Ypm
RMS r o u g h n e s s CLA roughness Peak d e n s i t y
Mean peak height Std. dev. p e a k h e i g h t
C~¢n
Mean peak curvature Std. dev. p e a k c u r v a t u r e
Mean slope Std. dev. slope Mean a b s o l u t e slope
-- 0.0418 3.469 55.93
(dy/dx)m (_.dy/dx) a
0
Cva
-- 5.887 10.85
0.8426 1.624
5.756
-- 3.988 9.537
1.690 8.242
Cwn
Cpa
Ca
Std. dev. c u r v a t u r e
M e a n valley c u r v a t u r e Std. dev. valley c u r v a t u r e
Yva
Y~n
M e a n valley h e i g h t Std. dev. valley h e i g h t
Ypa
GBIP1
Symbol
Name 8.374 6.948 126.1
Profile n a m e
Profile d e s c r i p t o r
-- 0.0358 3.792 58.76
-7.096 8.973
0.6316 0.4982
5.829
-- 5.747 10.18
1.754 8.314
8.594 6.943 105.9
GBIP2
-- 0.0381 4.388 59.75
-- 9.523 11.73
0.9428 1.447
7.347
-- 6.596 11.56
-- 0.4563 11.24
10.17 8.561 136.3
GB1P3
Glass ball m o d e l . A n a l y s i s o f r a w d a t a ( u n f i l t e r e d ) f o r 15 p r o f i l e d e s c r i p t o r s
TABLE 1
-- 0.0250 2.823 54.07
5.814
-- 6.034
0.6696 0.6368
4.278
-- 5.411 7.890
0.7294 8.247
8.288 6.737 110.4
GBIP4
-- 0.0291 3.240 54.99
-- 5.124 6.056
0.8073 0.6131
5.077
-- 5.673 8.428
0.3053 8.569
8.200 6.545 121.6
GBIP5
-- 0.0340 3.542 56.70
-- 6.733 8.684
0.7788 0.9638
5.657
-- 5.485 9.519
0.5671 8.922
8.725 7.147 120.1
Mean
0.0068 0.5899 2.448
1.711 2.702
0.1278 0.5282
1.133
0.9427 1.453
0.8950 1.302
0.8208 0.8079 12.21
5b
Std. Dev.
C~m Cpa
C~,m Cva
(dy/dx) m (dy/dx) a ~
Mean valley curvature Std. dev. valley curvature
Mean slope Std. dev. slope Mean absolute slope
Yvm Yva
Mean valley h e i g h t Std. dev. valley h e i g h t
Ca
Ypm Ypa
Mean peak h e i g h t Std. dev. peak h e i g h t
Std. dev. curvature
o Ra Dp
RMS roughness CLA r o u g h n e s s Peak d e n s i t y
Mean peak curvature Std. dev. peak curvature
AGIP1
Symbol
Name
0.0163 2.777 50.18
- - 4.141 7.406
1.685 2.455
4.758
- - 3.277 8.090
-- 0.1428 7.857
7.695 6.341 186.9
Profile n a m e
Profile d e s c r i p t o r
0.0033 3.321 54.59
- - 4.252 7.002
1.886 2.826
5.495
- - 2.493 7.968
1.020 7.020
7.921 6.320 191.4
AGIP2
0.0373 2.265 51.01
- - 3.032 4.266
1.872 2.281
4.223
- - 2.717 5.975
0.0987 5.792
6.073 4.743 214.0
AGIP3
Aggregate m o d e l . Analysis o f raw data ( u n f i l t e r e d ) for 15 profile d e s c r i p t o r s
TABLE 2
-
2.244 5.028
5.417
1.663 6.297
0.0159 3.237 53.62
- - 4.552 7.332
-
1.321 5.134
5.775 4.585 223.0
AGIP4
0.0059 2.751 52.42
- - 3.789 5.329
1.818 2.690
4.595
- - 2.452 8.122
0.5121 8.076
8.285 6.351 219.8
AGIP5
0.0157 2.870 52.36
- - 3.953 6.267
1.901 3.056
4.898
- - 2.520 7.290
0.5618 6.776
7.150 5.668 207.0
Mean
0.0134 0.4263 1.812
0.5828 1.401
0.2075 1.122
0.5461
0.5813 1.062
0.6123 1.283
1.143 0.9183 16.70
5a
Std. dev.
b~ Ob
descriptors ~ descriptors descriptors descriptors ~
Summary : 3 3 5 4
0
(_dy/dx)a
0.0067 0.3255 1.362
0.8084 1.361
0.1090 0.5954
0.5624
0.4969 0.8049
0.4850 0.8175
0.6293 0.5470 9.252
Std. dev. o f diff. o f m e a n s , •d • [(5~ + 5 a ) / 5 ] t n
99.8: Cpm, Dp, Yvm _ 9 8 - - 9 9 . 8 : Cpa , Cvm , 0 9 5 - - 9 8 : Yva, ( d y / d x ) m , Ra, Ypa, o 95
- - 0.0497 0.6720 4.34
(dy/dx)m
Cvo
- - 2.780 2.417
- - 1.122 - - 2.092
0.7590
- - 2.965 2.229
Cx~n
Cpa
C~
Yva Co
Ym~
Ypa
0.0053 2.146
1.575 1.479 - - 86.9
a Ra Dp
Y~n
D_ifference o f means, Xb - - X a
Profile d e s c r i p t o r symbol L/5 d
- - 2.715 2.065 3.186
- - 3.439 1.776
- - 10.30 - - 3.514
1.349
- - 5.967 2.769
0.0109 2.625
2.503 2.704 - - 9.393
t s_tatistic (X b -- Xa)/~d
95--98 ~ 95 98--99.8
98--99.8 <: 95
:> 99.8 98--99.8
~ 95
> 99.8 95--98
~ 95 95--98
95--98 95--98 :> 99.8
Confidence %
8 12 6
5 13
1 4
14
3 7
15 10
11 9 2
Ranking
C o m p a r i s o n o f 15 profile d e s c r i p t o r s f r o m the glass ball and aggregate m o d e l s using raw d a t a ( u n f i l t e r e d ) . C o n f i d e n c e limits based o n 2-tail t-test w i t h 8 degrees o f f r e e d o m - - see t e x t f o r discussion
TABLE 3
b~
Std. dev. o f diff. o f m e a n s
0.5624
0.760
- - 3.16:1 2.897
- - 0.0273 0.577 4.213
C~m Cva
(dy/dx)m (_dy/dx )~ 0
4 d e s c r i p t o r s ~ 95
(dy/dx)ra
0.0060 0.3061 1.352
0.5497 1.154
S u m m a r y : 6 d e s c r i p t o r s ~> 99.8: Yvm, Dp, Cvm , Cpm , Ra, 4 d e s c r i p t o r s 9 8 - - 9 9 . 8 : ~ , Yvo, Cpa, a 1 d e s c r i p t o r 9 5 - - 9 8 : Cva
- - 1.295 - - 2.378
Cpa
Cpm
0.2453 0.8051
0.3591 0.6205
- - 2.851 1.842
Yvo Ca
Yvm
0.3192 0.6261
0.4020 0.2356 12.47
(~d ---- [((~1~ -~- (~a2)/5] 1/2
0.607 1.414
1.180 1.082 - - 89.44
-~b --'~a
Difference of means
Ypm Ypa
a Ra Dp
Profile d e s c r i p t o r symbol
-- 4.550 1.885 3.116
- - 5.751 2.511
- - 5.279 - - 2.953
1.351
-- 7.940 2.968
1.901 2.258
2.935 4.592 - - 7.166
(ZYb - - 2 a ) ] ~ d
t statistic
> 99.8 < 95 98--99.8
> 99.8 95--98
> 99.8 98--99.8
< 95
> 99.8 98--99.8
< 95 < 95
98--99.8 > 99.8 > 99.8
%
Confidence
6 14 7
3 11
4 9
15
1 8
13 12
10 5 2
Ranking
C o m p a r i s o n o f 15 profile d e s c r i p t o r s f r o m the glass ball and aggregate m o d e l s using 18 m m high pass filtered data. C o n f i d e n c e limits based o n 2 tail t-test w i t h 8 degrees o f f r e e d o m - - see t e x t for discussion
TABLE 4
bO O~
268
Filtered data The filtering m e t h o d uses a moving-average technique which calculates the mean of the profile over a window of half the filter length each side of each x position. A cubic spline is interpolated through each calculated mean value to give a curve which represents the low pass filtered data. The high pass filtered data is then the raw data minus the low pass filtered data. In other words, the high pass filtered data has the longer wavelength (low frequency) height variations flattened out, referring its heights to a mean line which is in fact the low pass filtered data, (e.g. see Fig. 3). 18ram high pass filter. A length of 1 8 m m was chosen for the filter as this was the known diameter of the glass balls. By using this length of filter, it was hoped that elimination of the long-wavelength effects would enhance the differences between the model surfaces at the scale of the average particle size. Curvatures are not greatly affected by the filter although slopes and heights {especially valley heights) are affected considerably, see Figs. 3 and 4. The filtered ordinates were analysed using the same procedure as for the raw data. A comparison of the t test results in Table 4 with those in Table 3 shows that after filtering there are 6 descriptors rather than 3 which attain a confidence level of > 99.8%. These 6 descriptors appear to show up those differences between the two models' surfaces which are especially due to particle shape and texture. 3.2 m m low pass filter. With a sampling interval of 0.8 mm, a filter length of 3.2 mm is the shortest available for computation. Elimination of the very
I~ I
I
i~
24~
360
i
I I
48o
Fig. 5. Unfiltered and 3 . 2 m m filtered data f r o m profile R G B I P 5 of the glass sphere model. T o p : unfiltered profile with the effect of 3 . 2 m m high pass filtering shown superimposed. B o t t o m : the fine detail s m o o t h i n g effect of 3.2 m m low pass filtering.
269
0
i
,z0
,0
2~0
~\
'~(~ml ~ I'~
Fig. 6. Unfiltered and 3.2 m m filtered data from profile R A G I P 1 of the aggregate model. See Fig. 5 caption.
short wavelength effects virtually equalizes the peak density from the two models. The fine asperities in the aggregate model are removed while sharp peaks and valleys become less sharp, see Figs. 5 and 6. This filter enhances the differences in general form between the two surfaces. Table 5 indicates 2 descriptors that are perhaps worthy of special mention with confidence levels of 99.8% and which did n o t feature at this level in either the unfiltered or high pass filtered results. The mean absolute slope, O, is significantly higher in the surface generated from rounder particles. What is more surprising is that the mean peak height, Ypm, totally insignificant as a descriptor in the unfiltered and high pass filtered analysis, is now highly significant. DISCUSSION
There are a few important points with which the discussion should be prefaced. Although it may be of great importance to examine the set of ordinate height data that most closely resembles the true profile (i.e. the raw data), it must be appreciated that the sampling technique will have already included both long- and short-wavelength cut-offs within the raw data. The physical interpretation of profile analysis results must therefore incorporate some effects of filtering. Carefully selected filtering of the raw data, 'functional filtering', will be an additional tool for analysis. In this study it is possible that a bias has been introduced. The operator inaccuracy during digitizing of data from photographs tends to be biased so that particle profiles known to be smooth and rounded have fewer
- - 1.013 2.09
Y~m
- - 0.3940 0.3990
Cwn
Summary: 2 4 4 5
0
(dy/dx)m (_dy/dx)a
Cva
1.279
0.0074 0.1180
0.1221 0.2098
0.0749 0.1196
0.1053
0.4443 0.5817
0.2337 0.8228
0.6324 0.5267 7.220
~d --'--[(~l~ ~- ~2a)/511/2
Std. dev. o f diff. o f m e a n s
d e s c r i p t o r s > 99.8: 0-, Ypm d e s c r i p t o r s 9 8 - - 9 9 . 8 : ( d y / d x ) a , Yva, C~n, Cpm d e s c r i p t o r s 9 5 - - 9 8 : R a, Ca, ( d y / d x ) m , O d e s c r i p t o r s < 95
6.440
-0.0505 0.4980
- - 0.2321 - - 0.1061
Cpa
Cpm
Ca
Yva
0.2835
1.141 0.816
Ypa
Yp~n
1.535 1.428 -4.810
symbol
o Ra Dp
Difference of means
Zb -- Xa
Profile d e s c r i p t o r
5.036
- - 2.486 4.219
- - 3.227 1.902
- - 3.099 - - 0.8854
2.692
- - 2.280 3.593
4.882 0.9918
2.427 2.711 - - 0.6662
(Zb --Xa)/~d
t statistic
~ 99.8
95--98 98--99.8
98--99.8 < 95
98--99.8 < 95
95--98
~ 95 98--99.8
~ 99.8 < 95
95--98 95--98 <: 95
%
Confidence
1
9 3
5 12
6 14
8
11 4
2 13
10 7 15
Ranking
C o m p a r i s o n o f 15 profile d e s c r i p t o r s f r o m the glass ball a n d aggregate m o d e l s using 3.2 m m low pass f i l t e r e d data. C o n f i d e n c e limits based o n two-tail t t e s t w i t h 8 degrees o f f r e e d o m - - see t e x t f o r a discussion
TABLE 5
b~ Q
271
artificially introduced peaks than profiles of aggregate where the angular and spiked form is more random and unpredictable. This problem is unlikely to arise in future studies using automated image processing. In Table 3, the extremely high sensitivity indicated by the two parameters: mean peak curvature Cpm, and peak density Dp, to departure from sphericity of the surface's constituents, is a reassuring result. The mean peak curvature yields very useful information about the roundness/ angularity and even texture of the particles while also incorporating a function of average particle size. The peak density may be expected to yield a similar type of information (e.g. roundness etc.); however, the effect of average particle size (approximately equal in the two models) may prove to have a stronger influence generally on Dp than on Cpm. Further investigation will be necessary to determine under what circumstances Dp or Cpm is the best parameter for measuring particle roundness of the surface layer and what form of functional filtering, if any, is most appropriate. Speculation upon which set of descriptors is most likely to correlate with hydraulic stability, one of the long-term objectives of this research, is not instructive at this stage. It is not even known which of the two models has the more hydraulically stable surface. Nevertheless, it is satisfying to note that with the aid of functional filtering eight of the fifteen descriptors could discriminate between the glass ball and the aggregate models (where grain size differences were probably minimal) with only 5 samples from each, at a confidence level of better than 99.8%. It seems reasonable to suggest that subtle differences in surface geometry that are indicative of significant differences in hydraulic stability could be determined perhaps using a weighted combination of several descriptors. POSSIBLE P R A C T I C A L A P P L I C A T I O N S
Given that the field equipment and procedure for surveying breakwater profiles is developed and tested, a thoroughly statistical and objective method for monitoring the breakwater is available. Analysis of the profiles may be carried out at regular intervals and/or after severe storms during the life-time of a breakwater. On completion of the construction, quality control for block sizes and shapes could probably be checked using roughness descriptors. Having calibrated roughness descriptors from laboratory models it may be possible to assess placement technique for different packing (or compaction) of a given regular shape. Of geotechnical importance, the extent of subsidence and armour compaction could be rapidly assessed. Low pass filtering techniques could be useful in detecting areas of maximum subsidence, not noticeable from visual inspection. Topographic profiles sampled from the AC plane, with or without low
272
pass filtering can be used to give the type of profile data that is required in the powerful damage assessment technique used by van der Meer and Pilarczyk {1984). Furthermore, techniques for damage assessment and monitoring of movement and displacement of blocks for both models and p r o t o t y p e breakwaters would clearly benefit from an additional standardized technique which in principle can be applied to both p r o t o t y p e s and models identically. The rate of degradation and weight loss of breakwater armourstone by rounding could be assessed using descriptors such as peak curvature. The {rate of) change of certain descriptors might be used to define a {rate of) damage occurring to a breakwater. Several descriptors will be highly sensitive to an increase in the number of 'missing' or 'sub-sized' blocks, parameters used in the damage assessment criterion of Poole et al. (1984). In the laboratory, it is hoped that wave flume experiments, in which the surf similarity coefficient, ~, is accounted for in the determination of the stability factor, would show a correlation between certain roughness descriptors, block shape and the hydraulic stability and also the degree of run-up and run-down. Careful interpretation of roughness descriptor values as models approach failure could lead to insights into the symptoms of failure. The profile measurements would supplement or possibly replace the need to make block displacement measurements for damage assessment. For example, a precisely located AC, BC or BD profile plane could be monitored by topographic profile sampling at successive stages during a flume experiment or on a full size structure. Profile subtraction (preferably carried o u t by image processing) would yield an area measure of block movement and thus a highly sensitive objective measure of damage. Apart from direct application to breakwater armourstone research, there is a great benefit to be gained for the gravel and aggregate industry from being able to translate roughness descriptor information {e.g. from heaps of aggregate) into estimates concerning average particle sizes and shapes w i t h o u t need for sieving etc. ACKNOWLEDGEMENTS
Without the cooperation given by Dr. R.S. Sayles and the Meteorology Group at the Department of Mechanical Engineering, Imperial College, this research initiative could n o t have been pursued with such rapid progress. This research is funded by the S.E.R.C. Reference GR/C/00832. REFERENCES Ahrens, J.P., 1975. Large wave tank tests of rip-rap stability. TM°576, U.S. Army Corps of Engineers (USCE), Coastal Engineering Research Centre, (CERC), F o r t Belvoir, Va. Allsop, N.W.H., Bradbury, A.P., Poole, A.B., Dibb, T.E. and Hughes, D.W., 1985. Rock durability in the marine environment. Hydraulics Research Wallingford, Report S R l l .
273 Barends, B.J., Kogel, H., van der Uijttewall, F.J. and Hagenaar, J., 1983. West-Breakwater Sines, dynamic-geotechnical stability of breakwaters, Coastal Structures '83, Printed by the ASCE. Bergh, H., 1984. Riprap protection of a road embankment exposed to waves. Bull. No. TRITA-VBI-123, Hydraulics Laboratory, Royal Institute of Technology, Sweden. Bruun, P. and Giinbak, A.R., 1976. New design principles for rubble m o u n d structures, Proc. 15th Int. Conf. Coastal Eng., Honolulu, ASCE, pp. 2429--2473. Bruun, P. and Johannesson, P., 1976. Parameters affecting the stability of rubble mounds. J. Water, Harbors Coastal Eng. Div., ASCE, 102 (WW2): 141--164. Bruun, P., 1985. Discussion of "Rubble-mound breakwaters of composite slopes, by E. Naheer and V. Buslov". Coastal Eng., 9: 189--191. Giinbak, A.R., 1976. The stability of rubble mound breakwaters in relation to wave breaking and run-down characteristics and to the ~ ~ tans T/~/~I number. Division of Port and Ocean Engineering Rep. No. 1/76, Technical University of Norway, Trondheim. Giinbak, A.R., 1979. Wave mechanics principles on the design of rubble m o u n d breakwaters. Proc. of the POAC '79 Conf., Trondheim, Norway. Hudson, R.Y., 1959. Laboratory investigations of rubble-mound breakwaters. Proc. ASCE, J. Waterways Harbour Div., 85 (WW3). Losada, M.A. and Gimenez-Curto, L.A., 1979. The joint effect of wave height and period on the stability of rubble mound breakwaters using Iribarren's Number. Coastal Engineering, 3: 77--96. Meer, J.W. van der, and Pilarczyk, K.W., 1984. Stability of rubble mound slopes under random wave attack. Delft Hydraulics Laboratory, Publ No. 332. Naheer, E. and Buslov, V., 1983. On rubble-mound breakwaters of composite slope. Coastal Eng., 7 : 253--270. PIANC, 1976. Final report of the International Commission for the Study of Waves, Bulletin No 36, Vol II. Poole, A.B., Fookes, P.G., Dibb, T.E. and Hughes, D.W., 1984. Durability of rock in breakwaters. Proc. Conf. organized by the Institution of Civil Engineers, London, 4--6 May 1983, pp. 31--42. Sawaragi, T., Ryu, C. and Iwata, K., 1983. Consideration of the destruction mechanism of rubble m o u n d breakwaters due to the resonance phenomenon. 8th International Harbour Congress, Antwerp, Belgium. Sayles, R.S., 1976. The topography of surfaces. Ph.D. Thesis, Teeside Polytechnic, U.K. Thomas, T.R. (Editor), 1982. Rough Surfaces. Longman Inc., New York, N.Y., pp. 261.
253
THE QUANTIFICATION OF BREAKWATER ARMOUR PROFILES FOR DESIGN PURPOSES
J.P. LATHAM and A.B. POOLE
Centre for Applied Earth Science Research, Queen Mary College, London E1 4NS, U.K. (Received October 8, 1985; revised and accepted February 25, 1986)
ABSTRACT Latham, J.P. and Poole, A.B., 1986. The quantification of breakwater armour profiles for design purposes. Coastal Eng., 10: 253--273. A new approach for the evaluation of block shape effects in both artificial and rock armour layers is proposed. Topographic profiles based on high-resolution sampling frequencies of between 10 and 20 heights per nominal armour block width are considered. Model surfaces of (a) glass spheres and (b) rock aggregate, were prepared and examined by topographic profile sampling. A preliminary set of 15 statistical parameters or roughness descriptors were evaluated for each of 10 sets of profile height data. A statistical comparison between the surfaces of models (a) and (b) indicates the potential of roughness descriptors such as mean peak curvature and peak density to discriminate between surfaces generated from blocks of different shapes. Filtering of height data for discrimination enhancement is also illustrated. Nomenclature is introduced to distinguish the planar orientations of the principal profiles of the breakwater: the AC plane cross-cuts the long axis and is the plane observed in the well known studies of S-shaped profiles; the BC and BD planes parallel the axis and are the planes proposed for analysis. It is argued that the new monitoring method of topographic profile sampling and roughness descriptor analysis provides a promising additional means of assessing the relationship between block shape and hydraulic stability for model and prototype armour layers. The importance of further development and testing of these techniques for the quantitative evaluation of surface geometry is stressed in view of the many possible future applications of these methods.
INTRODUCTION
The success o f a rubble m o u n d breakwater will depend on the efficiency o f that structure to convert the energy o f incident waves into a harmless form, t h r o u g h o u t its design life. In general terms, the funct i on of the artificial or natural rock a r m o u r unit layer is to p r o m o t e dissipation of wave energy b y generating turbulence between the blocks whilst protecting the relatively weak core of the structure. In order t h a t the arm our blocks
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254 perform this function, they must remain hydraulically and structurally stable to the extent that they continue to serve as protection against the predicted storm and wave climate characteristics of the breakwater site, by virtue of their b o d y weight and interlocking properties. In simplistic terms, the design engineer therefore seeks a relationship between the size of armour blocks, the slope of the seaward face of the structure, the wave climate characteristics and the amount of damage that will occur. There may also be a range of possible block shapes and materials for the designer to consider. These will introduce additional important variables into the already complex relationship. The block shape or material property dependent bulk parameters of the armour layer such as macroporosity, interlock, skin friction, abrasion resistance for example, may take corresponding ranges of values, each with a different functional relationship to stability. The hydraulic importance of the macro-roughness and permeability of the armour layer has received somewhat greater study in relation to runup and run-down than to stability itself. Losada and Gimenez-Curto (1979} and Giinbak (1979) have used various sources of experimental data on runup (for example Ahrens, 1975 and Giinbak, 1976) to fit nonlinear relationships between run-up and the Iribarren (or surf similarity) coefficient, ~. These relationships involve two constants A and B which are different for each type of armour unit; an obvious influence from these studies being that A and B depend fundamentally upon the geometric form of the roughness and the permeability created by the armour units. Losada and Gimenez-Curto (1979) performed a similar (exponential) curve-fitting procedure on several sets of data for armour stability. They obtained another two constants, again different for each type of unit, which give the relationship between a stability coefficient, the seaward slope and the surf similarity coefficient. Roughness, interlock and permeability are generally recognised to be the most important factors excluded from such relationships and these omissions are probably because of the lack of appropriate parameters. However, some roughness parameters have been used in relation to rubble m o u n d materials. One empirical roughness parameter is the "run-up reduction relative to smooth slopes" (PIANC, 1976) which exhibits sensitivity to the type of breaker (i.e. G-value) and this obscures the independent role of the geometric roughness. Bruun and Johannesson (1976) implicitly recognising the importance of roughness and interlock used the angle of repose to evaluate interlayer friction between different sizes of crushed quartzite. They attempted with partial success to relate the significance of these static conditions to failure conditions in the wave flume. The angle of internal friction used in geotechnical analyses of slip surfaces (e.g. Barends et al., 1983) includes yet another empirical parameter for the influence o f porosity, smoothness, roundness and rock type. A highly damaging and unstable resonance condition was identified by
255 Bruun and Giinbak (1976). Sawaragi et al. (1983) have further investigated this condition which occurs when wave period and r u n - u p / r u n - d o w n period are repeatedly synchronized. They proposed limiting conditions for a "dimensionless roughness height" and a "void ratio of the surface" which when combined with the resonance condition for smoother slopes (2 ~ 3) would give the most dangerous conditions for permeable rough slopes. All these indications from the research c o m m u n i t y point towards an important role for such geometric parameters in future hydrodynamic investigations of breakwater stability. Seeking to simplify the complexity of the real situation, designers have often applied the well known Hudson equation (Hudson, 1959) and have used the stability coefficient K D which is primarily intended to account for block shape effects determined from physical model experiments. The interpretation o f such KD results without making corrections for the important influence of wave period and breaker type is now recognised to have severe shortcomings. K D values of 3.2 for natural stone and 9.5 for tetrapods were reported in Hudson's original study for conditions of no damage and no overtopping. The experimental determination of these K D values and other similar stability coefficients yields little information about the physical processes that lead to enhanced stability. The relative importance of void ratio and interlock in controlling the stability of dolosse or tetrapod armour layers for example, has not been evaluated. Not until it is possible to relate hydraulically and structurally sensitive geometric parameters of the armour layer pack of blocks to the fine and gross scale shapes of individual blocks will it become possible to select or design individual block shapes on all but the most generalized systematic lines. A preliminary search for just such sensitive parameters is the subject of this paper where we introduce the concept of profile roughness descriptors. The complementary study of shape descriptors is the subject of ongoing research. In contrast to the situation with artificial unit armour layers, the relative importance of the influence of block shape on the stability of natural rock armour layers is by no means clear. From an extensive series of model tests using random wave attack, van der Meer and Pilarczyk (1984) have set o u t new empirically derived practical design formulae. However, rubble shape was n o t a test variable and an assumption implicit in these design formulae is that typical shape variations from different sources of rip-rap have an insignificant effect upon stability. Wave period, number of waves and permeability of the core were found to be highly significant whereas armour grading, spectrum shape and groupiness of waves were not. Bergh (1984) has investigated rip-rap block shape in flume tests using roughly cubic blocks of granite and slate, flat slabs of slate and rounded glacier boulders but using an impermeable core in his models. Bergh's tests also confirmed a lack of sensitivity to grading of armour blocks. However, his result that flat slates gave zero damage wave heights of 20% less and rounded boulders 40% less than for cubic slates was significant. This would imply a 100%
256 increase in the required weight for the flatter slate and that in-service rounding of rocks, if rapid, could result in a serious reduction in stability. Anticipating the potential importance of in-service block degradation and shape modification regardless of the importance of the initial block shape, preliminary methods for the assessment of armour block shapes and statistical properties of the armour layer surface were investigated by Allsop et al. {1985). They suggest a set of damage assessment criteria on the basis of field data collected from breakwaters of known ages. The required data uses subjectively assessed quantities such as the number of sub-sized, unstable, fractured and missing blocks. Geometric properties such as block size, roundness, interlock and void ratio were also measured and their results have improved our understanding of the ageing process. Unfortunately, these measurements all require a very large investment of human energy in proportion to the a m o u n t of useful field data yielded. The data retrieved by photography was relatively unsystematic. This approach for the acquisition and assessment of shape data is therefore in need of review. TOPOGRAPHIC PROFILES FROM BREAKWATERS The term surface has a sufficiently obvious meaning for the present purpose although the particulate form of the armour layer requires that a precise definition be introduced when considering profiles. We now propose the following working hypothesis. The spatial form of the surface (i.e. its overall roughness characteristics) is largely a function of {a) the initial shape and statistical distribution of shapes and sizes of blocks prior to construction and (b) the history of their m o t i o n and deformation in response to forces applied from the time of construction to the time of observation. The information residing in this surface and how it responds to wave action is of course the source of all breakwater performance or damage assessment criteria. One obvious m e t h o d of extracting from this surface a set of meaningful quantitative parameters for use in design equations is the use of photographic techniques. However, because blocks overlap and obscure each other in photographs, objective quantitative data is difficult to obtain so that the derivation of bulk statistical parameters from imaging of individual blocks is fraught with difficulties, particularly from field surveys. However, we can define a set of data which can be directly measured mechanically and possibly by remote techniques such as photogrammetry or sonar devices. Within a chosen reference plane the breakwater's topographic profile is the profile obtained by plotting the coordinate positions of the highest solid/fiuid interface. Embayments or reentrants caused by overhangs are represented by 90 ° or high-angle slopes relative to a horizontal reference direction. Over the straight part of a breakwater the four reference directions
257 are: A width; B length; C vertical; D normal to mean seaward slope. The most useful reference planes for inspection are then the AC, BC and BD planes. The spatial configuration is shown in Fig. 1. The AC plane has of course been chosen for topographic profile examination by many researchers interested in the natural development and design of S-shap~:J profiles (see references cited by Bruun, 1985 and the work of Naheer and Buslov, 1983). In these studies, mapped profiles of both models and prototypes formed smoothed outlines due to sparsely sampled or imprecise height determinations. Van der Meer and Pilarczyk (1984), sampling 9 sections parallel to the AC plane for each model have recorded the heights of blocks at a sampling interval roughly equal to the nominal diameter of individual blocks. The smoothed S-shaped profiles obtained after cumulative wave attack were used to compute a statistically averaged measure of damage by considering certain 'areas' of material removed. This paper is concerned with detailed statistical techniques applied to highly resolved height data from any chosen reference plane.
~
~
~f'~
/
i
..s~-... Ac
Fig. 1. Topographic profile configuration of a breakwater. In the fields of research concerned with the mechanical properties of sliding contacting surfaces, known as tribology, the statistical description of machined (metal) surfaces has become highly sophisticated. See for example the b o o k 'Rough Surfaces' edited by Thomas (1982) The roughness can be described by a large number of statistical parameters which are loosely termed roughness descriptors. Given a sufficient data set of (x, y) co-ordinates of the profiles sampled, a set of descriptors may be c o m p u t e d which can distinguish between surfaces prepared by different machines, the degree to which they have been worn and their likely performance as bearing surfaces. Naturally, the amplitudes of roughness and the slopes of the asperities on both the model and p r o t o t y p e breakwater, are vastly different from those on machined metal surfaces. However, the same kind of statistical approach can be used to investigate hydraulic and
258
structural properties of the breakwater armour layers using roughness descriptors from the BC or BD and AC planes. In addition to the use of roughness descriptors in refining the initial breakwater design equations -- a long-term objective -- there is general agreement on the need for monitoring and assessment of long-term changes (e.g. over several years} and immediate storm-induced changes in the spatial distribution of armour blocks and in the block shapes themselves. Damage assessment obtained from sampling of topographic profiles would n o t necessarily require exact relocation surveying of the profile, merely a statistically valid sampling procedure which can be determined using laboratory models. Compaction of newly placed blocks will presumably correlate well with descriptors relating to roughness amplitudes or peak to valley height. Some national roughness standards also recognise a void coefficient and a similar type of coefficient to this might prove useful as a descriptor for monitoring specific hydraulic properties. Changes in shape of armourstone blocks occur in response to abrasion, dissolution and spalling, and crack propagation {Poole et al., 1984). The gradual removal of material from the armour layer, particularly in the intertidal zones, leaves behind armourstone which is progressively rounded with age. The rounding process will be particularly well monitored by descriptors such as peak curvature. By sampling topographic profiles across model particle packs (i.e. aggregates) of known average shape descriptors, roughness descriptors (e.g. peak density or average peak curvature) could be calibrated as measures of average roundness and therefore yield information on weight loss and loss rates. Block size is another important design parameter which, with the help of laboratory model work, could be described by an appropriate profile descriptor such as an average wavelength, or a correlation function. Points (a) and (b) from the above hypothesis immediately suggest several related research objectives which could provide an evaluation of presently speculative but promising new profiling t~chniques. METHOD E V A L U A T I O N USING MODELS
Before turning to wave flumes and models in search of descriptors that are sensitive to hydraulic stability, it is necessary to establish some familiarity with the suite of statistical parameters and their sensitivity to predetermined differences in surface topography. For this purpose, a glass ball model and an aggregate model were constructed. If the sampled value of a particular roughness descriptor can be just as easily assigned to the glass ball surface as to the aggregate surface, then that descriptor is unlikely to be of further practical value. In other words, the preliminary studies outlined here are required to establish the sensitivity of the various descriptors to changes in profile shape while accommodating the inevitable statistical variation associated with the profile.
259
Construction o f the laboratory models Glass balls A large quantity (1000) of spherical glass balls with equal diameters of 1 7 . 8 m m was used in the construction of the model. To provide an adhesive solution of relatively low viscosity, 1 part Butvar B98 powder (polyvinyl butyral) was dissolved in 3 parts methylated spirit (by bulk volume). A trough measuring about 500 x 150 x 1 0 0 m m was prepared using a malleable wire mesh. The glass balls were thoroughly coated with a thin film of the adhesive solution and poured into the trough. The trough was suspended to allow the adhesive solution to drain freely through the base of the model and to encourage rapid setting. No attempt was made to even o u t or 'flatten' the uppermost 'surface' of the balls and the well known regular packing geometries were deliberately inhibited from developing by the initial geometry imposed by the wire mesh at the base of the model. After 24 hours the entire model could be handled as a single rigid block until such time after analysis, when the model was broken up and the glass balls cleaned and recycled for further use. Aggregate The same procedure was used to make the aggregate model. However, it should be mentioned that the particle sizes of the aggregate were not sorted or measured for these preliminary experiments. Typically, the larger particles were of maximum and minimum dimensions of 40 and 15 mm, respectively, the great majority of particles having maximum and minimum dimensions between 30 and 10 mm. Very small grit particles were also present (unintentionally) on the model's surface. Data acquisition In these preliminary studies three precision carpenters profiling gauges were joined together to produce a linear profile gauge (length 4 6 0 m m ) of approximately 560 pins and pin diameter 0.8 mm. The gauge was clamped close to the model's surface with its axis approximately horizontal and its plane of pins vertical. Sampling of the profile topography required delicate manual contacting of each pin with the solid surface and the bonding of the particles of the model ensured that no particle movement occurred. Sampling of each model's surface was limited to 5 successive parallel profiles taken at 25-mm intervals. Photographs were taken of the pin positions corresponding to each profile and these were printed at considerable enlargement to give an image of true scale. Each full scale print of the profile gauge was digitized using a microphone array digitizer. The sparker source was placed over the photograph and located (to within 0.5 mm) successively at the end of each pin. The X and Y coordinates were automatically recorded (to an accuracy of better than
260 0.2 mm) and input to a computer data file. Each photograph too about 25 minutes to digitize.
Computer data analysis The data files containing approximately 560 pairs of X and Y coordinates for each profile are reformatted so that Y coordinates (the ordinates or heights) are held as integers and a regular X-interval is assumed. The data analysis is based on the program TPROFK, written by Dr. R.S. Sayles (1976) which has provided the vehicle for numerous research programmes and industrial applications in the field of tribology. In this study, the analysis of rough surface geometry, normally concerned with machined metal or fractured surfaces with irregularity amplitudes of several microns, has been applied to millimetre scale features with much steeper slopes. The full scope afforded by the range of analyses contained in TPROFK has yet to be explored. Some of the most important profile parameters have been chosen for investigation in this study and are described below. PROFILE
ANALYSIS
Profile analysis terms Roughness A straight mean-line is fitted by least-squares regression to the ordinates (z-values). This has the result that the areas enclosed above and below the mean line are equal. If the mean line is subtracted from z, the residual, y, is the mean line referred ordinate (see Fig. 2). It is this latter value y, which is used in the analyses of the profile. The centre line average (CLA) roughness, Ra, is given by the equation: L
1 r Ra = - - |dl y l d x L 0
and the root mean square (RMS) roughness, o, by: L
o =
L
y2 dx 0
t
In terms of the surface height distribution p(y), the RMS roughness is the standard deviation or, the square root of the variance or second m o m e n t of p(y). For a surface with a normal (Gaussian) distribution of ordinates, a --~ 1.25Ra. Although the RMS roughness is probably the most fundamental profile
261
0
Fig. 2. The profile coordinates, mean-line and sampling length. parameter, it is clearly possible to have two profiles from entirely different surfaces, with identical values of a.
Feature density, peaks and valleys The zero-crossing density, Do, is the number of times the profile crosses the mean-line per unit length. The profile peak density, Dp, is the number of peaks per unit length. Peaks and valleys are defined by examining three consecutive ordinates. Peaks are defined as points higher than their two respective neighbours. Valleys are similarly defined as a minimum. Curvature The curvature, C, of a valley or peak is defined using three consecutive ordinates as the negative of: y(i + 1) -- 2y(i) + y(i -- 1) (Ax) 2
(where ~ x is the sampling interval ~ 0.8 mm in this study), so that C > 0 for peaks and C < 0 for valleys.
8lope The slope, tan 0, is defined for any two consecutive ordinates as: tan0 =
y(i + 1) - - y ( i ) Ax
from which the mean absolute slope 0 in degrees can be computed.
Distribu tions From each profile, the distributions that are likely to contain important coded information and which have the simplest relationships to the surface geometry are the following: ordinates (y) peak curvature (Cp) peak ordinates (yp) valley curvature (Cv) valley ordinates (Yv) profile curvature (C) profile slope (tan0) For each profile sampled, any of the above distributions may be calculated
262
yielding four statistical parameters: the mean, standard deviation, skewness and kurtosis of the distribution.
Analytical results For the purposes of this exploratory study ten profiles were investigated, five from the glass bail model and five from the angular aggregate model. Typical profiles of each model are illustrated in Figs. 3 and 4. Tables 1 and 2 show a selection of fifteen statistically derived profile parameters (the profile descriptors of this study). The values of the descriptors vary considerably from one profile to the next for certain descriptors, see for example the mean peak height Yp~ in either of the models. Other descriptors such as profile peak density Dp are apparently more consistent. Bearing in mind the limitations of deriving statistics from five samples, for each descriptor, the mean and standard deviation of the mean has also been tabulated. It seemed reasonable to require that the mean value of any descriptor obtained from the glass ball model should be significantly different from that of the aggregate model, if there is to be any scope for that parameter as a profile descriptor. The simplest way to gain a measure of the significance in the difference in means of any one descriptor is to calculate the standard deviation of the difference of the means, and then to use a test such as Student's t test to obtain confidence limits. This procedure can be criticised
,,
i' ,~ ,,~
. 'i
"
!/!
~,
:
i,
=
/tJ'
t
!L L
,,! i:
I
"4
q:
LO
! HOpIZONrA~
[),~,T~1,%'C~
f IO'C
b,%,T ~)
~o'M'~
J
Fig. 3. Unfiltered and 18ram filtered data from profile RGB1P5 of the glass sphere model. Top: unfiltered profile with the gross smoothing effect of the 18ram low pass filtering shown superimposed. Bottom: effect of 18 mm high pass filtering giving a broad leveling of the profile.
263 zD 1
o
120
Z40
HORIZONTAL
D/STANCE
~60
(/~0
4e0
UIVIT5
=
80,'WM)
Fig. 4. Unfiltered and 18 mm filtered data from profile RAG1P1 of the aggregate model. See Fig. 3 caption.
on a number of grounds when it is applied to the sampling in this study. For example, it is n o t known whether for each descriptor, the five profiles give five values each of which has been taken from a normally distributed population -- a requirement of the t test's applicability. In Table 3, the t statistic is given for each of the descriptors. The confidence limits are calculated for eight degrees of freedom and the two-tail test is assumed to apply (which will give conservative confidence limits in most cases). A null hypothesis stating that there is no difference between the mean values of a descriptor for the glass ball surface and the aggregate surface can be rejected at different levels of confidence depending upon t. Thus t is a standardized measure of the difference in the sample means. Consider for example, peak density Dp (see Table 3). The difference in means that were sampled is 86.9. This a m o u n t of deviation is 9.4 times the expected deviation of 9.25, had there in fact been no difference in the means of the peak density. A table showing critical values of t for the Student's t distribution, at a significance level of 5% gives t = 2.31. It may be expected t h a t the difference in means will be up to but not exceeding 2.31 times its standard deviation in 95% of cases. In Table 3, 11 of the 15 descriptors have differences which do exceed 2.31 times their standard deviation and rejection of the null hypothesis at 95% confidence may be applied to all 11 of these descriptors. Rejection is at 98% confidence for t = 2.90 and 99.8% confidence for t = 4.50. The descriptors in Table 3 have been ranked according to their t value as well as grouped into confidence intervals. The mean peak curvature and peak density are predictably the most powerful of all the descriptors.
o Ra Dp
Ypm
RMS r o u g h n e s s CLA roughness Peak d e n s i t y
Mean peak height Std. dev. p e a k h e i g h t
C~¢n
Mean peak curvature Std. dev. p e a k c u r v a t u r e
Mean slope Std. dev. slope Mean a b s o l u t e slope
-- 0.0418 3.469 55.93
(dy/dx)m (_.dy/dx) a
0
Cva
-- 5.887 10.85
0.8426 1.624
5.756
-- 3.988 9.537
1.690 8.242
Cwn
Cpa
Ca
Std. dev. c u r v a t u r e
M e a n valley c u r v a t u r e Std. dev. valley c u r v a t u r e
Yva
Y~n
M e a n valley h e i g h t Std. dev. valley h e i g h t
Ypa
GBIP1
Symbol
Name 8.374 6.948 126.1
Profile n a m e
Profile d e s c r i p t o r
-- 0.0358 3.792 58.76
-7.096 8.973
0.6316 0.4982
5.829
-- 5.747 10.18
1.754 8.314
8.594 6.943 105.9
GBIP2
-- 0.0381 4.388 59.75
-- 9.523 11.73
0.9428 1.447
7.347
-- 6.596 11.56
-- 0.4563 11.24
10.17 8.561 136.3
GB1P3
Glass ball m o d e l . A n a l y s i s o f r a w d a t a ( u n f i l t e r e d ) f o r 15 p r o f i l e d e s c r i p t o r s
TABLE 1
-- 0.0250 2.823 54.07
5.814
-- 6.034
0.6696 0.6368
4.278
-- 5.411 7.890
0.7294 8.247
8.288 6.737 110.4
GBIP4
-- 0.0291 3.240 54.99
-- 5.124 6.056
0.8073 0.6131
5.077
-- 5.673 8.428
0.3053 8.569
8.200 6.545 121.6
GBIP5
-- 0.0340 3.542 56.70
-- 6.733 8.684
0.7788 0.9638
5.657
-- 5.485 9.519
0.5671 8.922
8.725 7.147 120.1
Mean
0.0068 0.5899 2.448
1.711 2.702
0.1278 0.5282
1.133
0.9427 1.453
0.8950 1.302
0.8208 0.8079 12.21
5b
Std. Dev.
C~m Cpa
C~,m Cva
(dy/dx) m (dy/dx) a ~
Mean valley curvature Std. dev. valley curvature
Mean slope Std. dev. slope Mean absolute slope
Yvm Yva
Mean valley h e i g h t Std. dev. valley h e i g h t
Ca
Ypm Ypa
Mean peak h e i g h t Std. dev. peak h e i g h t
Std. dev. curvature
o Ra Dp
RMS roughness CLA r o u g h n e s s Peak d e n s i t y
Mean peak curvature Std. dev. peak curvature
AGIP1
Symbol
Name
0.0163 2.777 50.18
- - 4.141 7.406
1.685 2.455
4.758
- - 3.277 8.090
-- 0.1428 7.857
7.695 6.341 186.9
Profile n a m e
Profile d e s c r i p t o r
0.0033 3.321 54.59
- - 4.252 7.002
1.886 2.826
5.495
- - 2.493 7.968
1.020 7.020
7.921 6.320 191.4
AGIP2
0.0373 2.265 51.01
- - 3.032 4.266
1.872 2.281
4.223
- - 2.717 5.975
0.0987 5.792
6.073 4.743 214.0
AGIP3
Aggregate m o d e l . Analysis o f raw data ( u n f i l t e r e d ) for 15 profile d e s c r i p t o r s
TABLE 2
-
2.244 5.028
5.417
1.663 6.297
0.0159 3.237 53.62
- - 4.552 7.332
-
1.321 5.134
5.775 4.585 223.0
AGIP4
0.0059 2.751 52.42
- - 3.789 5.329
1.818 2.690
4.595
- - 2.452 8.122
0.5121 8.076
8.285 6.351 219.8
AGIP5
0.0157 2.870 52.36
- - 3.953 6.267
1.901 3.056
4.898
- - 2.520 7.290
0.5618 6.776
7.150 5.668 207.0
Mean
0.0134 0.4263 1.812
0.5828 1.401
0.2075 1.122
0.5461
0.5813 1.062
0.6123 1.283
1.143 0.9183 16.70
5a
Std. dev.
b~ Ob
descriptors ~ descriptors descriptors descriptors ~
Summary : 3 3 5 4
0
(_dy/dx)a
0.0067 0.3255 1.362
0.8084 1.361
0.1090 0.5954
0.5624
0.4969 0.8049
0.4850 0.8175
0.6293 0.5470 9.252
Std. dev. o f diff. o f m e a n s , •d • [(5~ + 5 a ) / 5 ] t n
99.8: Cpm, Dp, Yvm _ 9 8 - - 9 9 . 8 : Cpa , Cvm , 0 9 5 - - 9 8 : Yva, ( d y / d x ) m , Ra, Ypa, o 95
- - 0.0497 0.6720 4.34
(dy/dx)m
Cvo
- - 2.780 2.417
- - 1.122 - - 2.092
0.7590
- - 2.965 2.229
Cx~n
Cpa
C~
Yva Co
Ym~
Ypa
0.0053 2.146
1.575 1.479 - - 86.9
a Ra Dp
Y~n
D_ifference o f means, Xb - - X a
Profile d e s c r i p t o r symbol L/5 d
- - 2.715 2.065 3.186
- - 3.439 1.776
- - 10.30 - - 3.514
1.349
- - 5.967 2.769
0.0109 2.625
2.503 2.704 - - 9.393
t s_tatistic (X b -- Xa)/~d
95--98 ~ 95 98--99.8
98--99.8 <: 95
:> 99.8 98--99.8
~ 95
> 99.8 95--98
~ 95 95--98
95--98 95--98 :> 99.8
Confidence %
8 12 6
5 13
1 4
14
3 7
15 10
11 9 2
Ranking
C o m p a r i s o n o f 15 profile d e s c r i p t o r s f r o m the glass ball and aggregate m o d e l s using raw d a t a ( u n f i l t e r e d ) . C o n f i d e n c e limits based o n 2-tail t-test w i t h 8 degrees o f f r e e d o m - - see t e x t f o r discussion
TABLE 3
b~
Std. dev. o f diff. o f m e a n s
0.5624
0.760
- - 3.16:1 2.897
- - 0.0273 0.577 4.213
C~m Cva
(dy/dx)m (_dy/dx )~ 0
4 d e s c r i p t o r s ~ 95
(dy/dx)ra
0.0060 0.3061 1.352
0.5497 1.154
S u m m a r y : 6 d e s c r i p t o r s ~> 99.8: Yvm, Dp, Cvm , Cpm , Ra, 4 d e s c r i p t o r s 9 8 - - 9 9 . 8 : ~ , Yvo, Cpa, a 1 d e s c r i p t o r 9 5 - - 9 8 : Cva
- - 1.295 - - 2.378
Cpa
Cpm
0.2453 0.8051
0.3591 0.6205
- - 2.851 1.842
Yvo Ca
Yvm
0.3192 0.6261
0.4020 0.2356 12.47
(~d ---- [((~1~ -~- (~a2)/5] 1/2
0.607 1.414
1.180 1.082 - - 89.44
-~b --'~a
Difference of means
Ypm Ypa
a Ra Dp
Profile d e s c r i p t o r symbol
-- 4.550 1.885 3.116
- - 5.751 2.511
- - 5.279 - - 2.953
1.351
-- 7.940 2.968
1.901 2.258
2.935 4.592 - - 7.166
(ZYb - - 2 a ) ] ~ d
t statistic
> 99.8 < 95 98--99.8
> 99.8 95--98
> 99.8 98--99.8
< 95
> 99.8 98--99.8
< 95 < 95
98--99.8 > 99.8 > 99.8
%
Confidence
6 14 7
3 11
4 9
15
1 8
13 12
10 5 2
Ranking
C o m p a r i s o n o f 15 profile d e s c r i p t o r s f r o m the glass ball and aggregate m o d e l s using 18 m m high pass filtered data. C o n f i d e n c e limits based o n 2 tail t-test w i t h 8 degrees o f f r e e d o m - - see t e x t for discussion
TABLE 4
bO O~
268
Filtered data The filtering m e t h o d uses a moving-average technique which calculates the mean of the profile over a window of half the filter length each side of each x position. A cubic spline is interpolated through each calculated mean value to give a curve which represents the low pass filtered data. The high pass filtered data is then the raw data minus the low pass filtered data. In other words, the high pass filtered data has the longer wavelength (low frequency) height variations flattened out, referring its heights to a mean line which is in fact the low pass filtered data, (e.g. see Fig. 3). 18ram high pass filter. A length of 1 8 m m was chosen for the filter as this was the known diameter of the glass balls. By using this length of filter, it was hoped that elimination of the long-wavelength effects would enhance the differences between the model surfaces at the scale of the average particle size. Curvatures are not greatly affected by the filter although slopes and heights {especially valley heights) are affected considerably, see Figs. 3 and 4. The filtered ordinates were analysed using the same procedure as for the raw data. A comparison of the t test results in Table 4 with those in Table 3 shows that after filtering there are 6 descriptors rather than 3 which attain a confidence level of > 99.8%. These 6 descriptors appear to show up those differences between the two models' surfaces which are especially due to particle shape and texture. 3.2 m m low pass filter. With a sampling interval of 0.8 mm, a filter length of 3.2 mm is the shortest available for computation. Elimination of the very
I~ I
I
i~
24~
360
i
I I
48o
Fig. 5. Unfiltered and 3 . 2 m m filtered data f r o m profile R G B I P 5 of the glass sphere model. T o p : unfiltered profile with the effect of 3 . 2 m m high pass filtering shown superimposed. B o t t o m : the fine detail s m o o t h i n g effect of 3.2 m m low pass filtering.
269
0
i
,z0
,0
2~0
~\
'~(~ml ~ I'~
Fig. 6. Unfiltered and 3.2 m m filtered data from profile R A G I P 1 of the aggregate model. See Fig. 5 caption.
short wavelength effects virtually equalizes the peak density from the two models. The fine asperities in the aggregate model are removed while sharp peaks and valleys become less sharp, see Figs. 5 and 6. This filter enhances the differences in general form between the two surfaces. Table 5 indicates 2 descriptors that are perhaps worthy of special mention with confidence levels of 99.8% and which did n o t feature at this level in either the unfiltered or high pass filtered results. The mean absolute slope, O, is significantly higher in the surface generated from rounder particles. What is more surprising is that the mean peak height, Ypm, totally insignificant as a descriptor in the unfiltered and high pass filtered analysis, is now highly significant. DISCUSSION
There are a few important points with which the discussion should be prefaced. Although it may be of great importance to examine the set of ordinate height data that most closely resembles the true profile (i.e. the raw data), it must be appreciated that the sampling technique will have already included both long- and short-wavelength cut-offs within the raw data. The physical interpretation of profile analysis results must therefore incorporate some effects of filtering. Carefully selected filtering of the raw data, 'functional filtering', will be an additional tool for analysis. In this study it is possible that a bias has been introduced. The operator inaccuracy during digitizing of data from photographs tends to be biased so that particle profiles known to be smooth and rounded have fewer
- - 1.013 2.09
Y~m
- - 0.3940 0.3990
Cwn
Summary: 2 4 4 5
0
(dy/dx)m (_dy/dx)a
Cva
1.279
0.0074 0.1180
0.1221 0.2098
0.0749 0.1196
0.1053
0.4443 0.5817
0.2337 0.8228
0.6324 0.5267 7.220
~d --'--[(~l~ ~- ~2a)/511/2
Std. dev. o f diff. o f m e a n s
d e s c r i p t o r s > 99.8: 0-, Ypm d e s c r i p t o r s 9 8 - - 9 9 . 8 : ( d y / d x ) a , Yva, C~n, Cpm d e s c r i p t o r s 9 5 - - 9 8 : R a, Ca, ( d y / d x ) m , O d e s c r i p t o r s < 95
6.440
-0.0505 0.4980
- - 0.2321 - - 0.1061
Cpa
Cpm
Ca
Yva
0.2835
1.141 0.816
Ypa
Yp~n
1.535 1.428 -4.810
symbol
o Ra Dp
Difference of means
Zb -- Xa
Profile d e s c r i p t o r
5.036
- - 2.486 4.219
- - 3.227 1.902
- - 3.099 - - 0.8854
2.692
- - 2.280 3.593
4.882 0.9918
2.427 2.711 - - 0.6662
(Zb --Xa)/~d
t statistic
~ 99.8
95--98 98--99.8
98--99.8 < 95
98--99.8 < 95
95--98
~ 95 98--99.8
~ 99.8 < 95
95--98 95--98 <: 95
%
Confidence
1
9 3
5 12
6 14
8
11 4
2 13
10 7 15
Ranking
C o m p a r i s o n o f 15 profile d e s c r i p t o r s f r o m the glass ball a n d aggregate m o d e l s using 3.2 m m low pass f i l t e r e d data. C o n f i d e n c e limits based o n two-tail t t e s t w i t h 8 degrees o f f r e e d o m - - see t e x t f o r a discussion
TABLE 5
b~ Q
271
artificially introduced peaks than profiles of aggregate where the angular and spiked form is more random and unpredictable. This problem is unlikely to arise in future studies using automated image processing. In Table 3, the extremely high sensitivity indicated by the two parameters: mean peak curvature Cpm, and peak density Dp, to departure from sphericity of the surface's constituents, is a reassuring result. The mean peak curvature yields very useful information about the roundness/ angularity and even texture of the particles while also incorporating a function of average particle size. The peak density may be expected to yield a similar type of information (e.g. roundness etc.); however, the effect of average particle size (approximately equal in the two models) may prove to have a stronger influence generally on Dp than on Cpm. Further investigation will be necessary to determine under what circumstances Dp or Cpm is the best parameter for measuring particle roundness of the surface layer and what form of functional filtering, if any, is most appropriate. Speculation upon which set of descriptors is most likely to correlate with hydraulic stability, one of the long-term objectives of this research, is not instructive at this stage. It is not even known which of the two models has the more hydraulically stable surface. Nevertheless, it is satisfying to note that with the aid of functional filtering eight of the fifteen descriptors could discriminate between the glass ball and the aggregate models (where grain size differences were probably minimal) with only 5 samples from each, at a confidence level of better than 99.8%. It seems reasonable to suggest that subtle differences in surface geometry that are indicative of significant differences in hydraulic stability could be determined perhaps using a weighted combination of several descriptors. POSSIBLE P R A C T I C A L A P P L I C A T I O N S
Given that the field equipment and procedure for surveying breakwater profiles is developed and tested, a thoroughly statistical and objective method for monitoring the breakwater is available. Analysis of the profiles may be carried out at regular intervals and/or after severe storms during the life-time of a breakwater. On completion of the construction, quality control for block sizes and shapes could probably be checked using roughness descriptors. Having calibrated roughness descriptors from laboratory models it may be possible to assess placement technique for different packing (or compaction) of a given regular shape. Of geotechnical importance, the extent of subsidence and armour compaction could be rapidly assessed. Low pass filtering techniques could be useful in detecting areas of maximum subsidence, not noticeable from visual inspection. Topographic profiles sampled from the AC plane, with or without low
272
pass filtering can be used to give the type of profile data that is required in the powerful damage assessment technique used by van der Meer and Pilarczyk {1984). Furthermore, techniques for damage assessment and monitoring of movement and displacement of blocks for both models and p r o t o t y p e breakwaters would clearly benefit from an additional standardized technique which in principle can be applied to both p r o t o t y p e s and models identically. The rate of degradation and weight loss of breakwater armourstone by rounding could be assessed using descriptors such as peak curvature. The {rate of) change of certain descriptors might be used to define a {rate of) damage occurring to a breakwater. Several descriptors will be highly sensitive to an increase in the number of 'missing' or 'sub-sized' blocks, parameters used in the damage assessment criterion of Poole et al. (1984). In the laboratory, it is hoped that wave flume experiments, in which the surf similarity coefficient, ~, is accounted for in the determination of the stability factor, would show a correlation between certain roughness descriptors, block shape and the hydraulic stability and also the degree of run-up and run-down. Careful interpretation of roughness descriptor values as models approach failure could lead to insights into the symptoms of failure. The profile measurements would supplement or possibly replace the need to make block displacement measurements for damage assessment. For example, a precisely located AC, BC or BD profile plane could be monitored by topographic profile sampling at successive stages during a flume experiment or on a full size structure. Profile subtraction (preferably carried o u t by image processing) would yield an area measure of block movement and thus a highly sensitive objective measure of damage. Apart from direct application to breakwater armourstone research, there is a great benefit to be gained for the gravel and aggregate industry from being able to translate roughness descriptor information {e.g. from heaps of aggregate) into estimates concerning average particle sizes and shapes w i t h o u t need for sieving etc. ACKNOWLEDGEMENTS
Without the cooperation given by Dr. R.S. Sayles and the Meteorology Group at the Department of Mechanical Engineering, Imperial College, this research initiative could n o t have been pursued with such rapid progress. This research is funded by the S.E.R.C. Reference GR/C/00832. REFERENCES Ahrens, J.P., 1975. Large wave tank tests of rip-rap stability. TM°576, U.S. Army Corps of Engineers (USCE), Coastal Engineering Research Centre, (CERC), F o r t Belvoir, Va. Allsop, N.W.H., Bradbury, A.P., Poole, A.B., Dibb, T.E. and Hughes, D.W., 1985. Rock durability in the marine environment. Hydraulics Research Wallingford, Report S R l l .
273 Barends, B.J., Kogel, H., van der Uijttewall, F.J. and Hagenaar, J., 1983. West-Breakwater Sines, dynamic-geotechnical stability of breakwaters, Coastal Structures '83, Printed by the ASCE. Bergh, H., 1984. Riprap protection of a road embankment exposed to waves. Bull. No. TRITA-VBI-123, Hydraulics Laboratory, Royal Institute of Technology, Sweden. Bruun, P. and Giinbak, A.R., 1976. New design principles for rubble m o u n d structures, Proc. 15th Int. Conf. Coastal Eng., Honolulu, ASCE, pp. 2429--2473. Bruun, P. and Johannesson, P., 1976. Parameters affecting the stability of rubble mounds. J. Water, Harbors Coastal Eng. Div., ASCE, 102 (WW2): 141--164. Bruun, P., 1985. Discussion of "Rubble-mound breakwaters of composite slopes, by E. Naheer and V. Buslov". Coastal Eng., 9: 189--191. Giinbak, A.R., 1976. The stability of rubble mound breakwaters in relation to wave breaking and run-down characteristics and to the ~ ~ tans T/~/~I number. Division of Port and Ocean Engineering Rep. No. 1/76, Technical University of Norway, Trondheim. Giinbak, A.R., 1979. Wave mechanics principles on the design of rubble m o u n d breakwaters. Proc. of the POAC '79 Conf., Trondheim, Norway. Hudson, R.Y., 1959. Laboratory investigations of rubble-mound breakwaters. Proc. ASCE, J. Waterways Harbour Div., 85 (WW3). Losada, M.A. and Gimenez-Curto, L.A., 1979. The joint effect of wave height and period on the stability of rubble mound breakwaters using Iribarren's Number. Coastal Engineering, 3: 77--96. Meer, J.W. van der, and Pilarczyk, K.W., 1984. Stability of rubble mound slopes under random wave attack. Delft Hydraulics Laboratory, Publ No. 332. Naheer, E. and Buslov, V., 1983. On rubble-mound breakwaters of composite slope. Coastal Eng., 7 : 253--270. PIANC, 1976. Final report of the International Commission for the Study of Waves, Bulletin No 36, Vol II. Poole, A.B., Fookes, P.G., Dibb, T.E. and Hughes, D.W., 1984. Durability of rock in breakwaters. Proc. Conf. organized by the Institution of Civil Engineers, London, 4--6 May 1983, pp. 31--42. Sawaragi, T., Ryu, C. and Iwata, K., 1983. Consideration of the destruction mechanism of rubble m o u n d breakwaters due to the resonance phenomenon. 8th International Harbour Congress, Antwerp, Belgium. Sayles, R.S., 1976. The topography of surfaces. Ph.D. Thesis, Teeside Polytechnic, U.K. Thomas, T.R. (Editor), 1982. Rough Surfaces. Longman Inc., New York, N.Y., pp. 261.