EXPERIMENTAL STUDIES OF SPECIALLY SHAPED CONCRETE BLOCKS FOR ABSORBING WAVE ENERGY

Laboratory tests were performed to determine wave energy absorbing ability of and stability characteristics against breaking waves of various shaped pre-cast concrete armor units used for protective cover layers on the seaward slopes of rubble^mound breakwaters and for parallel dykes placed the offshore sides of seawalls. A new shape of armor units, a hollow tetrahedron concrete block with a porosity of 25 percentages in the body was proved to have better characteristics for wave energy absorbing ability and attenuation of wave run-up, as well as for stability against breaking waves also than tetrapod or other armor units used up-to-date. EXPERIMENTAL EQUIPMENT AND PROCEDURE TESTS FOR PROTECTIVE COVER LAYERS OP RUBBLE-MOUND BREAKWATERS An open wave channel, which is 25 m. long, 2 m. wide, and 1 m. deep, was used for the experiments of the protective cover layers of rubble-mound breakwaters. Waves were generated by a flutter type wave generating machine, ranging the period T 1.2 to 1.9 sec, the height H « 10 to 24 cm., and the steepness H/L • 0.040 to 0.085. Since the scale ratio between the model and prototype is approximately l/20, the heights and periods of the model waves are scaled up approximately to H 2 to 4.8 m. and T * 5.4 to 8.5 sec. in sea by the use of Proude'.s law. A number of laboratory tests were performed of concrete armor units such as tetrahedrons, hexabars, tetrapods and hollow tetrahedrons made in l/20 scale ratio to prototype, comparing with quarry-stone armor units placed pell-mell and with moundsmade of wooden plates. The energy absorbing ability of armor units in these experiments was determined by use of the resultant forces of maximum simultaneous shock pressures^' exerted by breaking waves on the vertical walls of composite-type breakwaters, which were measured by pressure-gauges of strain-gauge type, and also by use of wave run-up along the vertical walls as well as reflection ratio from the walls, both of which were measured by visual observation. The shapes and characteristics of the specially shaped armor blocks used in the tests are shown in Figure 1 and Table 1. The armor units were in all tests constructed with the two layers of the specially shaped concrete blocks on a 1 t 1 ~2~ slope, because it was proved by the tests that the two-layer placing and the 1 1 1-^slope were the optimum condition for the stability of these

A number of laboratory tests were performed of concrete armor units such as tetrahedrons, hexabars, tetrapods and hollow tetrahedrons made in l/20 scale ratio to prototype, comparing with quarry-stone armor units placed pell-mell and with moundsmade of wooden plates.The energy absorbing ability of armor units in these experiments was determined by use of the resultant forces of maximum simultaneous shock pressures^1' exerted by breaking waves on the vertical walls of composite-type breakwaters, which were measured by pressure-gauges of strain-gauge type, and also by use of wave run-up along the vertical walls as well as reflection ratio from the walls, both of which were measured by visual observation.
The shapes and characteristics of the specially shaped armor blocks used in the tests are shown in Figure 1 and Table 1.The armor units were in all tests constructed with the two layers of the specially shaped concrete blocks on a 1 t 1 ~2~ slope, because it was proved by the tests that the two-layer placing and the 1 1 1-^-slope were the optimum condition for the stability of these     The types of composite breakwaters and rubble-mound breakwaters used in the tests are shown in Figures 2, 3 and 4. The protective cover layers composed of the two layers of cast concrete specially shaped armor units were placed in some orderly manner or pell-mell over a core of quarry-stones, the diameters of which d = 2.8 to 7.3 cm.. Figs. 2 and 3 are types of composite breakwaters with vertical walls sufficiently high to prevent overtopping by the test waves, and Fig. 4 is a type of composite breakwaters with low vertical walls subjected to overtopping at high water levels.In these law breakwaters cast concrete blocks are placed up to the crown of the vertical walls.

TESTS OF PARALLEL DYKES FOR THE PROTECTION OF RUN-UP ON SEAWALLS
A let of experiments was performed to determine the effect of parallel dykes, which/constructed with the two layers of concrete tetrapodsand hollow tetrahedrons and placed in front of seawalls, on the attenuation of wave run-up and of wave pressures on the seawalls.A wave channel used in these experiments was 23 m.long, 1 m.wide, and 1 m.deep, as shown in Fig. 5, and the nearly overall length of the channel was covered on the top with semicircular duralmin plates for generating winds of various speeds parallel with the direction of propagation of waves which were generated by a flutter type wave generator.The speed of revolution of a wind blower was varied by the use of a vari-pitch connected with a 15-horse power electric motor so as to generate winds of speed up to 20 m./sec..One typical type of the seawalls tested is shown in Fig. 6.
The characteristics of waves generated by the flutter type wave generator were T -1.2 to 1.9 sec., H -8~14 cm., H/L » 0.020 -0.070.The wave run-up as well as the behaviors of spray and overtopping were measured by the use of a 16 millimeter movie taken at 100 frames per second. (2)) Test results in composite breakwaters shown in Figs. 2 and 3 Figs.7, 8, 9 and 10 show maximum simultaneous shock pressures exerted by breaking waves of periods T =» 1.3 and 1.5 sec.on the vertical walls of the composite breakwaters shown in Fig. 2.

TESTS FOR THE PROTECTIVE COVER LAYERS OF RUBBLE-MOUND BREAKWATERS
The states of run-up in breaking waves with T « 1,5 sec, H • 16 cm., H/L *» O.060 impinged against the vertical walls placed on the various kinds of base-mounds are shown in Figs.11, 12, 13 and 14.
The test results are summarized in Tables 2 and 3   with the maximum intensities of shock pressures and the resultants of maximum simultaneous shock pressures exerted on the vertical walls of the composite breakwaters by the breaking waves, the heights of ware run-up, the ratioes of wave energy attenuation, and the stability of the armor units on the seaward slopes of the base-mounds.
The effect of the specially shaped concrete armor units on absorbing wave energy was also determined by use of the ratio of wave energy attenuation, « 2 , defined as follows.
The momentum per the unit width of the channel transported by a breaking wave for a period is obtained by f> Q 00 , where J 3 is the density of water, u) , the horizontal velocity of a water particle in a breaking wave, may equal to the celerity of the breaking wave with sufficient accuracy, and Q is the water mass per unit width of the channel transported for a period by the breaking wave.If the breaking wave is assumed that of a solitary wave, uj and Q are given by U) = Jf.ZbgH (1)   in which g is the acceleration of gravity, and H tke height of the breaking wave, and 0 = 4h.»IW. ( in which ho is a depth below the still water level at the horizontal bottom of the channel.
The resultant of the impulse exerted by the breaking wave on unit width of the vertical wall for a period is denoted by f 0 f 0 pdt-<jh where T is smaller than the period T of the breaking wave, and h the height from the top of the base-mound up to the highest point of th> wave pressure exerted by the breaking wave.If the ratio of the resultant of the impulse on the vertical wall to the momentum transported is denoted by «, Substituting Eqs.(l) and ( 2), into Eq.( 3), we obtain The right-hand side of Eq. (4) may be considered the momentum transported by a breaking wave with a height of aH.Since the net wave energy B ne t acted on the vertical wall by this breaking wave will be E ne t =^fg(<XHf the ratio of the net breaking wave energy acting on the vertical wall to the total breaking wave energy "before impinging against the breakwater should "be obtained by the equation By the use of the experimental data the values of a 2 were calculated from Eqs. (5) and (5).
From Tables 2 and 3 it is seen that the hollow tetrahedron armor units constructed with the two layers of cast concrete hollow tetrahedrons with a porosity of 25 percentages have the optimum characteristics of wave energy absorbing ability as well as of stability on the 1 on 1.5 slope, showingespecially 30 to 50 percentages greater attenuation of the maximum simultaneous shock pressures than that due to the tetrapod armor units.It ia considered that when the depth hj above the top of a base-mound covered with specially shaped concrete armor layers is small, the roughness on the surface of concrete block layers plays a greater role than the permeability of concrete block layers, on the contrary, the latter plays a greater role than the former when hj is large.Wave run-up on the vertical walls of composite breakwaters is also smaller ia the hollow tetrahedron armor layers than in the tetrapod armor layers.
Prom experiments in the composite breakwaters of such shapes as shown in Pig. 3, nearly the same trend as shown in Tables 2 and  3 was proved.
(b) Test results in composite breakwaters with low vertical walls shown in Fig. 4 Maximum simultaneous shock pressures exerted by breaking waves on the low vertical walls, up to the top of which the seaward slopes of the rubble-mound were covered with concrete tetrapod or hollow tetrahedron armor units, and the stability of those armor units on the slopes were measured by making breaking waves with the periods of T » 1.3 and 1.5 sec.on the slopes in the three different water levels.These experimental results are shown in Figs. 15, 16, 17, 18, 19 and 20.As it is known from the Figures, when waves break on the slopes in the cases of low water level, the magnitudes of shock pressures exerted by the breaking waves on the vertical walls are nearly the same in the two different armor units, indicating small values, but in the cases of high water level the effect of the^hollow tetrahedron armor units on the attenuation of wave pressures is distinguished, comparing with that of the tetrapod armor units.The quantity of overtopping in the hollow tetrahedron armor units is also smaller than that in the tetrapod armor units.The stability on the slopes was nearly the same in the two armor units.
(c) Test results of parallel dykes for the protection of wave run-up on sea-wall It was proved from a lot of experiments that if parallel dykes covered with the two layers of concrete hollow tetrahedron or tetrapod armor units were placed in front of seawalls, wave run-up on the slopes of the seawalls could be reduced to a
concrete armor units.

Fig. 7 ,Fig. 8 .
Fig.7, Maximum simultaneous shock pressures bybreaking waves of T = 1.5 sec (water depth above the top of the mounds hi is constantly 7 cm).

1 (
top* of the parallel dykes should be high stiffi cient to prevent a large amount of overtopping by the test wares at the design height of sea level, probably being 0.50 a. or more above the design sea level.The effect of the hollow tetrahedron armor units on the attenuation of wave run-up on the seawall slopes was proved more proainent than that due to the tetrapod araor units.Only the two exaaplea are shown in Figs.21 and 22to show the effeot of the attenuation of wave run-up due to the parallel dykes with the cover layers ooaposed of the hollow tetrahedron araor units.Fig.21is a case where a depth in front of a seawall at the design sea level is so large that the design waves do not break before arriving the sea-wall, on the contrary Fig.22is a ease where the design waves break at or in front of a sea-wall at the design sea level.(d)Stability of the hollow tetrahedron araor units on the slope of rabblC7mounds (3jAs aentioned above, the hollow tetrahedron araor uni£s on the slopes of rubble-aounds were proved to be in general nfere stable against the attack of waves than tetrapod araor units,because of wedge action caused by the upper layer blocks inversely set into aaong the lower layer blocks, as well as of the saall up-lift pressures of receding waves reduced due te the hollowness of the blocks.The curves of stability of the concrete hollow tetrahedron araor units were determined froa a number of experiments on the 1 i if slopes of rubble-aounds as shown inFig.23.(o) Tests of the strength of the oonerete hollow tetrahedron blocks Several field tests of prototype two-ton concrete hollow tetrahedron blocks with the porosity of 25 percentages ( with no reinforcement ) was performed t* know strength against very roughly dumping in seas by the measures of falling down on gravel layers and on hollow tetrahedron blocks froa some 3-meter height.Froa the tests the concrete hollow tetrahedron blocks were confirmed very tough against rough piling up or hard mutual colliding by atora waves because of resisting as Bahaen structures.CONCLUSIONS It is concluded froa the results of tests coapleted up to date that a) Two layers ooaposed of the concrete hollow tetrahedron araor units have better characteristics for absorbing wave energy or wave pressure and for stability against breaking waves than the other specially shaped concrete armor units which have been used up to date.(b) When the twe layers of hollow tetrahedron araor units are used for protective cover layers on the seaward slopes of the rubble-mound of composite-type breakwaters, it will be expected to obtain approximately 30 to 30 percentages greater attenuation of shock pressures exerted by breaking wares on the vertical walls than that due to tetrapod armor units.When the two layers of hollow tetrahedron armor units are used for the protective cover layers of parallel dykes located in front of sea-walls, the attenuation of ware run-up on the slopes of the sea-walls will be obtained to a great extent and be materially effective to prevent overtopping from the sea-walls.(e) The hollowness of a hollow tetrahedron block was proved optimum in the case of a porosity of 25 percentages, from the view points of wave energy absorbing ability as well as of the strength of a block* (d) The two layers of concrete hollow tetrahedron armor units have favorable characteristics for stability on 1 on 1-j-slopes^ because of wedge action caused between the two layers and of reduction of up-lift pressures caused by receding waves.(e) The number of concrete hollow tetrahedron blocks necessary for two-layer placing on a given area is on an average 15 percentages fewer than that of tetrapod blocks with the same dead weight.PRACTICAL USBS OF HOLLOW TETRAHEDRON ARMOR UNITS Interim report on the tests of the hollow tetrahedron armor units was first done at the 6th Conference of Coastal Engineering in Japan held at the begin^Lng of November.1959* One to two ton concrete hollow tetrahedron armor units have been in use or partly under construction for protective cover layers of rubble-mound breakwaters and for wave energy absorbing parallel dykes lecated in front of sea-walls at several harbors and coasts in Japan.The effect of absorbing wave energy of the hollow tetrahedron armor units will be checked when subjected to attack by heavy storm waves generated by typhoon at August and September this year.

Table 1 .
Characteristics of concrete armor units tested.

Table 3 .
Test results in Figures 9 and 10.