CHAPTER ONE HUNDRED SEVENTY FOUR FATIGUE IN BREAKWATER CONCRETE ARMOUR UNITS Hans F. Burcharth * ABSTRACT The reliability of rubble mound breakwaters depends on the hydraulic stability and the me- chanical strength of the armour units. The paper deals with the important aspect of fatigue related to the strength of concrete armour units. Results showing significant fatigue from impact tests with Dolosse made of unreinforced and steel fibre reinforced flyash concrete are presented. Moreover universal graphs for fa- tigue in armour units made of conventional unreinforced concrete exposed to impact load and pulsating load are presented. The effect of fibre reinforcement and the implementation of fatigue in a stochastic design process are discussed. INTRODUCTION Many of the recent failures of large rubble mound breakwaters are due to unexpected frac- ture of the concrete armour units. Traditionally the design process is based on hydraulic model tests and the design criterion chosen with consideration only to the hydraulic stabi- lity. Although progress has been made during the last years there exists no consistent ar- mour layer design method in which both the hydraulic and the mechanical stability are con- sidered. A discussion on the state of the art of this problem is given in Burcharth, 1983 (ref. 1 and 2). The different types of loads on armour units and their origin are listed in Fig. 1. TYPES OF LOADS ORIGIN OF LOADS Weight of units Prestressing due to: Settlement of underlayers Wedge effect and arching due to movements under dynamic loads Suspended material Rocking/rolling of units Impact Missiles of broken units Placing during construction Earthquake Pulsating Gradually varying wave force Stresses due to temperature differences during hardening process Freeze-thaw Corrosion of reinforcement CHEMICAL Sulfate reactions etc. Fig. 1. Types of loads on armour units. * Professor of Marine Civil Engineering, University of Aalborg, Denmark. 2592 CONCRETE ARMOUR UNITS 2593 This paper deals with fatigue due to repeated dynamic loads from the waves. Fatigue is the reduction in material strength by increasing number of load cycles. FATIGUE The waves will cause pulsating (gradually varying) flow forces and also impact forces when the units are rocking. The number of cycles of wave loadings will be in the order of 200 million during a 50 years' period in the North Atlantic period. Since 1903 it has been known that concrete shows significant fatigue. Considering the high stress level in the large slender types of units such as Dolosse and Tetrapods it is important to evaluate the fatigue effect on the stability. Fig. 2 shows the results from uniaxial fatigue tests with small specimens by Tepfers et al., 1979 (ref. 3 and 4), Fagerlund et al., 1979 (ref. 5), Zielinski et al., 1981 (ref. 6). The size of the specimens were 150 mm cubes, 100 mm and 74 mm diameter cylinders. UPPER STRESS LIMIT ULTIMATE STATIC STRENGTH 1.5 ^>. 1.0 /PULSATING (5-10Hz) TENSION AND COMPRESSION 150 MM CUBES IMPACT COMPRESSION7^ 0.5-- CYLINDERS 100 MM. DIAMETER •IMPACT TENSION CYLINDERS 74 MM DIAMETER 10 10 10 10 10 10 10 NUMBER OF CYCLES TO FAILURE N Fig. 2. Fatigue. Uniaxial impact and pulsating loading of small specimens (Tepfers et al. 1979, Fagerlund et al. 1979, Zielinski et al. 1981). The results of the static test shown in Fig. 2 compare very well to the results by Tait et al., 1980 (ref. 7) for 25 kg model Dolosse of 300 mm height exposed to a pulsating load which created mainly uniaxial tensile stresses in the critical section, see Fig. 3. Impact tests by M.G.A. Silva, 1983 (ref. 8) with full scale cubes in the range 1 ton to 27 tonnes also reveiled significant fatigue as shown in Fig. 4. In the tests one cube impacted side to side a resting cube of the same size. 2594 COASTAL ENGINEERING-1984 From the above mentioned tests it is seen that impact loads create the most drastic reduc- tion in strength. Regarding the application in practical breakwater design of the tests present- ed in Fig. 2 and 3 it might be argued that the size of the specimens could be too small to re- UPPER STRESS LIMIT ULTIMATE STATIC STRENGTH 100 90 ^»* 1 PULSATING LOAD-10 Hz 80 70 60 10 10' 10J 10 10 10 NUMBER OF CYCLES TO FAILURE N Fig. 3. Fatigue. Uniaxial pulsating tension loading of model Dolosse of 300 mm height (Taitetal. 1980). IMPACT VELOCITY (M/S) 12 5 10 20 50 N Fig. 4. Fatigue. Impact tests with full scale cubes (M. G.A. Silva 1983). present the properties of prototype concrete. Also the stresses are uniaxial whereas in proto- type the stresses in critical sections are often flexural stresses. To evaluate these questions series of impact fatigue flexural stress tests with 200 kg Dolosse were performed at the Uni- versity of Aalborg from 1981 to 1983. Both unreinforced and steel fibre reinforced concrete were tested. CONCRETE ARMOUR UNITS 2595 FATIGUE TEST SET UP AND TEST PROGRAMME The test set up is shown in Fig. 5. HYDRAULIC PISTON 40 KG CONCRETE- CYLINDER GREASED STEEL PLATES SAND CONCRETE BASE STEEL SUPPORT 2H H _ 3 M /\ QZ H H=790MM \ Fig. 5. Set up of Dolosse impact fatigue tests. The support of the Dolos compares to the set up used in prototype dynamic testing of Do- losse proposed by Burcharth 1980 and 1981 (ref. 9 and 10) and since widely used by other researchers. The set up is designed to generate mainly flexural stresses in the critical sections of the stem and the leg near the stem/leg corner. The pendulum was automatically operated by a hydraulic piston which could be set to any draw back distance from which the pendu- lum was released, thus reaching a specific impact speed. The number of impacts were recor- ded automatically. The operating speed was approximately one impact per 2 sec, somewhat dependent on the draw back distance. Apart from disintegration also the first sign of crack and a specific width of the crack were taken as failure modes to be registered. This necessitated careful visual observation of the Dolosse throughout the tests. To prevent material scale effects the size of the Dolosse was chosen such that concrete with normal size of aggregates could be used. This resulted in a Dolos height of 790 mm, a stem diameter of 261 mm giving a waist ratio of 0.33 and a mass of approximately 200 kg. The diagonal of the stem leg corner fillets was 48 mm. 2596 COASTAL ENGINEERING-1984 A total of 45 Dolosse were tested included some pilot tests. Two types of concrete, unrein- forced flyash concrete and steel fibre reinforced flyash concrete, were tested. The specifica- tions and the material properties are listed in Table 1. Table 1. Specifications of concretes. Unreinforced units Steelfibre reinforced units Cement content kg/m3 380 portland 435 portland flyash cement Flyash kg/m3 125 Sand kg/m3 525 788 4-8 mm pebbles kg/m3 80 none 8-16 mm pebbles kg/m3 1095 416 16-32 mm stones kg/m3 none 416 Water cement ratio 0.45 0.40 Additives app. 4% air 3.3kgplastisizerBV40 in Dolosse app. 6% air in Dolosse Reinforcement kg/m3 none 160, Wirex steel fibre 45 x 1 mm plain round (2% by volume) Mean static compressive strengtll 44.4 27.0 *) 100x200mmcyl. "o N/mm2 *) Mean static tensile strength 3.65 3.47 100 x 200 mm cyl. splitting test ^T split N'mm2 Mean modulus of elasticity deter- 4.4 x 10" mined by ultrasound measurement E N/mm2 Mean mass density of concrete in Dolosse p kg/m3 2330 2300 *' Absolute values not fully representative for the Dolosse concrete strength due to boundary effect of the small cylinders on the concrete containing large fibres and coarse aggregates. This resulted in app. 4% higher air content and accordingly lower strength properties for the cylinder specimens. On this base the strength of the concrete in the Dolosse is estimated to o = 30 N/m2 and o = 3.85 N/mm2. c T A fairly high fibre content of 160 kg per m3 of concrete or 2% by volume was used to make sure that it was well above the limit where fibre has no effect. According to full scale tests with 30 t Dolosse (static test and drop test) conducted by the author a steel fibre content below 70 kg/m3 has only negligible effect on the strength. CONCRETE ARMOUR UNITS 2597 Pilot's tests with beams reinforced with various types of steel fibres showed that a fibre length of app. 45 mm ensured a good toughness. A somewhat smaller diameter of the fibre than the applied 1 mm would probably have been more effective in terms of toughness per kilo of steel. Although the amount of fibres was high no problems with mixing of the fibres were ob- served and the distribution of the fibres in the concrete Dolosse was good. However, the air content came out higher than expected and the strengths lower. The age of all units when tested were approximately one year. THEORETICAL CONSIDERATIONS ON THE PROCESSING AND REPRESENTATION OF THE TEST RESULTS In fatigue tests each specimen is exposed to repeated load representing a specific stress range, ACT. Neglecting the influence of the rate of strain on stress and the variation of Poisson's ration Burcharth 1981 (ref. 10) derived formulae for the maximum tensile stress in a Dolosse ex- posed to impact load in a drop test and a pendulum test. Taking the waist ratio as a constant (0.33 in the present tests) the two formulae is given by "T R 0.5 mghH pgh where ~ means proportional to a the max tensile stress T m the pendulum mass (or the Dolos mass in the drop test) h the pendulum fall height (or the Dolos centre of gravity fall height in the drop test) H the Dolos height g the gravitional constant E the dynamic or static modulus of elasticity p the mass density of pendulum and Dolos In this it is assumed that for each type of concrete there is a constant ratio between the dy- namic and the static modulus of elasticity. Thus the variation of this ratio with the stress level and the amount of internal fracture is neglected. Eq. (1) is based on the assumption that the duration of the impact At can be taken as the time which elapses for a longitudinal shock wave to travel from the point of impact to a free edge of the concrete and back again, i.e. At is proportional to a characteristic length, H. However, actual recordings of the impact time in the present tests showed bigger values of At. A reanalysis based on the assumption of At being half of the natural period for the first mode of vibration of the Dolos when hit reveiled good agreement between measured and calculated values of At. Fortunately this finding do not change eq. (1) as also the vibration model involves proportionality between At and a characteristic length. Since the stresses range from approximately zero for each impact in the tests, the maximum stresses also represent the stress range. Thus in eq. (1) a = Acr . T T The present fatigue test results are presented in diagrams where the ratio of the ultimate dy- namic tensile stress range for N Impacts, Aa to the same quantity for one impact, Ao N N=1 2598 COASTAL ENGINEERING -1984 is plotted against the number of impacts at failure, N. Since the stresses were not directly re- corded in the tests the ratio Aa /Ao was determined from the impact speed (or fall N N=1 height) of the pendulum as follows: For a system with constant values of g, m and H eq (1) reduces to Eh 0.5 A» ~ (y1) (2) T Moreover since p and E were approximately constants for each type of concrete we get , 0-5 v AaTT ~ h = (2g)0„.-5? , (i. 3 )I where v is the pendulum impact velocity. Since the material properties of concrete produced to identical specifications vary, correc- tions for this variation should be implemented in the results. For this reason 6 cylinders (100 x 200 mm) were cast from the batch of each Dolos. 4 or 3 cylinders were used to de- termine the splitting tensile strength, CTT ut and 3 or 4 cylinders were used to determine the compressive strength, a . As testing of the cylinders and the corresponding Dolos took c place at the same time it is assumed that the mean values <J i; and o characterize the ac- Tsp t c tual strength properties of the Dolos. In the impact .fatigue tests the relevant strength property is the dynamic tensile strength aTd and not 0 |; which, due to the splitting test procedure, is a static tensile strength Tsp t property. However, in what follows the reasonable assumption of proportionality between the two tensile strengths is used for each specific type of concrete. To make it possible to compare fatigue in Dolosse of different concrete strength, corrections for the variations as found from the cylinder splitting test can be made by means of eq. (3). Thus a measure of a characteristic stress range for a tested Dolos is uO.5 Ao.-k^-S— (4) a aTsplit,a where k is an unknown constant and indices a corresponds to a specific Dolos. From this we obtain . .0.5 , „ AaN,a hN,a ' aT,split,a (5) ,0.5 . AoN = l,b nN=l,b ' aTsplit,b where indices b refers to a specific Dolos. It should be noted that the use of eq. (4) in the present tests is somewhat invalidated by the uncertainty on estimating o from relatively small cylinders, cf. the footnote in Table 1. T ut However, the test result presented by the graphs in Figs. 8 - 10 are based on eq. (5) which is not significantly biased because o appears both in the nominator and the denominator. T ]it h in eq. (5) could not be found directly from a test because it is impossible to determine N=1 the pendulum speed which in just one impact on an untested unit causes exactly the ulti- CONCRETE ARMOUR UNITS 2599 mate stress where the first crack appears. Therefore Ao was determined by extrapola- N=1 tion to N = 1 of the fatigue test results in a log-linear representation, see Figs. 6 and 7. LEGEND: •TEST RESULTS, FIRST SIGN OF CRACK. Acr_ fh N N k Oispiit A0N=1 - o 9 • • «w • • • ^•- ^_» • ~"i 1"' 9 ,-» i 0- 1 10 icr 10J 10" 103 10° NUMBER OF IMPACTS N Fig. 6. Determination of Ao for unreinforced flyash concrete Dolosse. Flexural stress. Ns!l LEGEND: -TEST RESULTS, FIRST SIGN OF CRACK. ACT = NfhTT k Cysplit 3.0 - AcrN=i_? 1 - • 1.5 • ^"^•^mm ~^*L*--^ # •^. • • • 10 10^ 10J 10* 10b 10b NUMBER OF IMPACTS N Fig. 7. Determination of Aa for steel fibre reinforced concrete Dolosse. Flexural w=J stress. 2600 COASTAL ENGINEERING- 1984 TEST RESULTS Fig. 8 shows the result of the fatigue tests with unreinforced Dolosse. LEGEND: • FIRST SIGN OF CRACK o DISINTEGRATION. MEAN OF FIVE TESTS. flQ-N . ULTIMATE DYN. STRESS RANGE FOR N IMPACTS Ao-N=1 ULTIMATE DYN. STRESS RANGE FOR ONE IMPACT • ^**S ••& .^. 0.5 • _ • ' '—•*. "-* o :. . .A DNOONLO BSRSOEK EN 1 10 102 103 104 10° 10° NUMBER OF IMPACTS N Fig. 8. Fatigue. Impact loaded Dolosse of unreinforced flyash concrete. Flexural stress. The ordinate represents the ratio between two dynamic stresses, namely the ultimate dyna- mic stress range for N impacts to the same quantity for one impact, N = 1. Very often in such Wohler diagrams the denominator is the static strength (cf. Fig. 2), but the presenta- tion in Fig. 8 demonstrates the fatigue effect more clearly. The full line corresponds to the first sign of crack, thus representing the design graph. The dotted line shows the state of disintegration. No sign of damage or indentation of the im- pacted Dolos-surfaces was seen in the test series with unreinforced concrete. The results for the fibre reinforced units are shown in Fig. 9. LEGEND: FIRST SIGN OF CRACK o 1 MM CRACK WIDTH ULTIMATE DYN. STRESS RANGE FOR N IMPACTS AcTN=i ULTIMATE DYN. STRESS RANGE FOR ONE IMPACT 1.0 • o ^ ^Cr--*_<£ 0.5 < i»"— • • O ( • 10 10 10 10 10 NUMBER OF IMPACTS N Fig. 9. Fatigue. Impact loaded Dolosse of steel fibre reinforced fly ash concrete. Flexural CONCRETE ARMOUR UNITS 2601 The full line corresponds to the first sign of crack and the dotted line to a crack width of 1 mm. For design purpose, the full line should be used since a crack width of 1 mm implies fast corrosion of the tiny steel fibres. If non-corrosive fibres are used cracks of some size might be acceptable. By large numbers of impacts an indentation was clearly seen on the im- pacted surface — quite contrary to the case of unreinforced concrete. A comparison of the fatigue properties of the two types of concrete is presented in Fig. 10. LEGEND: FLYASH CONCRETE FIBRE REINFORCED CONCRETE AtfN ULTIMATE DYN. STRESS RANGE FOR N IMPACTS A<rN=1 ULTIMATE DYN. STRESS RANGE FOR ONE IMPACT 1.0 • ^^^n '— — ~-a___ D 0.5 n • • ° a 10 10' 10J 10* 10J 10 NUMBER OF IMPACTS N TO FIRST SIGN OF CRACK Fig. 10. Comparison of fatigue in impact loaded Dolosse of unreinforced and steel fibre reinforced flyash concrete. Flexural stress. It is seen that the fatigue effect is smaller in the fibre reinforced units as it stabilizes at a stress range twice as big as for the unreinforced units for N > 10s. This better performance is properly partly due to the development of a more soft impact surface, cf. the observed in- dentation. Fig. 11 shows a comparison of the ultimate impact energy at the first sign of a crack. The impact energy, taken as the maximum kinetic energy of the pendulum, is dimensionless by dividing by gMH, where g is the gravitational constant, M the mass of the Dolos and H the height of the Dolos. It is seen that, the fatigue life of the steel fibre reinforced concrete is the best of the two ex- cept for small number of impacts. However, the difference is fairly small and probably much smaller than most people expect since it is often said in the literature that fibres increase the energy absorbtions at failure many times, compared to plain concrete. For example in ref. (11) a factor of "at least ten times" is related to a steel fibre content of 100 kg/m3. The reason for this discrepancy is the fact that most testing of fibre reinforced concrete re- ported in the literature is done with rather slender specimens, such as beams, where large de- flection creates only very small cracks, contrary to what is the case with stiff bodies like Do- losse and Tetrapods. Another important reason is that in the case of armour units failure must be defined as the appearance of a crack, while in the concrete literature failure of tested specimens is usually taken as the state of complete disintegration or some high level of deformation.