Abstract Considering the importance and preva‎lence of using statically Rubble Mound Breakwater in order to protect the shores, eva‎luating and investigating the stability of this type of structure requires careful study, in order to provide a stable and cost-effective design. Due to the main role of the toe in maintaining the stability of this type of breakwater and preventing scouring of the base of structure, toe design is mandatory. To achieve such a goal, laboratory study is necessary to establish a correct understanding of the effect of various environmental and geometric factors affecting the stability of the toe. In this study, a two-dimensional laboratory model of statically rubble mound breakwater with toe under the effect of irregular waves with Janswap spectrum was investigated. The experiments were performed in a canal 15 meters long, 1 meter high and 0.8 meters wide. The height of the breakwater was 0.45 m and its length was about 1.5 m. To measure the amount of toe degradation, the ratio of the eroded area of the toe to the square of the nominal diameter of the toe aggregates, as a parameter of toe damage, was used. The effect of wave height and period parameters, armour layer slope, water height in front of the structure, water height on the toe and toe width on the hydraulic stability of the breakwater toe was investigated. The results show that when the iribarren number of the front slope of the structure is greater than 3.35, the slope of the armour layer has almost no effect on the amount of toe damage. But for Iribarren number less than 3.35, wave breaking occurs and the amount of toe damage increases as the slope of the armour layer decreases. Wave height has a direct effect on the damage parameter. The effect of wave period on the damage parameter alone can not be investigated, so that along with the wave height and slope of the armour layer, it was considered as a dimensionless stability parameter. Another effective parameter in toe damage is the water depth in front of the structure, so that as it increases, the amount of toe damage increases. Increasing the water depth on the toe reduces the wave rundown on the toe and reduces the amount of damage to the toe. The simultaneous effect of these two parameters was presented as a dimensionless parameter of relative depth, ie the ratio of water depth on the toe to water depth in front of the structure. toe width does not affect the damage parameter. Finally, in order to apply the results obtained from this study, a relation for estimating the damage parameter in a statically rubble mound breakwater structure with toe was presented. The results of this relationship and the proposed Gerding relationship were validated using Gerding laboratory data. By comparing the error indices obtained from the relations with the laboratory data, the present relation shows up to about 10% better performance than the rounding relation. Key Words Statically Rubble Mound Breakwater, Toe, Hydraulic stability, wave Breaking, Irregular wave

محمد نويد مقيم، محمد رضا چمني

عبدالرضا كبيري ساماني، شهريار منصورزاده