Variational Solution of Coral Reef Stability Due to Horizontal Wave Loading

Abstract

This paper proposes a theoretical method that can be used in calculating the stability of coral reefs or artificial islands. In this work, we employ the variational limiting equilibrium procedure to theoretically determine the slope stability of coral reefs covered with hard reef shells as a result of horizontal wave loads. A reasonable functional is proposed and its extremum is calculated based on the conservation of energy. Then, we deduce the stability factor N_s of coral reefs under combined vertical self-gravity and horizontal wave loads, which is consistent with the published results. We compare some classic examples of homogeneous slopes without hard shells in order to analyze the accuracy of results generated by this variational procedure. The variational results are accurate and reliable according to the results of a series of detailed calculations and comparisons. Simultaneously, some other influence parameters on the reef stability, including the top-layer tensile strength of coral reef, the amplitude of wave loading, and the tensile crack, are calculated and discussed in detail. The analysis results reveal that the existence of a hard reef shell could enhance the stability of reef slope and that there is a nonlinear relationship between the stability factor N_s, the shear strength, and the thickness D_s of the covered coral reef shell. Furthermore, the emergence of top-layer tensile cracks on the coral reefs reduces their stability, and the action of horizontal wave loads greatly decreases the stability of coral reefs. Thus, the hard shell strength and its thickness D_s, surface tensile crack, and wave loading require more careful attention in the field of practical engineering.