Theoretical Analysis of Coral Reef Stability in South Sea

Abstract

In this paper, we utilize the variational limiting equilibrium (LE) procedure to theoretically determine the slope stability of homogeneous coral sand in the South China Sea. By establishing a reasonable functional and calculating its extremum, we can deduce the stability factor of a coral reef identical to that obtained by upper bound analysis. To determine the accuracy of the results obtained using the variational LE procedure, we present some classical examples of homogeneous sand slopes without a hard shell and compare our results with those obtained by the upper bound theorem of plasticity. A series of extensive calculations and comparisons reveal that the results obtained by our proposed analysis method and those obtained using classical methods are slightly different, but the variational results are believable. On the other hand, our method solves some stability factors for reef slopes covered with a hard shell, which indicates that the existence of a hard reef shell may significantly enhance the stability of a reef slope, and that there is strong nonlinear relationship between reef stability and the mechanical characteristics of the reef shell, such as its thickness and strength. Finally, based on the variational results presented in this paper, we present a useful chart that offers a convenient and straightforward way to determine the maximum stability factor of reef slopes. Taking into account the influence of the hard reef shell, we found that, in some limit equilibrium cases, the limit stability factor and critical height of a coral slope could be improved significantly. Therefore, this issue deserves careful attention in engineering practice.