Theoretical Analysis of Coral Reef Stability in South Sea

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.

Variational Solution of Coral Reef Stability Due to Horizontal Wave Loading

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 Ns 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 Ns,the shear strength,and the thickness Ds 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 Ds,surface tensile crack,and wave loading require more careful attention in the field of practical engineering.