This study introduces new analytical solutions for the one-line model of shoreline change on bounded coast whose both ends are fixed by the coastal structures or rocky cliffs (solid boundaries). A general analytical solution describing shoreline evolution on the bounded coast with the arbitrary initial shape of beach fill/cut is introduced. Subsequently, several shaped types of initial shorelines, such as trapezoid rectangle, and triangle are considered. The new solutions for the bounded coast (finite coast) were compared with the underlying analytical solutions, which describe shoreline evolution on an infinite coast. This shows the distinct differences in the cases without and with solid boundaries. The solid boundaries lead the shoreline to the equilibrium stage more quickly at a certain position instead of slow and 0 of the case without solid boundaries. The relationship showing the decaying process of sediment in the beach fill portion is presented. Results also highlight that when the value of L*, the ratio of bounded coast length to the width of beach fill portion, is large enough, the shoreline evolution of the cases without solid boundaries is asymptotic even at a large t*. Furthermore, the relationship between the dimensionless decay time, t*, and the dimensionless total length of the adjacent coasts to the beach fill portion is also provided, L-S*, If L-S* is large, then the t* is large and vice versa. The solutions proposed in this study have not been verified with the measured data, which could be a disadvantage. However, the derived solutions could be very useful and beneficial for preliminary design, education practices, and beach nourishment (beach fill), or the recovery of coastal morphology after the severe damages induced by natural disasters (beach cut).
展开▼
