Hydraulic Stability of Stone-Filled Coconut-Fibre Bags Installed on Sloping Riverbanks

Stone-filled coconut-fibre bags have the potential to serve as environmentally friendly riverbank protection elements, particularly where temporary mechanical stabilization is required before vegetation becomes sufficiently established to contribute to long-term bank stability. However, the practical applicability of such systems depends strongly on their ability to resist hydraulic displacement under the combined effects of gravity, hydrodynamic drag, hydrodynamic lift, and frictional resistance. Accordingly, this study develops an explicit closed-form analytical solution for predicting the incipient sliding velocity of a representative stone-filled coconut-fibre bag installed on an inclined riverbank. Hydrodynamic drag and lift forces are represented using conventional quadratic force formulations, while the submerged weight of the bag is resolved into normal and tangential components relative to the inclined bank surface. A general force-balance relationship is then formulated for an arbitrary angle between the hydrodynamic drag direction and the downslope gravitational component. From this formulation, an explicit expression for the critical velocity corresponding to the onset of sliding is obtained. Two limiting flow configurations, namely drag acting directly downslope and longitudinal river flow, are also considered to demonstrate the influence of flow orientation on hydraulic stability. The analytical results indicate that hydrodynamic lift indirectly reduces stability by decreasing the normal contact force and, consequently, the available frictional resistance. Furthermore, the relative orientation of drag and gravity significantly affects the predicted critical velocity. The proposed framework provides a theoretical basis for preliminary hydraulic stability assessment of stone-filled coconut-fibre bags and may support future parametric investigations and numerical simulations. Nevertheless, the formulation is based on idealized hydraulic assumptions and does not explicitly account for effects such as local scour and turbulence. Therefore, controlled laboratory experiments are required to validate the predicted critical sliding velocities and to calibrate the drag and lift coefficients before the framework can be reliably extended to practical riverbank protection systems.