An Analytical Solution for Wave Transformation Over Axi-Symmetric Topography

The present study considers wave scattering phenomena around a cylindrical island mounted on a general axisymmetric topography or a general submerged truncated axi-symmetric shoal based on the mild-slope equation. The method of separation of variables and Taylor series expansion are invoked to find the approximate solution to the variable water depth region which varies proportionally to an arbitrary power of radial distance. Validations against the solutions for the combined wave refraction and diffraction around a cylindrical island mounted on a paraboloidal shoal of Liu et al. in 2004 and the scattering and trapping of wave energy by a submerged truncated paraboloidal shoal of Lin and Liu in 2007 show excellent agreements as the power of radial distance being equal to two. For the solutions of wave refraction and diffraction around a cylindrical island mounted on a shoal with depth proportionally to an arbitrary power of radial distance, good agreements with Zhai et al.'s(2013) solutions are demonstrated. Since the robustness of the assumption of a general axi-symmetric geometry based on an arbitrary power variability of the radial distance, the present solution can be very conveniently employed to investigate the effects of bottom topography on wave scattering and trapping patterns.     

The mechanical behaviour and design concerns for a hybrid reinforced earth embankment built in limited width adjacent to a slope

This paper aims to investigate the mechanical behaviour of a hybrid reinforced earth embankment built in limited width adjacent to a slope. This embankment system incorporates reinforced earth embankments with soil nails, installed in the existing ground. Soil nails work to provide additional resisting forces to stabilize the embankment which may be unstable due to insufficient reinforcement length. Nail forces developed in the hybrid reinforced earth embankment with various geometric conditions in the fill space are analyzed. The FE method is used to simulate the construction of the hybrid reinforced earth embankment. Influence of reinforcement length, reinforcement stiffness, and slope gradient on the nail forces developed following the construction is analyzed and discussed. Additionally, design concerns for the hybrid reinforced earth embankment system are also studied. Simple charts for estimating the maximum nail force mobilized at back of the hybrid reinforced earth embankment are established in this research and can be helpful in the design of the soil nails in the system.     

Numerical solution of active earth pressures on rigid retaining walls built near rock faces

For retaining walls built in mountainous regions, narrow backfill spaces are often encountered. The space to fully develop the active wedge is restricted for walls with a limited backfill space. This paper presents a numerical study on the behaviour of active earth pressures behind a rigid retaining wall with limited backfill space of various geometries. The active earth pressure for a wall built with limited backfill space is considerably less than that of the Coulomb solution, and the location of the resultant of active earth pressures is noticeably higher than one-third of the wall height. The coefficient of active earth pressures is as low as 0.5–0.6 times the Coulomb solution and the h/H value reaches up to 0.4–0.37 if aspect ratio of the fill space is in the range from 0.1 to 0.2. A clear trend between the ratio of the coefficient of active earth pressures at constrained fill conditions over the Coulomb K_a value and the aspect ratio of the fill-space geometry is obtained.