Active earth pressure on retaining structures supporting a narrow column of soil cannot be properly analysed using Coulomb's theory. Finite-element limit analysis (FELA) shows that the soil forms multiple failure surfaces if the soil column is sufficiently narrow. This paper proposes a framework for active earth pressure estimation for narrow soils by combining an arched differential element method and a sliding wedge method. The analytical framework considers both soil friction and cohesion, soil arching effects and shear stress between adjacent differential elements. The solution obtained is validated against experimental data and FELA results. Through parametric studies, the effects on the active earth pressure of the aspect ratio, soil friction, soil cohesion and wall-soil interface roughness are examined. To facilitate the use of the proposed framework in design, a modified active earth pressure coefficient and an application height of active thrust are provided.

There is currently a lack of an available design approach to estimate the earth pressure in narrow backfills behind retaining walls rotated about the top (RT). The considerations of some significant factors, primarily load transfer mechanisms (soil arching effect and horizontal shear stress in soils), failure mechanisms (shape and number of slip surfaces) and soil cohesion are often neglected for brevity in routine design. Such simplifications may lead to significant deviations from reality. This paper first uses the finite element limit analysis (FELA) technique to identify the underlying failure mechanisms and load transfer mechanisms. The results observed in FELA models indicate that active rotation of walls about the top develops one curved slip surface, which can be approximated by the log-spiral function. Under the soil arching effect, the upper intermediate passive zone with major principal stress rotation trajectory and the lower active zone with minor one can be defined. The arched differential element method (ADEM) is then introduced to formulate the earth pressure calculation. The results from newly published tests, existing analytical approaches, and FELA are compared to validate the accuracy of the proposed approach in both purely-frictional and cohesive-frictional soils. Parametric studies are further conducted to thoroughly understand the earth pressure problems, considering the effects of sensitive design variables (e.g. aspect ratio, soil strength parameters, and wall-soil interface friction angle). The analytical approach presented here would be a great extension to the design guidelines for the retaining structures with narrow backfills.