Correct determination of the passive failure surface geometry is necessary for the design of retaining structures. The conventional theories assume linear passive failure surfaces even though it is known that the actual failure surfaces are non-linear. Many researchers claimed the appropriateness of a hybrid curved-linear method. This approach estimates the curved section by a log-spiral function, which then connects to the backfill surface with the conventional linear assumption. The main drawback here is that the geometric properties of the hybrid mathematical function is not directly related to the mechanical properties of soils. Thus, this study attempts to provide a mechanical description for the assumed geometrical parameters. For this purpose, a series of 1 g small scale retaining wall model tests, simulating passive failure, are conducted on two different backfill soils. The relative density is varied in the model tests and the resultant peak friction angles of the backfills are calculated as functions of failure stress state and relative density using a well-known empirical equation. Transparent sidewalls allow for visualization of the failure surface evolution, which is obtained by capturing images and analysing then through Particle Image Velocimetry (PIV) technique. Subsequently, the quantified slip zones are fitted with the hybrid curved-linear approach. The relationships between the peak friction angle and the geometrical characteristics of the best-fit log-spiral and linear functions are investigated. Obtained results are used to propose a set of equations that allow the estimation of non-linear passive failure surfaces as function of peak friction angle.

Discrete Element Modelling (DEM) is a virtual testing method that enables multiscale studies on granular materials. DEM provides a well-controlled testing environment, which enables precise systematic evaluation of the factors influencing the bulk response. The current study focuses on the behaviour of cohesionless backfills while a passive state of stress is simulated (i.e. rigid retaining wall translates toward backfill). Though particle-scale properties (e.g. size, shape and cohesion) play an important role on the macro response, the main objective in this study is to highlight the extent by which boundary conditions are important. Thus, identical dense packings are subject to the following boundary conditions: smooth/rough retaining wall and smooth/rough/periodic sidewalls (necessary for maintaining plain-strain conditions). Based on the DEM results, the failure surface geometries, wall pressure distribution and dilative response of the specimens are evaluated. It is seen that a curvilinear slip surface, similar to that observed in experiments, is only obtained once a rough retaining wall and periodic sidewalls are available. The overall observations suggest that the mobilisation of the passive state of stress, for a cohesionless granular assembly, is highly sensitive to the considered various boundary conditions.

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Masonry retaining walls are designed to resist lateral forces. Their stability is essentially warranted by the correct determination of the failure surface geometry. Accordingly, this study intended to investigate the influence of wall and backfill properties that control failure surface geometry of cohesionless backfills. For this purpose, the discrete element method (DEM) is utilized, and a series of parametric studies were conducted. As the wall-joint parameters reflect the mortar quality of the blocks that constitute the masonry wall, three binder types from weak to strong were defined. Additionally, loose to dense backfill soil conditions and wall-backfill interface properties were also investigated. The results indicate that in the case of a thin rigid wall, the failure surface of dense backfill is identical with the classical earth pressure theory. However, for the masonry walls with a higher foundation width, the failure surfaces are much deeper and wider; particularly on the active side compared to the classical earth pressure theories. In addition to that the deformation mechanism and the associated failure surfaces are greatly influenced from the mortar quality which results with either a deep-seated or sliding type of failure.