Stress and Strain Distributions Behind the Earth-Retaining Structure and the Corresponding Force-Displacement Behaviour


Student thesis: Doctoral Thesis

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Awarding Institution
Award date11 Apr 2019


Earth-retaining structures are widely used in civil engineering projects to maintain the stability of two adjacent, discontinued ground surfaces with a large, sudden elevation change in between. Safe and economical design of an earth-retaining structure relies on the understanding of the stress distribution, failure mechanism, and deformation in/of the backfill. Conventionally, these structures are designed following the force-based design (FBD) methods, which focus mostly on failure prevention and ignore the losses incurred by excessive deformation. In view of the deficiencies in FBD, an advanced design methodology, known as the performance-based design (PBD), has been introduced in the realm of earthquake/structural engineering, taking into consideration not only the strength/capacity of the structure but also the collateral losses attributable to the damage of the system. However, the application of the PBD approach in an earth-retaining structure is challenging, as it requires an accurate estimate of ground displacement, which may be unavailable in most of the prevailing earth pressure analysis models.

To tackle this issue, one may resort to commercial computer programs based on an advanced numerical theory such as the finite element method (FEM). Nonetheless, this type of modelling technique is computationally intensive and requires experienced engineers to retrieve the data and judge their reliability. Because the PBD adopts a stochastic approach to analyse and manage the seismic risks, the time-consuming nature of FEM renders it unfavourable in PBD. This study aims to pave the way towards the PBD approach for earth-retaining structures. A deterministic approach was first devised to estimate the stress distribution within the backfill; then, a semi-analytical formula capable of producing a satisfactory approximation to the resultant force is proposed to simplify the design procedure. Last, a computationally efficient model is developed to predict the force–displacement behaviour of earth-retaining structures.

This study extends a recently published analytical approach, the log-spiral-Rankine (LSR) method, to examine the stress distribution across the backfill. The LSR method inspected the stress state of soil at the failure to determine the geometry of a failure surface within the backfill. It discretized the mobilized soil mass into vertical slices and utilized the limit equilibrium concept to determine the force equilibrium conditions. In this study, the vertical slices were further broken into dices to allow for the stress variation in the vertical direction. A shear stress distribution shape function was proposed to provide additional equations required when solving for the unknown inter-dice forces. The normal and shear stress distributions predicted by the proposed dice method were verified, with the FEM simulation results showing good agreement.

The LSR method, although more accurate, relies on an iterative scheme to solve the nonlinear equilibrium equation sets. To release its complicity, a semi-analytical equation is derived to approximate the LSR’s solution using the well-known Mononobe–Okabe (MO) model coupled with two modification factors. The modification factors were introduced to account for the effects of a curvilinear failure surface and soil cohesion not considered in the MO model. The proposed simplified method is available for the passive case, and its error is around 2% overall.

This study also modified the log-spiral-hyperbolic (LSH) method to predict the nonlinear force–displacement behaviour of earth-retaining structures. The more realistic assumption for stress propagation in backfill was adopted in the formulation; the shear modulus reduction model was applied to calculate the strains of soil from the stresses, instead of using the Poisson’s ratio in the plane strain problem (which will result in a violation of the generalized Hooke’s law). The predictions of the revised LSH model were validated with several tests data as well as the solution obtained from FEM analysis. In addition, a reduced-scale retaining wall test program was conducted in this study to verify the aforementioned stress propagation assumption.