Shallow stability analysis of natural or man-made soil slopes requires accurate characterisation of soil strength at low effective stresses (5–20 kPa), corresponding to mechanisms expected at 1–2 m depth. This study focused on the intertwining effects of soil structures at different scales and low stresses on the undrained strength of fine-grained soils, by testing two natural plastic clays and a clay–sand mixed soil at different states (intact, reconstituted and compacted) in a series of constant-volume direct shear and hollow cylinder simple shear tests. The non-linearity of the Hvorslev bounding surface was expressed well by a power law function. The normalised strength and the degree of its non-linearity of the clays at intact states were higher than at equivalent reconstituted states, probably owing to true inter-particle cohesion, as confirmed by the hollow cylinder apparatus tests. The compacted states led to significantly lower normalised strength than the reconstituted state in both clays, while they did not show significant difference in the clay–sand mixed soil. This observation was explained by meso-scale discontinuities by X-ray micro-computed tomography images. Compacted clays’ shear strength is associated with a meso-fabric very different from that in more homogeneous intact and reconstituted clays, and the conventional state normalisation based on the equivalent pressure does not capture it.