Deep braced excavations are widely employed to support urban construction, with the axial stiffness of strut systems playing a crucial role in their structural performance. However, field observations have consistently shown that the effective axial stiffness of struts is often significantly lower than theoretical values, frequently attributed to slack arising from imperfections during assembly, gaps between structural elements, and initial curvatures. This paper presents a nonlinear model that captures the deformation-dependent stiffness behaviour arising from those initial imperfections. The model is governed by a single physically interpretable parameter, which controls the offset between effective and theoretical force–deformation curves and serves as an indicator of construction quality. A consistent unloading–reloading response and pre-stressing capability are incorporated within the same framework. The model is applied to a single-propped embedded wall to demonstrate its performance. The results confirm that the range of effective stiffness values reproduced by the model is consistent with instrumented case studies reported in the literature, and that pre-stressing improves average stiffness and reduces wall displacements. A straightforward calibration procedure based on monitored force–displacement data is proposed, enabling application within the Observational Method to improve predictions and inform installation practice.
Taborda et al. (2026) studied this question.