Main Formulas for Surface Settlement and Lateral Deformation in Excavations
The maximum surface settlement, denoted as δv(max), is commonly estimated using the maximum lateral deformation of the excavation wall, δH(max). Both values are typically normalized by the excavation height (H) for consistency and comparison.
Relationship Between Surface Settlement and Lateral Deformation
From empirical studies and graphical analysis, the following general relationship has been derived:
δv(max) ≈ 0.5 × δH(max) to 1.0 × δH(max)
This means that maximum surface settlement is usually between 50% to 100% of the maximum lateral wall displacement.
Findings by Researchers
Gassler & Gudehus (1981) and Shen et al. (1981), based on full-scale tests, established the following for nail walls and reinforced excavations:
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For reinforcement length-to-height ratios (L/H) between 0.7 to 1.0
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With a global factor of safety (FoS) around 1.5
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In absence of surcharge loads near the edge of the excavation
The maximum long-term horizontal and vertical deformations were observed to vary between:
0.1% to 0.3% of the vertical excavation height (H)
This data provides a reliable benchmark for estimating long-term deformation behavior of deep excavations stabilized using nail walls and similar retaining systems.
