Maximum Surface Settlement (Tunnel)
Calculate the maximum surface settlement, over the tunnel axis, S_max = Vs ÷ (i·√(2π)), from the settlement trough volume per metre of tunnel Vs (m³/m, the lost soil volume surfacing) and the trough-width parameter i (m, Peck's method). Since the trough is Gaussian, integrating the curve gives Vs = √(2π)·i·S_max, isolating the maximum settlement, which occurs right over the axis. This is the critical value for damage assessment: compared to allowable limits (typically 10-25 mm for sensitive structures), it decides whether the excavation is safe or needs mitigation. Enter the trough volume and the width parameter.
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Recalque máximo superficial de túnel
O recalque máximo de superfície, que ocorre exatamente sobre o eixo do túnel, é S_max = Vs ÷ (i·√(2π)), onde Vs é o volume da bacia de recalque por metro de túnel (o volume de solo perdido que aflora na superfície, em m³/m) e i é o parâmetro de largura da bacia de Peck. A fórmula sai da geometria da bacia gaussiana: como a área sob a curva de Gauss é √(2π)·i·S_max, e essa área é justamente o volume perdido Vs por metro, basta isolar o recalque máximo. Esse é o valor crítico de toda a análise de túneis urbanos, porque é o ponto onde a superfície mais afunda. Compara-se S_max com limites admissíveis — tipicamente 10 a 25 mm para edificações sensíveis, menos ainda para estruturas históricas ou ferrovias — para decidir se a escavação é segura ou se exige medidas de mitigação: injeções de compensação (compensation grouting, que reinjetam solo para reerguer o terreno), aumento da pressão de face da TBM, ou até congelamento artificial do solo. O recalque máximo, junto com a perda de volume, é o indicador que conecta a operação da máquina embaixo da terra aos danos potenciais nos edifícios na superfície — o coração do desafio geotécnico de tunelar sob cidades densas sem trincar prédios. Informe o volume da bacia e o parâmetro de largura.
Related Tools
Peck Settlement Trough Width
Calculate the trough-width parameter of the surface settlement induced by tunnelling, i = K·z₀, by Peck's method, from the trough-width parameter K (~0.5 for clays, ~0.25-0.35 for sands) and the tunnel axis depth z₀. The surface settlement from ground loss follows a Gaussian (inverted bell) curve, and i is its standard deviation — the horizontal distance from the tunnel axis to the inflection point, defining the trough width. Larger i means a wider, gentler trough (clays); smaller means narrower and deeper (sands). This parameter is essential to predict damage to nearby buildings in urban tunnels. Enter the K parameter and the tunnel depth.
Tunnel Volume Loss
Calculate the volume loss of a tunnel excavation, VL = Vs ÷ (π·D²/4)·100, the percentage ratio between the settlement trough volume per metre Vs (m³/m) and the excavated cross-section area (from diameter D). Volume loss quantifies how much soil 'disappeared' relative to the theoretical tunnel volume — caused by face relaxation, overexcavation, tail-gap closure behind the TBM shield and consolidation. It is the key control parameter for urban excavation: well-run EPB/slurry TBMs achieve 0.5-1.5% in soils; values above 2-3% indicate problems and excessive settlement. Enter the trough volume and the tunnel diameter.
Tunnel Convergence
Calculate a tunnel's convergence — the relative radial deformation of the excavation, ε = (u ÷ r)·100 — from the radial displacement u (the inward movement of the walls toward the center, measured by extensometers or total station) and the excavation radius r, in the same unit. Convergence is the primary monitoring indicator in NATM (New Austrian Tunnelling Method): it measures how much the rock mass deforms after excavation, reflecting stress mobilization and support effectiveness. Low, stabilized convergence indicates a stable mass; high, growing or accelerating convergence signals squeezing, instability or insufficient support, requiring immediate reinforcement. Enter the radial displacement and the tunnel radius.
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