Analytical approach for time‐dependent groundwater inflow into shield tunnel face in confined aquifer

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Summary This paper presents an analytical evaluation on the influence of foam conditioning on groundwater inflow at shield tunnel cutting face by the force‐equilibrium principle. Three key variables are highlighted, namely, the maximum foam infiltration distance, the critical infiltration distance, and the hydraulic conductivity of foam‐conditioned soil or rock fissure. To capture the variation of water level induced by foam injection, a dynamic water‐level equation is considered in the force‐equilibrium principle. The proposed analytical equations are employed to analyze a water inflow case during shield tunneling in a weathered mylonite fault. The results indicate that the hydraulic conductivity of foam‐conditioned mylonite and the infiltration distance decrease with an increase of shear stress of foam fluid. A three‐dimensional finite element model is employed to validate the analytical solutions. The comparison between the observed and calculated results confirms that the proposed method can predict groundwater inflow in foam‐conditioned soils.

Q ((), t) = \frac{16.11 k_{x} k_{y} λ S_{λ} ((), t)}{k_{z} ([], \frac{2}{M} \sqrt{\frac{{tk}_{z}}{S_{s}}} + \sqrt{π} ln \frac{k_{z} t}{S_{s} M^{2}})},

Section: Formulationmentioning

confidence: 99%

Section: Analytical Solutions Of a Groundwater Inflow Casementioning

confidence: 99%

“…Longitudinal geotechnical profiles of investigated tunnel section (data from Liu et al) [Colour figure can be viewed at wileyonlinelibrary.com]…”

Section: Analytical Solutions Of a Groundwater Inflow Casementioning

confidence: 99%

Section: Analytical Solutions Of a Groundwater Inflow Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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This paper presents an analytical model to investigate backfill grout diffusion behind tunnel segmental lining, in which the backfill grout is taken as a Bingham fluid. The analytical model of grout diffusion is derived based on force–equilibrium principle, Darcy's law, and the law of momentum conservation of the grout. Time‐dependent grout diffusion pressure and distance are highlighted in the model. The proposed grout diffusion model is applied in two field cases: Metro Lines No. 9 and No. 4 in Shanghai City. The results show that the proposed model agrees well with the measured grout diffusion distance in the field. Parametric studies are then conducted, implying that grout diffusion distance along the radial direction of tunnel lining is proportional to either hydraulic conductivity or initial grout pressure, whereas it is in inverse proportion to the yield stress of backfill grout. The distributions of initial grout pressure exert key influences on the grout diffusion distance and grout diffusion pressure behind tunnel segment lining.

A two‐dimensional analytical model for organic contaminant transport in cutoff wall and aquifer system

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