Determination of groundwater flow regimes based on the spatial non-local distribution of hydraulic gradient:Model and validation

The groundwater flow in natural aquifers can change from the Darcy flow to the non-Darcian flow due to a variety of causes,such as the increase of the Reynolds number in the highly permeable media or the decrease of the hydraulic gradient below a threshold in the low-permeability media,while the representative flow regime cannot be reliably determined using the traditional criteria.To address this challenge,this paper proposes a new term called the equivalent hydraulic gradient(EHG)by generalizing the differential form of the Darcy’s law using a spatial integral of the upstream hydraulic head.The nonlocal spatial variation of the hydraulic head difference between upstream and downstream zones is assumed to be the potential cause of the transition of the groundwater flow regimes.This assumption is analogous to the common assumption used for quantifying the anomalous pollutant transport in the geological media.Applications of this idea show that the EHG concept could distinguish three main flow regimes,namely the Super-Darcy flow,the Darcy flow,and the Sub-Darcy flow,although the Super-Darcy flow regime is rarely observed in the laboratory column flow experiments.Results of this study therefore shed lights on the interpretation of the fundamental dynamics of the groundwater moving in various heterogeneous aquifers,and may lead to the rebuilding of the hydrodynamics of the surface water,the groundwater,and the soil.

Influence of permeability anisotropy of seepage flow on the tunnel face stability

This paper focuses on the influence of permeability anisotropy of seepage flow on the face stability for a shied tunnel.An analytical model has been proposed to present the hydraulic head distribution around the tunnel face in the anisotropic ground,considering the difference of permeability coefficient in the horizontal direction and the vertical direction.The rationality of the proposed model is ver-ified by a series of numerical simulations.Then,an analytical model of face stability for a tunnel under the anisotropic seepage has been established based on the limit analysis upper bound method.Comparisons of the analytical solutions and the numerical simulations are conducted,and the limit support pressure of the two methods is consistent.The effect of permeability anisotropy and water pressure on the stability of the tunnel face is analyzed through the three-dimensional analytical solution.Anisotropy of permeability has a significant impact on the stability of the tunnel face,and its impact gradually decreases.It can also be found that the water pressure coefficient of the tunnel face has a significant effect on the limit support pressure and the failure area when the ratio of the horizontal permeability to the vertical permeability is large.

Three-dimensional theoretical analysis of seepage field in front of shield tunnel face

To evaluate hydraulic head distribution in front of a shield tunnel in a saturated soil layer,theoretical analysis and numerical simulations are carried out in this study.Based on the partial differential equilibrium equation of seepage flow,a three-dimensional(3D)theoretical analytical model of the shield tunnel face and the seepage field in front of it is established using the eigenfunction and the Fourier series expansion methods,and the hydraulic head calculation formula is derived.Combined with engineering cases,the theoretical analysis results and the 3D numerical simulation results are compared and analyzed.The effect of the water pressure of the tunnel face on the hydraulic head distribution is also analyzed.The results of the proposed analytical solution are in agreement with those of the numerical simulation solutions;moreover,the proposed analytical solution requires less time to calculate the seepage hydraulic head than the numerical simulation.The ratio of the initial water table to the diameter(D)of tunnel face has a more significant impact on the hydraulic head distribution at a position 0.5D above the tunnel vault.When the water pressure on the tunnel face is not considered,the values of the hydraulic head are significantly underestimated.