Impact d’une galerie étanche peu profonde sur l’écoulement d’une nappe

Résumé

On étudie la modification de la surface piézométrique d’une nappe, initialement en écoulement uniforme, liée à la présence d’un ouvrage linéaire d’axe horizontal perpendiculaire à la direction de l’écoulement. Pour une nappe captive, on propose des solutions analytiques approchées dans lesquelles la perte de charge supplémentaire introduite par l’ouvrage est proportionnelle au gradient hydraulique régional et fonction du rapport de la dimension de l’ouvrage à l’épaisseur de l’aquifère. Des simulations numériques établissent que, pour un milieu isotrope, la largeur d’influence de l’ouvrage, vers l’amont et l’aval est inférieure à trois fois le diamètre de l’ouvrage. On met en évidence l’importance d’une anisotropie des conductivités hydrauliques horizontale et verticale. Pour une nappe libre et un ouvrage entièrement submergé, une perturbation significative de la position de la surface libre de la nappe n’intervient que pour des valeurs relativement élevées du gradient hydraulique régional et lorsque la crête de l’ouvrage est proche de la surface libre.

Abstract

While many studies have been achieved on the interactions between groundwater and deep tunnels, in order to identify the evolution of pore pressure around the structure and to characterize the flow to its leaky parts, few studies have dealt with the impact of the carrying out of an impervious gallery in a shallow aquifer. The induced change in the piezometric level of the aquifer and the one in the hydraulic gradient of the flow however can, in this case, have significant consequences, in particular when the linear structure is located in an urban environment. This paper investigates, in steady state, the case of a straight tunnel having a horizontal axis perpendicular to the direction of the regional groundwater flow and a circular or square cross section. The aim is to determine the additional lost head Δh _s due to the tunnel (i.e. additional to that resulting from the regional flow, supposed to be uniform with a hydraulic gradient i ₀). In the context of a horizontal confined aquifer having a thickness 2B and of a tunnel of radius R located in the middle part of the aquifer, an analogy can be established with the flow above a hydraulic threshold resulting from a local rise of the elevation of the base of an aquifer, having a thickness B, on a width 2R and with a vertical maximum amplitude R. When neglecting the vertical component of the hydraulic gradient compared to its horizontal component, analytical solutions are developed for various hydraulic threshold shapes (rectangular, triangular and circular), based on the equivalence with a local change in the transmissivity of an aquifer keeping a constant thickness. The corresponding formulas take the form: ${\frac{{\Updelta h_{s} - \Updelta h_{0} }}{{\Updelta h_{0} }}} = f(a)$, with $a = {\frac{R}{B}}$ and Δh ₀ = 2Ri ₀. The use of these formulas shows that the additional lost head Δh _s due to the hydraulic threshold is proportional to i ₀ and that, for values of the ratio a < 0.5, the change in the piezometric surface is small. These conclusions are therefore limited by the fact that the vertical conductivity is supposed to be very large. In order to remove this hypothesis, numerical simulations are achieved using the MODFLOW code. It is considered a confined aquifer of length 2L = 110 m and thickness B = 10 m, a ratio $a = {\frac{R}{B}} = 0.25$ and a horizontal hydraulic conductivity $K_{H} = 10^{ - 5} \,{\text{m}}\,{\text{s}}^{ - 1}$. In the case of an isotropic medium ($\alpha = {\frac{{K_{H} }}{{K_{V} }}} = 1$), the simulations allow to check the linearity of the relationship between Δh _s and i ₀, with therefore a homogeneous variation in the proportionality coefficient compared to analytical solutions. Simulations also reveal that, in the case considered, the width of influence upstream and downstream L _i , corresponding to a value of the vertical component of the hydraulic gradient <1% of i ₀, is below 5.5R for the three hydraulic threshold shapes, and that it was few influenced by the hydraulic gradient i ₀. In the case of an anisotropy of the horizontal and vertical hydraulic conductivities, simulations reveal the significant importance of the anisotropy ratio $\alpha = {\frac{{K_{H} }}{{K_{V} }}}$ when it is more than 1, the most common case, and indicate that the proposed analytical solutions give an asymptotic value of ${\frac{{\Updelta h_{s} }}{{\Updelta h_{0} }}}$ for the isotropic case and for the values of the component α < 1. In the context of an unconfined aquifer, the hydraulic threshold model is not directly applicable. The model studied, using the Dupuit-Forchheimer assumption, is the one of a water table aquifer with a sloped base (slope value: p ₀). The simulations focus on an aquifer of length 2L = 85 m, with a tunnel of circular cross section having a diameter 2R = 5 m, bottom of which is located 5 m above the base of the aquifer, the isotropic hydraulic conductivity being equal to $K = 10^{ - 5} \,{\text{m}}\,{\text{s}}^{ - 1}$. The definitions of water heights d ₀ and d between the water table and the top of the tunnel are given in Fig. 7. The water table can be located above (fully submerged tunnel) or below (partially emerged tunnel) the top of the tunnel. The difference d ₀ − d represents the half of the additional lost head Δh _s due to the tunnel. Simulations are performed for various values of p ₀ and d ₀. They provide the values of i ₀, d and Δh _s . In the case of a fully submerged tunnel (d > 0), a significant rise of the water table upstream of the tunnel is obtained only for high values of the hydraulic gradient (5 and 10%), but, even in this case, it remains less than the tenth of the wetted height of the aquifer h _m . It is also highlighted that the ratio ${\frac{{\Updelta h_{s} }}{{i_{0} }}}$ varies as a linear function of (R + d) and that, in the studied case, there is no influence of the tunnel for d ≥ 4R. In the case of a partially emerged tunnel (d < 0), the aquifer is locally confined under the tunnel. It is suggested that an equivalence is possible with the case of a confined aquifer having a thickness equal to the wetted height in the unconfined aquifer. This is verified with one of the simulations. In the case of a partially emerged tunnel, the change in the water table due to the tunnel remains low.