Analytical Solution for Modeling Discharge into a Tunnel Drilled in a Heterogeneous Unconfined Aquifer

Predicting transient inflow rates into a tunnel is an important issue faced by hydrogeologists. Most existing analytical solutions overestimate the initial discharge due to the assumption that drilling was instantaneous over the entire tunnel length. In addition, they assume a homogeneous system. An alternative model was recently developed for tunnels intersecting heterogeneous formations, but its application was reduced to the case of confined flow to deep tunnels in weakly diffusive aquifers. In this paper, we adapt existing analytical solutions for drainage systems to the specific case of a tunnel progressively drilled in a highly diffusive heterogeneous unconfined aquifer. The case of a tunnel overlying an impervious layer is analytically solved by applying the superposition principle, while the case of a tunnel constructed some distance above an impervious layer is solved by discretizing the tunnel length into subsectors. Both models can simulate transient discharge into a tunnel drilled at various speeds through a heterogeneous unconfined aquifer, and allow the prediction of discharge rates in shallow tunnels located in highly diffusive aquifers. We successfully applied this approach to a tunnel in heterogeneous volcanic rock.     

Application of an Analytical Solution as a Screening Tool for Sea Water Intrusion

Sea water intrusion into aquifers is problematic in many coastal areas. The physics and chemistry of this issue are complex, and sea water intrusion remains challenging to quantify. Simple assessment tools like analytical models offer advantages of rapid application, but their applicability to field situations is unclear. This study examines the reliability of a popular sharp‐interface analytical approach for estimating the extent of sea water in a homogeneous coastal aquifer subjected to pumping and regional flow effects and under steady‐state conditions. The analytical model is tested against observations from Canada, the United States, and Australia to assess its utility as an initial approximation of sea water extent for the purposes of rapid groundwater management decision making. The occurrence of sea water intrusion resulting in increased salinity at pumping wells was correctly predicted in approximately 60% of cases. Application of a correction to account for dispersion did not markedly improve the results. Failure of the analytical model to provide correct predictions can be attributed to mismatches between its simplifying assumptions and more complex field settings. The best results occurred where the toe of the salt water wedge is expected to be the closest to the coast under predevelopment conditions. Predictions were the poorest for aquifers where the salt water wedge was expected to extend further inland under predevelopment conditions and was therefore more dispersive prior to pumping. Sharp‐interface solutions remain useful tools to screen for the vulnerability of coastal aquifers to sea water intrusion, although the significant sources of uncertainty identified in this study require careful consideration to avoid misinterpreting sharp‐interface results.     

An Analytical Method for Groundwater Inflow into a Drained Circular Tunnel

Groundwater inflow estimation is essential for the design and construction of tunnel and the assessment of the environmental impacts. Analytical solutions used in current engineering practice do not adequately account for the effect of the excavation‐induced drawdown, which leads to significant change in pore water pressure distribution and reductions of the water level beyond tunnel. Based on the numerical analysis results, this article proposes semianalytical method to predict the height of lowered water level and groundwater tunnel inflow. The tunnel problem is conceptualized as two‐dimensional flow in a plane perpendicular to the tunnel axis. The analytical formula, considering the effect of the excavation‐induced drawdown, provides a better prediction of the tunnel inflow compared to the existing analytical formulas, even for the cases with inclined groundwater level.     

饱和土半空间中地下圆形衬砌洞室对平面SV波的散射

在Biot饱和多孔介质动力学理论的基础上,利用Fourier-Bessel级数展开法,通过对舍有衬砌洞室的局部场地进行波场分析,得到饱和土半空间中圆柱形衬砌洞室对平面SV波的散射问题的解析解。经验证,本文得到的解可以退化为半空间单相介质的情况。通过与已有的单相弹性介质半空间中圆柱形衬砌洞室对平面SV波散射问题的解析解的对比,验证了此解的正确性。在解析解的基础上,数值计算给出洞口动应力集中放大系数,分析了入射频率和孔洞埋深对柱面上的应力集中因子的影响。     

A Field Test of Electromigration as a Method for Remediating Sulfate from Shallow Ground Water

Eloctromigraiion offers a potential tool for remediating ground water contaminated with highly soluble components, such as Na⁺, Cl, NO₃ and SO₄⁻. A field experiment was designed to lest the efficacy of electromigration for preconcontrating dissolved SO₄² in ground water associated with a fossil-fuel power plant. Two shallow wells, 25 feel apart (one 25 feel deep, the other 47 feet deep), were constructed in the upper portion of an unconfined alluvial aquifer. The wells were constructed with a double-wall design, with an outer casing of 4-inch PVC and an inner lube of 2-inch FVC; both were fully slotted (0.01 inch). Electrodes were constructed by wrapping the inner lulling with a 100-foot length of rare-earth metal oxide/copper wire. An electrical potential of 10.65 volts DC Was applied, and tests were run for periods of 12, 44, and 216 hours. Results showed large changes in the pH from the initial pH of ground water of about 7.5 to values of approximately 2 and 12 at the anode and cathode, respectively. Despite the fact that the test conditions were far from ideal, dissolved SO₄^2-; was significantly concentrated at the anode. Over a period of approximately nine days, the concentration of SO₄^2- at the anode reached what appeared to he a steady-state value of 2200 mg/L. compared lo the initial value in ground water of approximately 1150 mg/L. The results of this field lest should encourage further investigation of electromigration as a tool in the remediation of contaminated ground water.     

An analytical solution for predicting transient seepage into ditch drains from a ponded field

An analytical solution is provided for predicting time dependent seepage into an array of equally spaced parallel ditch drains in a homogeneous and anisotropic soil medium underlain by an impervious layer and receiving water from a ponded horizontal field of infinite extent. The solution can account for both unequal levels of water in the adjacent drains and variable depths of ponding at the soil surface. The validity of the developed model is tested by first reducing it to a steady state solution and then comparing predictions obtained from it for a few flow situations with corresponding predictions obtained from the analytical works of others. A numerical comparison of the developed model for a flow situation is also carried out using MODFLOW. The surface discharge distribution is found to show relatively greater uniformity at the early stages of simulation but with the progress of time, the extent of uniformity is found to reduce particularly for cases where the soil is subjected to a uniform depth of ponding. However, even when a soil surface is subjected to a constant depth of ponding, a high anisotropy ratio (ratio of horizontal to vertical hydraulic conductivity of soil) of the soil alone may lead to a marked improvement on the uniformity of the surface discharge distribution at all times in comparison to a soil having a low anisotropy ratio. A better uniformity of surface discharge may also be achieved by suitably adjusting the depths of ponding over the surface of the soil – regions close to the ditches be provided with zero or negligible depths of ponding and the ponding depths may be made to progressively increase with the increase in distance from the ditch faces. As the developed analytical model is of a general nature, it is hoped that the solution provided herein will lead to a better and realistic design of ditch drainage networks for controlling waterlogged areas and in reclaiming salt affected soils.     

A Laboratory Study of Electromigration as a Possible Field Technique for the Removal of Contaminants from Ground Water

A method for removing dissolved contaminants from ground water by emplacing electrodes in the aquifer has been tested using laboratory columns of pure quartz silty sand saturated with solutions of CuSO4 and copper-contaminated synthetic ground water. In the Soviet Union a similar method is commonly used in searching for hidden deposits of metallic minerals. In the Soviet method, electrodes are emplaced in the ground and ions of the metals being sought are caused to migrate along an imposed voltage gradient; the ions are collected for analysis in acid-filled ceramic cylinders which surround the cathodes.
In this study, quick-freezing was used to obtain the distribution of ions within the columns as a function of time and space. With voltages up to 2.5 V and cur-rents of a few tens of microamps, more than 50 percent of the dissolved copper was removed from the interstitial fluid in the porous columns in a period of five days. Current efficiencies ranged from more than 80 percent to less than 5 percent, depending on such factors as length of time of electrolysis, pH, concentration of Cu, and presence of other ions. The efficiency and economics of the technique of electromigration should be evaluated in additional laboratory studies and in the field, but in theory the method should be useful for removing any charged species in ground water, including some organics.