Subsurface Flow of Water in Soils and Geological Formations

Abstract

Henry Darcy was an engineer who built the drinking water supply system of the French city of Dijon in the mid-19th century. In doing so, he developed an interest in the flow of water through sands, and, together with Charles Ritter, he experimented (in a hospital, for unclear reasons) with water flow in a vertical cylinder filled with different sands to determine the laws of flow of water through sand. The results were published in an appendix to Darcy’s report on his work on Dijon’s water supply. Darcy and Ritter installed mercury manometers at the bottom and near the top of the cylinder, and they observed that the water flux density through the sand was proportional to the difference between the mercury levels. After mercury levels are converted to equivalent water levels and recast in differential form, this relationship is known as Darcy’s Law, and until this day it is the cornerstone of the theory of water flow in porous media. The development of groundwater hydrology and soil water hydrology that originated with Darcy’s Law is tracked through seminal contributions over the past 160 years. Darcy’s Law was quickly adopted for calculating groundwater flow, which blossomed after the introduction of a few very useful simplifying assumptions that permitted a host of analytical solutions to groundwater problems, including flows toward pumped drinking water wells and toward drain tubes. Computers have made possible ever more advanced numerical solutions based on Darcy’s Law, which have allowed tailor-made computations for specific areas. In soil hydrology, Darcy’s Law itself required modification to facilitate its application for different soil water contents. The understanding of the relationship between the potential energy of soil water and the soil water content emerged early in the 20th century. The mathematical formalization of the consequences for the flow rate and storage change of soil water was established in the 1930s, but only after the 1970s did computers become powerful enough to tackle unsaturated flows head-on. In combination with crop growth models, this allowed Darcy-based models to aid in the setup of irrigation practices and to optimize drainage designs. In the past decades, spatial variation of the hydraulic properties of aquifers and soils has been shown to affect the transfer of solutes from soils to groundwater and from groundwater to surface water. More recently, regional and continental-scale hydrology have been required to quantify the role of the terrestrial hydrological cycle in relation to climate change. Both developments may pose new areas of application, or show the limits of applicability, of a law derived from a few experiments on a cylinder filled with sand in the 1850s.