Analitical deriving of the field capacity through soil bundle model

The concept of field capacity as soil hydraulic parameter is widely used in many hydrologicalapplications. Althought its recurring usage, its definition is not univocal. Traditionally, field capacityhas been related to the amount of water that remains in the soil after the excess water has drainedaway and the water downward movement experiences a significant decresase. Quantifying thedrainage of excess of water may be vague and several definitions, often subjective, have beenproposed. These definitions are based on fixed thresholds either of time, pressure, or flux to whichthe field capacity condition is associated. The fluxbased definition identifies the field capacity as thesoil moisture value corresponding to an arbitrary fixed threshold of free drainage flux. Recently, manyworks have investigated the fluxbased definition by varying either the drainage threshold, thegeometry setting and mainly the description of the drainage flux. Most of these methods are based onthe simulation of the flux through a porous medium by using the Darcy’s law or Richard’s equation.Using the abovementioned fluxbased definition, in this work we propose an alternative analyticalapproach for deriving the field capacity based on a bundleoftubes model. The pore space of aporous medium is conceptualized as a bundle of capillary tubes of given length of different radii,derived from a known distribution. The drainage from a single capillary tube is given by the analyticalsolution of the differential equation describing the water height evolution within the capillary tube. Thisequation is based on the Poiseuille’s law and describes the drainage flux with time as a function oftube radius. The drainage process is then integrated for any portion of soil taking into account thetube radius distribution which in turns depends on the soil type. This methodology allows toanalytically derive the dynamics of drainage water flux for any soil type and consequently to definethe soil field capacity as the latter reachs a given threshold value. The theoretical model alsoaccounts for the tortuosity which characterizes the water pathways in real soils, but neglects thevoids mutual interconnections.