Watertable dynamics under capillary fringes: experiments and modelling

Watertable heights and total moisture content were measured in a sand colum n where the piezometric head at the base ("the driving head") varied as a s imple harmonic with periods in the range from 14.5 min to 6.5 h. The watert able height h(t) responded very closely to the driving head compared with t he predictions of previous analytical and numerical models. The total moist ure quantified as an equivalent, saturated height h(tot)(t) varied very lit tle compared with the watertable height. Neither h(t) nor h(tot)(t) deviate d significantly from simple harmonics when the driving head was simple harm onic. This indicates that non-linear effects are weak and hence that analys is based on linear solutions have fairly broad applicability. When h(t) and h(tot)(t) are simple harmonic, the ratio n(d) = [dh(tot)/dt]/[dh/dt] is a constant in the complex formalism. Its magnitude \n(d)\ is the usual effect ive porosity while its argument accounts for the phase shift which is alway s observed between h(t) and h(tot)(t). Within the current range of experime nts this dynamic, effective porosity nd appears to be almost independent of the forcing frequency, i.e., it is a function of the soil and its compacti on only. Introducing the complex nd enables analytical solution for the wat ertable height in the column which is simpler and more consistently accurat e over a range of frequencies than previous models including Richard's equa tion with van Genuchten parameters corresponding to the measured water rete ntion curve. The complex lid can be immediately adopted into linear waterta ble problems in 1 or 2 horizontal dimensions. Compared with "no fringe solu tions", this leads to modification of the watertable behaviour which is in agreement with experiments and previous models. The use of a complex nd to account for the capillary fringe in watertable models has the advantage, co mpared with previous models, e.g., [Parlange J-Y, Brutsaert W. A capillary correction for free surface flow of groundwater. Water Resour Res 1987; 23( 5):805-8.] that the order of the differential equations is lower. For examp le, the linearised Boussinesq equation with complex nd is still of second o rder while the Parlange and Brutsaert equation is of third order. The extra work of calculating the imaginary part of the initially complex solution i s insignificant compared to dealing with higher order equations. On the bas is of the presently available data it also seems that the "complex n(d) app roach" is more accurate. This is to be expected since the complex nd accoun ts implicitly for hysteresis while the Green-Ampt model does not. With resp ect to linear watertable waves, accounting for the capillary fringe through the complex n(d) is a very simple extension since the determination of wav e numbers already involves complex numbers. (C) 2000 Elsevier Science Ltd. All rights reserved.