NUMERICAL MODELLING OF TWO-DIMENSIONAL TRANSIENT SUBSURFACE FLOW TO DITCHES

Abstract

Inadequate natural subsurface drainage in an agricultural area results in a rise of water table up to the root zone of cultivated plants. This restricts the oxygen supply to the plant root system. The high water table also reverses the benefits of leaching of soluble salts from the root zone. An appropriate artificial subsurface drainage system can maintain the water table at a permissible depth, depending upon the crop and the soil. The prevalent theories of subsurface drainage, employing Dupuit-Forchheimer assumptions, ignore the loss of head due to vertical component of flow. This leads to an underestimation of water table rise and, thus, an overestimation of drain spacing. The effect is significant in the case of horizontally stratified soils, pipe drains and partially penetrating ditches due to higher vertical velocities. The vertical flow can be accounted for by numerical solution of the differential equation governing either two dimensional flow in a vertical plane or three dimensional flow. In the present study two numerical models of two-dimensional subsurface drainage, one analysing only the saturated domain (saturated flow model) and another analysing the entire unsaturated-saturated domain (Total Response Model) have been developed. In the saturated flow model (SFM) the two dimensional nature of the flow is accounted for by a finite differences based solution of the differential equation governing two-dimensional transient, unconfined saturated flow in a heterogeneous porous medium having vertical anisotropy (subjected to drainage boundary (v) conditions). The SFM requires among others the time variant distribution of recharge rate at the water table as input data and yields the time variant water table position. In the total response model (TRM), the two-dimensional flow is accounted for by a finite differences based solution of the differential equation governing two-dimensional transient unsaturated-saturated flow in a heterogeneous porous medium having vertical anisotropy (subjected to the drainage boundary conditions). The TRM requires among others, the time variant distribution of infiltration rate at ground surface as input data and yields the spatial and temporal distribution of capillary head (h ). This in turn yields the time variant water table position defined by h =0. c In chapter III the development of saturated flow model and total response model, along with their solution techniques have been presented. The saturated flow model has been implicitly validated by comparing its response with Donnan and Kraijenhaff analytical solutions. The model computed water table rises are found to converge to these analytical solutions as the ideal conditions (negligible relative resistance to vertical flow, i.e., K /K >>1) z x assumed in the analytical solutions are approached. However, under non-ideal conditions the analytical solutions are found to underestimate the water table rise. The model computed lateral flows (with K_/K >>1) into a ditch are also found to compare well with the Edelman solutions under different conditions, viz, (i) sudden lowering of water level in the ditch, (ii) constant lateral flow from aquifer to the ditch, (iii) linearly increasing lowering of water level in the ditch, and (iv) linearly (vi) increasing lateral flow to the ditch. The computed rises by the saturated flow model and the total response model have been compared with the corresponding field data from Haryana, India, reported by Chhedi Lai (1986). The two models have reproduced the water table rises quite well. As expected, the reproduction by the total response model is better. In chapter IV, the model validation, by comparing it with the analytical solutions and the reported field data, has been presented in detail. The model solution for partially penetrating ditch systems has been presented in the form of dimensionless design curves. The ratio Ah/Ah , i.e., the water table rise at the midsection computed by the model (Ah) divided by Kraijenhoff solution (Ah ), is expressed as a function of three dimensionless independent variables K /K , d/Yn, and d/L. The design curves along with Kraijenhoff solution permit graphical estimation of the steady state rise of water table (accounting for the vertical flows) within a practical range of geometric dimensions and parameters (i.e. 20 > K/Km> 0,1.0 > d/Y > 0.25, 0.5 > d/L X Cm U >0.075). The bank storage development and its subsequent release to a ditch has been studied by passing an assumed stage hydrograph of 7 days duration through the drain. For the case considered, it is found that for no infiltration on the ground surface 60% of the bank storage is released within a short period (20 days). The rest 40% is released slowly. The total response model developed in the present study is capable of simulating the generation of perched water table (vii) • condition (and associated throughflows to the drains) over an impeding layer in the unsaturated zone. The throughflow development has been studied by considering a horizontal clay layer in the unsaturated zone of a ditch system consisting of uniform loam soil above and below the clay layer. The applications of the two models, have been described in details in chapter V. The prominent conclusions drawn from the study have been presented in chapter VI.