Flow in Aquifers 2 Unconfined Aquifer Flow Groundwater

Flow in Aquifers – 2 Unconfined Aquifer Flow Groundwater Hydraulics Daene C. Mc. Kinney 1

Summary • Unconfined Aquifer Flow – Continuity Equation – Steady Horizontal Flow with Infiltration – Drains 2

Unconfined Aquifer • Flows bounded above by a water table occur in unconfined aquifers • Thickness of capillary fringe above the water table is assumed to be much smaller than the saturated domain below the water table • The water table is a nonlinear boundary and makes the exact solution of the governing equations almost impossible • Approximate solutions can be obtained based on a linearization of the boundary conditions or the nonlinear continuity equation. 3

Flow in an Unconfined Aquifer • Dupuit approximations – Slope of the water table is small – Velocities are horizontal – Considers a streamtube bounded by two streamlines: water table and impervious bottom Ground surface Water table Qx h(x) z K y Unconfined aquifer x Bedrock w 4

Continuity Equation in an Unconfined Aquifer N (accretion, infiltration) Water table h 5

Continuity Equation in an Unconfined Aquifer • 6

Continuity Equation in an Unconfined Aquifer • Homogeneous aquifer (K = constant) • Steady flow • No accretion (infiltration) • One-dimensional flow 7

1 -D Steady Flow in an Unconfined Aquifer • Find the head in a homogeneous, unconfined aquifer with steady flow from left to right Governing equation Simplifications: steady, 1 -D flow, K = Constant, No accretion Ground Surface Water Table Head in the aquifer Flow h. A h Bedrock x h. B L 8

Steady Flow in an Unconfined Aquifer • • • K = 10 -1 cm/sec L = 150 m h. A = 6. 5 m h. B = 4 m x = 150 m Find Q Ground Surface Water Table Flow h. A=6. 5 m h Bedrock x K=0. 1 cm/s h. B=4 m L=150 m 9

1 -D Steady Flow in an Unconfined Aquifer with Infiltration • Find the head in a homogeneous, unconfined aquifer with steady flow from left to right Governing equation Simplifications: steady, 1 -D flow, K = Constant, With accretion N, Infiltration Ground Surface Water Table h. A h. Max h Flow h. B Bedrock x L 10

Steady flow in an unconfined aquifer with infiltration N, Infiltration Ground Surface Water Table h. A h. Max h Flow h. B Bedrock x L 11

Example (Embankment) N, Infiltration • Given L = 3000 m K = 20 m/day h. A = 30 m h. B = 20 m N = 500 mm/yr Ground Surface Water Table h. A h. Max h Flow h. B Bedrock x L • Find: Flow to the streams and shape of water table 12

Example (Cont. ) N, Infiltration Ground Surface Water Table h. A h. Max h Flow h. B Bedrock x L 13

Unconfined Flow in an Aquifer with Horizontal Stratification Observation Well A Observation Well B Ground Surface Water Table K 2 h. A h. B a Bedrock x K 1 L 14

Example Observation Well A Observation Well B Ground Surface Water Table K 2 h. A h. B a Bedrock x K 1 L 15

Example (Drains) • • Subsurface drains are often used to prevent the water table elevation from increasing to an elevation where it would waterlog the roots of crops or bring unwanted salts and other chemicals in to the root zone. Steady, 1 -D flow , homogeneous, isotropic aquifer, w/infiltration N, Infiltration Ground Surface Water Table h. Max hd x L Lower Confining Layer 16

Summary • Unconfined Aquifer Flow – Continuity Equation – Steady Horizontal Flow with Infiltration – Drains 17