Ground Water Hydrology Introduction - 2005 Philip B. Bedient Civil & Environmental Engineering Rice University

GW Resources - Quantity Aquifer system parameters Rate and direction of GW flow Darcy’s Law - governing flow relation Dupuit Eqn for unconfined flow Recharge and discharge zones Well mechanics- pumping for water supply, hydraulic control, or injection of wastes

GW Resources - Quality Contamination sources Contaminant transport mechanims Rate and direction of GW migration Fate processes-chemical, biological Remediation Systems for cleanup

Trends in Ground Water Use

Ground Water: A Valuable Resource Ground water supplies 95% of the drinking water needs in rural areas. 75% of public water systems rely on groundwater. In the United States, ground water provides drinking water to approximately 140 million people. Supplies about 40% of Houston area

Regional Aquifer Issues

Typical Hydrocarbon Spill

Aquifer Characteristics Matrix type Porosity (n) Confined or unconfined Vertical distribution (stratigraphy or layering) Hydraulic conductivity (K) Intrinsic permeability (k) Transmissivity (T) Storage coefficient or Storativity (S)

Vertical Distribution of Ground Water

Vertical Zones of Subsurface Water Soil water zone: extends from the ground surface down through the major root zone, varies with soil type and vegetation but is usually a few feet in thickness Vadose zone (unsaturated zone): extends from the surface to the water table through the root zone, intermediate zone, and the capillary zone Capillary zone: extends from the water table up to the limit of capillary rise, which varies inversely with the pore size of the soil and directly with the surface tension

Typical Soil-Moisture Relationship

Soil-Moisture Relationship The amount of moisture in the vadose zone generally decreases with vertical distance above the water table Soil moisture curves vary with soil type and with the wetting cycle

Vertical Zones of Subsurface Water Continued Water table: the level to which water will rise in a well drilled into the saturated zone Saturated zone: occurs beneath the water table where porosity is a direct measure of the water contained per unit volume

Porosity Porosity averages about 25% to 35% for most aquifer systems Expressed as the ratio of the volume of voids Vv to the total volume V: n = Vv/V = 1- b/m where: b is the bulk density, and m is the density of grains

Porosity Water

Arrangement of Particles in a Subsurface Matrix Porosity depends on: • particle size • particle packing Cubic packing of spheres with a theoretical porosity of 47.65%

Rhombohedral packing of spheres with a theoretical porosity of 25.95%

Soil Classification Based on Particle Size (after Morris and Johnson) Material Particle Size, mm Clay <0.004 Silt 0.004 - 0.062 Very fine sand 0.062 - 0.125 Fine sand 0.125 - 0.25 Medium sand 0.25 - 0.5 Coarse sand 0.5 - 1.0

Soil Classification…cont. Material Particle Size, mm Very coarse sand 1.0 - 2.0 Very fine gravel 2.0 - 4.0 Fine gravel 4.0 - 8.0 Medium gravel 8.0 - 16.0 Coarse gravel 16.0 - 32.0 Very coarse gravel 32.0 - 64.0

Particle Size Distribution Graph

Particle Size Distribution and Uniformity The uniformity coefficient U indicates the relative sorting of the material and is defined as D60/D10 U is a low value for fine sand compared to alluvium which is made up of a range of particle sizes

Cross Section of Unconfined and Confined Aquifers

Unconfined Aquifer Systems Unconfined aquifer: an aquifer where the water table exists under atmospheric pressure as defined by levels in shallow wells Water table: the level to which water will rise in a well drilled into the saturated zone

Confined Aquifer Systems Confined aquifer: an aquifer that is overlain by a relatively impermeable unit such that the aquifer is under pressure and the water level rises above the confined unit Potentiometric surface: in a confined aquifer, the hydrostatic pressure level of water in the aquifer, defined by the water level that occurs in a lined penetrating well

Special Aquifer Systems Leaky confined aquifer: represents a stratum that allows water to flow from above through a leaky confining zone into the underlying aquifer Perched aquifer: occurs when an unconfined water zone sits on top of a clay lens, separated from the main aquifer below

Ground Water Flow Darcy’s Law Continuity Equation Dupuit Equation

Darcy’s Law Darcy investigated the flow of water through beds of permeable sand and found that the flow rate through porous media is proportional to the head loss and inversely proportional to the length of the flow path Darcy derived equation of governing ground water flow and defined hydraulic conductivity K: V = Q/A where: A is the cross-sectional area V  -∆h, and V  1/∆L

V= - K dh/dl Q = - KA dh/dl Darcy’s Law

Example of Darcy’s Law A confined aquifer has a source of recharge. K for the aquifer is 50 m/day, and n is 0.2. The piezometric head in two wells 1000 m apart is 55 m and 50 m respectively, from a common datum. The average thickness of the aquifer is 30 m, The average width of flow is 5 km.

Calculate: the Darcy and seepage velocity in the aquifer the average time of travel from the head of the aquifer to a point 4 km downstream assume no dispersion or diffusion

The solution Cross-Sectional area 30(5)(1000) = 15 x 104 m2 Hydraulic gradient (55-50)/1000 = 5 x 10-3 Rate of Flow through aquifer Q = (50 m/day) (75 x 101 m2) = 37,500 m3/day Darcy Velocity: V = Q/A = (37,500m3/day) / (15 x 104 m2) = 0.25m/day

Therefore: Seepage Velocity: Vs = V/n = 0.25 / 0.2 = 1.25 m/day (about 4.1 ft/day) Time to travel 4 km downstream: T = 4(1000m) / (1.25m/day) = 3200 days or 8.77 years This example shows that water moves very slowly underground.

Ground Water Hydraulics Hydraulic conductivity, K, is an indication of an aquifer’s ability to transmit water Typical values: 10-2 to 10-3 cm/sec for Sands 10-4 to 10-5 cm/sec for Silts 10-7 to 10-9 cm/sec for Clays

Ground Water Hydraulics Transmissivity (T) of Confined Aquifer -The product of K and the saturated thickness of the aquifer T = Kb - Expressed in m2/day or ft2/day - Major parameter of concern - Measured thru a number of tests - pump, slug, tracer

Ground Water Hydraulics Intrinsic permeability (k) Property of the medium only, independent of fluid properties Can be related to K by: K = k(g/µ) where: µ = dynamic viscosity  = fluid density g = gravitational constant

Storage Coefficient S = Vol/ (AsH) Relates to the water-yielding capacity of an aquifer S = Vol/ (AsH) It is defined as the volume of water that an aquifer releases from or takes into storage per unit surface area per unit change in piezometric head - used extensively in pump tests. For confined aquifers, S values range between 0.00005 to 0.005 For unconfined aquifers, S values range between 0.07 and 0.25, roughly equal to the specific yield

Regional Aquifer Flows are Affected by Pump Centers Streamlines and Equipotential lines

Derivation of the Dupuit Equation - Unconfined Flow

Dupuit Assumptions For unconfined ground water flow Dupuit developed a theory that allows for a simple solution based off the following assumptions: 1) The water table or free surface is only slightly inclined 2) Streamlines may be considered horizontal and equipotential lines, vertical 3) Slopes of the free surface and hydraulic gradient are equal

Derivation of the Dupuit Equation Darcy’s law gives one-dimensional flow per unit width as: q = -Kh dh/dx At steady state, the rate of change of q with distance is zero, or d/dx(-Kh dh/dx) = 0 OR (-K/2) d2h2/dx2 = 0 Which implies that, d2h2/dx2 = 0

Dupuit Equation Integration of d2h2/dx2 = 0 yields h2 = ax + b Where a and b are constants. Setting the boundary      condition h = ho at x = 0, we can solve for b b = ho2 Differentiation of h2 = ax + b allows us to solve for a, a = 2h dh/dx And from Darcy’s law, hdh/dx = -q/K

Dupuit Equation So, by substitution h2 = h02 – 2qx/K Setting h = hL2 = h02 – 2qL/K Rearrangement gives q = K/2L (h02- hL2) Dupuit Equation Then the general equation for the shape of the parabola is h2 = h02 – x/L(h02- hL2) Dupuit Parabola However, this example does not consider recharge to the aquifer.

Cross Section of Flow q

Adding Recharge W - Causes a Mound to Form Divide

Dupuit Example Example: 2 rivers 1000 m apart K is 0.5 m/day average rainfall is 15 cm/yr evaporation is 10 cm/yr water elevation in river 1 is 20 m water elevation in river 2 is 18 m Determine the daily discharge per meter width into each River.

Example L = 1000 m Dupuit equation with recharge becomes h2 = h02 + (hL2 - h02) + W(x - L/2) If W = 0, this equation will reduce to the parabolic Equation found in the previous example, and q = K/2L (h02- hL2) + W(x-L/2) Given: L = 1000 m K = 0.5 m/day h0 = 20 m hL= 28 m W = 5 cm/yr = 1.369 x 10-4 m/day

Example For discharge into River 1, set x = 0 m q = K/2L (h02- hL2) + W(0-L/2) = [(0.5 m/day)/(2)(1000 m)] (202 m2 – 18 m2 ) + (1.369 x 10-4 m/day)(-1000 m / 2) q = – 0.05 m2 /day The negative sign indicates that flow is in the opposite direction From the x direction. Therefore, q = 0.05 m2 /day into river 1

Example For discharge into River 2, set x = L = 1000 m: q = K/2L (h02- hL2) + W(L-L/2) = [(0.5 m/day)/(2)(1000 m)] (202 m2 – 18 m2 ) + (1.369 x 10-4 m/day)(1000 m –(1000 m / 2)) q = 0.087 m2/day into River 2 By setting q = 0 at the divide and solving for xd, the water divide is located 361.2 m from the edge of River 1 and is 20.9 m high

Flow Nets - Graphical Flow Tool Q = KmH / n n = # head drops m= # streamtubes K = hyd cond H = total head drop

Flow Net in Isotropic Soil Portion of a flow net is shown below Y Stream tube F Curvilinear Squares

Flow Net Theory Streamlines Y and Equip. lines  are . Streamlines Y are parallel to no flow boundaries. Grids are curvilinear squares, where diagonals cross at right angles. Each stream tube carries the same flow.

Seepage Flow under a Dam