1. Physical Properties of Aquifers
Groundwater Hydraulics
Daene C. McKinney

2. Outline Porous Medium Piezometric head in aquifers Aquifer Types
Porosity
Moisture Content
Particle Size
Distribution of water in subsurface
Capillary Pressure
Soil Moisture Characteristic Curves
Specific Yield and Retention
Piezometric head in aquifers
Aquifer Types
Aquifer Storage

3. Porous Medium Groundwater All waters found beneath the ground surface
Occupies pores (void space space not occupied by solid matter)
Porous media
Numerous pores of small size
Pores contain fluids (e.g., water and air)
Pores act as conduits for flow of fluids
Type of rocks and their
Number, size, and arrangement of pores
Affect the storage and flow through a formation.
Pores shapes are irregular
Differences in the minerals making up the rocks
Geologic processes experienced by them.

4. Continuum Approach to Porous Media
Pressure, density etc. apply to fluid elements that are large relative to molecular dimensions, but small relative to the size of the flow problem
We adopt a Representative Elementary Volume (REV) approach
REV must be large enough to contain enough pores to define the average value of the variable in the fluid phase and to ensure that the pore-to-pore fluctuations are smoothed out
REV must be small enough that larger scale heterogeneities do not get averaged out (layering, etc.)

5. Porosity
solid
Pore with water
Soil volume V
(Saturated)

6. Porosity Property of the voids of the porous medium
solid
Pore with water
Soil volume V
(Saturated)
Property of the voids of the porous medium
% of total volume occupied by voids
Rhombo
Packing
Cubic
Packing

7. Porosity Porosity: total volume of soil that can be filled with water
V = Total volume of element
Vi = Volume of Pores
Vs = Volume of solids
solid
Pore with water
Soil volume V
(Saturated)
rm = particles density (grain density)
rd = bulk density
Void Ratio:

8. Typical Values of Porosity
Material
Porosity (%)
Peat Soil
60-80
Soils
50-60
Clay
45-55
Silt
40-50
Med. to Coarse Sand
35-40
Uniform Sand
30-40
Fine to Med Sand
30-35
Gravel
Gravel and Sand
Sandstone
10-20
Shale
1-10
Limestone

9. Volumetric Water Content
Soil volume V
(Unsaturated)

10. Saturation
Soil volume V
(Unsaturated)

11. Particle Size of Some Soils

12. Particle Size Distribution
Poorly sorted silty fine to medium sand
Well sorted fine sand
Particle size distribution curves
Relative % of grain sizes
Soil classification standards
Soil texture

13. Particle Size Distribution
Sand
49%
Clay
40%
Soil Characteristics of Cyprus Soil Sample

14. Occurrence of Groundwater
Ground water occurs when water recharges the subsurface through cracks and pores in soil and rock
Shallow water level is called the water table

15. Distribution of Water in Subsurface
Moisture Profile
Soil Profile
Description
Different zones
depend on % of pore space filled with water
Unsaturated Zone
Water held by capillary forces, water content near field capacity except during infiltration
Soil zone
Water moves down (up) during infiltration (evaporation)
Capillary fringe
Saturated ar base
Field capacity at top
Saturated Zone
Fully saturated pores
Field capacity - Water remaining after gravity drainage
Wilting point - Water remaining after gravity drainage & evapotranspiration

16. Saturation Saturation Water Content Water Saturation Soil volume V
(Unsaturated)
Saturation
Water Content
Water Saturation

17. Surface Tension air water Below interface At interface
Forces act equally in all directions
At interface
Some forces are missing
Pulls molecules down and together
Like membrane exerting tension on the surface
Curved interface
Higher pressure on concave side
Pressure increase is balanced by surface tension
s = N/m 20oC)
Capillary pressure
Relates pressure on both sides of interface
water
air
No net force
Net force inward
Interface

18. Surface Tension sgl ssg b < 90o - liquid is wetting the solid
gas
liquid
ssg b
< 90o - liquid is wetting the solid
b > 90o - liquid is non-wetting the solid
solid
ssl Hg
solid
air b
water
solid
air b
Mercury nonwetting solid
Water wetting solid

19. Capillary Pressure
Two immiscible fluids in contact exhibit a discontinuity in pressure across the interface separating them.
This pressure difference is capillary pressure pc
It depends on the curvature of the interface.
pnw is the pressure in the nonwetting fluid (air, say)
pw is the pressure in the wetting fluid (water, say)

20. Capillary Pressure
Solid
Water
Air r
Rise of water in a capillary tube. Capillary forces must balance the weight of water
Capillary pressure head

21. Capillary Pressure B A (A) Below the water level
Solid
Water
Air r
Negative
pressure
Positive B A
(A) Below the water level
(B) Above the water level
Difference in pressure across the interface is

22. Drainage
Drainage occurs when the water pressure in the pores becomes less than the air pressure
Interfacial tension prevents displacement of water in the left pore r
solid
Pore water press. = -p
Pore air press. = 0
If pc increases, radius must decrease, or water occupies smaller pores.
Water recedes into pores small enough to support the interface with a radius required to balance the capillary force. Water drains from the large pores first.

23. Energy in Flow Systems Velocity head p/g Pressure head z
v2/(2g)
Velocity head
p/g
Pressure head z
Elevation head
v2/(2g)
EGL
p/g
HGL
v2/(2g) z
Hydraulic grade line (HGL) – height of water in piezometer tube
datum
Energy grade line (EGL) – Height of water in pitot tube

24. Piezometric Head
Confined aquifer
Unconfined aquifer
Pressure head = 0

25. Piezometric Head in Unsaturated Flow
Soil volume V
(Unsaturated)
Saturated Zone
Water Table
Unsaturated Zone
q = f
q < f
 < 0
 = 0
 > 0
pw > 0
pw = 0
pw < 0

26. Subsurface Pressure Distribution
Capillary pressure head in zone above water table
Hydrostatic pressure distribution exists below the water table (p = 0).
Ground surface
Pressure is negative above water table
Unsaturated zone
Water table
Pressure is positive below water table
Saturated zone

27. Soil Water Characteristic Curvesy
Vadose Zone
Porosity
Capillary Zone yb
Critacal
Head
(Bubbling
Press.) qo f
Capillary pressure head
Function of:
Pore size distribution
Moisture content
Irreducible
Water content
Porosity

28. Capillary Rise in Soils

29. Aquifer Types Confined aquifer Unconfined aquifer Aquifer Aquitard
Under pressure
Bounded by impervious layers
Unconfined aquifer
Phreatic or water table
Bounded by a water table
Aquifer
Store & transmit water
Unconsolidated deposits sand and gravel, sandstones etc.
Aquitard
Transmit don’t store water
Shales and clay

30. Aquifer Storage Storativity (S) - ability of an aquifer to store water
Change in volume of stored water due to change in piezometric head.
Volume of water released (taken up) from aquifer per unit decline (rise) in piezometric head.
Unit area
Unit decline in head
Released water

31. Aquifer Storage Fluid Compressibility (b) Aquifer Compressibility (a)
Confined Aquifer
Water produced by 2 mechanisms
Aquifer compaction due to increasing effective stress
Water expansion due to decreasing pressure
Unconfined aquifer
Water produced by draining pores

32. Unconfined Aquifer Storage
Storativity of an unconfined aquifer (Sy, specific yield) depends on pore space drainage.
Some water will remain in the pores - specific retention, Sr
Sy = f – Sr
Unit area
Unit decline in head
Released water

33. Porosity, Specific Yield, & Specific Retention

34. Confined Aquifer Storage
Storativity of a confined aquifer (Ss) depends on both the compressibility of the water (b) and the compressibility of the porous medium itself (a).
Unit area
Unit decline in head
Released water

35. Example Storage in a confined sandstone aqufier
f = 0.1, a = 4x10-7 ft2/lb, b = 2.8x10-8 ft2/lb, g = 62.4 lb/ft3
ga = 2.5x10-5 ft-1 and gbf = 1.4x10-7 ft-1
Solid  Fluid
2 orders of magnitude more storage in solid
b = 100 ft, A = 10 mi2 = 279,000,000 ft2
S = Ss*b = 2.51x10-3
If head in the aquifer is lowered 3 ft, what volume is released?
DV = SADh = 2.1x106 ft3

36. Summary Porous Medium Piezometric head in aquifers Aquifer Types
Porosity
Moisture Content
Particle Size
Distribution of water in subsurface
Capillary Pressure
Soil Moisture Characteristic Curves
Specific Yield and Retention
Piezometric head in aquifers
Aquifer Types
Aquifer Storage