Slide 1: GROUNDWATER
Freeze and Cherry: Groundwater
and
Fetter: Applied Hydrogeology
are the old and new testament of groundwater hydrology
Dingman has a good groundwater section (Chapter 8), which you will be responsible for by the end of the term
Slide 2: Properties of Aquifers
Aquifer  Geologic unit that can store enough water and transmit it at a rate fast enough to be significant
recall:
Porosity is
can be measured as 1 minus the ratio of the bulk density to the particle density of the material n = (Va + Vw)/V = Vv/V
Slide 3: Effective porosity is the fraction of the porosity that is available for transporting water (excludes fraction of pores too small to hold water, or those that are not interconnected
 can be measured in the lab directly by saturating a dried sample of known volume and measuring water uptake in a sealed chamber over time
 for unconsolidated coarsegrained sediments there is no significant difference
Slide 4: Uniformity coefficient  measure of sorting
On a grainsize vs %finer plot:
d60 is the grain size diameter that corresponds to 60% finer by weight
d10 is the grain size diameter that corresponds to 10% finer by weight
(i.e. d60 is coarser than d10)
 Cu less than 4 is well sorted, more than 6 is poorly sorted
Slide 5: Porosity of Sedimentary Rocks
 sedimentary rocks usually have lower porosity than unconsolidated sediment because of compaction, and infilling of cementing material (e.g. calcite, dolomite, silica), although dissolution can reverse the latter effect
Ground water can be associated with both:
Primary Porosity  porosity between grains
Slide 6: Secondary pores (fractures) can be enlarged through dissolution by the ground water flow
 sedimentary rock may have primary porosity from deposition and secondary porosity from fractures along bedding planes
 secondary porosity also possible in cohesive sediments through wetting/drying, tectonic activity, etc.
 limestones, dolomites, gypsum can all have deposition reversed
 when in groundwater zone dissolution can occur
 flow starts initially through limited pore spaces, fractures, and bedding planes, and porosity enlarges over time
Slide 7: Porosity of Plutonic and Metamorphic Rocks
 primary porosity extremely low, but often not zero
 porosity increased over time by weathering and fracturing
 fracturing increases porosity of crystalline rocks 2 to 5%
 chemical and physical weathering increases with porosity
 highly weathered plutonic and metamorphic rocks can have posities between 30 to 60%
 sheetlike structures of weathering minerals such as micas can have very high porosities
Porosity of Volcanic Rocks
 lava cools rapidly at surface, traps degassing products
 holes in rock (vesicular) may or may not be interconnected
 cracks form during cooling
 volcanic rocks vary in porosity but can be very high
 basalt has lower gas content with porosity between 1 and 12%
 pumice (very high gas content) can have porosity approaching 90% (but effective porosity if not this high)
 weathering of volcanic deposits will also increase porosity
Slide 8: Specific Storage (Ss) :
Storativity or Storage Coefficient (S):
where b is the saturated thickness of the aquifer
Specific Yield (Sy)
 volume of water that drains from a saturated rock by gravity to volume of rock
 in an unconfined aquifer, S=Sy
Slide 9: Specific Retention (Sr)
volume of water held behind by capillary forces to volume of rock
(this water is also referred to as “pendular” water)
 essentially identical to the concept of field capacity
 specific yield can be determined in the lab using soil column methods
 soil in column is saturated from below and allowed to drain without evaporation going on
 allowed to drain for months before equilibrium is reached
 volume of water drained to the volume of column is Sy
 above difficult to do with rock
 can also be measured in the field with pump tests (discussed later)
Slide 10: Hydraulic Conductivity of saturated media and Darcy’s Law
 ability of the rock to transmit and hold water are most important hydrologic properties
 as pointed out only effective porosity important with regards to groundwater flow (e.g. vesivcular basalt  lack of interconnectivity, Clays and shales  pores too small)
Slide 11: Darcy’s experiment
Reality
For educational purposes only
Slide 12: Darcy’s experiment
Henry Darcy in 1856 was playing around with movement of water through sand filtration columns for the City of Dijon, France.
Darcy found that the flow of water through a bed of “a given nature” is:
 proportional to the difference in the height of the two ends,
 inversely proportional to the length of the flow path
 proportional to the xsectional area of the pipe
 flow is further related to a coefficient dependant on the nature of the media
is Darcy’s Law for saturated flow through a pipe,
Where: ha and hb are heads at two ends of pipe
L is length pf flow path
K is hydraulic conductivity
A is the crosssectional area of the pipe
Q is discharge
Slide 13: or:
negative sign is for flow in direction of decreasing head
dh/dl is the hydraulic gradient recall Darcy’s Law for unsaturated flow from text is:
 we are not substituting Vx here, Q is discharge (remove A from above equation and we will have a velocity of flow)(see below).
 the term d(z+p/(w) is now combined into one term dh
Slide 14: Darcy’s Law Ohm’s Law (rearranged)
Where: i = current
K = electrical conductivity
K = 1/ ρ where ρ = resistivity
V = voltage
L = distance
A = area
Slide 15: Form of Darcy’s law we will use most often calculates specific discharge
v is not a true velocity
v is also known as the “Darcian Velocity”
K is also known as “Darcy’s proportionality constant” or “coefficient of permeability”
 whereas in unsaturated flow K is a function of soil moisture, soil and fluid properties, in saturated flow it a function of soil and fluid properties only
Slide 16:  discharge is proportional to the specific weight ( of the fluid
 Q% 1/: (dynamic viscosity of the fluid  resistance of fluid to shearing)
 Q%d2 (square of the diameter of pores)
Darcy’s law can be reexpressed as:
where C is a shape factor (because xsectional area of a pore is also related to it’s shape)
Slide 17:  intrinsic permeability (Ki) is representative of the character of the porous medium alone
 basically a function of the size of the openings through which the fluid moves
 larger the square of the pore diameter, the lower the resistance to flow
 Ki is essentially the “openess” of the flow path (in e.g. cm2)
 can also expressed in units called “darcys”
1 darcy=9.87x109 cm2 No fluid properties
Slide 19: By convention, if we always refer to K as the hydraulic conductivity, we can refer to Ki the permeability
(Note: Freeze and Cherry use k for permeability which is much more common)
 during the formation of clastic sedimentary rock, cementation and compaction can restrict throats between pores
 therefore, even though porosity may be reduced only slightly, permeability can be greatly reduced
 crystalline rocks have low permeability, although volcanics can have high permeability if connectiviy is good
 secondary permeability (like secondary porosity), through fracturing, weathering
Slide 20: Estimation of K
Hazen Method
 approximation
 for sandy sediments with d10 is betweem 0.1 and 3.0 mm
 developed on the basis of sand filtering for drinking water
 durable empirical equation
K is in cm/s
d10 is in cm
C is unitless coefficient which ranges from 40 in v. fine sand to 150 in coarse sand
Slide 21: KosenyCarmen Equation
for more nonuniform soils
 explicitly incorporates fluid properties and porosity
where n is porosity
Slide 22: FairHatch Equation
 uses first two terms in the KosenyCarmen equation and replaces the third with:
where: m is a packing factor (usually ~5)
C is the shape factor (6 for spheres, 7.7. for angular)
P is % of material held between adjacent seives
dm in this case is taken as the geometric mean of the rated sizes of adjacent seives
Slide 23: Permeameters
 tube filled with sample
 can be actual tube used to collect sample so minimal disturbance
2types of permeameter:
1. Constanthead
 used for noncohesive sediments (sands)
 best for samples with K>0.01cm/min
 rearranging Darcy’s law we can obtain:
where V is the volume of water discharging in time t
L is the length of sample
A is the xsectional areah is the hydraulic head
K is the hydraulic conductivity
 dh/dl should mimic field
h should never be greater than 0.5L (don’t want v to get too high. Why?)
Slide 25: 2. Fallinghead permeameter
 used for cohesive seds with lower K
 initial water level in a falling head tube is measured as h0
 after a period t (several hours), level is measured again as h
(See Fetter for derivation of these equations)
where At is xsectional area of falling head tube
Ac is the xsectional area of the sample tube
For both constanthead and fallinghead:
 make sure sample is fully saturated
 use dearied water if possible
Question: How would we arrive at Ki given a value for K above?
Slide 26: The Water Table
Question: How is the water table defined?
The following generalizations are valid:
1. In the absence of flow the water table will be flat
2. A sloping water table indicates flow
3. Groundwater discharge occurs in low zones
4. The water table has the same general shape as the surface topography (but less relief change)
5. Ground water generally flows from topographic highs to lows
Slide 27: Aquifers
 near the Earth’s surface there are few materials that are absolutely impermeable
Ki for aquifers is generally >102 darcy
Confining layer
 layer having low or no peremeability
 whether a layer is considered “confining” or not will depend on main aquifer material
 usually confining layers have some permeability, just very low
types of confining layers:
Aquiclude  layer of low permeability that can store and transmit groundwater slowly between aquifers (now more commonly referred to as “leaky confining layer”)
Aquifuge  absolutely impermeable and contains no water
Slide 28: Unconfined aquifer (water table aquifer)  layer where highly permeable material extends to the water table
 recharge can be from any direction
Confined aquifer (artesian aquifer)  aquifers overlain by confining layer
 recharge from recharge areas where strata tips up, or leakage through confining layer
 artesian wells are drilled into confined aquifers
 water from an artesian well can rise above surface
 potentiometric surface is the level to which water will rise in a cased well
Perched Aquifer  aquifer in the vadose zone because of a lens of impermeable material
 common in glacial outwash (clay from ponds), volcanic deposits (weathered ash deposits with low K sandwiched between high K basalt)
Slide 30: Water Table and Potentiometric Surface Maps
Question: What is the difference between the water table and the potentiometric surface?
 surfaces measured in wells open only to the aquifers of interest
 measurements should be made within a brief period of time
 each well needs to be tied into a common datum (e.g. sea level)
 datum should be same for surface topography (esp. ponds, springs, etc.)
 measurements in pumping wells should be made with no pumping and after enough time for rebound
 map should include location of lakes and streams
 potentiometric levels are not influenced by surface topography
 very important to know whether your well is measuring confined or unconfined aquifer
 also important if measuring potentiometric surface to know you are in same confined aquifer
Slide 31: Extrapolating Well Measurements
 often we want to map the direction of water flow in a confined or unconfined aquifer, but do not have enough wells
 graphical solution for 3 or 4points
1. Map scale drawing showing location of wells
2. Note water level at each well
3. Measure map distance and elevation change between each well
4. Find map distance for unit change in head between each pair
5. Mark even increments of head change along each line
6. Make lines of equal head
Slide 32: Piezometer and Piezometer Nests
 basic device for measuring head is a tube or pipe through which the water level can be measured
 open to water flow at bottom and open to atmosphere at top
 intake usually slotted pipe or commercially available well point
 must allow for intake of water, but not clastic material
 water levels measured by pressure transducers or with manual soundings
 nests are groups of peizometers at one location, but with well points going to different depths to obtain vertical hydraulic gradient
Slide 33: SteadyState flow vs Transient flow
Steadystate flow  when at any point in a flow field, magnitude and direction of flow are constant with time
 flow velocity may vary from point to point in the field, but the pattern is constant through time
Transient flow (unsteady flow, nonsteady flow)
Slide 34: Compressibility and Effective Stress
 at any point in an aquifer, the weight of overlying material applies downward stress on the aquifer material. This is Total stress
 upward stress on the aquifer material caused by fluid pressure counteracts total stress to a degree
 difference is the effective stress (i.e. the stress actually applied to the aquifer skeleton)
and of course
In confined aquifers P can change with little change in saturated thickness of aquifer. In these cases σT will remain essentially constant so that σe is what changes:
Question: What will happen to the effective stress acting on the aquifer skeleton if we pump water out of a confined aquifer?
Slide 35: Compressibility of water is constant at 4.4x1010 Pa1
Need a estimation of compressibility of the solid matrix
assume that the matrix acts as a elastic body:
 subject the matrix to a change in effective stress and it will deform
Aquifer compressibility is defined as:
where: α is aquifer compressibility
db is the change in aquifer thickness
b is the original aquifer thickness
Slide 36: There are 2 ways an aquifer can compress:
1. By compression of individual rock grains and crystals
2.
The first is negligible to nonexistent in most cases
If necessary, compressibility can be determined in the lab using loading cells
 aquifer compressibility will also depend on loading history of aquifer
 compressibility of water close to leastcompressible rock
 must be realized that stress field at depth is 3D, but changes in the horizontal stress field can be considered negligable
 i.e. large changes in stress only occur in the vertical direction
Summary of compaction:
when fluid pressure (head) is reduced in a confined aquifer, the following will occur:
1. Effective stress will increase
2. Aquifer material now bears an additional portion of the overburden load
3. Aquifer compacts a bit releasing water from storage
4. Reduction in water pressure also causes water to expand slightly releasing additional water
 if compaction is propagated to the surface, land subsidence can occur
Slide 41: Near Las Vegas Earth Fissures
Slide 42: Approximate maximum subsidence amounts as of 1997 for selected locations in the Southwest
Slide 44: Now we can use interferometric processing of Synthetic Aperture Radar (SAR) data.
Slide 45: Homogeneity and Isotropy
Homogeneous units
 values of Storativity and K similar throughout for sandstones: similar grain size, porosity, cemetation, thickness for plutonics and metamorphics: similar fracturing, strike and dip, etc.
 definition is usually arbitrary, but one common one is that the distribution of K must be monomodal
Heterogeneous units
 hydraulic properties change spatially
 can be changes in thickness, bedding of different hydraulic properties, etc.
 interlayered clay and sand deposits can create extreme layered heterogeneity
 limestones often heterogeneous because solution pathways form along bedding planes
discontinuous heterogeneity  occurs at faults or largescale stratigraphic features
Slide 47: trending heterogeneity  usually in units where deltas, alluvial fans, etc have formed

 trending heterogeneity in large sedimentary formations can cover 2 to 3 orders of magnitude in Ki
If a porous medium has equal intrinsic permeability in all directions it is said to be isotropic
If the pattern of voids allows for a path of least resistance (i.e. direction in which Ki is higher) the unit is said to be anisotropic
 fractured rocks, basalts often highly anisotropic
 sedimentary rocks may have many homogenous units
 directions of maximum and minimum anisotropy are the principal directions of anisotropy
If an xyz coordinate system is setup along the principal directions:
Kx=Ky=Kz is an isotropic situation
Kx…Ky…Kz is an anisotropic situation
Kx=Ky…Kz is a transversley isotropic situation (common in layered deposits