CSULA Chapter 7 Groundwater Fundamentals and One Dimensional Flow Essay Read chapter 7 and summarise it as points (outline). Expand on the main points by providing a brief explanation. 252
Chapter 7
Groundwater-Fundamentals and One-Dimensional Flow
Karl Terzaghi once wrote ” . . . in engineering practice, difficulties with soils are
almost exclusively due not to the soils themselves, but to the water contained in their
voids. On a planet without any water there would be no need for soil mechanics”
(Terzaghi, 1939). The presence of water, or at least the potential for its presence, is a
key aspect of most geotechnical analyses. Therefore, this is a topic worthy of careful
study.
Specific water-related geotechnical issues include the following:
•
•
•
•
•
•
•
The effect of water on the behavior and engineering properties of soil and rock
The potential for water fiOving into excavations
The potential for pumping water through wells or other facilities
The effect of water on the stability of excavations and embankments
The resulting uplift forces on buried stluctw·es
The potential for seepage-related failw-es, such as piping
The potential for transport of hazardous chemicals along with the water.
In this chapter, we explore the fundamental pliuciples of subsw1ace water.
Chapter 8 continues this discussion and applies these principles to practical engineering
problems.
7.1
HYDROLOGY
Hydrology is the study of water movements across the earth. It includes assessments of
rainfall iutensities, stream flows, and lake water levels, known as surface waJ.er hydrology, as well as studies of underground water, known as groundwater hydrology. These
various movements are part of the grand process called the hydrologic cycle.
The Hydrol ogic Cycle
The movement of water across the earth is ultimately dliven by energy received from
the sun. Thus, the hydrologic cycle begius with water 1ising into the sky from open bodies of water through the process of evaporation, as shown in Figure 7.1. This process
also draws water out of the near-sw-face soil, which dJies the soil. A related process,
called transpiration, acts through plants and draws water out of the ground through
their roots. The two processes are sometimes conceptually combiued and called
evapotranspiration.
Water iu the sky, which may be in the form of invisible water vapor or visible
clouds, eventually falls to the earth asp recipitation (rain, sleet, hail, and snow), much of
which goes directly iuto the oceans. The precipitation that falls onto land and onto
iuland bodies of water becomes the source of virtually all sw1ace water, much of which
flows overland until it reaches streams or rivers, where it becomes streamflow.
H owever, a significant portion of the sw1ace water soaks into the ground, either
while it is flowiug overland or after it has Teached rivers or lakes. This infili:ration
recharges the groundwater. Water applied to the ground by irligation also soaks in and
7.1
Hydrology
253
Precipitation
I I I
Precipitation
t
Transpiration
Evaporation
Evapo ration
+H
FIGURE 7.1
The hydrologic cyde.
can contiibute to the groundwater. Although some of the infiltrated water remains
near the ground surface, much of it penetrates down until it reaches the groundwater
table, which is the fully saturated zone.
These processes occur both in mountains and lowlands, so the groundwater eventually builds up and gains enough potential energy to begin flowing tin·ough the
ground. Eventually some of this water reappears at the ground surface as springs, or it
seeps directly into rivers or lakes. There it joins overland flows that eventually lead to
sinks (low spots in the land) or the ocean, where the hydrologic cycle begins anew.
Groundwater Hydrology
Geotechuical engineers are mostly interested in the portions of the hydrologic cycle
that occur underground. The term subsurface water encompasses all underground
water, virtually all of which is located within the soil voids or rock fissures. A very small
percentage of subsmface water is located in underground caverns, but this special case
is not of much interest to geotechuical engineers.
We use various kinds of infonnation to desclibe and understand subsmface
water. One of the most important is the groundwater table (also called the phreatic surface), which can be located by installing observation wells, as shown in Figure 3.22, and
allowing the groundwater to seep into them UJltil it reaches equilibrium. The water
level inside these wells is, by definition, the groundwater table, where the pore water
pressure is equal to zero. Soil profiles represent the groundwater table as a line marked
with a tiiangle, as shown in Figure 7.2. It also can be presented in plan view as a series
of contour lines on a map. The groundwater table location is important, and finding it
is one of the primary objectives of a site characterization program.
254
Chapter 7
Groundwater-Fundamentals and One-Dimensional Flow
·.. . . · .. : .
Pe rcbed
I
Artesian
weU
….··
: : · .. :
AquicludJ:
FIGURE 7.2
. …
. :. –
z one
: ,· .
Soil profile showing complex nature of groundwater.
The groundwater table elevation often changes with time, depending on the season of the year, recent patterns of rainfall, irrigation practices, pumping activities, and
other factors. At some locations, these fluctuations are relatively small (perhaps less
than 1m or 3ft), while in other places the groundwater table elevation has changed by
20m (60ft) or more in only a year or two. Thus, the groundwater conditions encountered in an exploratory boring are not necessarily those we use for design. Often we
need to use the observed conditions as a basis for estimating the worst-case conditions
that are likely to occur during the project life.
Water also is usually present in the soil above the groundwater table, but the
physical processes that control its movement are quite different. Thus, it is useful to
divide subsw1ace water into two zones:
• The portion below the groundwater table is called the phreatic zone. This water is
subjected to a positive pore water pressure as a result of the weight of the overlying water (and possibly due to other causes as well) . Most subsurface water is in
the phreatic zone.
• The portion above the groundwater table is called the vadose zone. This water
has a negative pore water pressure, and is held in place by capillary action and
other forces present in the soil.
Technically, only the water in the phreatic zone is true groundwater. However, we
often use the term groundwater to desclibe all subsurface water.
Some soils, such as sands and gravels, can transmit large quantities of groundwater. These are known as aquifers, and are good candidates for wells. Other soils, such as
clays, transmit water very slowly. They are known as aquidttdes. Intermediate soils, such
as silty sand, pass water at a slow-to-moderate rate and are called aquitards. All three
categories of soil might be present in a single soil profile, so the distribution and flow of
groundwater can be quite complex. R>r example, a perched groundwater condition can
7.2 Principles of Fluid Mechanics
255
occur when an aquiclude separates two aquifers, as shown in Figure 7.2. In this case,
there may be two or more groundwater tables.
An unconfined aquifer, such as the upper aquifer in Figure 7.2, is one in which
the bottom flow boundary is defined by an aquiclude, but the upper flow boundary
(the groundwater table) is free to reach its own natural level. The groundwater occupies the lower portion of the aquifer,just as water in a kitchen pot occupies the lower
part of the pot. n1e zone of soil through which the water flows is called the flow regime.
If more groundwater anived at the site, the groundwater table in an unconfined
aquifer would rise accordingly.
Conversely, a confined aquifer, such as the lower aquifer in Figure 7.2, is one in
which both the upper and lower flow boundaries are defined by aquicludes. This type of
aquifer is similar to a pipe that is flowing full. Most confined aquifers also are artesian,
which means the water at the top of the aquifer is under pressure. People often drill
wells into such aquifers, because the water will rise up through the aquiclude without
pumping. If the water pressure is high enough, artesian wells deliver water all the way to
the ground surface without pumping.
Figure 7.2 shows an example of an artesian condition. Groundwater enters the
confined aquifer from the left side of the cross-section, and then travels down and to
the light. By the time the water reaches the right side of the cross-section, it has developed an artesian condition. Artesian conditions are situations when the water inside
the well casing rise above the groundwater table as shown in the well in Figure 7.2.
Artesian conditions can occw· only in confined aquifers.
7.2
PRINCIPLES OF FLUID M ECHANICS
Our groundwater analyses will use the three-dimensional Cartesian coordinate system
shown in Figure 7.3, where the x and y axes are in a horizontal plane and the z-axis is
vertical. For some analyses, geotechnical engineers express vertical dimensions in
terms of elevation (z positive upward). However, it is usually more convenient to work
in terms of depth (z positive downward). For example, we often speak of depth below
the ground surface, depth below the groundwater table, or depth below the bottom of
••
l
l
dz
y
FIGURE 7.3
ef”J.
table
7
Coordinate s}’5tem used in groundwater analysis, along with typical soil element.
256
Chapter 7
Groundwater-Fundamentals and One-Dimensional Flow
a foundation. In addition, boring logs are always presented in terms of depth below the
ground surface. Therefore, in this book, all z-values are expressed as depths with the positive direction downward, as shown in Figure 7.3. A z-value with no subscript indicates
depth below the ground surface; Zw indicates depth below the groundwater table; and Zt
indicates depth below a foundation or other applied load The depth from the ground
surface to the groundwater table is Dw.
Groundwat er Flow Co nditions
One-, Two-, and Three-Dimensional F1ow For analysis. we need to distinguish
between one-, two-, and three-dimensional flow conditions. A one-dimensional flow
condition is one in which the velocity vectors are all parallel and of equal magnitude, as
shovm in Figure 7.4(a). In other words, the water always moves parallel to some axis
and through a constant cross-sectional area.
Two-dimensional flow conditions are present when all of the velocity vectors are
confined to a single plane, but vary in direction and magnitude within that plane. For
example, the flow into a long excavation, as shown in Figure 7.4(b), might be very close
to a two-dimensional condition described along a ve1tical plane through the excavation.
Three-dimensional flow is the most general condition. It exists when the velocity
vectors vary in thex,y,andz directions. Flow into multiple wells, as shown in Figure 7.4(c),
is an example. Most groundwater flow conditions are truly three-dimensional but for
analysis purposes can often be simplified to one- or two-dimensions with satisfactory
results.
Steady and Unsteady Flow
The term steady-state condition means a system has reached equilibrium. In the context
of groundwater analyses, it means the flow pattern has been established and is not in
the process of changing. We call this steady flow or steady-state flow. Under steady-state
condition, the direction and velocity of fluid flow is constant with time and, therefore,
the flow rate, Q, also remains constant with time.
In contrast, the unsteady condition (also known as the transient condition) exists
when something is in the process of changing. For seepage problems, unsteady flow (or
transient flow) occurs when the pore water pressures, groundwater table location, flow
rate, or other characteristics are changing, perhaps in response to a change in the
energy in the groundwater system. In other words, steady flow does not vary with time,
while unsteady flow does.
For example, consider a levee that protects a town from a nearby river. Some of
the water in the river seeps through the levee as shown in Figure 7.5, forming a groundwater table. 11lis is a steady-state condition. If the river rapidly rises, such as during a
flood, the groundwater table inside the levee also rises. However, the groundwater
inside the levee responds slowly, so some time is required to achieve the new steadystate condition. During this transition period, the flow is unsteady.
Analyses of unsteady flows are much more complex, and beyond the scope of this
chapter. However, we will study an important unsteady flow process called
consolidation in Chapters 10 and 11.
7.2 Principles of Fluid Mechanics
257
(b)
(a)
(c)
FIGURE 7.4 One-, two-, and three-dimensional flow conditions: (a) one-dimensional flow in a confined
aquifer; (b) two-dimensional flow into a long excavation; (c) three-dimensional flow into a pair of wells.
Laminar and TUrbulent Flow
Sometimes water flows in a smooth orderly fashion, known as laminar flow. This flow
pattem occurs when the velocity is low, and is similar to cars moving smoothly along an
interstate highway. The other possibility is caUed turbulent flow, which means the water
swirls as it moves. This happens when the velocity is high, and might be compared to an
interstate highway filled with vehicles who move too fast, weave back and forth, and
258
Chapter 7
Groundwater-Fundamentals and One-Dimensional Flow
Flood
Nonnal
Town
Rising groundwater table
FIGURE 7.5
Flow through a levee adjacent to a river.
occasionally make 360-degree turns. Thrbulent flow consumes much more energy, and
increases resi.stant:e to now.
In many civil engineering problems, such as design of water pipes or open channels, turbulent flow conditions control the flow. In contrast, for most soils, the velocity
is low, so the flow is laminar. This is important because many of our analyses are only
valid for laminar flow. There are cases in very coarse soils, such as clean, poorly-graded
gravels, in which velocities can be much higher and turbulent flow conditions apply.
Energy in Fluid M echanics
In a fluid mechanics or hydraulics course, you would have studied the concept of head
and its usefulness in analyzing the flow of water tluough pipes and open channels. We
will briefly review this concept in the context of pipe flow and then apply it to groundwater analyses.
Consider the pipe shown in Figure 7.6. It has a cross-sectional area A, and contains water flowing from left to right at a velocity v. The flow rate, Q, is the quantity of
water that passes through the pipe per unit of time:
Q = vA
(7.1)
This pipe also has a piezometer, which is simply a vertical tube vith one end
attached to the pipe and the other open to the atmosphere. Water from the pipe enters
the piezometer and rises to the level shown. If the flow rate through the pipe remains
constant, and the piezometer is sufficiently tall, the water level in the piezometer
remains stationary and will not flow out of the top.
We also have installed a Pitot tube, named after its inventor, Herui DePitot
(1695- 1771), which is similar to a piezometer except the tip is pointed upstream. The
opening of the Pitot tube is normal to the direction of flow and receives a dynamic
ramming effect from the flowing water. The water level in the Pi tot tube is affected by
the velocity of flow and thus is slightly higher than the water level in the piezometer
because the opening of the piezometer is parallel to the direction of flow and the
height of the water in the piezometer is not affected by the velocity of flow.
Fmally, Figure 7.6 shows a horizontal datum elevation, which is the level from
which elevations may be measured. This datum is arbitrary and might be set at sea
level, the laboratory floor, or some other suitable location.
7.2 Principles of Fluid Mechanics
259
1- Pi to t tube
i·
lip
Area =A
h
I’
Q–r
:cG
Point S
________
__________.
FIGURE 7.6 A pipe with a piezometer and a Pitot
tube. These instruments measure the heads at Point 8
in the pipe.
Head
An element of groundwater, such as the one at Point B in Figure 7.6, contains energy in
various forms, including the following:
• Potential energy, which is due to its elevation above the datum
• Strain energy, which is due to the pressure in the water (similar to the energy
contained in a spring that has been compressed under an external load)
• Kinetic energy, which is due to its velocity.
We could express these energies using Joules, BTUs, or some other suitable unit.
However, it is more convenient to do so using the concept of head, which is energy
divided by the acceleration of gravity, g. This method converts each form of energy to
the equivalent potential energy and expresses it as the conesponding height. Thus, we
express these three forms of energy as follows:
• The elevation head, hz, is the difference in elevation between the datum and
the point, as shoY.’Il in Figme 7.6. It describes the potential energy at that
point.
• The pressure head, hp, is the difference in elevation between the point and the
water level in a piezometer attache d to the pipe. It desclibes the strain energy.
260
Chapter 7
Groundwater-Fundamentals and One-Dimensional Flow
• The veloCity head, hv, is the difference in water elevations between the piezometer and the Pitot tube and describes the velocity head. It is related to the velocity,
-v, and acceleration due to gravity, g, as follows:
v2
(7.2)
hv=-
2g
The sum of these is the total head, h:
(7.3)
h=hz+hp+hv
Equation 7.3 is called the Bernoulli equation, and was named after the Swiss
mathematician Daniel Bernoulli (1700-1782). It is one of the cornerstones of fluid
mechanics and one of the most well-known equations in engineering, yet Bernoulli
developed only pait of the underlying theory and thus never wrote this equation. Later
investigators completed the work and developed the equation as we now know it, but
the credit has gone to Bernoulli.
The Bernoulli equation is a convenient way to compare the energy at two points.
For example, if the water at one point has an elevation head of 30m, a pressure head of
10m, and a velocity head of 5 m (h = 30 + 10 + 5 = 45 m ), it has the san1e total head
as the water at another point with an elevation head of 39m, pressure head of 2m, and
velocity head of 4 m ( h = 39 + 2 + 4 = 45 m). Flow occurs only when there is a total
head differential, so there would not be any flow of water between these two points.
Head Loss and Hydraulic Gradient
Figure 7.7 shows a pipe with piezometers and Pitot tubes at two points, A and B. Water
always flows from a point of high total head to a point of low total head. Thus, the water
-¥3.01 m
l:g
t _0.50m
1.60 Ill
L…-1—
l…-
Q-
I.
71
4.28m
3.62m
___
FIGURE 7.7
l______________________________________________,
________
Head loss between two points in a pipe.
7.2 Principles of Fluid Mechanics
261
in this pipe must be flowing from Point A to Point B because the total head at A is greater
than the total bead at BAs the water flows from A to B, some of its energy is lost due to
fiiction, a quantity known as the head wss, t:..h, which in this case is equal to hA – h8 .
The hydraulic gradient, i, is the change in total head per unit length in the direction
of flow:
.
dh
(7.4)
I = —
d/
where:
i = hydraulic gradient
h = total head
I = distance the water travels
The total head decreases as water moves downstream, or down gradient (i.e.,
dh < 0, dl > 0), so i is always a positive number. In addition, both h and l are lengths,
so i is dimensionless. A large hydraulic gradient reflects extensive friction, and thus
means either water is flowing very fast or the soil has a large resistance to flow (or a
combination of the two).
Example 7.1
Piezometers and Pitot tubes have been installed at Points A and B in the pipe
shown in Figure 7. 7. The water levels tmder steady-state flow are as s…
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