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Speleogenesis in carbonate rocks

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  • State University of New York, Oneonta

Abstract and Figures

This paper outlines the current views on cave origin in carbonate rocks, combining ideas from a variety of sources. A typical dissolution cave develops in several stages that grade smoothly from one to the next: (1) Initial openings are slowly enlarged by water that is nearly at solutional equilibrium with the local bedrock. (2) As the early routes enlarge, those with the greatest amount of flow grow fastest. (3) These favoured routes eventually become wide enough that groundwater is able to retain most of its solutional aggressiveness throughout the entire distance to the spring outlets. This breakthrough time usually requires times on the order of 104 to 105 years and ends the inception phase of speleogenesis. (4) Discharge along these selected routes increases rapidly, allowing them to enlarge into cave passages rather uniformly over their entire length. Maximum enlargement rates are roughly 0.001-0.1 cm/yr, depending on the local water chemistry and lithology. (5) The cave acquires a distinct passage pattern that depends on the nature of groundwater recharge, the geologic setting, and the erosional history of the region. Branchwork patterns dominate in most carbonate aquifers. Maze caves are produced by any of the following: steep hydraulic gradients (e.g. during floods), short flow paths, uniform recharge to many openings, and mixing of waters that contrast in chemistry. (6) Enlargement rate usually decreases as passages become air-filled, owing to loss of aggressiveness as carbon dioxide escapes through openings to the surface. (7) The cave typically evolves by diversion of water to new and lower routes as the fluvial base level drops. (8) The cave is eventually destroyed by roof collapse and by intersection of passages by surface erosion. At any given time, different parts of the same cave may be experiencing different stages in this sequence.
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Speleogenesis and Evolution of Karst Aquifers
The Virtual Scientific Journal
www.speleogenesis.info
Speleogenesis in carbonate rocks
Arthur N. Palmer
Department of Earth Sciences, State University of New York, Oneonta, NY 13820, USA
Re-published by permission from:
Gabrovšek, F. (Ed.), Evolution of karst: from prekarst to cessation.
Postojna-Ljubljana, Zalozba ZRC, 43-60.
Abstract
This paper outlines the current views on cave origin in carbonate rocks, combining ideas from a variety of sources. A typical
dissolution cave develops in several stages that grade smoothly from one to the next: (1) Initial openings are slowly enlarged by
water that is nearly at solutional equilibrium with the local bedrock. (2) As the early routes enlarge, those with the greatest amount of
flow grow fastest. (3) These favoured routes eventually become wide enough that groundwater is able to retain most of its solutional
aggressiveness throughout the entire distance to the spring outlets. This breakthrough time usually requires times on the order of 104
to 105 years and ends the inception phase of speleogenesis. (4) Discharge along these selected routes increases rapidly, allowing them
to enlarge into cave passages rather uniformly over their entire length. Maximum enlargement rates are roughly 0.001-0.1 cm/yr,
depending on the local water chemistry and lithology. (5) The cave acquires a distinct passage pattern that depends on the nature of
groundwater recharge, the geologic setting, and the erosional history of the region. Branchwork patterns dominate in most carbonate
aquifers. Maze caves are produced by any of the following: steep hydraulic gradients (e.g. during floods), short flow paths, uniform
recharge to many openings, and mixing of waters that contrast in chemistry. (6) Enlargement rate usually decreases as passages
become air-filled, owing to loss of aggressiveness as carbon dioxide escapes through openings to the surface. (7) The cave typically
evolves by diversion of water to new and lower routes as the fluvial base level drops. (8) The cave is eventually destroyed by roof
collapse and by intersection of passages by surface erosion. At any given time, different parts of the same cave may be experiencing
different stages in this sequence.
Keywords: cave origin in carbonate rocks
Introduction
Caves are present in all rather pure carbonate
rocks that are in geologic settings and climates that
allow abundant groundwater recharge. For this
reason, it is clear that cave origin requires no
special chemical mechanism beyond the circulation
of meteoric groundwater. Dissolution caves can
form by other processes, but this is the common
speleogenetic mode in most carbonate aquifers and
is the main topic of this paper. Most of the concepts
presented here are not new, but, where possible,
alternate viewpoints are given in the hope of
encouraging further discussion.
Cave inception
Speleogenesis requires one basic thing:
Groundwater must dissolve the bedrock rapidly
enough to produce caves before the rock is
removed by surface erosion. This requires the
through-flow of large amounts of solutionally
aggressive water along stable flow paths.
The earliest stages
At great depth beneath the surface there is very
little groundwater flow because openings in the
rock are narrow and few, and hydraulic gradients
are feeble. But as uplift and erosion expose these
rocks near the surface, increasing amounts of
groundwater pass through them. Along any given
flow path, the solutional enlargement rate is
controlled by a simple mass balance. The mass
removed from the walls of the growing conduits is
equal to that which is carried away in solution. The
increase in volume thus depends on how much
water passes through the conduit, and how rapidly
the water dissolves the rock. In other words, the
two major controls are discharge and chemical
kinetics.
Early in the development of a carbonate aquifer,
all groundwater becomes nearly saturated with
dissolved calcite and/or dolomite before it emerges
at the surface. The total amount of rock removed
along any flow path is nearly independent of
chemical kinetics, because the water has enough
time to equilibrate with the rock, regardless of
Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.2
dissolution rates. The saturation concentration
depends on the minerals present, CO2
concentration, type of system (open vs. closed),
temperature, and interactions with other dissolved
components. All these show considerable variation,
both spatially and temporally, but it is unlikely that
there will be major differences between
neighboring flow paths within a given aquifer. In
contrast, there are great variations in discharge
from one flow path to another – and this is the main
control over which the early paths are able to grow
into caves.
Most dissolution takes place at the upstream ends
of the flow paths, where aggressive water first
enters the carbonate rock. (“Upstream” and
“downstream” in the following discussion refer to
the up-gradient and down-gradient ends of the
system, even where the flow is only laminar
seepage.) With time and distance, there is an
increase in saturation ratio of the dissolved minerals
(actual concentration divided by saturation
concentration, C/Cs). At first the dissolution rate
decreases in a roughly linear manner. But as the
saturation ratio rises above approximately 60-90%
(the exact value depends on temperature and CO2
content), the dissolution rate decreases much more
rapidly. The result is that the final approach toward
saturation is very slow (see Berner and Morse,
1974; Plummer and Wigley, 1976; Plummer et al.,
1978; Dreybrodt, 1990; Palmer, 1991).
Dissolution is so rapid in the upstream sections
that if the remainder of the dissolution followed the
same trend, the water would lose virtually all its
aggressiveness after only a short distance of flow.
Dissolution would be so slow in the rest of the
aquifer that cave development would be almost
impossible (Palmer, 1984). Except in the most ideal
situations (wide, short fractures with steep
hydraulic gradients, e.g. along escarpments),
enlargement of the initial openings to cave size
would require many millions of years, during which
the carbonate rock is likely to be entirely removed
by erosion.
Interestingly, it would be unlikely for caves to
form with either the rapid dissolution at low
saturation ratios or the slow dissolution at high
saturation ratios. Early slow dissolution along the
entire flow path is essential for preparing the way
for the rapid dissolution that follows. But the slow
dissolution alone cannot enlarge the routes rapidly
enough to form caves within a geologically feasible
time. Rapid dissolution at low saturation ratios is
necessary to achieve this. But, as shown above, the
rapid dissolution by itself cannot form caves in
most situations.
Geological aspects of cave inception
The initial width of fissures (e.g. fractures and
partings) is perhaps the most uncertain of all field
conditions that influence cave inception. By the
time a cave is large enough for humans to enter, the
evidence has long disappeared. Initial fissure width
is a slippery concept, because the widths increase
with time even without being dissolved, simply by
release of stress as the overlying rocks are eroded
away. Field evidence suggests that a minimum
initial fissure width of about 0.01 mm is required
for cave development (Böcker, 1969). However,
this value depends on hydraulic gradient, flow
distance, water chemistry, and length of time
available, and so the threshold for initial fissure
width is not a fixed value, but instead depends on
the local setting.
To clarify how wide the initial fissures in
limestone might be, it is helpful to gather data from
relatively insoluble rocks that are approximately as
brittle as limestone. Intrusive igneous rocks such as
granite should give a close approximation. Water
wells in these rocks have fairly small yields,
especially at depths of more than 50 m below the
surface (Freeze and Cherry, 1979, p. 158). But even
with conservative estimates for hydraulic gradient
and fissure frequency, the observed well yields
require fissures that are roughly 0.1-0.5 mm wide.
Surely only a few of the many fissures are this
large, but they are important ones, which in soluble
rock would grow into caves.
Inception horizons were originally defined by
Lowe (1992) as beds or stratal interfaces that
provide a chemical environment that favours cave
development. The presence of pyrite along a
geologic contact was cited as a typical example,
whereby oxidation of the sulphide to sulphuric acid
might give a substantial boost to cave development.
One difficulty with this particular example is the
deficiency of oxygen in most deep groundwater.
Structural and hydraulic factors are also crucial in
determining which initial openings are able to
develop into caves.
The presence of interbedded sulphates within
carbonate rocks provides a suitable environment for
cave inception. Dissolution of the sulphates can
boost porosity, although this process forces calcite
to precipitate by the common-ion effect. Because of
differences in molar volume, the precipitated calcite
usually does not occupy all the porosity generated
by dissolution of gypsum or anhydrite. This process
is even more potent when limestone, dolomite, and
gypsum interact within the same system. As calcite
is forced to precipitate, the solubility of gypsum
rises to almost 1.5 times more than that of gypsum
alone, and the solubility of dolomite rises to several
Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.3
times its normal value. Because dolomite dissolves
so slowly, the process is drawn out over long
distances and times, potentially resulting in long,
continuous paths of increased porosity that may
pave the way for later cave development. The
geochemical process has been validated by field
measurements (e.g. Bischoff et al., 1994), but its
impact on cave development is still unclear.
Breakthrough
Eventually the entire length of an incipient cave
becomes large enough to allow water to pass all the
way through while still retaining most of its
aggressiveness. At this time there is a fairly sudden
transition (“breakthrough”) to rapid dissolution
throughout the entire flow path. From then on, the
entire route enlarges rapidly at a roughly uniform
rate of about 0.001-0.01 cm/yr, depending on the
water chemistry. This rate varies with the amount
of turbulence, but only at low saturation ratios
(Plummer and Wigley, 1976; White, 1984). At the
high saturation ratios of most karst water the effect
is minor. In mature caves, abrasion by coarse
sediment load can increase local rates of cave
development (Smith and Newson, 1974). These
factors are insignificant compared to the truly great
differences in growth rate that distinguish true cave
passages with low saturation ratios from narrow
flow paths whose water is nearly saturated with
dissolved carbonates.
Fig. 1 shows the mean enlargement rate in an
ideal fissure as a function of discharge and flow
length. The steep parts of the curves represent the
slow dissolution rates governed by the mass
balance, and the horizontal segments at the top
represent the rapid dissolution controlled mainly by
kinetics (Palmer, 1991). Because the enlargement
rates are not uniform throughout the fissure, the
rates shown in Fig. 1 cannot be translated directly
into the time required for an incipient cave to reach
breakthrough. To do this, finite-difference
modelling is necessary. The results are shown in
Fig. 2.
The time required for chemical breakthrough can
be considered the “gestation time” through which
an incipient cave must pass in order to allow it to
grow into a true cave. It is difficult to specify
exactly when this time begins. In some ways, it
involves the entire age of the carbonate aquifer, if
one includes all the effects of early diagenesis,
burial, and uplift in order to reach its present state
(Klimchouk and Ford, 2000). But before cave
growth can truly begin, there must be a substantial
hydraulic gradient. Thus it is customary to start the
clock when the carbonate rock is first exposed
above base level, at the time when both recharge
zones and discharge zones are well defined.
Computer models can track the growth of idealized
fissures of specified initial width, length, hydraulic
gradient, and chemical attributes. These show that
the breakthrough time is approximately
proportional to w-3 (
i/L)-1.4 P-1, where w = initial
fissure width, i = mean hydraulic gradient, L = flow
distance, and P = initial PCO2 (Palmer, 1988, 1991).
Dreybrodt (1996) provided an analytical derivation
arriving at nearly the same functional relationships.
Fig. 1. Mean enlargement rate of a fissure in limestone,
as a function of discharge (Q) and flow length (L). Q =
discharge per metre of fissure height (long dimension of
fissure cross section). Assumptions include closed
conditions, T = 10o C, initial PCO2 = 0.01 atm. (See
Palmer, 1991.)
Fig. 2. Approximate breakthrough times for cave incep-
tion along fissures in limestone. The main part of the
graph shows closed conditions at T = 10o C and initial
PCO2 = 1%. Variation of breakthrough time with initial
fissure width, temperature, and initial PCO2 are shown.
The combined variable i/L represents the hydraulic
gradient (h/L) divided by flow distance (L). Modified
from Palmer (1991). See also Dreybrodt (1996).
Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.4
Laminar discharge through the fissure is
proportional to w3 i, which is essentially the inverse
of two of the most important variables that
determine breakthrough time. Thus the paths that
develop most rapidly into caves are those with high
discharge and short flow distance. High PCO2 is also
favourable, as long as CO2 is not lost by degassing.
Temperature plays a complex role in determining
how long it takes for breakthrough to occur. Higher
temperatures speed the chemical reactions, but in
long flow systems this can increase the
breakthrough time by depleting most of the water’s
solutional capacity in the upstream parts, leaving
less for the downstream parts. High temperature
increases the flow velocity by reducing the
viscosity of the water, but it also decreases the
amount of limestone or dolomite that can be
dissolved. The net result is an increase in
breakthrough time with rising temperature.
However, another complication is that in warmer
climates the CO2 production in the soil is greater,
which shortens breakthrough times.
As shown in Fig. 2, breakthrough time decreases
as much as 5 times if the CO2 consumed by
carbonate dissolution is quickly replaced, for
example when the water is in close contact with a
CO2 source such as soil. This is rare. In general, the
early phase of growth takes place in an
approximately closed system, where CO2 is used up
as dissolution proceeds. In caves with open
atmospheres, CO2 is likely to be lost by air
exchange with the surface, which more than offsets
the apparent advantage of the open system.
Fig. 2 shows that initial fissures 0.01-0.1 cm
wide would require no more than a few thousand or
tens of thousands of years to reach the maximum
enlargement rates, from the time aggressive
groundwater first begins to flow through the
limestone. For example, in a fissure 1 kilometre
long, with an initial width of 0.02 cm, hydraulic
gradient of 0.02 (20 m/km), PCO2 of 0.05 atm,
temperature of 10o C, and closed to further uptake
of CO2, the maximum rate of enlargement is
reached in about 30,000 years. These conditions are
typical, perhaps even conservative. Lab work and
computer modelling by Dreybrodt (1990, 1996)
suggest even shorter breakthrough times that are
probably more valid. Acids can also be generated
within passages by oxidation of organic compounds
in the water or iron sulphide in the bedrock,
diminishing the breakthrough times. Water
chemistry and flow vary with the seasons, but their
effects average out over the years.
Time required for a cave to reach
traversable size
Beyond the breakthrough time, growth rate of a
cave depends chiefly on the nature of its water
input. In dense, rather pure limestone, the rate of
wall retreat (S) can be estimated with the equation
S = 11.7 k (1 – C/Cs)n cm/yr
where C/Cs is the saturation ratio, k is a reaction
coefficient, and n is the reaction order (see Palmer,
1991 for units and further details). Values for k and
n vary with PCO2, and k also varies with
temperature. For quick applications, some
representative averages can be given. At C/Cs <
~0.7, k and n are approximately 0.015 and 1.7
respectively. At C/Cs > ~0.7, k and n are roughly
0.24 and 4 respectively. Because (1-C/Cs) is less
than 1, the larger exponent gives a smaller value of
S.
For example, water that collects on insoluble
rock and then flows as a sinking stream directly
into a limestone cave usually has a PCO2 of about
0.001-0.005 atm. This value is higher than that of
the outside atmosphere (0.00036 atm) because even
though the stream is open to the atmosphere, it
acquires CO2 from seepage that enters the stream
through the soil. At ponors, most sinking streams
have saturation ratios of about 0.1-0.5. Under these
conditions, limestone surfaces in the cave will
dissolve as fast as 0.15 cm/yr. Ideally, a water-filled
cave can increase its diameter up to 2-3 m in 1000
years. (The diameter increases at twice the rate of
wall retreat, S.) Measurements with dial
micrometers, repeated over several years, have
verified these rates in caves fed by sinking streams
(High, 1970; Coward, 1975).
In contrast, many caves are fed by water that
infiltrates through soil and reaches the caves only
after having traveled for a considerable distance
along the soil-limestone contact and through
narrow fissures in the epikarst. This water has a
high PCO2 (about 0.01-0.05 atm) but has a high
saturation value, usually about 0.75-0.95 by the
time it reaches the caves. The diameter of a water-
filled passage grows no more than about 20 cm per
1000 years under those conditions.
Organization of conduits
It has been shown that caves in a typical karst
aquifer are able to form only along flow paths that
increase their discharge with time. This can be
achieved in either of two ways:
Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.5
By increasing the flow efficiency in a
system with a fixed head difference. An example is
leakage of water from a stream or other body of
water that drains to a lower outlet. As the initial
fissures widen, the discharge rises dramatically.
The upstream head begins to decrease only when
the conduit becomes large enough to transmit the
entire stream flow. By that time breakthrough has
already taken place.
By increasing the catchment area that feeds
an incipient cave passage. At first, water drains into
the growing caves as widely dispersed seepage.
Dolines form by subsidence into the rapidly
growing voids at the soil/bedrock interface. As
dolines increase their catchment area, their mean-
annual discharge increases to the caves that they
feed. Discharge to the caves increases in an
irregular manner, much less rapidly than in routes
fed by leaking streambeds, and hydraulic gradients
decrease with time, even during the earliest periods
of growth.
The difference between these two systems is
important. Because the routes fed by surface
streams can increase their flow much more rapidly,
they are usually the first parts of a cave to form.
Passages fed by depressions of limited catchment
area require longer times to form, and they usually
join the earlier passages as tributaries of a
branchwork system. The first passages to form in a
cave are usually short and direct, except where
short paths are prohibited by the geologic setting.
With time, these early passages serve as low-head
targets for passages having more remote recharge
sources (Ford and Ewers, 1978; Ford et al., 2000).
Less time is required for a cave to grow in small
steps (i.e. where new, relatively short upstream
passages link to earlier downstream ones) than for a
single long passage to form. This is partly due to
the non-linear relation between breakthrough time
and flow distance. Although the growth of any
single passage propagates in the downstream
direction, the overall system grows in the upstream
direction, away from the springs, by addition of
new passages (Ewers, 1982; Ford et al., 2000).
A typical sequence is shown in Fig. 3. Assume,
for simplicity, that passage segments B-A and C-B
have identical lengths and gradients. The
breakthrough time for a single passage from C to A
would be (LC-A
/ LB-A)1.4 longer than the
breakthrough time for either of the two segments –
i.e. about 2.6 times longer. This is 30% longer than
it would take for segments B-A and C-B to reach
breakthrough separately, one after the other. Just as
importantly, the gradient of C-B would normally be
less than that of B-A until the head dropped in B-A
(Ford et al, 2000). The tributary from doline (D)
has a smaller catchment area and is slower to reach
cave dimensions.
Fig. 3. Evolution of a typical branchwork cave by
successive piracy of sinking streams and development of
recharge sources through dolines. Segment B-A forms
first because of the short path length and steep gradient.
Segment C-B links up later, aided by steepening of the
gradient as segment B-A develops. (C-B does not
necessarily join B-A at point B.) The passage from
doline D is last to form because of its limited catchment
area. See Ford and Ewers (1978) and Ford et al. (2000)
for descriptions of hardware models that illustrate this
concept.
Since the flow of water through carbonate
aquifers is controlled partly by the history of river
entrenchment, the vertical arrangement of cave
passages also reflects this control. The traditional
view is that the largest passages are formed when
base level is relatively static (Sweeting, 1950;
Davies, 1960). At such times, rivers develop
floodplains, and springs are held at fairly constant
elevations for lengthy periods of time. Meanwhile
the passages that feed the springs are able to grow
large. In contrast, passages that form during rapid
river entrenchment are usually small. The major
passages form different levels, which in most cases
decrease in age downward. Fluvial aggradation may
cause some or all neighboring cave passages to fill
with sediment over the vertical range of base-level
rise.
This conceptual model has been well validated in
Mammoth Cave, Kentucky (Palmer, 1989; Granger
et al., 2001). However, in many caves there are
several complications that disrupt this simple
interpretation. Vadose passages may be perched on
insoluble strata and grow to large size above base
level. Most phreatic passages contain vertical loops
Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.6
that descend far below the local base level. Some
phreatic caves follow favourable stratigraphic units
such as zones of former sulphates. Even the ideal
cave levels controlled by pauses in fluvial
entrenchment are not perfectly “level”. For this
reason, many people prefer to call them storeys or
tiers, and either of these terms is preferred in
general applications. However, the term cave level
is still appropriate where there is a clear relation to
fluvial base level. But the critical elevation is not
the average elevation of a phreatic passage, but
instead where there is a clear transition from vadose
to phreatic morphology (for example, a transition
from canyon to tube). This transition is not clear in
some passages.
Fig. 4 is an idealized profile through a multi-
storeyed cave, as described by Ford (1971). Three
main stages of cave development are shown, with
decreasing loop amplitudes from the highest storey
to the lowest. This is not a characteristic of all
multi-storeyed caves, but it is a conceptual ideal.
Ford (1971) ascribed the decrease in amplitude to
increasing fissure frequency in the host rock with
time. Fissures are sparse at first, and passages are
constrained to only a few deeply descending loops.
As erosional unloading and cave development
persist, fissures become more numerous until
eventually the passages are able to form more or
less along the water table, with minimal phreatic
looping. In some caves the greater amplitude of
loops in upper passages is instead caused by
floodwaters, which superpose ungraded, looping
bypass routes around low-flow routes that have
more uniform gradients (Palmer, 1972). In the same
vein, on the basis of studies in the Alps, Audra
(1994) and Häuselmann et al. (2001) ascribe an
epiphreatic origin to looping passages.
Fig. 4. Vertical layout of a typical cave, showing
decreasing amplitude of phreatic loops with depth. This
trend has been interpreted by Ford (1971) and Ford and
Ewers (1978) to be the result of increasing fissure
frequency with time. Successive positions of the water
table are shown as gray lines. Some researchers consider
these lines to represent the upper extent of epiphreatic
flow (see text).
The earliest passages in a cave system (usually
fed by sinking streams) may not show a clear
distinction between vadose and phreatic
development, because their discharge fluctuates a
great deal, and because the initial potentiometric
surface is relatively high. As a result, most of these
passages are subjected to a variety of flow
conditions – phreatic at first, and then vadose and
epiphreatic at later times. Still, many of them show
a fairly sharp transition from vadose canyons (with
continuous downward trends) to phreatic tubes
(with low gradients and usually irregular looping
profiles). This transition is more sharply defined in
secondary passages fed by karst depressions of
limited catchment area, because the flow is more
uniform with time and the water sources are usually
well above the potentiometric surface.
Because of their gravitational flow, many vadose
passages have a strong down-dip component,
especially those in well-bedded rocks. Phreatic
passages show no consistent relation to the dip,
except where that is the only path to potential
outlets, or where prominent fractures also extend in
that direction. In well-bedded rocks, the
intersection between the dipping beds and low-
gradient water table encourage many phreatic
passages to develop nearly along the strike of the
beds. These relationships tend to be obscure where
the geologic structure is complex.
Origin of branching systems
Branching cave patterns are by far the most
common for several reasons:
As passages enlarge, the local hydraulic
head within them decreases. Groundwater flows
from surrounding smaller openings, where the
potentiometric surface is higher, toward the low
heads of the early conduits.
Vadose passages have no inherent tendency
to converge, because they are hydraulically
independent. However, the structures that they
follow often intersect, forcing independent streams
to join as tributaries. Examples include intersecting
fractures, and synclinal structures in bedding-plane
partings.
Water from broad recharge areas converges
toward outlets of limited extent, generally stream
valleys, which causes a natural tendency for
conduits to converge simply by competition for
space. After two streams have converged, there is
little opportunity for them to diverge farther
downstream. The exception is in the vicinity of the
spring outlet, where local distributary systems may
develop because of collapse, backflooding, and
widening of fissures by erosional stress release.
Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.7
Maze development
Besides branchworks, most other caves are
mazes in which all the passages form more or less
simultaneously. A maze cave can form only if the
growth rate is similar along many alternate flow
paths. This can happen if all passages evolve
simultaneously at the maximum rate shown in Fig.
1. If the ratio of discharge to flow distance (Q/L) is
large in many alternate flow routes, they will
enlarge at roughly the same rate (Palmer, 1991).
Specifically, this condition is achieved if Q/rL >
0.001 (cgs units), where r = mean conduit radius. In
fissures, this condition is reached if Q/bL > 0.001,
where b = long dimension of the fissure cross
section, perpendicular to the narrow dimension w.
Specific settings where this condition is met
include:
A. High-discharge or high-gradient flow during
floods. Water is forced into all fissures in adjacent
carbonate rocks under steep gradients, causing them
to enlarge at approximately the maximum possible
rate (Palmer, 2001). This process is most active in
the vicinity of constrictions in the main stream
passages, which result from collapse, sediment
chokes, or poorly soluble strata.
B. Short flow paths from where the water first
enters the soluble rock. Because of the short flow
distances, all fissures except for the narrowest
enlarge simultaneously at similar rates. The epikarst
is an example. Network mazes are also formed by
recharge through a permeable but insoluble
material such as quartz sandstone (Palmer, 1975,
2000).
C. Uniform recharge to all fissures, regardless of
their width. This can be achieved by seepage
through porous, insoluble materials, as in B above.
D. Sustained high gradients, for example beneath
dams.
E. Mixing zones, where the groundwater
aggressiveness is locally boosted by mixing of
waters of contrasting CO2 content or salinity, or by
oxidation of sulphide-rich water. Over short flow
distances, many alternate routes are enlarged.
Mixing of waters of varied CO2 content can
decrease breakthrough times, but large differences
in CO2 concentration are necessary (Gabrovšek,
2000).
The differences in maze types depend partly on
geologic structure. Network mazes consist of
intersecting fissures, with a pattern resembling city
streets. They require many intersecting fractures
(joints or faults), which are typical of massive or
thick-bedded rock. Most are formed by processes
B, C, or E above. Anastomotic mazes have a
braided pattern of intersecting tubes, usually
arranged two-dimensionally along a single parting
or fault. They are nearly all formed by process A
above. Spongework mazes form where primary
(matrix) porosity is dominant. In pattern they
resemble the intersecting holes in a sponge. Most of
them form by process E, and less commonly by
process A. A two-dimensional variety can form
along bedding-plane partings. Ramiform mazes
consist of rooms with offshoots extending outward
from them at various elevations. They usually
include areas of network or spongework maze
development and are formed mainly by process E.
Many network and anastomotic mazes, and a few
spongework mazes, are merely superimposed on a
basic branchwork pattern and represent only part of
the entire cave development.
Fig. 5 provides a summary of typical cave
patterns, showing their relation to source of
aggressive water and to dominant structural
characteristics.
Supporting evidence from computer models
Finite-difference computer models support and
clarify some of these relationships. Conspicuously
absent from the list of ways to form maze caves is
slow groundwater flow through artesian aquifers.
This origin seems logical, and many maze caves are
indeed located in aquifers that are partly artesian.
However, artesian conditions by themselves do not
produce maze caves. Modelling by Palmer (1991)
showed that different-sized branches of a loop are
least likely to enlarge at the same rate in slow-
moving water near saturation. Dreybrodt and
Siemers (2000) supported this idea by showing that
as breakthrough time increases, passages tend to
become unitary and exhibit less complexity.
Modelling by Clemens et al. (1997) verified the
development of network mazes by uniform seepage
through an insoluble caprock, as described in B
above. The insoluble cap encourages maze
development because it is permeable, rather than a
confining unit.
Conduit growth and modification
At the breakthrough time, when an incipient cave
reaches its maximum growth rate, several other
changes take place more or less simultaneously
(White, 1977). The cave water changes from
laminar to turbulent, which increases the solution
rate slightly (see earlier discussion). The flow also
becomes competent enough to transport detrital
sediment. For example, it is able to carry away the
soil that subsides into caves through karst
depressions, allowing the depressions to grow more
rapidly. The sediment load can also help to enlarge
Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.8
Fig. 5. Common patterns of solutional caves. Dot sizes show the relative abundance of cave types in each of the listed
categories. Single-passage caves are rudimentary or fragmentary versions of those shown here.
caves by mechanical abrasion, but, in places,
sediment accumulates in thick beds that retard
dissolution and erosion. Where sediment
accumulates, upward dissolution by paragenesis is a
possible consequence, especially in caves enlarged
by periodic floodwaters. However, water within the
sediment is often undersaturated and can still
dissolve the underlying rock (Vaughan et al., 1998).
When a cave is able to transmit the entire flow
from its recharge area, the average flow can
increase no further. Instead the head within the
passage decreases as the cross section continues to
enlarge. Much of the upstream part of the cave
becomes vadose, and streams may entrench
canyons in the passage floors.
As caves acquire entrances that allow air
exchange with the surface, many free-surface cave
streams lose part of their aggressiveness. Inflowing
water is fairly rich in soil-derived CO2, and may
acquire even more by oxidation of organic
materials as it flows through the caves (Bray,
1972). Loss of CO2 through entrances and other
openings can drive the stream water to
supersaturation with dissolved calcite or dolomite,
so that many vadose cave streams are aggressive
only during high flow. Some vadose stream
channels even acquire a thin coating of calcite in
sections of supercritical flow during dry seasons.
These deposits are usually removed during the
following wet season, but with only a small net
amount of solutional entrenchment each year.
Measurements in caves of New York State show
that the overall entrenchment rate of active stream
canyons of this type can be as slow as 10-20 mm
per thousand years (Palmer, 1996), despite the
continuous flow of water. During six months of
continuous monitoring in the largest stream in
Mammoth Cave, Meiman and Groves (1997) found
that 70% of the passage enlargement took place
during the highest 7% of flow.
Dating of cave sediments by 26Al/10Be isotope
ratios in quartz-rich cave sediment is a powerful
tool for interpreting rates of cave development.
Usually this sediment is deposited by the most
recent active stream flow and gives a minimum age
for the passage. At Mammoth Cave, 26Al/10Be
dating suggests that the development of each
passage level required at least 105 years (Granger et
al., 2001). This value is compatible with the range
of probable times required for breakthrough (Fig. 2)
and for later enlargement to the present diameters
of about 5-10 m in the major passages.
Headward erosion of resistant beds by cave
streams can require a surprisingly long time. For
example, sediment on ledges above an entrenched
canyon in Mammoth Cave were dated at 1.13
million years, validated by samples at similar
elevations elsewhere in the cave (Granger et al.,
2001). The passage is floored by a metre-thick
sequence of shaly and cherty limestone, which has
been breached by a deep canyon that post-dates the
sediment. Headward entrenchment has progressed
Arthur N. Palmer / Speleogenesis and Evolution of Karst Aquifers, 1 (1) January 2003, p.9
only 360 m along the passage, and only about half
of that has occurred upstream from the sampling
site. The entrenching stream is still active today and
is quite capable of transporting gravel. The rate of
headward entrenchment appears to be less than half
a metre per thousand years.
But under favourable conditions, diversion of
passages from one level to another can take place
rather rapidly. Post-glacial diversion of water in
New York State caves has formed traversable
passages up to a metre in diameter and 200 m long
since the last glacial retreat about 13,000 years ago
(Mylroie, 1977). In many vadose canyons
throughout the world, examples can be seen where
loops or cutoffs have developed along prominent
bedding-plane partings exposed in the canyon floor
(Fig. 6). As a result, the floor of the upper level
coincides with the ceiling of the lower level. The
new passage must develop before the parting is
bypassed by deepening of the original canyon. This
implies that the breakthrough time for the diversion
route is virtually nil, allowing the new narrow path
to enlarge competitively with the old well-
established one. Most such diversions are short.
As the land surface becomes dissected by
erosion, patterns of groundwater recharge change.
The few large initial water sources may be divided
into many smaller ones. Vadose water must travel
increasingly greater distances to reach the water
table, and extensive complexes of vadose canyons
and shafts can form. The resulting pattern of active
cave streams is much denser than that of the
original surface drainage. Growing dolines
eventually form a continuous karst surface.
Eventually the only surface streams that retain their
flow are the main entrenched rivers and the
ephemeral upstream ends of sinking streams.
Fig. 6. Stream diversion in an entrenching vadose
canyon. The lower loop illustrates nearly zero
breakthrough time along the guiding bedding-plane
parting, as shown by the minimal entrenchment of
segment A below the lower parting. This is a common
occurrence, especially in well-bedded carbonates, but it
is not a general rule.
The final stage
As the land erodes, the surface intersects
underlying cave passages, segmenting them and
eventually destroying them entirely. Evidence for
the cave may persist for a while as a canyon-like
feature or a rubbly zone of collapsed blocks. This
final episode in the life of a cave passage usually
occupies tens of thousands or even hundreds of
thousands of years. However, newer passages
continue to develop where the soluble rock extends
to lower elevations. In dipping carbonate rocks,
new areas of rock are uncovered by erosion at about
the same rate as they are eroded away in the up-dip
areas. This process ends when the entire soluble
rock in the cave region is eroded away.
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... In particular, we know that the curvilinear branchwork pattern is generally developed along the bedding planes with dominant point recharge. In contrast, the rectilinear branchwork pattern combines joint and fracture structures and point recharge conditions [25]. However, the porosity of joints and fractures under diffuse recharge is responsible for developing a network maze conduit pattern. ...
... However, conduits enlarge hierarchically in the branchwork pattern. The conduit's diameter tends to be larger, close to the discharging spring, compared to the recharge area far from the spring location [25]. The assumed specifications (i.e., order and diameter) for the three patterns of conduit are shown in Table 1. ...
... Common patterns of dissolution conduits in carbonate rocks. The size of the black circles shows the relative abundance of cave types in each of the listed categories[25]. ...
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Thesis
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