crack propagation on desert surface clasts by differential insolation of cracks

1
crack propagation on desert surface clasts by
differential insolation of cracks

• John E. Moores, Jon D. Pelletier and Peter H.
  Smith
• Lunar and Planetary Laboratory, University of
  Arizona 1629 E University Blvd Tucson, AZ
  85721-0092 Email jmoores_at_lpl.arizona.edu

abstract In the Southwest US, cracks in surface
clasts have a preferred orientation independent
of rock fabric, rock shape and local conditions.
Differential insolation of incipient cracks of
random orientations provides an explanation of
this preferred orientation through removal of
moisture held in the crack. A study of
differential insolation of cracks of different
orientations at 35N was undertaken using a
numerical radiative transfer code and idealized
crack geometry. The amount of energy reaching the
bottom of each crack was calculated at five
minute intervals over the day for several days of
the year to determine hourly, daily, seasonal and
annual deposition of energy depending only on
crack orientation and depth. By assuming that
only crack orientations which effectively shield
their interiors and minimize their water loss are
able to grow, the pattern of cracks produced,
including both expressed modes and their
deviations from pure North-South and East-West
behavior are consistent with observations in the
field. Given this formulation, the important
timescale for water retention is the annual
average insolation which is associated with both
modes of the aligned cracks while the effect of
daily recharge by summer monsoon rains is
consistent with the observed deviations of these
modes. This suggests that both the annual average
insolation and the daily pattern of rainfall
could be recorded in the cracking patterns of
surface rocks in the Southwest.
timescales The timescales over which water enters
and exits cracks is important to the analysis.
For instance, if more then a year is required to
discharge a crack, then only the annual average
insolation is significant. Similarly, the
timescale of the recharge of cracks is also
important. As such, the nature of water movement
through rock and the microstructure of the rock
itself must be considered to determine the
mechanisms by which water enters and exits the
rock in the vicinity of cracks. This is analyzed
using an order of magnitude approach. Equations
1 and 2 can be plotted for the pore size
range of interest (Figure 3) using values for the
various constants taken at 20C. The most
significant feature of this plot is the observed
roll off in the discharge rate for pores larger
then a few tens of nm. This means that for the
largest pores which represent the largest volume
of water and the major pathways into the smaller
pores and microcracks, recharge can happen very
quickly, on the order of hours, and occurs much
more rapidly then crack discharge. As a result,
unlike ponded water in a macroscopic crack which
will evaporate quickly due to direct contact with
the atmosphere, water in these pores and
microcracks is stable on long timescales and will
continue to recharge smaller microcracks and
pores during this period. The characteristic
timescale of discharge is of the order of 2x107
seconds or about two thirds of a year.
the role of water in thermal cycling The
breakdown mechanism of surface clasts in arid
environments has been a topic of debate for
almost a century. Unlike in other environments
where physical and chemical weathering by the
action of plentiful liquid water is clearly the
primary mechanism, arid environments largely lack
sufficient water in the form of precipitation for
typical weathering processes to dominate 2.
Instead rocks may remain on the surface for very
long periods, in excess of 30 Ma in the most arid
of deserts 3. As a result, it has been
suggested that rocks may be broken down by
thermal insolation cycling. However, this has
been difficult to show in experimental tests.
The situation changes once water is added.
Griggs 4 found that samples of rock which had
survived 244 years of diurnal cycling unchanged
when the cooled with dry air disintegrated
noticeably within ten days of cycling (equivalent
to about 2-3 years of exposure) when cooled with
a mist of water. Barton also observed this effect
in the field, noticing a correlation between the
presence of moisture and degree of disintegration
of monuments in Egypt 5,6. Even so, additional
evidence of the role of insolation is provided by
recent work by McFadden et al. 1 in which a
meticulous survey of a great many rocks at
various sites in the United States Southwest
found that there is a net preferred orientation
to all the crack population once the effects of
rock fabric and shape have been removed. This
preferred orientation is reproduced, after
McFadden et al., in Figure 1, and demonstrates
that some regional or possibly global actor is
affecting how rocks breakdown on a very small
scale. It seems highly likely, as suggested by
McFadden et al., that this actor is the sun. How
can the role of water be reconciled with the
crack preferred orientation observed by McFadden
et al. which suggests that the sun is primarily
responsible for rock failure? One possible
solution is that the cracks themselves, by
offering partial shielding from solar insolation,
can act as locations of enhanced water retention
by the rock. In this way, crack orientations
which offer the best shielding from solar
insolation will retain the most water and grow at
the expense of other orientations of cracks.
results There are three different regimes in
insolation for the annual average depending upon
the depth of the crack. The first regime (Fig 4,
panel A) is a monotonic increase with E-W
oriented cracks receiving the most insolation.
This is the result of a domination of the summer
months in the insolation curve in which E-W
cracks receive more insolation then the N-S
cracks. This regime extends from the shallow end
to relative depths of 1 to 1.2 units. At large
crack depths, greater then 2.5 to 2.8 units in
depth, the opposite relationship is true (Fig 4,
panel C) with N-S cracks receiving more
insolation as the winter regime dominates.
However, there is an interesting crossover region
between these two in which latitudinal effects
dominate and a minimum is observed at about 35 N
of E-W (Fig 4, panel B). To highlight the
possible resulting crack directionality, a
threshold in energy has been added beyond which
cracks are considered to be baked out. The effect
of the evaporation threshold (Fig 5) is to cause
N-S oriented cracks to propagate when the
incipient cracks are themselves shallow as E-W
cracks are permanently baked out due to the large
amounts of insolation received in the summer. If
the incipient cracks are deeper then 1.2 units, a
second population of cracks with ENE-WSW and
ESE-WNW orientations can be produced. Finally for
deep incipient cracks (3 units or more) E-W
orientations are favored. The secondary mode is
exhibited only along an ENE-WSW axis in Figure 1
instead of being symmetric around a north-south
axis (i.e. there is no WNW-ESE mode represented)
as seen in the results from section 4.3 and in
Figure 6. Since the position of the sun in the
sky is symmetric about a N-S axis, it cannot be
an insolation effect on an annual time scale and
must instead be a diurnal effect. As such, it is
necessary to determine whether there is any
orientation bias in the amount of available
recharge. During most of the year, there is no
hourly preference for rainfall, however, in the
summer months, at weather stations near the New
Mexico cluster studied by McFadden et al. 1
there is a strong peak at 2PM 9,10.This will
favor those orientations which receive most of
their insolation in the morning, before 2PM.
Since these cracks will typically be shielded
after precipitation has fallen, they should be
able to retain this water for a longer amount of
time (potentially overnight) which will allow
more water to diffuse into the rock for these
orientations.
Figure 3 Recharge and Discharge rates from
convoluted capillary pores of length 10cm
according to equations 1 and 2 respectively
for a constant crack temperature of 20C and a
relative humidity of 0. The rates of recharge
and discharge are similar for small pores, but
drastically different for large pores due to the
transition between the Knudsen and Molecular
Diffusion regimes.
Figure 1 10 binned rose diagram of crack
orientations unrelated to local conditions or
rock fabric after McFadden et al, 2005 using the
frame of reference as described in this
publication with North indicated at 0. The
cracks are oriented with two major modes
represented, a primary N-S mode and a weaker
ENE-WSW mode.
Figure 4 (left) Annual insolation on cracks
divided into three regimes. Cracks with a minimum
in insolation at N-S orientations (A), cracks
with a minimum in insolation away from E-W or N-S
(B) and cracks with a minimum at E-W orientations
(C). Open squares and circles indicate the
identity of the line, resolution is 1. Figure 5
(right) Rose diagrams of preferred orientations
for water retention corresponding to the three
regimes shown in Figure 6. Depending upon the
depth, cracks may be produced with any of the
three forms. Panel A corresponds to a crack depth
of 0.2, Panel B to 1.5 and Panel C to 4.0. The
energy thresholds used were 1.65x109J yr-1 m-²,
4.70x108 J yr-1 m-² and 1.12x108 J yr-1 m-² for
each panel respectively. Cracks which receive
more energy then this threshold are considered
baked out and are not shown.
hydration weathering and differential insolation
model Cracks, in general, represent areas of a
rock in which water can be retained for longer
times then directly on the surface (1) because of
their concave geometry provides a low point in
which water can accumulate, (2) because they
shield their interiors from solar insolation and
(3) if they are deep enough, they can shield
their interiors from the daily thermal wave
penetrating down from the surface. As such,
orientations which receive more insolation will
evaporate more water from their interiors and
will bake out entirely before other orientations
of cracks. This means that if water is required
for a crack to grow, those cracks which preserve
their internal water for the longest period will
grow preferentially. These preferential cracks
will be those with the lowest amount of
insolation over the timescale relevant to crack
formation. The solar insolation within the
cracks is modeled using a plane-parallel
radiative transfer code originally designed by
Martin Tomasko to perform calculations in the
atmosphere of Titan 7. The cracks themselves
are modeled as linear troughs with flat bottoms
and sides, as in Moores et al. 8 and shown
schematically in Figure 2. The assumption has
been made that the cracks are found on a flat,
horizontal surface, both for simplicity and
because this orientation of crack can retain the
largest amount of water. As the sun moves in the
sky, the model determines if it can be seen from
each of 200 individual area elements located on
the bottom of the trench. If the sun is not seen,
the incident flux on that panel is zero for that
configuration of the sun in the sky. The rock
surface is considered sufficiently dark that
reflections from the trench walls are not
significant. The energy variations to be
presented in section 3 describe the total energy
received at the trench bottom. As such, this can
be considered as characteristic of the amount of
down-welling radiation at a characteristic depth.
Trough deepening is accomplished by deepening the
floor of such a trench while keeping the cross
section constant. These trenches will be
described by their aspect ratios in the manner of
lengthwidthdepth. The final piece of
information required to plot the path of the sun
on each day of interest is the latitude of the
observer. Since this model will be tested against
the orientations shown in McFadden et al. 1, a
latitude of 35N, a typical value for the sites
surveyed in this study was chosen.In order to
build up diurnal, seasonal and yearly variations,
the model tracks the sun in the sky at 5-minute
intervals during the day for 8 values of the
solar longitude equally spaced over the year
(LS0 or vernal equinox, LS45, LS90 or
northern summer solstice, LS135, LS180 or
autumnal equinox, LS215, LS270 or northern
winter solstice, and LS315). Intermediate
values, when necessary, are obtained by
interpolating between these points.
Figure 6 (above) Cumulative Insolation by 1320
at Los Alamos, NM by crack orientation. ENE-WSW
cracks receive less insolation by the early
afternoon compared to WNW-ESE trending cracks at
all depths of the initial crack. The differential
is more extreme for the variation shown in Figure
6, panel C (120 vs 60) then for panel B (20 vs
170). Open squares and circles indicate the
identity of the line, resolution is 1.
Figure 2 Geometry of the simulated cracks with
aspect ratios of 811 (A) and 813 (B). Both
cracks are shown in an E-W configuration
corresponding to a rotation angle of 90. The
direction of increasing rotation angle is shown
in both panels and is consistent with the frame
of reference shown in Figure 1.
Background Image A surface clast in Southern
Iceland broken by freeze-thaw weathering (a form
of hydration weathering) along a preferred
direction. Photo by Till Niermann (1989), used
under the GNU Free Documentation Licence v1.2
conclusions Simulations of different orientations
of cracks show that certain orientations of
cracks can receive more insolation then other
cracks on all timescales. The pattern of
orientations that are favored changes for
different depths of crack under the same
conditions. By assuming that crack growth is
proportional to moisture content in a crack which
is itself inversely proportional to the received
insolation on the crack bottom, it was possible
to determine which orientations would propagate
most easily. For the US Southwest, three
different modes were exhibited, a north-south
population when the initial crack was shallow, an
ESE-WNW and ENE-WSW population when initial
cracks were of intermediate depth and an
east-west population when initial cracks were
deep. The first two modes correlate well to the
data retrieved by McFadden et al. 1 for cracked
rocks at several sites in the US Southwest. Thus,
the pattern of yearly average insolation in
selecting certain orientations for growth and not
others correlates well with the observed data.
The east-west mode predicted by the simulation is
not seen and could result from a lack of deep
initial cracks compared to shallow cracks and an
inability of the discharge of moisture to respond
to variations in insolation shorter then a year.
This relative lack of east-west cracks compared
to ENE-WSW cracks which are themselves less
common then north-south oriented cracks
correlates well with the idea that these modes
are associated with progressively shallower
initial cracks which are progressively more
common in the initial surface cracking of
rocks. The apparent offset in the north-south
mode and the lack of an ENE-WSW mode in the
dataset of McFadden et al. is also correlated
with the diurnal cycle of rainfall in the summer
which promotes recharge of certain crack
orientations and not others. This suggests that a
record of both the annual variation in insolation
and the daily pattern of rainfall could be
preserved in the orientations of cracks on rocks
in the US Southwest.
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