Lunar and Planetary Science XXXI
1647.pdf
A SIMPLE MODEL FOR LAVA FLOW QUARRYING: MECHANICAL EROSION OF THE SUBSTRATE. F. J. Ciesla,
L. Keszthelyi, Lunar and Planetary Laboratory, University of Arizona. Tucson, AZ 85721.
Introduction:
Erosion by flowing lava has been studied for decades because it has the potential to explain some of
the largest and most enigmatic volcanic features on the other
planets, including sinuous rilles and canali. However, the investigation of erosion by lava has focused completely on the
thermal effects [1,2,3]. Even when thermo-mechanical erosion is discussed, it is in the context of thermal softening of
the substrate before it is incorporated into the flowing lava [4].
The role of pure mechanical erosion has never been investigated quantitatively. Our initial examination of this problem
suggests that pure mechanical erosion is likely to be very effective. In this abstract we briefly discuss the qualitative requirements for mechanical erosion by flowing lava, then introuduce
a simple quantitative model of the stresses generated at the
base of an active lava flow, and conclude with a discussion of
the implications of our model.
For flowing lava to
be able to dislodge pieces of the substrate through mechanical
means certain conditions must be met. First, basal topography
is needed to the extent that it will cause a seperation of flow in
the lava. This is not unreasonable because even the smoothest
bases of pahoehoe lava flows contain 10 cm scale undulations
and protuberances. Lava channels and tubes often contain
meter-scale obstructions. Thus, mechanical erosion can be
ignored in a simplified model with a planar base, but can
operate in the real world. Once a piece of rock is broken off by
the flowing lava, it will easily be transported by the lava due
to the similar densities.
Another basic requirement for mechanical erosion is that
the liquid lava be in contact with the underlying substrate.
This means that the basal chill crust (a) never formed, (b) was
eroded away, or (c) is too thin to smooth out the undulations
in the flow base. Clearly, mechanical erosion will also be
confined to relatively large, fast moving lava flows.
The model used in this study is based
on Hallet’s study of glacial erosion [5]. The geometry of the
model is illustrated in Figure 1. We assume the lava flows over
a horizontal saw-toothed shaped substrate, where each tooth is
of length l, and each step rises at an angle to the horizontal
in the direction of flow. At the point at the top of each tooth the
flow will seperate, and a roughly parabolic cavity will form.
The cavity would not be empty, but rather would be filled with
a rotating pool of lava. The length of the cavity measured
along the horizontal is s.
The formation of cavities in viscous flows over steps has
been studied previously, and it has been found that the length of
the cavity grows linearly with the flow Reynolds number [6].
The pressure of the flow in this cavity, Pcav , is on the order of
the hydrostatic pressure at the cavity boundary, Phydro . The
normal stress imparted to the substrate is crucial in finding
how cracks would grow. The average stress at the flow/rock
contact, n is needed here. This can be found by the equation
(for a derivation see the 1996 paper by Hallet [5]):
Figure 1: Illustration of the geometry assumed in our
model.
Qualitative Requirements:
The Model:
n , Pcav = Pe
,
1
,s
1
0
where s0 is simply s=l and Pe is the effective pressure felt at
the flow/rock contact, given by:
Pe = Phydro + u2 sin2 + v2 cos2 where is the density of the lava, u is the horizontal flow
velocity of the lava, and v is the vertical velocity the lava gains
during cascading from the ledge of the previous tooth. The
flow is assumed to be laminar with a velocity profile of:
, 2
u (y) = g
y2
2 sin h
,
where g is the local acceleration due to gravity, is the dynamic
viscosity of the lava, h the height of the lava, and y is the depth
of interest, measured from the top of the flow.
Concentrating on the area near the ledge, and considering
the rock to be a linear elastic material, the stresses in the rock
would be close to those in an infinite elastic quarter-plane [5],
to which Hallet says the tensile stress in the rock would roughly
be:
T 2 (n Pcav ) =3
,
The stress would be most concentrated directly upstream of
the flow/rock contact zone.
The resultant tensile stress was found as a
function of step height and lava viscosity and can be seen in
figures 2 and 3. For the step height, the tooth length, l, was
varied with a constant step slope of =30o . The regional slope
was assumed to be 6 degrees (in other simulations, the regional
slope was found to not play a major role in determining the
stresses due to the slow variation of sin for small ).
As can be seen, for many cases, the maximum exerted
tensile stress is greater than a few million Pascals, and in
some cases, much greater. Because the strength of coherent
crystalline rock is roughly 10-20 MPa [5], we find we are close
to reaching the critical stresses to fracture rock. In addition, if
the bedrock is jointed or has its temperature rise significantly
Results:
Lunar and Planetary Science XXXI
1647.pdf
Mechanical Erosion by Lava: F. J. Ciesla and L. Keszthelyi
due to heat conduction from the lava, the rock will be weaker,
and the exerted tensile stresses will easily exceed the internal
strength of the rock. This would allow the lava to fracture the
bedrock and entrain the fragments in the flow.
Figure 2: Dependence of induced tensile stress with step
height
Figure 3: Dependence of induced tensile stress with lava
viscosity
Implications:
This model has many simplifications
that may affect its applicability to the real world. First, the
saw-tooth basal topography is obviously idealized, but it is
more realistic than a single step. For flows that are exposed
in cross-section, it will be possible to investigate the stresses
on the final, preserved basal topography. Second, the flow is
assumed to be laminar. In the case of the more fluid lavas,
the flow will be turbulent. Using the laminar flow equations
for the turbulent flow leads to significant overestimation of the
flow velocities [7]. However, offseting this is the fact that
flow velocities near the boundaries is much higer in turbulent
flow than in laminar. A more careful analysis of flow in the
turbulent regime is called for. Despite these problems with the
model, we are confident that it shows that, in many realistic
cases, the stresses on an irregular flow base are large enough
to fracture solid rock.
How does this relate to field observations? Kauahikaua et
al. [8] report up to 10 cm/day of erosion at the base of Hawaiian
lava tubes. Pure thermal or thermo-mechanical erosion of
basalt by basaltic flows cannot account for this high erosion
rate. We suggest that mechanical erosion may be the dominant
process to explain this observation.
This model also predicts that massive erosion is possible
at the base of thick flows such as continental flood basalts.
However, there is no field evidence for any erosion in the
Columbia River Basalts [9]. While the bases of most CRB
flows are quite smooth, even 40 m thick flows have not been
able to move 30 cm scale mounds of loose river gravel. We
suggest that this is strong evidence for the slow emplacement of
the CRB flows via inflation. The initial lobes to move over the
ground were probably on on the order of 50 cm thick and were
incapable of mechanical erosion. As the flows inflated, their
basal crusts thickened by cooling, gradually smoothing out the
underlying topographic undulations. The lack of mechanical
erosion in the CRB categorically rules out the possibility of
rapid turbulent emplacement.
The lunar sinuous rilles have been the focus of many studies on thermal erosion. Mechanical erosion should be particularly effective on the Moon because of the low viscosity of
the lavas (see Fig. 3). Where the lavas traversed impact fractured rock or pyroclastic deposits, mechanical erosion should
have been extremely rapid. It is interesting to note that the
sinuous rilles in the Aristarchus region terminate at margins of
pyroclastic deposits.
Finally, mechanical erosion may have implications for the
formation of canali on Venus.
[1] Greeley, R. (1971) Science, 172,
722-725; [2] Hulme, G. (1973) Mod. Geol., 4, 107-117; [3]
Jarvis, R. A. (1995) J. Geoph. Res., 100, 10127-10140;
[4] Williams, D. A. et al. (1998) J. Geoph. Res., 103
27533-27549; [5] Hallet, B. (1996) Ann. of Glaciol., 22,
1-8; [6] Hawken, D.M. et al. (1991) Computers and Fluids,
20, 59-75; [7] Keszthelyi L. and S. Self (1998) J. Geoph.
Res., 103, 27447-27464; [8] Kauahikaua, J. et al. (1998) J.
Geoph. Res., 103, 27303-27323; [9] Greeley R. et al. (1998)
J. Geoph. Res., 103, 27325-27345.
References: