Wosnitza, E. 2002. Data Analysis in Thermomechanical Analogue Modelling. Schellart, W. P. and Passchier, C. 2002. Analogue modelling of large-scale tectonic processes. Journal of the Virtual Explorer. | ||||||||||||||||||||||||||||||||||||||

Data
Analysis in Thermomechanical Analogue Modelling |
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The equation
governing heat transfer in thermally isotropic materials, without internal
heat production, is
During deformation,
thermal and mechanical velocities must be treated equally. Thus, it must
be ensured that the time needed by material particles or heat to move
over a certain distance is scaled by the same factor. For the scaling
factors of length
can be obtained, where
the scaling factors S The length and time
scales are also coupled by the request for kinematic similarity. All velocities
in the model must be scaled by the same factor
The thermal diffusivity
of rocks is about 10 The scaling of length
is limited by the size of the smallest particles used in the experiments.
The grains of the brittle material used are smaller than 200
and
the model is only
scaled to gravity when
This also implies the scaling factor for stresses to be
The mean densities
of the upper and lower crust are 2800 kg/m The scaling factor
for viscosity can be used to determine the viscosities needed in the analogue
model. For this, the viscosities of natural rocks must be calculated from
published flow parameters and an assumed geothermal gradient. Using a
geotherm of 20°C/km typical for a convergent collisional orogenic
setting (e. g. Decker et al., 1988), a wide range of viscosities can be
found. Basing on parameters from Carter & Tsenn (1987) for "wet"
dunite and a temperature of 720°C at a depth of 35km, a viscosity
of 3.1x10
According to Weijermars
& Schmeling (1986), rheological similarity also demands equality of
the dimensionless stress exponents for natural and analogue materials.
This exponent is between 1.8 and 5.1 for the materials shown in Table
2. For the paraffin waxes used, the measured data is consistent with
or more commonly as
(Means, 1990). This equation does not influence the scaling factors for stress or strain rate, but it requires the exponent
to be dimensionless.
Because of S
Using materials with
lower activation energies such as colophony (Cobbold & Jackson, 1992,
However, following an argument of Cobbold & Jackson (1992, p. 257), only the first two or three orders of magnitude of the overall strength variation are likely to have significant mechanical consequences. Whether the weaker layers are weaker by four or by five or even more orders of magnitude does not influence the stiffness of the overall scenario. Therefore, an attempt to perfectly scale the experiments for temperature is probably unnecessarily rigorous. Nevertheless, "pseudo-temperatures"
may be given for the model. These temperatures can be used in
Here, the thermal
gradient in the laboratory z .
Using the scaling factor for length _{L}S
is converted to a natural "depth"_{L}, z_{L} z. From
the latter, the natural temperature can be reconstructed using _{N}T.
"Depth" in this context is not to be taken literally since it
describes the depth in a scenario with a homogeneous geothermal gradient.
Instead of a simple scaling factor, the proposed work-around provides
the linear relationship_{N}(z_{N})
- Phase transitions
in either material are ignored, although they are essential in the reconstruction
of natural
*PTt*paths. Phase transitions also influence the overall rheology of crustal and mantle materials. - In some cases, unrealistically low temperatures are obtained for the upper crust. This is due to the thermal conductivity of the brittle material which is different from the conductivity of the waxes.
- The incorrect scaling
of temperature does not only obstruct the direct way from
*T*to_{N}*T*. It also causes the flow laws in the laboratory and in nature to be not exactly similar. Thus, only in the stronger parts of the materials does that relationship hold._{L}
Therefore, the temperatures obtained this way should be used with caution. Nevertheless, at the present stage of this work, this is the only way to gain temperature predictions from the analogue experiments.
σ from the
lithostatic pressure _{f}σ_{lith}
The angle of internal friction is dimensionless, therefore it must be equal in the model and in nature. Jet-Plast, the brittle material chosen has an angle of internal friction of (37±2)°. Natural brittle rocks show angles of internal friction of 25° - 35° (e. g. Lallemand et al., 1994). Although the scaling in this case is not perfect, the error bars overlap. Cohesion is a stress, consequently it needs to be scaled with the scaling factor for stresses. According to Hoshino et al. (1972), crustal rocks show cohesions of <20 MPa. In fact, these values were measured for rather small samples (some centimetres height). Due to pre-existing fractures, the bulk cohesion of the upper crust might be lower. Sand has cohesions of 20 -170 Pa (Lallemand et al., 1994). Due to the composition of the Jet-Plast, electrostatic forces can be assumed to lead to a lower cohesion. The upper limit of the natural cohesions scales down to 17 Pa which is well in the plausible range for the model material. |
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