In order to explore the thermal conductivity of the natural poly-mineral rock,numerical tests of rock models with randomly-distributed components were conducted and compared with each other.Elaborately designed Monte Carlo method was adopted to ingratiate the requirement of the random characteristics of grain size and the grains'spatial distribution.This requirement was fulfilled by clustering the randomly generated unstructured tetrahedral elements in full three dimensions.Natural rocks are consisted of randomly distributed crystal particles or intergranular minerals.Our primary results verify that the thermal conductivity of the rock is strongly sensitive to the ingredients' volume fraction and their spatial distribution.Furthermore,we proved that,in order to reduce the measurement error to a reasonable range,the numerical specimen must be large enough or include sufficient number of mineral particles.Our numerical test results are in accordance with a variety of empirical formulas which are currently employed in petrology.
The distribution and amount of ground ice on Mars is an important issue to be addressed for the future exploration of the planet.The occurrence of interstitial ice in Martian frozen ground is indicated by landforms,such as fluidized ejecta craters,softened terrain,and fretted channels.How-ever,experimental data on the rheology of ice-rock mixture under Martian physical conditions are sparse,and the amount of ground ice that is required to produce the viscous deformation observed in Martian ice-related landforms is still unknown.In our study,we put forward a three-dimensional non-Newtonian viscous finite element model to investigate the behavior of ice-rock mixtures numeri-cally.The randomly distributed tetrahedral elements are generated in regular domain to represent the natural distribution of ice-rock materials.Numerical simulation results show that when the volume of rock is less than 40%,the rheology of the mixture is dominated by ice,and there is occurrence of a brittle-ductile transition when ice fraction reaches a certain value.Our preliminary results contribute to the knowledge of the determination of the rheology and ice content in Martian ice-rock mixture.The presented model can also be utilized to evaluate the amount of ground ice on Mars.
