Abstract
When partial melting is parametrized in numerical thermo-mechanical models in a straightforward manner, it directly relates to variations in temperature. However, melt extraction is, to our knowledge rarely taken into account in these models, even if melt extraction and escape have a key influence on the mechanical behaviour of the entire system. Here, we propose a first step towards a numerical simulation for melt extraction in partially molten portions of the continental crust. We use a Lagrangian description, considering a discrete mineral distribution at sample scale. A cellular automaton mimics the mobile melt phase moving from cell to cell. An infinite source and sink for the melt and lateral periodic boundaries avoid melt accumulation. Time is represented by a proxy through successive iterations. The major controlling factors are the initial bulk melt percentage and a threshold controlling melt escape. We test pure and simple shear conditions to simulate strain partitioning between the melt and its matrix. The parameters, provided they do not vary, determine a regular or steady state amount of melt extraction after a few iterations. In contrast, for varying parameters during a single run, the quantity of melt extracted at each step presents alternate variations in amplitude (σμ) around an average value. Variations are neither periodic in the sense of a sinusoidal wave, nor of equal amplitude. Melt extraction behaves similar to a stick-slip motion in dry friction. Since we cannot have access to the prediction of melt amount, w test the origin of the sporadic motion. We examine variations of the input parameters (initial melt ϕ, permeability ζ, applied stress σ or τ). The transient effects mark by spikes (Δμ) with two contrasted situations. Return to a steady state is exponential, similar to the discharge of a capacitor. Nevertheless, a first mode occurs when the changes are made on separate runs, reinitializing the parameters between them. These experiments show a linear dependence of the variation in amplitude of σμ with the parameters. Alternatively, when the changes are successive during the same run, then σμ decreases accordingly. The exponential variation is interpreted as a memory effect or hysteretic behaviour of melt extraction. Similarly, the amplitude of the stiction spikes (Δμ) does not show the same behaviour when permeability increases or decreases. By analogy with friction, the change from sticking to slipping is interpreted as a manifestation of pinning and depinning, leading to an avalanche-like phenomena. Mechanically they correspond to a change in friction velocity. Physically, it points to the change in the free energy of the system, with a first derivative akin to velocity and a second derivative akin to acceleration. During melting, the mechanical barriers correspond to the energy variations due to chemical reactions between melt and crystals. Depinning corresponds to enhanced melting whereas pinning links with back reactions leading to garnet growth. The sporadic melt extraction links dry friction to poroelastic flow, or more generally to a consequence of two-phases rheology. Hence the sporadic motion of the weak phase originates from interactions with its matrix. Hence the flow (velocity) suffers modulations due to interactions with chemical potential (back-reaction, melting), entropy (ordering through dislocation creep), and strain (aperture of porous flow). Such interactions should be considered when dealing with quantitative mush (melt+ matrix) modeling (rejuvenation, extrusion).