Numerical model
This protocol is extracted from research article:
Tracking time with ricequakes in partially soaked brittle porous media
Sci Adv, Oct 12, 2018; DOI: 10.1126/sciadv.aat6961

The small strain assumption, which implies constant fluid saturation per carriage, can be removed by integrating the model numerically. For that purpose, we started by calculating the equilibrium length of the ith carriage, which follows a biphase value dependent on the Heaviside function H(x) = 1 if x > 0, H(x) = 0 otherwiseEmbedded Image(22)where, at the start of the simulation, Embedded Image. In removing the small strain assumption, we must now recall that, unlike the small strain analytic model before, the effective saturation corresponding to the ith carriage Embedded Image generally varies with time. This is because the position of that carriage Embedded Image varies as a function of carriage lengths l(i), itself varying with time. Specifically, during the simulation, the ith carriage effective degree of saturation and length areEmbedded Image(23)with the initial condition for the lengths given by Embedded Image. The constrained elastic moduli K(i) and the lengths l(i) are updated using a fourth-order Runge-Kutta algorithm, with a time step Δt such as Δtacr/α the characteristic time scale of the system. Simulations are nondimensionalized [with lm the unit length, Δt the unit time, and p*/(lmΔt2) the unit mass], but results are presented with dimensions for easier comparison with experiments.

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