Characterizing the physical properties of gelatin, a classic analog for the brittle elastic crust, insight from numerical modeling
Résumé
Precise characterization of the mechanical properties of gelatin, a classic analog of the elastic crust, is necessary for scaling the mechanical models of the Earth's crust behavior in laboratory experiments. Here we reassess how to accurately calculate the Young modulus (E) of gelatin contained in experimental tanks. By means of dedicated analog experiments and finite element simulations, we estimate the bias introduced by using equations appropriate for a half-space to interpret the subsidence due to a cylindrical surface load applied on the gelatin. In the case of a standard experimental setup with gelatin adhering to the tank wall, we find E is overestimated by at least 5/100 for a box with lateral size smaller than 20 times the cylinder diameter. In addition, we deduce a correction factor to be applied when using an analytical formula. We confirm that measuring the shear velocity leads to accurate estimates for the rigidity of gelatin. We also propose a new method for in situ Young's modulus estimation, relying on the length of air-filled propagating crack. Indeed, for a given injected volume, this length depends only on the density contrast between air and gelatin and on the Young's modulus of the gelatin. The fracture toughness of the gelatin is estimated independently. Direct comparison between fracture toughness and Young's modulus shows that for a given Young's modulus, salted gelatin has a higher fracture toughness than unsalted gelatin.
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