Abstract
We present a technique to measure the Young’s modulus of a gelatin, using shear waves. Gelatin is a commonly used material for analogue experiments in geophysics, investigating fluid-filled fractures like magmatic dikes, as well as fault slip. Using polarized filters, the deviatoric stresses in a block of gelatin become visible, as do the stress perturbation induced by waves propagating through the medium. We demonstrate how the wave velocity can be measured and related to the Young’s modulus, as well as processing techniques that improve the measurement precision. This methodology is simple to implement into a laboratory setting, can make precise, time-efficient estimates of the material strength and additionally is non-destructive and can be performed in situ.
Highlights
For samples prepared with low concentrations (15◦C), the resulting gelatin more readily deforms in a viscous way, so that if strain is applied for a prolonged period of time, the material is permanently deformed
The time scale associated to the shear wave experiments we describe is very short, so we assume they are dominated by elastic deformation
We present a method of measuring the Young’s modulus of gelatin, using shear wave velocity
Summary
Gelatin is commonly used in experiments as an analog for the Earth’s crust, typically when studying magmatic dike propagation (e.g., Fiske and Jackson, 1972; Takada, 1990; Menand and Tait, 2002; Taisne and Tait, 2009; Kavanagh et al, 2018; Urbani et al, 2018; Derrien and Taisne, 2019; Pansino and Taisne, 2019; Pansino et al, 2019; Sili et al, 2019) or modeling fault slip behaviors (Corbi et al, 2011; Rosenau et al, 2017). At concentrations greater than 3.0 wt%, it can be described by the Maxwell model, so that its elastic and viscous components are in series (van Otterloo and Cruden, 2016). Gelatin has a viscous component that can become prominent under certain circumstance, not usually associated to analog experiments of liquid-filled cracks. The characteristic time over which viscous deformation occurs is quantified by the Maxwell relaxation time, which van Otterloo and Cruden (2016) measure to be on the order of 0.1–1 s. Speaking, such estimates are extremely short, considering that the elastic behavior of gelatin can be observed over a time scale of seconds to tens of minutes. In the context of magma transport experiments, Sumita and Ota (2011) identified characteristic intrusion shapes associated to different types of deformation: liquid-filled cracks are associated to elastic deformation, diapir-like structures to ductile deformation, and dike-diapir
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