Time-varying stick-slip behaviors described by dehydration kinetics of gypsum

Dehydration embrittlement was proposed to account for intermediate or deep earthquakes (e.g., Raleigh and Paterson, 1965). Many researchers have investigated the frictional instability induced by dehydration of hydrous minerals, such as gypsum (e.g., Milsch and Scholz, 2005; Brantut et al., 2011; Leclère et al., 2016). In addition, time dependence of dehydration of hydrous minerals has been studied based on reaction kinetics (e.g., Sawai et al., 2013). Since kinetics controls the dehydration rate, the effect of dehydration-derived pore fluid pressure on the mechanical strength of rocks can also be represented by kinetics. However, there is no experimental study to quantitatively investigate how pore fluid pressure builds up and controls the mechanical strength of fault gouges in terms of kinetics. Here, we derived time function of pore fluid pressure based on dehydration kinetics of simulated gypsum (bassanite) gouges. First, we conducted friction experiments of simulated gypsum gouges using gas apparatus under eight different conditions of pressures from 10 MPa to 200 MPa and temperatures from room temperature to 180 °C, spanning dehydration condition of gypsum. Each stress-strain curve showed stick-slip behaviors with almost constant stress drops and recurrence intervals depending on the effective pressures under the conditions of room temperature (RT): larger stress drops and longer intervals for higher effective stresses. On the other hand, stress drops and recurrence intervals gradually decrease with time under 200 MPa and 110 °C, close to the dehydration boundary. These results suggested that the elevated pore fluid pressure by dehydration decreases effective pressure and reduces the stress drops and the intervals. We tested this hypothesis as follows. Microstructural observations illuminated marked development of Riedel shears (R1 shear) in samples deformed under the stability field of gypsums (RT and 70 °C), while scarce development of Riedel shears in the sample deformed under 110 °C, being consistent with Leclère et al. (2016)’s observations on that the elevated pore pressure suppress the development of Riedel shears. Based on the equation of state for water (He and Zoller, 1991), we calculated the porosity of the sample deformed under 110 °C. Although the estimated value was smaller than that obtained from dehydration under hydrostatic conditions (Bedford et al., 2017), this result indicates that shear compaction may have occurred due to deformation caused by higher differential stress. Considering that the decrease in effective pressure modulates the amount of stress drops and recurrence intervals, we analyzed frictional coefficients with Mohr’s circle assuming pore fluid pressure. The estimated value of about 0.6 is consistent with Byerlee (1978)’s law. Based on the results, we created a time function for evolution of pore fluid pressure controlled by Avrami-type dehydration kinetics (Avrami, 1940). The estimated Avrami exponent, the important parameter for crystallization, of 3.121 indicated that the dehydration proceeded with nucleation and three-dimensional growth. This function enables more accurate prediction of pore fluid pressure evolution controlled by dehydration kinetics and may contribute to better understanding the effect of hydrous minerals on frequency of intermediate and deep earthquakes.