Fracture healing and strength recovery in magmatic liquids

Cycles of fracture and healing in magma are important controls on outgassing time scales and repetitive seismicity at silicic volca-noes. Here, we experimentally drove silicate melts (at 10 9 –10 11 Pa∙s) to tensile failure, measuring the strength during fracture of the oth-erwise liquid material. We then took the same melts with parallel contact surfaces and closed the fracture under compressive stress and recorded the evolution of tensile strength of the interface healed for different times. We provide a semi-empirical model for fracture healing time scales useful for volcanic applications. As the time available for healing is increased, strength nonlinearly recovers toward that of unfractured glass. We parameterized the healing kinetics as a three-stage process: (1) relaxation of the compressive stress, (2) fracture surface–surface wetting, and (3) diffusive removal of the interface. During welding of these surfaces in air, we observed that micropores are trapped along the fracture plane, which may inhibit complete healing and provide a textural record of relict fracture planes in volcanic glasses. We conclude that at magmatic fracture is in crystal-poor it could rapidly seal outgassing pathways over time scales, contributing to cyclic behavior associated with recurring gas-and-ash explosions and outgassing events.


INTRODUCTION
In shallow volcanic conduits, ascending magmas can undergo multiple fracture and healing cycles (Tuffen et al., 2003), producing diagnostic relict fracture textures (Goto, 1999;Tuffen and Dingwell, 2005) thought to contribute to outgassing (e.g., Castro et al., 2012) and minor gas-and-ash venting episodes (e.g., Kendrick et al., 2016), which may generate lowfrequency seismic signals prior to large eruptions (Neuberg et al., 2006). Despite being important for interpreting geophysical and geochemical signals at active silicic volcanoes, the strength recovery of planar fractures has not been constrained, and studies have instead focused on how diffusive exchange of volatiles occurs across the fracture interface (e.g., Yoshimura and Nakamura, 2010). In both volcanic and tectonic settings, trails of microbubbles and microlites in flow bands, or fragments and glass inclusions in tuffisite veins (Tuffen and Dingwell, 2005;Cabrera et al., 2011;Castro et al., 2012;Kolzenburg et al., 2012;Kendrick et al., 2016;Gardner et al., 2017) have been interpreted as relict evidence for fracture healing processes. Magmas are viscoelastic materials that readily fracture when imposed shear stresses result in strain rates that exceed the inverse of the structural relaxation time τ (Dingwell and Webb, 1989).
The relaxation time τ is proportional to the viscosity η and shear modulus at infinite frequency G ∞ by τ = η/G ∞ , where G ∞ may be approximated as 10 10 Pa (Dingwell and Webb, 1989). Unrelaxed elastic behavior leading to failure occurs when strain rates locally exceed 10 -2 /τ (Dingwell and Webb, 1989). This strain-rate limit represents the critical transition to fractured magma, and open-system degassing (e.g., Gonnermann and Manga, 2003;Castro et al., 2012). While this critical time scale for fracturing is well constrained, the interfracture healing time scales have received comparatively less attention (Yoshimura and Nakamura, 2010). Sintering theory has been applied to healing and strength recovery of particulate material, relevant to fracture infill (e.g., Vasseur et al., 2013;Wadsworth et al., 2016), while for planar (particle-free) fractures, the healing and strength-recovery time scales are less well known. Nevertheless, Tuffen et al. (2003) proposed that magmas fracture and heal repetitively as they ascend through the crust. They suggested that healing and strength recovery might occur over times equal to the sum of a viscous period and a diffusive period. Here, we provide a framework for testing this hypothesis and a first quantitative predictive tool for scaling strength recovery in these repetitive fracture-healing processes.

MATERIALS AND METHODS
We performed fracture healing experiments on two standard borosilicate glasses with well-constrained temperature-viscosity relationships: (1) SRM 717a from the National Institute of Standards and Technology (NIST, USA), and (2) Duran ® glass (Schott Duran Glass Solutions [SDGS]) from Schott (GmbH, Germany).
First, we measured the tensile strength σ 0 of each glass by direct tensile tests on dog-bone samples (ISRM, 1978) using a 5969 Instron uniaxial press with a split furnace from Severn Thermal Solutions (UK). Each sample (16 mm diameter and a total length of 160 mm, with 35 mm in the center ground to 8 mm diameter) was loaded into the mechanical grips of the press and heated up at 5 °C min -1 to target temperatures that provided a viscosity of 10 10 Pa•s (560 °C for NIST and 630 °C for SDGS); the sample was thermally equilibrated over a period of 30 min, and direct pull was conducted at an axial strain rate of 10 −1 s −1 (which is greater than 10 −2 /τ), sufficient to ensure dominantly elastic behavior. The uncertainty on all sample temperatures was approximately 3 °C.
Fracture healing experiments were performed in air on samples in which an artificial fracture was cut through the center perpendicular to the long axis and the fracture surfaces were ground flat ( Fig. DR2 in the GSA Data Repository 1 ). We chose to use artificially cut fractures, rather than tensile fractures created in situ, to ensure repeatability of the results using a controlled fracture geometry. The sample pair was then loaded into the mechanical grips of the press, positioned parallel and not in contact (Fig. 1A, inset), heated up to the target temperature (560 °C for NIST and 590 °C, 630 °C, or 645 °C for SDGS), providing sample viscosities between 7 × 10 9 and 1.5 × 10 11 Pa•s (or 0.7 < τ < 15 s), and thermally equilibrated over a period of 30 min. After this time, the upper sample was forced into contact with the lower sample at 0.02 mm s -1 until an initial axial stress of between 1 and 6 MPa was reached, and the sample was held for variable experimental time scales of 0.5 < t < 8000 s. The low stresses used were selected to ensure minimal lateral flow of the sample; the evolving contact area due to flow was monitored through a window in the furnace to correct for bulging and changes in compressive stress (Fig. DR3). After the target time, the rods were pulled apart at a constant extension rate of 3.5 mm s -1 to attain a strain rate of 10 −1 s -1 to ensure a dominantly brittle response and to avoid viscous deformation. Here, the measured peak stress required to fracture the partially healed sample pair was measured and compared to the intact tensile strength of the melt as a measure of healing efficiency.

RESULTS AND A KINETIC MODEL FOR FRACTURE HEALING
Direct tension tests on NIST 717a and SDGS at a viscosity of 10 10 Pa•s constrained the tensile strength σ 0 of these glasses to be 24.99 ± 0.05 MPa and 32.19 ± 0.04 MPa, respectively (Fig. DR4). Fracture healing experiments showed that strength recovery, tracked by σ/σ 0 , is nonlinearly dependent on time (Fig. 1A), where σ is the strength of the partially healed fractured sample. We used a semi-empirical function that has been shown to capture strength recovery as a function of time t in polymers (Wool and O'Connor, 1981) where K (in s -1 ) and α (dimensionless) are constants that we optimized using a least-squares minimization technique. The efficacy of Equation 1 at capturing the data can be seen when σ/σ 0 is plotted against (1 + Kt) α , where the global goodness of fit is r 2 = 0.98 (Fig. 1B). Extrapolating the result from Equation 1 down to a value of σ/σ 0 at the detection limit of the press, we can compute an effective onset time, λ c , for fracture healing, before which the strength recovery is effectively zero. We also used the standard error computed from the residuals between Equation 1 and our data to propagate an error on λ c (see the Data Repository). This error accounts for the mismatch between the data and the model at short times. We interpret λ c to be the time before which the silicate liquid is unrelaxed, such that λ c ∝ τ. We find that, within the uncertainty on the model parameters, the onset time scales with this proportionality as λ c ≈ 10τ (Fig. 1C), providing a useful tool to find the critical time over which a magmatic fracture must be shut before nonzero strength will be achieved by healing. Furthermore, this implies that the applied stress will always be dissipated over times proportional to τ prior to strength recovery, confirming the hypothesis of Tuffen et al. (2003), and implying that the applied axial stress does not have a first-order effect on fracture healing within the range tested here.
To further understand the kinetics of this evolution, we can build a simplified physical picture of the operative mechanisms. During randomwalk diffusion in a silicate network, the length l traveled by an element in the network is l ~(Dt) 1/2 . Wool and O'Connor (1981) demonstrated that initial diffusion is influenced by a "wetting time," during which the rough fracture surfaces establish contact. They provided an example where this wetting of surface area proceeds linearly with time-a so-called "constant rate wetting." Following their model, we propose that the product of the diffusive and wetting times controls this first part of the process, resulting in l ~(Dt) 3/2 for initial-stage codiffusion wetting. At longer times, the surfaces are "fully wet," and there is near-complete surface area contact, meaning that only a single random-walk diffusive process is operative, with the standard result that l ~(Dt) 1/2 . Wool and O'Connor (1981) showed that the strength of a healing system is linearly dependent on the extent to which these diffusion mechanisms have occurred, such that σ/σ 0 ∝ l. We find that this simple theoretical constraint is consistent with our data and that the power-law exponent of the early stage (wetting and diffusion) is 3/2, while the late-stage exponent (diffusive only) is 1/2 (Fig. 2).

IMPLICATIONS FOR SILICIC VOLCANIC ERUPTIONS
Fracture healing may be an important control on the mechanisms of shallow silicic eruptions (e.g., Castro et al., 2012) and flow emplacement (Cabrera et al., 2011). Extensive, connected fracture networks are a primary outgassing pathway in silicic magmas (e.g., Cabrera et al., 2011;Berlo et al., 2013;Castro et al., 2014). Furthermore, fracturing and increased gas release have been argued to be important controls on shifts in eruptive style from explosive to effusive or hybrid explosive-effusive (e.g., Edmonds et al., 2003;Gonnermann and Manga, 2003;Yoshimura and Nakamura, 2010;Cabrera et al., 2011;Castro et al., 2012). As proposed by Cabrera et al. (2011) and Castro et al. (2012, and experimentally shown by Yoshimura and Nakamura (2010), the formation of dense, silicic obsidian might result from fracture-healing cycles. Once healed, the only remaining evidence for the fracture may be trails of isolated pores that trace the remnant fracture surface, which we reproduce here in Figure 3.
Our work has shown that healing is a kinetic process controlled first by structural relaxation and second by wetting and diffusion in silicate melts. The pressure acting on a closing fracture may shorten the total longevity of the initial wetting phase, and it can also impact the solubility of any volatiles trapped along the melt interfaces (cf. Zhang, 1999). As an explicit applied example, we considered the 2008 eruption of Volcán Chaitén (Chile), for which fractures have been shown to play a key role in the outgassing mechanisms (Castro et al., 2012). At the eruptive temperature of 825 °C, Castro and Dingwell (2009) constrained the melt viscosity at storage conditions and the conditions of shallow ascent to be in the range of 10 6 -10 8 Pa•s. Using the model presented herein, this results in a fracture healing onset time scale of 10 -3 ≤ λ c ≤ 10 -1 s. Then, applying the power-law model in Figure 2, we find the time for complete fracture healing is on the order of 10 0 -10 2 s. The key finding here is that this range of time scales is the same as those over which strength recovers toward that of intact glass. Over times much shorter than these healing and strength recovery time scales, the fracture is weak and prone to repeated rupture. Indeed, Figure 3 shows that even after thorough healing, trapped bubbles remain, which may suppress total strength recovery and permanently weaken the relict fracture (even low porosities can weaken silicate melts relative to a nonporous melt of the same composition; Vasseur et al., 2013).
As silicic magmas approach the surface and extrude as domes, they are often highly degassed (Castro et al., 2012), which, using the viscosity model of Hess and Dingwell (1996), results in viscosities that increase to 10 9 Pa•s (see the Data Repository for this calculation). In turn, this increases the fracture healing time scales to 10 3 -10 4 s. This shows that while fractures may rapidly heal during ascent (Gonnermann and Manga, 2003), once silicic magma is degassed, in-dome healing is far less efficient, and so the fractures may remain weak over long time scales and repetitively re-open during dome extrusion. This would imply that opensystem outgassing can be maintained for long periods in the upper conduit and dome. Our model also demonstrates that postemplacement cooling will extend fracture healing time scales significantly. Other examples of eruptions that have produced glassy rhyolites are good candidates for applications of the work presented here (e.g., Tuffen et al., 2003;Tuffen and Dingwell, 2005;Cabrera et al., 2011).
There is abundant textural evidence for healed or partially healed fractures in volcanic rocks produced from silicic eruptions (e.g., Tuffen and Dingwell, 2005;Cabrera et al., 2011). Some examples may be complicated by the presence of particulate material (fragments of magma and/ or country rock) trapped within fracture networks (Tuffen et al., 2003), which may obstruct fracture closure. In these cases, total healing is controlled by sintering of partly crystalline particles  or glass fragments (Vasseur et al., 2013), and it occurs over time scales  (Fig. 1C). Following relaxation of compressive stress, fracture healing is controlled by wetting of interfaces by diffusion, and then by diffusive mass exchange only, which have characteristic slopes of 3/2 and 1/2, respectively. Best-fit power-law equations for these regimes are shown on figure, which were used in the text to calculate total healing time; for example, of 2008 eruption of Volcán Chaitén (Chile). Uncertainties on σ/σ 0 (σ is strength of the partially healed fractured sample; σ 0 is tensile strength) are smaller than data points. proportional to the properties of the fracture fill at eruptive temperatures (Wadsworth et al., 2014) and the pressure acting on the fracture (Ryan et al., 2018), resulting in densification that reduces the system permeability Wadsworth et al., 2016Wadsworth et al., , 2017Ryan et al., 2018). We note that in the other end-member system of particle-free fractures constrained here, the permeability does not decay as slowly as with particle-bearing fractures. Instead, the gas permeability of the fracture can drop rapidly as the planar fracture seals shut, unimpeded by particles, and this healing scales with the strength recovery.
During ascent, viscosity can vary spatially across a conduit (Costa and Macedonio, 2003;Mastin, 2005), thus affecting the occurrence of fracture healing processes. Such variations may lead to variably efficient permeable pathway closure and strength recovery in marginal shear zones, thus affecting outgassing and pressure distribution in volcanic conduits.

CONCLUSIONS
Conducting novel fracture healing experiments on silicate liquids at magmatic viscosities, we demonstrated that healing initiates after a time scale proportional to the relaxation time scale (and therefore viscosity). Beyond this point, healing begins via wetting of the surface, which transitions into a purely diffusional regime. During this process, soluble volatiles may get trapped as a trail of bubbles, which may impact the strength recovery magnitude. The findings suggest that at volcanoes, fracture healing, even when partially complete, may be an efficient process, and we posit that this may contribute to eruptive time scales or cyclicity.