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Effect of grain size and grain size distribution on slip dynamics: An experimental analysis
Journal Pre-proof Effect of grain size and grain size distribution on slip dynamics: An experimental analysis
Jeremy Randolph-Flagg, Jacqueline E. Reber PII:
S0040-1951(19)30403-2
DOI:
https://doi.org/10.1016/j.tecto.2019.228288
Reference:
TECTO 228288
To appear in:
Tectonophysics
Received date:
12 August 2019
Revised date:
24 October 2019
Accepted date:
14 November 2019
Please cite this article as: J. Randolph-Flagg and J.E. Reber, Effect of grain size and grain size distribution on slip dynamics: An experimental analysis, Tectonophysics(2019), https://doi.org/10.1016/j.tecto.2019.228288
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© 2019 Published by Elsevier.
Journal Pre-proof Effect of grain size and grain size distribution on slip dynamics: An experimental analysis
Jeremy Randolph-Flagg1, Jacqueline E. Reber1 1 Department of Geological and Atmospheric Sciences, Iowa State University, Iowa, 50011, USA Corresponding author: Jacqueline Reber ([email protected]) Index Words: Slip dynamics, granular mechanics, rheology and friction of fault zones,
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Keywords: gouge, grain-size-distribution, slip dynamics, analog modeling
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Key Points: Grain size and grain size distribution affect slip dynamics in simple shear. For grains with a diameter < 1/10 of the shear zone width, larger grains lead to larger and faster stick-slip events. The fraction of small grains has no impact on slip dynamics when grains larger than 1/10 of the shear zone width are present. The grain size abundance controls their contribution to the bulk slip behavior of the system.
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Journal Pre-proof Abstract When faults form and slip they produce granular wear material that accommodates most of the strain. We investigate the effect of grain size and grain size distribution on slip dynamics by using sheared elliptical acrylic discs as a fault gouge proxy. Physical experiments on three different grain size assemblages are performed in a spring slider apparatus. Our results indicate that below a grain diameter threshold of 1/10 of the shear zone width, increasing grain size
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corresponds to faster slip velocities during slip events. In experiments with more than one grain
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size, the relative proportions of grain sizes and effective grain sizes control the bulk behavior.
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We show that shear zones with grains that are larger than 1/10 of the shear zone width show
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deformation dynamics that are independent of the small grain fraction. In shear zones where the grain sizes are below this threshold a high abundance of small grains promotes slower and
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smaller slip events.
1 Introduction
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Due to the presence of fault gouge and wear material in most fault zones, deformation of
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granular material has been used as a proxy for slip dynamics of natural faults [e.g., Abe et al., 2006; Abe and Mair, 2009; Hayman et al., 2011; Mair et al., 2002; Morgan and Boettcher, 1999]. Differences in granular characteristics such as grain shape, packing density, and grain size distribution, together with changing mineralogy and pore fluid pressure [Hubbert and Rubey, 1959; Schleicher et al., 2010], have been proposed as potential causes for the variability in slip dynamics of faults [Byerlee and Summers, 1976; Engelder, 1974; Johnson and Jia, 2005]. Similar to movement along faults, shear deformation in granular materials can be accommodated
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Journal Pre-proof by stable slip (constant creep) or via unstable, stick-slip, motion [e.g., Anthony and Marone, 2005; Daniels and Hayman, 2008; Morgan and Boettcher, 1999]. Frictional forces along faults break wall rock into wear material of various sizes ranging from coarse fault breccia to very fine ultracataclasite [Killick, 2003; Sibson, 1977; Woodcock and Mort, 2008]. This fault material accommodates the majority of deformation on the fault. A wide range of experimental studies, mostly using glass beads and quartz sand, as well as numerical
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studies have found that slip dynamics in granular material can vary with grain shape and
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angularity [Abe and Mair, 2009; Anthony and Marone, 2005; Guo and Morgan, 2004; 2006;
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Mair et al., 2002], grain size distribution [Mair et al., 2002; Morgan and Boettcher, 1999] and
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grain evolution through comminution [Guo and Morgan, 2006]. Mair et al. [2002] examined the effect of grain size distribution on the behavior of
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sheared granular materials using a biaxial shear apparatus and spherical glass beads. They
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performed experiments on beads with a narrow range of grain sizes (105 – 149 m) and beads with a wide range of grain sizes (1 – 800 m). The results of these experiments show that the
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narrow grain size range led to unstable stick-slip dynamics, while the wide range resulted in
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stable creep. These experiments are performed using a large number of grains and applying a controlled normal force. In contrast, here we present results from shear experiments where a quasi-two-dimensional granular layer is sheared between two parallel rigid walls in a volume conserving apparatus where we do not control normal forces during deformation. We report on the impact of the grain size in uniform and bimodal distributions on the slip dynamics. While Mair et al. [2002] compared a wide range to a narrow range of grain sizes, we investigate the impact of the relative grain sizes on slip dynamics. We suggest that the proportion of differently sized grains within a bimodal distribution affects the slip dynamics of the system.
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2 Methods We shear elliptical, acrylic discs of three sizes in a volume conserving simple shear machine (Figure 1). The apparatus approximates a two-dimensional plane (90 cm long, 30 cm wide, and 0.4 cm high) where one side is stationary and the other moves, leading to a discrete jump in velocity where the two plates meet [Daniels and Hayman, 2008; Hayman et al., 2011; Reber et
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al., 2014]. The deformation is driven by the moving base plate while the experimental chamber
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is attached to both base-plates and deforms from a rectangle to a parallelogram while preserving
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its volume. The width of the experimental chamber (30 cm) is also referred to as shear zone
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width. The experimental chamber is filled with a single layer of 4 mm thick, elliptical discs. The ellipses are randomly oriented in the experimental chamber. The three grain sizes have an aspect
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ratio of 1.57, and major axes of 4.4 cm (large grains), 2.2 cm (medium grains) and 1.1 cm (small
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grains), respectively. We use elliptical grains rather than circular ones to avoid geometric locking [Delaney et al., 2005]. The grains used in the presented experiments are idealized to isolate the
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impact of the grain size in relation to the shear zone width. All grains are the same shape and
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same aspect ratio to prevent effects from variable roughness or locking. Grains from experimentally produced gouge have an average long axis to short axis ratio of 1.5 while cracked quartz and feldspar show aspect ratios of 2.9 and 2.1 respectively [Heilbronner and Keulen, 2006]. The aspect ratio of grains used in this study, 1.57, is comfortably within the range of realistic values for fault rock. The sliding side of the table is driven by a stepper motor that pulls a spring at a constant velocity of 0.167 mm/s. The spring (k = 75 N/m) is attached to the mobile side of the apparatus and allows the system to respond elastically to frictional interactions of the grains (Figure 1). We
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Journal Pre-proof measure the pulling force with a Chatillon DFS II piezoelectric force gauge and the position of one corner of the sliding side of the table with a Celesco cable extensometer, both at 10 Hz. The extensometer precision is 0.155 cm and the precision of the force gauge is 0.536 N. To reduce the effect of noise, we apply a third order median filter (Figure 2). We deform the experiment to a total shear strain of γ = 0.5.
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The grains show negligible elastic deformation (bulk elastic modulus = 3 GPa) and no
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comminution at the stresses acting in the experiments. Even after multiple experiments we do not
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detect and scratches or polishing effects. Before each experiment, the grains are redistributed by
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hand to ensure no fabric or shape preferred alignment carries over from one experiment to the next. We set and record the global packing density and numbers of grains of each grain size
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before each experiment (Table 1). The void space and proportion of grains of different sizes are
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reported using percentage of the total area. For example, experiments with 50% small and medium grains do not have the same numbers of grains for both sizes, instead both sizes occupy
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the same area of the experimental table. Because of the pseudo two-dimensional nature of the
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experiment we neglect the third dimension when reporting void space. We report global and local void space where the term global void space describes the area of the total experimental chamber that is not occupied by grains. Local void space describes the area of a 12 cm wide band across the experiment (12 x 30 cm, see Figure 1) that is not occupied by grains. This investigation window was chosen to be 12 cm wide so that it is as far away from the corners of the apparatus as possible and at the same time is at least three grain diameters wide.
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Journal Pre-proof In a first experimental series, we perform experiments with homogeneous grain sizes (all small, all medium, or all large). In a second series, we mix grains and use three variations (25%75%, 50%-50%, and 75%-25%) for combinations of small and medium, and medium and large grains. To account for variability between individual experiments we run each experiment ~10 times. To ensure that the recorded signal is indeed resulting from the grain interaction we record
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the force and displacement curves of the empty apparatus. Experiments with no grains display no
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slip events, the displacement and velocity curves are linear and smooth (Figure 3 a). Physically, a
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slip event is a rapid reorganization of grains that accommodates net displacement. We define slip
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events using minimum peak prominence in the velocity curves where the minimum height of a local maxima above the nearest minima is larger than 0.05 cm/s. We observe a common slip
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duration of 0.4-0.5 s (Figure 2e, inset). We use the term creep to describe sliding whenever the
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velocity peaks are absent and the signal is similar to the signal of the experiment without grains. This means that indiscernibly small stick-slip events may be categorized as creep. To compile
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the data, we wrote a Matlab code that identifies slip events and records the peak velocity and the
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timestamp of each event (Figure 3).
3 Effect of packing density and evolution of void space In the first experimental series, we shear each grain size separately with percent global void space held constant. At a global void space of 13.0% of the total experiment area, large grains show a stick-slip signal (Figure 2 and Figure 3 d). At the same packing density, medium sized grains show very few, small slip events and small grains display no slip events at all (Figure 2). Medium and small grain experiments with a global void space of 13% are not packed
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Journal Pre-proof tightly enough to resists shear stresses and therefore do not exhibit stick-slip motion when sheared [Hayman et al., 2011; Onoda and Liniger, 1990]. This can be explained by the fact that smaller elliptical grains pack into the rectangular experimental chamber more efficiently than larger grains because smaller grains pack more tightly along the edges and corners of the rectangle [Galiev and Lisafina, 2013]. To be able to investigate the impact of the grain size on slip dynamics with a minimal contribution of the effects of the packing efficiency we pack
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experiments with smaller grains more tightly than experiments with larger grains. This, however,
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also means that we are not able to treat global void space as a constant in the experiments. With a
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global void space percentage of 13 for the experiments with large grains, 11.8 for experiments
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with medium grains, and 9.9 for experiments with small grains all systems show stick-slip behavior and the experiments reach a similar total strain before individual grains start escaping
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out of plane (Figure 3). Figure 4 shows the local void space distribution for three representative
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experiments of all small, medium, and large grains early in the experiments (shear strain γ = 0.2) and at a later stage (γ = 0.5). We analyze the distribution of void space along a 12 cm wide band
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between the rigid walls. We observe a larger local void space compared to the global void space
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in all experiments at both shear strains. In the experiments with only small grains the global void space is 9.9%. At a shear strain of 0.2 the measured local void space is 17.5% and at γ = 0.5 it is 15.7%. For the medium grain size experiment the void space increases from the global value of 11.8% to 15.7% at γ = 0.2 and 16.7% at γ = 0.5. Only a small change in void space can be seen for the large grain experiment where the local void space increase to 13.1% from the global value of 13% at γ = 0.2. At a shear strain of 0.5 the local void space is 14.0%. Because we keep the global void space constant throughout each experiment the change in local void space implies that grains are compacted outside of the 12 cm wide observation window. We do not observe an
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Journal Pre-proof alignment of the grains parallel to the velocity discontinuity imposed by the apparatus in any of the experiments but we do observe the tendency of a slightly larger local void space close to the shear plane at higher shear strains (Figure 4). Besides this change in the local void space we observe an additional heterogeneity in the packing density in our experiments due to the geometry of the experimental box. All the corners of the box change their angles during shear deformation. This leads to a denser packing in two corners and to a less dense packing in the
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other two corners.
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4 Effect of grain size
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In all experiments where we observe a stick-slip signal grain size impacts the onset, frequency, and velocity of slip events. We do not see any stick slip events during the first
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approximately 250 seconds of all the experiments. During this time the system is strengthening
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and builds a force chain network that is able to support shear forces [Daniels and Hayman, 2008]. The top row in Figure 5 shows cumulative slip velocities for experiments with small grains,
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medium grains, and large grains. We record the fastest slip speed for large grain experiments at
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0.97 cm/s, the fastest slip event for medium grained experiments at 0.95 cm/s, while for the smallest grain size it is 0.50 cm/s (Table 1). Slip events in experiments with small grain sizes are significantly slower and start later when compared to slip events in medium and large grain size experiments. There is no significant difference in slip velocities between experiments with medium and large grains. Slip events, however, appear sooner (< 300 s) for experiments with medium grains compared to experiments with large grains (> 300 s). In our experiments small grains have a long grain axis to shear box width ratio of 1/27.3, while medium grains have a ratio
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Journal Pre-proof of 1/13.6, and large grains have a ratio of 1/6.8 (Figure 5 c). All median and standard deviations are listed in table 1. Experiments containing a mixture of small and medium grains are conducted at a global void space of 9.75% (Figure 5 d, e, f). The first slip events occur between 250 and 350 seconds for all combinations of small and medium grains. Experiments with a higher percentage small grains show a higher abundance of slow slip velocities and a smaller maximum slip velocity.
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With a decrease in small grains the measured peak velocity increases and the abundance of slow
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slip velocities decreases. To calculate the average grain size to shear zone width (width of the
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experimental chamber) ratio we use the total number of grains used in each experiment (Table 1).
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This ratio is 0.039 for experiments with 75% small grains, 0.044 for 50% small grains, and 0.052 for 25% small grains (Figure 5 f).
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Experiments with a mixture of medium and large grains were conducted with a global
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void space of 11.8%. While experiments containing 75% medium sized grains show a higher percentage of slow slip velocities, the three different grain size distributions are otherwise very
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similar to each other. The first slip events occur between 250 and 280 seconds for all three grain
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size combinations. We do not detect a significant change in maximum speed between the different grain size distributions. The average grain size to shear zone width ratio is 0.078 for 75% medium grains, 0.088 for 50% medium grains, and 0.11 for 25% medium grains (Figure 5 i). 5 Discussion The experiments presented here belong to the category of spring slider experiments, which have been used before to investigate granular behavior [Daniels and Hayman, 2008; Hayman et al., 2011; Krim et al., 2011; Nasuno et al., 1998; Reber et al., 2014]. The
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Journal Pre-proof experimental setup is inspired by the simplified geometry of a fault gouge deforming between two parallel and rigid (non-dilatational) walls. Previous studies have shown that angular grains promote stable creep with a high shear resistance, while spherical grains under the same conditions lead to stick-slip and have a lower shear strength [Abe and Mair, 2009; Anthony and Marone, 2005; Mair et al., 2002]. The effect of grains breaking seems to be largely related to angularity; rounded grains become more angular through comminution and therefore the bulk
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behavior strengthens, while angular grains become more rounded and the bulk behavior weakens
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[Abe and Mair, 2009; Guo and Morgan, 2006]. Although breaking of wall rock and grain
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comminution are also widely observed and documented processes in natural fault zones [e.g.,
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Cashman and Cashman, 2000; Rawling and Goodwin, 2003] we do not take these effects into account in our experiments at this stage. We furthermore investigate the impact of grain sizes
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and distribution on slip dynamics in a two-dimensional setting. The two-dimensional nature of
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the experiments allows for direct observation of the evolution of the system through time, but may promote stick-slip and reduce frictional strength relative to an otherwise identical three-
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dimensional system [Hazzard and Mair, 2003]. Due to the volume conserving boundary
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condition the presented experiments are not able to reach steady state. Daniels and Hayman [2008] have conducted experiments on a similar apparatus where they tested the effect of constant volume and dilatational boundary conditions on the force evolution. They have found that in both systems the force slightly increases over time and neither could reach steady state. In experiments with a dilatational boundary condition this increase was, however, slower. Hayman et al. [2011] argue that the strengthening resulting from the constant volume boundary condition could be compared to the interslip strengthening periods on a natural fault that exhibits stick-slip deformation.
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In our experiments we observe that the local void space is heterogeneous and differs from the global average. The dilation of tightly packed granular systems under shear is a welldocumented phenomenon [e.g., Taylor 1956]. We observe local dilation near the slip plane in our constant area experiments. This dilation must be accommodated by local compaction elsewhere in the system. While we do not directly observe this compaction, it is a necessary inference.
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Variations across the experimental box perpendicular to the shear direction can be explained by
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the effect of higher packing order along boundaries of the experimental box (Figure 4). Particles tend to form layers along the walls of the box, which leads to greater order and a larger void
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space percentage [Desmond and Weeks, 2009]. The effect of increased order along the
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boundaries of the experimental frame is however only prominent to a distance of approximately
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one grain diameter from the wall. Its impact is largest for experiments with large grains. Desmond and Weeks [2009] suggest that this effect will be especially notable in experiments
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with less than 10 particle diameters across. In all our experiments we are unable to treat void
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space as a constant. While we are able to keep the global void space constant in experiments with mixed grain sizes, we cannot completely isolate its effect from the effect of the grain size
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distribution on slip dynamics. Furthermore, the global void space in our experiments does not change during deformation. This is at odds with many observations from nature where the porosity changes due to grain comminution [e.g., Kaproth et al., 2010]. The global void space in the experiments is small compared to, for example, undeformed and unlithified sand (27-28%) [Cashman and Cashman, 2000]. The global void space in the experiments is, however, comparable to the porosity in deformation bands and shear zones in unlithified sand (7-10% void space) [Cashman and Cashman, 2000] and deformation bands in sandstones (0-10% void space) [Antonellini et al., 1994].. Antonellini et al. (1994) documented that in deformation bands with 11
Journal Pre-proof little to no volume change the porosity is equivalent in the deformation band and the surrounding material and overall of the same order of magnitude as in our experiments.
During slip events grains rearrange and move past each other. This motion takes place via rearrangement of force chains, slipping of grains next to each other and some minor rotation of grains. Since reorganization of the grains is accommodated by grains sliding and rotating, the
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grain size has an impact on how the granular material deforms [Vangla and Latha, 2015].
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Dilation and movement of grains past each other has been described using the conceptual model
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of two saw-blades in contact. If the saw-teeth initially interlock they will push apart to
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accommodate shear [Bolton, 1986; Rowe, 1962]. Larger grains behave like larger saw-teeth. They can remain locked for longer, and when the pulling force becomes large enough to induce
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motion there is more displacement to make up in the slip event. Since reorganization of the
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grains is accommodated by grains sliding and rotating, larger grains will allow for larger and faster displacements when they slide or rotate. We observe faster slip velocities with an increase
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in grain size when comparing experiments with only small grains to experiments with only
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medium grains (Figure 5 c). Experiments with a mixture of small and medium sized grains also show that an increase in the abundance of medium sized grains leads to faster slip velocities. This trend, however, breaks down for experiments containing large grains with a shear zone width to grain diameter ratio of > 0.1 (Figure 6).
Soil engineering practice mandates that in direct shear experiments the largest grains should not be greater than 1/10 the height of the shear apparatus [Head, 1989] to obtain results that are independent of the boundaries of the testing apparatus. This is of the same order as the
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Journal Pre-proof expected shear band width in granular systems, which is between 6 and 10 grain diameters wide [Francois et al., 2002]. When the grain sizes in the experiment are below this threshold we observe an increase in the slip velocities with an increase in grain size. In experiments that contain grains with a diameter larger than 1/10 of the shear zone width (large grains) this trend is interrupted and slip velocities are smaller (Figure 6). Our results show that even though the average grain size is below the threshold of 1/10 of the shear zone width the deformation
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dynamics changes as soon as grains are present that have an aspect ratio that is larger than 1/10
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of the shear zone width.
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The grain sizes for the experiments were chosen deliberately on both sides of the 1/10 ratio. Natural fault zones are thought to develop a fractal grain size distribution at high strains
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because the probability of grain fracturing depends on the relative size of the grains nearest
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neighbors [Sammis et al., 1987]. Exhumed sections of faults however can show different grain size distributions even when samples are taken at nearby spots along the same fault [Anderson et
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al., 1983]. This indicates that while all fault rock may evolve towards a fractal distribution,
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diverse grain size distributions are common. Field observations show that in natural fault zones grains can temporarily exist that are larger than 1/10 of the shear zone width [Billi, 2005]. While these grains eventually will reduce their size due to comminution they may temporarily affect the slip dynamics of the fault.
Mair et al. [2002] found that experiments with a wide grain size distribution (1 – 800 m) show creep-like dynamics, while a narrow grain size distribution (105 – 149 m) exhibited stickslip behavior. Our findings here indicate that the impact of grain size distribution on granular
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Journal Pre-proof behavior is not only determined by the range in size, but also by the relative abundance of each grain size in the bulk granular material and the grain size to shear zone width ratios. Experiments with an identical range of grain sizes can show differences in slip frequency and velocity depending on the relative abundance of the two grain sizes (e.g., Figure 5 d, e, f).
6 Conclusions
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Displacement, force, and local void space are measured during shear experiments of
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granular systems. We use grains of three sizes to investigate the impact of the grain size to shear
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zone width ratio and grain size distribution on slip dynamics. We observe an increase in local
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void space in the center of the experiment when compared to the global void space. We do not however observe a significant increase of the local void space close to the velocity jump in the
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shear apparatus. The experiments show that below a grain size to shear zone width ratio of 1/10,
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an increase in grain size corresponds to an increase in slip velocities where the proportion of grains of each size controls the bulk behavior. Experiments containing grains with a diameter
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larger than 1/10 of the shear zone width show a decrease in slip velocity even when the average
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grain size diameter increases. This indicates that the presence of large grains has an impact on the deformation dynamics because of their interaction with the boundaries. We show that not only the range of grain sizes but also the relative proportion is relevant for the slip behavior. We propose that shear zones containing grains larger than 1/10 of the shear zone width show deformation dynamics that are independent of the fraction of smaller grains. In shear zones where all grains are smaller than 1/10 of the shear zone width a high abundance of smaller grains promotes smaller slip events.
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Journal Pre-proof Acknowledgements This work has partially been funded by a GSA Graduate Student Research Grant and by a UMass Geosciences Analog Modeling Workshop grant. We would like to thank Karen Daniels for hosting JRF in her lab and sharing insights on experimental materials and techniques. The thoughtful comments of Christoph von Hagke and an anonymous reviewer have improved this manuscript significantly. We acknowledge comments from Susan Cashman, Karen Daniels, and
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Ake Fagereng on an earlier version of this manuscript. The raw data and videos of the
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experiments can be accessed via the Iowa State University data repository
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(https://iastate.figshare.com/account/projects/59969/articles/10022984).
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Rawling, G. C., and L. B. Goodwin (2003), Cataclasis and particulate flow in faulted, poorly lithified sediments, Journal of Structural Geology, 25(3), 317-331.
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Reber, J. E., N. W. Hayman, and L. L. Lavier (2014), Stick-slip and creep behavior in lubricated granular material: insights into the brittle-ductile transition, Geophysical Research Letters, 41, 3471-3477. Rowe, P. W., 1962, The stress-dilatancy relation for static equilibrium of an assembly of particles in contact: Proc. R. Soc. Lond. A, v. 269, no. 1339, p. 500-527. Sammis, C., G. King, and R. Biegel (1987), The kinematics of gouge deformation Pure and Applied Geophysics, 125(5), 777-812. Schleicher, A. M., B. A. van der Pluijm, and L. N. Warr (2010), Nanocoatings of clay and creep of the San Andreas fault at Parkfield, California, Geology, 38(7), 667-670. Sibson, R. H. (1977), Kinetic shear resistance, fluid prssure and radiation efficiency during seismic faulting Pure and Applied Geophysics, 115(1-2), 387-400. 17
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Taylor, D. W. (1956). Fundamentals of Soil Mechanics: Griffin Vangla, P., and G. M. Latha (2015), Influence of Particle Size on the Friction and Interfacial Shear Strength of Sands of Similar Morphology, International Journal of Geosynthetics and Ground Engineering, 1(1), 6.
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Woodcock, N. H., and K. Mort (2008), Classification of fault breccias and related fault rocks, Geological Magazine, 145(3), 435-440.
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Figure captions
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Figure 1: Top row: Schematic top down view of the shear apparatus during loading phase, slip event, and subsequent loading phase. d(t) measures the displacement and F(t) the force over time (after Reber et al., 2014). Blue shaded rectangle shows 12 cm x 30 cm investigation window for local void space calculations. Bottom row: Measured displacement and velocity curves versus time. Shaded box indicates approximate duration of individual events.
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Figure 2: Force and displacement curves (a, c, & e), and velocity curves (b, d & f) for experiments run at 13.0% global void space with all small grains (a & b), all medium grains (c & d), and all large grains (e & f). Filtered force, displacement and velocity data are shown in red, green, and blue respectively. Raw force and displacement data are shown in gray underlying the filtered data. Inset: raw data of one slip event.
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Figure 3: Displacement and velocity versus time for representative experiments with no grains (a), small grains (b), medium grains (c) and large grains (d). Black circles indicate identified and recorded slip events. Figure 4: Local void space histograms plotted for a 12 cm wide band at a shear strain of 0.2 (left column) and a shear strain of 0.5 (right column). Experiment with small grains, top, medium grains, middle, and large grains, bottom. Black indicates area occupied by grains, white shows void space. Red dashed line indicates velocity discontinuity of the experimental table, small black arrows represent the shear direction.
Figure 5: Cumulative slip events for uniform grain size experiments (a, b, c), mixtures of small and medium grains (d, e, f), and mixtures of medium and large grain sizes (g, h, i). a, d, g) histograms of slip event velocity, bin size is 0.1 cm/s. b, e, h) slip event velocity versus time of event. c, f, i) slip event velocity versus ratio of grain size to shear zone width. Black dashed line indicates threshold of grain size to shear zone width of 0.1. 18
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Figure 6: Slip event velocity versus ratio of grain size to shear zone width. Black dashed line indicates threshold of grain size to shear zone width of 0.1. Gray shaded area indicates experiments containing large grains.
Table 1: Experimental parameters for different initial conditions. # of experiments
Global void space (%)
Max. slip velocity (cm/s)
Mean slip velcity (cm/s)
Standard deviation
Average # of slip events per experiment
Max grain diameter/ shear zone width
Total # of grains
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9.9
0.496
0.1338
0.0919
10.6
1/27.3
~4500
M
10
11.8
0.949
0.208
0.1626
28.3
1/13.6
~1100
L
9
13
0.97
0.1953
22.8
1/6.8
75%S 25%M
11
9.75
0.378
0.1077
0.0709
8.4
1/25.4
50%S 50%M
11
9.75
0.44
0.0961
18.1
1/22.7
25%S 27%M
10
9.75
0.1814
0.1224
18.6
1/19.1
75%M 25%L
7
11.8
0.606
0.1162
0.0776
15.6
1/12.7
50%M 50%L
7
0.443
0.1421
0.1008
20.8
1/11.4
~270 ~3400 S 280 M ~2250 S ~560 M ~1130 S ~840 M ~820 M 68 L ~550 M 205 L
0.795
0.136
0.1017
18.2
1/9.49
270 M 205 L
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11.8
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25%M 75%L
0.62
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S
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Journal Pre-proof Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
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Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Jeremy Randolph-Flagg, Jacqueline E. Reber PII:
S0040-1951(19)30403-2
DOI:
https://doi.org/10.1016/j.tecto.2019.228288
Reference:
TECTO 228288
To appear in:
Tectonophysics
Received date:
12 August 2019
Revised date:
24 October 2019
Accepted date:
14 November 2019
Please cite this article as: J. Randolph-Flagg and J.E. Reber, Effect of grain size and grain size distribution on slip dynamics: An experimental analysis, Tectonophysics(2019), https://doi.org/10.1016/j.tecto.2019.228288
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© 2019 Published by Elsevier.
Journal Pre-proof Effect of grain size and grain size distribution on slip dynamics: An experimental analysis
Jeremy Randolph-Flagg1, Jacqueline E. Reber1 1 Department of Geological and Atmospheric Sciences, Iowa State University, Iowa, 50011, USA Corresponding author: Jacqueline Reber ([email protected]) Index Words: Slip dynamics, granular mechanics, rheology and friction of fault zones,
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Keywords: gouge, grain-size-distribution, slip dynamics, analog modeling
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Key Points: Grain size and grain size distribution affect slip dynamics in simple shear. For grains with a diameter < 1/10 of the shear zone width, larger grains lead to larger and faster stick-slip events. The fraction of small grains has no impact on slip dynamics when grains larger than 1/10 of the shear zone width are present. The grain size abundance controls their contribution to the bulk slip behavior of the system.
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Journal Pre-proof Abstract When faults form and slip they produce granular wear material that accommodates most of the strain. We investigate the effect of grain size and grain size distribution on slip dynamics by using sheared elliptical acrylic discs as a fault gouge proxy. Physical experiments on three different grain size assemblages are performed in a spring slider apparatus. Our results indicate that below a grain diameter threshold of 1/10 of the shear zone width, increasing grain size
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corresponds to faster slip velocities during slip events. In experiments with more than one grain
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size, the relative proportions of grain sizes and effective grain sizes control the bulk behavior.
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We show that shear zones with grains that are larger than 1/10 of the shear zone width show
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deformation dynamics that are independent of the small grain fraction. In shear zones where the grain sizes are below this threshold a high abundance of small grains promotes slower and
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smaller slip events.
1 Introduction
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Due to the presence of fault gouge and wear material in most fault zones, deformation of
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granular material has been used as a proxy for slip dynamics of natural faults [e.g., Abe et al., 2006; Abe and Mair, 2009; Hayman et al., 2011; Mair et al., 2002; Morgan and Boettcher, 1999]. Differences in granular characteristics such as grain shape, packing density, and grain size distribution, together with changing mineralogy and pore fluid pressure [Hubbert and Rubey, 1959; Schleicher et al., 2010], have been proposed as potential causes for the variability in slip dynamics of faults [Byerlee and Summers, 1976; Engelder, 1974; Johnson and Jia, 2005]. Similar to movement along faults, shear deformation in granular materials can be accommodated
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Journal Pre-proof by stable slip (constant creep) or via unstable, stick-slip, motion [e.g., Anthony and Marone, 2005; Daniels and Hayman, 2008; Morgan and Boettcher, 1999]. Frictional forces along faults break wall rock into wear material of various sizes ranging from coarse fault breccia to very fine ultracataclasite [Killick, 2003; Sibson, 1977; Woodcock and Mort, 2008]. This fault material accommodates the majority of deformation on the fault. A wide range of experimental studies, mostly using glass beads and quartz sand, as well as numerical
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studies have found that slip dynamics in granular material can vary with grain shape and
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angularity [Abe and Mair, 2009; Anthony and Marone, 2005; Guo and Morgan, 2004; 2006;
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Mair et al., 2002], grain size distribution [Mair et al., 2002; Morgan and Boettcher, 1999] and
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grain evolution through comminution [Guo and Morgan, 2006]. Mair et al. [2002] examined the effect of grain size distribution on the behavior of
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sheared granular materials using a biaxial shear apparatus and spherical glass beads. They
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performed experiments on beads with a narrow range of grain sizes (105 – 149 m) and beads with a wide range of grain sizes (1 – 800 m). The results of these experiments show that the
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narrow grain size range led to unstable stick-slip dynamics, while the wide range resulted in
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stable creep. These experiments are performed using a large number of grains and applying a controlled normal force. In contrast, here we present results from shear experiments where a quasi-two-dimensional granular layer is sheared between two parallel rigid walls in a volume conserving apparatus where we do not control normal forces during deformation. We report on the impact of the grain size in uniform and bimodal distributions on the slip dynamics. While Mair et al. [2002] compared a wide range to a narrow range of grain sizes, we investigate the impact of the relative grain sizes on slip dynamics. We suggest that the proportion of differently sized grains within a bimodal distribution affects the slip dynamics of the system.
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2 Methods We shear elliptical, acrylic discs of three sizes in a volume conserving simple shear machine (Figure 1). The apparatus approximates a two-dimensional plane (90 cm long, 30 cm wide, and 0.4 cm high) where one side is stationary and the other moves, leading to a discrete jump in velocity where the two plates meet [Daniels and Hayman, 2008; Hayman et al., 2011; Reber et
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al., 2014]. The deformation is driven by the moving base plate while the experimental chamber
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is attached to both base-plates and deforms from a rectangle to a parallelogram while preserving
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its volume. The width of the experimental chamber (30 cm) is also referred to as shear zone
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width. The experimental chamber is filled with a single layer of 4 mm thick, elliptical discs. The ellipses are randomly oriented in the experimental chamber. The three grain sizes have an aspect
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ratio of 1.57, and major axes of 4.4 cm (large grains), 2.2 cm (medium grains) and 1.1 cm (small
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grains), respectively. We use elliptical grains rather than circular ones to avoid geometric locking [Delaney et al., 2005]. The grains used in the presented experiments are idealized to isolate the
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impact of the grain size in relation to the shear zone width. All grains are the same shape and
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same aspect ratio to prevent effects from variable roughness or locking. Grains from experimentally produced gouge have an average long axis to short axis ratio of 1.5 while cracked quartz and feldspar show aspect ratios of 2.9 and 2.1 respectively [Heilbronner and Keulen, 2006]. The aspect ratio of grains used in this study, 1.57, is comfortably within the range of realistic values for fault rock. The sliding side of the table is driven by a stepper motor that pulls a spring at a constant velocity of 0.167 mm/s. The spring (k = 75 N/m) is attached to the mobile side of the apparatus and allows the system to respond elastically to frictional interactions of the grains (Figure 1). We
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Journal Pre-proof measure the pulling force with a Chatillon DFS II piezoelectric force gauge and the position of one corner of the sliding side of the table with a Celesco cable extensometer, both at 10 Hz. The extensometer precision is 0.155 cm and the precision of the force gauge is 0.536 N. To reduce the effect of noise, we apply a third order median filter (Figure 2). We deform the experiment to a total shear strain of γ = 0.5.
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The grains show negligible elastic deformation (bulk elastic modulus = 3 GPa) and no
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comminution at the stresses acting in the experiments. Even after multiple experiments we do not
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detect and scratches or polishing effects. Before each experiment, the grains are redistributed by
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hand to ensure no fabric or shape preferred alignment carries over from one experiment to the next. We set and record the global packing density and numbers of grains of each grain size
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before each experiment (Table 1). The void space and proportion of grains of different sizes are
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reported using percentage of the total area. For example, experiments with 50% small and medium grains do not have the same numbers of grains for both sizes, instead both sizes occupy
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the same area of the experimental table. Because of the pseudo two-dimensional nature of the
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experiment we neglect the third dimension when reporting void space. We report global and local void space where the term global void space describes the area of the total experimental chamber that is not occupied by grains. Local void space describes the area of a 12 cm wide band across the experiment (12 x 30 cm, see Figure 1) that is not occupied by grains. This investigation window was chosen to be 12 cm wide so that it is as far away from the corners of the apparatus as possible and at the same time is at least three grain diameters wide.
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Journal Pre-proof In a first experimental series, we perform experiments with homogeneous grain sizes (all small, all medium, or all large). In a second series, we mix grains and use three variations (25%75%, 50%-50%, and 75%-25%) for combinations of small and medium, and medium and large grains. To account for variability between individual experiments we run each experiment ~10 times. To ensure that the recorded signal is indeed resulting from the grain interaction we record
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the force and displacement curves of the empty apparatus. Experiments with no grains display no
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slip events, the displacement and velocity curves are linear and smooth (Figure 3 a). Physically, a
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slip event is a rapid reorganization of grains that accommodates net displacement. We define slip
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events using minimum peak prominence in the velocity curves where the minimum height of a local maxima above the nearest minima is larger than 0.05 cm/s. We observe a common slip
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duration of 0.4-0.5 s (Figure 2e, inset). We use the term creep to describe sliding whenever the
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velocity peaks are absent and the signal is similar to the signal of the experiment without grains. This means that indiscernibly small stick-slip events may be categorized as creep. To compile
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the data, we wrote a Matlab code that identifies slip events and records the peak velocity and the
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timestamp of each event (Figure 3).
3 Effect of packing density and evolution of void space In the first experimental series, we shear each grain size separately with percent global void space held constant. At a global void space of 13.0% of the total experiment area, large grains show a stick-slip signal (Figure 2 and Figure 3 d). At the same packing density, medium sized grains show very few, small slip events and small grains display no slip events at all (Figure 2). Medium and small grain experiments with a global void space of 13% are not packed
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Journal Pre-proof tightly enough to resists shear stresses and therefore do not exhibit stick-slip motion when sheared [Hayman et al., 2011; Onoda and Liniger, 1990]. This can be explained by the fact that smaller elliptical grains pack into the rectangular experimental chamber more efficiently than larger grains because smaller grains pack more tightly along the edges and corners of the rectangle [Galiev and Lisafina, 2013]. To be able to investigate the impact of the grain size on slip dynamics with a minimal contribution of the effects of the packing efficiency we pack
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experiments with smaller grains more tightly than experiments with larger grains. This, however,
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also means that we are not able to treat global void space as a constant in the experiments. With a
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global void space percentage of 13 for the experiments with large grains, 11.8 for experiments
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with medium grains, and 9.9 for experiments with small grains all systems show stick-slip behavior and the experiments reach a similar total strain before individual grains start escaping
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out of plane (Figure 3). Figure 4 shows the local void space distribution for three representative
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experiments of all small, medium, and large grains early in the experiments (shear strain γ = 0.2) and at a later stage (γ = 0.5). We analyze the distribution of void space along a 12 cm wide band
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between the rigid walls. We observe a larger local void space compared to the global void space
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in all experiments at both shear strains. In the experiments with only small grains the global void space is 9.9%. At a shear strain of 0.2 the measured local void space is 17.5% and at γ = 0.5 it is 15.7%. For the medium grain size experiment the void space increases from the global value of 11.8% to 15.7% at γ = 0.2 and 16.7% at γ = 0.5. Only a small change in void space can be seen for the large grain experiment where the local void space increase to 13.1% from the global value of 13% at γ = 0.2. At a shear strain of 0.5 the local void space is 14.0%. Because we keep the global void space constant throughout each experiment the change in local void space implies that grains are compacted outside of the 12 cm wide observation window. We do not observe an
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Journal Pre-proof alignment of the grains parallel to the velocity discontinuity imposed by the apparatus in any of the experiments but we do observe the tendency of a slightly larger local void space close to the shear plane at higher shear strains (Figure 4). Besides this change in the local void space we observe an additional heterogeneity in the packing density in our experiments due to the geometry of the experimental box. All the corners of the box change their angles during shear deformation. This leads to a denser packing in two corners and to a less dense packing in the
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other two corners.
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4 Effect of grain size
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In all experiments where we observe a stick-slip signal grain size impacts the onset, frequency, and velocity of slip events. We do not see any stick slip events during the first
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approximately 250 seconds of all the experiments. During this time the system is strengthening
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and builds a force chain network that is able to support shear forces [Daniels and Hayman, 2008]. The top row in Figure 5 shows cumulative slip velocities for experiments with small grains,
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medium grains, and large grains. We record the fastest slip speed for large grain experiments at
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0.97 cm/s, the fastest slip event for medium grained experiments at 0.95 cm/s, while for the smallest grain size it is 0.50 cm/s (Table 1). Slip events in experiments with small grain sizes are significantly slower and start later when compared to slip events in medium and large grain size experiments. There is no significant difference in slip velocities between experiments with medium and large grains. Slip events, however, appear sooner (< 300 s) for experiments with medium grains compared to experiments with large grains (> 300 s). In our experiments small grains have a long grain axis to shear box width ratio of 1/27.3, while medium grains have a ratio
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Journal Pre-proof of 1/13.6, and large grains have a ratio of 1/6.8 (Figure 5 c). All median and standard deviations are listed in table 1. Experiments containing a mixture of small and medium grains are conducted at a global void space of 9.75% (Figure 5 d, e, f). The first slip events occur between 250 and 350 seconds for all combinations of small and medium grains. Experiments with a higher percentage small grains show a higher abundance of slow slip velocities and a smaller maximum slip velocity.
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With a decrease in small grains the measured peak velocity increases and the abundance of slow
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slip velocities decreases. To calculate the average grain size to shear zone width (width of the
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experimental chamber) ratio we use the total number of grains used in each experiment (Table 1).
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This ratio is 0.039 for experiments with 75% small grains, 0.044 for 50% small grains, and 0.052 for 25% small grains (Figure 5 f).
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Experiments with a mixture of medium and large grains were conducted with a global
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void space of 11.8%. While experiments containing 75% medium sized grains show a higher percentage of slow slip velocities, the three different grain size distributions are otherwise very
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similar to each other. The first slip events occur between 250 and 280 seconds for all three grain
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size combinations. We do not detect a significant change in maximum speed between the different grain size distributions. The average grain size to shear zone width ratio is 0.078 for 75% medium grains, 0.088 for 50% medium grains, and 0.11 for 25% medium grains (Figure 5 i). 5 Discussion The experiments presented here belong to the category of spring slider experiments, which have been used before to investigate granular behavior [Daniels and Hayman, 2008; Hayman et al., 2011; Krim et al., 2011; Nasuno et al., 1998; Reber et al., 2014]. The
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Journal Pre-proof experimental setup is inspired by the simplified geometry of a fault gouge deforming between two parallel and rigid (non-dilatational) walls. Previous studies have shown that angular grains promote stable creep with a high shear resistance, while spherical grains under the same conditions lead to stick-slip and have a lower shear strength [Abe and Mair, 2009; Anthony and Marone, 2005; Mair et al., 2002]. The effect of grains breaking seems to be largely related to angularity; rounded grains become more angular through comminution and therefore the bulk
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behavior strengthens, while angular grains become more rounded and the bulk behavior weakens
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[Abe and Mair, 2009; Guo and Morgan, 2006]. Although breaking of wall rock and grain
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comminution are also widely observed and documented processes in natural fault zones [e.g.,
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Cashman and Cashman, 2000; Rawling and Goodwin, 2003] we do not take these effects into account in our experiments at this stage. We furthermore investigate the impact of grain sizes
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and distribution on slip dynamics in a two-dimensional setting. The two-dimensional nature of
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the experiments allows for direct observation of the evolution of the system through time, but may promote stick-slip and reduce frictional strength relative to an otherwise identical three-
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dimensional system [Hazzard and Mair, 2003]. Due to the volume conserving boundary
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condition the presented experiments are not able to reach steady state. Daniels and Hayman [2008] have conducted experiments on a similar apparatus where they tested the effect of constant volume and dilatational boundary conditions on the force evolution. They have found that in both systems the force slightly increases over time and neither could reach steady state. In experiments with a dilatational boundary condition this increase was, however, slower. Hayman et al. [2011] argue that the strengthening resulting from the constant volume boundary condition could be compared to the interslip strengthening periods on a natural fault that exhibits stick-slip deformation.
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In our experiments we observe that the local void space is heterogeneous and differs from the global average. The dilation of tightly packed granular systems under shear is a welldocumented phenomenon [e.g., Taylor 1956]. We observe local dilation near the slip plane in our constant area experiments. This dilation must be accommodated by local compaction elsewhere in the system. While we do not directly observe this compaction, it is a necessary inference.
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Variations across the experimental box perpendicular to the shear direction can be explained by
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the effect of higher packing order along boundaries of the experimental box (Figure 4). Particles tend to form layers along the walls of the box, which leads to greater order and a larger void
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space percentage [Desmond and Weeks, 2009]. The effect of increased order along the
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boundaries of the experimental frame is however only prominent to a distance of approximately
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one grain diameter from the wall. Its impact is largest for experiments with large grains. Desmond and Weeks [2009] suggest that this effect will be especially notable in experiments
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with less than 10 particle diameters across. In all our experiments we are unable to treat void
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space as a constant. While we are able to keep the global void space constant in experiments with mixed grain sizes, we cannot completely isolate its effect from the effect of the grain size
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distribution on slip dynamics. Furthermore, the global void space in our experiments does not change during deformation. This is at odds with many observations from nature where the porosity changes due to grain comminution [e.g., Kaproth et al., 2010]. The global void space in the experiments is small compared to, for example, undeformed and unlithified sand (27-28%) [Cashman and Cashman, 2000]. The global void space in the experiments is, however, comparable to the porosity in deformation bands and shear zones in unlithified sand (7-10% void space) [Cashman and Cashman, 2000] and deformation bands in sandstones (0-10% void space) [Antonellini et al., 1994].. Antonellini et al. (1994) documented that in deformation bands with 11
Journal Pre-proof little to no volume change the porosity is equivalent in the deformation band and the surrounding material and overall of the same order of magnitude as in our experiments.
During slip events grains rearrange and move past each other. This motion takes place via rearrangement of force chains, slipping of grains next to each other and some minor rotation of grains. Since reorganization of the grains is accommodated by grains sliding and rotating, the
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grain size has an impact on how the granular material deforms [Vangla and Latha, 2015].
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Dilation and movement of grains past each other has been described using the conceptual model
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of two saw-blades in contact. If the saw-teeth initially interlock they will push apart to
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accommodate shear [Bolton, 1986; Rowe, 1962]. Larger grains behave like larger saw-teeth. They can remain locked for longer, and when the pulling force becomes large enough to induce
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motion there is more displacement to make up in the slip event. Since reorganization of the
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grains is accommodated by grains sliding and rotating, larger grains will allow for larger and faster displacements when they slide or rotate. We observe faster slip velocities with an increase
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in grain size when comparing experiments with only small grains to experiments with only
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medium grains (Figure 5 c). Experiments with a mixture of small and medium sized grains also show that an increase in the abundance of medium sized grains leads to faster slip velocities. This trend, however, breaks down for experiments containing large grains with a shear zone width to grain diameter ratio of > 0.1 (Figure 6).
Soil engineering practice mandates that in direct shear experiments the largest grains should not be greater than 1/10 the height of the shear apparatus [Head, 1989] to obtain results that are independent of the boundaries of the testing apparatus. This is of the same order as the
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Journal Pre-proof expected shear band width in granular systems, which is between 6 and 10 grain diameters wide [Francois et al., 2002]. When the grain sizes in the experiment are below this threshold we observe an increase in the slip velocities with an increase in grain size. In experiments that contain grains with a diameter larger than 1/10 of the shear zone width (large grains) this trend is interrupted and slip velocities are smaller (Figure 6). Our results show that even though the average grain size is below the threshold of 1/10 of the shear zone width the deformation
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dynamics changes as soon as grains are present that have an aspect ratio that is larger than 1/10
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of the shear zone width.
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The grain sizes for the experiments were chosen deliberately on both sides of the 1/10 ratio. Natural fault zones are thought to develop a fractal grain size distribution at high strains
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because the probability of grain fracturing depends on the relative size of the grains nearest
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neighbors [Sammis et al., 1987]. Exhumed sections of faults however can show different grain size distributions even when samples are taken at nearby spots along the same fault [Anderson et
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al., 1983]. This indicates that while all fault rock may evolve towards a fractal distribution,
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diverse grain size distributions are common. Field observations show that in natural fault zones grains can temporarily exist that are larger than 1/10 of the shear zone width [Billi, 2005]. While these grains eventually will reduce their size due to comminution they may temporarily affect the slip dynamics of the fault.
Mair et al. [2002] found that experiments with a wide grain size distribution (1 – 800 m) show creep-like dynamics, while a narrow grain size distribution (105 – 149 m) exhibited stickslip behavior. Our findings here indicate that the impact of grain size distribution on granular
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Journal Pre-proof behavior is not only determined by the range in size, but also by the relative abundance of each grain size in the bulk granular material and the grain size to shear zone width ratios. Experiments with an identical range of grain sizes can show differences in slip frequency and velocity depending on the relative abundance of the two grain sizes (e.g., Figure 5 d, e, f).
6 Conclusions
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Displacement, force, and local void space are measured during shear experiments of
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granular systems. We use grains of three sizes to investigate the impact of the grain size to shear
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zone width ratio and grain size distribution on slip dynamics. We observe an increase in local
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void space in the center of the experiment when compared to the global void space. We do not however observe a significant increase of the local void space close to the velocity jump in the
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shear apparatus. The experiments show that below a grain size to shear zone width ratio of 1/10,
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an increase in grain size corresponds to an increase in slip velocities where the proportion of grains of each size controls the bulk behavior. Experiments containing grains with a diameter
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larger than 1/10 of the shear zone width show a decrease in slip velocity even when the average
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grain size diameter increases. This indicates that the presence of large grains has an impact on the deformation dynamics because of their interaction with the boundaries. We show that not only the range of grain sizes but also the relative proportion is relevant for the slip behavior. We propose that shear zones containing grains larger than 1/10 of the shear zone width show deformation dynamics that are independent of the fraction of smaller grains. In shear zones where all grains are smaller than 1/10 of the shear zone width a high abundance of smaller grains promotes smaller slip events.
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Journal Pre-proof Acknowledgements This work has partially been funded by a GSA Graduate Student Research Grant and by a UMass Geosciences Analog Modeling Workshop grant. We would like to thank Karen Daniels for hosting JRF in her lab and sharing insights on experimental materials and techniques. The thoughtful comments of Christoph von Hagke and an anonymous reviewer have improved this manuscript significantly. We acknowledge comments from Susan Cashman, Karen Daniels, and
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Ake Fagereng on an earlier version of this manuscript. The raw data and videos of the
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experiments can be accessed via the Iowa State University data repository
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(https://iastate.figshare.com/account/projects/59969/articles/10022984).
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References
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Reber, J. E., N. W. Hayman, and L. L. Lavier (2014), Stick-slip and creep behavior in lubricated granular material: insights into the brittle-ductile transition, Geophysical Research Letters, 41, 3471-3477. Rowe, P. W., 1962, The stress-dilatancy relation for static equilibrium of an assembly of particles in contact: Proc. R. Soc. Lond. A, v. 269, no. 1339, p. 500-527. Sammis, C., G. King, and R. Biegel (1987), The kinematics of gouge deformation Pure and Applied Geophysics, 125(5), 777-812. Schleicher, A. M., B. A. van der Pluijm, and L. N. Warr (2010), Nanocoatings of clay and creep of the San Andreas fault at Parkfield, California, Geology, 38(7), 667-670. Sibson, R. H. (1977), Kinetic shear resistance, fluid prssure and radiation efficiency during seismic faulting Pure and Applied Geophysics, 115(1-2), 387-400. 17
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Figure captions
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Figure 1: Top row: Schematic top down view of the shear apparatus during loading phase, slip event, and subsequent loading phase. d(t) measures the displacement and F(t) the force over time (after Reber et al., 2014). Blue shaded rectangle shows 12 cm x 30 cm investigation window for local void space calculations. Bottom row: Measured displacement and velocity curves versus time. Shaded box indicates approximate duration of individual events.
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Figure 2: Force and displacement curves (a, c, & e), and velocity curves (b, d & f) for experiments run at 13.0% global void space with all small grains (a & b), all medium grains (c & d), and all large grains (e & f). Filtered force, displacement and velocity data are shown in red, green, and blue respectively. Raw force and displacement data are shown in gray underlying the filtered data. Inset: raw data of one slip event.
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Figure 3: Displacement and velocity versus time for representative experiments with no grains (a), small grains (b), medium grains (c) and large grains (d). Black circles indicate identified and recorded slip events. Figure 4: Local void space histograms plotted for a 12 cm wide band at a shear strain of 0.2 (left column) and a shear strain of 0.5 (right column). Experiment with small grains, top, medium grains, middle, and large grains, bottom. Black indicates area occupied by grains, white shows void space. Red dashed line indicates velocity discontinuity of the experimental table, small black arrows represent the shear direction.
Figure 5: Cumulative slip events for uniform grain size experiments (a, b, c), mixtures of small and medium grains (d, e, f), and mixtures of medium and large grain sizes (g, h, i). a, d, g) histograms of slip event velocity, bin size is 0.1 cm/s. b, e, h) slip event velocity versus time of event. c, f, i) slip event velocity versus ratio of grain size to shear zone width. Black dashed line indicates threshold of grain size to shear zone width of 0.1. 18
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Figure 6: Slip event velocity versus ratio of grain size to shear zone width. Black dashed line indicates threshold of grain size to shear zone width of 0.1. Gray shaded area indicates experiments containing large grains.
Table 1: Experimental parameters for different initial conditions. # of experiments
Global void space (%)
Max. slip velocity (cm/s)
Mean slip velcity (cm/s)
Standard deviation
Average # of slip events per experiment
Max grain diameter/ shear zone width
Total # of grains
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9.9
0.496
0.1338
0.0919
10.6
1/27.3
~4500
M
10
11.8
0.949
0.208
0.1626
28.3
1/13.6
~1100
L
9
13
0.97
0.1953
22.8
1/6.8
75%S 25%M
11
9.75
0.378
0.1077
0.0709
8.4
1/25.4
50%S 50%M
11
9.75
0.44
0.0961
18.1
1/22.7
25%S 27%M
10
9.75
0.1814
0.1224
18.6
1/19.1
75%M 25%L
7
11.8
0.606
0.1162
0.0776
15.6
1/12.7
50%M 50%L
7
0.443
0.1421
0.1008
20.8
1/11.4
~270 ~3400 S 280 M ~2250 S ~560 M ~1130 S ~840 M ~820 M 68 L ~550 M 205 L
0.795
0.136
0.1017
18.2
1/9.49
270 M 205 L
6
11.8
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25%M 75%L
0.62
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S
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Journal Pre-proof Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
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Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6