Supplementary information for: Permeability changes in experimentally fractured
granite during and after frictional sliding
Wataru Tanikawa a,*
Osamu Tadai b
Hideki Mukoyoshi b,c
a
Kochi Institute for Core Sample Research, Japan Agency for Marine-Earth Science and
Technology, 200, Monobe-otsu, Nankoku, Kochi 783-8502, Japan
b
Marine Works Japan Ltd., 200, Monobe-otsu, Nankoku, Kochi 783-8502, Japan
c
Faculty of Education and Integrated Arts and Sciences, Waseda University, 1-6-1,
Nishiwaseda, Shinjuku, Tokyo 169-8050, Japan
*Corresponding author
Address: Kochi Institute for Core Sample Research, Japan Agency for Marine-Earth
Science and Technology, Nankoku 783-8502, Japan
Tel: +81-88-878-2203; fax: +81-88-878-2192
E-mail: tanikawa@jamstec.go.jp
Supplementary Information item 1: Mineral composition of Aji granite
The mineral composition of Aji granite used in our friction tests is listed in Table S1.
Supplementary Information item 2: Calculation of temperature and gas viscosity at
slip plane during friction tests
We used numerical modeling to calculate the temperature distribution in specimens
during frictional sliding. We assumed an axisymmetric two-dimensional problem (Fig.
S1a) and used a computer program based on the finite-element method developed by
Kuroda (2001). In our modeling the half-specimen on one side of the slip plane was
represented by 600 elements, each 0.5 × 0.5 mm (Fig. S1b). The time step we used was
such that temperature changes were less than 1 K for each time step.
Temperature on the top of the specimen (boundary A, Fig. S1b) was fixed to room
temperature in our modeling. Heat transfer to the surrounding atmosphere from the rock
specimen (boundary B, Fig. S1b) followed Newton’s law of cooling, which states that the
rate of heat loss from the rock specimen is proportional to the difference between the
surface temperature and the surrounding temperature (room temperature in our model).
This relationship is
qs = α(T – Ts),
(S1)
where qs is the heat flux per unit are to the surroundings, α is the heat transfer coefficient,
T is the temperature on the rock surface, and Ts is the surrounding temperature. We
assumed a heat transfer coefficient of 10 W/m2 K. The heat flux per unit area of slip
surface generated by friction at boundary C (Fig. S1b), qf, is described in terms of shear
stress and slip velocity as
qf = σf ×v/2,
(S2)
where σf and v are the shear stress and slip velocity, respectively. We assumed constant
shear stress on the surface during sliding to simplify the model setting, even though the
shear stress changes with slip in our friction test. We used 1.28 MPa of shear stress in our
model based on the average friction coefficient of 0.64 in our friction tests. The thermal
properties of Aji granite, listed in Table S2, were measured by using a commercial
instrument (TPS1500, Hot Disk AB Ltd., Sweden) and used in the model calculation.
Assuming that shear stress is constant across the entire slip surface, heat flux is
greatest at the external edge of the specimen. As the rate of heating was not uniform
across the slip surface, the temperature increased radially from the center of the slip
surface and deviated markedly from the average temperature, especially for high-velocity
friction tests (Figs. S1c and S1d). The lowest and highest temperature rise across the slip
surface were observed in the internal and external edges of the specimen, respectively, at
all velocities (Fig. S1d). The deviation of temperature at the slip surface increases with
slip velocity, and the deviation is greater than 30 K for 97 mm/s of slip velocity. The
deviation of temperature induces the deviation of gas viscosity due to the temperature
dependence on the viscosity described in equation (3). According to equation (3) the
deviation of viscosity reaches 6% for a friction test at 97 mm/s slip velocity, and gas
viscosity is greatest at the external edge of the specimen. For lower slip rates (< 9.7 mm/s
of slip velocity), though, the deviation is less than 1%.
Supplementary Information item 3: Reproducibility of our results
The experimental results for an additional series of friction tests using a different set
of cylindrical specimens from the same Aji granite block are shown in Figs. S2 to S4.
Sample sizes and experimental conditions for this series were almost the same as those
for the experiment described in this paper, although the sequence of slip velocities was
different (Fig. S3a). Normal stress was applied at 2 MPa with 1.5 m of slip displacement
for a series of friction tests. We pre-rotated 53 m at 5 mm/s slip velocity and 2 MPa of
normal stress before conducting friction tests. Normal stress dependence on the
permeability of this specimen (Fig. S2a) was similar to that of the specimen discussed in
the main text. Even though the data were fewer than those for the main test, transmissivity
during sliding was proportional to the friction coefficient (Fig. S4b). The overall trends of
slip velocity dependencies (Fig. S4a to S4c) and initial transmissivity dependencies (Fig.
S4d to S4f) were similar to those presented in the main text. These additional data
confirm the reproducibility of our results.
Supplementary Information item 4:
The thermomechanical properties of Aji granite were measured by a Thermomechanical
Analyzer (TMA-60, Shimazu Corporation, Japan), and the calculated thermal property
was used to estimate the thermal stress from the heating test. We applied 0.1 MPa of
normal stress during the thermomechanical test.
References
Everl DD (2003) User’s Guide to RockJock: A Program for Determining Quantitative
Mineralogy from Powder X-Ray Diffraction Data. USGS Open-File Report,
2003-78.
Kuroda H (2001) Two-Dimensional Heat Flow Analysis Program Using Finite Element
Method, 255 pp., CQ, Tokyo (in Japanese).
Captions
Supplementary Fig. S1. Model calculation of temperature and viscosity change during
friction tests. (a) Illustration of the area used for modeling of the temperature distribution
within specimens during friction tests. (b) Detail of the area modeled showing mesh
geometry and boundaries used. (c) Snapshot of the modeled thermal distribution for an
Aji granite specimen after 1.5 m slip displacement for an average slip rate of 97 mm/s (=
100 rpm). (d) Snapshot of temperature distribution of the slip surface after 1.5 m slip
displacement at various slip rates. (e) Change of maximum temperature difference along
slip surface during shearing at various slip rates. (f) Change of maximum deviation of gas
viscosity on slip surface at various slip rates. Constant shear stress of 1.28 MPa and
constant slip ratio were assumed during frictional sliding.
Supplementary Fig. S2 (a) Permeability as a function of normal stress for an intact
specimen and for simulated fault rocks before and after slip. Loading and unloading were
applied to the same samples. (b) Gas flow rate, measured in the flow line before entry to
the shearing apparatus, as a function of differential pore pressure (Pu2 – Pd2)/Pu. Inset
graph is a magnified view at low flow rate.
Supplementary Fig. S3. (a) Friction coefficient and (b) slip velocity as a function of
cumulative slip displacement for a series of successive friction tests performed on the
second pair of hollow granite specimens. (c) Average coefficient of friction during slip
displacement of 1.5 m as a function of slip velocity. (d) Average friction coefficient
during slip as a function of average fracture transmissivity during slip (T1) for different
slip velocities.
Supplementary Fig. S4. Relative fracture transmissivity (a)–(c) as a function of slip
velocity and (d)–(e) as a function of initial transmissivity. T0, initial fracture
transmissivity; T1, average fracture transmissivity during slip; T2, fracture transmissivity
after slip; T3, fracture transmissivity approaching steady state 15 min after slip.
Supplementary Fig. S5. Thermal expansion of Aji granite during heating.
Supplementary Table S1. Mineral composition of Aji granite (%) determined using the
RockJock program (Everl, 2003).
Supplementary Table S2. Thermal and physical properties used for numerical modeling
of the temperature distribution during friction tests.