Contrasting hydrological and mechanical properties of clayey and silty muds cored from the shallow Nankai Trough accretionary prism

Tectonophysics 600 (2013) 63–74

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Contrasting hydrological and mechanical properties of clayey and silty muds cored from the shallow Nankai Trough accretionary prism Miki Takahashi a, Shuhei Azuma b, 1, Shin-ichi Uehara c, Kyuichi Kanagawa b,⁎, Atsuyuki Inoue b a b c

Active Fault and Earthquake Research Center, Geological Survey of Japan, AIST Tsukuba Central 7, 1-1-1 Higashi, Tsukuba 305-8567, Japan Department of Earth Sciences, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan Department of Environmental Science, Toho University, 2-2-1 Miyama, Funabashi 274-8510, Japan

a r t i c l e

i n f o

Article history: Received 2 July 2012 Received in revised form 22 December 2012 Accepted 16 January 2013 Available online 31 January 2013 Keywords: Clayey mud Silty mud Nankai Trough accretionary prism Permeability Failure strength Friction

a b s t r a c t Two mud samples cored from the shallow (≈1000 mbsf) Nankai Trough accretionary prism at Site C0002 of IODP Expedition 315 are found to be distinctly different in hydrological and mechanical properties. At confining pressures, pore water pressures and temperatures close to their in situ conditions, a clayey mud sample has lower permeability of 2.92× 10−19 m2, while a silty mud sample has higher permeability of 2.29× 10−18 m2. Triaxial compression experiments at these conditions and an axial displacement rate of 10 μm/s reveal that the clayey mud sample exhibits lower failure strength of 14.2 MPa followed by a slow failure lasting for ≈40 s, while the silty mud sample exhibits higher failure strength of 20.1 MPa followed by a rapid failure within ≈5 s. Friction experiments at these conditions and axial displacement rates changed stepwise among 0.1, 1 and 10 μm/s reveal that the clayey mud sample has a much lower steady-state friction (μss ≈ 0.25) than the silty mud sample (μss ≈0.53). Although both samples exhibit velocity strengthening, the former has more than three times larger velocity-dependence of steady-state friction than the latter. Such contrasting hydrological and mechanical properties of the clayey and silty mud samples as revealed in this study suggest the following implications for deformation and faulting in the shallow mud-dominant Nankai Trough accretionary prism. Deformation results in a possible increase in pore pressure, and hence, in strength reduction in clayey mud, but not in silty mud. Faulting would preferentially occur in the weaker clayey mud, and its slow failure may result in a slow slip. Faults formed in clayey mud are weak and easily reactivated, but stable and not seismogenic. In contrast, once the stronger silty mud is faulted, its rapid failure may become a seismic slip. Faults formed in silty mud are strong and not easily reactivated, but possibly unstable and seismogenic. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Sediments on the incoming oceanic plate at subduction zones are mainly composed of hemipelagic sediments and terrigenous turbidites, and they together are off-scraped to form an accretionary prism (e.g. Underwood, 2007). This is also true in the Nankai Trough subduction zone, as revealed by recent Integrated Ocean Drilling Program (IODP) Expeditions 316 and 322 (Screaton et al., 2009; Underwood et al., 2010), part of the Nankai Trough Seismogenic Zone Experiment (NanTroSEIZE). NanTroSEIZE IODP Expeditions 315, 316 and 319 also revealed that the shallow Nankai Trough accretionary prism is largely composed of mud with subordinate sand and volcanic ash (Ashi et al., 2009; Expedition 319 Scientists, 2010a; Screaton et al., 2009). Hence the hydrological and mechanical properties of the shallow

⁎ Corresponding author. Tel.: +81 43 290 2857; fax: +81 43 290 2859. E-mail address: [email protected] (K. Kanagawa). 1 Present address: SK Engineering, Co., Ltd., 2-1-15 Iwamoto-cho, Chiyoda-ku, Tokyo 101-0032, Japan. 0040-1951/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.tecto.2013.01.008

Nankai Trough accretionary prism are likely controlled by those of mud. Here we report the results of permeability measurements, and triaxial compression and friction experiments of two mud samples, which are cored from the shallow (≈1000 mbsf) Nankai Trough accretionary prism, at confining pressures, pore water pressures and temperatures close to their in situ conditions. They are found to be distinctly different not only in lithology but also in hydrological and mechanical properties, which and their implications for deformation and faulting in the shallow mud-dominant Nankai Trough accretionary prism will be discussed. 2. Geologic setting The Nankai Trough is a convergent plate margin where the Philippine Sea plate is subducting northwestward beneath the Eurasian plate at a rate of 4–6.5 cm/y (Heki, 2007; Seno et al., 1993; Fig. 1). An accretionary prism is developed landward from the Nankai Trough (Fig. 1). The Shikoku Basin sediments composed of hemipelagic sediments and terrigenous turbidites are actively accreting at the deformation front (Screaton et al., 2009; Underwood et al., 2010; Fig. 1b). An in-sequence thrust package of

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M. Takahashi et al. / Tectonophysics 600 (2013) 63–74

35°N

(a)

34°

33°

136°

137°

(b)

Depth (km)

2

C0002

C0001

138°

C0004 C0008 Slope sediments

Kumano Basin sediments

0

139°E

5 km

Trench sediments

C0006 C0007

5 Accretionary prism

fault splay Mega

10

Shikoku Basin sediments

ent Décollem ts g sedimen ubductin

S

st anic cru the oce Top of

Fig. 1. Locality map (a) and seismic profile (b) showing Site C0002 of the IODP Expedition 315 off Kii Peninsula, Japan, where mud samples tested in this study were cored. Six other sites referred in text are also indicated. Inset at the top right in (a) is an index map of Japan (©2012 Google and ©2012 TerraMetrics) showing the location of map area of (a). NAP: North American plate, PP: Pacific plate, and PSP: Philippine Sea plate. Line X–X′: composite seismic line for the seismic profile shown in (b). Yellow arrows: computed far-field convergence vectors between Philippine Sea plate and Japan (Heki, 2007; Seno et al., 1993). Modified after Moore et al. (2009) and Underwood et al. (2010).

accreted sediments occupies between this deformation front and the outer ridge (Fig. 1b), the latter of which was likely formed by outof-sequence thrusting along the “megasplay” fault branching from the master décollement (Moore et al., 2007; Park et al., 2002; Fig. 1b). Landward from this outer ridge off Kii Peninsula, the fore-arc Kumano Basin sediments unconformably cover the older accreted sediments (Fig. 1b). The Nankai Trough subduction zone has been the site of recurring, typically tsunamigenic great earthquakes larger than Mw > 8.0, including the 1944 Tonankai Mw 8.2 and 1946 Nankai Mw 8.3 earthquakes (Ando, 1975; Hori et al., 2004). Recent tsunami and seismic waveform inversions, seismic reflection studies and mud breccia analyses suggest that the coseismic slip during the 1944 Tonankai earthquake occurred

along the megasplay fault (Kikuchi et al., 2003; Park et al., 2002; Sakaguchi et al., 2011; Tanioka and Satake, 2001). In addition, very low frequency earthquakes have recently been found to occur within the accretionary prism between the outer ridge and the deformation front (Ito and Obara, 2006). 3. Sample descriptions 3.1. Location and in situ conditions of samples We tested two mud samples cored by the D/V Chikyu from the shallow Nankai Trough accretionary prism at Site C0002, located at the

M. Takahashi et al. / Tectonophysics 600 (2013) 63–74

Depth (mbsf)

Table 1 In situ temperatures (T), pressures (P) and pore pressures (Pp) of two mud samples tested.

Unconformity 500

Slump Ash Sand Silt Mud

Quaternary

600

700

65

Kumano Basin sediments

Sample

Site/Hole/Core/Section Depth (mbsf)

T (°C)

C2516 C2652

C0002/B/51R/6 C0002/B/65R/2

32.6 35.2

944.64 1048.99

a

P (MPa) 36.2 38.3

b

Pp (MPa)

c

28.3 29.3

a Estimated from the temperature profile based on downhole temperatures and thermal conductivity on cores measured during the Expedition 315 (Expedition 315 Scientists, 2009). b Estimated from the overburden stress calculated from the least-squares fitted profile of densities measured onboard D/V Chikyu (Expedition 315 Scientists, 2009) and the water column above the seafloor. c Estimated assuming a hydrostatic condition.

during the IODP Expedition 319 at Site C0009 located ≈20 km northwest away from Site C0002 (Expedition 319 Scientists, 2010b; Fig. 1a), in situ pore pressures of samples C2516 and C2652 are estimated to be 28.3 MPa and 29.3 MPa, respectively (Table 1).

3.2. Sample characterization

Pliocene

800

900

Miocene

C2516 Accretionary sediments 1000

C2652 Fig. 2. Columnar section of Hole B at Site C0002 (Expedition 315 Scientists, 2009) showing the locations of two mud samples C2516 and C2652 tested in this study. mbsf: meters below seafloor.

southeastern margin of the Kumano Basin, during the IODP Expedition 315 (Fig. 1). At this site, the unconformity boundary between the Miocene accretionary sediments and the overlying Pliocene–Quaternary Kumano Basin sediments occurs at a depth of ≈922 mbsf (meters below seafloor) (Expedition 315 Scientists, 2009; Fig. 2). Sample C2516 comes from 944.64 mbsf, while sample C2652 comes from 1048.99 mbsf (Fig. 2 and Table 1). According to a temperature profile based on downhole temperatures and thermal conductivity on cores measured at Site C0002 (Expedition 315 Scientists, 2009), in situ temperatures of samples C2516 and C2652 are estimated to be 32.6 °C and 35.2 °C, respectively (Table 1). From the overburden stress calculated from the leastsquares fitted profile of densities measured onboard D/V Chikyu (Expedition 315 Scientists, 2009) and the water column above the seafloor, in situ pressures of samples C2516 and C2652 are estimated to be 36.2 MPa and 38.3 MPa, respectively (Table 1). Assuming a hydrostatic condition, which was found to be true down to 1460 mbsf when tested

We have made petrographic thin sections of the two mud samples, and observed optical and backscattered electron microstructures. We also conducted powder X-ray diffraction analyses of the two mud samples. We have not only prepared powder samples from specimens after triaxial compression experiments, but also used powder samples for triaxial friction experiments. After qualitative analyses to check constituent minerals, we have conducted quantitative analyses following the method described by Chung (1974). We used quartz as the reference mineral, and prepared a powder mixture of equally weighing synthetic quartz and each constituent mineral within the sample to be analyzed. From an X-ray diffraction profile of each mixture, the peakheight ratio of a specific diffraction plane of each mineral to that of quartz was obtained. The peak-height ratio of the same diffraction planes from an X-ray diffraction profile of the sample to be analyzed then provides an estimate of relative weight of that specific mineral with respect to quartz. This method, although not so precise, gives a rough estimate of the modal composition in weight%. In addition, we have measured porosities of the two mud samples at an unconfined condition by using a mercury bath and a helium porosimeter for bulk and pore volume measurements, respectively, at the Technology and Research Center of Japan Oil, Gas and Metals National Corporation. Sample C2516 is a very fine-grained and homogeneous, clayey mud (Fig. 3a, b). This sample is strongly bioturbated, and no bedding-related fabric was recognized (Fig. 7a). It contains ≈13 wt% quartz and ≈23 wt% feldspar as clastic grains, and 27–32 wt% smectite, 5–6 wt% illite, ≈1.5 wt% chlorite and ≈3 wt% kaolinite as clay minerals (Table 2). The porosity of this sample is 11.2% (Table 3), which is unusually low compared with 30–50% porosities of accretionary sediments measured onboard at Site C0002 (Expedition 315 Scientists, 2009). In contrast, sample C2652 is a coarser-grained and more poorly sorted, silty mud (Fig. 3c, d). This sample has a weak bedding-parallel fabric (Fig. 7b). It contains not only abundant angular clastic grains but also rounded mud clasts (arrows in Fig. 3c, d), and contains 28–31 wt% quartz and 24–27 wt% feldspar as clastic grains, and 21–25 wt% smectite, 5–6 wt% illite, ≈1 wt% chlorite and ≈2 wt% kaolinite as clay minerals (Table 2). The porosity of this sample is 38.5% (Table 3), which is within the porosity range of accretionary sediments measured onboard at Site C0002 (Expedition 315 Scientists, 2009). Thus, the two mud samples distinctly differ in lithology, modal composition and porosity. As for modal composition, the two samples show major differences in quartz and smectite contents, but only minor differences in contents of other minerals (Table 2).

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(a)

(b)

(c)

(d)

Fig. 3. Microstructures of two mud samples tested in this study. (a) and (c) are optical micrographs (plane polarized light), while (b) and (d) are backscattered electron micrographs. (a) and (b) are from sample C2516, and (c) and (d) are from sample C2652. White arrows in (c) and (d) indicate mud clasts.

4. Permeability measurements, and triaxial compression and friction experiments 4.1. Experimental methods For permeability measurements, and triaxial compression and friction experiments, we used a gas-medium, high-pressure, high-temperature triaxial apparatus at Active Fault and Earthquake Research Center of Geological Survey of Japan (Masuda et al., 2002). Pressure mediums for confining pressure and pore pressure were argon gas and distilled water, respectively. Hollow pistons enable pore water to flow through the specimen tested (Fig. 4). Two independent servo-controlled pressure intensifiers enable us to apply both confining and pore pressures up to 200 MPa. Axial load was measured by a load cell attached to the lower piston inside the pressure vessel. For permeability measurements and triaxial compression experiments, we used cylindrical specimens cored horizontally from the vertical core samples in order to deform them horizontally as in the accretionary prism. The specimen assembly for permeability measurements and triaxial compression experiments consisted of a cylindrical

Table 2 Modal compositions of mud samples determined by quantitative powder X-ray diffraction analyses. Sample

Qz

Fs

Cc

Hb

Pr

Gs

Smt

Ill

Chl

Kln

C2516-1 C2516-2 C2652-1 C2652-2

13.4 13.0 30.7 27.6

23.3 23.0 26.8 24.2

4.2 3.4 2.7 2.7

13.6 11.6 8.5 8.3

8.4 5.9 1.9 3.1

0.9 1.2 0.0 0.0

26.7 32.0 21.1 24.7

5.2 5.8 4.9 6.4

1.4 1.5 1.0 1.1

2.8 2.7 2.4 1.9

C2516-1 and C2652-1 are powder samples from specimens used for triaxial compression experiments, while C2516-2 and C2652-2 are powder samples used for triaxial friction experiments. Qz: quartz, Fs: feldspar, Cc: calcite, Hb: hornblende, Pr: pyrite, Gs: gypsum, Smt: smectite, Ill: illite, Chl: chlorite, and Kln: kaolinite.

specimen with 20 mm in diameter and 40 mm in length, a pair of porous WC spacers, a pair of alumina spacers, and upper and lower stainlesssteel pistons (Fig. 4a). Stainless-steel mesh sheets were inserted between the specimen and the WC spacer to make the pore water flow uniform (Fig. 4a). This assembly was then jacketed by a heat-shrink Teflon® tube (Fig. 4a). We applied silicone sealant on the lateral side of the cylindrical specimen in order to prevent the pore water flow between the specimen and the Teflon® jacket. For triaxial friction experiments, we prepared simulated gouges with grain sizes smaller than 250 μm from crushed and sieved mud samples. The specimen assembly consisted of a cylinder of porous Shirahama sandstone with 20 mm in diameter and 40 mm in length, containing a 0.65 g (≈0.5 mm thick) gouge layer along a sawcut inclined at 30° to the cylinder axis, a pair of porous WC spacers, a pair of alumina spacers, and upper and lower stainless-steel pistons (Fig. 4b). Teflon® sheets were inserted between spacers in order to reduce the friction (Fig. 4b). This assembly was then jacketed by a heat-shrink Teflon® tube (Fig. 4b). Permeability measurements, and triaxial compression and friction experiments have been conducted at a room temperature (≈15 °C), and the confining and pore pressures equivalent to their in situ conditions, i.e. 36 MPa and 28 MPa, respectively for the clayey mud sample (C2516), and 38 MPa and 29 MPa, respectively for the silty mud sample (C2652) (Table 4). Thus, the effective confining pressure was 8 MPa for

Table 3 Summary of porosity measurements. Sample

Vbulk (cm3)

Vpore (cm3)

ϕ (%)

C2516 C2652

1.56 1.58

0.175 0.608

11.22 38.48

Vbulk: bulk volume determined by using a mercury bath, Vpore: pore volume determined by using a helium porosimeter, and ϕ: porosity.

M. Takahashi et al. / Tectonophysics 600 (2013) 63–74

Pore-water access hole

67

Pore-water access hole

Stainless-steel piston

Stainless-steel piston

Sealing tape

Sealing tape

Teflon® jacket

Teflon® jacket

Porous WC spacer

Porous WC spacer

Specimen

Shirahama sandstone 30°

Gouge layer

Stainless-steel mesh sheet

Teflon® sheet

Alumina spacer

Alumina spacer

Teflon® sheet

(a)

(b)

Fig. 4. (a) Specimen assembly for permeability measurements and triaxial compression experiments. (b) Specimen assembly for triaxial friction experiments.

the former and 9 MPa for the latter. Although the experimental temperature was about 20 °C lower than the in situ temperatures (Table 1), the difference is very minor at this temperature range and the duration time of experiments, i.e. ≈4 min for compression experiments and ≈70 min for friction experiments. Thus, we have conducted experiments at confining pressures, pore water pressures and temperatures almost equivalent to their in situ conditions.

We have measured permeability of the two mud samples by the pore pressure oscillation method of Fischer and Paterson (1992). We applied a sinusoidal change in upstream pore pressure with an amplitude of 0.4 MPa and a frequency of 0.001 Hz, which resulted in a different sinusoidal change in downstream pore pressure with a smaller amplitude and a lagging phase (Fig. 5). Provided that the dynamic viscosity of pore fluid (distilled water in this case) and the storage of the downstream

Table 4 Summary of experimental conditions and results. Sample

T

Pc Pp (MPa) (MPa)

k (m2)

β (/MPa)

Triaxial compression experiment

Triaxial friction experiment

Vaxial σfail σres (μm/s) (MPa) (MPa)

Vaxial (μm/s)

Δσ/Δε (MPa/%)

C2516

RT 36

28

2.92±0.06×10−19

1.31±0.06×10−4 10

14.2

11.1

2.09

C2652

RT 38

29

2.29±0.02×10−18

2.40±0.08×10−4 10

20.1

17.3

13.33

Vsliding (μm/s)

0.1, 1, 10 0.1155, 1.155, 11.55 0.1, 1, 10 0.1155, 1.155, 11.55

μss@Vaxial =1 μm/s a−b

Δμss / ΔlnVsliding

0.25

0.004±0.001 0.014±0.001

0.53

0.003±0.001 0.004±0.002

T: temperature, RT: room temperature, Pc: confining pressure, Pp: pore pressure, k: permeability, β: storage capacity, Vaxial: axial displacement rate, σfail: failure strength, σres: residual strength, Δσ/Δε: stress drop ratio, Vsliding: sliding velocity, μss: steady-state friction coefficient, a − b: difference in direct and evolutionary effects after an e-times stepwise change in sliding velocity, and Δμss /ΔlnVsliding: dependence of steady-state friction coefficient on logarithmic sliding velocity.

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M. Takahashi et al. / Tectonophysics 600 (2013) 63–74

reservoir (≈8.2×10−9 m3/MPa in this case) are known, sample permeability k (m2) and storage capacity β (/MPa) can then be calculated from the amplitude ratio and phase shift between these sinusoidal changes in upstream and downstream pore pressures (Fischer and Paterson, 1992). Subsequently after permeability measurements, we have conducted triaxial compression experiments of the same specimens until failure at a constant axial displacement rate (Vaxial) of 10 μm/s (Table 4), i.e. at a constant strain rate of 2.5 × 10−4/s, and monitored differential stress with increasing axial displacement, which was converted into axial strain. After experiments, the specimens were vacuum-impregnated with epoxy and cut normal to fractures formed, from which petrographic thin sections were made. We then observed optical microstructures of fractured specimens. We also conducted friction experiments on simulated gouges as prepared above at axial displacement rates (Vaxial) changed stepwise among 0.1, 1, and 10 μm/s, i.e. at sliding velocities (Vsliding) along the sawcut changed stepwise among 0.1155, 1.155, and 11.55 μm/s (Table 4), and monitored differential stress with increasing axial displacement. Shear and normal stresses acting on the gouge layer were calculated from the differential stress and effective confining pressure, and corrected for Teflon® jacket strength. Their ratio gave friction coefficient (μ) of the gouge. Axial displacement was converted into sliding displacement (d) along the sawcut.

4.2. Experimental results At the experimental conditions described above, we obtained k = 2.92 × 10 −19 m 2 and β = 1.31 × 10 −4/MPa for the clayey mud sample (C2516), and k = 2.29 × 10 −18 m 2 and β = 2.40 × 10 −4/MPa for the silty mud sample (C2652) (Table 4). Thus, the former is about ten times less permeable than the latter.

Pore pressure Pp (MPa)

(a) C2516 @Pc = 36 MPa 28.5

28.0

Upstream P p

27.5 0

1000

Downstream P p

2000

3000

During the triaxial compression experiment, the clayey mud sample (C2516) exhibited a slow failure lasting for ≈ 40 s after reaching lower failure strength of 14.2 MPa, and subsequently deformed at constant strength of 11.1 MPa (Fig. 6 and Table 4). In contrast, the silty mud sample (C2652) exhibited a rapid failure within ≈ 5 s after reaching higher failure strength of 20.1 MPa, and then slightly strain hardened to reach steady-state strength of 17.3 MPa (Fig. 6 and Table 4). Thus, two samples differ not only in strength, but also in time required for failure. Mesoscopic fractures oblique to the cylindrical specimen axes were formed in both samples after failure (Fig. 7). The fracture in the clayey mud sample (C2516) is curved (Fig. 7a), while the one in the silty mud sample (C2652) is planar (Fig. 7b). During the triaxial friction experiment, the clayey mud sample (C2516) exhibited slip softening after reaching maximum μ ≈ 0.38 at d ≈ 0.3 mm and Vaxial = 1 μm/s, until μ ≈ 0.25 at d ≈ 2.8 mm and Vaxial = 1 μm/s (Fig. 8 and Table 4). In contrast, the silty mud sample (C2652) exhibited quasi steady-state slip after reaching maximum μ ≈ 0.56 at d ≈ 0.7 mm and Vaxial = 1 μm/s, until μ ≈ 0.53 at d ≈ 3.2 mm and Vaxial = 1 μm/s (Fig. 8 and Table 4). Thus, these two samples are different not only in frictional strength, but also in slip-dependent frictional behavior. Although both samples showed an increase in μ when Vaxial was increased and vice versa (Figs. 8 and 9), i.e. velocity strengthening, the response after a stepwise change in Vaxial is different between the two samples. When Vaxial of the clayey mud sample (C2516) was increased or decreased, μ not only instantaneously increased or decreased (direct effect) and subsequently decayed (evolutionary effect), as predicted by the rate- and state-dependent friction constitutive law (Dieterich, 1979, 1981), but also asymptotically increased or decreased thereafter (Fig. 9a). In contrast, such an asymptotic increase or decrease in μ after the evolutionary effect was not obvious in the silty mud sample (C2652) (Fig. 9b). The observed frictional behavior of the clayey mud sample (C2516) after a stepwise change in Vaxial cannot be explained by the rate- and state-dependent friction constitutive law alone, and is attributable to a contribution of a certain type of flow as for frictional behavior of serpentinite (Reinen et al., 1992; Takahashi et al., 2011). We have therefore fitted the observed friction data by the mixed friction–flow law proposed by Takahashi et al. (2011), and estimated the velocitydependent friction parameter (a − b) as the difference in direct and evolutionary effects for an e-times change in Vsliding, as well as the steady-state friction coefficient (μss) after the flow response at each Vsliding (see Appendix A for details). Estimated (a − b) values of the clayey mud sample (C2516) are 0.0027–0.0065 with an average of 0.004 and a standard deviation of 0.001, while those of the silty mud sample (C2652) are 0.0004–0.0038 with an average of 0.003 and a

4000 25

Time (sec)

Differential stress (MPa)

Pore pressure Pp (MPa)

(b) C2652 @Pc = 38 MPa 29.5

29.0

28.5

Upstream P p

0

1000

C2652 @Pc = 38 MPa, Pp = 29 MPa, Vaxial = 10 µm/s 5.3 s

20

15

39.6 s

10

C2516 @Pc = 36 MPa, Pp = 28 MPa, Vaxial = 10 µm/s

5

Downstream P p

2000

3000

4000

Time (sec)

0

0

1

2

3

4

5

6

Axial strain (%) Fig. 5. Sinusoidal changes in upstream pore pressure given in permeability measurements and observed changes in downstream pore pressure. (a) Sample C2516. (b) Sample C2652. Pc: confining pressure, and Pp: pore pressure. See Table 4 for experimental conditions.

Fig. 6. Differential stress plotted against axial strain for two mud samples C2516 and C2652. Duration times required for failure of two samples are also indicated. Pc: confining pressure, Pp: pore pressure, and Vaxial: axial displacement rate.

M. Takahashi et al. / Tectonophysics 600 (2013) 63–74

(a)

69

(b)

5 mm

5 mm

Fig. 7. Microstructures of samples C2516 (a) and C2652 (b) after failure. The maximum compression direction is vertical. White arrows indicate fractures formed during failure.

standard deviation of 0.001 (Fig. 10 and Table 4). Although the (a − b) values of the clayey mud sample (C2516) are slightly larger than those of the silty mud sample (C2652), the difference is small. However, when we plot μss against Vsliding, it is evident that the clayey mud sample (C2516) has μss much more dependent on Vsliding than the silty mud sample (C2652) (Fig. 11). The least-squares fitting of these data gives Δμss / ΔlnVsliding of 0.014 for the clayey mud sample (C2516), and that of 0.004 for the silty mud sample (C2652) (Table 4). Thus, Δμss / ΔlnVsliding of the former is more than three times larger than that of the latter. It should be also noted that the difference between (a − b) value and Δμss / ΔlnVsliding is large for the clayey mud sample (C2516), while it is very small for the silty mud sample (C2652) (Table 4).

less abundant quartz (≈13 wt%) and more abundant smectite (27–32 wt%) than the silty mud sample (C2652) (Table 2). These characteristics suggest that this sample is of hemipelagic origin. In contrast, the silty mud sample (C2652) is relatively coarse-grained and poorly sorted (Fig. 3c, d). It contains abundant terrigenous clastic grains (Fig. 3c, d), and much more abundant quartz (28–31 wt%) and less abundant smectite (21–25 wt%) than the clayey mud sample (C2516) (Table 2). These characteristics suggest that this sample is of turbidite origin. Thus, the two mud samples cored from the shallow (≈1000 mbsf) Nankai Trough

(a) C2516 @Pc = 36 MPa, Pp = 28 MPa 0.30

5.1. Origin of mud samples The clayey mud sample (C2516) is very fine-grained and homogeneous (Fig. 3a, b). It contains fewer clastic grains (Fig. 3a, b), and much 0.8

Friction coefficient µ

5. Discussion

1

10

1

10 µm/s

0.27 0.26 1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

Sliding displacement d (mm)

0.6

C2652 @Pc = 38 MPa, Pp = 29 MPa

(b) C2652 @Pc = 38 MPa, Pp = 29 MPa

0.5 Vaxial = 1

0.4

10

1 .1 1 .1 1

0.57 10

1

10

1 .1 1 µm/s

0.3 C2516 @Pc = 36 MPa, Pp = 28 MPa

0.2 0.1 0

0.5

1.0

1.5

2.0

2.5

3.0

Sliding displacement d (mm)

Friction coefficient µ

Friction coefficient µ

0.1

0.28

0.25 1.2

0.7

0

Vaxial = 1

0.29

Vaxial = 0.1

1

0.1

1

10 µm/s

0.56 0.55 0.54 0.53 0.52 1.0

1.1

1.2

1.3

1.4

1.5

1.6

Sliding displacement d (mm) Fig. 8. Friction coefficient μ plotted against sliding displacement d for gouges of two mud samples C2516 and C2652. Pc: confining pressure, Pp: pore pressure, and Vaxial: axial displacement rate.

Fig. 9. Enlarged parts of the curves shown in Fig. 8. (a) Sample 2516. (b) Sample 2652. Pc: confining pressure (MPa), Pp: pore pressure (MPa), and Vaxial: axial displacement rate.

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M. Takahashi et al. / Tectonophysics 600 (2013) 63–74

0.008 C2516 C2652

a−b

0.006

0.004

0.002

0 0.8

1.0

1.5

2.0

2.5

3.0

3.2

Sliding displacement d (mm) Fig. 10. (a − b) value plotted against sliding displacement d for two samples C2516 and C2652. Vertical bars are error bars. See Appendix A for details to determine (a − b) values.

accretionary prism are different not only in lithology, but also possibly in origin. 5.2. Hydrological properties of mud samples Although the permeability of the clayey mud sample (C2516) has been measured at an effective confining pressure 1 MPa lower than that of the silty mud sample (C2652), the former permeability was one order of magnitude lower than the latter permeability (Table 4). The clayey mud sample (C2516) has a porosity as low as 11.2%, while the silty mud sample (C2652) has a porosity as high as 38.5% (Table 3). Such large difference in porosity between these two samples must be largely responsible for the difference in permeability as observed. Permeability is also known to decrease with decreasing grain size and increasing clay fraction even if the porosity is constant (e.g. Schön, 1996; Takahashi et al., 2007). Hence finer grain size and a 0.6

larger smectite content of the clayey mud sample (C2516) than those of the silty mud sample (C2652) (Table 2) should also make the former sample less permeable. Although the clayey mud sample (C2516) has an isotropic fabric, the silty mud sample (C2652) has a weak beddingparallel fabric oblique to the specimen by ≈30° (Fig. 7). This difference in anisotropy may also contribute to the difference in permeability between the two samples, but it remains unknown how much the effect is. Permeability of mud samples cored during the IODP Expeditions 315 and 316 has also been measured by Guo et al. (2011), Ikari and Saffer (2012), and Tanikawa et al. (2012). Guo et al. (2011) measured permeability of mud samples cored at Sites C0002, C0006 and C0007 (Fig. 1), and reported permeability values of 10 −17–10 −18 m 2 at a vertical effective stress of 8 MPa, which is comparable to our measurement conditions. Although we used distilled water as pore fluid, Guo et al. (2011) used seawater as pore fluid which may have suppressed swelling of smectite to have resulted in their permeability values one order of magnitude higher than those of our samples. It should be noted, however, that their samples are grouped into two possibly reflecting the difference in lithology as our samples; samples with higher permeability values of ≈ 10 −17 m 2 and those of lower permeability values of ≈10 −18 m 2. Ikari and Saffer (2012) measured permeability of mud samples cored at Sites C0001, C0004 and C0008 (Fig. 1), and reported permeability values of the order of 10 −18 m 2 at a vertical effective stress of ≈10 MPa, which are similar to the permeability value of our silty mud sample. Ikari and Saffer (2012) also measured permeability of two mud samples cored during the Ocean Drilling Program Site 1173, ≈ 200 km SW away from the IODP sites off Kii Peninsula, and reported permeability values of ≈10 −18 m 2 for one mud sample and of ≈10 −19 m 2 for the other at a vertical effective stress of ≈10 MPa. These permeability values are well correlatable with those of our mud samples. Tanikawa et al. (2012) reported permeability values of the order of 10−16–10−17 m 2 for mud samples cored at Sites C0004 and C0007 (Fig. 1), which are two orders of magnitude higher than the permeability values of our mud samples. However, these are values measured at an effective confining pressure of 3.3 MPa, and therefore would be lower at effective confining pressures of 8–9 MPa as in this study. 5.3. Failure properties of mud samples

C2652

Steady-state friction coefficient µss

0.5

0.4

C2516

0.3

0.2

0.1

0

0.1

1

10

Sliding velocity Vsliding (µm/s) Fig. 11. Steady-state friction coefficient μss plotted against sliding velocity Vsliding for two mud samples C2516 and C2652. Least-squares fitted lines are also shown. See Appendix A for details to determine μss values.

Triaxial compression experiments revealed that the failure and residual strengths of the silty mud sample (C2652) were about 6 MPa higher than those of the clayey mud sample (C2516) (Fig. 6 and Table 4). Although the effective confining pressure of the former was 1 MPa higher than that of the latter (Table 4), this difference cannot be explained by the difference in effective confining pressure alone and implies an intrinsic difference in strength. In spite of bedding suitably oriented for fracturing in the silty mud sample (C2652) (Fig. 7b), this sample is much stronger than the clayey mud sample (C2516) so that anisotropy of samples does not noticeably affect the sample strength. These two samples also differ in time required for failure. The clayey mud sample (C2516) failed slowly lasting for ≈40 s while the silty mud sample (C2652) failed rapidly within ≈5 s (Fig. 6 and Table 4). The mesoscopic fracture formed during failure is curved in the former while planar in the latter (Fig. 7), which may be related with the difference in time required for failure. The silty mud sample (C2652) contains clastic grains of quartz and feldspar more than 50 wt% (Table 2). This sample is likely grainsupported and stiff, and therefore was strong and failed rapidly. In contrast, the clayey mud sample (C2516) contains clastic grains of quartz and feldspar less than 40 wt%, while it contains clay minerals as much as ≈40 wt% (Table 2). This sample is likely matrix-supported and soft, and therefore was weak and failed slowly. In addition, the low porosity and permeability of this sample as described above likely resulted in an increase in pore pressure during its triaxial compression as discussed

M. Takahashi et al. / Tectonophysics 600 (2013) 63–74

below, which would have further weakened this sample. Frictional behavior of this sample suggests a contribution of flow during the frictional sliding of this sample, as described above. Such flow possibly occurred also during the triaxial compression deformation of this sample partly due to the increased pore pressure, and may be responsible for the slow failure of this sample. Kitajima et al. (2012) estimated the maximum strain rate e˙ max (/s) for pore pressure equilibrium during deformation experiments using the following equation.

e˙ max ¼

0:1k l2 ηw ðβ−ϕχ w Þ

where l (m) is sample length, ηw (Pa·s) is pore water viscosity, χw (/Pa) is pore water compressibility, ϕ is porosity, k (m2) is permeability, and β (/Pa) is storage capacity. Strain rate faster than e˙ max would result in imperfect drainage and hence an increase in pore pressure during a deformation experiment. Inputting ϕ, k and β values obtained in this study (Tables 3 and 4), l=0.04 m, and ηw =1.1×10−3 Pa·s and χw = 4.3×10−10/Pa at pressures of 28–29 MPa and a temperature of 15 °C into the above equation, we obtain e˙ max =2.0×10−4/s and 1.8×10−3/s for the clayey (C2516) and silty (C2652) mud samples, respectively. In addition, the porosities of these samples during their triaxial compression experiments at effective confining pressures of 8–9 MPa should be lower than the porosities we measured at an unconfined condition, which would result in lower e˙ max values than those estimated above. Therefore, our experimental strain rate (2.5×10 −4/s) is faster than the expected e˙ max for the clayey mud sample so that the pore pressure inside the clayey mud sample (C2516) likely increased during its triaxial compression experiment. In contrast, even if the porosity of the silty mud sample (C2652) is decreased to 20% from its original porosity of 38.5%, the estimated e˙ max is still faster than our experimental strain rate so that the pore pressure inside this sample would not have increased during its triaxial compression experiment. Triaxial compression experiments on mud samples cored during the IODP Expeditions 315 and 316 have also been conducted by Chang et al. (2010) and Kitajima et al. (2012). Chang et al. (2010) reported uniaxial compressive strength of 3.2–7.5 MPa and internal friction coefficients of 0.28–0.54 for mud samples cored at Sites C0001, C0002, C0006 and C0007 (Fig. 1). Failure envelopes drawn from these data yield failure strength of 10–22 MPa at effective confining pressures of 8–9 MPa, which is comparable to the failure strength of our samples. Kitajima et al. (2012) reported uniaxial compressive strength of 2.7–3.1 MPa for mud samples cored at Sites C0002, C0004 and C0006 (Fig. 1), which is lower than the uniaxial compressive strength reported by Chang et al. (2010). Kitajima et al. (2012) conducted triaxial compression experiments at a strain rate of ≈10−7/s three orders of magnitudes lower than that of our experiments, which may have resulted in their lower uniaxial compressive strength. 5.4. Frictional properties of mud samples Triaxial friction experiments revealed that the two mud samples tested are not only different in frictional strength, but also in slip-dependent frictional behavior (Fig. 8). Although both samples showed velocity strengthening upon a stepwise change in sliding velocity (Figs. 8 and 9), the dependence of steady-state friction on sliding velocity was quite different between the two samples (Fig. 11). These differences in frictional strength and behavior are attributable to their difference in amount of clay minerals relative to quartz and feldspar, as discussed below. The amount of clay minerals relative to the total amount of quartz, feldspar and clay minerals is 50–54 wt% in the clayey mud sample (C2516), while it is 34–40 wt% in the silty mud sample (C2652) (cf. Table 2).

71

The clayey mud sample (C2516) has low frictional strength with a steady-state friction coefficient μss ≈ 0.25 at Vaxial = 1 μm/s, while the silty mud sample (C2652) has high frictional strength with μss ≈ 0.53 at Vaxial = 1 μm/s (Fig. 8 and Table 4). Previous friction experiments on gouges of quartz–clay mixtures revealed that frictional strength decreases with increasing clay content relative to quartz (Logan and Rauenzahn, 1987; Moore and Lockner, 2011; Rutter et al., 1986; Saffer and Marone, 2003; Shimamoto and Logan, 1981; Takahashi et al., 2007; Tembe et al., 2010). The difference in frictional strength between our mud samples is therefore attributable to their difference in amount of clay minerals relative to quartz and feldspar. However, the low frictional strength of the clayey mud sample (C2516) may also be partly attributable to an increase in pore pressure inside the gouge layer during its frictional sliding, as discussed for its failure strength. The clayey mud sample (C2516) exhibited slip softening, while the silty mud sample (C2652) exhibited quasi steady-state slip (Fig. 8 and Table 4). In both direct shear experiments on gouges of quartz–smectite mixtures by Saffer and Marone (2003) and triaxial friction experiments on gouges of quartz–talc mixtures by Moore and Lockner (2011), gouges with ≥ 50 wt% smectite or talc exhibited slip softening, while gouges with b50 wt% smectite or talc exhibited steady-state slip to slight slip hardening. Such systematic change in slip-dependent frictional behavior according to the amount of clay minerals is consistent with the above difference in slip-dependent frictional behavior observed in this study. Both mud samples exhibited velocity strengthening upon a stepwise change in sliding velocity (Figs. 8 and 9). Although (a − b) values determined as the difference between the direct and evolutionary effects after a stepwise change in sliding velocity are always positive and not much different between the two samples (Fig. 10 and Table 4), the dependence of steady-state friction on logarithmic sliding velocity, Δμss / ΔlnVsliding, of the clayey mud sample (C2516) is more than three times larger than that of the silty mud sample (C2652) (Fig. 11 and Table 4). In addition, the difference between (a − b) value and Δμss / ΔlnVsliding is large for the clayey mud sample (C2516), while it is very small for the silty mud sample (C2652) (Table 4). This implies that the contribution of flow was large during the frictional sliding of the clayey mud sample (C2516), while it was very small for the silty mud sample (C2652) (see Appendix A). This is also noticed by that an asymptotic increase or decrease in μ followed after the evolutionary effect in the former, while such an asymptotic increase or decrease in μ was not obvious in the latter (Fig. 9b). Saffer and Marone (2003) reported that (a − b) values were negative at smectite contents less than 30 wt% while positive at smectite contents more than 30 wt% when the siding velocity was changed from 10 or 20 μm/s to 100 or 200 μm/s. Moore and Lockner (2011) also reported that (a − b) values were negative at talc contents less than 30 wt% while positive at talc contents more than 30 wt% when the siding velocity was changed from 0.01 μm/s to 0.1 μm/s as well as from 0.1 μm/s to 1 μm/s. Both studies also showed that gouges of quartz–clay mixtures have similar positive (a − b) values irrespective of the clay content. The two mud samples tested in this study contain clay minerals more than 30 wt% relative to the total content of quartz, feldspar and clay minerals, and their estimated (a − b) values are consistent with the results of these two studies in that (a − b) values are not only positive, but also similar in the two samples with different clay contents. If Saffer and Marone (2003) and Moore and Lockner (2011) applied a mixed friction–flow law to their friction data as done in this study, the velocity dependence of steady-state friction, Δμss / ΔlnVsliding, would be expected to increase with increasing clay content due to the increasing contribution of flow. Thus, increasing clay contents further from 30 wt% likely results in an increase in flow component, but not in an increase in (a − b) value. However, the large contribution of flow for the clayey mud sample (C2516) may also be partly due to an increase in pore pressure during its frictional sliding as discussed above.

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Friction experiments of mud samples cored at Sites C0004 and C0007 (Fig. 1) during the IODP Expedition 316 have also been conducted by Hirose et al. (2008), Ikari et al. (2009) and Tsutsumi et al. (2011). From direct shear experiments at sliding velocities ranging from 0.01 μm/s to 100 μm/s on wet gouges of mud samples cored at Site C0004, Ikari et al. (2009) reported μss = 0.37–0.47 and (a − b) = 0.0004–0.0069, both of which are within the ranges of μss and (a − b) values obtained in this study. From rotary shear experiments at sliding velocities ranging from 1 μm/s to 1 cm/s on wet gouges of mud samples cored at Sites C0004 and C0007, Hirose et al. (2008) and Tsutsumi et al. (2011) distinguished two types of frictional strength and behavior; one with lower μss (0.25–0.35) and velocity strengthening and the other with higher μss (≥0.38) and velocity weakening. The former type is comparable with the frictional strength and behavior of our clayey mud sample (C2516). In fact, a sample of this type is a clayey mud showing a very-fine-grained and homogeneous microstructure (Hirose et al., 2008). Thus, low μss ≤ 0.35 and velocity strengthening are likely characteristic of clayey mud. In contrast, another sample with higher μss (≥0.38) and velocity weakening is a silty mud rich in clastic grains, coarser-grained and more poorly sorted (Hirose et al., 2008). Ikari et al. (2012) recently reported from their direct shear experiments that (a − b) values of gouges with μss ≥ 0.5 evolve from positive (velocity strengthening) to negative (velocity weakening) with increasing displacement. Displacements in rotary shear experiments conducted by Hirose et al. (2008) and Tsutsumi et al. (2011) reached more than 25 cm. Such large displacements of silty mud gouges with high μss may have resulted in their velocity weakening behavior. This implies that our silty mud sample (C2652) with μss ≈ 0.53 may also exhibit velocity weakening after displacements larger than 25 cm. 5.5. Implications for deformation and faulting in the shallow Nankai Trough accretionary prism The contrasting hydrological and mechanical properties of the clayey and silty mud samples as revealed in this study suggest important implications for deformation and faulting in the shallow (≈1000 mbsf) mud-dominant Nankai Trough accretionary prism, as discussed below. Our permeability measurements revealed that clayey mud is relatively impermeable, while silty mud is relatively permeable (Table 4). Deformation of these mud sediments therefore would result in a possible increase in pore pressure, and hence a reduction in strength in clayey mud, which would not be seen in silty mud. Such difference in permeability between clayey and silty muds also affects the efficiency of thermal pressurization during seismic slip. Tanikawa and Shimamoto (2009) demonstrated that thermal pressurization occurs more efficiently in gouges with lower permeability. When a seismic rupture is propagated upward to the shallow accretionary prism, thermal pressurization would therefore occur more efficiently in clayey mud than in silty mud, promote strength reduction and hence enable a large displacement in the former, which may result in a tsunamigenic earthquake (e.g. Noda and Lapusta, in press). Our triaxial compression experiments revealed that clayey mud is intrinsically weak and fails slowly, while silty mud is intrinsically strong and fails rapidly (Fig. 7 and Table 4). Possible increase in pore pressure during deformation would further weaken the clayey mud and promote its slow failure, as discussed above. In the shallow accretionary mud sediments, faulting would therefore preferentially occur in the weaker clayey mud, and its slow failure may be a source of slow slip events or very low frequency earthquakes as recently found by Ito and Obara (2006). On the other hand, once the stronger silty mud is faulted, its rapid failure may become a seismic slip. Our triaxial friction experiments also revealed frictional sliding of clayey mud with low strength, strong velocity strengthening and a large contribution of flow, while frictional sliding of silty mud with high strength, weak velocity strengthening and a negligible contribution of flow (Figs. 8–11 and Table 4). Faults formed in clayey mud are

therefore weak and easily reactivated, but stable and not seismogenic. In contrast, faults formed in silty mud are strong and not easily reactivated, but possibly unstable and seismogenic. Such contrasting hydrological and mechanical properties of clayey and silty muds as revealed in this study are, however, based on the experimental results of only two samples. Further experimental study using more samples is definitely needed in order to explore how general these properties are. 6. Conclusions We present permeability measurements, and triaxial compression and friction experiments of two mud samples, which are cored at Site C0002 of the IODP Expedition 315 from the shallow (≈1000 mbsf) Nankai Trough accretionary prism, at conditions close to their in situ conditions. The results led us to draw the following conclusions. 1. The two mud samples are different in lithology; one is a clayey mud and the other is a silty mud. The clayey mud sample contains fewer clastic grains, and is poorer in quartz (≈13 wt%), richer in smectite (27–32 wt%) and uniformly fine-grained, while the silty mud sample contains abundant terrigenous clastic grains, and is richer in quartz (28–31 wt%), poorer in smectite (21–25 wt%), coarsergrained and more poorly sorted. The former has a low porosity of 11%, while the latter has a high porosity of 38%. These characteristics suggest that the clayey mud sample is of hemipelagic origin, while the silty mud sample is of turbidite origin. 2. The clayey mud sample has lower permeability of 2.92 × 10−19 m 2, while the silty mud sample has higher permeability of 2.29 × 10 − 18 m 2. Much lower porosity, finer grain size and larger clay content of the clayey mud sample than the silty mud sample make the former permeability much smaller than the latter permeability. 3. The clayey mud sample has lower failure strength of 14.2 MPa and exhibits a slow failure lasting for ≈40 s, while the silty mud sample has higher failure strength of 20.1 MPa and exhibits a rapid failure within ≈5 s. The silty mud sample is likely grain-supported and stiff, and therefore is strong and fails rapidly. In contrast, the clayey mud sample is likely matrix-supported and soft, and therefore is weak and fails slowly. In addition, the low porosity and permeability of this sample likely result in an increase in pore pressure during its compression, which may further weaken this sample and promote its slow failure. 4. The clayey mud sample exhibits slip softening and has lower frictional strength (μss ≈0.25 at Vaxial =1 μm/s), while the silty mud sample exhibits quasi steady-state slip and has higher frictional strength (μss ≈0.53 at Vaxial =1 μm/s). These differences in frictional strength and slip-dependent behavior between the clayey and silty mud samples likely arise from their difference in amount of clay minerals relative to quartz and feldspar, and also partly from a pore pressure increase in the former sample. Both samples exhibit velocity strengthening with similar positive (a−b) values upon a stepwise change in sliding velocity. However, a larger amount of clay minerals relative to quartz and feldspar as well as a possible increase in pore pressure in the clayey mud sample result in a larger contribution of flow during its frictional sliding, so that its velocity dependence of steady-state friction, Δμss /ΔlnVsliding, is more than three times larger than that of the silty mud sample. Previous friction experiments suggest that the silty mud sample with high frictional strength (μss ≈0.53) possibly exhibits velocity weakening after large displacements. 5. The contrasting hydrological and mechanical properties of the clayey and silty mud samples as revealed in this study suggest important implications for deformation and faulting in the shallow mud-dominant Nankai Trough accretionary prism. Deformation of these mud sediments results in a possible increase in pore pressure and hence in strength reduction in clayey mud, but not in silty mud. Faulting would preferentially occur in the weaker clayey

M. Takahashi et al. / Tectonophysics 600 (2013) 63–74

We used samples and data provided by the Integrated Ocean Drilling Program (IODP). KK thanks the support provided by the operation staff of D/V Chikyu and by the onboard laboratory technicians of Marine Works Japan while he was onboard D/V Chikyu. We also thank M. Shimogawara for her assisting with porosity measurements, KANAME members for their advice for thin section preparation and discussions, H. Kitajima for her advice on the potential pore pressure increase during our triaxial compression experiments, T. Mitchell and D. Saffer for their helpful reviews, and G. Di Toro for his editorial handling. This study was supported by a MEXT KANAME grant # 21107004 to MT and KK. Appendix A The rate- and state-dependent friction constitutive law proposed by Dieterich (1979, 1981) can be written as follows. μ¼

 μ ss



   V V θ þ a ln  þ b ln V Dc

ðA1Þ

where μ is friction coefficient, V is sliding velocity (μm/s), μ*ss is steady-state friction coefficient at a reference sliding velocity V*, θ is state variable (s), Dc is characteristic distance (μm), and a and b are positive constants. Second term of the right-hand side in Eq. (A1) describes the rate dependence of μ called “direct effect”, while third term describes the state dependence of μ called “evolutionary effect”. When sliding velocity is changed from V* to eV*, friction coefficient changes with sliding displacement as shown in Fig. A1a so that the direct effect is a and the evolutionary effect is b. The state variable θ is a function of time, and its time derivative is described as follows. θ˙ ¼ 1−

Vθ : Dc

ðA2Þ

˙ 0 and θ = Dc / V. Inputting this θ During steady-state sliding, θ= into Eq. (A1), we get the steady-state friction coefficient μss at sliding velocity V as follows. 

μ ss ¼ μ ss þ ða−bÞ ln



 V :  V

ðA3Þ

Velocity dependence of friction can then be described as follows. dμ ss ¼ a−b dð ln V Þ

ðA4Þ

which is equal to the difference in direct and evolutionary effects after an e-times change in sliding velocity (Fig. A1a). Frictional sliding with (a − b) > 0 is called velocity strengthening and stable, while that with (a − b) b 0 is called velocity weakening and possible unstable (Rice and Ruina, 1983). Elastic deformation of the experimental system affects the transient behavior as follows.   μ˙ ¼ k V lp −V

ðA5Þ

where Vlp is velocity of a load point and k (/μm) is machine stiffness normalized by normal stress. Eqs. (A1), (A2) and (A5) are solved

Friction coefficient µ

Acknowledgments

(a) V*

V = eV*

b a µss µ*ss

Sliding displacement d

(b) V* Friction coefficient µ

mud, and its slow failure may be a source of slow slip events or very low frequency earthquakes. Faults formed in clayey mud are weak and easily reactivated, but stable and not seismogenic. In contrast, once the stronger silty mud is faulted, its rapid failure may become a seismic slip. Faults formed in silty mud are strong and not easily reactivated, but possibly unstable and seismogenic.

73

V = eV*

b a

a

µss µ*ss

Sliding displacement d Fig. A1. Schematic diagrams showing friction coefficient μ versus sliding displacement d across a stepwise change in sliding velocity from V* to V = eV* for the rate- and state-dependent constitutive law (a) and for the mixed friction–flow law (b). See Appendix A for details.

simultaneously in order to get optimized values, a, b, Dc and k (e.g. Reinen and Weeks, 1993). In the mixed friction–flow law proposed by Takahashi et al. (2011), equations in addition to Eqs. (A2) and (A5) to be solved simultaneously are as follows. V˙flow ¼

˙ V¼

k′ V flow ðV−V flow Þ a′

    V θ˙ ′ k V lp −V −k ðV−V flow Þ−b a θ

ðA6Þ

ðA7Þ

where Vflow is flow velocity, and a′ and k′ are flow response and normalized stiffness for flow, respectively. The steady-state friction coefficient μss at sliding velocity V in this mixed friction–flow law is then given as follows.   V   ′ μ ss ¼ μ ss þ a−b þ a ln  : V

ðA8Þ

When sliding velocity is changed from V* to eV*, friction coefficient changes with sliding displacement as shown in Fig. A1b. In this mixed friction–flow law, steady-state friction is reached after a flow response of a′ following the direct and evolutionary effects of a and b (Fig. A1b). Velocity dependence of friction is then described as follows. dμ ss ′ ¼ a−b þ a : dð ln V Þ

ðA9Þ

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Optimum values of a, a′, b, Dc, k and k′ in Eqs. (A2) and (A5)–(A7) are obtained using an iterative least-squares inversion method (Noda and Shimamoto, 2009; Reinen and Weeks, 1993; Takahashi et al., 2011). References Ando, M., 1975. Source mechanisms and tectonic significance of historical earthquakes along the Nankai Trough, Japan. Tectonophysics 27, 119–140. Ashi, J., Lallemant, S., Masago, H., the Expedition 315 Scientists, 2009. Expedition 315 summary. In: Kinoshita, M., Tobin, H., Ashi, J., Kimura, G., Lallemant, S., Screaton, E.J., Curewitz, D., Masago, H., Moe, K.T., the Expedition 314/315/316 Scientists (Eds.), Proceedings of the Integrated Ocean Drilling Program 314/315/316. Integrated Ocean Drilling Program Management International, Washington, DC. http://dx.doi.org/ 10.2204/iodp.proc.314315316.121.2009. Chang, C., McNeill, L.C., Moore, J.C., Lin, W., Conin, M., Yamada, Y., 2010. In situ stress state in the Nankai accretionary wedge estimated from borehole wall failures. Geochemistry, Geophysics, Geosystems 11, Q0AD04. http://dx.doi.org/10.1029/2010GC003261. Chung, F.H., 1974. Quantitative interpretation of X-ray diffraction patterns. I. Matrixflushing method of quantitative multicomponent analysis. Journal of Applied Crystallography 7, 519–525. Dieterich, J.H., 1979. Modeling of rock friction. 1. Experimental results and constitutive equations. Journal of Geophysical Research 84, 2161–2168. Dieterich, J.H., 1981. Constitutive properties of faults with simulated gouge. In: Carter, N.L., Friedman, M., Logan, J.M., Stearns, D.W. (Eds.), Mechanical Behavior of Crustal Rocks. Geophysical Monograph, 24. American Geophysical Union, Washington, DC, pp. 103–120. Expedition 315 Scientists, 2009. Expedition 315 Site C0002. In: Kinoshita, M., Tobin, H., Ashi, J., Kimura, G., Lallemant, S., Screaton, E.J., Curewitz, D., Masago, H., Moe, K.T., Expedition 314/315/316 Scientists (Eds.), Proceedings of the Integrated Ocean Drilling Program 314/315/316. 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