Developments in Heat Transfer Part 3 docx

6.1 Effect of axial magnetic field on convective heat transfer In case of flow of liquid metals in heated channels under the influence of a uniform axial magnetic field shows a decrease

6.1 Effect of axial magnetic field on convective heat transfer

In case of flow of liquid metals in heated channels under the influence of a uniform axial magnetic field shows a decrease of convective heat transfer at low and moderate Hartmann numbers whereas the convective heat transfer and hence Nu increases at higher Hartmann numbers as shown in Miyazaki (1988) It was stated in section 4 that an axial magnetic field does not affect the mean velocity distribution so the modification of convective heat transfer

is due the variation in the turbulent fluctuations in time and space

Reynolds number Hartmann Number Nu/NuB=0

Table 2 Variation of Nusselt Number with Axial Magnetic Field, Miyazaki (1988)

The values of Nu for various value of Hartmann numbers is shown in table 2 It can be seen that the values of Nu decreases from its value, Nu/NuB=0= 1, at Ha = 0 The decrease in Nu value for small and moderate Ha is more when the Reynolds number is high because of the higher turbulence content in the flow At lower values of Reynolds numbers, the flow will

be inherently laminar and therefore the reduction in Nu due to suppression of turbulent fluctuations will be low

At high values of Hartmann numbers, the Nusselt number was found to increase, violating the earlier theories and studies, see Miyazaki (1988) Miyazaki attributes the increase in the Nusselt number is due to the increase in turbulence levels in the flow as the effect of buoyancy can be ruled out because the flow direction upwards

6.2 Effect of transverse magnetic field on convective heat transfer

The studies in the field of effect of magnetic field on convective heat transfer in ducts subjected to transverse magnetic field can be classified into two cases

1 Absence of high velocity jets near the side walls

2 Presence of high velocity jets near the side walls

6.2.1 Case 1: Absence of high velocity jets near the side walls

In case of ducts having Hartmann walls with zero conductivity, high velocity jets will not be formed near the side walls Gardener and Lykoudis (1971b) performed experiments with flow of Mercury in horizontal electrically insulated pipe subjected to transverse magnetic field It was found that the velocity profile near the Hartmann wall becomes flat with increase in magnetic field as discussed in section 4.1 and the velocity profile near side walls becomes round as discussed in sections 4.2.1 and 4.2.2 The mean velocity distribution is not much different with the increase in magnetic field, so the modification of turbulence phenomenon by the magnetic field will affect the convective heat transfer predominantly for this case The Nusselt number distribution near the Hartmann and side walls for a range of Reynolds numbers and Hartmann numbers is shown in figure 12 The decrease of Nusselt number with increase in magnetic field is lesser at lower Reynolds number because the turbulence content in the flow at low Reynolds number will be lesser

Magneto Hydro-Dynamics and Heat Transfer in Liquid Metal Flows 71

Re

Fig 12 Nusselt number with magnetic field intensity, Gardener and Lykoudis (1971b)

The reduction in Nusselt number with increase in magnetic field is because of the reduction

in turbulence quantified using turbulence kinetic energy as shown in figure 13 It was found

that the turbulent kinetic energy decreases both near the Hartmann and side walls with

increase in magnetic field where r/R = 0 represents the centre of the duct and r/R = 1

represents the walls The damping force within the Hartmann layer is much higher than at

the side region due to the high local electric current density The turbulence in core is

suppressed initially and then the turbulence in the Hartmann layer followed by the

turbulence near the side wall

Fig 13 Turbulent kinetic energy vs r/R for Re = 50,000, Gardener and Lykoudis (1971a)

A correlation for Nusselt number values is created from various experimental results by Ji

and Gardener (1997) and is given using the following relation as a function of Peclet number

Pe and Hartmann number Ha

( )

0.811 1.5

6.2.2 Case 2: Presence of high velocity jets near the side walls

In case of ducts having Hartmann walls with finite conductivity, high velocity jets will be formed near the side walls The side layers with high velocity jets (M shaped profile, figure 8 case 3) carry high mass flux is the prime reason for increase of heat transfer near the side walls Miyazaki et al (1986) performed experiments to determine the heat transfer characteristics for liquid metal Lithium flow in annular duct with electrically conducting walls under the influence of transverse magnetic fields The Nusselt number plotted with magnetic field is shown in figure 14 It can be seen that the Nusselt number increases near the side walls and decreases near the Hartmann walls A singular rise of Nusselt number can be seen near both the walls

Fig 14 Nusselt number plotted with magnetic field intensity, Miyazaki (1986)

This effect of heat transfer enhancement near the side walls is caused by the generation and

development of large scale velocity fluctuations in the near wall area The reduction in Nusselt number near the Hartmann walls is created due to the turbulence reduction as shown in figure 15

Magneto Hydro-Dynamics and Heat Transfer in Liquid Metal Flows 73

7 Application of numerical codes

A difficulty in experimental study of the flow of liquid metals arises as the visualization is not possible because of the opaque nature of liquid metals Application of closed form analytical solutions is limited to simple cases where the equations are not very complex This makes the application of numerical simulations useful for the study of liquid metal magneto-hydro-dynamic flows An example of application of a numerical code to explain the mechanisms affecting heat transfer for flow subjected to transverse magnetic field is explained using a series of simulations given in Rao and Sankar (2010), see figure 16

1.651.1

1.651.1

Height of the first cell = 1μm

Fig 16 (a) Schematic of model (b) Details of the computational mesh, Rao and Sankar (2010)

A numerical study is conducted in an annular duct formed by a SS316 circular tube with electrically conducting walls and a coaxial heater pin, with liquid Lithium as the working fluid for magnetic field ranging from 0 – 1 Tesla The Hartmann and Stuart number of the study ranges from 0 – 700 and 0 – 50 respectively The Reynolds number of the study is 104

It was shown that the convective heat transfer and hence the Nusselt number decreases near the walls perpendicular to the magnetic field due to reduction in turbulent fluctuations with increase of magnetic field It was observed that the Nusselt number value increases near the walls parallel to the magnetic field as the mean velocity increases near the walls A singular rise was observed near both the walls near Stuart number ~ 10 which is due to the increase

of turbulence levels in the process of changing from turbulent to electromagnetically laminarized flow, see figure 17

When a very low Reynolds number ~ 300 is used, the reduction in Nusselt number near the Hartmann walls is less as shown in figure 18 This shows that the reduction in Nusselt number near the Hartmann walls for the high Reynolds number study is due to the reduction in turbulent fluctuations The Nusselt number was found to increase near the side walls as the mean velocity increases near the walls When an insulating duct is used the Nusselt number near the parallel walls did not increase for the case with insulating walls as

in the case with conducting walls showing the contribution of the ‘M’ shaped velocity profile in the Nusselt number increase near the parallel walls The Nusselt number near the perpendicular walls was found to decrease at a higher rate in case of insulating walls than that of the study with conducting walls as shown in figure 19

0.6 0.8 1.0 1.2 1.4

Hartmann wall Side wall

uB=

TeslaSt

Hartmann wall Side wall

uB=

TeslaSt

Hartmann wallSide wall

Hartmann wallSide wall

Fig 19 High Reynolds number with insulating walls, Rao and Sankar (2010)

Magneto Hydro-Dynamics and Heat Transfer in Liquid Metal Flows 75

8 Application of liquid metal MHD studies in nuclear fusion reactors

International Thermo-nuclear Experimental Reactor is an international organization formed

in 1985 comprising of researchers from US, EU, China, Japan, India, Korea and Russia working towards development of a test reactor (TOKOMAK) which is expected to be developed by 2020 The test reactor will be installed in France where the head office of ITER

is situated Salient details of the reactor to be developed are shown in figure 20 The reactor height will be close to 100 ft and would weigh around 38000 tons The cryostat is the external chamber around the TOKOMK which maintains high vacuum inside it to reduce the heat load from atmosphere through conduction and convection The fusion of Deuterium and Tritium happens inside the plasma chamber The magnets are used to confine the plasma created inside the plasma chamber using a magnetic field of 4-8 Tesla

Plasma Chamber Cryostat

Central Solenoid Toroidal Magnets

Plasma Chamber Cryostat

Central Solenoid Toroidal Magnets

Fig 20 Details of the TOKOMAK

Tritium breeding modules are used in fusion reactors to produce Tritium by reacting Lithium with neutrons a byproduct of the nuclear fusion reaction The two basic breeder concepts developed by ITER are liquid breeder and solid breeders The advantages of liquid breeder over solid breeder are the high Tritium breeding ratio and the Lead-Lithium eutectic can also act as a coolant inside the breeding module which is subjected to high heat

from plasma and the heat generated in itself due to bombardment of neutrons The major disadvantages of liquid breeders over solid breeders is the pressure drop in the form of Lorentz force and the reduction in convective heat transfer characteristics of the liquid metal when it is flowing in the presence of intense magnetic field produced by the cryogenic super-conducting magnets

Wong et al (2008) has mentioned about the various liquid metal breeders being developed

around the world details of which is given in the table 3 All the liquid breeder design uses Lithium as the breeding material though most of them use a eutectic of Lead and Lithium because of the lower electrical conductivity and the neutron multiplication ability of Lead

India LLCB - Lead-Lithium Cooled Ceramic Breeder PbLi

Table 3 Details of the liquid TBM developed in the various countries, Wong et al (2008)

First Wall Pb-Li Inlet

PbLi

First Wall Pb-Li Inlet

PbLi

First Wall Pb-Li Inlet

PbLi

Fig 21 Details of LLCB- TBM, Wong et al (2008)

Magneto Hydro-Dynamics and Heat Transfer in Liquid Metal Flows 77

Indian Lead lithium Cooled Ceramic Breeder (LLCB) – The design description of LLCB is given

in Rao et al (2008) The details of the exploded and cut section views of the LLCB – TBM is

shown in figure 21 The two coolants used in LLCB are Helium and a eutectic of Lithium, Pb-Li The two coolants are of different molecular properties as Pb-Li has very low Prandtl Number of the order 10-2 and Helium gas has Prandtl number of ~0.65 The thermal diffusivity of the two fluids were different as the main temperature difference for Helium in straight ducts were concentrated at the viscous sub layer where as the temperature difference for Pb-Li was also present in the mean core region

Lead-The material of construction of the cooling channels is Ferritic-Martensitic Steel (FMS) having electrical conductivity of the order 106 1/Ώ-m, so the pressure drop associated with the flow was very high Hence a coating of Alumina (Al2O3), which has very low electrical conductivity (~10-8 1/ Ώ-m) is used on the wet surfaces of the cooling channels This makes the configuration similar to the rectangular channel of Shercliff’s case with all walls

insulating i.e dA = 0 and dB = 0 and hence as mentioned in 4.2.1, the velocity profiles will not have a high velocity jet near the side walls So the effect of turbulence modification is more significant on the heat transfer characteristics as mentioned in section 6.2.1 The flow will be electromagnetically laminarized and the heat transfer capacity of the Pb-Li deteriorates at high Hartmann numbers

9 Nomenclature

2a Distance between Hartmann walls

2b Distance between side walls

c Speed of light

dA Electrical conductivity of wall AA

dB Electrical conductivity of wall BB

keff Effective thermal conductivity

kΤ Turbulent thermal conductivity

Prm Magnetic Prandtl number

q '' Volumetric heat generation

Rem Magnetic Reynolds number

σ Electrical conductivity of fluid

η Non-dimensionalized distance in y direction

ξ Non-dimensionalized distance in x direction

ν Kinematic viscosity of fluid

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Technical Note, Washington D C., 1968

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of a magnetic field on heat transfer in a slotted channel Journal of Fusion Engineering

and Design, Vol 27, (1995), pp 587-592

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McGraw Hill, ISBN 0070220050

Gardener, R A & Lykoudis, P S (1971a) Magneto-fluid-mechanic pipe flow in a transverse

magnetic field Part 1 Isothermal flow Journal of Fluid Mechanics, Vol.47, (1971), pp

737-764

Gardener, R A & Lykoudis, P S (1971b) Magneto-fluid-mechanic pipe flow in a transverse

magnetic field Part 1 Heat Transfer Journal of Fluid Mechanics, Vol.48, (1971), pp

129-141

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9001371159

Magneto Hydro-Dynamics and Heat Transfer in Liquid Metal Flows 79

Hartmann, J (1937) Theory of the laminar flow of electrically conductive liquid in a

homogeneous magnetic field, Hg-Dynamics, Kgl Danske Videnskab Selskab

Mat.-fus Medd., Vol.15, No.6, (1937)

Hartmann, J & Lazarus P (1937) Experimental investigation of flow of Mercury in a

homogeneous magnetic field, Kgl Damske Videnskabernes Selskab, Math-,Fys Med,

Vol.14, No 7, (1937)

Hunt, J C R (1965) Magnetohydrodynamic flow in rectangular ducts Journal of fluid

mechanics, Vol 21, No 4, (1965), pp 577-590

Hunt, J C R & Stewartson, K (1965) Magnetohydrodynamic flow in rectangular ducts II

Journal of fluid mechanics, Vol 23, No.3, (1965), pp 563-581

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magnetic field International Journal of Heat and Mass Transfer, Vol.40, No.8, (1997),

pp 1839-1851

Kirillov, I R.; Reed, C B.; Barleon, L & Miyazaki, K (1994) Present understanding of MHD

and heat transfer phenomenon for liquid metal blankets, Proceedings of 3rd

International Symposium of Fusion Nuclear Technology, Los Angeles, 1994

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Publishers Group, ISBN 079230344X, Dordrecht, Boston

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characteristics under transverse field gradients Journal of Fusion Science and Technology, Vol 44, (July 2003), pp 85-93

Miyazaki, K.; Inoue, h.; Kimoto, T ; Yamashita, S.; Inoue, S & Yamaoka, N (1986)

Heat transfer and temperature fluctuation of lithium flowing under transverse

magnetic field Journal of Nuclear Science and Technology, Vol.23, (1986), pp

582-593

Miyazaki, K.; Yokomizo, K.; Nakano, M.; Horiba, T & Inoue, S et al (1988) Heat Transfer

and Pressure Drop of Lithium Flow under Longitudinal Strong Magnetic Field,

Proceedings of LIMET’88, Avignon, 1988

Moffatt, H K (1967) On the suppression of turbulence by a uniform magnetic field Journal

of Fluid Mechanics, Vol 28, (1967), pp 571–592

Muller, U & Buhler, H (2001), Magneto-fluid-dynamics in Channels and Containers (1st

Edition), Springer, ISBN 978-3-540-41253-3

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module, Report to the ITER test blanket working group (TBWG), (2008), Institute of

Plasma Research, India

Rao, J S & Sankar, H (2011) Numerical Simulation of MHD Effects on Convective Heat

Transfer Characteristics of Flow of Liquid Metal in Annular Tube Journal of Fusion

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1967, ISBN 978-0-582-44728-8

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pp 936-943

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5

Thermal Anomaly and Strength of Atotsugawa Fault, Central Japan, Inferred from Fission-Track Thermochronology

1National Research Institute for Earth Science and Disaster Prevention

2Central Research Institute of Electric Power Industry

Japan

1 Introduction

Frictional slip induces temperature rise in a fault zone Abundant frictional heat during an earthquake sometimes produces melt of rocks (i.e pseudotachylyte; e.g., Sibson, 1975) The amount of heat production along faults provides the essential information to investigate frictional strength of the faults that characterizes the earthquake generation processes Lachenbruch and Sass (1980) first estimated the coefficient of friction of the San Andreas Fault to be 0.1-0.2 from the measurement of surface heat flow along the fault Kano et al (2006) found a temperature rise of ~ 0.06 °C measured in a borehole drilled across the Chelungpu fault six years after the 1999 Chi-Chi, Taiwan earthquake associated with this fault They found that very low coefficient of friction of 0.04-0.08 can explain the heat anomaly along the Chelungpu fault The above observations along the natural faults have suggested a very low friction level compared with that of 0.6-0.8 evaluated in laboratory rock friction experiments (Byerlee, 1978)

Fission-track (FT) thermochronology is an effective method to detect heat anomaly caused

by past faulting (e.g., Scholz et al., 1979; Camacho et al., 2001; Murakami et al., 2002; Murakami and Tagami, 2004; Yamada et al., 2007a) In order to constrain the frictional properties of faults, d’Alessio et al (2003) measured apatite FT ages and lengths for samples adjacent to and within the San Gabriel fault zone that is thought to be an abandoned major trace of the San Andreas Fault system active from 13 to 4 Ma They found no evidence of a localized thermal anomaly in FT data even in samples within just 2 cm of the ultracataclasite, and concluded that either there has never been an earthquake with > 4 m of slip at this locality, or the average apparent coefficient of friction is < 0.4 based on the modelling of heat generation and transport

In this paper, we estimate the frictional strength of the Atotsugawa fault, central Japan, using the method similar to that used by d’Alessio et al (2003) In the Atotsugawa fault, Yamada et al (2009) performed FT thermochronologic analysis at an outcrop without visible pseudotachylyte layers, and revealed a thermal anomaly at a several cm thick gouge whose apatite age is significantly younger than those of other samples in the vicinity Assuming that the thermal anomaly is cause by frictional heating during a single earthquake, the frictional coefficient and the ancient depth of gouge samples are evaluated by the thermal

modelling to satisfy the constraints given by the FT thermochronological data with respect

to the geometry and alignment of the gouges in the outcrop

2 Fission-track thermochronology in Atotsugawa fault zone

The Atotsugawa fault is a right-lateral strike-slip one with a strike of N60°E and almost vertical dip, located in the Hida metamorphic belt, central Japan (Fig 1) From the trenching surveys, a number of historical large earthquakes were detected along the Atotsugawa fault; the most recent one is the 1858 Hietsu earthquake The estimate of the magnitude ranges 7.0 (Usami, 1987), 7.3 (Matsu'ura et al., 2006) and 7.9 (Doke and Takeuchi, 2009) Geographical Survey Institute, Japan (GSI; 1997) reported a creeping slip with a rate of 1.5 mm/yr in the central section of the fault

Fig 1 Distribution of active fault around the Atotsugawa fault An open circle (centre) and an open triangle (bottom left) symbols indicate the locations of an outcrop and a reference site

of R2 in Fig 2, respectively

In the creeping section, Yamada et al (2009) performed FT thermochronologic analysis by measuring ages of apatite and zircon grains separated from gouges and fractured rocks at six fracture zones within a 15 m-wide fault zone without visible pseudotachylyte layers (Fig 2a) This fault zone consists of six fault gouges (name, thickness; gouge-1, 10 cm; gouge-2, 8-

20 cm; gouge-3, 8-25 cm; gouge-4, 10 cm; gouge-5, 10-30 cm; gouge-6, 20 cm) FT ages of zircon (c 120-150 Ma) and apatite (c 44-60 Ma) for samples except "gouge-1" agree well with emplacement ages for the Funatsu granitic rocks that intruded the Hida Belt (Matsuda et al., 1998) The discordance in zircon and apatite FT ages is interpreted to reflect the rock cooling due to the regional uplift and associated erosion A thermal anomaly was identified at the gouge sample of "gouge-1" that showed an exceptionally young apatite age (32.1 ± 3.2 Ma, 1σ) with a unimodal FT length distribution, although its zircon age (121 ± 6 Ma, 1σ) was well concordant with other samples (Fig 2b; after Yamada et al., 2009) The creeping slip

Thermal Anomaly and Strength of Atotsugawa Fault,

Central Japan, Inferred from Fission-Track Thermochronology 83 observed in the central section of the Atotsugawa fault (GSI, 1997) could be a possible source for this heat anomaly Such a low slip rate of 1.5 mm/yr, however, causes much smaller increase in temperature (< 20 °C; d’Alessio et al., 2003) in the fault zone This disagreement can therefore be attributed to the secondary heating induced by frictional slip during an associated earthquake, and the young apatite age possibly gives a younger limit

of the initiation of the activity in the Hida Belt

Fig 2 (a) Sketch of the outcrop of the Atotsugawa fault zone and (b) fission-track age variation

in apatite (lower) and zircon (upper) across the outcrop (after Yamada et al., 2009) Open circle, solid circle and square symbols indicate data of fault gouge, fractured rock and host Hida metamorphic rock, respectively Dashed lines indicate locations of the fault gouge

zones Two reference samples of R1 and R2 (an open triangle in Fig 1) were also collected

where no fractures were observed Length distribution of apatite FTs for sample ATG1G is also shown Shaded bands behind the plot indicate the apatite and zircon FT age distributions

of the granitic rocks that intrude into the Hida Belt (Matsuda et al 1998) Error bars show 2σ

uncertainty in age

3 Thermal modelling associated with frictional heating and estimation of

frictional strength

In order to estimate the frictional strength of the Atotsugawa fault based on the FT

thermochronological data, we modelled the temporal change in the temperature in and out

of the "gouge-1" where an exceptionally young apatite age was found (Yamada et al., 2009)

The FT data and the geometry of the occurrence of gouges in the outcrop indicate that the

apatite FT age in the 10 cm thick “gouge-1” zone was thermally reset but that in the

fractured rock 10 cm apart from “gouge-1” was not Therefore, the model space for the thermal

modelling is composed of a central slip zone of 10 cm thickness and the surrounding rock

zone of 10 m thickness with a homogeneous temperature distribution at a certain depth in

the initial state (Fig 3) It is assumed that a single fault slip occurs at a constant rate and all

of the frictional work converts into heat One-dimensional heat transfer model is used to

describe the heat diffusion into the surrounding zone at a direction normal to the slip zone

The effect of thermal diffusion by fluid flow is not considered because hydraulic properties

of the Atotsugawa fault zone at depth have not yet been investigated

The equation of thermal diffusion with frictional heat source term for the slip zone is given

by

2 2

where T is temperature, t is the lapse time after a slip occurs, V is the slip rate of the fault, µ

is the coefficient of friction, σn is the effective normal stress on the fault, C p is the heat

capacity of rock, Wc is the width of a slip zone, k is the thermal conductivity of rock, ρr is the

density of rock, and x is the distance normal to the fault from the centre of the slip zone

The effective normal stress σn is equivalent to the effective overburden pressure given by

(ρr - ρw )·H·g, where ρw is the density of water, H is depth and g is gravity For the surrounding

zone, Equation (1) without the heat source term (i.e., the first term in the right hand side) is

used

Fig 3 Fault model for thermal calculation associated with frictional heating Distance is

measured from the centre of the fault

Thermal Anomaly and Strength of Atotsugawa Fault,

Central Japan, Inferred from Fission-Track Thermochronology 85

Table 1 Parameters used for thermal calculations

Constants of typical physical properties of rocks are used in the thermal modelling as shown

in Table 1 (c.f., Schön, 1996) W c is set as 10 cm that is equivalent to the thickness of the

“gouge-1” The initial temperature at a certain depth H is obtained from a geothermal

gradient of 30 °C/km (typical value for the upper crust in Japan; e.g., Tanaka et al., 1999)

multiplied by H plus a surface temperature of 20 °C, and the temperature distribution over

the fault zone is assumed to be uniform The boundary condition of the temperature at the edge of the model space is fixed at the initial value Total slip of 5 m long is given for this fault system because the estimate of the magnitude of the associated earthquake ranges from 7.0 to 7.9 (Usami, 1987; Matsu'ura et al., 2006; Doke and Takeuchi, 2009) that corresponds to the total slip of the order of 1-10 m, based on the empirical relationship

between the fault displacement and the magnitude (Matsuda, 1975) V is set at 1 m/s (e.g.,

Heaton, 1990) and therefore the slip duration is 5 sec Considering the closure temperature

of apatite FT (100 ± 20 °C; e.g., Wagner and Van den Haute 1992), H should be shallower

than 3 km which corresponds to the environment temperature of 110 °C, and therefore restricted to the three cases of 1, 2 and 3 km for the modelling assuming a geothermal gradient of 30°C/km (e.g., Tanaka et al, 1999)

Fig 4 Temperatures at the centre of the fault (T 0, solid line) and at 10 cm apart from the

centre (T 10, dashed line) are plotted as a function of time since a slip occurs

(a)

(b)

Fig 5 Maximum temperature at the centre of the fault (T 0; a) and at the location 10 cm apart

from the centre (T 10; b) during an earthquake are plotted as a function of friction coefficient of 0.1 ~ 0.9 in cases of depth from 1 to 3 km Square, triangle and circle symbols denote the data

at 1, 2 and 3 km, respectively Shaded areas in (a) and (b) indicate ranges of T 0 (upper) and

T 10 (lower) inferred from apatite and zircon FT thermochronological analyses, respectively

Calculation results of the temporal change in temperature at the two locations of x = 0 cm (D 0 ) and x = 10 cm (D 10 ) for the combination of µ (0.6) and H (3 km) parameters are shown as

representative cases in Fig 4 These locations are chosen to approximate the positions of the

"gouge-1" and a surrounding rock sample, respectively For any combinations of µ and H

parameters, the time during which the temperature in a specific location is maintained at its

maximum is almost invariant The temperatures at D 0 and D 10 are preserved at the

Thermal Anomaly and Strength of Atotsugawa Fault,

Central Japan, Inferred from Fission-Track Thermochronology 87

maximums of T 0 and T 10 (named T max0 and T max10) for the order of ~10^2 sec and ~10^4 sec,

as indicated by shaded bands in Fig 4, respectively Fig 5 shows the variations of T max0 and

T max10 for the combinations of µ (0.1-0.9) and H (1-3 km) parameters

Whether FTs in apatite and zircon are annealed or not depends on the temperature and duration of heating Assuming that the frictional heat caused by an associated single palaeo-earthquake event was responsible for the thermochronologic difference between the “gouge-1” and other samples, calculation results above indicate that the effective heating duration

for the samples at D 0 and D 10 at T max0 and T max10 are estimated as the order of ~10^2 sec and

~10^4 sec, respectively Note that the effective heating time is significantly longer than the slip duration, and that FTs in minerals in the distance to the frictional centre are not necessary annealed instantly due to the frictional slip event The estimates of heating durations and the kinetic relation of time-dependent FT annealing temperature of apatite and zircon (Laslett and Galbraith, 1996; Yamada et al., 2007b) give the following constraints

on the T max0 and T max10 at the secondary heating event (Yamada et al., 2009) For the D 0

sample, the fact that apatite FT age was totally reset although zircon FT age was not

indicates that T max0 is in the range of 400°C to 750°C (for the heating duration of ~10^2 sec)

For the D max10 sample, the fact that both apatite and zircon FT ages were not reset indicates

that T max10 does not exceed 250 °C (for ~10^4 sec) These constraints on T max0 and T max10 are

satisfied with the limited cases of µ > 0.6 for H = 2 km, and 0.4 < µ < 0.7 for H = 3 km, shown

as shaded areas in Fig 5

4 Discussion

The effect of the pore water is not taken into account in the modelling above If the pore water exists at the “gouge-1” zone, the temperature will be less than that in the dry condition calculated above, because the pore pressure decreases the stress applied on the fault and the frictional heat is diffused by fluid flow Therefore, the estimate of the frictional strength in the dry condition can be regarded as a lower bound The increase in the total amount of slip with the same slip velocity will considerably raise the temperature in the fault zone If the total amount of slip is doubled compared with the case for the above

calculation (= 5 m), the estimated increase in T 0 and T 10 is almost doubled and the estimate

of the coefficient of friction is reduced to almost half Even in this case, however, the estimated coefficient of friction is still large (µ > 0.3 for H = 2 km; 0.2 < µ < 0.4 for H = 3 km) compared with that of 0.1-0.2 (Lachenbruch and Sass, 1980) and 0.04-0.08 (Kano et al., 2006) Our estimates are obtained by assuming that the thermal anomaly found in “gouge-1” zone

is attributed to the frictional heating during a single earthquake associated at ~32 Ma (Yamada et al., 2009) Although a number of earthquakes should have occurred thereafter along the Atotsugawa Fault that remains active to date, an amount of heat generated by each of these quakes might be insufficient to reduce FT length in apatite because the partially annealed tracks are not observed for the "gouge-1" sample The coefficient of

friction for the earthquakes occurred after 32 Ma are, therefore, inferred as < 0.6 for H = 2

km, and < 0.4 for H = 3 km In addition, the effect of accumulated residual heat generated by

a number of earthquakes should be taken into account if the next heat generation may occur before the temperature in the fault zone is reduced to the ambient temperature due to the thermal diffusion in rocks This effect should, however, be negligible considering the recurrence interval of general active faults in Japan, ranging from 1000 to 10000 years

(Research Group for Active Faults of Japan, 1991) that would be sufficiently long for the thermal diffusion

Our modelled estimates of the coefficient of friction are approximately consistent with that obtained in laboratory friction experiments on rocks (Byerlee, 1978) As for the Atotsugawa fault, Mizoguchi et al (2007) obtained the similar frictional strength of 0.5-0.6 by laboratory friction experiments using fault gouge samples taken from the Atotsugawa borehole core samples at a depth of 326 m, located near to the FT samples of Yamada et al (2009) This coincidence of frictional strength between the nature and laboratory has rarely reported in the past In previous studies, frictional strengths of natural faults are estimated much lower than those in the laboratory (Lachenbruch and Sass, 1980; Kano et al., 2006; d’Alessio et al., 2003) At the outcrop of the Atotsugawa fault in Yamada et al (2009), however, the other five gouges were not heated enough by frictional slip to reset their ages We suggest that the frictional strengths of the fault during earthquakes when the other gouges were activated were less than that for the “gouge-1” The variety of frictional strength of fault with every event might reflect the complicated earthquake generation processes

5 Conclusions

The fission-track analysis on fault-related rocks collected from a outcrop of the Atotsugawa fault without visible pseudotachylyte layers revealed that the apatite FT age of the a gouge sample is exceptionally younger than those of the surrounding other rocks (fault gouge, fractured rocks and host rocks) in the vicinity, although the zircon FT age is well concordant with other samples To explain the thermal anomaly identified at this gouge sample, we modelled the temporal change in the temperature in and out of the gouge after an associated earthquake generated the frictional heat The calculation results indicate that the effective heating time is significantly longer than the slip duration, and that FTs in minerals in the distance to the frictional centre are not necessary annealed instantly due to the frictional slip

event The estimate of frictional strength for the “gouge-1” is larger than 0.6 for H = 2 km, and between 0.4 and 0.7 for H = 3 km, which is similar to that obtained in laboratory friction

experiments using the gouge samples taken from the Atotsugawa Fault

6 Acknowledgment

We are grateful to Drs E Fukuyama, H Negishi and N Hasebe for useful discussion and help in preparing the manuscript

7 References

Byerlee, J D (1978) Friction of rocks, Pure Appl Geophys., Vol 116, pp 615-626

Camacho, A., McDougall, I., Armstrong, R., Braun, J (2001) Evidence for shear heating,

Musgrave block, central Australia, J Struct Geol Vol 23, pp 1007-1013

d’Alessio, M A., Blythe, A E., Bürgmann, R (2003) No frictional heat along the San Gabriel fault,

California: Evidence from fission-track thermochronology, Geology Vol 31, pp 541-544

Doke, R., Takeuchi, A (2009) The latest event at the eastern part of the Atotsugawa fault, inferred

from the outcrops at Sako, Hida City, central Japan (in Japanese with English abstract),

The Quaternary Res., Vol 48, pp 11-17