A Conventional straddle-sliding-packer system as a borehole extensometer; Monitoring shear displacement of a fault during an injection test

A constant-head step injection test using a conventional straddle-packer system was performed for a normal fault in siliceous mudstone. The test applied a new method whereby axial displacements of isolated test sections in a borehole during injection are monitored by measuring the pressures of sliding packers and the pore pressure in the test section. The measured pressures and axial displacement, and the injection ﬂ ow rate, were used to estimate the hydraulic aperture, shear displacement, normal compliance, normal stress, shear sti ﬀ ness and hydraulic dilation angle of the fault during the test. The injection successfully yielded a large shear displacement during normal faulting of up to 13.3 – 49.5 mm (including the estimation error), which left residual shear displacement of 2.8 – 10.4 mm after a remarkable shear-slip event. The shear sti ﬀ ness during faulting is estimated to be 2.3 × 10 7 to 8.4 × 10 7 Pa m − 1 (considering the estimation error), which is consistent with empirically predicted values based on previous studies. The hydraulic dilation angle was inferred to be e ﬀ ectively zero as the residual shear displacement did not leave any increase in hydraulic aperture. The experimental method applied here does not require specialized equipment and could aid in the investigation of the hydromechanical behavior of subsurface fractures or aquifers.


Introduction
The safe disposal of radioactive waste must consider host-rock permeability following closure of the underground repository.The host rock is likely to include some (minor) faults, whose transmissivities must be properly assessed.A conservative assessment must consider any possible increase in transmissivity that could occur following fault reactivation, for example caused by thermal-hydro-mechanically induced shear stresses and thermal pressurization due to the release of heat from radioactive waste (Birkholzera et al., 2019;Rutqvist, 2020;Rutqvist and Stephansson, 2003;Urpi et al., 2019).
According to the parallel-plate model (cubic law) of Snow (1968), the transmissivity T of a fracture (m s −2 ) can be related to the hydraulic aperture of the fracture δ H (m) as follows: where ρ w is the density of water (kg m −3 ), g is the acceleration due to gravity (m s −2 ), and μ is the dynamic viscosity of water (Pa s).The hydraulic aperture increment Δδ h (m) during shearing is expressed as follows: where Δu s is the shear displacement increment (m), and d h is the dilation angle for hydraulic aperture (°) (McClure and Horne, 2014a).Therefore, if a fault is artificially sheared, in situ measurement of the hydraulic dilation angle at that time can help to assess a possible increase in the fault's transmissivity during fault reactivation.
Artificially induced fault reactivation due to increasing groundwater pressure has been observed in earthquakes that were triggered by wastewater fluid injection (Ellsworth, 2013;Healy et al., 1966;Hsieh and Bredehoeft, 1981).Recently, numerous injection activities have been carried out on a large scale for a variety of purposes such as geothermal exploitation, natural oil/gas production, and geological carbon storage, where artificially induced fault reactivation has been observed and focused in terms of seismic hazard (Davies et al., 2013;Dempsey et al., 2015;Evans et al., 2005;McClure and Horne, 2014b;Rutqvist et al., 2015;Tezuka and Niitsuma, 2000;Vilarrasa et al., 2019;Zakharova and Goldberg, 2014).Small-scale injection tests are also actively conducted in underground research laboratories, where detailed hydromechanical behavior of faults is carefully studied by artificially inducing fault reactivation (Guglielmi et al., 2015a(Guglielmi et al., , 2015b(Guglielmi et al., , 2017(Guglielmi et al., , 2020;;Jeanne et al., 2018).Based on these previous activities/ tests, small-scale injection testing is expected to be a useful technique to investigate the hydraulic dilation angle of faults (cf., Guglielmi et al., 2015b;Nguyen et al., 2019).However, measuring the shear displacement during injection typically requires specialized equipment such as a borehole extensometer (Schweisinger et al., 2007), a borehole tiltmeter (Burbey et al., 2012), or a three-component borehole deformation sensor (Guglielmi et al., 2014).
This work reports the results of an injection test using a conventional straddle-sliding-packer system performed on a fault in Neogene siliceous mudstone from the Wakkanai Formation in the Horonobe area of Hokkaido, Japan (Fig. 1a).During testing, a new method was applied in which shear displacement along the fault during injection was monitored by measuring water pressure in the sliding packers.This method does not require specialized equipment and can be employed along with the usual hydraulic tests, as described below.

Materials
In the Horonobe area, borehole investigations and the construction of an underground facility have been ongoing since 2001 for research and development relevant to radioactive waste disposal.Consequently, conductive faults have been found within the Wakkanai Formation (Ishii, 2015;Ishii et al., 2011), although their hydraulic connectivity in the deeper parts of the formation (generally deeper than 400 m below ground level, mbgl) is limited (Ishii, 2018).The injection tests were performed on a fault (shear fracture) at 99.5 m along the borehole (mabh; 479.3 mbgl) in vertical borehole 350-FZ-02 (borehole length 119.7 m; drilling diameter 101 mm; drillcore diameter 63.5 mm) that was drilled from the bottom face (380 mbgl) of the East Shaft in the underground facility (Fig. 1b).This depth corresponds to the uppermost level of the lower Wakkanai Formation where the hydraulic connectivity of faults is limited (Ishii, 2018).
In situ stress measurements in boreholes (HDB-1, −3, and − 6) near the underground facility showed the far-field maximum principal stress to be oriented E-W and the stress regime to be generally characterized by reverse/strike-slip faulting (Fig. 3; Sanada et al., 2010Sanada et al., , 2012)).However, a normal faulting stress regime (E-W-directed horizontal maximum principal stress) was also observed within a range of decameters from the test section (HDB-6_416.0 m in Fig. 3), which is consistent with the sense of displacement of the fault (Fig. 2d).The pore pressure around the test section before excavation of the underground facility and subsequent pumping was ~4.9 MPa (Yoshino et al., 2015), but dehydration due to the pumping has reduced this to the current value of 3.9-4.5MPa.

Injection
A constant-head step injection test was performed on the fault for two days (29 and 30 October 2018).The test used a conventional straddle-sliding-packer system and considered the section from 87.8 to 101.9 mabh (467.7-481.7 mbgl) (Fig. 1b).A plunger pump (plus an accumulator tank) was used for injection, and the water pressure in the test section (called "the test-section pressure") was increased and decreased in steps of ~0.5 MPa while the test-section pressure was manually controlled by adjusting a regulating valve on the pump (i.e., adjusting the injection flow rate) at 350 mbgl (Fig. 1b).During each step, water injection was continued at a constant head until the flow rate was nearly stable.During pressure decrease steps, the test-section pressure was forcibly decreased by opening the regulating valve.At this time, back-flows occasionally occurred into the water tank at 350 mbgl.Stainless steel rods (outer diameter 41 mm; inner diameter 34 mm) with strainers (plus a pressure-resistance hose) were used as an injection line into the test section to reduce pressure loss during injection (Fig. 1b), and the injection flow rate was monitored by a mass flow meter installed on the downstream side of the pump at 350 mbgl.The test-section pressure, and the water pressures in the upper and lower packers (called "the upper-packer pressure" and "the lower-packer pressure", respectively), were monitored by pressure sensors installed at 350 mbgl, connected by poly-ether-ether-ketone (PEEK) tubes (length 150 m).The recording interval was 1 s.After the 29th of October injection, the test section was shut in, and the test-section pressure recovered under natural conditions.

Function of the packer system
Sliding packers with a tube length of 0.9 m were used.The packers are inflated with water, and the bottom end slides as the packer tube expands, while the top end is fixed (Fig. 4a).When a sliding packer is inflated in a borehole and the top end is pulled upward, the packer tube is extended upward and the volume of the packer increases, reducing the packer pressure (Fig. 4b).Conversely, when the top end is pulled downward, the packer tube is shortened, the volume of the packer reduces, and its pressure increases (Fig. 4c).However, when the borehole wall is elastically soft, shortening the packer tube expands the borehole wall, and the packer pressure decreases.This is because the packer rubber contains steel wire fabric with a constant stiffness.
The displacement of the packer's top end (Δu p , m, positive sign when the top end is pulled upward), the change in its pressure (Δp p , Pa), and the axial force increment (ΔF, N, positive sign when the top end is pulled upward) can be related as follows:  measured by the hydraulic fracturing method, and the vertical (overburden) stress (σ v ) calculated using rock density in boreholes HDB-1, −3, and − 6 located near the underground facility (Sanada et al., 2010(Sanada et al., , 2012)).The distance between the injected fault zone in 350-FZ-02 (−419.3masl, meters above sea level) and the location of HDB-6_416.0m (−355.8masl) is 64 m.
where the coefficients a and b can be determined from a laboratory experiment (N m −3 and m N −1 , respectively), V p is the volume of the packer plus PEEK tubes filled with packer water (m 3 ), and c p is the compressibility of water (Pa −1 ).

Laboratory experiment to determine coefficients a and b
During the laboratory experiment, the packer was inflated in pipes that have the same inner diameter as the borehole (~104.5 mm for the upper packer and ~103.9 mm for the lower packer, as measured by caliper logging) and the same elasticity as the borehole wall.Inflation continued until the packer pressure was similar to that used during the in situ injection test, and at that stage the top end of the packer was pulled to the top or to the bottom by a jack (Fig. 4b, c).Following this, the coefficients a and b were determined from the measured displacement of the top end, the change in packer pressure, and the axial force increment (Fig. 4b, c).
The pipes were selected based on the following equation derived from the theory of linear elasticity for isotropic media: where r p is the pipe inner radius (m), Δr p is the change of r p (m), Δp p is an increment of the packer pressure (Pa), and E p , ν p , and t p are Young's modulus (Pa), Poisson's ratio, and thickness (m) of the pipe, respectively.Assuming infinite thickness for the borehole wall gives the following: Here, r w is for the borehole, and is 0.052 m; E and ν are for the borehole wall, and are 1-5 GPa and ~0.2, respectively, according to the results from previous laboratory tests and in situ pressuremeter tests (Miyazawa et al., 2011;Niunoya and Matsui, 2007).Generic acrylic pipe (E = 3.0 GPa, ν = 0.36, inner diameter 52.5 mm, thickness 10 mm) and generic aluminum pipe (E = 68.6GPa, ν = 0.34, inner diameter 52.0 mm, thickness 3 mm) were selected based on Eqs. ( 5) and ( 6).They are equivalent to a borehole with walls having E = 0.6 and 4.5 GPa, respectively, assuming ν = 0.2.Thus, these pipes represent the possible upper and lower limits of the elastic stiffness of the borehole wall, and the effective coefficients a and b for the borehole wall are expected to be within the ranges of the coefficients for these model pipes.Fig. 4d-i shows the results of the laboratory experiment; the values of aV p c p and b are −0.232N Pa −1 and 4.86 × 10 −8 m N −1 for the acrylic pipe and − 0.092 N Pa −1 and 4.09 × 10 −8 m N −1 for the aluminum pipe, respectively, when the top end is pulled upward (Fig. 4d, f).When the top end is pulled downward, these values are 0.154 N Pa −1 and 1.84 × 10 −7 m N −1 for the acrylic pipe and − 0.054 N Pa −1 and 1.17 × 10 −7 m N −1 for the aluminum pipe, respectively (Fig. 4e, g).The coefficient a can be derived from these results using the known compressibility of water c p and the volume of packer water V p during the laboratory experiment (5 × 10 −10 Pa −1 and 1.3 × 10 −3 m 3 , respectively).When the top end is pulled upward a is −3.56 × 10 11 N m −3 for the acrylic pipe and − 1.41 × 10 11 N m −3 for the aluminum pipe.When the top end is pulled downward it is 2.36 × 10 11 N m −3 for the acrylic pipe and − 0.83 × 10 11 N m −3 for the aluminum pipe.Although the displacement increased nonlinearly during the first axial force increment up to 1-2 kN when the top end was pulled downward (Fig. 4g), this initial increase was small enough to be ignored.As a result, the gray zones shown in Fig. 4d-i represent the possible ranges for the relationships between the displacement of the packer's top end, the change in packer pressure, and the axial force increment during the injection test.

Calculation of axial displacement of the test section during injection
The change in test-section length during injection (Δl, m) is defined as follows: where Δu pu and Δu pl are the displacements of the upper and lower packers' top ends (m), respectively.The displacement of the top end of the packer that is pulled upward can be calculated from the change in its packer pressure and the coefficients a and b (i.e., the combinations of −3.56 × 10 11 N m −3 and 4.86 × 10 −8 m N −1 for the acrylic pipe and of −1.41 × 10 11 N m −3 and 4.09 × 10 −8 m N −1 for the aluminum pipe) (Fig. 4d, f).On the other hand, the displacement of the top end of the packer that is pulled downward cannot be determined from the change in its packer pressure.This is because the two empirical lines (i.e., the gray zone) shown in Fig. 4e do not provide constraints on axial force increments during changes in packer pressure.However, the displacement can be calculated from the change in packer pressure for the other packer whose top end is pulled upward, because the scalars of axial force increments imposed on the two top ends of the upper-and lower-packers during testing are always the same.Therefore, the used coefficients a and b are the combinations of −3.56 × 10 11 N m −3 and 1.84 × 10 −7 m N −1 for the acrylic pipe, and − 1.41 × 10 11 N m −3 and 1.17 × 10 −7 m N −1 for the aluminum pipe (Fig. 4d, g).In summary, Δl (m) can be calculated from the following equation: where a ⁎ is the coefficient for the packer whose top end is pulled upward (i.e., −3.56 × 10 11 N m −3 for the acrylic pipe and − 1.41 × 10 11 N m −3 for the aluminum pipe), b u and b l are the coefficients for the upper and lower packers (m N −1 ), respectively, (b u + b l ) is 2.33 × 10 −7 m N −1 for the acrylic pipe and 1.58 × 10 −7 m N −1 for the aluminum pipe, V p is the volume of packer water during the injection test (i.e., 3.2 × 10 −3 m 3 considering the PEEK tubes of 150 m), c p is the compressibility of water (i.e., 5 × 10 −10 Pa −1 ), and Δp p ⁎ is the change in packer pressure for the packer whose top end is pulled upward.The criteria for judging which packer's top end is pulled upward are summarized in Table 1.
As the packer pressure can also change during elastic expansion/ contraction of the packer tube due to changes in test-section pressure, it is necessary to remove this effect by identifying the linear relationship between the packer pressure and test-section pressure during lowpressure phases of injection to the fault (or intact rock).Strain of the stainless steel rods is disregarded because steel is more resistant to strain than the packer.

Estimation of shear displacement along the fault during injection
Shear displacement along the fault during injection (Δu s , m, positive sign when the sense of displacement is normal faulting) is defined by the following equation: where Δδ m is the mechanical (or void) aperture increment of the fault (m), θ is the dip angle of the fault (i.e., 71°), and Δl is the change in testsection length (m) calculated from Eq. ( 8).This equation assumes a simple geometry, ignoring any tilt of the borehole during the test.In addition, the equation gives a minimum estimate of the possible shear displacement, because the strike-slip component cannot be measured by this method.
The mechanical aperture δ m can be related to the hydraulic aperture δ h by the following equation (Barton et al., 1985): where JRC 0 is the joint roughness coefficient (JRC) on the laboratory scale.The units of δ m and δ h in this equation are microns, and this equation is only valid for δ m ≥ δ h .When the δ m value calculated from δ h is smaller than the δ h value, the δ m value is assumed to be the same as the δ h value (Barton, 1982).Although numerous correlations between δ m and δ h have been proposed (see reviews by Li et al., 2019;Shahbazi et al., 2020;Sun et al., 2020), Eq. ( 10) is one popular correlation (Li et al., 2014;Pan et al., 2010;Zhan et al., 2016).
The hydraulic aperture δ h can be calculated from the transmissivity of the fault, based on Eq. (1).To estimate the transmissivity of the fault, the test-section pressure and injection flow rate were analyzed using well test analysis software (nSIGHTS, n-dimensional Statistical Inverse Graphical Hydraulic Test Simulator; Beauheim et al., 2014;Nuclear Waste Management Program, 2011).This program simulates a singlephase, one-dimensional radial/non-radial flow regime or a two-dimensional radial flow regime, with a borehole at the center of the modeled flow system.The present study determined the transmissivity of the test section for each injection step by fitting the measured and simulated flow rates, while the simulation considered entire injection sequences as the pressure history (Fig. 5).The fault was modeled as a 0.1 m thick, homogeneous, horizontal and infinite aquifer, where a transient, radial, and laminar flow was assumed.The fitting parameters were the fault transmissivity, fault storativity, static formation pressure, and test-section compressibility, and the last two parameters were given narrow fitting ranges near the best estimates based on measurement data as follows.The best estimate of the static formation pressure during each injection step was given as follows: (1) the mean test-section pressure and the mean injection flow rate during the last minute of each injection step were measured and plotted, (2) regression lines were derived from the intervals showing a linear relationship between the test-section pressure and injection flow rate, and (3) the pressure on the regression lines for zero injection flow rate was given as the best estimate of the static formation pressure during each step (cf., Huang et al., 2018).The best estimate of the test-section compressibility was 2.38 × 10 −10 Pa −1 based on data from a pulse test.
The JRC 0 of the fault can be calculated based on the maximum height of the fracture-surface profile (R z , mm; equal to the vertical distance between the highest peak and the lowest valley in the profile) (Li and Zhang, 2015).Although numerous methods for determining JRC 0 have been proposed, the method using R z is simple and practical, and less sensitive to the problem of the sampling interval of data points (e.g., Bao et al., 2020;Liu et al., 2017;Zheng and Qi, 2016), according to Li and Zhang (2015).Four profiles parallel to the striations on the fault surface were traced using a profile gauge, which resulted in R z of 0.3-0.7 mm.These values can be converted to a JRC 0 of 2-4 using the following empirical equation (Li and Zhang, 2015): In this study, the JRC 0 of the fault was assumed to be 3 (JRC 0 is commonly within 0-20 and higher JRC 0 indicates rougher surfaces).

Assessment of axial/normal compliance and normal stress
Assessing the compliance of equipment is important, as it may restrict the normal displacement of the fault.The axial compliance of equipment can be used as a measure of its compliance, and it should be greater than the normal compliance of the tested fault.From Eq. ( 4), the axial compliance C a (m Pa −1 ) of the packer system is given by the following equation: where Δu pu and Δu pl are the displacements of the upper and lower packers' top ends (m), respectively, r w is the borehole radius (m), ΔF is the axial force increment (m), and b u and b l are the coefficients in Eq. ( 4) for the upper and lower packers (m N −1 ), respectively.As (b u + b l ) is 1.58 × 10 −7 m N −1 for the acrylic pipe and 2.33 × 10 −7 m N −1 for the aluminum pipe (Fig. 4f, g), and r w is 0.052 m, the axial compliance of the packer system is estimated to be between 1.3 × 10 −9 and 2.0 × 10 −9 m Pa −1 .The normal compliance of the fault C n (m Pa −1 ) is defined as follows: where δ m is the mechanical fracture aperture (m) and σ' n is the effective normal stress (Pa).The σ' n is given as follows: where σ n is the total normal stress (Pa), α is the effective stress coefficient (or Biot's coefficient), and p is the pore pressure (Pa).The coefficient α is assumed here to be 1, as usual for a fracture.The σ n can be approximated to the test-section pressures below which the back-flows occurred during the pressure decrease steps after high-flow-rate injection (Rutqvist and Stephansson, 1996).This appoximation can be further optimized from the relationship between the test-section pressures p and the mechanical aperture δ m during injection, as the effective normal stress σ' n (Pa) and the mechanical aperture of a sheared fracture δ m (m) can be expressed as the following semi-log relationship (Bandis et al., 1983): where q is a coefficient (Pa m −1 ).Parametric analysis of σ n to minimize the negative correlation coefficient between log 10 σ' n and δ m results in a regression line between log 10 σ' n and δ m that gives the best estimates for σ n and q.Using this result, Eq. ( 13) can be further developed to give the following equation (Bandis et al., 1983): Note that this model assumes normal displacement upon fractures that occurs as a result of changes in effective normal stress, regardless of shear-induced dilation.As the effective change in fracture aperture during injection tests may also include a component of shear-induced dilation (Hsiung et al., 2005;Lei et al., 2016;Rinaldi and Rutqvist, 2019), the normal compliance derived from Eq. ( 16) may overestimate the normal compliance of the fault.However, the estimated σ n is reliable, as the σ' n at which the mechanical aperture asymptotically increases according to Eq. ( 15) is largely insensitive to the component of shear-induced dilation.

Test-section pressure and injection flow rate
The changes in test-section pressure and injection flow rate during injection are summarized as follows.Although the flow rate increased linearly from 0 to 397 mL min −1 , and the test-section pressure increased from 3.9 to 5.5 MPa (tests 1-3 in Figs.6a and 7a), the flow rate increased non-linearly when the test-section pressure increased to 6.0 MPa, and the flow rate was 1584 mL min −1 when the test-section pressure was 6.1 MPa (test 4 in Figs.6a and 7a).Then, as the testsection pressure decreased and increased, the test-section pressure and the flow rate again changed linearly (tests 5-9 in Figs.6a and 7b) (the back-flow occurred when the test-section pressure decreased to 6.04 MPa after test 4).The flow rate again increased non-linearly when the test-section pressure increased to 6.0 MPa, increasing the flow rate from 238 to 1479 mL min −1 (test 10 in Figs.6a and 7b).Further increasing the test-section pressure to ≥6.1 MPa further increased the flow rate (7473 mL min −1 : test 11 in Figs.6a and 7b).As injection continued, the test-section pressure suddenly dropped by 0.5 MPa (from 6.09 to 5.61 MPa) during a period of 22 s (event A in Fig. 6a) without a significant change in the flow rate (Fig. 6a).Then, the test-section pressure stabilized at ~5.6 MPa after some fluctuations (test 12 in Fig. 6a), and the flow rate varied non-linearly (tests 12-17 in Figs.6a  and 7c) (after tests 12 and 13, the back-flows occurred when the testsection pressure decreased to 5.52 MPa and 5.51 MPa, respectively).After test 17, the test section was shut in, and its pressure recovered under natural conditions.The next day, reinjection into the test section showed the same results as those of the previous day; that is, the flow rate increased linearly with test-section pressure up to 4.9 MPa (tests 18-20 in Figs.6b and 7d), and then increased non-linearly when the test-section pressure was ≥5.3 MPa (tests 22-25 in Figs.6a and 7b) (the back-flow occurred when the test-section pressure decreased to 5.55 MPa after test 25).

Packer pressures and axial strain of the test section
Injection caused changes in the upper-packer pressure.Here, changes are described only after test 5, because the change in packer pressure during the early phase of the test was mainly affected by the additional inflation performed from 2300 s after the start (Fig. 6a).When the test-section pressure was ≤6.0 MPa, the packer pressure changed linearly with varying test-section pressure on account of the elastic response (tests 5-10 in Figs.6a and 8a).At this time, the elastic relationship between the packer pressure and test-section pressure was as follows (Fig. 8a where p p and p are the packer pressure (Pa) and test-section pressure (Pa), respectively.When the test-section pressure increased to ≥6.0 MPa, the packer pressure decreased.After the packer pressure decreased by 0.06 MPa during test 11, it suddenly dropped by 0.19 MPa during event A (Figs. 6a and 8a).It then slowly decreased by 0.18 MPa and stabilized at 6.6 MPa with no significant change in the test-section pressure during test 12 (Figs.6a and 8a).After that, when the testsection pressure was approximately > 5.0 MPa, the packer pressure began to change inversely with the test-section pressure during tests 13-25 (Figs. 6 and 8a, b).
For the lower-packer pressure, an elastic response was observed following changes in the test-section pressure, similar to the upperpacker pressure (Figs.6a and 8c).However, it did not show the remarkable changes as observed in the upper-packer pressure after test 11 (Figs.6a and 8c).After test 17, the lower-packer pressure decreased significantly owing to a leak from a connector in the PEEK tubes (Fig. 8c).This leak might have started to occur intermittently during injection and could have decreased the lower-packer pressure slightly, as a slight decrease was observed with time (Fig. 8c).During tests 18-25, the lower packer was inflated only to maintain hydraulic isolation of the test section.Its pressure during these tests is therefore not shown in Fig. 6b.
The upper-packer pressure significantly decreased, while the lowerpacker pressure remained almost constant, except for the elastic response following changes in the test-section pressure (Fig. 8).Such changes in packer pressures indicate that the test section shortened and the upper packer's top end was pulled upward during the test (Table 1).By removing the elastic component due to the change in the test-section pressure using Eqs.( 17), ( 8) can be expressed as follows: where a u is the coefficient in Eq. ( 3) for the upper packer (i.e., −3.56 × 10 11 N m −3 from the acrylic pipe and − 1.41 × 10 11 N m −3 from the aluminum pipe), b u and b l are the coefficients in Eq. ( 4) for the upper and lower packers, respectively (i.e., b u + b l = 1.58 × 10 −7 m N −1 from the acrylic pipe and 2.33 × 10 −7 m N −1 from the aluminum pipe), V p is the volume of packer water during the in situ injection test (i.e., 3.2 × 10 −3 m 3 ), c p is the compressibility of water (i.e., 5 × 10 −10 Pa −1 ), p pu is the upperpacker pressure (Pa), and p is the test-section pressure (Pa).
Fig. 6 shows the calculated shortening of the test section, where the maximum estimate represents the values calculated using the coefficients a and b for the acrylic pipe, while the minimum estimate gives the values calculated using the coefficients for the aluminum pipe.This shortening can be attributed to shear movement along the fault by normal faulting, as other factors cannot be considered.

Hydraulic aperture increment of the fault
The best estimate of the static formation pressure at each injection step is 3.85 MPa for tests 1-4, 4.49 MPa for tests 5-11, and 4.38 MPa for tests 18-25, based on the regression lines in Fig. 7.For tests 12-17, a pressure of 4.38 MPa based on tests 18-25 was assigned because no linear relationship between the test-section pressures and injection flow rates was identified from tests 12-17 (Fig. 7c).According to these assumed static formation pressures, the transmissivities of the test section for tests 1-4, 8-11, and 18-25 were estimated as shown in Fig. 9a (pressure-decrease steps in tests 5-7 were not calculated, considering the back-flows observed during the tests).Furthermore, applying Eq.
(1) to those transmissivities, the hydraulic apertures of the fault at different test-section pressures were calculated as shown in Fig. 9b.Results are as follows: • A significant increase in hydraulic aperture was observed at high test-section pressure (Fig. 9b).
• The test-section pressure at which the hydraulic aperture asympto- tically increases was ~6.1 MPa before event A and ~5.6 MPa after event A (Fig. 9b).
• The hydraulic apertures at low test-section pressures before and after event A are similar (Fig. 9b).

Shear displacement along the fault
For tests 8-25 where the packer pressures and the hydraulic apertures were evaluated, the total shear displacement of the fault during the last 10 s of each injection step (Δu s , m) was calculated by Eq. ( 9).The mechanical aperture δ m of the fault was calculated by applying Eq. ( 10) (all δ m were assumed to be equal to δ h because all the δ m calculated from δ h were smaller than the δ h ).The calculated total shear displacement is plotted in Fig. 9c.The main results concerning the shear displacement are as follows: • The calculated total shear displacement has a maximum of 13.3-49.5mm (Fig. 9c).
• The total shear displacements at low test-section pressures after event A confirmed a residual shear displacement of 2.8-10.4mm after event A (Fig. 9c).
• The onset of shearing occurred at a test-section pressure of ~6.0 MPa before event A, while after event A the onset occurred at a test-section pressure of ~4.7 MPa (Fig. 9c).

Normal compliance and normal stress
The relationship between fault displacement and test-section pressure was different before and after event A (section 4.3 and 4.4); the test-section pressure at which the hydraulic aperture asymptotically increases decreased after event A (Fig. 9b), and the test-section pressure at which the onset of shearing occurs also decreased after event A (Fig. 9c).This observation indicates a possibility that normal and shear stiffnesses of the fault both decreased after event A, indicating that a loss of cohesion occurred at cohesive asperities (e.g., healed part) within the fault through event A (cf., the break-up of a fracture: Rutqvist, 2015;Rutqvist and Stephansson, 1996).Given the possibility that the fault was partly cohesive before event A, the back-flow method described in section 3.6 and the empirical method using Eqs.( 15) and ( 16) might not be valid to estimating the normal stress acting across the fault before event A, as those methods basically assume a cohesionless fracture.Therefore, this study estimated only the normal stress and normal compliance of the fault after event A as below.
After tests 12, 13, and 25, the back-flows occurred when the testsection pressure decreased to 5.51, 5.52, and 5.55 MPa, respectively (section 4.1).These pressures are very close to each other and are inferred to represent the normal stress across the fault.For each pressure, the regression line was derived as shown in Fig. 10a by applying Eqs. ( 14) and ( 15) to the mechanical aperture δ m and test-section pressure p, which resulted in the best estimate of 5.55 MPa for σ n to minimize the  negative correlation coefficient between log 10 σ' n and δ m (the correlation coefficients were − 0.91, −0.96, and − 0.97 for σ n of 5.51, 5.52, and 5.55 MPa, respectively).From the slope of the regression line at σ n = 5.55 MPa (Fig. 10a) and Eqs. ( 15) and ( 16), the normal compliance of the fault after event A was estimated as shown in Fig. 10b and was found to be significantly smaller than the axial compliance of the packer system.

Reliability of shear displacements estimated using the applied packer method
The lower-packer pressure did not change significantly during the test, except for the elastic response following changes in test-section pressure (Figs. 6 and 8c).This observation is compatible with results from the laboratory experiment (Table 1) showing that one packer may remain constant while the pressure in the other packer decreases (as shown by the gray zones in Fig. 4h, i).Furthermore, the estimated shortening of the test section reflects shear movement along the fault in the sense of normal faulting (section 4.2), which is consistent with the previous displacement interpreted from observations of drill cores (Fig. 2d).
The estimated shear displacement (Fig. 9c) is considered reliable because the measured and empirically predicted shear stiffnesses of the fault (K s , Pa m −1 ) are consistent, as described further below.The measured K s during tests 18-24 (i.e., the pressure-increase step when the test-section pressure was less than the total normal stress across the fault on 30th October 2018) can be defined as follows (Guglielmi et al., 2014): where Δτ, Δu s , and Δp ⁎ are the excess-shear-stress increment (Pa), shear-displacement increment (m), and pressure increment (Pa), respectively, and ϕ is the friction angle of the fault (°).Here, those increments are defined as the increments from test 18 to test 24.The ϕ can be estimated by the following equation (Barton et al., 1985): where JRC and JCS are, respectively, the joint roughness coefficient and joint wall compressive strength (Pa) at an in situ scale, and ϕ r is the residual friction angle (°).The JRC and JCS can be related to values at a laboratory scale using the following equations (Barton et al., 1985): where L is the length of the fracture (m), and JRC 0 and JCS 0 are those values for L = 0.1 m.For unweathered fractures, JCS 0 and ϕ r are equal to the unconfined compressive strength of the intact rock (UCS) and the basic friction angle ϕ b , respectively, and ϕ b can be obtained from tilt tests performed on samples with saw-cut surfaces (Barton and Choubey, 1977).Adopting the following parameters: ϕ b = ~26°(results from the tilt tests); L = 0.1-10.0m (assumption); JRC 0 = 3 (section 3.5); and UCS = 22.4 MPa (section 2), and by approximating the friction angle ϕ to be 32°based on Eqs. ( 21)-( 23), the measured K s during tests 18-24 is calculated to be 2.3 × 10 7 to 8.4 × 10 7 Pa m −1 using Eqs.( 19)-( 20).
The empirically predicted K s during tests 18-24 is defined as follows (Barton and Choubey, 1977): where u sp is the shear displacement required to reach the peak shear strength (m).The u sp can be derived from the following empirical equation suggested by Asadollahi and Tonon (2010): By using Eqs.( 24) and ( 25) with the effective normal stress at test 24, the empirically predicted K s is calculated to be 0.8 × 10 7 to 7.1 × 10 7 Pa m −1 , which is comparable to the measured K s .The clearance of ≥32 mm between the test rod and borehole wall in the test section (as measured by caliper logging; the borehole diameter is mostly ~104 mm in the test section but is enlarged up to ~124 mm near the fault due to the fault damage) is also sufficient to accommodate relatively large shear displacements during normal faulting at a dip angle of 71°(the maximum possible accommodation is ≥98 mm).Therefore, the estimated shear displacement is considered to be reliable.The estimated maximum shear displacement of 13.3-49.5mm (Fig. 9c) is very large and comparable to the maximum of previously reported values (centimeters or less) for injection tests in other fields (De Barros et al., 2016;Derode et al., 2013;Evans et al., 2005;Guglielmi et al., 2015aGuglielmi et al., , 2015bGuglielmi et al., , 2017;;Jeanne et al., 2018).

Applicability of the packer-pressure-based extensometer
This study has developed and demonstrated a new method for monitoring axial displacements of isolated test sections in a borehole during injection by utilizing sliding-packer pressures.However, the method has some disadvantages that are outlined below.
• The estimation error is large, as shown in Fig. 6.
• Whether the test section lengthens or shortens cannot be determined by changes in packer pressure when the upper and lower packerpressures both decrease by similar amounts (e.g., the case of 0.6 ≤ Δp pu /Δp pl ≤ 1.5 in Table 1 for this study).
• When the normal compliance of the fault is comparable to the axial compliance of the packer system (~2 × 10 −9 m Pa −1 in this study), the equipment may restrict normal displacement on the fault.Normal compliance of fractures is commonly ~1 × 10 −12 to ~1 × 10 −9 m Pa −1 , based on previous field investigations (Burbey  et al., 2012;Cappa et al., 2006;Guglielmi et al., 2015b;Jeanne et al., 2018;Murdoch et al., 2009;Rutqvist et al., 1998;Schweisinger et al., 2009Schweisinger et al., , 2011;;Svenson et al., 2007Svenson et al., , 2008)).Due to the potential similarity between the normal compliance of fractures and the axial compliance of the packer, it is necessary to carefully check the compliances of the testing equipment and the fault, as shown in Fig. 10b.Despite these disadvantages, this method does not need specialized equipment and can be conducted along with standard hydraulic tests.A sliding packer is a commonly available item, and the length of the test section is not restricted (14.1 m in this study).These advantages in the method's application may offset the disadvantages described above.

Implications for the hydraulic dilation angle of the fault
The hydraulic dilation angle of the fault can be estimated as follows.
A residual shear displacement of 2.8-10.4mm was observed after event A (Fig. 9c).However, the hydraulic aperture showed no significant change as a result of that displacement (Fig. 9b).Therefore, the hydraulic dilation angle of the fault is estimated to be effectively zero.The increments of hydraulic aperture observed at high test-section pressures are interpreted to be due to normal displacement of fractures caused by pore-pressure increase, regardless of shear-induced dilation (e.g., Rutqvist and Stephansson, 1996).

Summary
• A constant-head step injection test using a conventional straddle- packer system was performed on a normal fault (shear fracture) in siliceous mudstone.
• The tests applied a new method whereby axial displacements of isolated test sections in a borehole during injection are calculated from the pressures of sliding packers and the pore pressure in the test section, calibrated using a simple laboratory experiment.
• The hydraulic aperture, shear displacement, normal compliance, normal stress, and shear stiffness of the fault during the test were estimated using the new method.
• The hydraulic dilation angle is inferred to have been effectively zero, because the residual shear displacement observed after event A did not result in any increase in hydraulic aperture.
• The method developed and applied here does not require specialized equipment and is expected to aid investigation of the hydromechanical behavior of fractures or aquifers.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 4 .
Fig. 4. (a) Photograph of a sliding packer.When the packer tube is inflated, the bottom end slides toward the top while the top end is fixed.(b, c) Schematic diagrams of the laboratory experiment for measuring u p , p p , and F when the top end is pulled (b) upward (to the borehole mouth) and (c) downward (toward the bottom).(d,e) Measured F and p p during the experiment when the top end is pulled (d) upward and (e) downward.(f, g) Measured u p and F during the experiment when the top end is pulled (f) upward and (g) downward.(h, i) Measured u p and p p during the experiment when the top end is pulled (h) upward and (i) downward.The regression lines are also shown in (d) to (i).These diagrams refer to both upper and lower packers.

Fig. 5 .
Fig. 5. Representative fitting analysis between measured (red) and simulated (blue) flow rates for each injection step.Test 20 is the given example.(For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6 .
Fig. 6.Test-section pressure, packer pressures, injection flow rate, and shortening of the test section during injection tests performed on (a) 29th October 2018 and (b) 30th October 2018.The numbers (1 to 25) in the graphs refer to the test numbers of constant-head injection tests.A sudden pressure drop in the test section occurred between 11,478-11,500 s after the start of injection (labeled "event A" in the figure).

Fig. 7 .
Fig. 7. Injection flow rate vs. test-section pressure determined by constant-head injection tests for tests (a) 1-4, (b) 5-11, (c) 12-17, and (d) 18-25.Solid circles denote data used to determine the regression lines for deriving the static formation pressure during each step.Each gray number indicates the constant-head injection test number.

Fig. 9 .
Fig. 9. (a) Transmissivity, (b) hydraulic aperture, and (c) total shear displacement of the fault with respect to test-section pressure.

Fig. 10 .
Fig. 10.(a) Regression line between log 10 σ' n and δ m for tests 13-24 (excluding test 17) after event A when σ n is 5.55 MPa and (b) the estimated normal compliance of the fault with respect to the estimated effective normal stress.

Table 1
Criteria for assessing which packer's top end is pulled upward.