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A Conventional straddle-sliding-packer system as a borehole
Title

extensometer; Monitoring shear displacement of a fault during an
injection test

Author(s)Ishii Eiichi

Citation

Engineering Geology,275,p.105748_1-105748_12

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Published Journal Article

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https://jopss.jaea.go.jp/search/servlet/search?5066005

DOI

https://doi.org/10.1016/j.enggeo.2020.105748© 2020 The Author. Published by Elsevier B.V. This is an open
Right

access article under the CC BY license(http://creativecommons.org/licenses/BY/4.0/).

Japan Atomic Energy Agency

Engineering Geology 275 (2020) 105748

Contents lists available at ScienceDirect

Engineering Geology
journal homepage: www.elsevier.com/locate/enggeo

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

T

Eiichi Ishii
Horonobe Underground Research Center, Japan Atomic Energy Agency, Horonobe-cho, JapanA R T I C LE I N FO

A B S T R A C T

Keywords:
Borehole extensometer
Fault displacement
Hydraulic dilation angle
Injection test
Siliceous mudstone
Sliding packer

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 aborehole 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 ﬂow rate, were used toestimate the hydraulic aperture, shear displacement, normal compliance, normal stress, shear stiﬀness andhydraulic 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 stiﬀness during faulting is estimated tobe 2.3 × 107 to 8.4 × 107 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 eﬀectively zero as theresidual 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 behaviorof subsurface fractures or aquifers.

1. Introduction
The safe disposal of radioactive waste must consider host-rockpermeability following closure of the underground repository. The hostrock 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 ofheat 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 hydraulicaperture of the fracture δH (m) as follows:

T = ρw gδh3/12μ(1)−3where ρw is the density of water (kg m ), g is the acceleration due togravity (m s−2), and μ is the dynamic viscosity of water (Pa s). The
hydraulic aperture increment Δδh (m) during shearing is expressed asfollows:∆δh = ∆us tan(dh )(2)where Δus is the shear displacement increment (m), and dh is thedilation angle for hydraulic aperture (°) (McClure and Horne, 2014a).
Therefore, if a fault is artiﬁcially sheared, in situ measurement of thehydraulic 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 groundwaterpressure has been observed in earthquakes that were triggered bywastewater ﬂuid injection (Ellsworth, 2013; Healy et al., 1966; Hsieh
and Bredehoeft, 1981). Recently, numerous injection activities havebeen carried out on a large scale for a variety of purposes such as
geothermal exploitation, natural oil/gas production, and geologicalcarbon 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, 2015b,
2017, 2020; Jeanne et al., 2018). Based on these previous activities/
tests, small-scale injection testing is expected to be a useful technique toinvestigate 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

E-mail address: ishii.eiichi@jaea.go.jp.
https://doi.org/10.1016/j.enggeo.2020.105748
Received 29 April 2020; Received in revised form 22 June 2020; Accepted 24 June 2020
Available online 27 June 2020
0013-7952/ © 2020 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license(http://creativecommons.org/licenses/BY/4.0/).

Engineering Geology 275 (2020) 105748

E. Ishii

Fig. 1. (a) Location of the Horonobe area. (b) Layout of borehole 350-FZ-02 and the underground facility. Mabh = meters along borehole; mbgl = meters below
ground level.

identiﬁed. A splay crack (hybrid fracture; Ishii, 2016) is also observed
as a secondary fracture (Fig. 2a, c), which propagates at an angle of
30°–40° from the main fault surface (Fig. 2d). The orientations of the
splay crack and striations on the fault surface indicate that the fault is anormal fault without a strike-slip component (Fig. 2d). Although theshear displacement of this fault is unknown, Ishii et al. (2010) reported
the shear displacements of similar faults exposed on a surface outcrop
to be up to 0.6 m (exceptionally ~10 m for a largest fault).
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., 2010,2012). 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 isconsistent with the sense of displacement of the fault (Fig. 2d). The porepressure around the test section before excavation of the undergroundfacility 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 3.9–4.5 MPa.

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 areaof Hokkaido, Japan (Fig. 1a). During testing, a new method was appliedin which shear displacement along the fault during injection wasmonitored by measuring water pressure in the sliding packers. Thismethod does not require specialized equipment and can be employed
along with the usual hydraulic tests, as described below.
2. Materials
In the Horonobe area, borehole investigations and the constructionof an underground facility have been ongoing since 2001 for researchand 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 inthe 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) thatwas drilled from the bottom face (380 mbgl) of the East Shaft in theunderground 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).
The host rock (siliceous mudstone) contains opal–cristobalite/tridymite (opal–CT) (40–45 wt%), clay (19–33 wt%), quartz (9–13 wt%),
and feldspar (7–13 wt%) (Ishii et al., 2011). Its physical properties are
as follows: tensile strength = 1.8 ± 0.7 MPa ( ± 1σ), unconﬁned
compressive strength = 22.4 ± 5.4 MPa ( ± 1σ), Young's modulus = 1–5 GPa, Poisson's ratio = ~0.2, porosity = ~40%, and intrinsic permeability = 10−19 m2 (Ishii et al., 2011; Miyazawa et al.,2011; Niunoya and Matsui, 2007). The fault at 99.5 mabh (479.3 mbgl)
exhibits a dip direction/dip angle of 181°/71° (Fig. 2a), a thin layer offault breccia (millimeters or less) (Fig. 2b, c), and striations (rake ≈90°) on the fault surface (Fig. 2d), although slickensteps are not clearly

3. Methods
3.1. 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 anaccumulator tank) was used for injection, and the water pressure in thetest section (called “the test-section pressure”) was increased and decreased in steps of ~0.5 MPa while the test-section pressure wasmanually 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 thistime, back-ﬂows occasionally occurred into the water tank at 350 mbgl.
Stainless steel rods (outer diameter 41 mm; inner diameter 34 mm)
2

Engineering Geology 275 (2020) 105748

E. Ishii

Fig. 2. (a) Image of borehole wall and (b–d) the drill core containing the injected fault in borehole 350-FZ-02.

packers (called “the upper-packer pressure” and “the lower-packer
pressure”, respectively), were monitored by pressure sensors installedat 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.
3.2. 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 (Δup, m, positive signwhen the top end is pulled upward), the change in its pressure (Δpp,Pa), and the axial force increment (ΔF, N, positive sign when the top
end is pulled upward) can be related as follows:

Fig. 3. Maximum and minimum horizontal stresses (σH and σh, respectively)
measured by the hydraulic fracturing method, and the vertical (overburden)
stress (σv) calculated using rock density in boreholes HDB-1, −3, and − 6 located near the underground facility (Sanada et al., 2010, 2012). The distance
between the injected fault zone in 350-FZ-02 (−419.3 masl, meters above sea
level) and the location of HDB-6_416.0 m (−355.8 masl) is 64 m.

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∆F = aVp c p ∆pp ,3(3)

Engineering Geology 275 (2020) 105748

E. Ishii

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 up, pp, 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 pp during the experiment when the top end is pulled (d)upward and (e) downward. (f, g)
Measured up and F during the experiment when the top end is pulled (f)upward and (g) downward. (h, i)
Measured up and pp 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 upperand lower packers.

4

Engineering Geology 275 (2020) 105748

E. Ishii∆u p = b∆F,

2.36 × 1011 N m−3 for the acrylic pipe and − 0.83 × 1011 N m−3 forthe 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 enoughto 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.

(4)

where the coeﬃcients a and b can be determined from a laboratory
experiment (N m−3 and m N−1, respectively), Vp is the volume of thepacker plus PEEK tubes ﬁlled with packer water (m3), and cp is thecompressibility of water (Pa−1).
3.3. Laboratory experiment to determine coeﬃcients a and b
During the laboratory experiment, the packer was inﬂated in pipesthat have the same inner diameter as the borehole (~104.5 mm for theupper packer and ~ 103.9 mm for the lower packer, as measured bycaliper logging) and the same elasticity as the borehole wall. Inﬂation
continued until the packer pressure was similar to that used during thein 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:

Δrp/ rp = Δpp (((rp + tp )2 + rp2)/((rp + tp )2 − rp2) + νp)/ Ep

3.4. Calculation of axial displacement of the test section during injection
The change in test-section length during injection (Δl, m) is deﬁned
as follows:∆l = ∆u pl − ∆u pu

where Δupu and Δupl 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 inits packer pressure and the coeﬃcients a and b (i.e., the combinations of−3.56 × 1011 N m−3 and 4.86 × 10−8 m N−1 for the acrylic pipe andof −1.41 × 1011 N m−3 and 4.09 × 10−8 m N−1 for the aluminumpipe) (Fig. 4d, f). On the other hand, the displacement of the top end of
the packer that is pulled downward cannot be determined from thechange 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, thedisplacement can be calculated from the change in packer pressure forthe other packer whose top end is pulled upward, because the scalars of
axial force increments imposed on the two top ends of the upper- andlower-packers during testing are always the same. Therefore, the used
coeﬃcients a and b are the combinations of −3.56 × 1011 N m−3 and1.84 × 10−7 m N−1 for the acrylic pipe, and − 1.41 × 1011 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:(5)

where rp is the pipe inner radius (m), Δrp is the change of rp (m), Δpp is
an increment of the packer pressure (Pa), and Ep, νp, and tp 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:Δrw / rw = Δpp (1 + ν )/ E

(7)

(6)

Here, rw 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 resultsfrom 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 = 68.6 GPa, ν = 0.34, innerdiameter 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 thepossible 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 valuesof aVpcp and b are −0.232 N Pa−1 and 4.86 × 10−8 m N−1 for theacrylic pipe and − 0.092 N Pa−1 and 4.09 × 10−8 m N−1 for thealuminum 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 pipeand − 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 theseresults using the known compressibility of water cp and the volume of
packer water Vp during the laboratory experiment (5 × 10−10 Pa−1
and 1.3 × 10−3 m3, respectively). When the top end is pulled upward ais −3.56 × 1011 N m−3 for the acrylic pipe and − 1.41 × 1011 N m−3
for the aluminum pipe. When the top end is pulled downward it is∆l = −a∗ (bu + bl ) Vp c p ∆pp∗(8)

where a⁎ is the coeﬃcient for the packer whose top end is pulled upward (i.e., −3.56 × 1011 N m−3 for the acrylic pipeand − 1.41 × 1011 N m−3 for the aluminum pipe), bu and bl are thecoeﬃcients for the upper and lower packers (m N−1), respectively,(bu + bl) is 2.33 × 10−7 m N−1 for the acrylic pipe and1.58 × 10−7 m N−1 for the aluminum pipe, Vp is the volume of packer
water during the injection test (i.e., 3.2 × 10−3 m3 considering the
PEEK tubes of 150 m), cp is the compressibility of water (i.e.,
5 × 10−10 Pa−1), and Δpp⁎ is the change in packer pressure for the
packer whose top end is pulled upward. The criteria for judging whichpacker'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, itis necessary to remove this eﬀect by identifying the linear relationshipbetween the packer pressure and test-section pressure during lowpressure phases of injection to the fault (or intact rock). Strain of thestainless steel rods is disregarded because steel is more resistant tostrain than the packer.

Table 1
Criteria for assessing which packer's top end is pulled upward.
Upper-packer pressure (ppu)

Lower-packer pressure (ppl)Test-section strain

Packer whose top end is pulled upward

Increase/no change
Decrease
Decrease (Δppu/Δppl > 1.5)
Decrease (Δppu/Δppl < 0.6)
Decrease (0.6 ≤ Δppu/Δppl ≤ 1.5)

Decrease
Increase/no change
Decrease
Decrease
Decrease

Lengthen
ShortenShortenLengthenLengthen/shorten

Lower packer
Upper packer
Upper packer
Lower packer
Upper/lower packer

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E. Ishii

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 JRC0 of the fault can be calculated based on the maximum
height of the fracture-surface proﬁle (Rz, mm; equal to the verticaldistance between the highest peak and the lowest valley in the proﬁle)(Li and Zhang, 2015). Although numerous methods for determining
JRC0 have been proposed, the method using Rz 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 thefault surface were traced using a proﬁle gauge, which resulted in Rz of
0.3–0.7 mm. These values can be converted to a JRC0 of 2–4 using thefollowing empirical equation (Li and Zhang, 2015):

3.5. Estimation of shear displacement along the fault during injection
Shear displacement along the fault during injection (Δus, m, positive
sign when the sense of displacement is normal faulting) is deﬁned by
the following equation:∆us = (∆δm cosθ − ∆l)/ sinθ(9)where Δδm 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 δm can be related to the hydraulic apertureδh by the following equation (Barton et al., 1985):

δm =δh JRC0 2.5

JRC0 = 4.4192Rz0.6482

(10)

(11)

In this study, the JRC0 of the fault was assumed to be 3 (JRC0 is
commonly within 0–20 and higher JRC0 indicates rougher surfaces).

where JRC0 is the joint roughness coeﬃcient (JRC) on the laboratory
scale. The units of δm and δh in this equation are microns, and thisequation is only valid for δm ≥ δh. When the δm value calculated fromδh is smaller than the δh value, the δm value is assumed to be the sameas the δh value (Barton, 1982). Although numerous correlations between δm and δh 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 δh can be calculated from the transmissivityof 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 themodeled ﬂow system. The present study determined the transmissivityof the test section for each injection step by ﬁtting the measured andsimulated 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 atransient, 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 pressureduring each injection step was given as follows: (1) the mean test-section pressure and the mean injection ﬂow rate during the last minute ofeach injection step were measured and plotted, (2) regression lines
were derived from the intervals showing a linear relationship between

3.6. 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 ofequipment can be used as a measure of its compliance, and it should begreater than the normal compliance of the tested fault. From Eq. (4), theaxial compliance Ca (m Pa−1) of the packer system is given by thefollowing equation:

Ca = (∆u pu + ∆u pl ) rw2 π / ∆F = (bu + bl ) rw2 π(12)where Δupu and Δupl are the displacements of the upper and lower
packers' top ends (m), respectively, rw is the borehole radius (m), ΔF isthe axial force increment (m), and bu and bl are the coeﬃcients in Eq.
(4) for the upper and lower packers (m N−1), respectively. As (bu + bl)
is 1.58 × 10−7 m N−1 for the acrylic pipe and 2.33 × 10−7 m N−1 forthe aluminum pipe (Fig. 4f, g), and rw is 0.052 m, the axial complianceof the packer system is estimated to be between 1.3 × 10−9 and2.0 × 10−9 m Pa−1.
The normal compliance of the fault Cn (m Pa−1) is deﬁned as follows:

Cn = dδm/ dσn′(13)where δm is the mechanical fracture aperture (m) and σ'n is the eﬀective
normal stress (Pa). The σ'n is given as follows:

σn′ = σn − αp(14)where σn 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 σn can beapproximated 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 pressuresp and the mechanical aperture δm during injection, as the eﬀective
normal stress σ'n (Pa) and the mechanical aperture of a sheared fractureδm (m) can be expressed as the following semi-log relationship (Bandis
et al., 1983):

log10 σn′ ∝ qδm (σ ′n > 0)

(15)
−1

where q is a coeﬃcient (Pa m ). Parametric analysis of σn to minimize
the negative correlation coeﬃcient between log10 σ'n and δm results in aregression line between log10 σ'n and δm that gives the best estimates forσn and q. Using this result, Eq. (13) can be further developed to give thefollowing equation (Bandis et al., 1983):

Fig. 5. Representative ﬁtting analysis between measured (red) and simulated(blue) ﬂow rates for each injection step. Test 20 is the given example. (Forinterpretation of the references to colour in this ﬁgure legend, the reader isreferred to the web version of this article.)
6

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E. Ishii

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).

Cn = dδm/ dσn′ = log10 e /(qσn′ ) = 0.4343/(qσn′ )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 andthe ﬂow rate again changed linearly (tests 5–9 in Figs. 6a and 7b) (theback-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 ratefrom 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 theﬂow 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 (from6.09 to 5.61 MPa) during a period of 22 s (event A in Fig. 6a) without asigniﬁcant change in the ﬂow rate (Fig. 6a). Then, the test-section
pressure stabilized at ~5.6 MPa after some ﬂuctuations (test 12 inFig. 6a), and the ﬂow rate varied non-linearly (tests 12–17 in Figs. 6aand 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(16)Note that this model assumes normal displacement upon fracturesthat occurs as a result of changes in eﬀective normal stress, regardlessof shear-induced dilation. As the eﬀective change in fracture apertureduring 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 σn is reliable, as the σ'n at which the mechanical aperture asymptotically increases according to Eq. (15) is largely insensitive to the component ofshear-induced dilation.
4. Results
4.1. 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 rate7

Engineering Geology 275 (2020) 105748

E. Ishii

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. Solidcircles denote data used to determine the regression
lines for deriving the static formation pressureduring each step. Each gray number indicates theconstant-head injection test number.

pressure using Eqs. (17), (8) can be expressed as follows:

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 to5.55 MPa after test 25).

∆l = −a u (bu + bl ) Vp c p [ppu − (0.0815p + 6.6514 × 106)]

where au is the coeﬃcient in Eq. (3) for the upper packer (i.e.,−3.56 × 1011 N m−3 from the acrylic pipe and − 1.41 × 1011 N m−3
from the aluminum pipe), bu and bl are the coeﬃcients in Eq. (4) for the
upper
and
lower
packers,
respectively(i.e.,
bu + bl = 1.58 × 10−7 m N−1 from the acrylic pipe and2.33 × 10−7 m N−1 from the aluminum pipe), Vp is the volume of
packer water during the in situ injection test (i.e., 3.2 × 10−3 m3), cp isthe compressibility of water (i.e., 5 × 10−10 Pa−1), ppu is the upperpacker pressure (Pa), and p is the test-section pressure (Pa).
Fig. 6 shows the calculated shortening of the test section, where themaximum 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.

4.2. 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 theadditional inﬂation performed from 2300 s after the start (Fig. 6a).
When the test-section pressure was ≤6.0 MPa, the packer pressurechanged linearly with varying test-section pressure on account of theelastic 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):

pp = 0.0815p + 6.5145 × 106

(18)

(17)
4.3. Hydraulic aperture increment of the fault

where pp 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 notshown 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). Suchchanges in packer pressures indicate that the test section shortened andthe 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

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 MPafor tests 18–25, based on the regression lines in Fig. 7. For tests 12–17, apressure 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 hightest-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 andafter event A are similar (Fig. 9b).

4.4. 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
8Engineering Geology 275 (2020) 105748

E. Ishii

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

test-section pressure of ~4.7 MPa (Fig. 9c).

4.5. 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); thetest-section pressure at which the hydraulic aperture asymptoticallyincreases 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 aloss 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 thefault before event A, as those methods basically assume a cohesionlessfracture. Therefore, this study estimated only the normal stress andnormal 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 δm and test-section pressure p,
which resulted in the best estimate of 5.55 MPa for σn to minimize theFig. 8. Packer pressure vs. test-section pressure during the injection tests.
Upper-packer pressure during (a) tests 5–17 and (b) tests 18–25, and (c) lowerpacker pressure during tests 5–17. The regression line in (a) was obtained from6400 to 10,237 s during tests 5–10.

the last 10 s of each injection step (Δus, m) was calculated by Eq. (9).
The mechanical aperture δm of the fault was calculated by applying Eq.
(10) (all δm were assumed to be equal to δh because all the δm calculated from δh were smaller than the δh). 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
13.3–49.5 mm (Fig. 9c).
• The total shear displacements at low test-section pressures after•

event A conﬁrmed a residual shear displacement of 2.8–10.4 mm
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
9

Engineering Geology 275 (2020) 105748

E. Ishii

Fig. 10. (a) Regression line between log10 σ'n and δm for tests 13–24 (excluding test 17) after event A when σn is 5.55 MPa and (b) the estimated normal compliance ofthe fault with respect to the estimated eﬀective normal stress.

negative correlation coeﬃcient between log10 σ'n and δm (the correlation coeﬃcients were − 0.91, −0.96, and − 0.97 for σn of 5.51, 5.52,
and 5.55 MPa, respectively). From the slope of the regression line at
σn = 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 ofthe packer system.

to the unconﬁned compressive strength of the intact rock (UCS) and thebasic friction angle ϕb, respectively, and ϕb can be obtained from tilt
tests performed on samples with saw-cut surfaces (Barton and Choubey,1977). Adopting the following parameters: ϕb = ~26° (results from thetilt tests); L = 0.1–10.0 m (assumption); JRC0 = 3 (section 3.5); andUCS = 22.4 MPa (section 2), and by approximating the friction angle ϕto be 32° based on Eqs. (21)–(23), the measured Ks during tests 18–24 is
calculated to be 2.3 × 107 to 8.4 × 107 Pa m−1 using Eqs. (19)–(20).
The empirically predicted Ks during tests 18–24 is deﬁned as follows(Barton and Choubey, 1977):

5. Discussion
5.1. Reliability of shear displacements estimated using the applied packer
methodK s = 1/ usp σn′ tan(JRC log10 (JCS / σn′ ) + ϕr )The lower-packer pressure did not change signiﬁcantly during thetest, except for the elastic response following changes in test-section
pressure (Figs. 6 and 8c). This observation is compatible with resultsfrom the laboratory experiment (Table 1) showing that one packer may
remain constant while the pressure in the other packer decreases (asshown by the gray zones in Fig. 4h, i). Furthermore, the estimatedshortening of the test section reﬂects shear movement along the fault inthe sense of normal faulting (section 4.2), which is consistent with theprevious displacement interpreted from observations of drill cores(Fig. 2d).
The estimated shear displacement (Fig. 9c) is considered reliablebecause the measured and empirically predicted shear stiﬀnesses of thefault (Ks, Pa m−1) are consistent, as described further below. The
measured Ks during tests 18–24 (i.e., the pressure-increase step when
the test-section pressure was less than the total normal stress across thefault on 30th October 2018) can be deﬁned as follows (Guglielmi et al.,2014):

usp = 0.0077L0.45 (σn′ / JCS )0.34cos(JRC log10 (JCS / σn′ )).

Δτ = ∆p∗ tan ϕ(25)

By using Eqs. (24) and (25) with the eﬀective normal stress at test
24, the empirically predicted Ks is calculated to be 0.8 × 107 to
7.1 × 107 Pa m−1, which is comparable to the measured Ks. The
clearance of ≥32 mm between the test rod and borehole wall in the test
section (as measured by caliper logging; the borehole diameter ismostly ~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 13.3–49.5 mm(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., 2015a, 2015b, 2017; Jeanne et al., 2018).

(19)

K s = Δτ /Δus(24)

where usp is the shear displacement required to reach the peak shear
strength (m). The usp can be derived from the following empiricalequation suggested by Asadollahi and Tonon (2010):(20)
5.2. Applicability of the packer-pressure-based extensometer⁎

where Δτ, Δus, 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):

ϕ = JRC log10 (JCS / σn′ ) + ϕrThis study has developed and demonstrated a new method formonitoring axial displacements of isolated test sections in a boreholeduring injection by utilizing sliding-packer pressures. However, themethod has some disadvantages that are outlined below.

(21)• The estimation error is large, as shown in Fig. 6.
• Whether the test section lengthens or shortens cannot be determined

where JRC and JCS are, respectively, the joint roughness coeﬃcient andjoint wall compressive strength (Pa) at an in situ scale, and ϕr is theresidual friction angle (°). The JRC and JCS can be related to values at alaboratory scale using the following equations (Barton et al., 1985):

JRC = JRC0 (L/0.1)−0.02JRC0(22)

JCS = JCS0 (L/0.1)−0.03JRC0

(23)

•

where L is the length of the fracture (m), and JRC0 and JCS0 are thosevalues for L = 0.1 m. For unweathered fractures, JCS0 and ϕr are equal10

by changes in packer pressure when the upper and lower packerpressures both decrease by similar amounts (e.g., the case of
0.6 ≤ Δppu/Δppl ≤ 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

Engineering Geology 275 (2020) 105748

E. Ishii

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., 2009, 2011; Svenson et al., 2007, 2008). Due tothe 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, asshown in Fig. 10b.

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model into ﬁnite-discrete element analysis of the geomechanical behaviour ofDespite 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 themethod's application may oﬀset the disadvantages described above.
5.3. 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 2.8–10.4 mm was observed after event
A (Fig. 9c). However, the hydraulic aperture showed no signiﬁcantchange 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 bypore-pressure increase, regardless of shear-induced dilation (e.g.,
Rutqvist and Stephansson, 1996).
6. Summary• A constant-head step injection test using a conventional straddle••••

packer system was performed on a normal fault (shear fracture) insiliceous mudstone.
The tests applied a new method whereby axial displacements ofisolated test sections in a borehole during injection are calculated
from the pressures of sliding packers and the pore pressure in thetest 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.
Acknowledgments
The author thanks engineers of the Taisei Corporation, Asano
Taiseikiso Engineering, and Mitsubishi Materials Techno Corporation
for the borehole investigation, and Yoichi Samata, Nobukatsu Miyara,
and Akitaka Sakurai of JAEA for performing the laboratory experiment.
The author also thanks Larry Murdoch for valuable comments on the
new packer method, an anonymous reviewer for insightful and detailed
review, and Janusz Wasowski for editorial handling of the manuscript.
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