1 Introduction

High-level radioactive wastes (or spent fuel) are planned to be disposed of deep underground with engineered barriers, such as metallic overpacks and bentonite buffer materials, based on the respective country’s disposal concept (Faybishenko et al. 2017; Organisation for Economic Co-operation and Development/Nuclear Energy Agency 2019). The host rock where the wastes will be emplaced should have low effective permeability to isolate radionuclides that might be released from the wastes into the groundwater. However, even if the effective permeability of the rock is low, minor faults (or shear fractures) might develop (Mazurek et al. 1998; Ozaki et al. 2022; Patriarche et al. 2004a, b). When the wastes are emplaced in such a low-permeability faulted rock, the waste’s heat might increase the water pressure and differential stress in the surrounding rock (Rutqvist 2020), causing elastic shear displacement of the surrounding minor faults. Emplacing the wastes in a faulted rock must consider the risk of possible damage to the engineered barriers by shear displacement along faults (Chapman et al. 2012; Nuclear Waste Management Organization of Japan 2021; Radiation and Nuclear Safety Authority 2015; Svensk Kärnbränslehantering AB 2008). Thus, investigating the shear capability of minor faults is crucial when considering the emplacement of the wastes in low-permeability faulted rock.

To investigate the shear capability of minor faults, it is helpful to perform borehole tests to artificially shear the faults by injecting water into them and increasing the water pressure and shear capability. Meanwhile, it is necessary to measure the shear movement along the faults, which requires specialized equipment such as a borehole extensometer (Schweisinger et al. 2007), borehole tiltmeter (Burbey et al. 2012), or three-component borehole deformation sensor [step-rate injection method for fracture in situ properties (SIMFIP)] (Guglielmi et al. 2014). The borehole extensometer and tiltmeter have been widely used to characterize the normal displacement of fractures (Hisz et al. 2013; Murdoch et al. 2009; Schweisinger et al. 2009; Svenson et al. 2007, 2008). The SIMFIP has been actively applied to study the detailed hydromechanical behavior of faults (Cappa et al. 2019, 2022; Guglielmi et al. 2015; Guglielmi et al. 2021; Rutqvist et al. 2020).

Recently, the author developed a straightforward method using a conventional straddle-sliding-packer system for hydraulic tests as a borehole extensometer (Ishii 2020). In this method, during injection, an axial displacement of a packered-off test section can be estimated from a change in the packer pressures through a calibration based on simple laboratory experiments. This method cannot measure a slight displacement of 10−5 m or less but can measure an axial displacement of 10−4 m or more without any special device (Ishii 2020). Thus, this method might help investigate the shear capability of minor faults. However, this method is applicable for investigating the effect of fault shear displacement on hydraulic transmissivity (i.e., hydraulic dilation angle) (Ishii 2020) or hydraulic connectivity (Ohno and Ishii 2022), but the applicability for assessing the shear capability of faults with fault rocks/filling materials has yet to be verified.

This study used the packer-pressure-based extensometer method to two neighboring minor faults in Neogene siliceous mudstone hosting the underground facility of the Horonobe Underground Research Laboratory (URL; Figs. 1a–c) to verify the applicability of this method to investigate the shear capability of minor faults. Herein, the tested faults are A and B, intersecting boreholes 350-FZ-01 and 350-FZ-02 (Fig. 1b–d) and have fault breccias of different thicknesses. Furthermore, the applied method includes estimating the in situ (far-field) stress state.

Fig. 1
figure 1

a Location of the Horonobe Underground Research Laboratory (URL). b Layout of boreholes 350-FZ-01 and 350-FZ-02 and the underground facility; mbgl meters below ground level. c Geological cross-section and locations of boreholes 350-FZ-01, 350-FZ-02, and HDB-6 and the underground facility. d Interpreted geometry of the tested faults A and B based on geological information obtained from boreholes 350-FZ-01 and 350-FZ-02

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2 Material

The tests were performed on bedding-oblique faults A and B, encountered at 476.7 m below ground level (mbgl) [96.8 m along borehole (mabh)] of a vertical borehole 350-FZ-01 and at 479.3 mbgl (99.5 mabh) of a vertical borehole 350-FZ-02, respectively. Both boreholes were drilled from the bottom of the east access shaft (drilling diameter 101 mm; drill core diameter 63.5 mm) (Figs. 1b–d and 2a and b). Fault A has a dip direction/dip angle of 159°/71° and a fault breccia of centimeter-thickness (Fig. 2a). The fault surface on the footwall exhibits two-directed striations (rake ≈ 20° and 70°; dip direction/dip angle ≈ 76°/19° and ~ 208°/63°, respectively) (Fig. 2c). The lower part of the fault surface shows a plumose structure (Fig. 2c), indicating that the fault surface was originally a hybrid fracture (Ishii 2016a). Fault B has a dip direction/dip angle of 181°/71° and a thin layer of fault breccia (millimeters or less thick) (Fig. 2b and d). Striations with a rake of ~ 90° (dip direction/dip angle ≈ 181°/71°) are observed on the fault surface on the footwall (Fig. 2d). Additionally, a splay crack (hybrid fracture) propagating at an angle of 30°–40° from the fault surface indicates that fault B is a normal fault without a strike-slip component (Ishii 2020). Although the shear displacements and sizes of the tested faults cannot be directly measured, Ishii et al. (2010) reported that the shear displacements of similar faults exposed on a surface outcrop were up to 0.6 m (~ 10 m for the largest fault); the lengths of those faults were 100–101 m.

Fig. 2
figure 2

a and b Images of borehole walls and photographs of drill cores in boreholes 350-FZ-01 and 350-FZ-02. c and d Occurrence on the fault surfaces for faults A and B

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The host rock is massive, siliceous mudstone with weakly developed bedding (dip direction/dip angle ≈ 225°/35°) and 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). The tensile strength (MPa) and shear modulus (GPa) of intact rock samples near the test sections are 1.0–1.2 MPa and 0.5–0.8 GPa, respectively, based on laboratory experiment results (Ishii 2021; Miyazawa et al. 2011).

Previous in situ stress measurements (hydrofracturing method) and borehole breakout observations in a vertical borehole HDB-6 near boreholes 350-FZ-01 and 350-FZ-02 (Fig. 1c) showed an E–W far-field horizontal maximum principal stress, and the stress regime was generally characterized by reverse/strike-slip faulting (Fig. 3a and b; Sanada et al. 2010, 2012). However, a normal faulting stress regime was also observed at ~ 110 m from the test section (416.0 mbgl in Fig. 3a), consistent with the sense of displacement of fault B. Figure 3c shows the unconfined compressive strengths (UCSs, MPa) measured by laboratory tests using core samples from borehole HDB-6, and their strengths are lower near 416.0 mbgl, although the UCSs might be lowered by the effects of bedding planes, given the loading axis during the UCS tests was oblique to bedding planes (potential weak planes) in core samples (Ishii et al. 2011). Borehole breakouts were observed also near faults A and B, which similarly indicate an E–W horizontal maximum principal stress (Fig. 4).

Fig. 3
figure 3

a 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, b directions (directional locations) of borehole breakouts observed by borehole televiewer surveys, and c unconfined compressive strengths (UCSs) measured by laboratory tests in borehole HDB-6 (Sanada et al. 2010, 2012; Yamamoto et al. 2004)

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Fig. 4
figure 4

Borehole wall acoustic imageries obtained by borehole televiewer surveys near a fault A in borehole 350-FZ-01 and b fault B in borehole 350-FZ-02

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The water pressure around the test sections before excavating the underground facility and subsequent pumping was ~ 4.8 MPa (Honda et al. 2022). However, dehydration due to the pumping reduced the water pressure to the current values of 4.1 MPa for the 350-FZ-01 and 4.0 MPa for the 350-FZ-02 test sections.

3 Method

3.1 Injection

A constant-head step-injection test was performed on fault B (October 29 and 30, 2018) and then on fault A (March 12, 2021). A plunger pump (plus an accumulator tank) was used for injection, and the water pressure in the test sections (called the test-section pressure) was increased in steps of 0.04–0.50 MPa. 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). The test-section pressure was sometimes forcibly decreased by opening the regulating valve after pressure-increase steps or a shut-in of the test sections. Stainless steel rods (outer diameter 41 mm; inner diameter 34 mm) with strainers (plus a pressure-resistance hose) were used as injection lines into the test sections to reduce pressure loss during injection (Fig. 1b). 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- and lower-packer pressures, 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. Table 1 shows the details of the test sections for faults A and B, which further show the borehole diameters measured by caliper logging.

Table 1 Details of the test sections (meters below ground level (mbgl) derived from dipmeter logs; inner diameter of the borehole (Φbor) measured by caliper logging)
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3.2 Calculation of Axial Displacement of the Test Sections During Injection

The basis of the packer-pressure-based extensometer method relies on the mechanical characteristics of a sliding packer (Ishii 2020). The bottom end slides as the packer tube expands by inflating a sliding packer with water, while the top end is fixed (Fig. 5a). Moreover, two sliding packers are inflated in a borehole to straddle each fault (Fig. 5b). For example, the top end of the upper packer is pulled upward by shortening the test section due to fault shear displacement (Fig. 5c); the packer tube is extended upward and the volume of the packer increases, reducing the packer pressure (Fig. 5d). Conversely, the top end of the lower packer is pulled downward; the packer tube is shortened; the volume of the packer reduces; and the packer pressure increases (Fig. 5e). However, when the borehole wall is elastically soft, the shortening of the packer tube expands the borehole wall. The packer pressure might decrease because the packer rubber contains steel wire fabric with a constant stiffness. Vice versa, there is a case where the test-section lengthens due to fault shear displacement.

Fig. 5
figure 5

a Photographs of a sliding packer. b Layout of a conventional straddle-sliding-packer system in a borehole. c–e Diagrams for the primary functions of sliding packers

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The change in test-section length during injection (Δl, mm, and positive sign when the test-section length increases) can be calculated from the following equation (Ishii 2020):

$$\Delta l=ab{V}_{\text{p}}\Delta {p}_{\text{p}}/{K}_{\text{p}},$$
(1)

where the coefficients a and b can be determined from a laboratory experiment (N/m3 and m/N, respectively), which depend on the elastic strength of the borehole wall. The a and b values for the tested boreholes range from − 3.56 × 1011 to − 1.41 × 1011 N/m3 and 1.58 × 10−7 to 2.33 × 10−7 m/N, respectively (Ishii 2020). Vp is the volume of the packer plus PEEK tubes filled with packer water (i.e., 3.2 × 10−3 m3); Δpp is the change in packer pressure (MPa) for the packer whose top end is pulled upward; and Kp is the bulk modulus of water (i.e., 2.0 GPa). Table 2 summarizes the criteria for determining which packer’s top end is pulled upward.

Table 2 Criteria for assessing which packer’s top end is pulled upward (Ishii 2020)
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The packer pressure can also change during elastic expansion/contraction of the packer tube owing to changes in inner-borehole water pressures above and below the packer. Hence, it is necessary to remove these effects by identifying the linear relationship between the packer pressure and the water pressure. The corrected Δpp can be calculated using the following empirical formulation:

$$\Delta {p}_{\text{p}}={\Delta p}_{\text{pmeas}}-0.1168{\Delta p}_{\text{above}}-0.0815{\Delta p}_{\text{below}},$$
(2)

where Δppmeas is the change in the measured packer pressure (MPa), and Δpabove and Δpbelow are the inner-borehole water pressures above and below the packer (MPa), respectively. The coefficients for Δpabove and Δpbelow (i.e., 0.1168 and 0.0815 in Eq. 2) are obtained by measuring the relationship between the packer pressure and Δpabove (or Δpbelow), while Δpbelow (or Δpabove) is almost constant (Fig. 6). The strain of the stainless steel rods is disregarded because steel is more resistant to strain than the packer.

Fig. 6
figure 6

a Packer pressure and inner-borehole water pressures above and below the packer when the water pressure above the packer changed while the water pressure below the packer was almost constant. b Linear relationship between packer pressure and the inner-borehole water pressure above the packer, as shown in a and the approximation line. c Packer pressure and inner-borehole water pressures above and below the packer when the water pressure below the packer changed while the water pressure above the packer was almost stable. b Linear relationship between the packer and inner-borehole water pressures below the packer, as shown in c and the approximation line

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3.3 Estimation of the In Situ (Far-Field) Stress State

Estimating the shear capability of faults requires knowing the shear stress acting on the faults. Thus, the in situ far-field stress state around the test sections was estimated from the axial displacement of the test sections during injection and the following assumptions:

  1. (i)

    One of the principal stresses is vertical (overburden), as determined by the rock density (Zoback et al. 2003). This study derives the vertical stress σv (MPa) from the following equation (Fig. 3a):

    $${\sigma }_{\text{v}}=0.0167D,$$
    (3)

    where D is the depth (mbgl). However, the in situ water pressure around the test sections has been reduced by 0.7–0.8 MPa due to dehydration during the construction of the underground facility, which can poroelastically decrease the vertical stress. Referring to a decrease in the vertical stress at the 350 m gallery (Fig. 1b) due to a reduction in water pressure (Aoyagi and Ishii 2019), the vertical stress is estimated as,

    $${\sigma }_{\text{v}}=0.0167D-0.51\Delta p,$$
    (4)

    where Δp is the reduction in water pressure by long-term drainage in the URL construction (MPa). D and Δp are 476.7 m and 0.7 MPa for fault A and 479.3 m and 0.8 MPa for fault B, respectively.

  2. (ii)

    The horizontal maximum principal stress is oriented in the typical direction of the investigated area (Heidbach et al. 2010). The typical direction in and around the Horonobe URL is E–W (Fig. 3b; Sanada et al. 2010, 2012) due to the direction of the Eurasian and Pacific plate motions (Fig. 1a). The E–W horizontal maximum principal stress is also confirmed from borehole breakouts near faults A and B (Fig. 4). Thus, in this study, the horizontal maximum and minimum principal stresses σH and σh (MPa) were assumed to be E–W and N–S, respectively.

  3. (iii)

    The total normal stress acting on the tested fault corresponds to the test-section pressure, where the injection flow rate asymptotically increases during pressure-increase steps. Such an increase in injection flow rate indicates fracture opening; thus, the test-section pressure at that time can be approximated as the total normal stress near the test sections (Guglielmi et al. 2014). The total normal stress σn (MPa) acting on the fault surface can be related to the principal stresses as follows (Jaeger et al. 2007):

    $${\sigma }_{\text{n}}={\sigma }_{1}{l}^{2}+{\sigma }_{2}{m}^{2}+{\sigma }_{3}{n}^{2},$$
    (5)

    where σ1, σ2, and σ3 are the maximum, intermediate, and minimum principal stresses (MPa), respectively. l, m, and n are the direction cosines of the line perpendicular to the fault surface for σ1, σ2, and σ3 in the principal coordinate system, respectively.

  4. (iv)

    The shear displacement along the fault induced by injection is along the line where a shear stress acting on the fault surface is maximum (Morris et al. 1996). The direction of shear displacement is consistent with that of the observed axial displacement of the test section during injection. Here, the direction of shear displacement has the following direction ratios (Ramsay and Lisle 2000):

    $$l{m}^{2}\left({\sigma }_{1}-{\sigma }_{2}\right)+l{n}^{2}\left({\sigma }_{1}-{\sigma }_{3}\right):m{n}^{2}\left({\sigma }_{2}-{\sigma }_{3}\right)-{ml}^{2}\left({\sigma }_{1}-{\sigma }_{2}\right):-n{l}^{2}\left({\sigma }_{1}-{\sigma }_{3}\right)-{nm}^{2}\left({\sigma }_{2}-{\sigma }_{3}\right).$$
    (6)
  5. (v)

    The borehole-radial component of shear displacement during injection cannot exceed the clearance between the borehole wall and rod. The borehole-radial component of shear displacement Δur (mm) is expressed by

    $$\Delta {u}_{\text{r}}=\left|\Delta l-\Delta {\delta }_\text{m}\text{cos}\theta \right|/\text{tan}\theta ,$$
    (7)

    where Δδm is the mechanical aperture increment of the faults during injection (mm, positive sign when the mechanical aperture increases), and θ (°) is the acute angle of the direction normal to the borehole axis to the direction of the shear displacement determined by Eq. 6. Equation 7 assumes a simple geometry, ignoring any tilt of the borehole during the tests. When Δδm is largely smaller than Δl (e.g., when Δl is millimeters or more), Δδm is negligible as follows:

    $$\Delta {u}_{\text{r}}\approx \left|\Delta l\right|/\text{tan}\theta .$$
    (8)

    The upper limit of the borehole-radial component of shear displacement Δurlim (mm) determined by the clearance between the borehole wall and the rod is defined as follows:

    $$\Delta {u}_{\text{rlim}}={{\varPhi }}_{\text{bor}}-{{\varPhi }}_{\text{rod}},$$
    (9)

    where Φbor is the inner diameter of the borehole in the test sections (106 mm for fault A and 105 mm for fault B; Table 1), and Φrod is the outer diameter of the rod (41 mm).

  6. (vi)

    The in situ stress ratio σv:σH:σh around the test sections can be estimated by searching for the best stress ratio while following the requirements of (i)–(v). Then, the stress states σ1, σ2, and σ3 are determined for faults A and B using Eq. 4.

3.4 Calculation of the shear capabilities of the faults

The effective shear capability of the fault at test section Cs (mm/MPa) can be calculated using the following formulas (Jaeger et al. 2007):

$${C}_{\text{s}}=u/\tau,$$
(10)
$$\tau ={({\sigma }_{1}-{\sigma }_{2})}^{2}{l}^{2}{m}^{2}+{({\sigma }_{2}-{\sigma }_{3})}^{2}{m}^{2}{n}^{2}+{({\sigma }_{3}-{\sigma }_{1})}^{2}{l}^{2}{n}^{2},$$
(11)

where u is the elastic shear displacement of the fault at the test section (mm), and τ is the maximum shear stress acting on the fault surface (MPa). During elastic shear deformation, Cs can be controlled by asperities in the fault and can increase by injection because an increase in water pressure reduces the contact areas in the fault. As the test-section pressure increases, the Cs and u increase (Fig. 7a).

Fig. 7
figure 7

Relationship between shear capability (log Cs) and elastic shear displacement (u) of the fault during injection for the a high Cs and b low Cs cases

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The u in Eq. 10 is expressed as follows:

$$u={u}_{0}+\Delta u,$$
(12)
$$\Delta u\approx \left|\Delta l\right|/\text{sin}\theta ,$$
(13)

where u0 is the initial elastic shear displacement that existed before injection (mm), and Δu is the elastic shear displacement induced by injection (mm) (Fig. 7a). Whether the induced shear displacement is elastic or inelastic can be assessed by analyzing the plot of shear displacement vs. test-section pressure. A reversible relationship between shear displacement and test-section pressure during repeated injection cycles indicates that the induced shear displacement is elastic. In the u0 in Eq. 12, if an increase in the test-section pressure cannot detect Δu, Cs can be interpreted to be very low, and the u0 can be approximated to be zero (Fig. 7b). Therefore, the possible maximum Cs can be calculated using the detection limit of Δl and Eqs. 10–13. However, if Δu is detected by the increase in the test-section pressure but u0 is unknown, we can estimate the possible minimum Cs by assuming u0 = 0 mm. Therefore, the greater the Δu, the smaller the influence of u0 on u, as defined by Eq. 12. Thus, the possible minimum Cs is better determined when Δu is as large as possible.

4 Results

4.1 Axial Displacement of the Test Sections During Injection into Fault B

Figure 8 shows the test-section pressure, packer pressures, injection flow rate, and test-section shortening in borehole 350-FZ-02 during injection into fault B since test 7. The axial displacement of the test section was not detected during tests 7–10, even when the test-section pressure increased from the initial pressure (4.0 MPa; Ishii 2020) to 6.0 MPa (Fig. 8a). The injection flow rate nonlinearly increased from 0.2 to 1.5 L/min when the test-section pressure was ≥ 5.5 MPa (Fig. 9). The dispersion (a standard error) of the axial displacement of the test section during tests 7–10 was 0.2–0.8 mm, indicating the detection limit of the axial displacement of the test section. Then, the test section was shortened by 2–7 mm when the test-section pressure increased to 6.1 MPa during test 11 (Fig. 8a), and the injection flow rate asymptotically increased up to 7.5 L/min (Fig. 9). Subsequently, the test-section pressure suddenly dropped from 6.1 to 5.6 MPa during 22 s, and the test-section further shortened by 5–20 mm without a substantial change in the flow rate (event A in Fig. 8a). After event A, the test-section pressure stabilized at ~ 5.6 MPa after some fluctuations (test 12 in Fig. 8a). The test-section shortening reached a maximum of 14–51 mm, and the test-section length reversibly changed with the change in the test-section pressure (tests 12–17 in Figs. 8a and 10). Meanwhile, a response was detected at the test section in borehole 350-FZ-01 for fault A, with an increase in water pressure of ~ 0.013 MPa and a test-section shortening (1/10 of the amount at the test section of fault B) during test 11 (Fig. 11a). However, after event A, a test-section axial displacement was monitored at fault A with an opposite displacement to that for fault B. The test-section axial displacement at fault A was approximately 1%–10% of that at fault B (tests 12–25 in Fig. 11a).

Fig. 8
figure 8

Packer pressures, test-section pressure, injection flow rate, and test-section shortening in borehole 350-FZ-02 during injection into fault B for a tests 7–17 and b tests 18–25 (Ishii 2020). The numbers (7–25) in the graphs refer to the test numbers of constant-head steps. A sudden test-section pressure drop occurred between 11,478 and 11,500 s after the start of injection (labeled “event A” in the figure). Lower-packer pressure for b is not shown in the figure due to a leak. Raw data are available in Ishii (2024)

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Fig. 9
figure 9

Mean injection flow rate vs. mean test-section pressure during the last minute of each injection step for injection into fault B (Ishii 2020). The gray numbers indicate the test numbers. Raw data are available in Ishii (2024)

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Fig. 10
figure 10

Test-section shortening vs. the test-section pressure in borehole 350-FZ-02 during injection into fault B. Raw data are available in Ishii (2024)

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Fig. 11
figure 11

Test-section pressures and the minimum estimates of the test-section shortenings in boreholes 350-FZ-01 and 350-FZ-02 during injection into fault B for tests a 7–17 and b 18–25. Raw data are available in Ishii (2024)

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The next day, after a shut-in of the test section in borehole 350-FZ-02 for fault B, the test-section pressure decreased to 4.4 MPa, and a test-section shortening of 3–10 mm was left in fault B. When the test-section pressure increased from 4.4 to 5.6 MPa, test-section shortening occurred with the inception of injection (tests 18–25 in Fig. 8b). It reached 12–46 mm, where the relation between the test-section shortening and pressure was similar to that during tests 12–17 (Fig. 10). Meanwhile, similar to the previous day, a response was observed in the test section in borehole 350-FZ-01 for fault A, which detected a test-section axial displacement opposite to that for fault B (Fig. 11b).

The injection flow rate at fault B after event A linearly increased with an increase in the test-section pressure of 4.4–5.0 MPa, similar to that before event A (Fig. 9). However, it nonlinearly increased when the test-section pressure was ≥ 5.1 MPa; it asymptotically increased when the test-section pressure approached ~ 5.6 MPa (Fig. 9).

4.2 Axial Displacement of the Test Sections During Injection into Fault A

Figure 12 shows the measured data in the test section in borehole 350-FZ-01 during injection into fault A. A test-section shortening occurred with the start of injection and reached 9–32 mm when the test-section pressure increased from 4.10 to 4.35 MPa (tests 1–6 in Fig. 12). Then, after the valve-opening of the test section, the test-section pressure and shortening recovered to 4.15 MPa and 3–12 mm, respectively. The test-section shortening again reached 13–47 mm with the increase in the test-section pressure from 4.15 to 4.40 MPa (tests 7–12 in Fig. 12). Comparing the test-section shortenings between tests 1–6 and 7–12, the shortening for the latter tests was several percent larger than that for the former tests under a given test-section pressure. However, the relation between the test-section length and pressure was generally reversible (Fig. 13). During injection into fault A, a test-section axial displacement opposite to that of fault A was observed at the test section in borehole 350-FZ-02 for fault B. The amount of displacement at fault B was approximately 1%–6% of that at fault A (Fig. 14). The injection flow rate linearly increased with the increase in the test-section pressure although tests 1–6 exhibited slightly larger flow rates than those of tests 7–12 at a given test-section pressure (Fig. 15).

Fig. 12
figure 12

Packer pressures, test-section pressure, injection flow rate, and test-section shortening in borehole 350-FZ-01 during injection into fault A for tests 1–12. The numbers (1–12) in the graphs refer to the test numbers of the constant-head steps. Raw data are available in Ishii (2024)

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Fig. 13
figure 13

Test-section shortening vs. the test-section pressure in 350-FZ-01 during injection into fault A. Raw data are available in Ishii (2024)

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Fig. 14
figure 14

Test-section pressures and the minimum estimates of the test-section shortenings in boreholes 350-FZ-01 and 350-FZ-02 during injection into fault A for tests 1–12. Raw data are available in Ishii (2024)

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Fig. 15
figure 15

Mean injection flow rate vs. the mean test-section pressure during the last minute of each injection step for injection into fault A. Raw data are available in Ishii (2024)

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4.3 In Situ (Far-Field) Stress State

Assuming the stress ratio σv:σH:σh to be 1.0:0.8:0.7 (case 1) or 1.0:0.9:0.7 (case 2) satisfied the requirements of (i)–(v) of Sect. 3.3. Thus, the in situ stress states for faults A and B were estimated, as shown in Table 3, along with the acute angles of the direction normal to the borehole axis to the direction of shear displacement calculated from Eq. 6.

Table 3 Estimated in situ (far-field) stress states and the acute angles θ of the direction normal to the borehole axis to the direction of shear displacement calculated from Eq. 6 (cases 1 and 2 assuming the stress ratio σv:σH:σh = 1.0:0.8:0.7 and 1.0:0.9:0.7, respectively)
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4.4 Shear Displacements and Shear Capabilities of Faults A and B

The axial displacement of the test section for fault B was not detected, even when the test-section pressure reached the normal stress acting on fault B (i.e., 5.6 MPa; Table 3) during tests 7–10 before event A (Fig. 8a). Thus, the shear capability of fault B was very low, and the u0 in Eq. 12 can be approximated to be zero for fault B (Fig. 7b). Hence, considering the dispersion (standard error) of 0.2–0.8 mm of the test-section axial displacement during tests 7–10 to be the detection limit of the axial displacement for the test section, the shear capability of fault B is estimated to be lower than 3 × 10−1 to 1 × 100 mm/MPa based on Eqs. 10–13 and θ in Table 3. During test 11, the shear displacement and capability of fault B increased to 2–9 mm and 3 × 100 to 1 × 100 mm/MPa, respectively; during event A, the shear displacement increased by 6–21 mm. Figure 16a shows that the shear displacement and capability were 3–10 mm and 4 × 100 to 2 × 101 mm/MPa, respectively, since event A under the test-section pressure of 4.4 MPa. However, they largely increased against a given test-section pressure of ≥ 5.1 MPa and reached 14–54 mm and 2 × 101 to 8 × 101 mm/MPa at a test-section pressure of 5.6 MPa. The estimated shear capability could be an overestimate if the calculated shear displacement includes a plastic shear displacement or a hysteretic elastic shear displacement left by repeated injection cycles.

Fig. 16
figure 16

Shear displacement and capability vs. the test-section pressure for a fault B during injection into fault B and b fault A during injection into fault A, assuming case 1 in Table 3. The shear capability of b shows the possible minimum shear capability. Raw data are available in Ishii (2024)

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The shear displacement of fault A during injection into fault A reached 15–54 mm at a test-section pressure of 4.4 MPa (Fig. 16b), given a θ of 61° (case 1 in Table 3). The u0 in Eq. 12 for fault A is unknown, and the possible minimum shear capability is 2 × 101 to 8 × 101 mm/MPa against the test-section pressure of 4.4 MPa (Fig. 16b). If θ is 46° (case 2 in Table 3), the shear displacement and possible minimum shear capability are 18–66 mm and 3 × 101 to 9 × 101 mm/MPa, respectively.

5 Discussion

5.1 Hydromechanical Evolution of Fault B During Injection into Fault B

Based on the axial displacement of the test section in borehole 350-FZ-02 for fault B, this section interprets the hydromechanical evolution of fault B during injection into fault B because it is key information to assess the shear capability of fault B. The test section did not show axial displacement, even when the test-section pressure increased from 4.0 to 6.0 MPa during tests 7–10 but shortened when the test-section pressure increased to 6.1 MPa during test 11 (Fig. 8a). The test-section shortening demonstrates a fault shear displacement with a component of normal faulting. During event A, the test section was shortened by 5–20 mm for 22 s (Fig. 8a). This shortening indicates that a shear displacement of 6–21 mm or more occurred along the fault near the test section, considering the dip angle of the fault (71°; Fig. 2c). This shear displacement rate is 3 × 10−4 to 1 × 10−3 m/s or more and could be within a range of seismic slip (≥ 10−4 m/s; Rowe and Griffith 2015). Such a fast shear displacement can occur with an instant increase in shear capability in fault B due to a failure occurring at an asperity in fault B. This failure was a dilatant shear failure, considering that a test-section shortening had already started during test 11, immediately before event A (Fig. 8a), and an injection flow rate asymptotically increased against a given test-section pressure during test 11 (Fig. 9); i.e., the shearing and opening of fault B started in fault B during test 11. The occurrence of the dilatant shear failure indicates that fault B had cohesion. Although the detail of the cohesive part is unknown, healing by pressure solution or sealing by minerals (Gratier 2011) might yield cohesion in the fault around the test section because the studied siliceous mudstone contains abundant opal-CT, which is susceptive to pressure solution (Ishii 2016b). Faults sealed by carbonates are also observed (Ishii 2016b).

A loss of cohesion by the dilatant shear failure enabled a fast opening of fault B near the test section and rapidly reduced the test-section pressure from 6.1 to 5.6 MPa by dilatancy hardening (Brace and Martin 1968) during event A (Fig. 8a). Referring to the shut-in pressure in the hydraulic fracturing method (Haimson and Cornet 2003), the test-section pressure of ~ 5.6 MPa during test 12 (Fig. 8a) indicates a water pressure in the fault that was in temporal equilibrium with the normal stress acting on the fault. This test-section pressure was consistent with the test-section pressure at which the injection inflow rate asymptotically increased during pressure-increase steps since event A (Fig. 9). As the dilatant shear failure increased the shear and normal capabilities of fault B, the test section shortened at a lower test-section pressure (4.4 MPa; Fig. 8a) after event A. Moreover, the injection flow rate increased nonlinearly against a given test-section pressure at a lower test-section pressure (5.1 MPa; Fig. 9).

5.2 Range of Mechanical Influence During the Tests

The range of the mechanical influence/disturbance during the tests is assessed from the mutual responses between the test sections of faults A and B. During injection into fault B before event A, both test sections of faults A and B shortened during test 11 (Fig. 11a). Meanwhile, as the test-section pressure of fault A increased (Fig. 11a), the shear capability of fault A decreased, causing fault A to shear with a component of normal faulting. However, after event A, the test-section axial displacement of fault A varied with an opposite displacement to that of fault B during injection into fault B (Fig. 11). This is because the shear capability of fault B increased after event A and the resulting large shear displacement of fault B caused the opposite shear displacement (Fig. 17a). Furthermore, during injection into fault A, the test-section axial displacement of fault B varied with an opposite displacement to that of fault A (Figs. 14 and 17b). These observations indicate that the range of the mechanical influence/disturbance during injection into fault A and post-failure fault B was 100 m or more because the distance between the test sections was 4.5 m (Fig. 17).

Fig. 17
figure 17

a Synchronous shear movement of fault A with an opposite displacement to that of fault B during injection into post-failure fault B, and b synchronous shear movement of fault B with an opposite displacement to that of fault A during injection into fault A

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5.3 In Situ (Far-Field) Stress State

The estimated stress ratios σv:σH:σh = 1.0:0.8:0.7 (case 1) or 1.0:0.9:0.7 (case 2) agree well with a stress ratio of 1.0:0.9:0.7 obtained by a previous hydraulic fracturing test at ~ 110 m from the present test sections (i.e., 416.0 mbgl in borehole HDB-6; Fig. 18a). Furthermore, the normal stress of fault B estimated by this study (5.6 MPa; Table 3) is consistent with the value estimated by previous studies (5.6 MPa; Ishii 2020) using the back-flow method (Rutqvist and Stephansson 1996); the normal stress is interpreted to correspond to the test-section pressure at which back-flows occurred during pressure decrease steps after high-flow-rate injection. The UCSs near faults A and B calculated by the borehole breakout method (Barton et al. 1988) using the estimated stress ratios are also concordant with the UCSs measured by previous laboratory tests in HDB-6 (Fig. 18b). Thus, the estimated stress state (Table 3) is reasonable. Although all the estimated stress states at 416.0 mbgl in HDB-6 and at faults A and B in 350-FZ-01 and 350-FZ-02 indicate a normal faulting stress regime, their small horizontal stresses might attribute to the lower rock strength in ~ 400–480 mbgl compared with the rock strengths in the overlying and underlying domains (Fig. 18b).

Fig. 18
figure 18

a Maximum and minimum horizontal stresses and the vertical stress (σH, σh, and σv, respectively) in borehole HDB-6 shown in Fig. 3a, and those in boreholes 350-FZ-01 (fault A) and 350-FZ-02 (fault B) calculated applying 0 MPa to Δp in Eq. 4 for comparison with the values in HDB-6. b Unconfined compressive strengths (UCSs) measured by laboratory tests using core samples from HDB-6 shown in Fig. 3c, and UCSs near fault A in 350-FZ-01 and fault B in 350-FZ-02 estimated by the borehole breakout (BB) method using the stress ratios shown in Table 3 (see Table 4 for details)

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Table 4 Details of the borehole breakout method-based unconfined compressive strengths (UCSs) shown in Fig. 18b
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Following the stress state (Table 3) and Eq. 6, the calculated shear displacement direction on fault A has a dip direction/dip angle of 228°/46°–210°/61° (rake = 50°–68°), close to one of the striation directions observed on the fault surface (i.e., ~ 208°/63°; rake ≈ 70°; Fig. 2c). The calculated shear displacement direction for fault B is 181°/71° (rake = 90°), consistent with the striation directions observed on the fault surface (i.e., ~ 181°/71°; rake ≈ 90°; Fig. 2d). These results indicate that the observed striations were formed in the same stress state as the current stress state. Furthermore, fault B had cohesion (Sect. 5.1). Thus, fault B should have been long-term inactive or had already halted fault activity, with the stress state unchanged. The current activity for shear movement of fault A is unknown.

5.4 Shear Displacements of the Faults

The calculated shear displacement reached 15–66 mm for fault A and 14–54 mm for post-failure fault B and was largely elastic as it approximately reversibly varied with a change in the test-section pressure (Fig. 16). Furthermore, the range of the mechanical influence/disturbance during the tests was 100 m or more (Sect. 5.2). Such elastic shear displacements of 10−2 m on a scale of 100 m or more do not contradict the previous laboratory experimental results. Barton (1981, 1982) showed that clay-bearing discontinuity samples and unfilled joint samples of a 3–12 m length can accommodate an elastic shear displacement of 10−3–10−2 m.

A shear displacement of 10−2 m should exceed the limit of capable elastic shear displacement (probably 10−4–10−3 m; Barton 1982) in the limited area of 10−2 m from the test section. Thus, the shear stress is interpreted to have reached the shear strength in the limited area near the test section. However, considering a scale of 100 m or more around the test section, hydraulically pressurized areas in the faults during injection might be limited to near the test sections or flow channels in the faults (Ohno and Ishii 2022). Besides, asperities (e.g., contact areas or cohesive zones) might remain at a distance from the test sections or from the flow channels in the faults. Furthermore, the shear strength of a fault might be higher near the fault tip (Bürgmann et al. 1994; Cowie and Scholz 1992). Hence, the elastic shear displacement of 10−2 m could occur without the shear stress reaching the shear strength across the entire fault, even when the test-section pressure reached the normal stress acting on the faults near the test sections.

5.5 Shear Capability of the Faults

The shear capability was estimated to be 2 × 101 to 9 × 101 mm/MPa or more for fault A at a test-section pressure of 4.4 MPa. The shear capability of fault B was 3 × 10−1 to 1 × 100 mm/MPa or less at a test-section pressure of < 6.0 MPa before event A but increased to 4 × 100 to 2 × 101 mm/MPa at a test-section pressure of 4.4 MPa and 2 × 101 to 8 × 101 mm/MPa at a test-section pressure of 5.6 MPa after event A. These shear capabilities are consistent with previous laboratory experimental results. Bandis et al. (1983) and Barton (1982) showed that the shear capabilities of clay-bearing discontinuity samples and unfilled joint samples of a 1–10 m length are 100–102 mm/MPa under a normal stress of < 10 MPa. The shear capabilities of fault A and post-failure fault B are consistent with those of the samples, and the shear capability of pre-failure fault B is lower than those of the samples.

The shear capability of post-failure fault B increased against a given test-section pressure of ≥ 5.1 MPa (Fig. 16a), indicating that the contact areas in fault B reduced by elastic fracture-normal displacement in fault B as the injection flow rate nonlinearly increased against a given test-section pressure of ≥ 5.1 MPa (Fig. 9).

The shear capability of a fault should not be higher than the maximum shear capability Csmax (mm/MPa) determined by the shear modulus G (GPa) of the surrounding rock:

$${C}_{\text{smax}}\approx a/G,$$
(14)

where a is the smallest dimension of the sheared region (m) (Jaeger et al. 2007). Assuming that a is 5–10 m based on the mechanical influence/disturbance during the tests (i.e., 100 m or more; Sect. 5.2) and G is 0.5 GPa based on the shear modulus of the intact rock (Sect. 2), Csmax is 10–20 mm/MPa. This value, for example, is lower than the estimated shear capability of 2 × 101 to 8 × 101 mm/MPa for post-failure fault B at a test-section pressure of 5.6 MPa, which is contradictory as the Csmax is not maximum. However, the apparent shear modulus of the surrounding rock can be substantially lower than the shear modulus of the intact rock due to damage-zone fracture and neighboring fault development by a factor of 100 or more (Cappa et al. 2007; Griffith et al. 2009; Stanton-Yonge et al. 2020). As faults A and B synchronously sheared during injection after event A (Fig. 17), the apparent shear modulus of the surrounding rock should be considerably lower than the shear modulus of the intact rock, which can reconcile the estimated shear capabilities with the maximum shear capability.

6 Conclusions

This study performed constant-head step-injection tests with a recently developed packer-pressure-based extensometer method to investigate the shear capabilities of fault A with centimeter-thick fault breccia and fault B with millimeters or less-thick fault breccia in siliceous mudstone. The results showed that the shear capability is high for fault A but low for fault B despite containing an incohesive fault rock. An elastic shear displacement occurred for fault A with the inception of injection into fault A at the initial test-section pressure of 4.1 MPa and reached 15–66 mm when the test-section pressure increased from 4.1 to 4.3 MPa, where the shear capability was 2 × 101 to 9 × 101 mm/MPa or more. Fault B had cohesion, and a shear displacement was not detected, even when the test-section pressure increased from 4.0 to 6.0 MPa, where the shear capability was 3 × 10−1 to 1 × 100 mm/MPa or less. Subsequently, after the test-section pressure increased to 6.1 MPa, the dilatant shear failure (event A) occurred in fault B; then, an elastic shear displacement occurred with the start of injection at a test-section pressure of 4.4 MPa and reached 14–54 mm when the test-section pressure increased from 4.4 to 5.6 MPa due to the increased shear capability (e.g., 4 × 100 to 2 × 101 mm/MPa at the test-section pressure of 4.4 MPa and 2 × 101 to 8 × 101 mm/MPa at the test-section pressure of 5.6 MPa). The range of the mechanical influence/disturbance during injection into fault A and post-failure fault B was 100 m or more, and the estimated shear capabilities were consistent with previous laboratory experimental results using 1–10-m long fracture samples. The applied method helps investigate the shear capabilities of minor faults in advance when considering the emplacement of high-level radioactive wastes in a low-permeability faulted rock.