Rock Stress Measurements for Unlined Pressure Tunnels: A True Triaxial Laboratory Experiment to Investigate the Ability of a Simplified Hydraulic Jacking Test to Assess Fracture Normal Stress

The HF test method includes the pressurization, usually by water, of a short, isolated section of borehole, devoid of fractures, until a fracture is created. The pressures at which the borehole ruptures, termed the breakdown pressure (P_b), the pressure required to reopen the fracture at consecutive pressure cycles (P_r) and the pressure measured immediately after pumping stops, termed the instantaneous shut-in pressure (P_s) are all recorded throughout the test, see Fig. 1.

The in situ state of stress can be assessed from such measurements by applying the classical hydraulic fracturing criterion, introduced by Hubbert and Willis (1957):orwhere T is the tensile strength of the rock, P₀ the initial pore pressure in the rock and σ₁ and σ₃ are the maximum and minimum principal stresses, respectively. Guidelines on how to measure the tensile strength of the rock, T, are provided in Haimson and Cornet (2003), including laboratory tests on extracted core, such as the hollow cylinder test or the Brazilian test, or, when core is not available, by looking at the difference between breakdown pressure in the first pressure cycle, P_b, and the reopening pressure, P_r, found during subsequent cycles.

Calculation of the magnitude of σ₁ based on Eq. (1) has proven rather uncertain due to the difficulty in assessing the tensile strength from such tests (Zoback 2007). Magnitude of σ₃, however, require no calculation since in the classical interpretation of the HF test, it is assumed that the created fracture opens normal to the minimum principal stress, and consequently that:

Several techniques for assessing the minimum principal stress from analysis of hydraulic fracturing tests are described in the literature, and reference is made to Zoback and Kohli (2019) for an overview of such methods.

When a fracture has been created, it can be assumed that for consecutive pressurization cycles T = 0, and that P_b in Eq. (1) can be replaced by the reopening pressure, P_r such that (Bredehoeft et al. 1976):or

There is also some uncertainty related to this method of calculating σ₁, mainly due to the difficulty of picking the exact pressure at which the fracture re-opens (Ito et al. 1999). In addition, in cases with negative tangential stresses around the borehole, i.e. where 3σ₃ < σ₁, the fracture will never completely close, and no meaningful estimate on reopening pressures can be identified (Haimson 1992).

An important requirement for the proper execution and interpretation of the HF test is that the borehole axis is in the same direction as one of the principal stresses, or at least deviating less than 15° from it. Tests performed in deviating boreholes invalidate the classical method of interpreting results, potentially causing considerable error (Warren and Smith 1985). This requirement necessitates, in principle, reliable information of the stress directions, which for hydroelectric projects—often situated at relatively shallow depths in mountainous regions, would require 3D stress measurements since the in situ stress orientation might vary considerably over short distances. The additional cost and time required for 3D stress measurements limit the applicability of the HF test in such cases.

To circumvent some of the limitations associated with the HF method, the HTPF test was developed by Cornet and Valette (1984). The objective of the HTPF method is to determine the normal stress supported by pre-existing fracture planes with known orientations and, by inversion of the test results, determining the complete stress field.

The magnitude of normal stress is found in much the same way as done for assessing σ₃ during the HF test, i.e. by assessing shut-in pressure after full fracture opening. However, since the stimulated fracture is not necessarily oriented normal to σ₃, Eq. (2) can be rewritten as follows:where σ_n is the normal stress acting across the fracture. The HTPF test is performed by pressurizing the test section at a pre-determined constant flow until fracture opening, followed by a shut-in phase, similar to the HF test. After this first cycle is either: (1) a stepwise increase (forward-step) in flow rate conducted until full fracture opening, followed by another shut-in phase; or (2) an initial forward-step flow increase followed by a stepwise flow decrease (backward-step). By plotting pressure data vs. flow rate from the step-rate tests can a bilinear curve be obtained, the intersection of which can be taken as the normal stress (Haimson and Cornet 2003). Determining the regional stress field is then done by finding a best fit function to the measured normal stresses, together with the fracture orientation, as presented by Cornet (1993).

Testing a minimum of eight individual fractures of various orientation is required for a complete stress determination with the HTPF test. Since each tested fracture needs to be isolated it is further a requirement that the rock mass cannot be too fractured (Amadei and Stephansson 1997). The number of tests required can, however, be reduced by combining the HF test with the HTPF test, provided ideal testing conditions (Cornet 2016). The relatively large number of tests combined with the extensive formulae required to find the complete stress field is arguably the main drawback of the HTPF method in the context of assessing σ₃ for unlined pressure tunnel design purposes.

The basic principle of the various hydraulic jacking tests is to pressurize a section of a borehole intersected by one or several pre-existing fractures, and by monitoring fluid pressure and flow to find the fluid pressure at which the fracture can be kept opened. This pressure is taken as a measure of the normal stress acting across the stimulated fracture, since once the fracture is opened, the stress concentration which previously surrounded the borehole is reduced and the pressure, P_inj, required to hold the fracture open is equal to that of the in situ normal stress across the fracture (Hubbert and Willis 1957).

According to Rutqvist and Stephansson (2003), the first hydraulic jacking tests were performed during the investigation of the Malpasset dam failure in the 1960s. During these investigations, it was demonstrated how the permeability of the rock mass was affected by the effective normal stresses on the fractures, with permeability decreasing with increasing effective stress (Londe and Sabarly 1966). These tests thus provided some of the first insights on the hydromechanical (HM) coupling in fractured rock masses. Many variants of hydraulic jacking tests have since been developed, including: the step-rate test (Felsenthal 1974); the aforementioned HTPF test (Cornet and Valette 1984); a hydraulic jacking test developed specifically for pressure tunnel investigations (Brekke and Ripley 1987); the cyclic hydraulic jacking test (Rutqvist and Stephansson 1996) and; though not strictly a hydraulic jacking test, the modified Lugeon test (Philippe et al. 2019).

Hydraulic jacking tests are considered highly relevant for assessing stresses in connection with unlined pressure tunnel design since they are relatively simple to execute and they simulate the effect imposed on the rock mass by the pressurized water (Doe and Korbin 1987; Benson 1989; Broch et al. 1997; Merritt 1999). Testing is commonly performed during the constructional phase of hydroelectric projects, with number and location of tests based on local conditions.

The normal testing procedure is to drill boreholes in various directions into the rock mass surrounding the tunnel, and then install a single packer at a depth where stress influence from the tunnel can be ignored, to isolate a section of borehole. This borehole section, which typically is 5–15 m long, is then injected by water until the water pressure (P_inj) exceeds the in situ normal stress acting across the fracture most favourably oriented for opening, effectively providing a single measure of the magnitude of normal stress supported by the stimulated fracture, see Fig. 2. Tests are typically pressure controlled with pressure increments of 0.3–1 MPa, and with each increment held a few minutes until steady-state conditions are achieved. Each test cycle consist of a stepwise pressure increase followed by stepwise decrease with the same pressure increments. Testing in several holes and repeated cycles in each hole are commonly performed to improve the reliability of the measurements.

The interpretation of hydraulic jacking tests traditionally has been based on assumption of a distinct fracture opening or closure when P_inj equals or just barely exceeds the normal stress acting across the fracture. This assumption is, however, not necessarily valid, since it has been found that fracture opening and closure are gradual, rather than distinct, which affects the interpretation of test results (Rutqvist and Stephansson 1996). Still, the pressure at the transition from a gradual to a linear pressure decline might serve as a reasonable, lower bound, normal stress estimate (Hartmaier et al. 1998).

The test rig, shown in Fig. 3, consists of the following main units: a custom built true triaxial test frame with an integrated crane; a monitoring system for monitoring fluid pressure, fluid flow and acoustic emission (AE) signals, and a high-pressure reciprocating injection pump.

The modular test frame, made to order by Sollie Solutions AS, is made of structural steel (S355) and consists of a quadratic bottom plate on which a circular spacer element and the main steel body rests, see Fig. 4. The main steel body has an outer diameter of 820 mm and the minimum material thickness is 80 mm. On top is an 80-mm-thick lid which can be hoisted with the integrated hydraulic crane. The top lid is fixed with four Ø60 mm high strength (S165M) tension bolts running from the bottom plate through the top plate. Three 30 mm openings, angled 0°, 15° and 30° from the vertical, run through both top lid and the upper sensor platen, enabling drilling into the specimen under confinement and used also for installation of the injection packer into a confined specimen. The rock specimen is located centrally in the loading frame, surrounded by platens of different thicknesses, including six 19 mm sensor platens, housing acoustic emission (AE) sensors; five 40-mm-thick rigid platens, ensuring even load transfer from the cylinder to the specimen; and two 60 mm dummy platens, serving as rigid spacer elements, see Fig. 4. All platens are 290 mm wide, slightly smaller than the specimen width, to avoid contact between neighbouring platens during testing. Three hydraulic cylinders were used to load the specimen sides. Each cylinder is pressurized with a hand pump, allowing for individual control of the three stress directions according to the desired stress configuration. Since the stresses are intended to simulate a tectonic stress situation, no adjustment of stress was made during the test. The hydraulic cylinders have an integrated tilting function, where the plunger can be tilted up to 4° from the loading axis, thus accommodating minor rotations between the moving and stationary parts of the cylinder to prevent uneven loading, similar to the effect of spherical seats. To enhance load transfer was the diameter of the hydraulic piston was chosen such that it would be close to that of the specimen. Similar design choices for true triaxial rigs have been described by Zhang and Fan (2014) and Shi et al. (2013).

Confining pressures (P_jack) and injection pressures (P_inj) were monitored by four pressure transmitters, each having a 1 kHz sampling rate. The pressure data were displayed real-time throughout testing and data was stored for post-test analysis and processing. As a backup, the fluid pressure in the hydraulic lines could also be monitored by separate gauges, in the form of a 10 Hz pressure transmitter integrated with the injection pump, and three Bourdon pressure gauges for the confining pressures. A simplified overview of the monitoring system is shown in Fig. 5.

A dual piston reciprocating pump capable of providing 28 MPa injection pressure, at a maximum flow of 100 ml/min, was used to pressurize the borehole test section. The pump was factory configured to flow-control mode. The flow was controlled through a programme developed in LabVIEW, and was adjustable in 0.1 ml/min increments within the full flow range from 0.1 to 100 ml/min. A high-pressure stainless steel fluid injection line was used to transfer water from the pump to the packer, where the water entered the test section via the packer rod. Return flow, when needed, was directed through a separate return line equipped with two autoclave needle valves marked as “A” and “B” in Fig. 6. This valve arrangement serves the dual purpose of venting the system as well as enabling flow-back over a constant choke by fixing valve “B” at a pre-determined choke and shutting the flow on and off with valve “A” (though this latter option was not been employed for the experiments described in this paper). The total water volume in the tubing and test section was approximately 44 ml, distributed between the high-pressure tubing (10 ml), the packer rod (14 ml) and the open-hole sections (20 ml).

A 19 mm high-pressure, mechanical injection packer was used to isolate the test section during testing. This kind of packer is structurally similar to the single-use packers commonly used for both field-scale hydraulic jacking tests and rock mass grouting, and has the advantage of being easy to handle, durable and highly efficient in sealing the borehole. The injection line tubing was connected to the packer by a sliding coupling connection, enabling a fast and watertight connection. The downstream section of steel tubing was given an expansion loop to ensure better manoeuvrability of the tubing when connecting to the packer. The packer and steel pipe with the sliding connection are shown in Fig. 6.

AE monitoring was used as an aid in the analysis of pressure and flow data, enabling linking of AE activity with the mechanical behaviour of the stimulated fractures during hydraulic testing. The orientation of the fracture could also be mapped by 3D event localization, where each hypocentre represented a single point in a point cloud representing the fracture. During all tests, AE signals were monitored using eight broadband AE sensors with a 500 kHz operating frequency. The sensors, AE-HTRX type, were connected to an AE measurement system consisting of eight 2/4/6 voltage preamplifiers and an eight-channel acoustic emission PCI card configured with AEwin software, version E5.90. The preamplifiers gain was set to 40 dB for all channels.

Two holes for the AE sensors, with appurtenant grooves for the AE cables, were machined in each sensor platen to protect the sensors from the cylinder load. This arrangement enabled direct contact with the specimen side without damaging the specimen, see Fig. 7. Each AE sensor is 18.7 mm high with 22.2 mm diameter. Each sensor was wrapped with a 3-mm-thick rubber jacket to minimize acoustic contact between the side of the sensor and the steel platen. In addition, on the passive side of each sensor, a penny-shaped piece of rubber was placed to ensure that a gentle pressure was transmitted from the rigid platen to the sensor, promoting good acoustic coupling with the specimen.

The specimens used in all experiments were cubes of Iddefjord granite, cut from a quarry in south-eastern Norway. The approximately 920 Ma old granite was chosen due to its homogeneity, low permeability, and availability. The side lengths of the tested rock cubes were 300 mm ± 0.5 mm. Opposing sides of the cubical specimens were sawn parallel to ± 0.4°, as measured by a precision protractor. Main index properties of the Iddefjord granite are given in Table 1.

Each rock specimen was visually inspected for damage before testing, and the P-wave sound velocity (V_P) measured. A vertical, 180-mm-deep borehole was drilled with a hand-held percussion drill from the top centre of the specimen through the specimen centroid such that a 60 mm open-hole test section could be established in the middle of the sample, as shown in Fig. 8. After drilling, the borehole was flushed thoroughly with water until clear return water could be observed. The selected 20 mm hole diameter was considered an optimal dimension as it is large enough to be comparable to field-scale operations (Haimson and Zhao 1991), but at the same time small enough to avoid stress perturbation away from the borehole.

To facilitate the hydraulic jacking tests, a new fracture had first to be made in the initially intact rock specimens. This was done by confining the specimen inside the rig and hydraulically fracturing it, using the same equipment used for later hydraulic jacking tests. To promote the development of a vertical fracture a stress configuration with σ_H > σ_v > σ_h was chosen. Despite omitting, any pre-slotting of the borehole to control the fracture direction the fractures developed fairly planer and close to vertical, in a classic bi-wing (i.e. to both sides of the borehole) manner.

Before lowering the specimen inside the test frame, a thin layer of acoustic couplant was applied to the active side of the AE sensors, i.e. the surface in contact with the specimen. A paving slab lifter was used to clamp the specimen as it was lowered into the test frame using the integrated crane. Once the specimen had been placed inside the test frame, and the four sensor platens placed in contact with the specimen, the remaining platens could be installed, ensuring both a snug fit and that the specimen was maintained centrally in the test frame, as shown in Fig. 8. An initial check of the acoustic coupling was then made by first confining the specimen to 1 MPa in both horizontal directions, and then performing a pencil-lead test to ensure satisfactory acoustic contact between specimen and sensor.

For all tests, the true triaxial stress field, with σ_H = 7 MPa, σ_h = 3 MPa and σ_v = 4 MPa, was kept constant throughout the test. The chosen stress magnitudes were considered representative for stress conditions at typical depths of Norwegian hydroelectric projects where, due to the predominantly compressional tectonic regime in Norway, the maximum horizontal stress commonly exceeds the magnitude of the vertical stress. The stress directions were set to promote hydraulic jacking of the existing hydraulic fracture, and not creating new fractures, i.e. by ensuring that the direction of minimum horizontal stress was closest to normal to the fracture, and that the maximal horizontal stress was closest to parallel to the fracture. The stress directions, stress magnitude and fracture orientation for all specimens are shown in Fig. 9.

After confinement of the specimen, the packer could be installed and tightened, thus representing the actual field condition. The packer rod was topped off with water and the injection line thoroughly flushed prior to connecting the high-pressure injection line to the packer, to avoid trapped air in the system. Low-pressure injection into the test section was performed prior to each test to check for any leaks, causing the fracture to be wetted prior to testing. The specimen itself was unsaturated prior to testing. Ordinary tap water at ambient temperatures was used in all tests. Any water reaching the sample boundaries during testing is effectively drained along the sensor platen–specimen interface before being drained out of the test rig. The packer rod was anchored to the crane yoke prior to testing, a final safety measure to avoid sudden release and ejection of the packer during testing.

Two types of hydraulic jacking experiments have been conducted as part of this study. The first is a rapid variant of the step-rate test, hereafter termed the rapid step-rate test (RSRT), where water is injected in a series of pre-determined flow steps, and the corresponding response in injection pressure, P_inj is registered. The test starts with forward-step flow increments until hydraulic jacking occurs, interpreted in the test as a distinct deviation from the initial linear stage in the pressure–time plot. After hydraulic jacking, the test continues with backward-step flow reduction down to zero flow, similar to that of the Fracture reopening—option 3 of the HTPF method (Haimson and Cornet 2003).

The stepwise flow change, and relatively small flow increment of each step, ensures that the pressure in the test interval can be raised steadily, even when the initial permeability of the test section is unknown.

For the second test type, termed Type B, the first part of the procedure is basically identical with the RSRT, using the same ascending flow increments. In the second half of the test follows a brief period of constant flow before the pump is stopped without venting the injection line, similar to that of the Fracture reopening—option 2 of the HTPF method (Haimson and Cornet 2003). It should be noted that, due to the experimental setup, no traditional shut-interpretation to assess the fracture normal stress is intended, since it is believed that the leaky periphery (fracture extending to specimen edges) would cause gradual fracture closure and thus indistinct shut-in pressure interpretation (Rutqvist and Stephansson 1996). The shut-in phase is instead performed to investigate the acoustic emission (AE) response to fracture closure. The idealized, flow/time curves for the two test types are shown in Fig. 10.

An important feature of both test procedures is that the flow change for each step, and the duration of which each flow step is maintained, is kept constant throughout the test. For the experiments presented in this paper, each flow step is fixed at 1 ml/min, and the duration of each flow step is 1 s, giving a flow rate change of 1 ml/min/s. Consecutive tests on the same specimen were made without removing the specimen from the test rig between tests. The RSRT was performed first, and, after waiting a minimum of 0.5 h, Test B was performed.

To enable calculation of the normal stress across the different fractures, the orientation of each fracture had to be known. This was done by investigating the AE hypocentre location from 3D AE data and, where applicable, by direct measurements of visible fracture trace on the specimen sides. Though the fracture itself rarely was visible to the naked eye, it could be traced on the specimen sides either by post-test injection of water with methylene blue, a water-soluble dye, or from the colour contrast from the wetted fracture against the otherwise dry specimen. This combined fracture mapping provided an efficient and non-destructive means of identifying the fracture orientation and shape. To illustrate the ability of the AE system to locate the fracture, an AE hypocentre plot has been draped on a photo of the actual specimen immediately after removing the sample from the test rig after testing, see Fig. 11.

The fracture surfaces were not perfectly planar, and one single value for the orientation had to be chosen for the normal stress calculation. This orientation is termed the Representative Dip/dip-direction. The combined uncertainty due to variation in fracture orientation (the fact that the fracture is not entirely planar), and due to inaccuracy of orientation measurement, is estimated to be max ± 5° for dip-direction and ± 2° for dip, representing a max. error of about 0.28 MPa in the normal stress calculation. The dip- and dip-direction for each fracture, relative to the local north (see Fig. 9), is provided in Table 2, together with a brief description of the fracture.

A total of four tests based on the Type B test procedure have been performed. Injection pressures, flow rates and AE event rates from these tests are plotted as functions of time in Fig. 16. The event rate activity during the first half of each test evidently is lower than what observed for the RSRT (cf. Fig. 15), even though the initial flow stage for each test type is identical. The reason for this difference in AE behaviour may be associated with the gradual reduction of acoustic contact, caused by partial removal of the water-soluble acoustic couplant, and possibly also with changes in how well the two surfaces fit together, i.e. the fracture surface matedness. Despite this, a strong correlation between fracture closure during the shut-in period and AE activity was observed for all tests, as shown by Fig. 16.

Starting with test 001-B in Fig. 16, an initial linear pressure increase can be observed until P_inj = 3.6 MPa, from where deviation from linearity indicates leak-off. Full hydraulic jacking can be seen from about t = 27 s. No distinct AE response is observed prior to shut-in, but a very distinct AE response can be seen after shut-in when the fracture starts to close at t = 55.7 s, when P_inj = 4.5 MPa. An AE activity peak can then be seen at t = 57 s, when P_inj = 3.8 MPa. The AE event rate then gradually fades out as the pressure drops further and the fracture closes. For test 004-B a gradual deviation from the initially linear pressure–time curve can be seen from P_inj = 1.6 MPa, but with no corresponding AE activity. Full hydraulic jacking can be seen from about t = 63 s, when P_inj = 3.1 MPa. Immediately following shut-in a distinct AE response be observed at t = 95.5 s, also marking the event rate peak occurring at P_inj = 2.4 MPa. The AE event rate then gradually fades out as the pressure drops further and the fracture closes. For test 005-B a distinct breakdown, occurring at P_inj = 4.4 MPa can be observed after an initial linear pressure increase. A clear AE response to the breakdown can be seen with a sudden onset of AE activity. Some AE activity persists all the way to the shut-in phase, but a distinct increase in AE event rate can be observed after shut-in, the onset of which occurring at t = 104 s and P_inj = 2.4 MPa. The AE activity peak occurs at t = 106 s, when P_inj = 1.7 MPa. In test 006-B a gradual deviation from the linear pressure–time curve can be seen when P_inj = 3.4 MPa, but with no AE activity. Full hydraulic jacking can be seen from about t = 37 s, when P_inj = 4.7 MPa. Immediately following shut-in a distinct AE response can be observed from t = 76 s when P_inj = 2.9 MPa. Immediately afterwards follows the AE event rate peak at t = 76.5 and P_inj = 2 MPa, before the AE activity gradually fades out when the fracture closes. A summary of the pressure observed at the fracture opening, AE activity onset and AE activity peak for Type B tests is presented in Table 4.

From the above observations, it can be inferred that fracture closure is associated with a distinct AE response, but that AE data alone cannot be used to pinpoint the magnitude of normal stress, since the distinct AE response seems to appear when the fluid pressure is below the normal stress.

The hydraulic jacking experiments presented in this paper are aimed at investigating the ability of a simplified hydraulic jacking test to assess fracture normal stresses in an effort to facilitate more frequent stress measurements for the final design of unlined pressure tunnels. The results from the laboratory-scale hydraulic jacking experiments performed as part of this study, have indicated that the magnitude of normal stresses acting across fractures in rock can be measured efficiently, and to a reasonable level of accuracy, by the rapid step-rate test. The RSRT procedure is similar to ordinary step-rate tests but differ by the relatively small flow increments combined with the short and fixed duration of each step, enabling rapid and semi-automated testing. This represents a major benefit for field-scale operations since the time for testing can be reduced to minutes for individual tests rather than hours as sometimes can be seen in field tests.¹ The semi-automated testing procedure can further reduce operator bias and make testing more efficient since the fixed steps easily can be programmed in a computer-controlled pump. Therefore, it is believed that the RSRT can serve as one way to approach to the ideal of measuring stress regularly along the pressure tunnel rather than at a few locations only, following up the idea outlined in Ødegaard and Nilsen (2018). The short duration of each flow step does not guarantee steady-state conditions during the RSRT, but this does not invalidate the test approach since step-rate tests can be performed without reaching stabilized pressures at each step, provided that equal step-durations are used throughout the test, as discussed by several authors, e.g. (Nolte 1982; Singh et al. 1987; Economides and Nolte 2000; Lizak et al. 2006; Smith and Montgomery 2014).

The experimental results suggests that the most accurate estimate of fracture normal stresses is made by assessing data from the backward-step phase, i.e. the fracture closure phase. These findings are in qualitative agreement with those presented by Rutqvist and Stephansson (1996), who found that reopening pressures were influenced by gradual opening of the fractures—and that interpretation of fracture normal stresses from hydraulic jacking tests should be made from the fracture closure stages to avoid effects of non-linear fracture stiffness.

An additional argument for assessing normal stress from the fracture closure stages is the fact that fractures can dilate at hydraulic pressures lower than the fracture normal stress due to shear movement (Rancourt 2010). Even though this can affect the interpretation of the fracture-opening pressure, the shear stress will be released upon fracture opening, and a stiffness contrast can still be observed during the fracture closure stage.

On a pressure–time plot of the fracture closure phase, the normal stress can then be estimated from the transitional point between gradual pressure decline and linear decline. In a plot of flow vs. pressure, a qP-plot, the same pressure can be found by picking the transitional point between a gradual to a linear trend when flow- and pressure data are plotted for the fracture closure phase. This interpretation can be linked to the idea of system stiffness, originally proposed by Raaen et al. (2001), where the slope of the pressure–time graph observed prior to fracture closure represents the less stiff system associated with an open fracture, and the succeeding, steeper, linear pressure decline represents the system stiffness when the fracture is closed, as discussed in further detail in Sect. 5.2. The same way of reasoning has been presented by Thörn et al. (2015), who proposed that stiffness difference also could be associated with the matedness of fracture surfaces, where poorly fitted surfaces have low normal stiffness whilst well-mated fractures large normal stiffness. This difference in matedness might explain the observed reduction of system stiffness represented by the difference of slope between the pre-opening and post-closure stages for all four hydraulic jacking tests, see Fig. 12. The same mechanism can also explain the observed distinct difference in fracture opening pressure between tests 004-A and 004-B, which would otherwise be expected to be similar since the pressurization rate and confining pressures were identical. This assumed change in matedness might have been caused by minor shear dislocation of the fracture during testing, or by particles dislodged from the fracture surface during the hydraulic jacking, as has been suggested by Chitrala et al. (2011).

Fracture closure following hydraulic stimulation can be described as a three-stage process (Hayashi and Haimson 1991): stage 1, hinge-like fracture closure, i.e. closure by width reduction but at constant fracture length; stage 2, fracture starting to close at the tip and gradual fracture length reduction, and ultimately; stage 3, where the fracture closes fully, or to its residual aperture depending on the fracture characteristics, see Fig. 17. This understanding of fracture closure behaviour has been used by Raaen et al. (2001) to explain the different stages of pressure decline during flow-back tests. Referring to Fig. 17, the essence of their interpretative model is that the initial linear pressure decay (stage 1) represents the system stiffness when the fracture is open, and when the asperities of the fracture surfaces start to touch (point A), there is a gradual increase in system stiffness (stage 2), until the fracture finally closes (point B) and a new linear pressure decay is observed (stage 3), representing the system stiffness with a closed fracture.

There has been some debate as to which of the two inflection points best represents fracture closure and corresponding fracture normal stress. Arguments have been put forward for picking the point of first inflection (A) (Raaen et al. 2001), picking the intersection point of the lines drawn through the two linear segments (Plahn et al. 1997) and (Jung et al. 2016), or picking the lower inflection point (B) (Shlyapobersky 1989) and (Savitski and Dudley 2011).

In the experimental data, it has been found that the pressure at the lower inflection point corresponds reasonably well with the expected normal stress, as discussed in Sect. 4.3.1. An initial linear pressure decline, corresponding to stage 1 of Fig. 17, cannot be identified in the pressure–time graphs of tests 001-A and 004-A, but is partially visible for tests 005-A and 006-A, as can be seen in Fig. 12. This might suggest that picking the upper inflection point would overestimate the normal stress.

Picking the inflection points presented in Fig. 12 was done by fitting straight lines to the linear trend of each graph, to find the point of deviation. This approach, common in field applications, will introduce some subjectivity to the fracture closure determination. To reduce this subjectivity, plots of the time derivative of pressure versus time have been used, since the time derivative of pressure is linear when the system stiffness is constant, and stiffness changes thus may be detected from such plots (Raaen et al. 2001). However, since the pressure–time graphs are quasi-linear, the derivative plots offer only limited guidance on finding the exact inflection points, as no distinct breaks in the derivative plot can be found, see Fig. 18.

The authors believe that simple graphical methods for finding the inflection point, as illustrated in Figs. 12 and 14, are well suited for the purpose as they can provide estimates of fracture normal stresses that are reasonably accurate, whilst at the same time maintaining the intended simplicity of the RSRT procedure.

The observed link between AE response and the mechanical behaviour of the fracture represents a useful supplement to hydraulic jacking tests, potentially enabling a more robust assessment of fracture normal stresses. Similar observations of AE events associated with fracture closure have been reported by several authors (Ishida et al. 1997, 2012; Chitrala et al. 2011; Zhuang et al. 2020). Upon investigating the reported link between AE activity and fracture closure Bunger et al. (2014), however, did not find the same correlation during unconfined laboratory experiments, and concluded that it was not appropriate to link post shut-in AE events with fracture closure. From our experiments, we firmly believe that such a link does exists, and that the reported absence of AE events might be linked to the unconfined conditions of which the test was performed.

The AE event rate response does not seem to be sufficiently distinct to assess the exact moment of fracture closure, and the fracture normal stress, hence, could not be assessed from AE data alone. It is believed that the indistinct AE response primarily is caused by the repeated dynamic contact of fracture wall asperities, caused by the dilated fractures response to the incremental flow steps. In addition, when fluid percolates through the fracture there can be local and temporal pressure fluxes caused by repeated cycles of pressure build-up and deflation. Still, AE monitoring during hydraulic jacking tests is considered highly promising, not only for identifying the moment of fracture closure, but also to delineate the orientation of the stimulated fracture, as originally suggested by Tanaka et al. (1997), and later demonstrated by (Zang et al. 2017). The “tail” of AE events observed long after the fracture appears to be closed is believed to be associated with the further, slow, closure of the fracture as water without hydraulic connection to the test section slowly is drained from the fracture.

Investigation of hydraulic fracturing processes at laboratory scale requires proper scaling to adequately represent field conditions (De Pater and Weijers 1994). Results obtained from laboratory-scale hydraulic jacking experiments are, however, more easily transferred to field conditions as no material strength parameters, such as fracture toughness need to be considered. Still, some adaptions must be made when upscaling the proposed test procedure to field conditions, mainly related to the equipment used during testing, as will be discussed in the following.

First, is it required that the pump can be operated in flow-control mode without significant pressure pulses, so that the test sequence can be programmed to the desired flow steps and that fluid flow and pressure can be accurately measured and logged. A potential limiting factor for hydraulic jacking tests may be represented by the flow capacity of the pump, especially in the case of high rock mass permeability. One example is what was experienced at the Kihansi HPP in Tanzania, where measurements performed in an extensional tectonic regime required a pump capable of delivering 100 l/min at 20 MPa (Dahlø et al. 2003). Sufficient pumping capacity has also been addressed by Benson (1989), and the practical reason is clear: should the pumping capacity be too low for a given test hole, no pressure build-up can be achieved, and hence, no meaningful estimate of fracture normal stresses can be made. A common practical mitigating measure to this problem is simply to shorten the test section by deeper packer placements, or alternatively omitting holes with too high permeability altogether, moving to the next. Should still the permeability be too high can either shorter holes be drilled, or viscosity adjustments made to the injection fluid (Dr. B. Buen, personal communication May 2019).

During the laboratory experiments described in this paper, it has been found that the native 1 kHz sampling rate of the pressure transmitters should be downsampled to reduce noise, in line with the findings of Kakurina et al. (2020). By looking at the data at various degrees of downsampling, it seems that 100 Hz sampling rate would be optimal, and that sampling rates lower than 10 Hz should be avoided, since important details are lost. Therefore, we recommend sampling rates ranging from 10 to 100 Hz for field-scale hydraulic jacking tests. The transmitter itself should ideally be located as close to the test section as possible to minimize the effect of friction losses, especially at high flow rates (Wandke and Cooper 2016).

To enhance the sensitivity to minor changes in system stiffness during hydraulic testing it has been suggested to minimize the fluid volume used during testing, and to use a piping system with high stiffness (Ito et al. 2006). Even though this theoretically can enhance the sensitivity, it is hard to realize in the field due to the minimum requirements of the borehole dimensions, causing the bulk of the fluid volume to be in the open-hole section and only a fraction in the tubing/piping.

In the introduction, it was argued that distributed measurements along the entire length of a pressure tunnel can provide better insight regarding stress variability, and thus reduce the risk of hydraulic failure. To enable timely adjustments of the tunnel design (if stresses are too low), these measurements should be performed not too far behind the advancing excavation front. This requires that the measurements can be made quite regularly, such that they in a sense are an integral part of the tunnelling activities—and not as per current practice an occasional specialist activity requiring planned stops in other tunnelling activities. Performing standardized HF/HTPF tests regularly along the pressure tunnel would be prohibitively costly, due to the specialist nature of such tests. Though relatively cost-effective, the simplified hydraulic jacking tests commonly used as an alternative to HF/HTPF tests are somewhat impractical due to the long test duration (typically ~ 1–2 h for each test), causing undesirable hindrance to other tunnelling activities. The semi-automated and rapid nature of the proposed RSRT enable highly efficient tests (minutes, rather than hours), and since operator bias can be minimized—there is no strict requirement for specialist crews.