Simplified Hydraulic Jacking Test to Assess Fracture Normal Stress for Unlined Pressure Tunnels: A Field Experiment Using the Rapid Step-Rate Test

Abstract

This paper describes an experimental campaign where a simplified test method. The Rapid Step-Rate Test (RSRT) has been investigated in a full-scale field setting. The test, originally developed to assess rock stresses for pressure tunnel considerations, had in an earlier laboratory study demonstrated a promising ability to assess the magnitude of fracture normal stress. The field campaign presented herein was therefore aimed at assessing the field applicability of this test. The field experiments were conducted inside the pressure tunnel of the Løkjelsvatn Hydroelectric Power Plant in Norway, under field conditions identical to those for which the test originally was developed. A total of 29 individual tests were conducted in 7 boreholes, providing 20 test cycles with interpretable test results. The stress estimates made from the test cycles not affected by the near-field stress of the tunnel showed good correlation with the magnitude of minimum principal stress found from a preceding hydraulic fracturing and over-coring stress measurement campaign. The experience from the field campaign suggests that the RSRT can represent an efficient and reliable method to assess the magnitude of minimum principal stress, particularly useful for the final design of unlined pressure tunnels.

Highlights

• A first field verification of a new flow-controlled hydraulic jacking test protocol, the Rapid Step-Rate Test, is presented

• The test protocol enables estimation of fracture normal stress through analysis of the pressure decline curve during fracture closure stages

• The onset of fracture closure can be identified as a distinct brake of slope, passing from an initial linear pressure decline to a more gradual decline

1 Introduction

Assessing the magnitude of minimum principal stress, σ₃, is highly important for the design of unlined pressure tunnels since it governs the maximum allowable water pressure that the tunnel can sustain without failing (Benson 1989; Merritt 1999). The basic design idea is to locate the section of unlined pressure tunnel in a volume of rock mass where σ₃ exceeds the internal water pressure. This will minimize construction costs by limiting the length of steel liner to a relatively short section of tunnel upstream the power station, where it in any case is needed to ensure the controlled conveyance of water into the turbine. The main length of tunnel, from intake to the start of the steel liner, can thus be kept essentially unlined, as schematically shown in Fig. 1a. This design concept represents a highly cost-efficient design solution for the conveyance of pressurized water in hydropower projects, but only if hydraulic failure is avoided. Naturally, there are other design requirements which also need consideration before choosing an unlined concept. But in this paper, main emphasis is given to the stress requirement, which in most cases is the key design issue. For an in-depth review of the general design process of unlined pressure tunnels, reference is made to the significant contribution of Brekke and Ripley (1993).

Fig. 1

Conceptual overview of main elements of a hydroelectric power plant (HPP) using unlined pressure tunnels, including picture examples from various HPPs. a idealized long section showing the water tunnels, with the unlined sections shown in blue and the steel-lined sections in red, b intake structure, c section of unlined tunnel, d start of steel liner and, e power station with horizontal Francis turbines

The significance of stress estimates for safe pressure tunnel design is now well established among engineers working with the design of unlined pressure tunnels, and stress measurement techniques based on hydraulic methods are commonly employed, such as the hydraulic fracturing (HF) test (Hubbert and Willis 1957), the hydraulic testing of pre-existing fractures (HTPF) test (Cornet and Valette 1984), as well as other variants of hydraulic jacking tests (Brekke and Ripley 1993; Rutqvist and Stephansson 1996; Quirion and Tournier 2010).

Typically, stress measurements are performed only at a few key test locations, aimed at verifying design and the tender assumption on stress magnitudes. Once these assumptions are verified, by measurements performed at the selected locations, further testing is often limited, leaving hundreds, or even thousands, of tunnel meters without any stress measurements. One reason for the relatively limited scope of stress measurements is certainly related to costs, but based on the authors’ experience, it can also be attributed to an inherent overconfidence on the reliability of stress estimates based on overburden weight. With relatively few test sites, often located far apart, the designer has to make assumptions on the stress gradient beyond measurement locations, leaving the untested sections of pressure tunnel at risk of hydraulic failure. This is an unsatisfactory situation owing to the fact that in situ rock stress can vary significantly over short distances, independently of the surface topography above the point of observation (Marulanda et al. 1986; Haimson 1992; Amadei and Stephansson 1997; Martin and Chandler 1993; Christiansson and Janson 2003; Ødegaard et al. 2020).

To mitigate this undesirable situation, the authors believe that the number of measurement locations should be increased compared to current practice, to achieve a better coverage and distribution of stress measurement locations along the entire length of the unlined tunnel, as also suggested in Ødegaard and Nilsen (2018). Though it can be argued that it is economically and practically unfeasible to get a continuous stress log along the pressure tunnel, the authors believe that it is still possible to get closer to this goal, by adopting a simplified and cost-effective method for assessing stresses. One test method which potentially could make more testing possible, is the new hydraulic jacking test protocol termed the Rapid Step-Rate Test (RSRT), which was developed specifically with the goal of enabling such simple stress assessments (Ødegaard and Nilsen 2021). As the RSRT in laboratory-controlled conditions demonstrated a promising ability to assess fracture normal stresses, it was considered of great interest to investigate how the test protocol would perform in the field. The aim of the field campaign described in this study was therefore to assess the field applicability of the RSRT, by performing testing in a full-scale field setting.

The main field campaign of this study includes hydraulic testing in 7 boreholes drilled from the unlined section of the pressure tunnel of Løkjelsvatn HPP, currently under construction in southern Norway. These field experiments, comprising 29 individual test cycles, were designed in such a way that a comparison could be made between the stress estimates obtained from the RSRT experiments and stress estimates originating from the more well-established hydraulic fracturing (HF) and over-coring (OC) stress measurements. This was possible since HF and OC tests had already been conducted at the same location as part of the plant Owners final design considerations. These preceding tests had been performed by an independent specialist company, SINTEF Community, and access to the test report were granted by the plant Owner, Sunnhordaland Kraftlag AS (SKL).

Originally, it was intended to include data from hydraulic jacking tests performed at another plant, the Leikanger HPP, owned by Leikanger Kraft A/S, but equipment failure unfortunately made these tests unsuccessful. The experience gained during the initial field trials at the Leikanger plant did, however, prove valuable for the planning of the subsequent field campaign at Løkjelsvatn HPP, and some detail from these failed tests will therefore be included in Sect. 2.1.

The experiments performed at the Løkjelsvatn HPP are, to the authors best knowledge, the first time the Rapid Step-Rate Test protocol have been executed in field-scale conditions.

2 Description of the Test Sites

2.1 Initial Field Trials—Leikanger HPP

The Leikanger HPP is a run-of-river hydroelectric plant located 116 km north-east of Bergen, in the region of western Norway. The plant has an underground powerhouse equipped with a single Pelton turbine and the installed capacity is 77 MW, with a planned yearly production of 208 GWh once the last stage of development is completed by 2021. The tests, comprising 13 individual test cycles, were performed in 5 different boreholes, all drilled from within the access tunnel of the plant, close to Chainage 550, see Fig. 2. Access to the test site was granted by the plant owner, Sognekraft AS.

Fig. 2

Leikanger HPP long section (top) and plan view (bottom). The long section has been shortened to promote the visibility of the downstream high-pressure section of the water tunnels. Note that plan view and long section have different scales. Background map from the Norwegian Water Resources and Energy Directorate (NVE) (2020)

The tests were performed with a custom-built, dual-piston, reciprocal pump, using pressure-controlled hydraulic jacking test protocol, similar to the test approach of Doe and Korbin (1987). The test protocol included the stepwise increase in pressure, in a series of rapid 0.1 MPa pressure increments, until hydraulic jacking (or fracturing) occurs, and then reducing the pressure following the same steps down to ambient pressure while continuously monitoring the resulting pressure and flow. Analysis of the test data was, however, inhibited by excessive flow- and pressure pulsations. The pulsations were caused by a significant drop in flow rate occurring at each piston reversal, causing a corresponding drop in pressure. When the pressure dropped below the set point, the control system of the pump would immediately try to compensate for the loss of pressure, resulting in even more pulsations. Attempts of manually operating the pump, to override the PID (proportional–integral–derivative controller) of the pump, did not succeed. To worsen the situation, it was also discovered that the ordered hydraulic packers did not have the proper pressure rating, rendering them useless for the tests. Ordinary mechanical grouting packers found at site had therefore to be used, but packer seating depth was limited to 6 m (maximal length of the available grouting rods), considered too short to stay away from the perturbed stress field surrounding the 6.5 m wide access tunnel.

In summary, the test results from the Leikanger HPP could not be used for any meaningful assessment of in situ stresses, but the challenges faced during the pressure-controlled tests did influence the later development of the flow-controlled RSRT protocol, where no PID-control is needed.

2.2 Main Field Trials—Løkjelsvatn HPP

The main field experiments were all conducted inside the tunnel system of the Løkjelsvatn HPP, a storage hydroelectric plant currently under construction some 90 km south of the city of Bergen, Norway. The plant is equipped with a single 60 MW vertical Francis turbine placed in an underground powerhouse and will, once in operation, provide an annual production of 163 GWh. Planned commissioning of the plant is 2022.

The Løkjelsvatn plant was deemed well-suited for the planned field experiments since the in situ conditions corresponded well with typical conditions for which the test was originally developed, i.e., measurements performed inside unlined pressure tunnels during the construction stage. A longitudinal section and plan layout of the plant is presented in Fig. 3, and the main components of the tunnel system will be briefly described in the following.

Fig. 3

Løkjelsvatn HPP; longitudinal section (top) and plan view (bottom). The longitudinal section has been shortened to enhance the legibility. Note that plan view and long section have different scales. Background map from NVE (2020)

From the intake at the Løkjelsvatn reservoir, shown to the right in the plan overview, the water will be conveyed through a short horizontal headrace tunnel before entering the 480 m deep vertical pressure shaft. A 300 m long pressure tunnel connects the shaft bottom with the start of the steel liner. From this point, the transition zone between the unlined tunnel and the steel-lined, the water is conveyed through an approximately 60 m long section of concrete embedded steel liner before entering the turbine. The 3 200 m long tailrace leads the water to the lower Litledalsvatnet reservoir, shown to the left in the plan overview in Fig. 3. The maximum water pressure sustained by the unlined section of the tunnels is 548 m, equivalent to 5.4 MPa.

The test location, where all RSRT experiments were conducted, can be found at the lower end of the pressure tunnel, immediately upstream of the planned steel liner start, as shown in Fig. 3.

2.2.1 Rock Mass Condition

According to the tender stage geological map, the tunnels of Løkjelsvatn HPP were expected to pass mainly through Cambro-Silurian phyllites and mica schists. Some Precambrian amphibolite was also expected, mainly in the western reaches of the project. At the test location, only phyllite was observed, which, from laboratory testing of core specimens, could be classified as strong with a uniaxial compressive strength around 70 MPa, and Brazil Tensile Strength of 8 MPa. The rock mass quality was generally good with no signs of weathering. In addition to random joints, two joint sets were observed: the foliation, with a typical orientation (dip/dip direction) of 30/170, though with the dip locally varying between 20 and 50°, and a steep joint set with orientation 80/060. Only minor leaks and drips could be observed at the test location, though significantly larger leakages could be observed in the upper parts of the access tunnel.

Generally, the rock mass conditions at the test site were considered excellent for the drill and blast (D&B) excavation, allowing for full round lengths (~ 5 m) and full-face excavation, which is standard for most hard rock tunneling in Norway. The rock support in the water tunnels consisted mainly of scaling, spot bolting and occasional application of steel fiber reinforced sprayed concrete.

The underground state of stress at the test location had been assessed during the aforementioned HF and OC stress measurements. The σ₃ estimates made from these tests are summarized here, based on the test report (Sintef Byggforsk 2021):

• σ₃ from HF: 7.3 MPa, based on picking the lowest shut-in (P_ISIP) value from a total of 11 tests performed in boreholes H1, H3 and H4.

• σ₃ from OC tests: 9.4 ± 1.0 MPa, based on tests in borehole H7

The magnitude of all three principal stresses, as estimated from the OC tests are presented in Table 1, and an overview of all boreholes at the test location is provided in Fig. 4.

Table 1 Stress values found from 3D over-coring stress estimation performed in borehole H7 (Sintef Byggforsk 2021)

Fig. 4

Detailed view of the test location in the downstream end of the pressure tunnel. The blue colored numbers represent the chainage of each of the two tunnel branches. The access tunnel ends at Ch. 170, where it meets the unlined pressure tunnel. Chainage 0 marks the downstream end of the unlined pressure tunnel

The likely range of minimum principal stress σ₃ at the test location, based on the HF and OC stress estimation, would therefore be about 7–9.5 MPa. It can be noted that, according to the OC tests, the major principal stress σ₁ is close to vertical and has a magnitude that corresponds fairly well with that which can be calculated based on pure gravitational loading from the weight of the 591 m column of rock above the test site.

It should also be noted that, even though it is concluded that the minimum principal stress found from the HF measurements is 7.3 MPa, the test report offers no explanation for the considerable spread in shut-in estimates, with P_ISIP values varying between 7.3 and 17.3 MPa.

2.2.2 Test Location

The tests were all performed at the junction between the access tunnel and the downstream end of the pressure tunnel of Løkjelsvatn HPP, see Fig. 4. As mentioned in Chapter 1, stress measurements had already been performed at this location for the plant owner’s final liner design considerations. The boreholes used for this purpose are given the prefix “H”, and they are all located along the southern tunnel wall, as can be seen in Fig. 4. The boreholes on the opposite tunnel wall, marked with the prefix “L”, are the boreholes drilled exclusively for the field experiments described herein.

A company specializing in hydraulic testing and grouting works, Injeksjonsteknikk AS, was engaged to aid in the practical execution of the RSRT field tests. The company provided all equipment required for the tests and had made several modifications and adaptions to the pump setup and monitoring system to accommodate the specifications required for the planned RSRT protocol. Arguably the most important adaption was the software programming, enabling semi-automated control of the test procedure, in pre-determined flow-increments. The company also contributed with experienced personnel as support during the test execution.

The normal width of the pressure tunnel is 4.5 m but is somewhat larger at the junction with the access tunnel. At the time of testing, the pressure tunnel had been excavated from Ch. 0 to 80.

When rigging up for the RSRT experiments, it was discovered that the directions of the “L” boreholes deviated somewhat from what was originally planned. Therefore, it was deemed necessary to perform a rough field control of azimuth and inclination for all boreholes. This was done using a geological compass and clinometer. The depth of observation was typically limited to a couple of meters; thus, any borehole deviation deeper than this could not be detected. The easy downhole deployment of rigid steel tubes of 8 to 10 m length into the boreholes suggested, however, that the boreholes were fairly straight. The measured azimuths and inclinations of all boreholes are shown in Table 2. Unfortunately, it was discovered that borehole L4 had been moved from the planned location and given a direction that made the borehole alignment very close to the tunnel periphery, as can be seen in Fig. 4.

Table 2 Borehole geometry for all exploratory boreholes at the test location

Due to a rather tight construction schedule, access to the test site could only be granted during a brief holiday standstill of the tunneling activities. Despite the somewhat limited available time for testing, only two days, the halt in tunneling activities ensured good testing conditions and effective testing.

3 Test Protocol and Test Setup

3.1 General

Hydraulic jacking tests are often described as simple borehole tests used to estimate the magnitude of rock stress for various engineering purposes. Such tests commonly involve the pressurization of a sealed-off section of borehole until hydraulic failure occurs, typically from the hydraulic opening, or jacking, of pre-existing fractures, and then to analyze the pressure required to just barely keep the stimulated fracture open. Through various interpretative techniques and repeated test cycles can then the normal stress acting across the stimulated fracture be inferred, see (Felsenthal 1974; Nolte 1982; Doe and Korbin 1987; Rutqvist and Stephansson 1996; Hartmaier et al. 1998). Although the term “jacking” implies the mobilization of a pre-existing fracture, can the same principles for estimating fracture normal stress be followed for newly created fractures and pre-existing fractures alike.

Since the hydraulic jacking test in principle only measures fracture normal stress, and not necessarily the minimum principal stress, σ₃, has the common approach to such tests—at least when used for the purpose of final liner design in hydropower projects—been to perform tests in many boreholes with various orientation to increase the likelihood of stimulating the “critical” fractures, i.e., those oriented normal to σ₃. Somewhat simplified, the assembly of the lowest normal stress estimates from many such tests is then taken as a representative estimate of σ₃ (Hartmaier et al. 1998).

3.2 Test Protocol—The Rapid Step-Rate Test

The Rapid Step-Rate test is a hydraulic jacking test variant originally developed through a series of laboratory-controlled hydraulic jacking experiments, presented in Ødegaard and Nilsen (2021). During these experiments were hydraulic jacking tests conducted on cubical rock granite specimens, each specimen containing a pre-existing fracture of known orientation. Prior to each test could the specimen be subjected to a pre-set polyaxial stress field, thus allowing control of the normal stress acting across the fracture. This then provided “ground-truth” in the form of a known normal stress acting across the stimulated fracture, enabling efficient experimentation of various hydraulic jacking test protocols to investigate which best captured the true normal stress—eventually resulting in the RSRT protocol.

The RSRT is basically a rapid variant of the well-known step-rate test (SRT), used for decades as a tool for rock stress estimation in the petroleum industry Felsenthal (1974). Having adapted a novel interpretative technique to detect fracture closure from the resulting pressure data, the essence of which is outlined in Chapter 3.1.4 of this article, Ødegaard and Nilsen (2021) proceeded to demonstrate how the RSRT in the lab produced stress estimates that were in good agreement with the true normal stress.

The RSRT protocol involves injection of water into a sealed-off section of borehole, using pre-determined flow stages, or steps, while monitoring the corresponding response in water pressure, P_inj. The test starts with increasing flow steps, the forward-step stage, which is continued until a sudden pressure drop or a distinct deviation from the initial linear stage in a pressure–time plot can be observed, indicative of the creation or re-opening of a fracture, respectively. After fracture opening is the forward-step continued for a certain period before the flow steps are reversed to a stage of decreasing flow steps, termed the backward-step stage. The backward-step stage is then continued down to zero flow. By analysis of the resulting pressure, development during the backward-step stage can fracture normal stress be assessed according to the principles described in Chapter 3.1.4.

The RSRT protocol is defined by the two parameters step height, Δq (l/min), and the step duration, Δt, which together define the rate of flow-rate change (l/min × s⁻¹), see Fig. 5. The rate of flow-rate change is positive, i.e., increasing, in the forward-step stage, and negative during the backward-step stage.

Fig. 5

Conceptual overview of different RSRT flow steps. The rate of flow change can be adjusted by individually changing the flow rate, Δq, or flow step duration, Δt, as shown schematically by graphs a–c

Once the test parameters are defined the test sequence can be run automatically, only requiring the operator to reverse the flow steps after fracture opening, simply by pressing a single button on the touch-screen display of a programmable logic controller (PLC), an industrial-type computer. The required operator intervention is thus limited to defining the timing of flow reversal and to find the proper Δq and Δt values. Typical values for the tests performed at the Løkjelsvatn HPP were step heights ranging from 0.05–0.2 l/min and a step duration between 2 and 4 s. As the RSRT interpretation is based on an assessment of fracture behavior during the backward-step stage, there is no strict requirement on how the pressurization rate during the forward-step cycle is designed, as long as a fracture is created and opened against the normal stresses acting across it. For simplicity, it was, however, decided to maintain the same rate of flow change for both forward- and backward stages within each test cycle, though with some exceptions.

3.3 Field Experiments—Test Setup

An overview of the test setup including the borehole, the hydraulic packer assembly, fluid lines, pump and monitoring system is shown in Fig. 6. The pump used to pressurize the borehole is a CAT 550 pump, a plunger-type, positive-displacement pump configured to flow-control mode. The simplicity of flow-controlled tests, where no flowmeter or PID-control systems are required, was considered a benefit compared to pressure-controlled tests. Not only is the cost directly reduced when omitting the cost associated with the flowmeter, but the test system is also considered more robust and simpler to operate and maintain. The pump is computer controlled and can be operated and monitored through a touch-screen PLC. A pressure transmitter with a sampling rate of 5 Hz was used to monitor the test pressure, P_inj, during testing, and the flow rate, q_in, was calculated directly from the rotational speed of the electromotor driving the pump. As can be seen in Figs. 6 and 7, a flowmeter was connected to the hydraulic lines, but this was only for use in pressure-controlled tests, and thus not used during the tests at Løkjelsvatn HPP. The maximal flow capacity, 20 l/min according to specifications, was occasionally exceeded by the operator by increasing the RPM of the electromotor beyond the recommended speed. The 20 MPa maximal pressure rating of the hydraulic system was, however, never exceeded.

Fig. 6

Schematic overview of the experimental setup for the hydraulic jacking tests using the RSRT protocol

Fig. 7

Overview of the pump and packer assembly. Packer assembly during installation (top) and the pump (bottom), where the following components can be seen: (1) the pump head, (2) pressure transmitter, (3) Bourdon gage, (4) the electromotor, (5) pressure relief valve, (6) the connection box, and (7) an accumulator tank. The direction of flow is indicated with small arrows

All boreholes were visually inspected for leakage prior to testing, to be able to have a reference to detect any cross-hole leaks during testing. The following general test procedure was then followed:

• 1. Thorough flushing of the borehole, to remove cuttings and particles left after the drilling

• 2. Connecting the packer to the hydraulic tubes, placing packer at the desired depth

• 3. Connecting the packer assembly to the pump with hydraulic hoses

• 4. Packer inflation, to seal off the test section

• 5. Starting test protocol with the forward-step stage, continuing until a fracture is formed or re-opened. If P_inj still increased after fracture opening, the forward-step stage was continued until it exceeded the opening pressure by about 30%, and then

• 6. A constant flow was maintained for a brief period before

• 7. Reversing the test such that a backward-step cycle was followed all the way down to zero flow, and finally

• 8. Testing was terminated and the test section vented.

For consecutive cycles in the same borehole, steps 5 through 8 were repeated.

The boreholes used for testing were drilled in directions that not necessarily coincided with any of the principal stress directions, and it was thus expected that the stimulated fractures could twist and re-align away from the borehole, following the fracture mechanical principles mentioned in Chapter 5.2. This would significantly reduce the usefulness the use of any downhole tool for the delineation of the fracture trace, such as impression packers or televiewers, since these tools only indicate the fracture orientation on the borehole wall, and not the true orientation away from the borehole.

As a safeguard against the consequences of sudden packer ejection, known to have caused fatal accidents during similar stress measurement campaigns (Evans et al. 2003), no personnel were allowed in front of the borehole during testing. In field settings where passage in front of the borehole cannot be forbidden, anchoring of the rod directly to the tunnel wall has to be performed. In Norway, mechanical anchoring of grouting rods has become a mandatory safety measure during all rock mass grouting operations. The effectiveness of even simple mechanical anchorage was experienced during the initial field trials at the Leikanger HPP, where the packer assembly was prevented from shooting out of the hole following a sudden release of the mechanical-type rubber packer. The kinetic energy, and potential risk, associated with such events, should be evident from looking at the example in Fig. 8.

Fig. 8

Example of packer anchoring. Upper photograph showing how the packer rod is mechanically secured to the tunnel wall using expansion anchors and a chain. The lower photo shows how a packer rod was bent after a sudden packer release

During the RSRT experiments, attempts were initially made to save time by omitting the push-rods and only using the hydraulic hose itself to push the packer into the hole, but these attempts were not successful. Even though it worked fine in downward slanting boreholes, it was not possible to push the packer to the desired depth in upwards slanting boreholes without the use of rods.

The total length of hydraulic hose, as measured from the rods to the pump, is 36 m, and the total volume in the sealed-off system, prior to starting the pump, is about 70–90 L, depending on the packer placement depth. The open borehole constitutes the bulk of the volume, with the hose and rod together only accounting for 10–15% of the total. All tests were conducted with water at ambient temperatures, using the same water source as used for service water in various tunneling operations, which for the purpose of a hydraulic jacking test, could be characterized as clean water.

The volume or rock being tested, roughly some tens of meters outside the tunnel periphery, was effectively drained by the tunnel itself; thus, the tests were performed in drained conditions.

3.4 Fracture Closure Determination from the RSRT

Determining fracture closure is of great interest when assessing the underground state of stress since it has been shown that the hydraulic pressure required to keep the fracture open will be equal to the in situ normal stress acting across it (Hubbert and Willis 1957). Since fracture closure is not instant, interpretative techniques are required to find the pressure which best represents the actual normal stress across the fracture. The technique adopted for the assessment of fracture closure from the RSRT is based on the system stiffness approach of Raaen et al. (2001), who observed that when the pressure inside a hydraulically opened fracture is lowered, in a controlled manner, the resulting pressure decline curve will show distinct breaks caused by changes in the stiffness of the hydraulic system. A premise for this approach is that the stimulated fracture is less stiff (i.e., more compliant) than the overall system stiffness, effectively meaning that there is a detectable stiffness contrast as the fracture starts to close. They further explained how these breaks could be linked to the normal stress acting across the fracture, using the fracture closure model of Hayashi and Haimson (1991). In this model, fracture closure is described as a three-stage process:

• Stage 1: Fracture closes in a hinge-like manner, i.e., closure by width reduction but with constant fracture length

• Stage 2: Fracture closure by length reduction, meaning that the asperities of the fracture surfaces progressively will make contact, starting from the tip continuing toward the borehole

• Stage 3: The fracture is fully closed

Raaen et al. (2001) showed how these stages could readily be detected in pressure vs. volume (PV) or pressure vs. time (Pt) plots from flowback tests. Referring to the schematic pressure decline curve shown in Fig. 9, they argued that the initial linear pressure decay represents the constant stiffness associated with hinge-like fracture closure (Stage 1), and that the gradual pressure decline starting at Point A represent the onset of mechanical closure, where the asperities of the fracture start to make contact, causing a corresponding increase of stiffness (Stage 2), which ends at Point B, where a new linear decay can be seen, representing the system stiffness with a closed fracture, termed hydraulic closure (Stage 3). It should be noted that even though the term hydraulic closure originally indicated a fracture closed for flow, it will be expanded in this paper to include fractures closing back to their residual aperture, and thus not necessarily full closure in the sense that fluid cannot permeate the fracture.

Fig. 9

Typical pressure decline curve during controlled fracture closure. The borehole with a fully open fracture (top) indicates the schematic situation during the first linear pressure decline, the partially closed fracture (middle) indicates the closing fracture resulting in a gradually increasing pressure decline, and the closed fracture (bottom) indicates the last linear stage. Figure modified after Savitski and Dudley (2011) and Raaen et al. (2001)

Raaen et al. (2001) further suggested that the best estimate of fracture normal stress was found by picking the pressure at the end of Stage 1, Point A in Fig. 9, when the fracture starts to close by length reduction, indicating the onset of mechanical closure. Other authors have suggested to pick the point where the lines drawn through the two linear segments intersect, as seen in Fig. 9 (Plahn et al. 1997; Jung et al. 2016), or picking the point where the fracture is hydraulically closed, i.e., Point B in Fig. 9, (Shlyapobersky 1989; Savitski and Dudley 2011).

Instead of flowing back fluid at the surface, as is done during a flowback test, a slightly different method to achieve the same controlled fracture closure is used in the RSRT protocol, by reducing the injected flow rate q_inj in a controlled and stepwise manner, effectively reducing the system volume since the ratio of q_inj to q_leak (leakage into the rock mass) diminishes as the test progresses.

Since the interpretative model described by Raaen et al. (2001) is considered directly relevant also for the interpretation of the RSRT, some details of their original arguments will be iterated in the following. Their interpretation is linked to the concept of system stiffness, i.e., the how changes in pressure, dP, relates to changes in system volume, dV, described by

$$S=\frac{dP}{d\mathrm{V}},$$

(1)

where S is the stiffness of the test system, including the combined stiffnesses of hoses, borehole, water, and the stimulated fracture. As the system volume change originating from the deformation of hydraulic lines, borehole and the water itself can be considered negligible compared to the volume change caused by fracture closure, the latter will dominate the system stiffness during fracture closure. It is therefore useful to look only at the fracture stiffness, S_f, during closure.

$${S}_{f}=\frac{dp}{d{V}_{f}},$$

(2)

where dV_f is the fracture volume change. Sneddon and Mott (1946) showed that the maximum fracture width of an idealized disk-shaped fracture, an ellipsoid, as a function of the net pressure acting on the fracture, would be:

$${w}_{f}=\frac{8}{\pi }\left(1-{\nu }^{2}\right){r}_{f}\frac{{P}_{\mathrm{inj}}-{\sigma }_{n}}{E},$$

(3)

where w_f is the fracture width, ν the Poisson’s ratio, r_f the fracture radius, P_inj the test interval pressure, E Young’s modulus of the rock and σ_n the normal stress acting across the stimulated fracture. The fracture volume, V_f, can then be expressed as the volume of an ellipsoid with w_f as the minor axis, such that:

$${V}_{f}=\frac{2}{3}\pi {{r}_{f}}^{2}{w}_{f,}$$

(4)

which, when inserting for w_f gives:

$${V}_{f}=\frac{16}{3}\left(1-{\nu }^{2}\right){{r}_{\mathrm{f}}}^{3}\frac{{P}_{\mathrm{inj}}-{\sigma }_{n}}{E}.$$

(5)

Using Eq. 2, it can then be shown that the system stiffness is constant during Stage 1 when the fracture length is constant:

$${S}_{f}=\frac{\mathrm{d}p}{\mathrm{d}{V}_{f}}= \frac{3E}{16{{r}_{f}}^{3}(1-{\nu }^{2})}.$$

(6)

This also shows that the fracture stiffness is not affected by fracture width, and consequently that fracture opening or closing at constant fracture length, i.e., hinge-like closure, will have constant stiffness (Raaen et al. 2006). A linear pressure decline is thus expected when the fracture closes in a hinge-like manner, and any reduction of fracture length must cause an increase in system stiffness.

In Chapter 3.1.3, it was described how the forward-step stage of the test was maintained for some time when the pressure was increasing after fracture opening. The main reason why this is done is to ensure that P_inj sufficiently exceeds the normal stress acting across the stimulated fracture, so that a longer stage of linear pressure decline can be achieved during the backward-step stage, making it easier to pick the breakpoint at the end of Stage 1.

4 Results from the Field Testing at Løkjelsvatn HPP

4.1 Rapid Step-Rate Tests

During the course of the field testing campaign, a total of 29 individual test cycles, from 7 boreholes, were performed, all using the RSRT protocol. In the following sub-chapters, test results will be presented as graphs showing injection pressure (P_inj), flow rate (q_inj) and the time derivative of pressure (dP/dt) plotted versus time. The derivative plot is included to reduce the subjectivity associated with picking the point best representing the onset of mechanical fracture closure, i.e., the transition from linear to gradual pressure decline. Derivative plots are useful since the time derivative of pressure versus time is linear when the system stiffness is constant, and thus stiffness changes may be detected from distinct breaks in such plots (Raaen et al. 2001).

An individual graph for each test cycle is presented, but graphs from consecutive cycles in the same borehole are collected in one figure for ease of comparison, see Fig. 10 through Fig. 14. The number of test cycles performed in each borehole varied but was typically 3–4. In borehole L1, however, were 9 cycles performed, primarily as an initial check of the rate-dependency of fracture closure determination.

Fig. 10

Test results from borehole L1, including test cycles L1-1 through L1-9. A dashed line is drawn to show the deviation from linearity, and a double arrow to indicate the interpreted onset of mechanical fracture closure

The start point of each test, t = 0 s, is defined by the start of the pumping, and the test ends at the time when the backward-step flow cycle reaches zero flow, q_inj = 0. Data are, however, plotted for some time after zero flow, for the sake of clarity. It can be commented that the somewhat jagged appearance of the pressure graphs is caused mainly by the 0.1 MPa resolution of the pressure monitoring system. An overview of all boreholes at the test location, including and the number of RSRT cycles executed for each borehole, is provided in Table 3.

Table 3 Overview of the boreholes at the test location

Tests in boreholes L2 and H2 turned out inconclusive and therefore will not be presented here. Instead, an extract of the results from these boreholes will be presented in Chapter 5.3 together with a discussion on the characteristic pressure development.

The following sub-chapters include a description of the characteristic pressure development observed during the tests, including an assessment of the fracture closure pressures based on the principles outlined in Chapter 3.1.4. The pressure observed at the breakpoint from the initial linear pressure decay, i.e., Point A in Fig. 9, will hereafter be termed P_CL1, and the pressure observed at the onset of hydraulic closure, i.e., Point B in Fig. 9, will be referred to as P_CL2. A dashed straight line is drawn to highlight the interpreted linear stages of the graphs, and vertical arrows are used to indicate P_CL1—believed to best represent the fracture normal stress across the stimulated fracture. The fracture re-opening pressures, (P_RO), are also presented for reference, but is generally not considered a reliable measure for the magnitude of normal stress, due to its rate-dependency, and gradual nature (Cornet 1981; Rutqvist and Stephansson 1996; Zoback 2007; Ødegaard and Nilsen 2021).

To avoid tedious repetition of pressure data, we refrain from providing detailed text descriptions of all test cycles in the same borehole, but instead prioritize to comment the main observations, considered of interest for the understanding of the tests and the pressure behavior.

4.1.1 Borehole L1

A total of 9 RSRT cycles were carried out in borehole L1, with test results as presented in Fig. 10. The first test cycle, test L1-1, is characterized by an initial linear pressure increase until approximately t = 62 s, where a sudden pressure drop from the peak P_inj = 12.8 MPa indicates a breakdown event, i.e., the creation of a new fracture. After this event, the pressure is stabilizing at a 10.5 MPa plateau, suggesting further fracture propagation until the backward-step stage is initiated at t = 320 s, followed by a linear pressure decline until about t = 480 s, where a deviation from the initial linear trend can be observed in both the P–t graph and in the dP/dt plot, suggesting the onset of mechanical fracture closure and that P_CL1 = 7.8 MPa. Then, a rather long period of gradual pressure decay can be seen, lasting until t = 595 s where the onset of a second linear pressure decay indicates hydraulic closure and that P_CL2 = 5.2 MPa.

During the next test cycle, L1-2, an initial linear pressure increase can be seen until P_inj = 6.7, where a distinct deviation from the initial linear trend indicates re-opening of the fracture created during the first cycle. After fracture re-opening, a gradual pressure increase can be seen until t = 310 s, when the backward-step stage starts. Thereafter, a stage of linear pressure decline can be observed until t = 445 s, when deviation from the initial linear pressure decline suggesting that P_CL1 = 7.6 MPa. Following a period of gradual pressure decline, a new linear decline can be observed from t = 580 s, and that P_CL2 = 5.0 MPa. As the remaining test cycles executed in borehole L1 for the most part show very similar behavior as L1-2, the following examination of the test data for this borehole will be limited to highlighting some key observations.

To investigate the effect of a slower flow-rate change was the step duration, Δt, increased from 2 to 3 s for tests L1-4, L1-5 and L1-6. The resulting graphs show that, even though P_RO are seen to gradually decrease for consecutive tests, P_CL1 remain essentially the same, see also Table 4.

Table 4 Test results from RSRT performed in Borehole L1

After the conclusion of the initial six tests cycles in borehole L1 it was decided to add an additional 2 m rod extension to enable packer placement at 10.5 m depth, two meters deeper than the first six cycles in this borehole. This was done to investigate if the test results would be affected by this deeper packer placement. Three additional test cycles, L1-7, L1-8 and L1-9 were therefore conducted the following day. Test cycles L1-8 and L1-9 showed essentially the same results as the first six test cycles, but the premature flow reversal during test L1-7, caused by an operator mistake, provided some interesting new insights: A very different pressure response can be observed during test cycle L1-7, including the striking absence of any initial linear pressure decay. This behavior is believed to be caused by the fact that the interval pressure, due to the operator mistake, never sufficiently exceeded the normal stress of the stimulated fracture. Hence, no initial linear pressure decay associated with hinge-like closure could be observed, since the fracture more or less directly entered the stage of closure by length reduction.

In the succeeding tests, L1-8 and L1-9, where the pressure was sufficiently increased, curves with a distinct break following an initial linear pressure decay could be observed, suggesting P_CL1 values of 6.6 MPa and 7 MPa, respectively. The interpreted opening- and closure pressures for all test cycles in L1 are summarized in Table 4.

4.1.2 Borehole L3

Three RSRT cycles were performed in borehole L3, the resulting graphs from which are presented in Fig. 11. The first test cycle, L3-1, is characterized by initial steep pressure increase to a peak at P_inj = 16.8 MPa, followed by a sudden drop in pressure, first to an intermittent 11 MPa level, then further down to 7.5 MPa, suggesting two breakdown events. The fairly stable pressure plateau of P_inj ≈ 7.5 MPa suggests fracture propagation. The backward-step stage starts at t = 315 s and is followed by a fairly linear pressure decline until t = 460 s, where a distinct deviation from the initial linear pressure decline suggests the onset of mechanical fracture closure and that P_CL1 = 7.1 MPa. After a brief period of pressure decline can a new stage of linear pressure decay be seen at t = 500 s, suggesting that P_CL2 = 7.0 MPa.

Fig. 11

Test results from borehole L3, including tests L3-1 through L3-3

The succeeding two test cycles did not show equally distinct breaks in the backward-step stage, making fracture closure uncertain. Starting with the second test cycle, L3-2, a linear pressure increase can be observed until re-opening is indicated with P_RO = 4.3 MPa. Thereafter, the pressure can be seen to increase steadily until the maximum capacity of the pump is reached, forcing the end of the forward-step stage at t = 400 s. The backward-step stage is initiated at t = 420 s and is followed by an initial period of almost constant pressure, before starting to decline gradually from t = 550. Even though a slight change of curvature can be observed both in Pt- and dP/dt plots at t = 670 s, possibly suggesting that P_CL1 = 7.6 MPa, the response is considered too uncertain to firmly conclude that it is the onset of fracture closure. Similar behavior is observed for the last test cycle L3-3, but here the forward-step stage was again stopped prematurely, so that the backward-step stage started when the pressure was almost the same as the anticipated normal stress found from test cycle L3-1. The somewhat erratic pressure fluctuations seen at the end of test cycle L3-3 were caused by the operator performing some manual maneuvering of the outlet valve. A summary of the interpreted opening- and closure pressures is given in Table 5.

Table 5 Interpreted pressure values from the tests performed in Borehole L3

4.1.3 Borehole L4

Testing in borehole L4 comprised 3 RSRT cycles, which are all presented in Fig. 12. A summary of the interpreted pressure values is provided in Table 6. Starting with test cycle L4-1 a steep pressure increase can be observed until t = 220 s, where a deviation from the linear trend indicates that some fluid starts to leak from the test section, often termed leak-off. Following the leak-off a further pressure rise can be seen to until t = 275 s, where a small pressure drop indicates fracture opening. Two additional pressure drop events can also be observed, at t = 400 s and t = 525 s, suggesting fracture propagation events. After the backward-step stage is initiated at t = 545 s, a linear pressure decline can be seen until a breakpoint is observed at t = 765 s, suggesting that P_CL1 = 4.4 MPa. After a short period of gradual pressure decline can a second linear pressure decline be seen, suggesting that P_CL2 = 3.9 MPa. The backward-step stage of the last two tests L4-2 and L4-3 are very similar to that of the first, with P_CL1 of 4.5 MPa and 4.4 MPa, respectively, in close agreement with that of the first test cycle.

Fig. 12

Test results from borehole L4. The double arrow indicates the interpreted point of mechanical closure

Table 6 Test results from RSRT performed in Borehole L4

It must be noted that due to the unfavorable borehole orientation of L4, running fairly close to the tunnel periphery, it is considered likely that the tests are affected by the stress perturbations of the tunnel, i.e., the near-field stress. The too short distance between borehole and tunnel was also evident from the observation of a slight water leakage showing on the tunnel wall both upstream and downstream of the borehole during testing, suggesting a hydraulic communication between the test section and the tunnel.

4.1.4 Borehole H1

Starting with test H1-1, the first RSRT cycle in this borehole, see Fig. 13, shows a linear pressure increase developing from t = 190 s, following an initial stage of fairly slow pressure increase. After this linear pressure increase, a pressure drop can be observed when the pressure reaches 11.8 MPa. Even though this pressure drop resembles a breakdown event, the rather blunt pressure peak and relatively low pressure drop after the peak indicate that the event is fracture re-opening. The succeeding 11 MPa pressure plateau could, however, indicate that a new fracture is created, alternatively that a pre-existing fracture is further propagated (several pre-existing fractures should be present in the borehole due to the HF tests). After the backward-step stage is initiated at t = 340 s, a linear pressure decline can be seen until t = 570 s where a downward break in the Pt-curve suggests onset of mechanical fracture closure with P_CL1 = 8.2 MPa. A brief period of gradual pressure decay is then followed by a new linear decay, suggesting hydraulic closure and that P_CL2 = 8.0 MPa. Quite similar pressure development can be observed during the three consecutive RSRT cycles, indicating P_CL1 values within an 8.6–9.0 MPa range. It is interesting to observe that the value of P_CL1 remained rather unchanged when Δt was increased from 2 to 4 s during the backward-step stage of test cycle H1-4. A summary of the interpreted pressure values is provided in Table 7.

Fig. 13

Test results from borehole H1

Table 7 Test results from RSRT performed in Borehole H1

4.1.5 Borehole H4

Testing in borehole H4 comprises 3 RSRT cycles, the results from which are presented in Fig. 14, and with a summary of the interpreted opening and closure pressures provided in Table 8. The first test cycle, H4-1, displays a linear pressure increase before a distinct deviation from this trend, occurring at t = 275 s, suggesting re-opening of a pre-existing fracture when P_inj reaches 6.1 MPa. The backward-step cycle starts at t = 470 s and is followed by a fairly linear pressure decline until t = 670 s where the deviation from the initial linear pressure suggests that P_CL1 = 6.2 MPa. After a period of gradual pressure decay a second linear pressure decline can be seen developing from t = 830 s, suggesting that P_CL2 = 4.2 MPa. Similar behavior could be observed during the backward-step cycle of the next two test cycles H4-2 and H4-3, with P_CL1 = 6.0 and P_CL1 = 5.9 MPa, respectively.

Fig. 14

Test results from borehole H4

Table 8 Test results from RSRT performed in Borehole H4

Though not as extreme as borehole L4, it can be commented that H4 also runs quite close to the tunnel periphery, which might cause the test section to be affected by the stress re-distribution of the tunnel, and consequently that the stress estimates also could be affected by the near-field stresses.

4.1.6 Summary of Results

A summary of the interpreted closure pressures, averaged for each borehole, is provided in Table 9. As can be seen, the P_CL1 values range from 4.4 to 8.7 MPa, with an average value across the boreholes of 6.7 MPa. Disregarding the tests performed in boreholes L4 and H4, considered less representative for the in situ stress due to the proximity of the tunnel, narrows this range to 7.2–8.7 MPa, which is quite comparable to the σ₃ estimate of 7–9.5 MPa, found from the preceding HF and OC stress measurements. The corresponding values for P_CL2, range between 4.8 and 8.5 MPa, the low range of which is clearly lower than the σ₃ estimate from the HF and OC stress measurements.

Table 9 Summary of test results from interpretation of the backward-step stage, average value for each borehole

5 Discussion

5.1 Fracture Behavior During Testing

A series of hydraulic jacking experiments were conducted to assess the ability of a new hydraulic jacking test protocol, the RSRT, to assess fracture normal stresses under field-scale conditions. Through analysis of the test results several encouraging observations could be made, strengthening the theory that reliable normal stress estimates can be made by assessing pressure decline curves during the backward-step stage of the RSRT, in the same manner as done for flowback tests.

During the backward-step stage of the tests two characteristic downward slope breaks could usually be observed, displaying pressure decline curves that are similar to those seen during the preceding laboratory campaign, also corresponding with the pressure decline observed during successful flowback tests. The pressure at which the breakpoints occur are repeatable for consecutive test cycles in the same borehole, even when the step-rate change is varied between consecutive cycles. Since the breaks occur without any other concurrent changes to the hydraulic system (the flow rate is reduced at a constant rate), it is believed that the distinct changes in the rate of pressure decline are caused by the fracture closing process, and that the RSRT successfully captures the fracture behavior predicted by the fracture closure model of Hayashi and Haimson (1991).

In the traditional interpretation of flowback tests, the accelerated pressure decline was observed at fracture closure attributed to a flow restriction introduced when the asperities of the fracture surfaces started to close (Nolte 1982). However, since the exact same behavior is seen during the RSRT, where water always is injected and not flowed back, we tend to favor the explanation that this effect is caused by the asperities touching, causing an increase in the fracture stiffness (Shlyapobersky (1989); Raaen et al. (2001); Jung et al. (2016)). Another way to explain the same effect is that when the fracture is open, the full normal stress will act across it as “push-back” on the fluid, but once the asperities start to touch, some of the normal stress will be carried by the asperities, thus in a sense shielding the fluid and causing a more rapid pressure drop as the fluid leaks into the rock mass.

A simplified sketch, intended to explain our conceptual understanding of the system behavior during the RSRT is shown in Fig. 15. While entirely conceptual, the sketch might provide some overall understanding of the pressure development during a RSRT cycle: In (A) an isolated borehole is injected with water according to the stepwise flow increase of the RSRT protocol, causing a corresponding increase in pressure until; (B), a fracture is created, causing a pressure drop since volume is added to the system by the fracture opening, and then; (C) the fracture propagates further, ideally in a plane normal to σ₃, until the operator reverses the flow steps, whereupon in; (D) the stepwise reduction of flow, and corresponding linear pressure decay, cause the fracture to close in a hinge-like manner, before; (E) the pressure inside the fracture drops below the normal stress acting across it, causing the fracture to start to close by length reduction (mechanical closure), seen as a distinct downward break from the linear pressure decay in the pressure decline curve at P_CL1, before the gradual pressure decline continues until (F) hydraulic fracture closure is indicated by the start of a second stage of linear pressure decay, P_CL2.

Fig. 15

Principal sketch (“cartoon representation”) of the idealized fracture behavior and corresponding pressure development during the RSRT. The array of small arrows signifies the direction of the minimum principal stress

In cases where there is significant re-orientation of the fracture away from the borehole, a tortuous flow path can be created, potentially causing a bottleneck for flow (Zoback (2007); Jung et al. (2016)). Such a near-borehole flow restriction will cause a pressure drop between the borehole and the fracture, thus potentially causing the interpretation of the RSRT to over-estimate the magnitude of minimum principal stress since the measured pressure exceeds that inside the fracture. This effect will, however, be largest when the fracture is narrowest since it is known from the cubic law that the pressure drop is inversely proportional to the cube of the fracture width (Witherspoon et al. (1980); Economides and Nolte (2000)). This suggests that the effect of near-borehole flow restrictions generally is less prominent when picking the P_CL1 values from the RSRT, since the fracture at this stage of the test is fully open.

5.2 Estimating Minimum Principal Stress from the RSRT

The test results from the RSRT cycles yielded P_CL1 values varying between 7.2 and 8.7 MPa for tests in boreholes L1, L3 and H1, where effects of the tunnel near-field stress were considered minimal. This estimate is surprisingly close to the σ₃ estimate of 7–9.5 MPa found from the HF and OC measurements, suggesting that the stimulated fractures must have aligned rather normal to the direction of σ₃, instead of following some pre-existing weakness plane. This assumption is also supported by the fact that the σ₃ magnitude is substantially (about 6–9 MPa) lower than the two other principal stresses, making fracture propagation in a plane that is not normal to σ₃ unlikely, and in any case requiring higher pressures than were observed during the tests. Consequently, the P_CL1 value found from the RSRT should provide reasonable estimates of the minimum principal stress, σ₃.

The results from the preceding laboratory trials did, however, suggest that the upper breakpoint, P_CL2, could over-estimate the normal stress, thus seemingly in contradiction with the interpretation from the field experiments. It is, however, believed that the reason for the deviating interpretations is linked to limitations in the laboratory conditions. Specifically, the difficulty of maintaining an open fracture due to the leaky periphery, thus masking the stage of hinge-like fracture closure (Stage 1), could make the detection of mechanical fracture closure difficult.

From the lack of knowledge on the orientation of the stimulated fractures, the above conjecture of fractures propagating normal to σ₃ cannot be confirmed, but it finds support in the literature: Close to the borehole will the orientation of the newly created fracture be governed by the local stress field surrounding the borehole, and to some extent also by local weaknesses in the rock and borehole irregularities, causing the fracture to initiate in a direction that is not normal to the far-field σ₃ direction. Outside the influence of the borehole, however, the fracture will tend to twist and re-align such that it ends up propagating in a plane approximately normal to σ₃ since this is what requires the least amount of energy (Zoback 2007). This phenomenon has been demonstrated in mine-back studies Warren and Smith (1985), microseismicity studies Zang et al. (2017), in laboratory experiments (Abass et al. 1994; Mao et al. 2017), as well as numerically (Zangeneh et al. 2015; Lavrov 2016). The same fracture behavior was also convincingly demonstrated in a recent study conducted at the Sanford Underground Research Facility (Guglielmi et al. 2021): Based on microseismic monitoring and continuous borehole displacement monitoring, the authors were able to show how a hydraulic fracture re-oriented away from the borehole and propagated in a plane normal to σ₃, even when the fracture first initiated along a foliation plane with a different orientation. During the fracture closure stages of these tests, the fracture closed in a direction normal to the main fracture, and only during the final stages of closure displacement aligned to the foliation plane normal where the fracture first initiated. This is relevant for the interpretation of the RSRT data since it demonstrates how the normal stress estimates made from identifying the pressure at onset of mechanical closure (which is early in the fracture closure process) is representative for σ₃ even when the fracture initiated in a plane that is not normal to the σ₃ direction.

While P_CL1 was considered quite representative for the magnitude of σ₃, the pressure found at the second breakpoint, P_CL2, was usually less representative, in accordance with the findings of Raaen et al. (2001). Assuming a pervious rock mass, and that the pre-excavation groundwater table at the test location corresponded with the level of the numerous lakes situated directly above, the undisturbed groundwater pressure at the test location would be about 5.8 MPa. This is significantly higher than the average P_CL2 value found in borehole L1, suggesting that P_CL2 in this case must be less than σ₃, since groundwater pressures in excess of the minimum principal stress would be inadmissible due to the occurrence of natural hydro-fracturing (Dahlø et al. (2003); Zoback (2007)).

5.3 Failed Tests in Boreholes L2 and H2

Tests in boreholes L2 and H2 all turned out inconclusive, preventing assessments of fracture closure stress due to anomalous pressure development. The reason for the irregular test behavior is believed to be linked to unfavorable test conditions, as will be described in the following. Looking at the start of the backward-step stage of test cycle L2-1 in Fig. 16, one can see an almost linear, or gently decreasing slope all the way down to zero flow—contrary to the expected downward break in the P_inj–t curve associated with fracture closure. The same type of irregular pressure decline was observed during all three test cycles, and it is believed to be caused by air trapped in the borehole. The presence of air inside the hydraulic system could effectively dominate the system stiffness, thus masking any stiffness contrast during the backward-step cycle. That air can have detrimental effect on fracture closure assessments was pointed out by Raaen and Brudy (2001). It can be questioned, however, why tests in boreholes L4, H1 and H4 all yielded interpretable results, despite also being air-filled at the start of the test (they are all upwards slanting and hence drained). This can be explained by the air being expelled sufficiently far during testing to avoid the negative effect of the less stiff air in hydraulic contact with the test system. The proximity of borehole L4 to the tunnel surface, and the presence of several pre-existing fractures in boreholes H1 and H4, would make it easier for air to leak out of the test section than in borehole L2.

Fig. 16

Two examples of failed tests. Test results from the first test cycles of boreholes L2 (left) and H2 (right)

Testing in borehole H2 was seriously hampered by a cross-hole hydraulic communication where water leaked from the H2 test section into the neighboring borehole H7. This leakage is believed to have entirely dominated the pressure response, effectively preventing the controlled fracture opening and closure, resulting in a gradual pressure decline during the backward-step stage of the test, devoid of discernible breaks in all test cycles. That a hydraulic communication could be created between the two boreholes, with borehole H2 crossing above borehole H7 with only 1–2 m spacing, was expected—but it was still considered worthwhile to try testing in this borehole. The reason why this borehole arrangement was originally chosen for the preceding HF and OC stress measurements is not known to the authors.

5.4 Suggestions for Proper Test Execution

Based on the field experiments conducted at the Løkjelsvatn HPP, we believe that the following three conditions should first be addressed when planning stress estimates using the RSRT protocol:

• 1. Ensure that the test section is established outside the stress perturbations of the tunnel. Though site specific, keeping the test section away from the tunnel periphery with a distance equivalent to two times the tunnel will in most cases be sufficient.

• 2. Minimize risk of cross-hole leakage by ensuring sufficient distance between neighboring boreholes. A minimum distance of about 10 m is recommended.

• 3. Avoid air in the test system by flushing hydraulic lines prior to testing and by ensuring that all boreholes are given a sub-horizontal inclination so that they can be water-filled prior to placing the packer.

Adherence to these three basic requirements will significantly reduce the risk of test failure, but there are also other considerations of importance. One aspect is to ensure that the fracture is fully opened against the in situ normal stress, so that the initial linear pressure decay can be detected during the backward-step stage of the test. This means that the stimulated fracture should extend sufficiently far away from the borehole to not be affected by the near-field stress concentration of the borehole, but also that the fracture volume is sufficiently large to create the stiffness contrast when opening and closing. As a rough guide, based on the field data from testing at Løkjelsvatn HPP, it is believed that the fracture will have extended sufficiently far once the forward-step stage has been continued to about 30% above the fracture re-opening pressure. This must, however, be adjusted by trial and error in the field, simply by adjusting the test variables (Δq, Δt and test duration) until test cycles show an initial linear pressure decline from the start of the backward-step stage. This requires the pump to be able to provide sufficient flow, which it in some cases during the field campaign did not. To increase the robustness of the testing system, it is therefore recommended to have a pump with a somewhat higher pumping capacity than the 20 l/min limitation of the pump used during our tests.

Even though a straddle-packer arrangement could be used with the RSRT, single packers were preferred due to their simplicity and low cost. A drawback of using single packers is that this introduces the risk of sudden packer ejection, caused by slippage of the packer during testing, as experience by the authors during testing. Similar events are also known from rock mass grouting, even with fatal consequences. It is therefore of utmost importance that the packer assembly is physically restrained from being ejected from the borehole, e.g., by mechanical anchorage. If this cannot be done, an alternative can be to establish a zone of no entry in front of the packer during testing.

6 Conclusion

A series of experimental hydraulic jacking tests were conducted underground at the Løkjelsvatn HPP, in an effort to assess the field applicability of the RSRT, a novel hydraulic jacking test protocol first presented in the laboratory study of Ødegaard and Nilsen (2021). The experimental results confirm the preceding laboratory findings, suggesting that rapid and reliable estimates of fracture normal stress can be made using the RSRT, thus providing a successful first field verification of the test.

It has also been found that the normal stress estimates correspond fairly well to the magnitude of minimum principal stress σ₃, provided that measurements were done sufficiently far from the tunnel contour to actually measure the far-field stress. This suggests that the stimulated fractures in these cases may have propagated in a plane that is normal to σ₃, thus enabling direct estimates of σ₃ from the RSRT.

The RSRT protocol allows for fairly rapid test execution, with average test duration of approximately 10 min and test cycles rarely exceeding 15 min. Even with three test cycles, which is usually recommended, testing in one borehole will last less than one hour. Test interpretation can be made on-site, and quite rapidly, not requiring specialized software—only standard spreadsheets. When it comes to the equipment required for the test, all components are readily available (off the shelf), though the computer control of the pump requires some programming. Boreholes for the tests can be drilled using drilling jumbos, which for D&B excavated tunnels are readily available. Combined, this makes the RSRT highly cost- and time-efficient.

Overall, the experience from the field campaign suggests that, provided proper execution, the RSRT represents an efficient and reliable method to assess the normal stress magnitude, particularly useful for the final design of unlined pressure tunnels. Still, since the performed experiments are relatively few, and limited to a single test location, more field tests are required to further verify the aptness of the RSRT, ideally by performing a comparison with an independent stress estimation technique in the same borehole.

Though we cannot offer any concrete advice on the optimal spacing between tests performed as part of the stress estimation campaign for unlined pressure tunnels, it will be a major step in the right direction if measurements are done at regular intervals, rather than only at a few select locations. Ideally, one could envisage that the RSRT was incorporated in the normal excavation cycle so that one or two boreholes for RSRT was drilled every 20–50 m of tunnel, or even closer—depending on risk acceptance, economy, and rock mass complexity of the project.

As a potential extension to the original intended scope of the RSRT, it could be interesting to try out this test during grouting operations, as a potential way to delineate the “safe” grouting pressures during pre-excavation grouting in tunnels. This is particularly relevant for infrastructure projects where high-pressure pre-excavation grouting is performed, known to quite frequently produce undesirable hydraulic fracturing events (Strømsvik et al. 2018).