In situ measurements of rock mass deformability using fiber Bragg grating strain gauges

International Journal of Rock Mechanics & Mining Sciences 71 (2014) 350–361

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International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms

In situ measurements of rock mass deformability using fiber Bragg grating strain gauges JoAnn R. Gage a,n,1, Herbert F. Wang a, Dante Fratta b, Alan L. Turner c,2 a

Department of Geoscience, University of Wisconsin—Madison, 1215 W. Dayton St., Madison, WI 53706, USA Department of Civil and Environmental Engineering, Geological Engineering Program, University of Wisconsin—Madison, 1415 Engineering Drive, Madison, WI 53706, USA c Micron Optics Inc., 1852 Century Place NE, Atlanta, GA 30345, USA b

art ic l e i nf o

a b s t r a c t

Article history: Received 1 April 2013 Received in revised form 22 July 2014 Accepted 25 July 2014 Available online 7 September 2014

In order to examine how the mechanical properties of a rock mass vary from the centimeter to meter scale, we performed two field point-loading tests (89 kN and 890 kN) to determine the in situ modulus of deformation of a rock mass. The experimental setup is analogous to plate jacking-type tests, but instead, using a point load. The experiments were done in the Poorman formation on the 4100 level (
1250 m underground) of the Sanford Underground Research Facility (SURF) at the site of the former Homestake gold mine in Lead, SD. For comparison with in situ values, we also conducted laboratory mechanical tests and used two geotechnical classification systems to evaluate rock stiffness. The in situ modulus of deformation increases with depth into the rock mass. This increase in stiffness is a result of the differences in mechanical properties due to the effect of excavation of the underground space. Near the surface (0–1.2 m depth), the rock is softest due to induced fractures and damage from blasting. Beyond this damaged zone is the stress-relief zone (1.2–1.5 m depth), where open joint sets affect rock stiffness, and beyond that lies the undisturbed zone ( 41.5 m depth) where the rock is the stiffest. If done properly, in situ measurements of rock stiffness are a valuable tool to fully characterize the gradient in stiffness of a rock mass, which laboratory tests or geotechnical classification systems do not fully capture. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Fiber Bragg grating Strain gauges In situ strain Modulus of deformation Rock strain strips

1. Introduction Deformability and strength are the most important geotechnical variables used to predict the behavior of a rock mass in response to loading or construction. The modulus of deformation (Em) is one of the parameters that represents the mechanical behavior of a rock mass. However, there is no clear consensus on the most accurate method to determine a representative modulus of deformation. There has been significant work done on this problem using three main approaches: (1) extrapolation of laboratory mechanical tests to the field scale, (2) development of geotechnical classification systems that incorporate laboratory results and field observations, and (3) in situ measurements of rock mass deformability. The results of laboratory mechanical tests frequently cannot be used to predict the behavior of an intact rock mass. Small laboratory samples cannot capture the effect of structural heterogeneities, such

n

Corresponding author. Tel.: þ 1 832 854 5638. E-mail address: [email protected] (J.R. Gage). 1 Currently at Chevron Energy Technology Company, 1500 Louisiana St., Houston, TX 77002, USA. 2 Currently at Lloyd’s Register Drilling Integrity Services Inc. 1330 Enclave Pkwy, Houston, TX 77077, USA. http://dx.doi.org/10.1016/j.ijrmms.2014.07.021 1365-1609/& 2014 Elsevier Ltd. All rights reserved.

as joints and fractures, on the mechanical behavior of a larger-scale rock mass [1,2]. In addition to using laboratory measurements, several authors have also used geotechnical classification systems to predict rock mass deformability. These classification systems incorporate field observations with the laboratory-measured rock moduli. The three main classification systems are the rock mass rating (RMR) [3], the tunneling quality index (Q) [4], and the geological strength index (GSI) [5]. Instead of using indirect classification systems or extrapolating laboratory results, it would be preferable to measure the deformability of a rock mass directly, in the field. However, in situ deformation measurements are time consuming, expensive, and often produce inconsistent results. The reliability and accuracy of in situ measurements largely depend on the experimental methods [6–8]. There are three standard tests commonly used to measure the in situ deformation modulus; they are the plateloading test (PLT), plate-jacking test (PJT) and Goodman jack test [8]. The Goodman jack test is the least reliable when compared to the PLT and PJT [9] primarily because of complications associated with accurately measuring the displacement of the jack’s plates and modeling the applied stress field [10]. Furthermore, Goodman jack test results typically show significant scatter because only a

J.R. Gage et al. / International Journal of Rock Mechanics & Mining Sciences 71 (2014) 350–361

small volume of rock is deformed [11]. Plate-loading tests can also produce unreliable results because of the difficulty in accurately measuring displacement of the surface of the rock mass [12,13]. Plate-jacking tests produce the most reliable results because the embedded extensometers allow strain to be measured at depth within the rock mass and hopefully beyond any damaged zone surrounding the opening [14]. Although the database of in situ modulus of deformation measurements is not extensive, several authors have tried to combine the in situ measurements with the geotechnical classifications systems. Both the RMR and GSI systems can be linked to in situ measurements with reasonable reliability [8,15]. Other authors suggest that it is important to integrate field observations of joints, weathering and general rock mass character with any geotechnical classification scheme and in situ measurements [6,16,17]. Without a well-defined and agreed upon method to predict the behavior of a rock mass during deformation, it is important to critically assess both experimental methods and classification techniques and continue to examine how the mechanical properties of rock vary over spatial scales. In this paper we present the results of two point-loading tests performed
1250 m underground in a quartz and mica-rich amphibolite. We applied both a 89 kN (10 t) and 890 kN (100 t) point load to the rock surface, and utilized a dense array of fiberoptic strain gauges to measure strain at depth in the intact rock mass [18–20]. The resulting in situ moduli of deformation (Em) are compared to laboratory measurements of Young’s modulus and stiffness estimates from geotechnical classification systems, which allow us to examine how the mechanical properties of the rock vary from the centimeter to the meter scale. We also discuss several important experimental considerations to improve future in situ rock deformability measurements.

geotechnical strength classification for comparison to laboratory and in situ results. The Poorman formation has a well-developed foliation that is often mineralized with pyrite and chalcopyrite. The most prominent joint set (J1) in the experiment alcove is parallel to the foliation, and its strike/dip orientation is 044/50 SE (Fig. 2). There are several sets of quartz veins from 0.2 cm to 10 cm thick that are oblique to foliation. Some of the quartz veins also have sulfide mineralization. In addition to foliation-parallel joints, the experiment alcove contains three other joint sets (Fig. 2). The two more prominent joint sets (J2 and J3) are, in general, steeply dipping and cut obliquely though the alcove. J4 is less prominent than J1, J2, and J3; it is moderately dipping and oblique to foliation. J2 is oriented 161/86 W and J3 is 075/87 SE. The sub-vertical joint sets (J2 and J3) are not mineralized. J4 is oriented 205/39 NW. The joint spacing in the Poorman formation for sets J2 and J3 in the alcove is 0.3 m. In general, joint aperture is less than 1 mm, and the joint surfaces are slightly rough. The rock surface is completely dry and no groundwater is observed.

Canada

0 200 km

United StatesMN

ND

MT

South Dakota

WY NE CO Yates Shaft

West

2. Geologic background

Ross Shaft

East No. 5 Shaft

4100’ 4850’

c.

4850’ 7400’ 8000’

7400’

10 m

Drift To R

oss

N

Sha

ft

Drift

Experiment Alcove

Tr (20 ace o 5/3 f 9N J W)

Fig. 1. Location of experiment in SURF. (a) Gray box denotes the location of the Black Hills; (b) schematic cross section of SURF. Black star denotes approximate experiment location; (c) map view of experiment alcove on the 4100 level.

T (0 rac 44 e /5 of 0 J SE )

Our loading tests were conducted at the Sanford Underground Research Facility (SURF) at the site of the former Homestake gold mine in Lead, SD. SURF is an underground laboratory that is being built to house physics experiments and research [21]. In conjunction with the South Dakota Science and Technology Authority (SDSTA) and the Department of Energy (DOE), the Homestake gold mine is being converted to SURF. When commercial mining stopped in 2002, the Homestake gold mine was the largest and deepest (48000 ft.;
2500 m) gold mine in North America. SURF is located in the northern Black Hills of South Dakota (Fig. 1). The area was subjected to several episodes of Precambrian tectonism, resulting in metamorphism, foliation development, complex folding, shear zones, and the emplacement of dikes and veins [22]. Fluid influx during deformation and metamorphism produced economic gold deposits along the structures [23]. Uplift during the Laramide orogeny caused brittle deformation in the area of SURF [24] and created several joint sets and brittle faults. Our experiment was located in the Precambrian Poorman formation, which consists of metamorphosed tholeiitic basalt and metasedimentary rocks [25]. In the area of our experiment, the Poorman formation is a strongly foliated and lineated, amphibolite-grade mica schist that contains visible quartz, muscovite, and garnet. The Poorman formation also contains several quartz veins and vein arrays.

351

1m

FROSTS OS3600

X

89 kN Load

Trace of J (161/86 SW)

X 89 kN Load and 890 kN Load Location #1

X Trace of J (075/87 SE)

To Ross Shaft

3. Rock mass geotechnical classification Detailed field descriptions of the Poorman formation in the area of the experiment were completed in order to determine the

Legend:

X 890 kN Load Location #2

DRIFT Fig. 2. Map of experiment alcove showing orientation of joint sets, location of FROSTS, embedded OS3600 sensors, and loads applied during the 89 kN and 890 kN point-loading tests.

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Using the rock mass rating (RMR) classification scheme [3] the Poorman formation in the experiment alcove has a rating of 74 (good). On the 2.1 km (6950 ft.) level of the Homestake mine, the Poorman formation was determined to have a RMR of 70 [26,27]. It is important to note that we did not have access to core from the Poorman formation, so we used the rock quality designation (RQD) parameter from Golder’s previous analyses [28] where RQD ¼75% for our RMR classification. Using the geological strength index (GSI) classification [5], the Poorman formation has a rating of 80.

4. Point-loading tests In order to measure the in situ modulus of deformation (Em) with the embedded strain sensors, we performed two pointloading tests, which are analogous to plate-jacking tests (PJT) [8]. The major difference between our point-loading tests and traditional PJTs, is that we applied a point load directly to the rock mass instead of a load distributed across a plate. 4.1. Strain sensor array

Anchoring Disk

5 cm Fig. 3. Photograph of OS3600 strain gauge embedded in the ceiling of the alcove. Gauge length is 25.4 cm.

Serrated sections used to grip the grout and couple the FROSTS to the rock mass

Fiber optic strain sensor

5 cm

Fig. 4. Photograph of a section of a FROSTS instrument.

We installed a dense array of fiber Bragg grating (FBG) fiberoptic strain and temperature sensors on the 4100 level of SURF in an alcove measuring 2 m deep by 3 m wide and 2 m tall. Gage et al. [18–20] provide a detailed discussion of the sensor array. For this experiment, we primarily utilized the strain gauges embedded in the ceiling of the alcove, which were grouted into vertically oriented boreholes. These fiber-optic strain sensors measure onedimensional shortening and elongation in the vertical direction, and are accurate to 1 mε and 0.1 1C. Two types of fiber-optic strain gauges were embedded in the ceiling of the experiment alcove. The first type is the Micron Optics Inc. OS3600 temperature compensated strain gauge. This gauge consists of an FBG strain gauge anchored between two metal disks (5 cm diameter) and surrounded by a 1.5 cm diameter Teflon tube (Fig. 3). The gauge length of the OS3600 sensor is 25.4 cm. The nearedge of the OS3600 was 32 cm from the roof of the alcove. The OS3600 sensor was grouted into a
9 cm (3.5 in.) diameter borehole. The second type of strain gauge is a Fiber-optically Instrumented Rock Strain and Temperature Strip, or FROSTS embedded in the roof of the alcove [20]. FROSTS are in situ strain measuring tools that are
183 cm (6 ft) long and have six strain and temperature sensors installed at 30 cm intervals along its length. The strain gauges are installed in the center of the 10 cm long sections of the FROSTS that are separated by wider serrated sections [20,29] (Figs. 4 and 5). The ridges on the serrated sections grip the grout that embeds the FROSTS in the borehole and divide the FROSTS into six discrete sections that measure strain independently along the length of the FROSTS. The FBG gauges on each of the six sections of the FROSTS measure the average strain between the two serrated sections on either end. The FROSTS use Micron Optics Inc. OS3200 strain gauges and OS4310 absolute temperature sensors. The OS3200 strain gauges have a gauge length of 1.0 cm. The FROSTS was pretensioned prior to installation [19,20], which allows the tool to measure the shortening strains associated with the point-loading tests. The near-end of the FROSTS was 45 cm from the surface. The FROSTS was grouted into a

3m

2m

2m

Fig. 5. Set up for 89 kN (10 t) point-loading test. (a) Sketch of experimental plan. (b) Photograph of experimental set up.

J.R. Gage et al. / International Journal of Rock Mechanics & Mining Sciences 71 (2014) 350–361


7 cm (2.75 in.) diameter borehole. The location of each individual strain gauge was measured to 0.5 cm accuracy.

353

the applied load than the deepest embedded strain gauge. Thus, we can treat the experiment as a point load on a semi-infinite half space and utilize Boussinesq’s solution to determine the vertical stress (σzz) within the rock mass at each strain gauge location, which is:

4.2. Stress during point-loading tests σ zz ¼ In order to calculate the in situ modulus of deformation (Em) for the rock mass, the applied surface load must be extrapolated into the rock mass to determine the magnitude of stress at each sensor location. Because only the instrument (either FROSTS or OS3600) nearest the applied load for each loading location recorded a detectable strain during the loading cycles of the 890 kN test, we can assume that the shape of the alcove and edge effects of nearby walls do not affect the stress field because the adjacent walls of the alcove are further from

Q 3z2 2π R5

ð1Þ

where Q is the applied load, z is the vertical distance from the surface to the sensor, and R is the distance from the load to the sensor [30]. The Boussinesq solution is a simplified and idealized approximation for the actual stress in the rock mass during loading. There are many variables in our experimental setup that will influence the stress at each sensor such as the presence and orientation of macroscopic fractures and microcracks, the non-linear elastic nature

Table 1 Deformation modulus (Em) results for 89 kN point-loading test. FROSTS

Stress (MPa)

0.62 0.92 1.23 1.53 1.84 2.14 0.50

0.02 0.02 0.02 0.01 0.01 0.01 0.02

OS3600 (με) Sensor F (με) Sensor E (με) Sensor D (με) Sensor C (με) Sensor B (με) Sensor A (με)

Sensor A Sensor B Sensor C Sensor D Sensor E Sensor F OS3600

Depth (m)

Em (GPa)

Strain (mε) Loading cycle 1

Loading cycle 2

Loading cycle 3

Loading cycle 4

Average

2 1 0.5 0.25 0 0 2

2 1.5 1 0.5 0 0 2

2 1.5 1 0.5 0.5 0.25 2

2 1.5 1 0.5 0 0 2

2.00 1.38 0.88 0.44 0 0 2

12 17 21 32 – – 8

4 0 -4 -8 4 2 0 -2 6 4 2 0 -2 4 2 0 -2 4 2 0 -2 -4 2 0 -2 -4 2 0 -2 -4

18:40

19:10

19:40

20:10

20:40

21:10

Time (UTC) Fig. 6. Strain data from 89 kN point-loading test. Loads were applied at 18:30, 18:55, 19:40, 20:30, and 21:05 (denoted by vertical dashed black lines). Shortening is negative and elongation is positive. For the FROSTS, sensor A is closest to the surface (0.62 m) and sensor F is deepest in the rock mass (2.14 m). The OS3600 is embedded in the ceiling of the alcove. See Fig. 2 for FROSTS, OS3600, and load locations. Data was collected at 5 Hz. The black line is a 1 s moving average of the raw strain data (gray area). The load was applied linearly over a 30 s period.

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J.R. Gage et al. / International Journal of Rock Mechanics & Mining Sciences 71 (2014) 350–361

of the rock mass at low strains, the grout surrounding the FROSTS and OS3600, and the actual contact area of the load on the rock mass. While we recognize these uncertainties, and are unable to quantitatively account for their effect on the applied stress, we think the Boussinesq model is still applicable for estimating the stress in the rock mass during the loading experiments. 4.3. 89 kN (10 t) Point-loading test For the first experiment, we used two 89 kN (10 t) capacity hydraulic rams to apply a load to the floor and ceiling of the alcove (Fig. 2). The rams were Strata Products Inc. Rocprops, which are portable roof supports used primarily in coal mines. The Rocprops are able to apply an 89 kN (10 t) load to the rock mass using 6.9 MPa (1000 psi) hydraulic pressure. The tops of the Rocprops are hemispherical, and they were placed directly against the rock mass, thus applying an 89 kN point force during loading. Each of the two Rockprops was placed near one of the two sensors (FROSTS and OS3600) embedded in the ceiling of the alcove (Fig. 2). We performed five loading cycles holding the maximum load on the rock mass for between 5 and 20 min during each cycle. The load was applied linearly over a 30 s period in each test and each Rockprop was loaded at the same time. All loading cycles were completed during a 4 h period during which we monitored the air temperature using a FBG temperature sensor. The temperature of the mine and the rock mass did not change more than 1 1C during the experiment. Thus, there should be negligible thermal strain component in the measurements, and

Steel

all strain recorded by the FBG gauges is mechanical strain and is a result of the load applied during the experiment. 4.3.1. Results: 89 kN (10 t) point-loading test For the 89 kN test, the stress, calculated using Eq. (1), decreased along the FROSTS from 0.02 MPa at the FROSTS sensor closest to the surface of the rock mass (sensor A) to 0.01 MPa at the deepest sensor (sensor F) (Table 1). The stress at the embedded OS3600 was 0.02 MPa (Table 1). The stress–strain curves during loading were linear for each sensor that recorded measurable strain. In general, the 89 kN load was too small to induce substantial strain in either the FROSTS or the embedded OS3600 sensor (Fig. 6). The embedded OS3600 measured
2 mε during each 89 kN loading cycle. On the FROSTS, sensor A, closest to the surface, also measured 2 mε for each loading cycle. Sensors E and F, deepest in the rock mass, did not measure any strain, except in loading cycle #3 (Fig. 6 and Table 1). All deformation measured during the 89 kN loading test by the FROSTS was near or below the 1 mε resolution of the fiber-optic strain gauges. However, the recorded changes in strain correlated temporally to the application and removal of the load, which suggests that the measured strain is a result of the loading experiment. Using the stress determined by Boussinesq’s solution and the measured strain at each FBG gauge along the FROSTS, we can calculate the modulus of deformation for the rock mass. For sensor A, at a depth of 0.62 m in the rock mass, Em ¼12 GPa. For the four sensors on the FROSTS that recorded strain during the loading cycles, the Em increases with depth (Table 1). The modulus of deformation

10 cm

Post Hydraulic Cylinder

0.5 m Fig. 7. (a) Photograph of experimental setup for 890 kN point-loading test. (b) Close-up photograph of rounded head of steel post.

J.R. Gage et al. / International Journal of Rock Mechanics & Mining Sciences 71 (2014) 350–361

increases by
7.3% for each sensor (Table 1). The OS3600 sensor, at a depth of 0.5 m in the rock mass, recorded Em ¼8 GPa. 4.4. 890 kN (100 t) Point-loading test To induce larger strains in the rock mass, we performed a second point-loading test using an 890 kN (100 t) hydraulic ram. The experimental set up was similar to the 89 kN loading test. For the 890 kN test, we used a single load that consisted of a specially machined steel column atop a 890 kN (100 t) capacity hydraulic cylinder (Fig. 7a). The steel column had a rounded head to apply a point load to the rock mass (Fig. 7b). We loaded the rock mass in two different locations near our embedded strain sensors (Fig. 2). An 89 kN load was held on the rock mass continuously so that the steel column would not lose contact with the rock and become misaligned. In the first location, we performed four loading cycles from 89 kN to 890 kN. The maximum load was held on the rock mass for 10 min during each cycle. At the second location, we performed three loading cycles holding the maximum load on the rock mass for 10 min during each cycle. Except for cycle 2, the load was applied linearly over a 60 s period. In cycle 2, the load was applied in a step-wise pattern with a 60 s rest after each 10 t increase. All loading cycles were completed during a six-hour period during which we monitored the air temperature using a FBG temperature sensor. The temperature of the mine and the rock mass did not change more than 2 1C during the experiment. Thus, there should be negligible thermal strain component in the measurements, and all strain recorded by the FBG gauges is mechanical strain resulting from the load applied during the experiment. 4.4.1. Results: 890 kN (100 t) point-loading test For the 890 kN experiment, at the first loading location, the stress, calculated using Eqn. 1, decreased from 0.23 MPa at sensor A to 0.07 MPa at the deepest strain gauge (Table 2). The stress at the embedded OS3600 was 0.02 MPa. For the second loading location, the stress along the FROSTS was 0.02 MPa at sensor A and 0.01 MPa at sensor F. The stress at the embedded OS3600 was 0.57 MPa. For the first loading location, the FROSTS recorded a clear gradient of decreasing strain into the rock mass (Fig. 8). Sensor A, closest to the surface, recorded approximately 6 mε more than

355

Sensor F, the deepest strain gauge in the rock mass (Table 2). The strain magnitude at each sensor on the FROSTS was above the resolution of the fiber-optic strain gauges. The embedded OS3600 sensor did not record any statistically significant strain during the loading cycles at the first location (Fig. 8). For the 890 kN loading test at the first loading location, Em for sensor A on the FROSTS is 29 GPa. The modulus of deformation increases with depth into the rock mass by
18% for each sensor (Table 2). Sensor F at 2.14 m in the rock mass has Em ¼65 GPa. The stress–strain curves during loading were linear for each sensor along the FROSTS and the OS3600 (Fig. 9). Also, the slope of the stress–strain curve for each sensor was distinct, and similar in magnitude to the modulus of deformation determined for each sensor from the average maximum strain for all four loading cycles (Fig. 9 and Table 2). For the second loading location, the embedded OS3600 recorded an average of 12.7 mε for the three loading cycles (Fig. 8). The FROSTS did not record any significant strain response during the loading cycles at the second location. Sensors C, D, E, and F showed some strain response (Fig. 8), but the discrete loading events were indiscernible, and thus cannot be accurately analyzed. For the 890 kN loading test at the second location, the Em calculated by the embedded OS3600 sensor is 45 GPa.

5. Laboratory mechanical testing We tested six specimens from a sample of the Poorman formation collected in the sensor alcove on the 4100 level of SURF. Three specimens were cored perpendicular to foliation and three were cored parallel. Each specimen was 2.5 cm in diameter and 5 cm tall. The specimen preparation and laboratory testing followed ASTM D702-10 specifications. Each specimen had four electrical resistance strain gauges installed along its circumference with two strain gauges oriented axially and two radially. The gauges were Micro-Measurements CEA-06-250UW-120 foil strain gauges installed with M-Bond 200 epoxy. The specimens were unconfined and loaded until failure. 5.1. Results: Laboratory mechanical testing The average Young’s modulus measured for the Poorman formation perpendicular to foliation is 43.5 GPa and the average Poisson’s

Table 2 Deformation modulus (Em) results for 890 kN point-loading test. Loading location 1

Strain (mε)

FROSTS

Depth (m)

Stress (MPa)

Loading cycle 1

Loading cycle 2

Loading cycle 3

Loading cycle 4

Average

Em (GPa)

Sensor A Sensor B Sensor C Sensor D Sensor E Sensor F OS3600

0.62 0.92 1.23 1.53 1.84 2.14 0.50

0.22 0.20 0.16 0.12 0.09 0.07 0.02

9 4.5 3 2 1.5 1.5 0

6 5 3 2 1.5 1 0

8 6 3 2 1.5 1 0

8 6 3.5 2 1.5 1 0

7.8 5.4 3.3 2.0 1.5 1.1 –

29 38 49 60 61 65 –

Loading location 2

Strain (mε)

FROSTS

Depth (m)

Stress (MPa)

Loading cycle 1

Loading cycle 2

Loading cycle 3

Average

Em (GPa)

Sensor A Sensor B Sensor C Sensor D Sensor E Sensor F OS3600

0.62 0.92 1.23 1.53 1.84 2.14 0.50

0.04 0.03 0.03 0.02 0.02 0.01 0.57

0 0 0 0 0 0 12

0 0 0 0 0 0 13

0 0 0 0 0 0 13

0 0 0 0 0 0 12.7

45

Sensor F (με) Sensor E (με) Sensor D (με) Sensor C (με) Sensor B (με) Sensor A (με)

J.R. Gage et al. / International Journal of Rock Mechanics & Mining Sciences 71 (2014) 350–361

10 5 0 -5 -10 -15 8 4 0 -4 -8

OS3600 (με)

356

0 -4 -8 -12 -16

12 8 4 0 -4 0 -4 -8 4 2 0 -2 -4 2 0 -2 -4 -6 -8

16:00

17:00

18:00

19:00

20:00

21:00

22:00

Time (UTC) Fig. 8. Strain data from 890 kN point-loading test. Loads were applied at location #1 at16:00, 18:40, 19:40, 20:20 and at location #2 at 20:40, 21: 20, and 21:45 (denoted by vertical black dashed lines). Shortening is negative and elongation is positive. For the FROSTS, sensor A is closest to the surface (0.62 m) and sensor F is deepest in the rock mass (2.14 m). The OS3600 is embedded in the ceiling of the alcove. See Fig. 2 for FROSTS, OS3600, and load locations. Data was collected at 5 Hz. The black line is a 1 s moving average of the raw strain data (gray area). The load was applied linearly over a 60 s period.

ratio is 0.23 in the linear range of the stress–strain curve between 10 MPa and 100 MPa (Fig. 10). For the specimens cored parallel to foliation, the average Young’s modulus is 53.7 GPa, and Poisson’s ratio is 0.16 in the linear range of the stress–strain curve between 10 MPa and 100 MPa (Table 3). The Young’s modulus and average Poisson’s ratio from each strain gauge pair on individual specimens are relatively consistent; however, for the parallel orientation, there is significant scatter in the data among specimens (standard deviation¼11.9 GPa). The stress–strain curves for each specimen are generally linear after
10 MPa until failure (Fig. 10). Because the load was applied obliquely to foliation during the point-loading tests, the mechanical properties of the rock mass are likely somewhere between the end members measured in our laboratory experiments [31]. The foliation dips 501 in the alcove; therefore following the construction of Nye [32], the laboratory value for Young’s modulus at 501 to foliation is approximately 50.8 GPa. These values are consistent with those measured by Johnson et al. [33] for the Poorman formation and higher than those measured by Pariseau et al. [26].

6. Discussion 6.1. Comparison of in situ and laboratory deformability results A major criticism of in situ measurements of the modulus of deformation is that the results are generally unreliable. Field measurements typically produce results that are significantly lower, and in

some cases unreasonably lower than values measured in the laboratory. For example, in situ modulus of deformation measurements of sandstones and siltstones at the Mingtan pumped storage site in Taiwan were up to 90% more compliant than laboratory-determined Young’s moduli measurements [7]. However, much of this inaccuracy can be eliminated by the use of a proper in situ testing methodology [8]. Different types of in situ tests (plate-jacking, plate-loading, Goodman jack, etc.) give significantly different results for the same rock mass [6,34]. Plate-jacking tests produce the most accurate and reliable results, and should be the method of choice [8,35]. Both our 89 kN and 890 kN point-loading tests are analogous to plate-jacking tests; however the 89 kN and 890 kN tests yielded significantly different results for the modulus of deformation for the Poorman formation. For the 89 kN, Em ¼ 12 GPa at sensor A at a stress of 0.02 MPa, and for the 890 kN experiment Em ¼29 GPa at sensor A at a stress of 0.22 MPa. A similar relationship is seen for sensors B–D on the FROSTS and the OS3600 (Tables 1 and 2). The rock mass appears significantly more compliant when a small magnitude load is applied. This is likely caused by the closure of fractures and microcracks in the damaged zone surrounding the experiment alcove [36]. The data from the 890 kN test is more robust than the 89 kN test because all the sensors along the FROSTS measured strain and all the recorded strains were above the resolution of the FROSTS. If the 890 kN test, was not performed, the in situ modulus of deformation for the rock mass would appear to be significantly lower than the likely actual value. Thus, in in situ experiments, it is important to use a load that is sufficiently large to induce significant strain in the rock mass. Therefore, it is possible that the relatively small load magnitudes during

J.R. Gage et al. / International Journal of Rock Mechanics & Mining Sciences 71 (2014) 350–361

Sensor A

0.30

0.20

0.15

Un

loa

0.10

din

0.20

ad

ing

Stress (MPa)

Stress (MPa)

Lo

Sensor B

0.25

0.25

g

Lo

ad

ing

0.15

Un

0.10

loa

din

g

0.05

0.05

Slope = - 3 0 .2 M Pa

Slope = - 32 .9 M Pa 0

0

-4

-3

-2

-1

0

1

2

3

4

-3

-2

-1

0

Strain x 10 -6

3

4

0.14

ad

0.12

0.12

ing

Stress (MPa)

Lo

0.14

0.10

Un

0.08

loa

0.06

din

g

Lo

0.10

ad

ing

0.08

Un

0.06

loa

din

0.04

0.04

0 2.5

2

Sensor D

0.16

0.16

0.02

1

Strain x 10 -6

Sensor C

0.18

Stress (MPa)

357

g

0.02

Slope = - 50 .4 M Pa

Slope = - 41.3 M Pa 3.0

3.5

4.0

4.5

5.0

5.5

6.0

0 -6.0

6.5

-5.5

-5.0

Strain x 10 -6 Sensor E

0.12

-4.5

-4.0

-3.5

-3.0

Strain x 10 -6 Sensor F

0.09 0.08

0.10

0.08

ad

Stress (MPa)

Stress (MPa)

0.07

Lo

ing

0.06

Un

0.04

loa

din

g

Lo

0.06

ad

ing

0.05 0.04

Un

0.03

loa

din

g

0.02

0.02 0.01

Slope = - 6 0 .3 M Pa 0 -1.0

-0.8

-0.6

-0.4

-0.2

Slope = - 68.2 M Pa 0.0

0.2

0.4

0.6

0.8

Strain x 10 -6

0 -4.0

-3.8

-3.6

-3.4

-3.2

-3.0

-2.8

-2.6

Strain x 10 -6

Fig. 9. Loading and unloading stress–strain curves for the six FBG sensors on the FROSTS embedded in the roof of the alcove during the 18:40 UTC, 890 kN point-loading test (Fig. 8). To reduce the amount of data, stress and average strain are plotted for every 10 t increase in applied load.

testing contributed to the anomalously low Em values reported in some previous in situ tests [7,8,15]. The laboratory value for Young’s modulus for the Poorman formation of 51 GPa is similar to the in situ modulus of deformation values measured for the 890 kN experiment. Using the relationship of Em and depth determined from the 890 kN field experiment, the laboratory value would correspond to the Em at


1.2 m depth in the rock mass (Fig. 11). The results of the 89 kN test significantly underestimate Em because the applied load was too small to close the open fractures in the rock mass surrounding the alcove (Table 2). By using a point-loading test setup and applying a sufficiently large load, we have improved the results of the in situ experiments and more closely approximated the laboratory-measured value.

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6.2. Comparison of in situ rock mass deformability measurements and empirical estimates Many studies have tried to develop empirical methods for determining a representative modulus of deformation of a rock

180 160 140

Stress (MPa)

120 100

Axial gage #2 80

Axial gage #1 60 40 20

Young’s modulus 1 = 52.7 GPa Young’s modulus 2 = 47.5 GPa

0 0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0.0035

0.004

Strain Fig. 10. Representative stress–strain curve for two axial gauges on specimen during laboratory testing. Young’s modulus is noted on graph.

Em ðMPaÞ ¼

Table 3 Moduli from laboratory mechanical testing on the Poorman Formation. Sample Core Orientation

PM1 PM3 PM5

Poisson’s Young’s Young’s modulus gage modulus gage ratio gage no. 1 no. 2 (GPa) no. 1 (GPa)

Perpendicular 35.4 Perpendicular 52.7 Perpendicular 44.8

Average PM2 Parallel PM4 Parallel PM6 Parallel

43.5 GPa 56.7 53.5 74.3

Average

57.3 GPa

Poisson’s ratio gage no. 2

32.9 47.5 47.4

0.34 0.17 0.26

0.24 0.16 0.23

52.7 40.0 66.3

0.23 0.16 0.14 0.18

0.14 0.19 0.17

0.16

80

70

Modulus of Deformation; E (GPa)

mass using the results of the RMR and GSI classification systems for reviews see [8,15]. Both Bieniawski [6] and Serafim and Pereira [16] determined empirical relationships producing Em from the RMR classification of a rock mass. For rock masses with an RMR455, Bieniawski’s [6] relationship has been shown to be more accurate [8]. For the Poorman formation, where RMR¼ 74, Em ¼48 GPa. This is equivalent to the Em measured at
1 m depth in the rock mass during our 890 kN loading experiment, and is similar to the laboratory results. The empirical relationship developed by Hoek and Diederichs [15] uses the GSI classification and the disturbance factor (D) [37]. The disturbance factor is an attempt to quantify the effect of the damaged zone on the results of in situ deformability measurements. The damaged zone is the volume of rock surrounding an underground space that has been damaged due to excavation of the opening from blasting or boring [8]. Rock damage due to blasting significantly decreases the measured deformation modulus of a rock mass [38,39]. The size of the damage zone is dependent on several variables such as the rock properties, amount of explosive used, and distance between blast holes [40], and thus is very difficult to quantify [15]. The increase of rock stiffness and Em with depth in the rock mass is, in part, a result of the transition from the damaged rock surrounding the alcove to the undisturbed rock mass [8]. Using the relationship in eq. (2) from Hoek and Diederichs [15] with different values for D (the disturbance factor; see [37]), we can quantify the damaged zone around the experiment alcove using: 100; 000½1  ðD=2Þ 1 þ exp½ð75 þ 2D  GSIÞ=11

ð2Þ

where D is the disturbance factor, and GSI is the geological strength index. At the depth of sensor A (0.62 m) D¼ 0.44. At D¼0, Em ¼61.2 GPa, which corresponds to a depth of
1.5 m in the intact rock mass (Tables 4 and 5). Thus, in the Poorman formation on the 1250 m level of SURF, the damaged zone is interpreted to extend
1.5 m deep. Previous studies suggest that the damage zone in a relatively competent rock only extends up to 0.5 m and is dependent on the scale and method of excavation [41]. The transition from the damaged zone into the intact rock mass is gradual [8]; thus it is useful to record a detailed strain gradient during in situ testing. FROSTS are an ideal monitoring tool because they can be embedded through the length of the damage zone and used to document the change in rock properties with depth (Table 4). For example, the six strain gauges along the FROSTS allow for the accurate characterization of the damaged zone, whereas the OS3600 only provides one Em measurement. Thus, embedded multipoint borehole extensometers (such as FROSTS) are more

60

Table 4 Comparison of in situ modulus of deformation results and Em from [15] as a function of Disturbance Factor.

Slope = 9.2 GPa/m

50

40

Slope = 33.5 GPa/m

30

20

10

In situ E from FROSTS sensors A-C In situ E from FROSTS sensors D-F

0 0

0.5

1

1.5

2

Disturbance factor (D)a

Em (GPa) Hoek and Diederichs [15]b

0.5 0.44 0.4 0.3 0.2

25.2 28.7 31.1 37.7 45.0

0.1 0

52.9 61.2

2.5

Depth in the rock mass (m) Fig. 11. Plots of modulus of deformation (Em) and depth in intact rock mass as measured during the 890 kN point-loading test.

a b

From Hoek et al. [7]. From Eq. (2) [15].

In situ Em (GPa) 890 kN loading experiment

Depth (m)

29

0.62

38

0.92

50.8 49 60 61 65

LAB 1.23 1.53 1.84 2.14

J.R. Gage et al. / International Journal of Rock Mechanics & Mining Sciences 71 (2014) 350–361

Table 5 Vertical stress for each strain gage along the FROSTS embedded in the roof of the experiment alcove prior to applied loads. Sensor

Depth (m)

σv (MPa)

A B C D E F

0.62 0.92 1.23 1.53 1.84 2.14

0 0 6.31 10.2 12.4 13.7

favorable than single-point borehole extensometers for producing more detailed and complete in situ deformation modulus results. The stiffness profile provided by the FROSTS during the 890 kN point-loading test shows that the rate of increase of the modulus of deformation varies with depth. The plot of in situ deformation modulus versus depth in the rock mass has two distinct data populations (Fig. 11). Sensors A–C on the FROSTS measure a relatively low modulus, and have a steep slope (Fig. 11), which shows that the stiffness of the rock mass increases quickly in the damaged zone. Sensors D–F on the FROSTS measure higher moduli and have a shallow slope (Fig. 11), which suggests that, in the undisturbed zone, the deformation modulus of the rock mass asymptotically approaches a stable value. The change in slope also appears to occur in the stress–relief zone. An alternate explanation for the apparent increase in stiffness with depth into the rock mass is that the strain measurements on the FROSTS occur at different initial stress levels along a nonlinear stress–strain curve. Stress–strain curves are often nonlinear, especially at low stresses [42], and the apparent Young’s modulus becomes stiffer as the applied load increases. The stress–strain curves measured in the laboratory (Section 4; Fig. 10) are nonlinear for the Poorman formation below
10 MPa, which is greater than the applied stress in our experiments. Thus, it is possible that the trend of increasing stiffness with depth is a result of the strain gauge locations along the borehole being at different initial stress states before the point-loading experiment. However, the stress–strain curves observed in the 890 kN point-loading test are linear for the applied stresses (Fig. 9). The FROSTS and OS3600 also record significantly different values for the modulus of deformation during both the 89 kN and 890 kN loading experiments. The OS3600 is 0.5 m deep in the rock mass and records an Em ¼45 GPa, whereas sensor A on the FROSTS records an Em ¼29 GPa at 0.62 m during the 890 kN experiment. This discrepancy is likely due to the difference in gauge length of the FROSTS and OS3600 sensors. The OS3600 provides a single strain measurement averaged over a 24.5 cm gauge length. Thus, the difference in strain and Em is expected because the OS3600 averages the strain over a larger volume of rock (in which the stress and discontinuities in the rock mass vary) whereas the individual strain gauges on the FROSTS provide point measurements. The difference in the recorded strain for the OS3600 and FROSTS could also be due to different construction of the two sensors. The materials of the gauges’ packaging are different, which create contrasting mechanical properties of the gauges and affect the way each measures strain e.g. [29,43]. Thus, it is important to understand the mechanical properties of the extensometers. The coupling between the sensors and the rock mass could also create the differences between the FROSTS and OS3600, since the sensors have different anchoring mechanisms. 6.3. Scale and rock mass stiffness Discontinuities in a rock mass (e.g. fractures, joints, and faults) are the biggest influence on rock stiffness when moving from

359

small-scale laboratory results to the cubic meter-scale of an underground excavation (such as the experiment alcove). In our work, the laboratory value for the Young’s modulus of the Poorman formation is 51 GPa, which would correspond to a depth of
1.2 m as measured by the 890 kN point-loading experiment (Table 2). The meter-scale rock mass contains two main types of fractures that influence both its mechanical behavior and deformation modulus. First, fractures created during blasting weaken the rock mass [38,39]. The stiffness of the damaged zone surrounding an excavation (up to a depth of 1.2 m, as measured in the 890 kN experiment) is lower than the laboratory measured results. Second, fractures that are structural features of the rock mass (e.g. pervasive joint sets or foliation) also influence how the larger scale rock mass behaves e.g. [44]. Beyond the damaged zone is an area where rock stiffness increases (Table 2). This zone is close enough to the free surface of the excavation that some stress is relieved, causing opening of the joint sets [45]. At this depth in the Poorman formation (between
1.2 m and 1.5 m), the rock has a similar stiffness to the Young’s modulus measured in the laboratory. As depth into the rock mass increases ( 41.5 m) the rock mass is stiffer than laboratory values (Table 2), this represents the undisturbed rock mass where it behaves as massive, unjointed rock mass because the confining stress is sufficient to close all the joint sets [8]. The size and extent of these zones will vary significantly by rock type. Also, the degree to which laboratory measurements will approximate the mechanical properties of the stress-relief zone depends on joint configurations [46,47]. The stiffness characteristics of a rock mass are complex and no single measurement will accurately characterize its response to deformation. The three documented zones (damaged zone, stressrelief zone, and undisturbed zone) all have different implications for the behavior of underground openings. Near-surface rock stiffness in the damaged zone will influence the required ground control as well as the potential for surface failure hazards. The deeper undisturbed rock stiffness will determine the size, orientation, depth, and construction methods of the openings [48]. The stiffness gradient in a rock mass is important on the larger scale and cannot be captured by a single laboratory value. Thus, in situ testing using an embedded multipoint borehole extensometer (such as the FROSTS), allows for the characterization of the different zones of rock behavior and provides a fuller understanding of rock mass deformability and its variation on a scale comparable to typical excavation sites.

7. Conclusions When combined with laboratory analyses, in situ measurements of rock mass deformability can be a valuable tool to understand how a rock mass responds to deformation. However, the literature contains several examples of in situ tests that report significantly different laboratory and field results, which has led to the impression that in situ tests generally do not produce quality data that are worth the time and expense. Our work shows that there are several elements of the experimental setup that can be augmented to improve overall results. First, utilizing an embedded extensometer eliminates many of the errors associated with strain measurement because strain is measured within the rock mass as opposed to on the surface. Embedded multipoint extensometers provide multiple strain measurements at different depths within the rock mass, which allow for the calculation of the modulus of deformation at several locations. Multiple measurements of Em are useful for quality and accuracy checks, as well as defining any trends within the rock mass. Second, the load applied during the experiment needs to be large enough to induce significant strain in

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the rock mass that will completely close any open fractures and then measure the deformability of the rock mass. The strain measured by the deeper strain gauges on a multipoint extensometer can be used to determine if a sufficient load was applied. The results of in situ loading experiments and laboratory mechanical tests are presented to examine how the mechanical properties of a rock mass vary from the cm3 to the m3 scale. Laboratory results, in situ tests, and empirical relationships give similar, but not the same results for the Em of the Poorman formation. However, no single value of Em accurately describes the behavior of the rock mass around an excavation because discontinuities such as joint and microcracks, both natural and induced, cause the modulus of deformation to vary within a rock mass. The gradient of Em in a rock mass surrounding an underground excavation has three zones with different mechanical properties: the damaged zone, the stress-relief zone, and the undisturbed zone. The transition between these zones is gradual, but it is important to characterize rock deformability over these three zones to accurately understand how the rock mass responds to deformation.

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