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Quality control of overcoring stress measurement data
ARTICLE IN PRESS
International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159
Quality control of overcoring stress measurement data M. Hakalaa,*, J.A. Hudsonb, R. Christianssonc b
a Gridpoint Finland Oy, Karkkila 03600, Finland Imperial College and Rock Engineering Consultants, UK c Svensk Karnbr anslehantering AB, SKB, Sweden . .
Accepted 20 July 2003
Abstract The in situ state of stress is one of the key rock mechanics factors related to the safety and stability of underground excavations for civil and mining engineering purposes. However, measurement and interpretation of stress have their difficulties. In particular, practical and objective tools have not been developed to judge transient strain behaviour during overcoring. The work described in this paper was set up by the nuclear waste management companies Posiva Oy (Finland) and Svensk K.arnbr.anslehantering AB (Sweden) to improve the quality of interpretation of overcoring stress measurement results. Thus, the primary product of the project is a quality control capability for overcoring stress measurement data. For this purpose, a computer program was developed which can simulate the transient strains and stresses during the overcoring process for any in situ stress and coring load conditions. The solution is based on superposition of elastic stresses and the basic idea can be applied for different overcoring probes with minor modifications and recalculation of stress tensors. The measured strains can be compared to the calculated ones to check whether the measured transient behaviour accords with the interpreted in situ state of stress. If not, the in situ state of stress can be calculated based on any transient or final strain values. The transient stresses can also be compared to a strength envelope of intact rock and thereby the core damage potential can be estimated. r 2003 Elsevier Ltd. All rights reserved.
1. Introduction When designing an underground excavation at great depth, i.e. for high stress conditions, it is important to have reliable knowledge of the: *
* *
*
magnitude and orientation of the in situ state of stress; strength and critical stress states of intact rock; pre- and post-failure deformation behaviour of rock; and rock mass quality.
for larger volumes by reopening of existing fractures (HTPF) [1]. With increasing depth and rock stress–strength ratio, the core sample for laboratory testing can be damaged but far more difficult and vulnerable is the measuring of the in situ state of stress [2,3]. In crystalline rock, reasons for unsatisfactory in situ stress measurements can be one or more of the following: * * * *
In practice, only vertical boreholes can be used if the target area is deep below the ground surface. The threedimensional stress tensor can be measured at one measurement point using the overcoring method (Borre Probe, CSIRO-HI cell, CSIR-cell, modified CSIR-cell, ANZI-cell, conical-cell or spherical-cell) or interpreted
*Corresponding author. E-mail address: matti@gridpoint.fi (M. Hakala). 1365-1609/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2003.07.005
*
* *
discontinuity closes stress cell, unrecognized anisotropy of rock [4], heterogeneity of rock, stress or strain induced damage of pilot hole wall or core, unacceptable behaviour of glue, glue–rock or glue–cell contact [5], change in temperature [6], and other technical problems of various kinds.
This study was set up by Posiva Oy (Finland) and Svensk K.arnbr.anslehantering AB SKB (Sweden) in order to enhance the quality of overcoring stress measurement interpretation methods. Both companies,
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who are responsible for management of spent nuclear fuel, have a need to define the in situ state of stress at around 400–500 m depth at potential repository locations with high confidence. The initial idea was to interpret the situ state of stress based on early strains, when the core damage potential is low [7,8]. A suitable approach for this solution was introduced by Fouial et al. [9]. As a result of the initial project phase, it was decided to focus the work on verifying that measured transient strains correspond to the interpreted in situ state of stress and on estimating core damage potential based on transient stresses at the strain gauge locations. For this purpose, a computer program was developed which can simulate the transient strains and stresses during the overcoring process for any in situ stress and coring load conditions. To be a practical quality control tool, the calculations of transient strains and stresses for any in situ state of stress should be implementable in a relative short time. For this reason, the solution is based on superposing precalculated secondary stresses caused by each relevant primary load component. This approach assumes that the rock is continuous, homogeneous and linearly elastic. Further, the rock is assumed to be isotropic, although the solution can be applied for known anisotropy also. The precalculation of secondary stresses presumes that the overcoring geometry and Poisson’s ratio are known. Similar superposition solutions have been previously used in core damage studies by Li and Hakala [7,8]. For this project, the Borre Probe (SwedPower’s Leeman-Hiltscher probe) geometry was selected, where the pilot hole diameter is 36 mm and the inner and outer overcoring diameters are 62 and 76 mm (see Figs. 1 and 2) [10]. The rosettes are installed 160 mm from the collar of the pilot hole. The orientation of rosettes is read after installation. The total overcoring length is at least 400 mm. The code can be modified to any other overcoring probe by recalculating the stress tensors. There is the intention to extent the computer code for transverse isotropy in the next phase of the project. With the developed code, a sensitivity study for selected overcoring cases was undertaken and two in situ . o. Hard Rock stress measurement cases from the Asp Laboratory site in Sweden were analysed. The reported work includes an extensive list of factors to be considered in overcoring measurements [11]. In particular, the studied cases demonstrate that it is extremely important to have technical auditing and quality assurance methods for overcoring stress measurement—because the measurement assumptions are easily forgotten and the measured magnitudes are small and sensitive to various errors and disturbances.
Fig. 1. Phases of Borre probe overcoring measurement (modified from Ref. [10]). (1) Advance +76 mm main borehole to measurement depth, (2) drill +36 mm pilot hole and recover core for appraisal, (3) insert Borre probe in installation tool into hole, (4) probe releases from installation tool. Gauges bonded to pilot-hole wall under pressure from the nose cone, (5) pull out installation tool. Probe bonded in place, and (6) overcore the Borre probe and recover in core barrel.
Strain gauge rosette (R1) seen from center of borehole
0 90°
R2 120° 120°
G2 (G5, G8)
R1 120°
R3
G3 (G6, G9) G1 (G4, G7)
Borehole axis Fig. 2. Borre probe strain gauge rosette (left) and strain gauge configuration (right) (modified from Ref. [10]).
2. Overcoring method In pilot hole probe methods, normally nine or 12 strain gauges with different orientations on the pilot
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hole wall are monitored when the stresses on the borehole wall are released by overcoring, Figs. 1–3. Because the stress state around a circular hole is known in closed-form solution, the in situ state of stress can then be calculated from the released strains assuming that the rock is continuous, homogeneous and behaves in a linearly elastic manner around the circular hole (Fig. 4) [12]. The material has to be either isotropic, transversely isotropic or orthotropic. Further, it is assumed that the bottom of the pilot hole or full-scale hole does not have any effect on the secondary stress state at probe level before overcoring. The calculation of the in situ stress requires at least six independent final strain readings and the elastic parameters of the rock. For isotropic rock, we need two elastic parameters: conventionally, Young’s modulus and Poisson’s ratio; but, for transversely isotropic rock, we need five parameters: conventionally, two Young’s moduli, two Poisson’s ratios and a shear modulus. The elastic parameter values for isotropic rock are defined by
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biaxial testing of the overcored rock cylinder but, for transverse isotropy or orthotropy, at least three uniaxial or indirect tensile test specimens at different tested anisotropy angles are needed [13,14]. The success of measurement is defined by the continuity and stability of strain gauge readings during the overcoring and linearity during the biaxial testing. The judgement of continuity and stability is subjective. The loading and unloading cycle in the biaxial cell provides information on linear elasticity and the comparison of different axial, circumferential and inclined strain gauge readings provides information on the degree of anisotropy or heterogeneity. Based on the ISRM 1987 suggestions and complemented by experiences of the authors, a successful overcoring in situ stress measurement in hard crystalline rock conditions requires that the phases shown in Fig. 5 are implemented and/or considered [15]. Further, a reliable interpretation of stress from the measured strains has to be based on a full understanding of the
In situ stress stress trajectories
σ1, max deformed shape σ1, min
contours for maximum In situ principal stress
(a)
(b)
unstressed hollow core
(c) Fig. 3. Stress state at the vicinity of pilot hole at different phases in overcoring in situ stress measurement: (a) in situ state; (b) after pilot hole drilling; and (c) after overcoring.
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Fig. 4. Stress system around a hole in the rock mass (modified from Ref. [12]).
evolution of the measured strains and the cell temperature—from cell installation to the end of biaxial testing (Fig. 6). The quality control code developed in this work is applicable for Phases 15 and 16, although this paper provides ideas for Phases 1–3, 5, 7 and 9–14 also. It must be remembered that the measured in situ stress is a point tensor quantity and the defined values have uncertainties related to geological factors, the accuracy of each measurement method and data analyses. Therefore, it is important to understand and control all known error sources. Based on Amadei and Stephansson [1] 10–20% scatter in magnitude and 720 scatter in orientations must be accepted when in a series of stress measurements in typical rock conditions. The
World Stress Map, the global repository for contemporary tectonic stress data from the Earth’s crust, divides overcoring in situ stress measurement results into five categories based on the number of tests, standard deviation and measuring depth [16]. These do not cover systematic human errors or mistakes.
3. Overcoring (OC) quality control tool In order to control the quality of overcoring data, a computer program was developed. It can simulate the transient strains and stresses during the overcoring process for any in situ stress and coring load conditions.
ARTICLE IN PRESS
Site considereation
M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159
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(1) site characterization (2) estimation of potential for suggesfull measurement (3) drill hole position and orientation
Location considereation
(4) drilling of full size hole (5) starting level for measurement (6) pilot drilling (7) acceptance of pilot hole
Prior OC
(8) cell installation
During OC
(10) overcoring
After OC
(9) hardening of glue and cell monitoring
(11) stabilizing the cell, breaking core (12) biaxial testing
Interpretation
(13) geological logging of core (14) biaxial test interpretation (15) transient strain check (16) stress calculation, sensitivity study (17) guidelines for further use
Fig. 5. Flowchart for phases of overcoring for in situ stress measurement.
The program assumes CHILE rock conditions (continuous, homogeneous, isotropic and linearly elastic). The developed program can be used: (a) for a strain check, i.e. comparing the measured strains with the computed ones, (b) to identify erroneous strain gauges and estimate the amount of error for individual strain gauges, or unexplained strains for all strain gauges, (c) to estimate core damage potential by comparing elastic principal stresses at the pilot hole wall to the strength of the rock, and (d) to estimate the in situ state of stress based on the early strains readings by using an inverse solution. For secondary stresses at the vicinity of the hole bottom, no analytical solutions exist. Therefore, numerical simulation was the only choice for this work. Normally, a 3-D numerical calculation with an adequate number of coring steps will take one to two days with a 1 GHz Pentium PC but, with pre-calculation results, it is
possible to pre-produce transient strain curves for any loading condition in 1 min. As input data for the transient strain curve calculation, the following are needed: (a) Orientation of borehole (trend and plunge). (b) Position and orientation of strain gauges (angular location on pilot hole perimeter and dip related to borehole axis). (c) The in situ state of stress, usually given in the form of principal stress s1 ; trends1 ; plunges1 ; s2 ; trends2 ; plunges2 ; s3; trends3 ; plunges3 which can be transformed into tensor form sN ; sE ; sV ; sNE ; sEV ; sVN ; where N, E and V refers to the north and east compass points and vertical. (d) Young’s modulus and Poisson’s ratio from the biaxial test on overcored core. (e) Optionally, drilling loads: axial stress (PA), shear stress (PS) at drill bit–rock interface and drilling fluid pressure (PW) on the drill and pilot hole walls.
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1146 500
10
A0
Readings resetted
A90
300
A45
9
B45 B135 8
-100
7
-300
6
-500
5
B90 C0 C90 C45 D135 E90 F90 Temp
End of coring Flushing off
Flushing on Coring started -700
-900 -80
Cell temperature (degrees)
Microstrain
100
4 Hardening 38 h -40
Flushing 30 min
Coring 50 min 0
40
Core out Flushing of borehole Biaxial testing 30 min 20 min 30 min 80
120
3 160
Hardening ( h ), Flushing (min ), Coring ( cm ), After coring (min ), Biaxial ( min )
Fig. 6. The evolution of measured strains and cell temperature from cell installation to end of biaxial testing. Total time for presented CSIRI-HI cell measurement was approximately 40 h (A, B, C, D, E, F are identifiers for different rosettes and value is the orientation of strain gauge, i.e. 0 is for axial strain gauge and 90 for tangential).
Similarly as for the in situ stress measurement, the code is based on CHILE conditions. For CHILE conditions, the secondary stress state ssx ; ssy ; ssz ; ssxy ; ssyz ; sszx at the borehole wall corresponding to a certain overcoring advance x in a known in situ state of stress (sN ; sE ; sV ; sNE ; sEV ; sVN ) and drilling loading condition (PA ; PS ; PW ) can be reproduced by superimposing the secondary stresses from each primary load ssx ðiÞ; ssy ðiÞ; ssz ðiÞ; ssxy ðiÞ; ssyz ðiÞ; sszx ðiÞ; i ¼ sN ; sE ; sV ; sNE ; sEV ; sVN ; PA ; PS ; PW ). The secondary stresses are nonlinearly dependent on Poisson’s ratio; therefore, secondary stresses from each primary load have to be calculated with an adequate number of Poisson’s ratio values to obtain good estimates for secondary stresses for any Poisson’s ratio. For this code, 0.15, 0.5 and 0.35 were selected. Young’s modulus does not affect the secondary stresses; instead, it has a linear effect on the strains. From the secondary stresses at gauge position and Young’s modulus, the strain for any known strain gauge can be calculated. The secondary stresses in the strain gauge area are calculated using the 3-D finite difference method code FLAC3D [17]. The flowchart of the developed code is shown in Fig. 7. The developed code is a Microsoft Excel workbook. The programming is done with Visual Basic for Application macros. The workbook code includes a quick guide and a more detailed manual. The session is started by reading in precalculated stress tensors and is continued by inputting case data and measured strain data. Then the inputted transient strains corresponding
to the given in situ state of stress can be calculated and compared to measured ones. The comparison can be made in the form of absolute transient values, transient differences or transient unexplained strains. The stress path for maximum compression, deviatoric stress and tension in the strain gauge area can be studied and compared to the strength of the intact rock. The strength plot includes user-defined envelopes for peak strength, crack damage strength, crack initiation strength and s3 ¼ 5% s1 (Fig. 8). The Hoek–Brown peak strength envelope is defined by the uniaxial compressive strength (sUCS ) and tensile strength (sT ) assuming s ¼ 1 [18]. The crack damage envelope is defined by the uniaxial crack damage strength (sCD ) and the same m-value as for peak strength. For the crack initiation envelope, the deviatoric stress (s1 2s3 ) is assumed to be equal to the uniaxial crack damage strength (sCI ). Based on the presentation of Read et al. [19], the crack damage strength is assumed to be the true strength of the rock The rock is assumed to become damaged if the state of stress reaches the crack initiation surface and the confinement is less than 5% of the maximum stress. The rate of strength reduction is not given, but it can be defined from in situ observations. Finally, the in situ state of stress can be calculated from early strains using an inverse method. In the inverse solution, the unwanted strain gauges can be rejected from the solution. Any input value can be changed and the calculations repeated without again reading the stress tensors. The visibility of resulting and
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(1) read stress tensor files for three Poisson's rato values
(2) spread tensor values around pilot hole if symmetry was used in tensor calculation
(3) Input case data - bearing and dip of borehole - in situ principal stresses in form of magnitude, bearing and dip - drilling loads: Pa, Ps and Wp - strain gauge rosette bearings - Young's modulus and Poisson's ratio (4) convert in situ stress to global tensor form to get tensor multipliers (5) global tensor form to borehole tensor form to get tensor multipliers (6) check if inverse solution is asked to be done
(7a) superimpose borehole cartesian stress tensors by taking account in situ stress multipliers and poisson's ratio
(8a) calculate average strain gauge stresses by taking account true angular position
Repeat phases 7a to 11a nine times, in each time one primary load multiplier is set to one and the others are equal to zero
Produce unit load-strain matrix for inverse solution
(9a) transforms secondary stresses in cartesian borehole coordinate system to borehole polar coordinate system
(10a) transforms stresses in borehole polar system into strain gauge stresses
(11a) calculate strain gauge strains (12) calculate and find maximum principal stresses
(13) find calculated strain vaues for measured ones
(14) If asked, do inverse solution for in situ state of stress (15) produce plots (16) modify plots
(17) If asked, reject strain gauges and redo inverse solution
(18) change input values and recalculate (19) end
Fig. 7. Flowchart of developed code.
measured data can be controlled, calculated values can be copied to other applications, and resulting figures can be copied or plotted. The maximum error of the code includes the accuracy of the stress tensor calculation, error caused by strain gauge location interpolation and error caused by Poisson’s ratio interplolation/extrapolation. The maximum error was studied with one real set of measure-
ment data and with 10 MPa uniaxial in situ stress. In both cases, Poisson’s ratio was varied from 0.05 to 0.5. The maximum error in the real case was –0.6 to 0.4 MPa, which is –3.7% to 3.1% of the mean in situ stress. With a uniaxial in situ stress, the maximum error was –0.5 to 0.5 MPa, being –5.1% to 5.1% of the mean in situ stress. The mean total error was 71% of the mean in situ stress.
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Strength envelope, defined by σucs, σt and s = 1
DA M AG E E VIDE NT
Major Principal Stress (MPa)
σucs
Stress path during overcoring in location where maximum compression takes place
Crack damage envelope, defined by σcd, s = 1 and m (strength envelope)
HIGH DAMAGE POTENTIAL σcd
Stress path during overcoring in location where maximum tension takes place
DAMAGE POSSIBLE σci
Envelope for σ3 = 0.05 σ1 Crack initiation envelope, σ3 - σ1 = σcl
Secondary stress on pilot hole wall with bigger signal
0.0 Minor Principal Stress (MPa)
Fig. 8. Interpretation of elastic stress paths during the overcoring at strain gauge location when superimposed over strength envelopes.
4. Sensitivity studies
*
The sensitivity study conducted is not all inclusive, but aimed at understanding the effect of certain factors on the transient strains and interpreting the in situ state of stress. Three different types of sensitivity studies were completed. A real in situ stress measurement from . o. borehole KK0045G01, distance 34.77 m at the Asp Hard Rock Laboratory, Sweden, was selected as a reference case for all the sensitivity studies The first study in which the loading conditions and material parameter values were slightly varied showed the following:
*
*
*
*
*
*
*
Young’s modulus is an important parameter having close to a 100% proportional effect on the stress magnitudes. The effect of Poisson’s ratio is moderate for all strains and interpreted stress; the effect is 20–60% for the principal stress magnitude and a few degrees in orientation. 10 uncertainty in strain gauge orientation can produce, at a maximum, 20% error in strain values. The rotation of the whole gauge system produces an equal error in the principal stress orientations. 10% change in the major principal stress requires 5–10% general change in strains. 10 MPa drill bit pressure has a general 5% to 20% effect on transient strains when the coring has not yet passed the strain gauge position.
*
*
The drill bit shear stress has a minor effect on transient strains. Drill bit loads do not have an affect on the final strains. 1 MPa (=100 m water) drilling fluid pressure decreases all strains generally by 5–10% and all interpreted in situ principal stresses by this magnitude. For the studied factors, there is no general trend that the effect is higher and lower for transient stresses than for final stresses, except in the case of drilling loads—which do not affect the final strain.
The second study with heterogeneous or anisotropic rock or modified pilot hole geometry showed the following: *
*
*
735% random deviation of elastic parameters, 2 cm spherical crystal at rosette 1 location with 20% lower Young’s modulus or 10% transverse anisotropy in Young’s modulus does not have a clear effect on the measured strains. 2 cm spherical crystal at rosette 1 location with 80% lower Young’s modulus has a clear effect on the measured strains and interpreted in situ state of stress. If 96 mm overcoring instead of 76 mm is used, the transient phase is longer, the evolution of strains is smoother, but the final strains are the same. The maximum and minimum principal stresses at the
ARTICLE IN PRESS M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159
strain gauge location were 53.2 and 7.1 MPa for 96 mm overcoring and 57 and –18 MPa for 76 mm overcoring. This means that the thin walled overcoring is clearly more sensitive in terms of core damage than the thicker one. The developed code has the capability to solve for the in situ state of stress based on any measured transient (early strains) or final strains. Based on exact calculated strain values and corresponding coring advance, the inverse solution is exact. In the real case, there is always some error relating to measurement of coring advance, drilling loads and measuring accuracy. The sensitivity study was undertaken for coring advance only. It is based on calculated strain values for . o. case. Three coring the previously used reference Asp advances of 60, 15 and 5 mm before the strain gauge location were studied. The resulting stress tensors showed that, if there is some uncertainty in measurement of coring advance, the solution is very sensitive and it is most sensitive close to the strain gauge position. If the inverse solution is going to be used, the coring advance has to be measured to better than 71 mm accuracy.
5. Case study . o. Hard Rock The selected cases are from the Asp Laboratory (HRL) where the Swedish Nuclear and Fuel Waste Mangement Co (SKB) has tested the reliability of different in situ stress methods under controlled conditions. The HRL is located below an island close to the coast of south-east Sweden (Fig. 9). The host rock is a diorite with a Young’s modulus of 75–80 GPa and a uniaxial compressive strength in the range of 160– 210 MPa. The stress measurement campaigns have been
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carried out through various phases. The first investigation phase up to 1990 was undertaken from the surface, and included hydraulic fracturing and overcoring using the Borre probe. The next phase up to 1995 covered stress measurements during excavation of the tunnels, using the CSIRO gauge. During the operational phase after 1995, stress measurements been carried out from the tunnels using overcoring with the CSIRO and Borre gauges, as well as hydraulic fracturing. By comparing the results from the various stress measuring campaigns between levels 320 and 500 m, it was concluded that data from different measurement projects, and from different locations at the site, could display significant differences in orientations, magnitudes and repeatability. Differences in stress magnitudes with depth of 50% and variations in trend of the major principal stress of 730–40 within the test locations were considered to indicate a problem with the reliability of the stress measurement data [20]. The case data was from borehole KK0045G01. Two sequential measurements were studied: Level 2:2 (34.77 m) and Level 2:3 (35.48 m) (Figs. 10 and 11). The procedure in the case study was to study the measured strains, analyse the biaxial data, execute the closed-form solution, compare measured transient strains with calculated ones, and obtain the inverse solution for the in situ state of stress and compare the transient strains to the measured ones again. 5.1. Measurement data Studying the transient strain data from both measurements the following points are noted. * *
The 4.5 C temperature increases in both cases. The time-dependent behaviour of most extended strain gauges (34.77 m: G5, G6, G8 and 35.48 m: G2, G5).
. o. HRL (left) and general layout of the HRL facilities (right). Fig. 9. Geographical location of Asp
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700
24
600
22
500
20
400
18
300
16
200
14
100
12
G1, R1-axi G2, R1-tan G3, R1-45 G4, R2-axi G5, R2-tan G7, R3-axi Temp (degrees)
Micro strain
G6, R2-45 G8, R3-tan G9, R3-t45 G1sc, R1-axi G2sc, R1-tan G3sc, R1-45 G4sc, R2-axi G5sc, R2-tan G6sc, R2-45
10
0
G7sc, R3-axi
OC-start -200 -20
G8sc, R3-tan
8
-100
0
SG-position 20
G9sc, R3-t45
OC-stop 40
SG temp 60
80
6 100
Advance (cm) or time before and after overcoring (s)
. o. KK0045G01 34.77 m, measured strain gauge readings during the overcoring measurement and the values originally selected for the Fig. 10. Asp in situ stress calculation (Gn is for measured and Gnsc is for stress calculation value). 24
700
G1, R1-axi G2, R1-tan
600
22
500
20
400
18
300
16
200
14
G3, R1-45 G4, R2-axi G5, R2-tan G6, R2-45 G7, R3-axi
12
100
Temp (degrees)
Micro strain
G8, R3-tan G9, R3-t45 G1sc, R1-axi G2sc, R1-tan G3sc, R1-45 G4sc, R2-axi G5sc, R2-tan
0
10
G6sc, R2-45 G7sc, R3-axi
OC-start
SG-position
OC-stop
G8sc, R3-tan
-100
8 G9sc, R3-t45 SG temp
-200 -20
0
20
40
60
80
6 100
Advance (cm) or time before and after overcoring (s)
. o. KK0045G01 35.44 m, measured strain gauge readings during the overcoring measurement and the values originally selected for in situ Fig. 11. Asp stress calculation (Gn is for measured and Gnsc is for stress calculation value). *
*
*
Sudden large changes after overcoring (not reported, but probably caused by core break). Definition of calculation values basically from the position where the drill bit is 5–6 cm beyond the gauge position. For the original stress calculation, judgement in selecting selected strain values has been used (34.77 m: G2 and 35.48: G7 and G8).
The temperature seems to have minor effect on the readings of the Borre probe, because the effect is not manifested on all tangential nor inclined strain gauges. The most strained strain gauges suffer probably from debonding because no time-dependent behaviour is shown on the less strained strain gauges. The definition of strain values for stress calculation are reasonable because in the ideal case (simulation) the strain readings
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two cases, we cannot be sure that the strain gauge response in the biaxial test was the same as it was during the overcoring.
are relatively stable when coring has passed the gauge position by 5 cm. Also, the effect of debonding is probably lowest at this position. Another question is the value for the axial strain; in both measurements, the lowest measured value was ignored (actually it has been decided to use the average of the two highest values). Also the stress calculation value for gauge 8 in level 35.48 m is not clear. It is not acceptable that measured values are ignored if no evidence for erroneous reading can be clearly shown. In this case, there is no such clear evidence, only the G1 in level 34.77 m has a different transient path. In the studied cases, there has been large changes in the strain readings between the end of overcoring and the beginning of biaxial testing (Table 1). Possible reasons are strain gauge drift, hardening of glue, timedependent behaviour of rock or temperature change. If they are caused by gauge drift or temperature change, they do not affect the stress calculation but, in the other
5.2. Biaxial testing In both biaxial measurements, slight hysteresis is seen, but no permanent deformation (Figs. 12 and 13). In the axial gauges, the deviation is minor; in the inclined gauges, it is moderate; but gauge 5 deviates from other tangential gauges in both cases. Normally, the calculation of elastic parameters is based on the unloading portion of the biaxial test, which is closer to the unloading process during overcoring. In the calculation, different stress ranges or averaging methods can be used (Table 2). The calculation of Young’s modulus and Poisson’s ratio for CHILE material requires only axial and tangential strain responses. In the ideal case, the strain for the 45
Table 1 . o. KK0045G01. Strain gauge readings at the end of overcoring, at the beginning of biaxial testing, and the difference Asp G1, R1 axi 34.77 m End of OC Beg. of biaxial Delta 35.44 m End of OC Beg. of biaxial Delta
G2, R1 tan
G3, R1 45
G4, R2 axi
G5, R2 tan
G6, R2 45
G7, R3 axi
G8, R3 tan
303 233
245 3
422 41
250 318
1404 1273
760 777
639 269
902 362
2284 1706
70
242
381
68
131
17
370
540
578
397 386
664 656
1242 945
178 85
124 465
675 569
274 543
631 704
1189 774
11
8
297
263
341
106
269
73
415
200 G1, R1_axi G2, R1_tan
100
G3, R1_45 G4, R2_axi
0
G5, R2_tan -100
Microstrain
G9, R3 45
G6, R2_45 G7, R3_axi
-200 G8, R3_tan G9, R3_45
-300
-400
-500
-600 0
2
4
6
8
Cell pressure (MPa)
. o. KK0045G01 34.77 m, biaxial test response. Fig. 12. Asp
10
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200 G1, R1_axi G2, R1_tan
100
G3, R1_45 0
G4, R2_axi G5, R2_tan
Microstrain
-100
G6, R2_45 G7, R3_axi
-200 G8, R3_tan G9, R3_45
-300
-400
-500
-600 0
2
4
6
8
10
Cell pressure (MPa)
. o. KK0045G01 35.48 m, biaxial test response. Fig. 13. Asp
Table 2 . o. KK0045G01. Resulting elastic parameters and the amount of unexplained strain for 45 aligned strain gauge defined from the unloading part Asp of the biaxial test using two different methods (AoUS=amount of unexplained strain) Depth
34.77
Parameter
E
n
66
0.26
63 90 63 70 63 64 92 64 71 64
0.26 0.39 0.26 0.29 0.26 0.26 0.40 0.27 0.30 0.27
Method, stress regime, case Average of point values 3y8 MPa, all gauges Linear fit 0y10 MPa, Rosette 1 0y10 MPa, Rosette 2 0y10 MPa, Rosette 3 0y10 MPa, all gauges 0y10 MPa, G5 ignored 3y8 MPa, Rosette 1 3y8 MPa, Rosette 2 3y8 MPa, Rosette 3 3y8 MPa, all gauges 3y8 MPa, G5 ignored
35.48 AoUS 45 (%)
0 17 27
2 17 28
inclined strain gauge should be the mean value of the corresponding axial and tangential strains; thereby, the measured and calculated values can be used to estimate the degree of heterogeneity, anisotropy or general degree of measurement success (Fig. 14) AoUS ¼
ðe45 0:5ðeaxi þ etan gential Þ : e45
ð1Þ
The study of the biaxial test result showed that: (a) there is a significant differences in the deformation parameter values for the different rosettes; (b) in both measurements, the highest difference is caused by tangential gauge number 5 in rosette 2;
E
n
56
0.17
64 54 66 61 65 65 55 67 62 66
0.23 0.19 0.23 0.21 0.23 0.23 0.19 0.24 0.22 0.23
AoUS 45 (%)
7 29 10
6 27 11
(c) there is an indication of anisotropy, but the response of gauge 5 is not clear; (d) the calculation method can have a 5–10% effect on Young’s modulus value, and hence on the interpreted in situ stress magnitudes also; (e) generally, the SwedPowers method gives a lower modulus and Poisson’s ratio and it does not assume linear elastic behaviour; and (f) the pressure range used for calculation has minor effect. 5.3. Closed-form solution Based on the analytical closed-form solution for the in situ state of stress, it is possible to back calculate the
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Äspö x-axis - 120°
αi = angular position of strain rosette relative to Äspö x-axis - 120°
30° /0%
ri = AoUS W 270° / 17%
329° /-29%
89° / 7% AoUS -20% -10% 157° / -27%
+10%
+20%
209° / -10%
S
. o. KK0045G01 34.77 m and 35.48 m biaxial tests. The Fig. 14. Amount of unexplained strain (AoUS) for different strain gauge rosettes for both Asp angle from North corresponds with angular position of rosette and radial distance is the amount of unexplained strain.
axial, tangential and 45 inclined strains on the pilot hole wall, i.e. the used strains without fixing the angular position. Further, to compare the measured and back calculated strains, the measured values are superimposed on the pilot hole strain plot (Figs. 15 and 16). The difference between the measured and back calculated strains and the location of the strain rosette readings compared to the calculated strain pattern can be used to estimate the sensitivity of individual strain reading in relation to the closed-form solution. The result of the closed-form solution indicates the following: (a) The absolute and relative differences and the amount of unexplained strains are quite small in both cases and the correlation between the measured and back calculated strains is almost perfect. (b) The degree of anisotropy or heterogeneity of the rock is probably not strong because the calculated and measured strains are close to each other. (c) The defined Poisson’s ratio value is reasonable or the effect of Poisson’s ratio is minor. (d) The accuracy of the tangential strain for rosettes 2 and 3 at level 34.77 m and rosettes 1 and 2 at level 35.48 m can have a remarkable effect on the resulting in situ state of stress, because the
tangential and inclined strain gauge gradient is high at these strain gauge positions. (e) The orientation of the stress field is well known, although the magnitudes can vary in a range of defined Young’s modulus values. In both measurements, Young’s modulus is about 64 GPa and Poisson’s ratio 0.25—if the gauge 5 reading is ignored. On the other hand, no evidence of erroneous response exists. (f) Based on the two measurements and the elastic parameters defined by SwedPower, the magnitude of s1 and s2 is known with 720% and s3 with 730% accuracy. The orientation of the principal stresses is known with 77 accuracy (Table 3).
5.4. Transient strain analysis Comparing the measured and calculated transient strains, the following conclusions can be made (Figs. 17 and 18): (a) The majority of strain gauges exhibit trends close to the simulated response. (b) A relatively long interval (min 2 cm) in the measurements makes the comparison uncertain, for example Gauge 4 in Fig. 17.
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M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159 Äspö KK0045G01 34.77
Äspö x-axis - 120°
Analytical - 0, axi
800
Analytical - 90, tan angular position for Rosette 1
600
Analytical - 45, incl. Stress calc value - 0, axi Stress calc value - 90, tan Stress calc value - 45, incl. SG reading at +10cm - 0, axi
400
SG reading at +10cm - 90, tan SG reading at +10cm - 45, incl.
angular position for Rosette 2
200
0 -800
-600
-400
-200
0
200
400
600
800 s1
-200
-400
Principal stresses relative to Äspö x-axis -120°: σ1 = 26.1 MPa, dip 39°, bearing 27° σ2 = 17.3 MPa, dip 28°, bearing 271° angular position σ3 = 8.9 MPa, dip 38°, bearing 156° for Rosette 3
-600
-800
. o KK0045G01 34.77 m. Strain values used to calculate the in situ state of stress, measured strain values when drill bit is 10 cm ahead of Fig. 15. Asp. the gauge position and back calculated axial, tangential and 45 inclined strains around the pilot hole.
Äspö x-axis - 120°
Äspö KK0045G0 135.48 angular position for Rosette 2
Analytical - 0, axi
800
Analytical - 90, tan Analytical - 45, incl. Stress calcvalue - 0, axi
600
Stress calcvalue - 90, tan Stress calcvalue - 45, incl. SG reading at +10cm - 0, axi
400
SG reading at +10cm - 90, tan SG reading at +10cm - 45, incl.
200
0 -800
-600
-400
-200
0
200
-200
400
600
800 angular position for Rosette 1 s1 - 120°
-400
angular position for Rosette 3
-600
Principal stresses relative to Äspö x-axis - 120°: σ1 = 18.1 MPa, dip 29°, bearing 24° σ2 = 12.3 MPa, dip 35°, bearing 271° σ3 = 5.0 MPa, dip 41°, bearing 143°
-800
. o KK0045G01 35.48 m. Strain values used to calculate the in situ state of stress, measured strain values when drill bit is 10 cm ahead of Fig. 16. Asp. the gauge position and back calculated axial, tangential and 45 inclined strains around the pilot hole.
(c) It seems that measured coring advance is about 2 cm ahead of the calculated one. This is possible because the advance is defined from the starting and ending time of overcoring and the total overcoring length. Further, normally the overcoring speed is 3–5 cm/min. (d) Because of uncertainty in the coring advance, it would be extremely hard to implement stress interpretation based on early strains.
(e) The final simulated strain values are close to the measured strain values around +50 mm coring advance, which were used for interpretation of the in situ state of stress. 5.5. Transient stress analysis In both cases, there is a high potential for core damage (Figs. 19 and 20). At 34.77 m depth, the tensile
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Table 3 . o. KK0045G01. In situ principal stresses and the angular direction of both measurements, average in in situ principal stress based on average Asp tensor components and differences compared to average Measuring point
Dip (deg)
s1
Bearing (deg)
s2
Dip (deg)
Bearing (deg)
s3
Dip (deg)
Bearing (deg)
Interpreted in situ state of stress (MPa) Depth 34.77 m 26.1 39 Depth 35.48 m 18.1 29
27 24
17.0 12.0
28 35
271 271
8.9 5.0
38 41
156 143
Average in situ state of stress (MPa) 22.0 35
25
15.0
31
270
7.1
39
150
Absolute difference (MPa) Depth 34.77 m-ave. 4.1 Depth 35.48 m-ave. 3.9
2 1
2.5 2.5
3 4
1 1
1.8 2.1
1 2
6 7
4 6
Relative difference (%) Depth 34.77 m-ave. 19 Depth 34.48 m-ave. 18
17 17
26 29
700 Measured
600
G6
m G4 ( r2_axi ) m G5 ( r2_tan )
G5 500
m G6 ( r2_incl ) Calculated
400
G4 ( r2_axi )
µStrain ( )
G5 ( r2_tan )
300
G6 ( r2_incl )
200
G4 100
0
-1 00
-2 00 -200
-150
-100
-50
0
50
100
150
200
Coring advance (mm)
. o KK0045G01 34.77 m. Measured and calculated strain gauge responses in Rosette 2. Zero advance is equal to strain gauge position. Fig. 17. Asp.
stress exceeds the tensile strength and, at 35.48 m depth, the tensile stress is beyond the crack damage envelope.
5.6. Inverse solution For both cases, the inverse solution with two different elastic parameter values (Table 2) was obtained. It was reasonable to obtain the solution only for strains 50 mm after the strain gauge position because the coring advance was not directly measured and is thus not
accurate enough (Figs. 21 and 22). Also, the point interval is not adequate. The inverse solution gives principal stresses within –1.9 to 1.5 MPa and their orientations within –4 to +6 compared to the closed-form solution. The deviation in resulting values can be considered small. 5.7. Summary . o. KK0045G01 cases showed The study of the two Asp that these two sets of measurements can be considered
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1156 600
Measured m G4 (r2_axi) 500
G5
m G5 (r2_tan) m G6( r2_incl) Calculated
400
G4 (r2_axi) G6
µStrain ( )
G5 (r2_tan) 300
G6 (r2_incl)
200
G4
100
0
-100 -200
-150
-100
-50
0
50
100
150
200
Coring advance (mm)
. o KK0045G01 35.48 m. Measured and calculated strain gauge responses in Rosette 2. Zero advance is equal to strain gauge position. Fig. 18. Asp.
250 σPEAK
Stress path for point: σ1,MAX
200
Stress path for point: σ3,MIN Intact rock parameters:
Major Principal Stress (MPa)
σucs = 195 MPa σt = 16.0 MPa 150
σCRACK DAMAGE
σcd = 123 MPa σci = 75 MPa Position of monitring points:
σ3 = 0.05 σ1
100
σCRACK INITIATION
σ1,MAX at 135° σ3,MIN at 217° 50
0 -20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
Minor Principal Stress (MPa)
. o. KK0045G01 34.77 m. Elastic stress path for maximum compression and tension superimposed on intact rock strength envelopes. Fig. 19. Asp
relatively successful and fulfill the assumptions of continuous, homogenous, isotropic and linearly elastic rock. Major uncertainty concerns the time-dependent behaviour of most of the strained strain gauges, changes in strain readings between core removal and
biaxial testing, and the deviation of gauge 5 in the biaxial test. Based on the two measurements and the elastic parameters defined by SwedPower, the magnitude of s1 and s2 is known with 720% and s3 with 730%
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250 Stress path for point: σ1,MAX
σPEAK
Stress path for point: σ3,MIN 200 Intact rock parameters:
Major Principal Stress (MPa)
σucs = 195 MPa σt = 16.0 MPa 150
σCRACK DAMAGE
σcd = 123 MPa σci = 75 MPa
Position of monitring points: σ3 = 0.05 σ1
100
σCRACK INITIATION
σ1,MAX at 127° σ3,MIN at 207° 50
0 -20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
Minor Principal Stress (MPa)
. o. KK0045G01 35.48 m. Elastic stress path for maximum compression and tension superimposed on intact rock strength envelopes. Fig. 20. Asp
60
40
σN
σNE
σE
σEV
σV
σVN
Stress (MPa)
20
0
-20
-40 Inverse solution for coring advance of 160 mm:
-60
-80 -200
-150
-100
-50
component
value (MPa)
bearing (°)
σ1
24.7
32
36
σ2
16.7
277
30
σ3
8.1
158
39
0
50
100
dip (°)
150
200
Coring advance (mm)
. o. KK0045G01 34.77 m. Inverse solution for stress tensor components. Fig. 21. Asp
accuracy. The orientation of principal stresses is known with 77 accuracy.
6. Discussion and conclusions Technically the developed code fulfilled all the objectives. It can be used to interpret the in situ state
of stress of a CHILE rock based on early strains, compare measured transient strains to the calculated ones, and estimate the core damage potential based on the elastic stresses in the strain gauge regions. The code is quick enough to be a practical tool and it can be used as one of the main components in an overall quality control procedure for overseeing overcoring measurements and their data reduction. The basic idea can be
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M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159 40 Inverse solution for coring advance of 160mm: component 30
Stress (MPa)
20
value (MPa) bearing (°)
dip (°)
σ1
17.1
25
σ2
11.6
272
38
σ3
3.5
141
40
27
10
0
-10
-20
-30 -200
σN
σNE
σE
σEV
σV
σVN
-150
-100
-50
0
50
100
150
200
Coring advance (mm )
. o. KK0045G01 35.48 m. Inverse solution for stress tensor components. Fig. 22. Asp
applied also to other overcoring probes—with minor modifications and recalculation of stress tensors. Based on the case studies, the interpretation of the in situ state of stress from early strains is difficult because the solution is very sensitive to the measured strains and coring advance. The heterogeneity of so-called homogeneus rock, changes in rock temperature, and accuracy in defining the coring advance can ruin the interpretation. On the other hand, the comparison of measured strains to the calculated ones, finding unreliable strain responses, estimation of core damage potential and using the inverse solution for final strains worked well. The estimation of core damage potential of course requires laboratory test results on intact rock strength. The work showed clearly that good quality in situ overcoring stress measurement involves an understanding of all the affecting factors and the quality of preparation, measuring and interpretation work. Key matters are: *
* *
*
* *
knowledge of the local geology, i.e. is the rock continuous, homogeneous, isotropic and linearly elastic, both at the strain gauge and pilot hole scales; selection, stability and control of the glue; temperature control during and after overcoring, depending on the probe used, even a 1 C change in core temperature can have a clear effect on the resulting in situ state of stress; measurement of coring advance, depending on the device the interval should be close to 5 mm and accuracy 71 mm; interpretation of biaxial test results; and strain monitoring from probe installation to after the biaxial test to identify possible sources of unexpected response.
The current version of the developed code cannot take account of thermal effects and anisotropy. With minor development and calculation of new tensor files, it is possible to simulate thermal strains with reasonable accuracy by interpolating the effects of flush water temperature, drill bit contact temperature, overcoring speed and thermal properties of the rock. The capability to include transverse isotropy and free orientation can also be developed.
Acknowledgements The authors thank Heikki Hinkkanen from Posiva Oy and Rolf Christianson from Svensk K.arnbra. nslehantering AB for funding the study and Jonny . Sjoberg from SwedPower AB and Erik Johansson from Saanio & Riekkola Oy for their contributions.
References [1] Amadei B, Stephansson O. Rock stress and its measurement. London: Chapman & Hall; 1997. [2] Martin CD, Stimpson B. Sample disturbance and laboratory properties of Lac du Bonnet granite. Can Geotech J 1994;31: 692–702. [3] Martino JB, Chandler NA, Thompson PM, Read RS. The in situ stress program at AECL’s Underground Research Laboratory, 15 Years of Research (1982–1997). NWMD, Ontario Hydro, Canada, 1997. [4] Martin CD, Christiansson R. Overcoring in highly stressed granite—the influence of microcracking. Int J Rock Mech Min Sci Geomech Abstr 1991;28(1):53–70. [5] Irwin RA, Garritty P, Farmer IW. The effect of boundary yield on the results of in situ stress measurement using overcoring
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[6]
[7]
[8]
[9]
[10]
[11]
[12]
techniques. Int J Rock Mech Min Sci Geomech Abstr 1987; 24(1):89–93. Cai M, Thomas LJ. Performance of overcoring stress measurement device in various rock types and conditions. Trans Inst Min Metall 1993;102. Li Y. Drilling-induced core damage and its relationship to crystal in situ state of stress and rock properties. PhD thesis, University of Alberta, Edmonton, Alta., 1997. Hakala M. Numerical study on core damage and interpretation of in situ state of stress. Helsinki, Finland: Posiva Oy, Posiva-99-25, 1999. Fouial K, Alheib M, Baroudi H, Trentsaux C. Improvement in the interpretation of stress measurements by use of the overcoring method: development of a new approach. Eng Geol 1998;49: 239–52. . L, Ingevald K, Martna J, Strindell L. New automatic Hallbjorn probe for measuring triaxial stresses in deep boreholes. Tunneling Underground Space Technol 1990;5(1/2):141–5. Hakala M. Quality control for overcoring stress measurement. Helsinki, Finland: Posiva Oy, Posiva-03-xx 2003, in press. Leeman ER. The CSIR Doorstopper and triaxial rock stress measuring instrument. Rock Mech 1970;3:25–50.
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[13] Amadei B. Importance of anisotropy when estimating and measuring in situ stress in rock. Int J Rock Mech Min Sci Geomech Abstr 1996;33(3):293–325. [14] Chen C, Pan E, Amadei B. Determination of deformability and tensile strength of anisotropic rock using Brazian test. Int J Rock Mech Min Sci Geomech Abstr 1998;35(1):43–61. [15] Kim K, Franklin JA. Suggested methods for rock stress determination. Int J Rock Mech Min Sci Geomech Abstrs 1987;24(1):53–73. [16] Mueller B, Reinecker J, Heidbach O, Fuchs K. The 2000 release of the World Stress Map, 2000 (available online at www. world-stress-map.org). [17] Fast Lagrangian Analysis of Continua in 3 Dimension. User’s manual, version 2.0. Minneapolis, MN, USA: Itasca Consulting Group, Inc., 1997. [18] Hoek E, Brown ET. Practical estimates of rock mass strength. Int J Rock Mech Min Sci Geomech Abstr 1997;34(8):1165–86. [19] Read RS, Chandler NA, Dzipk EJ. In situ strength criteria for tunnel design in highly stressed rock masses. Int J Rock Mech Min Sci 1998;35(3):261–78. [20] Christiansson R, Hudson JA. Quality control of in situ rock stress . o. Hard Rock measurements. Sweden: Lessons from the Asp Laboratory; 2002.
International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159
Quality control of overcoring stress measurement data M. Hakalaa,*, J.A. Hudsonb, R. Christianssonc b
a Gridpoint Finland Oy, Karkkila 03600, Finland Imperial College and Rock Engineering Consultants, UK c Svensk Karnbr anslehantering AB, SKB, Sweden . .
Accepted 20 July 2003
Abstract The in situ state of stress is one of the key rock mechanics factors related to the safety and stability of underground excavations for civil and mining engineering purposes. However, measurement and interpretation of stress have their difficulties. In particular, practical and objective tools have not been developed to judge transient strain behaviour during overcoring. The work described in this paper was set up by the nuclear waste management companies Posiva Oy (Finland) and Svensk K.arnbr.anslehantering AB (Sweden) to improve the quality of interpretation of overcoring stress measurement results. Thus, the primary product of the project is a quality control capability for overcoring stress measurement data. For this purpose, a computer program was developed which can simulate the transient strains and stresses during the overcoring process for any in situ stress and coring load conditions. The solution is based on superposition of elastic stresses and the basic idea can be applied for different overcoring probes with minor modifications and recalculation of stress tensors. The measured strains can be compared to the calculated ones to check whether the measured transient behaviour accords with the interpreted in situ state of stress. If not, the in situ state of stress can be calculated based on any transient or final strain values. The transient stresses can also be compared to a strength envelope of intact rock and thereby the core damage potential can be estimated. r 2003 Elsevier Ltd. All rights reserved.
1. Introduction When designing an underground excavation at great depth, i.e. for high stress conditions, it is important to have reliable knowledge of the: *
* *
*
magnitude and orientation of the in situ state of stress; strength and critical stress states of intact rock; pre- and post-failure deformation behaviour of rock; and rock mass quality.
for larger volumes by reopening of existing fractures (HTPF) [1]. With increasing depth and rock stress–strength ratio, the core sample for laboratory testing can be damaged but far more difficult and vulnerable is the measuring of the in situ state of stress [2,3]. In crystalline rock, reasons for unsatisfactory in situ stress measurements can be one or more of the following: * * * *
In practice, only vertical boreholes can be used if the target area is deep below the ground surface. The threedimensional stress tensor can be measured at one measurement point using the overcoring method (Borre Probe, CSIRO-HI cell, CSIR-cell, modified CSIR-cell, ANZI-cell, conical-cell or spherical-cell) or interpreted
*Corresponding author. E-mail address: matti@gridpoint.fi (M. Hakala). 1365-1609/$ - see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijrmms.2003.07.005
*
* *
discontinuity closes stress cell, unrecognized anisotropy of rock [4], heterogeneity of rock, stress or strain induced damage of pilot hole wall or core, unacceptable behaviour of glue, glue–rock or glue–cell contact [5], change in temperature [6], and other technical problems of various kinds.
This study was set up by Posiva Oy (Finland) and Svensk K.arnbr.anslehantering AB SKB (Sweden) in order to enhance the quality of overcoring stress measurement interpretation methods. Both companies,
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who are responsible for management of spent nuclear fuel, have a need to define the in situ state of stress at around 400–500 m depth at potential repository locations with high confidence. The initial idea was to interpret the situ state of stress based on early strains, when the core damage potential is low [7,8]. A suitable approach for this solution was introduced by Fouial et al. [9]. As a result of the initial project phase, it was decided to focus the work on verifying that measured transient strains correspond to the interpreted in situ state of stress and on estimating core damage potential based on transient stresses at the strain gauge locations. For this purpose, a computer program was developed which can simulate the transient strains and stresses during the overcoring process for any in situ stress and coring load conditions. To be a practical quality control tool, the calculations of transient strains and stresses for any in situ state of stress should be implementable in a relative short time. For this reason, the solution is based on superposing precalculated secondary stresses caused by each relevant primary load component. This approach assumes that the rock is continuous, homogeneous and linearly elastic. Further, the rock is assumed to be isotropic, although the solution can be applied for known anisotropy also. The precalculation of secondary stresses presumes that the overcoring geometry and Poisson’s ratio are known. Similar superposition solutions have been previously used in core damage studies by Li and Hakala [7,8]. For this project, the Borre Probe (SwedPower’s Leeman-Hiltscher probe) geometry was selected, where the pilot hole diameter is 36 mm and the inner and outer overcoring diameters are 62 and 76 mm (see Figs. 1 and 2) [10]. The rosettes are installed 160 mm from the collar of the pilot hole. The orientation of rosettes is read after installation. The total overcoring length is at least 400 mm. The code can be modified to any other overcoring probe by recalculating the stress tensors. There is the intention to extent the computer code for transverse isotropy in the next phase of the project. With the developed code, a sensitivity study for selected overcoring cases was undertaken and two in situ . o. Hard Rock stress measurement cases from the Asp Laboratory site in Sweden were analysed. The reported work includes an extensive list of factors to be considered in overcoring measurements [11]. In particular, the studied cases demonstrate that it is extremely important to have technical auditing and quality assurance methods for overcoring stress measurement—because the measurement assumptions are easily forgotten and the measured magnitudes are small and sensitive to various errors and disturbances.
Fig. 1. Phases of Borre probe overcoring measurement (modified from Ref. [10]). (1) Advance +76 mm main borehole to measurement depth, (2) drill +36 mm pilot hole and recover core for appraisal, (3) insert Borre probe in installation tool into hole, (4) probe releases from installation tool. Gauges bonded to pilot-hole wall under pressure from the nose cone, (5) pull out installation tool. Probe bonded in place, and (6) overcore the Borre probe and recover in core barrel.
Strain gauge rosette (R1) seen from center of borehole
0 90°
R2 120° 120°
G2 (G5, G8)
R1 120°
R3
G3 (G6, G9) G1 (G4, G7)
Borehole axis Fig. 2. Borre probe strain gauge rosette (left) and strain gauge configuration (right) (modified from Ref. [10]).
2. Overcoring method In pilot hole probe methods, normally nine or 12 strain gauges with different orientations on the pilot
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hole wall are monitored when the stresses on the borehole wall are released by overcoring, Figs. 1–3. Because the stress state around a circular hole is known in closed-form solution, the in situ state of stress can then be calculated from the released strains assuming that the rock is continuous, homogeneous and behaves in a linearly elastic manner around the circular hole (Fig. 4) [12]. The material has to be either isotropic, transversely isotropic or orthotropic. Further, it is assumed that the bottom of the pilot hole or full-scale hole does not have any effect on the secondary stress state at probe level before overcoring. The calculation of the in situ stress requires at least six independent final strain readings and the elastic parameters of the rock. For isotropic rock, we need two elastic parameters: conventionally, Young’s modulus and Poisson’s ratio; but, for transversely isotropic rock, we need five parameters: conventionally, two Young’s moduli, two Poisson’s ratios and a shear modulus. The elastic parameter values for isotropic rock are defined by
1143
biaxial testing of the overcored rock cylinder but, for transverse isotropy or orthotropy, at least three uniaxial or indirect tensile test specimens at different tested anisotropy angles are needed [13,14]. The success of measurement is defined by the continuity and stability of strain gauge readings during the overcoring and linearity during the biaxial testing. The judgement of continuity and stability is subjective. The loading and unloading cycle in the biaxial cell provides information on linear elasticity and the comparison of different axial, circumferential and inclined strain gauge readings provides information on the degree of anisotropy or heterogeneity. Based on the ISRM 1987 suggestions and complemented by experiences of the authors, a successful overcoring in situ stress measurement in hard crystalline rock conditions requires that the phases shown in Fig. 5 are implemented and/or considered [15]. Further, a reliable interpretation of stress from the measured strains has to be based on a full understanding of the
In situ stress stress trajectories
σ1, max deformed shape σ1, min
contours for maximum In situ principal stress
(a)
(b)
unstressed hollow core
(c) Fig. 3. Stress state at the vicinity of pilot hole at different phases in overcoring in situ stress measurement: (a) in situ state; (b) after pilot hole drilling; and (c) after overcoring.
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M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159
Fig. 4. Stress system around a hole in the rock mass (modified from Ref. [12]).
evolution of the measured strains and the cell temperature—from cell installation to the end of biaxial testing (Fig. 6). The quality control code developed in this work is applicable for Phases 15 and 16, although this paper provides ideas for Phases 1–3, 5, 7 and 9–14 also. It must be remembered that the measured in situ stress is a point tensor quantity and the defined values have uncertainties related to geological factors, the accuracy of each measurement method and data analyses. Therefore, it is important to understand and control all known error sources. Based on Amadei and Stephansson [1] 10–20% scatter in magnitude and 720 scatter in orientations must be accepted when in a series of stress measurements in typical rock conditions. The
World Stress Map, the global repository for contemporary tectonic stress data from the Earth’s crust, divides overcoring in situ stress measurement results into five categories based on the number of tests, standard deviation and measuring depth [16]. These do not cover systematic human errors or mistakes.
3. Overcoring (OC) quality control tool In order to control the quality of overcoring data, a computer program was developed. It can simulate the transient strains and stresses during the overcoring process for any in situ stress and coring load conditions.
ARTICLE IN PRESS
Site considereation
M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159
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(1) site characterization (2) estimation of potential for suggesfull measurement (3) drill hole position and orientation
Location considereation
(4) drilling of full size hole (5) starting level for measurement (6) pilot drilling (7) acceptance of pilot hole
Prior OC
(8) cell installation
During OC
(10) overcoring
After OC
(9) hardening of glue and cell monitoring
(11) stabilizing the cell, breaking core (12) biaxial testing
Interpretation
(13) geological logging of core (14) biaxial test interpretation (15) transient strain check (16) stress calculation, sensitivity study (17) guidelines for further use
Fig. 5. Flowchart for phases of overcoring for in situ stress measurement.
The program assumes CHILE rock conditions (continuous, homogeneous, isotropic and linearly elastic). The developed program can be used: (a) for a strain check, i.e. comparing the measured strains with the computed ones, (b) to identify erroneous strain gauges and estimate the amount of error for individual strain gauges, or unexplained strains for all strain gauges, (c) to estimate core damage potential by comparing elastic principal stresses at the pilot hole wall to the strength of the rock, and (d) to estimate the in situ state of stress based on the early strains readings by using an inverse solution. For secondary stresses at the vicinity of the hole bottom, no analytical solutions exist. Therefore, numerical simulation was the only choice for this work. Normally, a 3-D numerical calculation with an adequate number of coring steps will take one to two days with a 1 GHz Pentium PC but, with pre-calculation results, it is
possible to pre-produce transient strain curves for any loading condition in 1 min. As input data for the transient strain curve calculation, the following are needed: (a) Orientation of borehole (trend and plunge). (b) Position and orientation of strain gauges (angular location on pilot hole perimeter and dip related to borehole axis). (c) The in situ state of stress, usually given in the form of principal stress s1 ; trends1 ; plunges1 ; s2 ; trends2 ; plunges2 ; s3; trends3 ; plunges3 which can be transformed into tensor form sN ; sE ; sV ; sNE ; sEV ; sVN ; where N, E and V refers to the north and east compass points and vertical. (d) Young’s modulus and Poisson’s ratio from the biaxial test on overcored core. (e) Optionally, drilling loads: axial stress (PA), shear stress (PS) at drill bit–rock interface and drilling fluid pressure (PW) on the drill and pilot hole walls.
ARTICLE IN PRESS M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159
1146 500
10
A0
Readings resetted
A90
300
A45
9
B45 B135 8
-100
7
-300
6
-500
5
B90 C0 C90 C45 D135 E90 F90 Temp
End of coring Flushing off
Flushing on Coring started -700
-900 -80
Cell temperature (degrees)
Microstrain
100
4 Hardening 38 h -40
Flushing 30 min
Coring 50 min 0
40
Core out Flushing of borehole Biaxial testing 30 min 20 min 30 min 80
120
3 160
Hardening ( h ), Flushing (min ), Coring ( cm ), After coring (min ), Biaxial ( min )
Fig. 6. The evolution of measured strains and cell temperature from cell installation to end of biaxial testing. Total time for presented CSIRI-HI cell measurement was approximately 40 h (A, B, C, D, E, F are identifiers for different rosettes and value is the orientation of strain gauge, i.e. 0 is for axial strain gauge and 90 for tangential).
Similarly as for the in situ stress measurement, the code is based on CHILE conditions. For CHILE conditions, the secondary stress state ssx ; ssy ; ssz ; ssxy ; ssyz ; sszx at the borehole wall corresponding to a certain overcoring advance x in a known in situ state of stress (sN ; sE ; sV ; sNE ; sEV ; sVN ) and drilling loading condition (PA ; PS ; PW ) can be reproduced by superimposing the secondary stresses from each primary load ssx ðiÞ; ssy ðiÞ; ssz ðiÞ; ssxy ðiÞ; ssyz ðiÞ; sszx ðiÞ; i ¼ sN ; sE ; sV ; sNE ; sEV ; sVN ; PA ; PS ; PW ). The secondary stresses are nonlinearly dependent on Poisson’s ratio; therefore, secondary stresses from each primary load have to be calculated with an adequate number of Poisson’s ratio values to obtain good estimates for secondary stresses for any Poisson’s ratio. For this code, 0.15, 0.5 and 0.35 were selected. Young’s modulus does not affect the secondary stresses; instead, it has a linear effect on the strains. From the secondary stresses at gauge position and Young’s modulus, the strain for any known strain gauge can be calculated. The secondary stresses in the strain gauge area are calculated using the 3-D finite difference method code FLAC3D [17]. The flowchart of the developed code is shown in Fig. 7. The developed code is a Microsoft Excel workbook. The programming is done with Visual Basic for Application macros. The workbook code includes a quick guide and a more detailed manual. The session is started by reading in precalculated stress tensors and is continued by inputting case data and measured strain data. Then the inputted transient strains corresponding
to the given in situ state of stress can be calculated and compared to measured ones. The comparison can be made in the form of absolute transient values, transient differences or transient unexplained strains. The stress path for maximum compression, deviatoric stress and tension in the strain gauge area can be studied and compared to the strength of the intact rock. The strength plot includes user-defined envelopes for peak strength, crack damage strength, crack initiation strength and s3 ¼ 5% s1 (Fig. 8). The Hoek–Brown peak strength envelope is defined by the uniaxial compressive strength (sUCS ) and tensile strength (sT ) assuming s ¼ 1 [18]. The crack damage envelope is defined by the uniaxial crack damage strength (sCD ) and the same m-value as for peak strength. For the crack initiation envelope, the deviatoric stress (s1 2s3 ) is assumed to be equal to the uniaxial crack damage strength (sCI ). Based on the presentation of Read et al. [19], the crack damage strength is assumed to be the true strength of the rock The rock is assumed to become damaged if the state of stress reaches the crack initiation surface and the confinement is less than 5% of the maximum stress. The rate of strength reduction is not given, but it can be defined from in situ observations. Finally, the in situ state of stress can be calculated from early strains using an inverse method. In the inverse solution, the unwanted strain gauges can be rejected from the solution. Any input value can be changed and the calculations repeated without again reading the stress tensors. The visibility of resulting and
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(1) read stress tensor files for three Poisson's rato values
(2) spread tensor values around pilot hole if symmetry was used in tensor calculation
(3) Input case data - bearing and dip of borehole - in situ principal stresses in form of magnitude, bearing and dip - drilling loads: Pa, Ps and Wp - strain gauge rosette bearings - Young's modulus and Poisson's ratio (4) convert in situ stress to global tensor form to get tensor multipliers (5) global tensor form to borehole tensor form to get tensor multipliers (6) check if inverse solution is asked to be done
(7a) superimpose borehole cartesian stress tensors by taking account in situ stress multipliers and poisson's ratio
(8a) calculate average strain gauge stresses by taking account true angular position
Repeat phases 7a to 11a nine times, in each time one primary load multiplier is set to one and the others are equal to zero
Produce unit load-strain matrix for inverse solution
(9a) transforms secondary stresses in cartesian borehole coordinate system to borehole polar coordinate system
(10a) transforms stresses in borehole polar system into strain gauge stresses
(11a) calculate strain gauge strains (12) calculate and find maximum principal stresses
(13) find calculated strain vaues for measured ones
(14) If asked, do inverse solution for in situ state of stress (15) produce plots (16) modify plots
(17) If asked, reject strain gauges and redo inverse solution
(18) change input values and recalculate (19) end
Fig. 7. Flowchart of developed code.
measured data can be controlled, calculated values can be copied to other applications, and resulting figures can be copied or plotted. The maximum error of the code includes the accuracy of the stress tensor calculation, error caused by strain gauge location interpolation and error caused by Poisson’s ratio interplolation/extrapolation. The maximum error was studied with one real set of measure-
ment data and with 10 MPa uniaxial in situ stress. In both cases, Poisson’s ratio was varied from 0.05 to 0.5. The maximum error in the real case was –0.6 to 0.4 MPa, which is –3.7% to 3.1% of the mean in situ stress. With a uniaxial in situ stress, the maximum error was –0.5 to 0.5 MPa, being –5.1% to 5.1% of the mean in situ stress. The mean total error was 71% of the mean in situ stress.
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Strength envelope, defined by σucs, σt and s = 1
DA M AG E E VIDE NT
Major Principal Stress (MPa)
σucs
Stress path during overcoring in location where maximum compression takes place
Crack damage envelope, defined by σcd, s = 1 and m (strength envelope)
HIGH DAMAGE POTENTIAL σcd
Stress path during overcoring in location where maximum tension takes place
DAMAGE POSSIBLE σci
Envelope for σ3 = 0.05 σ1 Crack initiation envelope, σ3 - σ1 = σcl
Secondary stress on pilot hole wall with bigger signal
0.0 Minor Principal Stress (MPa)
Fig. 8. Interpretation of elastic stress paths during the overcoring at strain gauge location when superimposed over strength envelopes.
4. Sensitivity studies
*
The sensitivity study conducted is not all inclusive, but aimed at understanding the effect of certain factors on the transient strains and interpreting the in situ state of stress. Three different types of sensitivity studies were completed. A real in situ stress measurement from . o. borehole KK0045G01, distance 34.77 m at the Asp Hard Rock Laboratory, Sweden, was selected as a reference case for all the sensitivity studies The first study in which the loading conditions and material parameter values were slightly varied showed the following:
*
*
*
*
*
*
*
Young’s modulus is an important parameter having close to a 100% proportional effect on the stress magnitudes. The effect of Poisson’s ratio is moderate for all strains and interpreted stress; the effect is 20–60% for the principal stress magnitude and a few degrees in orientation. 10 uncertainty in strain gauge orientation can produce, at a maximum, 20% error in strain values. The rotation of the whole gauge system produces an equal error in the principal stress orientations. 10% change in the major principal stress requires 5–10% general change in strains. 10 MPa drill bit pressure has a general 5% to 20% effect on transient strains when the coring has not yet passed the strain gauge position.
*
*
The drill bit shear stress has a minor effect on transient strains. Drill bit loads do not have an affect on the final strains. 1 MPa (=100 m water) drilling fluid pressure decreases all strains generally by 5–10% and all interpreted in situ principal stresses by this magnitude. For the studied factors, there is no general trend that the effect is higher and lower for transient stresses than for final stresses, except in the case of drilling loads—which do not affect the final strain.
The second study with heterogeneous or anisotropic rock or modified pilot hole geometry showed the following: *
*
*
735% random deviation of elastic parameters, 2 cm spherical crystal at rosette 1 location with 20% lower Young’s modulus or 10% transverse anisotropy in Young’s modulus does not have a clear effect on the measured strains. 2 cm spherical crystal at rosette 1 location with 80% lower Young’s modulus has a clear effect on the measured strains and interpreted in situ state of stress. If 96 mm overcoring instead of 76 mm is used, the transient phase is longer, the evolution of strains is smoother, but the final strains are the same. The maximum and minimum principal stresses at the
ARTICLE IN PRESS M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159
strain gauge location were 53.2 and 7.1 MPa for 96 mm overcoring and 57 and –18 MPa for 76 mm overcoring. This means that the thin walled overcoring is clearly more sensitive in terms of core damage than the thicker one. The developed code has the capability to solve for the in situ state of stress based on any measured transient (early strains) or final strains. Based on exact calculated strain values and corresponding coring advance, the inverse solution is exact. In the real case, there is always some error relating to measurement of coring advance, drilling loads and measuring accuracy. The sensitivity study was undertaken for coring advance only. It is based on calculated strain values for . o. case. Three coring the previously used reference Asp advances of 60, 15 and 5 mm before the strain gauge location were studied. The resulting stress tensors showed that, if there is some uncertainty in measurement of coring advance, the solution is very sensitive and it is most sensitive close to the strain gauge position. If the inverse solution is going to be used, the coring advance has to be measured to better than 71 mm accuracy.
5. Case study . o. Hard Rock The selected cases are from the Asp Laboratory (HRL) where the Swedish Nuclear and Fuel Waste Mangement Co (SKB) has tested the reliability of different in situ stress methods under controlled conditions. The HRL is located below an island close to the coast of south-east Sweden (Fig. 9). The host rock is a diorite with a Young’s modulus of 75–80 GPa and a uniaxial compressive strength in the range of 160– 210 MPa. The stress measurement campaigns have been
1149
carried out through various phases. The first investigation phase up to 1990 was undertaken from the surface, and included hydraulic fracturing and overcoring using the Borre probe. The next phase up to 1995 covered stress measurements during excavation of the tunnels, using the CSIRO gauge. During the operational phase after 1995, stress measurements been carried out from the tunnels using overcoring with the CSIRO and Borre gauges, as well as hydraulic fracturing. By comparing the results from the various stress measuring campaigns between levels 320 and 500 m, it was concluded that data from different measurement projects, and from different locations at the site, could display significant differences in orientations, magnitudes and repeatability. Differences in stress magnitudes with depth of 50% and variations in trend of the major principal stress of 730–40 within the test locations were considered to indicate a problem with the reliability of the stress measurement data [20]. The case data was from borehole KK0045G01. Two sequential measurements were studied: Level 2:2 (34.77 m) and Level 2:3 (35.48 m) (Figs. 10 and 11). The procedure in the case study was to study the measured strains, analyse the biaxial data, execute the closed-form solution, compare measured transient strains with calculated ones, and obtain the inverse solution for the in situ state of stress and compare the transient strains to the measured ones again. 5.1. Measurement data Studying the transient strain data from both measurements the following points are noted. * *
The 4.5 C temperature increases in both cases. The time-dependent behaviour of most extended strain gauges (34.77 m: G5, G6, G8 and 35.48 m: G2, G5).
. o. HRL (left) and general layout of the HRL facilities (right). Fig. 9. Geographical location of Asp
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700
24
600
22
500
20
400
18
300
16
200
14
100
12
G1, R1-axi G2, R1-tan G3, R1-45 G4, R2-axi G5, R2-tan G7, R3-axi Temp (degrees)
Micro strain
G6, R2-45 G8, R3-tan G9, R3-t45 G1sc, R1-axi G2sc, R1-tan G3sc, R1-45 G4sc, R2-axi G5sc, R2-tan G6sc, R2-45
10
0
G7sc, R3-axi
OC-start -200 -20
G8sc, R3-tan
8
-100
0
SG-position 20
G9sc, R3-t45
OC-stop 40
SG temp 60
80
6 100
Advance (cm) or time before and after overcoring (s)
. o. KK0045G01 34.77 m, measured strain gauge readings during the overcoring measurement and the values originally selected for the Fig. 10. Asp in situ stress calculation (Gn is for measured and Gnsc is for stress calculation value). 24
700
G1, R1-axi G2, R1-tan
600
22
500
20
400
18
300
16
200
14
G3, R1-45 G4, R2-axi G5, R2-tan G6, R2-45 G7, R3-axi
12
100
Temp (degrees)
Micro strain
G8, R3-tan G9, R3-t45 G1sc, R1-axi G2sc, R1-tan G3sc, R1-45 G4sc, R2-axi G5sc, R2-tan
0
10
G6sc, R2-45 G7sc, R3-axi
OC-start
SG-position
OC-stop
G8sc, R3-tan
-100
8 G9sc, R3-t45 SG temp
-200 -20
0
20
40
60
80
6 100
Advance (cm) or time before and after overcoring (s)
. o. KK0045G01 35.44 m, measured strain gauge readings during the overcoring measurement and the values originally selected for in situ Fig. 11. Asp stress calculation (Gn is for measured and Gnsc is for stress calculation value). *
*
*
Sudden large changes after overcoring (not reported, but probably caused by core break). Definition of calculation values basically from the position where the drill bit is 5–6 cm beyond the gauge position. For the original stress calculation, judgement in selecting selected strain values has been used (34.77 m: G2 and 35.48: G7 and G8).
The temperature seems to have minor effect on the readings of the Borre probe, because the effect is not manifested on all tangential nor inclined strain gauges. The most strained strain gauges suffer probably from debonding because no time-dependent behaviour is shown on the less strained strain gauges. The definition of strain values for stress calculation are reasonable because in the ideal case (simulation) the strain readings
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two cases, we cannot be sure that the strain gauge response in the biaxial test was the same as it was during the overcoring.
are relatively stable when coring has passed the gauge position by 5 cm. Also, the effect of debonding is probably lowest at this position. Another question is the value for the axial strain; in both measurements, the lowest measured value was ignored (actually it has been decided to use the average of the two highest values). Also the stress calculation value for gauge 8 in level 35.48 m is not clear. It is not acceptable that measured values are ignored if no evidence for erroneous reading can be clearly shown. In this case, there is no such clear evidence, only the G1 in level 34.77 m has a different transient path. In the studied cases, there has been large changes in the strain readings between the end of overcoring and the beginning of biaxial testing (Table 1). Possible reasons are strain gauge drift, hardening of glue, timedependent behaviour of rock or temperature change. If they are caused by gauge drift or temperature change, they do not affect the stress calculation but, in the other
5.2. Biaxial testing In both biaxial measurements, slight hysteresis is seen, but no permanent deformation (Figs. 12 and 13). In the axial gauges, the deviation is minor; in the inclined gauges, it is moderate; but gauge 5 deviates from other tangential gauges in both cases. Normally, the calculation of elastic parameters is based on the unloading portion of the biaxial test, which is closer to the unloading process during overcoring. In the calculation, different stress ranges or averaging methods can be used (Table 2). The calculation of Young’s modulus and Poisson’s ratio for CHILE material requires only axial and tangential strain responses. In the ideal case, the strain for the 45
Table 1 . o. KK0045G01. Strain gauge readings at the end of overcoring, at the beginning of biaxial testing, and the difference Asp G1, R1 axi 34.77 m End of OC Beg. of biaxial Delta 35.44 m End of OC Beg. of biaxial Delta
G2, R1 tan
G3, R1 45
G4, R2 axi
G5, R2 tan
G6, R2 45
G7, R3 axi
G8, R3 tan
303 233
245 3
422 41
250 318
1404 1273
760 777
639 269
902 362
2284 1706
70
242
381
68
131
17
370
540
578
397 386
664 656
1242 945
178 85
124 465
675 569
274 543
631 704
1189 774
11
8
297
263
341
106
269
73
415
200 G1, R1_axi G2, R1_tan
100
G3, R1_45 G4, R2_axi
0
G5, R2_tan -100
Microstrain
G9, R3 45
G6, R2_45 G7, R3_axi
-200 G8, R3_tan G9, R3_45
-300
-400
-500
-600 0
2
4
6
8
Cell pressure (MPa)
. o. KK0045G01 34.77 m, biaxial test response. Fig. 12. Asp
10
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200 G1, R1_axi G2, R1_tan
100
G3, R1_45 0
G4, R2_axi G5, R2_tan
Microstrain
-100
G6, R2_45 G7, R3_axi
-200 G8, R3_tan G9, R3_45
-300
-400
-500
-600 0
2
4
6
8
10
Cell pressure (MPa)
. o. KK0045G01 35.48 m, biaxial test response. Fig. 13. Asp
Table 2 . o. KK0045G01. Resulting elastic parameters and the amount of unexplained strain for 45 aligned strain gauge defined from the unloading part Asp of the biaxial test using two different methods (AoUS=amount of unexplained strain) Depth
34.77
Parameter
E
n
66
0.26
63 90 63 70 63 64 92 64 71 64
0.26 0.39 0.26 0.29 0.26 0.26 0.40 0.27 0.30 0.27
Method, stress regime, case Average of point values 3y8 MPa, all gauges Linear fit 0y10 MPa, Rosette 1 0y10 MPa, Rosette 2 0y10 MPa, Rosette 3 0y10 MPa, all gauges 0y10 MPa, G5 ignored 3y8 MPa, Rosette 1 3y8 MPa, Rosette 2 3y8 MPa, Rosette 3 3y8 MPa, all gauges 3y8 MPa, G5 ignored
35.48 AoUS 45 (%)
0 17 27
2 17 28
inclined strain gauge should be the mean value of the corresponding axial and tangential strains; thereby, the measured and calculated values can be used to estimate the degree of heterogeneity, anisotropy or general degree of measurement success (Fig. 14) AoUS ¼
ðe45 0:5ðeaxi þ etan gential Þ : e45
ð1Þ
The study of the biaxial test result showed that: (a) there is a significant differences in the deformation parameter values for the different rosettes; (b) in both measurements, the highest difference is caused by tangential gauge number 5 in rosette 2;
E
n
56
0.17
64 54 66 61 65 65 55 67 62 66
0.23 0.19 0.23 0.21 0.23 0.23 0.19 0.24 0.22 0.23
AoUS 45 (%)
7 29 10
6 27 11
(c) there is an indication of anisotropy, but the response of gauge 5 is not clear; (d) the calculation method can have a 5–10% effect on Young’s modulus value, and hence on the interpreted in situ stress magnitudes also; (e) generally, the SwedPowers method gives a lower modulus and Poisson’s ratio and it does not assume linear elastic behaviour; and (f) the pressure range used for calculation has minor effect. 5.3. Closed-form solution Based on the analytical closed-form solution for the in situ state of stress, it is possible to back calculate the
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Äspö x-axis - 120°
αi = angular position of strain rosette relative to Äspö x-axis - 120°
30° /0%
ri = AoUS W 270° / 17%
329° /-29%
89° / 7% AoUS -20% -10% 157° / -27%
+10%
+20%
209° / -10%
S
. o. KK0045G01 34.77 m and 35.48 m biaxial tests. The Fig. 14. Amount of unexplained strain (AoUS) for different strain gauge rosettes for both Asp angle from North corresponds with angular position of rosette and radial distance is the amount of unexplained strain.
axial, tangential and 45 inclined strains on the pilot hole wall, i.e. the used strains without fixing the angular position. Further, to compare the measured and back calculated strains, the measured values are superimposed on the pilot hole strain plot (Figs. 15 and 16). The difference between the measured and back calculated strains and the location of the strain rosette readings compared to the calculated strain pattern can be used to estimate the sensitivity of individual strain reading in relation to the closed-form solution. The result of the closed-form solution indicates the following: (a) The absolute and relative differences and the amount of unexplained strains are quite small in both cases and the correlation between the measured and back calculated strains is almost perfect. (b) The degree of anisotropy or heterogeneity of the rock is probably not strong because the calculated and measured strains are close to each other. (c) The defined Poisson’s ratio value is reasonable or the effect of Poisson’s ratio is minor. (d) The accuracy of the tangential strain for rosettes 2 and 3 at level 34.77 m and rosettes 1 and 2 at level 35.48 m can have a remarkable effect on the resulting in situ state of stress, because the
tangential and inclined strain gauge gradient is high at these strain gauge positions. (e) The orientation of the stress field is well known, although the magnitudes can vary in a range of defined Young’s modulus values. In both measurements, Young’s modulus is about 64 GPa and Poisson’s ratio 0.25—if the gauge 5 reading is ignored. On the other hand, no evidence of erroneous response exists. (f) Based on the two measurements and the elastic parameters defined by SwedPower, the magnitude of s1 and s2 is known with 720% and s3 with 730% accuracy. The orientation of the principal stresses is known with 77 accuracy (Table 3).
5.4. Transient strain analysis Comparing the measured and calculated transient strains, the following conclusions can be made (Figs. 17 and 18): (a) The majority of strain gauges exhibit trends close to the simulated response. (b) A relatively long interval (min 2 cm) in the measurements makes the comparison uncertain, for example Gauge 4 in Fig. 17.
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M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159 Äspö KK0045G01 34.77
Äspö x-axis - 120°
Analytical - 0, axi
800
Analytical - 90, tan angular position for Rosette 1
600
Analytical - 45, incl. Stress calc value - 0, axi Stress calc value - 90, tan Stress calc value - 45, incl. SG reading at +10cm - 0, axi
400
SG reading at +10cm - 90, tan SG reading at +10cm - 45, incl.
angular position for Rosette 2
200
0 -800
-600
-400
-200
0
200
400
600
800 s1
-200
-400
Principal stresses relative to Äspö x-axis -120°: σ1 = 26.1 MPa, dip 39°, bearing 27° σ2 = 17.3 MPa, dip 28°, bearing 271° angular position σ3 = 8.9 MPa, dip 38°, bearing 156° for Rosette 3
-600
-800
. o KK0045G01 34.77 m. Strain values used to calculate the in situ state of stress, measured strain values when drill bit is 10 cm ahead of Fig. 15. Asp. the gauge position and back calculated axial, tangential and 45 inclined strains around the pilot hole.
Äspö x-axis - 120°
Äspö KK0045G0 135.48 angular position for Rosette 2
Analytical - 0, axi
800
Analytical - 90, tan Analytical - 45, incl. Stress calcvalue - 0, axi
600
Stress calcvalue - 90, tan Stress calcvalue - 45, incl. SG reading at +10cm - 0, axi
400
SG reading at +10cm - 90, tan SG reading at +10cm - 45, incl.
200
0 -800
-600
-400
-200
0
200
-200
400
600
800 angular position for Rosette 1 s1 - 120°
-400
angular position for Rosette 3
-600
Principal stresses relative to Äspö x-axis - 120°: σ1 = 18.1 MPa, dip 29°, bearing 24° σ2 = 12.3 MPa, dip 35°, bearing 271° σ3 = 5.0 MPa, dip 41°, bearing 143°
-800
. o KK0045G01 35.48 m. Strain values used to calculate the in situ state of stress, measured strain values when drill bit is 10 cm ahead of Fig. 16. Asp. the gauge position and back calculated axial, tangential and 45 inclined strains around the pilot hole.
(c) It seems that measured coring advance is about 2 cm ahead of the calculated one. This is possible because the advance is defined from the starting and ending time of overcoring and the total overcoring length. Further, normally the overcoring speed is 3–5 cm/min. (d) Because of uncertainty in the coring advance, it would be extremely hard to implement stress interpretation based on early strains.
(e) The final simulated strain values are close to the measured strain values around +50 mm coring advance, which were used for interpretation of the in situ state of stress. 5.5. Transient stress analysis In both cases, there is a high potential for core damage (Figs. 19 and 20). At 34.77 m depth, the tensile
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Table 3 . o. KK0045G01. In situ principal stresses and the angular direction of both measurements, average in in situ principal stress based on average Asp tensor components and differences compared to average Measuring point
Dip (deg)
s1
Bearing (deg)
s2
Dip (deg)
Bearing (deg)
s3
Dip (deg)
Bearing (deg)
Interpreted in situ state of stress (MPa) Depth 34.77 m 26.1 39 Depth 35.48 m 18.1 29
27 24
17.0 12.0
28 35
271 271
8.9 5.0
38 41
156 143
Average in situ state of stress (MPa) 22.0 35
25
15.0
31
270
7.1
39
150
Absolute difference (MPa) Depth 34.77 m-ave. 4.1 Depth 35.48 m-ave. 3.9
2 1
2.5 2.5
3 4
1 1
1.8 2.1
1 2
6 7
4 6
Relative difference (%) Depth 34.77 m-ave. 19 Depth 34.48 m-ave. 18
17 17
26 29
700 Measured
600
G6
m G4 ( r2_axi ) m G5 ( r2_tan )
G5 500
m G6 ( r2_incl ) Calculated
400
G4 ( r2_axi )
µStrain ( )
G5 ( r2_tan )
300
G6 ( r2_incl )
200
G4 100
0
-1 00
-2 00 -200
-150
-100
-50
0
50
100
150
200
Coring advance (mm)
. o KK0045G01 34.77 m. Measured and calculated strain gauge responses in Rosette 2. Zero advance is equal to strain gauge position. Fig. 17. Asp.
stress exceeds the tensile strength and, at 35.48 m depth, the tensile stress is beyond the crack damage envelope.
5.6. Inverse solution For both cases, the inverse solution with two different elastic parameter values (Table 2) was obtained. It was reasonable to obtain the solution only for strains 50 mm after the strain gauge position because the coring advance was not directly measured and is thus not
accurate enough (Figs. 21 and 22). Also, the point interval is not adequate. The inverse solution gives principal stresses within –1.9 to 1.5 MPa and their orientations within –4 to +6 compared to the closed-form solution. The deviation in resulting values can be considered small. 5.7. Summary . o. KK0045G01 cases showed The study of the two Asp that these two sets of measurements can be considered
ARTICLE IN PRESS M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159
1156 600
Measured m G4 (r2_axi) 500
G5
m G5 (r2_tan) m G6( r2_incl) Calculated
400
G4 (r2_axi) G6
µStrain ( )
G5 (r2_tan) 300
G6 (r2_incl)
200
G4
100
0
-100 -200
-150
-100
-50
0
50
100
150
200
Coring advance (mm)
. o KK0045G01 35.48 m. Measured and calculated strain gauge responses in Rosette 2. Zero advance is equal to strain gauge position. Fig. 18. Asp.
250 σPEAK
Stress path for point: σ1,MAX
200
Stress path for point: σ3,MIN Intact rock parameters:
Major Principal Stress (MPa)
σucs = 195 MPa σt = 16.0 MPa 150
σCRACK DAMAGE
σcd = 123 MPa σci = 75 MPa Position of monitring points:
σ3 = 0.05 σ1
100
σCRACK INITIATION
σ1,MAX at 135° σ3,MIN at 217° 50
0 -20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
Minor Principal Stress (MPa)
. o. KK0045G01 34.77 m. Elastic stress path for maximum compression and tension superimposed on intact rock strength envelopes. Fig. 19. Asp
relatively successful and fulfill the assumptions of continuous, homogenous, isotropic and linearly elastic rock. Major uncertainty concerns the time-dependent behaviour of most of the strained strain gauges, changes in strain readings between core removal and
biaxial testing, and the deviation of gauge 5 in the biaxial test. Based on the two measurements and the elastic parameters defined by SwedPower, the magnitude of s1 and s2 is known with 720% and s3 with 730%
ARTICLE IN PRESS M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159
1157
250 Stress path for point: σ1,MAX
σPEAK
Stress path for point: σ3,MIN 200 Intact rock parameters:
Major Principal Stress (MPa)
σucs = 195 MPa σt = 16.0 MPa 150
σCRACK DAMAGE
σcd = 123 MPa σci = 75 MPa
Position of monitring points: σ3 = 0.05 σ1
100
σCRACK INITIATION
σ1,MAX at 127° σ3,MIN at 207° 50
0 -20.0
-15.0
-10.0
-5.0
0.0
5.0
10.0
Minor Principal Stress (MPa)
. o. KK0045G01 35.48 m. Elastic stress path for maximum compression and tension superimposed on intact rock strength envelopes. Fig. 20. Asp
60
40
σN
σNE
σE
σEV
σV
σVN
Stress (MPa)
20
0
-20
-40 Inverse solution for coring advance of 160 mm:
-60
-80 -200
-150
-100
-50
component
value (MPa)
bearing (°)
σ1
24.7
32
36
σ2
16.7
277
30
σ3
8.1
158
39
0
50
100
dip (°)
150
200
Coring advance (mm)
. o. KK0045G01 34.77 m. Inverse solution for stress tensor components. Fig. 21. Asp
accuracy. The orientation of principal stresses is known with 77 accuracy.
6. Discussion and conclusions Technically the developed code fulfilled all the objectives. It can be used to interpret the in situ state
of stress of a CHILE rock based on early strains, compare measured transient strains to the calculated ones, and estimate the core damage potential based on the elastic stresses in the strain gauge regions. The code is quick enough to be a practical tool and it can be used as one of the main components in an overall quality control procedure for overseeing overcoring measurements and their data reduction. The basic idea can be
ARTICLE IN PRESS 1158
M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159 40 Inverse solution for coring advance of 160mm: component 30
Stress (MPa)
20
value (MPa) bearing (°)
dip (°)
σ1
17.1
25
σ2
11.6
272
38
σ3
3.5
141
40
27
10
0
-10
-20
-30 -200
σN
σNE
σE
σEV
σV
σVN
-150
-100
-50
0
50
100
150
200
Coring advance (mm )
. o. KK0045G01 35.48 m. Inverse solution for stress tensor components. Fig. 22. Asp
applied also to other overcoring probes—with minor modifications and recalculation of stress tensors. Based on the case studies, the interpretation of the in situ state of stress from early strains is difficult because the solution is very sensitive to the measured strains and coring advance. The heterogeneity of so-called homogeneus rock, changes in rock temperature, and accuracy in defining the coring advance can ruin the interpretation. On the other hand, the comparison of measured strains to the calculated ones, finding unreliable strain responses, estimation of core damage potential and using the inverse solution for final strains worked well. The estimation of core damage potential of course requires laboratory test results on intact rock strength. The work showed clearly that good quality in situ overcoring stress measurement involves an understanding of all the affecting factors and the quality of preparation, measuring and interpretation work. Key matters are: *
* *
*
* *
knowledge of the local geology, i.e. is the rock continuous, homogeneous, isotropic and linearly elastic, both at the strain gauge and pilot hole scales; selection, stability and control of the glue; temperature control during and after overcoring, depending on the probe used, even a 1 C change in core temperature can have a clear effect on the resulting in situ state of stress; measurement of coring advance, depending on the device the interval should be close to 5 mm and accuracy 71 mm; interpretation of biaxial test results; and strain monitoring from probe installation to after the biaxial test to identify possible sources of unexpected response.
The current version of the developed code cannot take account of thermal effects and anisotropy. With minor development and calculation of new tensor files, it is possible to simulate thermal strains with reasonable accuracy by interpolating the effects of flush water temperature, drill bit contact temperature, overcoring speed and thermal properties of the rock. The capability to include transverse isotropy and free orientation can also be developed.
Acknowledgements The authors thank Heikki Hinkkanen from Posiva Oy and Rolf Christianson from Svensk K.arnbra. nslehantering AB for funding the study and Jonny . Sjoberg from SwedPower AB and Erik Johansson from Saanio & Riekkola Oy for their contributions.
References [1] Amadei B, Stephansson O. Rock stress and its measurement. London: Chapman & Hall; 1997. [2] Martin CD, Stimpson B. Sample disturbance and laboratory properties of Lac du Bonnet granite. Can Geotech J 1994;31: 692–702. [3] Martino JB, Chandler NA, Thompson PM, Read RS. The in situ stress program at AECL’s Underground Research Laboratory, 15 Years of Research (1982–1997). NWMD, Ontario Hydro, Canada, 1997. [4] Martin CD, Christiansson R. Overcoring in highly stressed granite—the influence of microcracking. Int J Rock Mech Min Sci Geomech Abstr 1991;28(1):53–70. [5] Irwin RA, Garritty P, Farmer IW. The effect of boundary yield on the results of in situ stress measurement using overcoring
ARTICLE IN PRESS M. Hakala et al. / International Journal of Rock Mechanics & Mining Sciences 40 (2003) 1141–1159
[6]
[7]
[8]
[9]
[10]
[11]
[12]
techniques. Int J Rock Mech Min Sci Geomech Abstr 1987; 24(1):89–93. Cai M, Thomas LJ. Performance of overcoring stress measurement device in various rock types and conditions. Trans Inst Min Metall 1993;102. Li Y. Drilling-induced core damage and its relationship to crystal in situ state of stress and rock properties. PhD thesis, University of Alberta, Edmonton, Alta., 1997. Hakala M. Numerical study on core damage and interpretation of in situ state of stress. Helsinki, Finland: Posiva Oy, Posiva-99-25, 1999. Fouial K, Alheib M, Baroudi H, Trentsaux C. Improvement in the interpretation of stress measurements by use of the overcoring method: development of a new approach. Eng Geol 1998;49: 239–52. . L, Ingevald K, Martna J, Strindell L. New automatic Hallbjorn probe for measuring triaxial stresses in deep boreholes. Tunneling Underground Space Technol 1990;5(1/2):141–5. Hakala M. Quality control for overcoring stress measurement. Helsinki, Finland: Posiva Oy, Posiva-03-xx 2003, in press. Leeman ER. The CSIR Doorstopper and triaxial rock stress measuring instrument. Rock Mech 1970;3:25–50.
1159
[13] Amadei B. Importance of anisotropy when estimating and measuring in situ stress in rock. Int J Rock Mech Min Sci Geomech Abstr 1996;33(3):293–325. [14] Chen C, Pan E, Amadei B. Determination of deformability and tensile strength of anisotropic rock using Brazian test. Int J Rock Mech Min Sci Geomech Abstr 1998;35(1):43–61. [15] Kim K, Franklin JA. Suggested methods for rock stress determination. Int J Rock Mech Min Sci Geomech Abstrs 1987;24(1):53–73. [16] Mueller B, Reinecker J, Heidbach O, Fuchs K. The 2000 release of the World Stress Map, 2000 (available online at www. world-stress-map.org). [17] Fast Lagrangian Analysis of Continua in 3 Dimension. User’s manual, version 2.0. Minneapolis, MN, USA: Itasca Consulting Group, Inc., 1997. [18] Hoek E, Brown ET. Practical estimates of rock mass strength. Int J Rock Mech Min Sci Geomech Abstr 1997;34(8):1165–86. [19] Read RS, Chandler NA, Dzipk EJ. In situ strength criteria for tunnel design in highly stressed rock masses. Int J Rock Mech Min Sci 1998;35(3):261–78. [20] Christiansson R, Hudson JA. Quality control of in situ rock stress . o. Hard Rock measurements. Sweden: Lessons from the Asp Laboratory; 2002.