linear variable differential transformer= is an electromechanical sensor used to convert mechanical motion or vibrations, specifically rectilinear motion, into a variable electrical current, voltage or electric signals, and the reverse.

1. In situ rock stress measurements
from existing tunnels with LVDT-cell

2. LVDT-cell version II
Eight radial
LVDT sensors
Rock and cell
temperature sensors
Electronics
O-ring based
mounting system
Mounting
tool
Batteries & USB-memory
Online cable

3. Measurement location and hole layout
Mine niche
-400 m
Raisebored shaft
-310 m

4. OC
-12 cm
- 63 cm
SC 80 cm
- 10 cm
- 50 cm
SC 90 cm
- 66 cm
- 10 cm
SC 75 cm
- 46 cm
-15 cm
OC
- 50 cm
- 10 cm
R1
R2
R3
R4
R6
R5
S-tunnel
TBM
Measurement location and hole layout
TBM-tunnel
-450
Drill and blast
S-tunnel
-450 m

5. LVDT measurement
Measurement holes
Selecting measurement location
- sparcely fractures
- middle of blast round

6. Overcoring to by pass EDZ
- raise bore or TBM: 0 cm
- drill and blast: 25-50cm
Pilot / installation hole
- Ø 126 mm
- min free length 35 cm
Overcoring
- Ø ≥ 200 mm
min 5 cm
Min OC length 35 cm
EDZ
LVDT-probe
Hole dimensions

7. Calibration of the cell
Measurement phases
Drilling the 126 mm pilot hole

8. Overcoring
Cooling
Biaxial testing
Measurement phases
Biaxial testing

9. 3D photogrammetry
3D-photogrammetry
Profiles

10. Defining the measurement hole
Locations and orientations
Y=North
R1
R3
R4
R5
Building the 3D-model
Building the 3D-model for inversion

11. Calculation of in situ state of stress
- best fit inverse solution between measured and simulated convergences
- requires 3D-numerical simulations of geometries ( BEM, FEM, DEM )
- assumes linear elastic isotropy or known transverse isotropy
- analytical solution for surface measurements on circular excavation
( considered as gigantic overcoring measurement )
For 3D-model
- 3D-photogrammetric model
- all holes can be in the same model if
far enough from each other
Interpretation

12. For the inversion
To get orthogonal displacements components
at each LVDT sensor head
- i.e., 6 × 3 displacements for each head location
Six runs:
1) sEE = 1MPa
2) sNN = 1MPa
3) sUU = 1MPa
4) sEN = 1MPa
5) sNU = 1MPa
6) sUE = 1MPa
- other five components are set to zero
- measured mean E and n
u1
N,sij
u1
E,sij
u1
U,sij
Interpretation

13. Inversion
In the case of linear elasticity the LVDT sensor head displacements caused
by any in situ stress state, ie. ( k×sEE, l×sNN, m×sUU, n×sEN, o×sNU, p×sUE ),
can be constructed by superimposing the multiplied displacement components
caused by each unit stress tensor:
ui(ksEE, lsNN, msUU, nsEN, osNU, psUE ) = k×ui(sEE=1) + l×ui(sNN=1) + m×ui(sUU=1) +
n×ui(sEN=1) + o×ui(sNU=1) + p×ui(sUE=1),
i=E,N,U
-> Best fit between measured and calculated convergence can be found
using a focused iterative search
Interpretation

14. -> side coring can be used
- to prevent ring disking
4.98e-002
9.10e-002
1.21e-001
9.10e-002
4.98e-002
2.82e-002
2.17e-002
2.82e-002
126.700
200.000
36.650
0
3
2
2
2
2
2
2
2
2
2
2
1
1
1
1
-300 -250 -200 -150 -100 -50 0 50 100 150
deformed shapes
orignal shapes
Solution method does not require full stress release,
because solution uses displacement differences
between the phases before and after coring
Side coring

15. Side coring

16. CASE 1
Äspö Hard rock laboratory

17. Äspö Hard Rock Laboratory
measurements in well known stress state (-450m level)
Experience with a new LVDT-Cell to measure in-situ stress from an existing tunnel
TBM
- bearing 248°, plunge 8°
TASS
- bearing 218°, plunge 0.6° (up)
- drill and blast
TBM
TASS
TBM
TASS

18. Sidecoring responce
Experience with a new LVDT-Cell to measure in-situ stress from an existing tunnel

19. Stability of LVDT probe readings
Experience with a new LVDT-Cell to measure in-situ stress from an existing tunnel
LVDTs looking from tunnel
to the measurement hole
Measurement
location
OC_Start
OC_End, 35 cm
0
5
10
15
20
25
30
35
40
45
50
-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
18:00 19:30 21:00 22:30 0:00 1:30 3:00 4:30 6:00 7:30 9:00
Temperature
(C)
Diametric
deformation
(mm)
R1-50 - 90 (1+5)
R1-50 - 135 (2+6)
R1-50 - 00 (3+7)
R1-50 - 45 (4+8)
OC_Start
OC_End, 35 cm
Values for calc.
Measured convergences
LVDT pair dL at OC-stop (µm) dL/1 h (µm) dL/12 h (µm)
(1+5) 41 2 0
(2+6) 63 0 -2
(3+7) 19 2 2
(4+8) -2 3 3

20. Results - TASS biaxial tests
Experience with a new LVDT-Cell to measure in-situ stress from an existing tunnel
0
20
40
60
80
100
R1 R2 R3 R4 R6
Young's
Modulus
(GPa)
Sample
SurfaceA
SurfaceB
Deep A
Deep B
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
R1 R2 R3 R4 R6
Poisson's
ration
()
Sample
SurfaceA
SurfaceB
Deep A
Deep B R1
R2
R3
R4
R6
R5
Elastic parameters from LVDT pilot cores
- no diffrence in mean values
between EDZ and deep samples
- no difference related to location
( stress state )
- EDZ samples have higher variation

21. Results - in situ stress orientation
Experience with a new LVDT-Cell to measure in-situ stress from an existing tunnel
Sigma_1
Sigma_2
Sigma_3
North
East
Trend 90
dip=60 dip=30 dip=0
Sigma_1
Sigma_2
Sigma_3
North
East
Trend 90
dip=60 dip=30 dip=0
TASS Axis
TASS TBM
TBM Axis
248°
Deep
solid signals
Surface
open signals
Christiansson &
Jansson (2003)
Christiansson &
Jansson (2003)
Constrained
to be H/V

22. Results - in situ stress magnitude
Note, Vertical bars are for sH, sh and sV according to Christiansson & Jansson (2003)
Experience with a new LVDT-Cell to measure in-situ stress from an existing tunnel
24.6
18.9
13.6
13.4
9.2
9.8
0 10 20 30
Deep,
Final values
Deep,
OC Stop values
Surface,
Final values
Surface,
OC Stop values
Principal stress ( MPa )
Sigma 1 Sigma 2 Sigma 3
TASS, drill and blast
Deep,
Final values
Surface,
Final values
Principal stress (MPa)
TBM
25.6
22.0
14.1
0 10 20 30
Final, All
Final, All, H/V
All, OC-Stop
Principal stress ( MPa )
Sigma 1 Sigma 2 Sigma 3
Final values
OC stop values
Final values,
constrained
to be H/V
Principal stress (MPa)
Deep,
OC stop values
Surface,
OC stop values

23. Quality of the solution
Experience with a new LVDT-Cell to measure in-situ stress from an existing tunnel
TASS, drill and blast TBM
y = 1.01x
R² = 0.84
y = 0.67x
R² = 0.82
-60
-40
-20
0
20
40
60
80
100
-60 -40 -20 0 20 40 60 80 100
Calculated
Convergence
(microstrain)
Measred Convergence (microstrain)
Deep, final
Surface, final
y = 0.98x
R² = 0.97
-100
-50
0
50
100
150
200
-100 -50 0 50 100 150 200
Measured convergence (microstrain)
Measured convergence (microstrain)
Calculated
convergence
(microstrain)
Calculated
convergence
(microstrain)

24. Summary
Experience with a new LVDT-Cell to measure in-situ stress from an existing tunnel
- deep measurements have excellent agreement with traditional borehole
techniques
- the higher internal error and distortion of surface measurement solution
supports the existence of an excavation disturbed zone (EDZ)
-> minimum measurement depth should be 50 cm
- clear advantages of the methodology are the capability to manage with short
boreholes and a compact drill rig, and avoiding the issues associated with
gluing and the time needed for curing
- method also involves large volume, avoids effect of small scale heterogeneity
σH
MPa
σH trend
(RT90)
σh
MPa
σv
MPa
Christiansson &
Jansson (2003) 24 ±5 136° 10 - 13 12
This study
Deep, > 0.5 m 23-24 136°-139° 12-13 10-11

25. www.smcoy.fi
matti.hakala@smcoy.fi