1 Introduction
Strain measurement devices/techniques | Measurement Ranges and Resolutions | Benefits/Limitations | References |
---|---|---|---|
Local measurements/techniques | |||
Strain Gauges | 0.3 – 150 mm range Less than 1 µm resolution | -Flexible, submersible, -Requires complete sealing, not reusable, strain drifting, time intensive installation | |
Local Linear Variable Differential Transformer (LVDT) | Up to 10 mm range Less than 1 µm resolution | -Good resolution, stability, linear calibration, reusable, submersible -Costly, susceptible to jamming, slippage errors | |
Electro Level Inclinometer | Resolution up to 1 µm | -Submersible, compatible with unconsolidated specimens -Bulky, prone to tilting effects, hysteresis effects | |
Hall Effect Local Strain Transducers | 4–6 mm range Less than 0.1 µm resolution | -Fixed or floating type -Difficulties in sensor alignment, and sensitive to lower pad rotations | Clayton and Khatrush (1986) |
Digital Image Correlation using Digital Camera | Ranges and resolutions dependent on camera specifications | -Straight forward operation -Edge effects, requires clear confining fluid and transparent pressured vessel | |
Local Strain Transducers-LST | Up to 1.5 mm range 1 µm resolution | -Reusable -Non-linear calibration, slippage error due to clamping on the jacket | Tatsuoka (1988) |
Proximity Sensors | Up to 5 mm range Up to 10 nm resolution | -Fixed/floating, high resolution -Expensive, complex setup, mostly non-submersible | Hird and Yung (1989) |
Fiber Bragg Grating—FBG | Up to 80 mm range. 4.45 µm resolution | -Less expensive than LDT -Bulky, and slippage error due to clamping on the jacket | Xu (2017) |
Global measurements/techniques | |||
Cap-to-cap LVDT | Up to 1 m range Less than 1 µm resolution | -Submersible, easy to install, linear calibration, reusable -Prone to seating and bending effects |
2 Experimental Studies
2.1 Test Protocol
2.2 Standard Aluminum Specimen
Specimen | Length | Diameter | L:D | Mass | Estimated UCS | Confining Pressure | Peak Stress [MPa] | ||
---|---|---|---|---|---|---|---|---|---|
[mm]b | [mm]b | Ratio | [gr]c | [MPa] | [MPa] | 1st cycle | 2nd cycle | 3rd cycle | |
Aluminum | 50.230 | 25.105 | 2.00:1 | 67.132 | 310a | 0, 10, 30, 60 | 60 | 60 | 60 |
Eagle Ford Shale | 50.896 | 25.435 | 2.00:1 | 65.639 | 130–150 | 0 | 58 | 58 | 58 |
Berea Sandstone | 51.349 | 25.385 | 2.02:1 | 55.194 | 62–78 | 0 | 35 | 35 | – |
Jubaila Carbonate 1 (Packstone) | 57.841 | 26.813 | 2.16:1 | 78.752 | 24–48 | 0 | 21 | 21 | – |
Jubaila Carbonate 2 (Wackestone) | 53.953 | 26.714 | 2.02:1 | 72.989 | 24–48 | 0 | 10 | 15 | 20 |
2.3 Rock Specimens
3 Experimental Results
3.1 Local Strain vs. Global Deformation
3.2 Instrumentation on the Sleeve–Compliance
3.3 Surface Roughness
Specimen | ASTM International D4543-08 (2008) (1 mm tip) | Profilometer (7 μm spot size) | ||
---|---|---|---|---|
Max amplitude | Standard deviation | Max amplitude | Standard deviation | |
[μm] | [μm] | [μm] | [μm] | |
Aluminum | 23 | 12 | 38 | 13 |
Eagle Ford shale | 11 | 5 | 20 | 6 |
Jubaila carbonate | 10 | 4 | 13 | 4 |
Berea Sandstone | 23 | 11 | 41 | 11 |
Endcaps | 21 | 11 | 34 | 11 |
4 Analyses and Discussion
4.1 Seating Effects and Surface Roughness
4.2 Ultrasonic Velocity
4.3 Impact on Static and Dynamic Moduli
Methods | Frequency range | Measurements | Excitation |
---|---|---|---|
Impulse response ASTM International E (1876)-15 (2015) | 100 Hz–50 kHz (depends on specimen stiffness and size) | Fundamental resonant frequency | Mechanically by a singular elastic strike with an impulse tool |
Ultrasonic ASTM International E494-15 (2015) | 1–20 MHz | Pulse transit time | Low strain pulse using piezo transducers |
Sonic resonance ASTM International E (1875)-13 (2013) | 100–30,000 Hz | Resonant frequency | Variable-frequency audio oscillator. A speaker of the tweeter type or a magnetic cutting head |
Resonance column ASTM International D4015-15e1 (2015) | 0.1–300 Hz (for soils) (depends on specimen stiffness and size) | Fundamental resonant frequency | Flexural and longitudinal vibration using electromagnetic devices |
Cyclic loading ASTM International D5311/D5311M-13 (2013) | 0.1–2 Hz | Strain and phase shift | Loading–unloading using tri/uniaxial compression device |