Method for laboratory determination of dynamic modulus of rock core specimens

IS 10782: Scope and Key Specifications

• Scope: Covers testing of concrete specimens for specific properties using ultrasonic pulse velocity methods.

Specimen Dimensions (Clause 2.3)

• Specimen preferably a right circular cylinder.
• Tolerances as per Clause 2.3.
• Other regular geometries acceptable.
• Preparation per IS 9179-1979.

Oscilloscope Requirements (Clause 3.3.4)

• Double beam oscilloscope with:
  • Bandwidth: DC to 15 MHz
  • Rise time: ≤ 0.02 µs
• Must have:
  • Inbuilt delay time marker or external marker generator (preferably movable).
  • Time base sweep rate: max 0.1 µs/cm on at least one channel.
  • X-amplification: at least 10× in addition to normal Y-amplifier.

Reporting (Rounding off)

• Follow IS 2-1960 for rounding values.

Summary Table

This ensures accurate ultrasonic pulse velocity testing per IS 10782.

IS 10782: Rock Core Specimen - Key Formulas & Specifications

This standard focuses on determining the dynamic modulus of rock cores using ultrasonic wave velocities.

Specimen Requirements:

• Shape: Cylindrical core specimens.
• Dimensions: Typically diameter 38 mm or 50 mm, length 2–3 times diameter.
• Surface: Smooth, parallel ends for accurate wave transmission.

Key Formulas:

1. Dynamic Young’s Modulus (E_d):

[ E_d = \rho V_p^2 (1 + \mu)(1 - 2\mu) / (1 - \mu) ]

Where:

• ( \rho ) = density of the rock (kg/m³)
• ( V_p ) = longitudinal ultrasonic wave velocity (m/s)
• ( \mu ) = Poisson’s ratio (dimensionless)

2. Poisson’s Ratio (μ):

[ \mu = \frac{V_p^2 - 2V_s^2}{2(V_p^2 - V_s^2)} ]

Where:

• ( V_s ) = shear wave velocity (m/s)

3. Dynamic Shear Modulus (G):

[ G = \rho V_s^2 ]

Typical Table for Wave Velocities and Moduli:

Summary:

• Measure ( V_p ) and ( V_s ) using ultrasonic pulse velocity apparatus.
• Calculate ( \mu ), ( G ), and finally ( E_d ).
• Ensure specimen preparation per IS 10782 for accuracy.

IS 10782: Apparatus Key Points

• Specimen Shape & Dimensions (Clauses 2.1 & 2.3):

  • Preferably a right circular cylinder with tolerances as per 2.3.
  • Other regular geometry shapes allowed.
  • Preparation as per IS 9179-1979.

• Coupling Media (Clause 4.1):

  • Use media like light oil, soft grease, phenolic jelly, resin, salol, epoxy compounds for acoustic coupling between specimen and piezo-transducers.
  • Maintain a nominal stress of ~10 N/cm² using a jig for uniform contact.

• Rounding Off Results (Clause 0.3):

  • Follow IS 2-1960 for rounding off test values.

Typical Specimen Dimensions (Example from IS 10782 & IS 9179)

Acoustic Coupling Stress

[ \sigma = \frac{F}{A} \approx 10 , \text{N/cm}^2 ]

• Where:
  • (F) = applied force (N)
  • (A) = contact area (cm²)

flowchart LR
    A[Test Specimen] --> B[Coupling Media]
    B --> C[Piezo-transducer]
    C --> D[Signal Generation & Detection]
    style B fill:#f9f,stroke:#333,stroke-width:2px

This ensures good acoustic contact and reliable test results.

IS 10782: Acoustic Coupling - Key Points & Specifications

1. Acoustic Coupling Media (Clause 4.1)

• Use light oil, soft grease, phenolic jelly, resin, salol (phenyl salicylate), epoxy compounds for coupling.
• Maintain a nominal contact pressure ≈ 10 N/cm² using a jig to ensure uniform acoustic contact.

2. Transducers (Clause 3.3.2)

• Transmitter: Converts electrical pulses → mechanical (acoustic) pulses.
• Receiver: Converts mechanical pulses → electrical pulses.
• Use matched pairs of transducers with the same fundamental frequency (100 kHz – 10 MHz) for best waveform and amplitude.
• Piezo-elements: barium titanate or lead zirconate titanate, polarized for:
  • Thickness mode for compressional waves.
  • Shear mode for shear waves or use mode conversion/angle probes.
• End faces must be smooth and polished (Clause 2.3.2) for effective coupling.

3. Oscilloscope Requirements (Clause 3.3.4)

• Double beam oscilloscope with:
  • Bandwidth: DC to 15 MHz
  • Rise time: ≤ 0.02 μs
  • Delay time markers for transit-time measurement.
  • Time base sweep rate: max 0.1 μs/cm
  • X-amplification ≥ 10× for pulse observation.

Summary Table: Acoustic Coupling Parameters

flowchart LR
    A[Electrical Pulse] --> B[Transmitter (Piezo-element)]
    B --> C[Acoustic Wave]
    C --> D

IS 10782: Test Procedure Key Points

• Specimen Shape & Dimensions (Clause 2.1 & 2.3):

  • Preferably a right circular cylinder.
  • Dimensions and tolerances as per Clause 2.3 (refer IS 10782 for exact tolerances).
  • Alternative shapes allowed if geometry is regular.
  • Preparation as per IS 9179-1979.

• Acoustic Coupling (Clause 4.1):

  • Use coupling media such as light oil, soft grease, phenolic jelly, resin, salol, epoxy compounds to ensure effective ultrasonic wave transmission.
  • Apply a nominal stress of ~10 N/cm² using a jig to maintain uniform contact.

• Rounding Off Results (Clause 0.3):

  • Round off final values according to IS 2-1960 standard.

Typical Test Specimen Dimensions (Example)

Summary Diagram: Test Setup

flowchart LR
    A[Piezo Transducer (Generator)] -->|Ultrasonic Wave| B[Test Specimen]
    B -->|Wave Transmission| C[Piezo Transducer (Receiver)]
    B -->|Coupling Media (Oil/Grease)| B
    style B fill:#f9f,stroke:#333,stroke-width:2px

Use uniform pressure (~10 N/cm²) to keep coupling consistent.

For detailed tolerances and specimen preparation, refer directly to IS 10782 Clauses 2.3 and IS 9179-1979.

IS 10782: Key Formulas & Specifications for Measurements and Calculations

1. Specimen Dimensions (Clause 2.3)

• Specimen dimensions must be accurately measured as per IS 10782 for valid test results.
• Dimensions affect wave travel time and dynamic modulus calculations.

2. Measurement of Shear Wave Travel Time (Clause 5.9)

• For shear waves, measure apparent travel time on standard materials (steel, aluminium, quartz).
• Transmitter & receiver must be in direct contact to avoid errors in first arrival time (t₁).

3. Dynamic Moduli Relations (Clause 6.2)

Given:

• ( p ) = density (kg/m³)
• ( V_p ) = velocity of longitudinal waves (m/s)
• ( V_s ) = velocity of shear waves (m/s)

Formulas:

[ E = p V_s^2 \frac{3V_p^2 - 4V_s^2}{V_p^2 - V_s^2} \quad \text{(Young's Modulus, Pa)} ]

[ G = p V_s^2 \quad \text{(Shear Modulus, Pa)} ]

[ \nu = \frac{V_p^2 - 2V_s^2}{2(V_p^2 - V_s^2)} \quad \text{(Poisson's Ratio)} ]

[ K = \frac{p (3V_p^2 - 4V_s^2)}{3} \quad \text{(Bulk Modulus, Pa)} ]

[ \beta = \frac{1}{K} \quad \text{(Compressibility, Pa}^{-1}\text{)} ]

4. Rounding Off (Clause 0.3)

• Final values must be rounded as per IS 2-1960 standards.

Summary Table

IS 10782: Reporting of Results – Key Specifications

• Rounding Off: Final values must be rounded per IS 2:1960 rules.

• Specimen Dimensions: Follow IS 9179:1979 for specimen size and shape.

• Pulse Travel Distance:
  [ \text{Pulse travel distance} \geq \max(10 \times \text{average grain size}, 10 \times \text{wavelength}) ]

• Report Must Include:

  • Rock Core Particulars: Location (latitude, longitude, geological formation, quarry, drill hole).
  • Sample Dimensions & Geometry.
  • Sample Collection Method: Quarrying, drilling, blasting, etc.
  • Orientation: North, dip, strike details.
  • Microscopy: Petrography, microfracture distribution.
  • Preparation Details: Core quality, number, orientation.
  • Electronic Setup: Pulse generator, amplifier, oscilloscope settings.
  • Acoustic Transducers: Size, frequency, excitation mode, mounting.
  • Physical Properties: Density (ρ), porosity, permeability, absorption.
  • Measurements:
    • Length (e.g., 1 cm)
    • Initial delay ( t_1 ) (ps)
    • Delay with sample ( t_2 ) (ps)
    • P-wave velocity ( V_p ) (m/s)
    • S-wave velocity ( V_s ) (m/s)
    • Stress (Pa)
    • Accuracy/repeatability of ( t_1, t_2 ) (by interchanging faces).
  • Transit Time Measurement Method.
  • Elastic Moduli: Computer program output or CRO trace/photograph.
  • Laboratory and Observer Name.

Typical Velocity Calculation

[ V = \frac{L}{t_2 - t_1} ]

Where:

• ( L ) = sample length (m)
• ( t_1 ) = initial delay (s)
• ( t_2 ) = delay with sample (s)

flowchart TD
    A[Sample Collection