Method for the determination of modulus of elasticity and Poisson's ratio of rock materials in uniaxial compression

IS 9221: Scope Summary

• Scope: IS 9221 covers methods for testing and analyzing mechanical properties of materials, focusing on stress-strain behavior.
• Specimen Dimension (Clause 3.2): Specifies dimensions for test specimens to ensure uniformity and comparability of results.
• Reporting (Clause 6.1): Test reports must include:
  • Stress-strain curve plot
  • Young's modulus (E)
  • Poisson's ratio (ν)
  • Method of determination
  • Stress levels applied

Rounding Off Results: Follow IS 2-1960 for rounding off numerical values.

Key Formulas

• Young’s Modulus (E):
  [ E = \frac{\sigma}{\epsilon} ] where (\sigma) = stress, (\epsilon) = strain (in elastic region)

• Poisson’s Ratio (ν):
  [ \nu = -\frac{\epsilon_{\text{lateral}}}{\epsilon_{\text{longitudinal}}} ]

Typical Specimen Dimensions (Example)

graph LR
A[Specimen Preparation] --> B[Testing]
B --> C[Stress-Strain Data]
C --> D[Calculate E & ν]
D --> E[Plot Curve & Report]

This standard ensures uniform testing for reliable material characterization.

IS 9221: Key References & Reporting Requirements

Test Report Must Include (Clause 6.2)

• Number of specimens tested
• Mode of failure
• Lithological description of rock
• Orientation of loading axis relative to anisotropy (bedding, foliation)
• Sample source, location, depth, orientation, date
• Storage history/environment
• Date of testing & machine type
• Specimen diameter & height
• Moisture content & room temperature
• Test duration & stress rate
• Other physical properties (specific gravity, absorption, permeability, porosity) with methods
• Any other observations
• Note if specimen size < 45 mm or length/diameter ratio < 2-3

Additional Report Data (Clause 6.1)

• Stress-strain curve plot
• Young’s modulus (E) and Poisson’s ratio (v) with determination method
• Stress levels

Important Related Indian Standards

Notes

• Round off results per IS 2-1960.
• Ensure specimen size and aspect ratios are within recommended limits or mention deviations.

flowchart TD
    A[Sample Collection] --> B[Specimen Preparation]
    B --> C[Laboratory Testing]
    C --> D[Record Data: Stress-Strain, E, v]
    D --> E[Report Compilation]
    E --> F[Include: Specimen Details, Failure Mode, Physical Properties]
    F --> G[Submit Report per IS 9221]

This ensures standardized, comprehensive rock testing and reporting as per IS 9221.

IS 9221: Test Specimens Key Points

1. Specimen Shape & Preparation (Clause 3.1)

• Shape: Right circular cylinder preferred; other regular geometries allowed.
• Preparation: As per IS 9179-1979.

2. Dimensions & Tolerances (Clause 3.2 & 3.2.7)

• Diameter measurement: Average of two diameters at right angles at upper, mid, and lower heights.
• Tolerance: Diameter variation ≤ 0.3 mm over specimen length.
• Measurement accuracy: Diameter to nearest 0.1 mm.

3. Strain Measurement (Clause 2.4)

• Strain gauges: Use electrical resistance strain gauges, compressometers, or optical devices.
• Positions: At least 2 axial + 2 circumferential strains, equally spaced around mid-height circumference.
• Distance from ends: Measurements not within D/2 from specimen ends (D = diameter).
• Gauge length: ≥ 5 × grain size diameter.
• Accuracy: ±2% of reading.
• Precision: 0.2% full scale.

Summary Table for Specimen Dimensions & Strain Measurement

flowchart LR
    A[Test Specimen] --> B{Shape}
    B --> C[Right Circular Cylinder]
    B --> D[Other Regular Geometry]
    A --> E[Diameter Measurement]
    E --> F[Average 2 diameters @ upper, mid, lower height]
    E --> G[Variation ≤ 0.3 mm]
    A --> H[Strain Measurement]
    H --> I[2 Axial + 2 Circumferential gauges]
    H --> J[Positions > D/2 from ends]
   

IS 9221: Test Procedure Key Points

• Specimen Dimensions (Clause 3.2.7 & 3.1):

  • Shape: Right circular cylinder (or regular geometry).
  • Diameter measured at 3 heights (upper, mid, lower) by averaging two diameters at right angles.
  • Diameter tolerance: Variation ≤ 0.3 mm over specimen length.
  • Preparation as per IS 9179-1979.

• Strain Measurement (Clause 2.4):

  • Use electrical resistance strain gauges, compressometers, or optical devices.
  • Measure at least 2 circumferential + 2 axial strains per load increment.
  • Positions equally spaced around circumference, near mid-height, avoiding ends within D/2.
  • Measurement length ≥ 5 × grain size diameter.
  • Accuracy: ±2% of reading; Precision: ±0.2% full scale.

• Reporting Results (Clause 0.4):

  • Round off final values per IS 2-1960 standard.

Diameter Measurement Formula

[ D_{avg} = \frac{1}{6} \sum_{i=1}^{3} (d_{i1} + d_{i2}) ]

• (d_{i1}, d_{i2}): diameters at right angles at height (i) (upper, mid, lower).

Strain Gauge Placement Diagram

circle
    title Specimen Cross-section (Mid-height)
    strain1((Axial Strain 1))
    strain2((Axial Strain 2))
    strain3((Circumferential Strain 1))
    strain4((Circumferential Strain 2))
    strain1 --- strain3
    strain2 --- strain4

This ensures balanced strain measurement around the specimen circumference.

IS 9221 Key Formulas & Specifications for Modulus of Elasticity and Poisson's Ratio

1. Modulus of Elasticity (E)

• Calculated from the stress-strain curve in uniaxial compression.

• Commonly used moduli (Clause 5.5):

  • Initial Tangent Modulus (M): Slope of the initial linear portion of the stress-strain curve.
  • Secant Modulus: Slope from origin to a specified stress level.
  • Tangent Modulus at 50% Ultimate Stress: Recommended for design purposes.

• Typical stress-strain behavior (Fig. 1 & 2):

  • Stage I: Closure of cracks and pores.
  • Stage II: Linear elastic compression.
  • Stage III: Internal cracking.

2. Poisson's Ratio (ν)

• Defined as the ratio of lateral (diametric) strain to axial strain at a given stress level (Clause 5.6):

[ \nu = \frac{\varepsilon_{\text{lateral}}}{\varepsilon_{\text{axial}}} ]

• Usually taken at 50% of ultimate stress for standardization.

Summary Table

Visual Concept (Mermaid Diagram)

graph LR
A[Axial Stress] --> B[Axial Strain (ε_axial)]
A --> C[Lateral Strain (ε_lateral)]
B --> D[Calculate E = ΔStress / ΔStrain]
B & C --> E[Calculate ν = ε_lateral / ε_axial]

Note: Use uniaxial compression tests per IS methods for accurate measurement.

IS 9221: Test Report Key Points

Clause 6.1 — Stress-Strain Curve & Parameters

• Plot stress-strain curve relevant to use.
• Report Young's modulus (E) and Poisson's ratio (ν).
• Specify method of determination and stress levels used.

Clause 6.2 — Test Report Contents

Include the following details:

Additional Notes

• Strain measurements must be averaged from at least 2 axial + 2 circumferential gauges placed mid-height, outside D/2 from ends.
• Strain length ≥ 5 × grain size.
• Accuracy: ±2% reading; precision: 0.2% full scale.
• Final values rounded per IS 2-1960.

Summary Table of Report Requirements

IS 9221: Accuracy and Precision Requirements Summary

• Strain Measurement Accuracy:

  • Both axial and circumferential strains must be measured with an accuracy of ±2% of the reading.
  • Precision (repeatability) must be within ±0.2% of full scale.

• Measurement Setup:

  • Use at least two circumferential and two axial strain gauges per load increment.
  • Gauges should be equally spaced around the specimen circumference, near mid-height, but not within D/2 from specimen ends (D = specimen diameter).
  • Strain measurement length ≥ 5 × grain size diameter.

• Specimen End Preparation:

  • Ends must be perpendicular within 0.001 radians (3.5 minutes) or 0.05 mm for 45 mm diameter specimens.

• Rounding Off Results:

  • Follow IS 2-1960 for rounding off numerical results.

Key Specification Table

flowchart LR
    A[Specimen] --> B{Measurement Positions}
    B --> C[At least two axial strain gauges]
    B --> D[At least two circumferential strain gauges]
    C & D --> E[Equally spaced around circumference]
    E --> F[Located near mid-height, > D/2 from ends]
    F --> G[Measurement length ≥ 5 × grain size diameter]

This ensures reliable, repeatable strain data within IS 9221 standards.

IS 9221: Specimen Preparation and Dimensions

• Shape: Right circular cylinder preferred; other regular geometries allowed (Clause 3.1).
• Diameter (d):
  • Minimum diameter ≥ 10 × largest mineral grain size.
  • Preferably 45 mm, never less than 30 mm (Clause 3.2.2).
• Diameter Measurement:
  • Measure diameter at upper, mid, and lower heights.
  • Take two measurements at right angles at each height.
  • Average all six readings to nearest 0.1 mm (Clause 3.2.7).
  • Diameter variation along length ≤ 0.3 mm.
• Length:
  • Typically, length-to-diameter ratio (L/d) as per IS 9179-1979 (referenced in Clause 3.1).
• Tolerances:
  • Follow IS 9179-1979 for detailed tolerances on dimensions and preparation.
  • If diameter < 45 mm, tolerances are relaxed accordingly (Clause 3.2.2).

Diameter Measurement Summary

flowchart LR
    A[Specimen] --> B[Measure Diameter at Upper Height]
    A --> C[Measure Diameter at Mid Height]
    A --> D[Measure Diameter at Lower Height]
    B --> E[Two perpendicular diameters]
    C --> F[Two perpendicular diameters]
    D --> G[Two perpendicular diameters]
    E & F & G --> H[Average all 6 readings]
    H --> I[Check diameter variation ≤ 0.3 mm]

This ensures specimen uniformity and compliance with IS 9221 for reliable test results.

IS 9221: Measurement Techniques – Key Points

1. Measurement Positions & Setup (Clause 2.4)

• Use ≥ 2 circumferential and ≥ 2 axial strain gauges per load increment.
• Gauges must be equally spaced around specimen circumference near mid-height.
• Avoid placing gauges within D/2 (half diameter) from specimen ends.
• Strain measurement length ≥ 5 × grain size diameter.
• Accuracy: ±2% of reading; Precision: ±0.2% full scale.

2. Strain Types & Recording (Clause 5.1)

• Axial strain, ( s_a ), and diametric strain, ( E_d ), can be:
  • Recorded directly from strain gauges.
  • Calculated from measured deformations.

3. Specimen Dimensions (Clause 3.2)

• Specimen dimensions must comply with IS 9221 specifications (refer to Clause 3.2 for detailed sizes).

4. Reporting Results

• Round off results per IS 2-1960 rounding rules.

Typical Strain Calculation Formulas:

[ \text{Axial strain}, s_a = \frac{\Delta L}{L} ] [ \text{Diametric strain}, E_d = \frac{\Delta D}{D} ]

Where:

• ( \Delta L ) = change in length
• ( L ) = original gauge length
• ( \Delta D ) = change in diameter
• ( D ) = original diameter

flowchart LR
    A[Specimen] --> B[Strain Gauges]
    B --> C{Positions}
    C -->|Axial| D[≥2 gauges equally spaced]
    C -->|Circumferential| E[≥2 gauges equally spaced]
    D & E --> F[Measure strain per load increment]
    F --> G[Calculate average strains]
    G --> H[Report results per IS 2-1960]

Summary: Use multiple, equally spaced strain gauges away from specimen ends, measure over sufficient length, ensure precision, and report results per IS standards.

IS 9221: Equipment and Apparatus Key Points

1. Measurement of Strains (Clause 2.4)

• Use electrical resistance strain gauges, compressometers, optical devices, or equivalent.
• Measure at least two circumferential and two axial strains per load increment.
• Measuring points:
  • Equally spaced around specimen circumference.
  • Located near mid-height, avoiding ends within D/2 (D = diameter).
• Strain measurement length ≥ 5 × grain size diameter.
• Accuracy: ±2% of reading; Precision: ±0.2% of full scale.

2. Loading Machine (Clause 2.1)

• Must have adequate capacity for specimen size.
• Provide controlled loading rate per Clause 4.3.
• Must be calibrated periodically.

3. Test Report Requirements (Clause 6.2)

Include:

• Number of specimens, failure mode, lithology.
• Loading axis orientation vs. anisotropy.
• Sample source, date, storage history.
• Specimen dimensions (diameter, height).
• Moisture content, temperature.
• Test duration, stress rate.
• Physical properties (specific gravity, porosity, etc.).
• Note if specimen size <45 mm or length/diameter ratio <2-3.

Summary Table: Strain Gauge Placement

flowchart LR
    A[Specimen] --> B{Strain Measurement Points}
    B --> C[Circumferential Strains (≥2)]
    B --> D[Axial Strains (≥2)]
    C & D --> E[Equally spaced around circumference]
    E --> F[Located near mid-height, > D/2 from ends]
    F --> G[Strain length ≥ 5 × grain size diameter]

This ensures reliable and standardized strain data critical for rock testing per IS 9221.

IS 9221: Data Interpretation - Key Points

IS 9221 primarily guides reporting and data interpretation for rock testing. Key specifications include:

Reporting Requirements (Clause 6.2)

Test reports must include:

• Number of specimens tested
• Mode of failure
• Lithological description
• Loading axis orientation vs. anisotropy (bedding, foliation)
• Sample source, location, depth, orientation, date
• Storage history/environment
• Date of testing & machine type
• Specimen dimensions (diameter, height)
• Moisture content & room temperature
• Test duration & stress rate
• Other physical properties (specific gravity, absorption, permeability, porosity) with methods
• Any other observations
• Specimen size notes if less than 45 mm diameter or length/diameter ratio < 2–3

Rounding Off (Clause 0.4)

• Follow IS 2-1960 for rounding numerical results.

Specimen Dimensions (Clause 3.2)

• Standard specimen size typically:
  • Diameter ≥ 45 mm
  • Length to diameter ratio: 2 to 3

Common Formulae for Rock Tests (from related IS codes referenced)

• Unconfined Compressive Strength (UCS):
  [ \sigma_c = \frac{P}{A} ]
  Where:
  ( P ) = maximum load at failure (N)
  ( A ) = cross-sectional area (mm²)

• Point Load Strength Index (IS 8764):
  [ I_s = \frac{P}{D^2} ]
  Where:
  ( P ) = failure load (N)
  ( D ) = diameter or core size (mm)

Summary Diagram: Data Reporting Flow

flowchart TD
    A[Test Execution] --> B[Record Specimen Details]
    B --> C[Measure Dimensions & Properties]
    C --> D[Perform Test & Observe Failure]
    D --> E[Calculate Strength Parameters]
    E --> F[Round off Results (IS 2-1960)]
    F --> G[Prepare Test Report with all details]

References:

• IS 2-

IS 9221 does not explicitly detail Safety and Handling formulas or tables. However, based on standard engineering practice and related IS codes:

Key Safety & Handling Points for Test Specimens (per IS 9221 & IS 9179):

• Specimen Shape: Right circular cylinder or regular geometry (Clause 3.1).
• Specimen Dimension Tolerances: As per Clause 3.2 (refer IS 9179-1979 for specifics).
• Handling: Specimens must be handled carefully to avoid damage or alteration before testing.
• Rounding Off Results: Follow IS 2-1960 for rounding off numerical test results (Clause 0.4).

General Safety Guidelines (Industry Practice):

• Use personal protective equipment (PPE) when handling specimens.
• Ensure secure gripping and support during testing to prevent specimen ejection.
• Follow standard operating procedures for mechanical testing machines.

Example: Specimen Dimension Tolerances (from IS 9179-1979)

flowchart TD
    A[Specimen Preparation] --> B[Dimension Check (IS 9179)]
    B --> C[Safe Handling & Storage]
    C --> D[Testing Procedure]
    D --> E[Result Reporting (IS 2-1960)]

For detailed safety handling, refer to IS 9179 and machine-specific manuals.

IS 9221: Key Specifications & Reporting Requirements (Annexures & Figures)

Test Report Must Include (Clause 6.2):

• Specimen details: Number, diameter, height, size deviations (<45 mm or L/D < 2-3)
• Failure mode and stress-strain curve (Clause 6.1)
• Rock description: Lithology, anisotropy orientation (bedding, foliation)
• Sampling info: Source, location, depth, orientation, date
• Test conditions: Storage history, environment, moisture, temperature, stress rate, duration
• Machine type used for testing
• Physical properties: Specific gravity, absorption, permeability, porosity (with methods)
• Other observations as necessary

Key Parameters to Report:

Related IS Codes for Reference:

• IS 7292: In-situ rock properties by flat jack
• IS 7317: Uniaxial jacking test
• IS 7746: In-situ shear test on rock
• IS 8764: Point load strength index
• IS 9143: Unconfined compressive strength
• IS 9179: Specimen preparation

flowchart TD
    A[Test Specimen] --> B[Measure Diameter (d) & Height (h)]
    B --> C[Conduct Compression Test]
    C --> D[Record Stress-Strain Data]
    D --> E[Calculate Young's Modulus (E) & Poisson's Ratio (ν)]
    E --> F[Prepare Test Report]
    F --> G[Include Rock Description, Test Conditions, Observations]

Summary: IS 9221 emphasizes detailed reporting of specimen characteristics, test conditions, and mechanical properties with stress-strain curves to ensure consistent rock strength evaluation.