Method for the quantitative description of discontinuities in the rock mass, Part 4: Roughness

IS 11315 Part 4 (1987) — Introduction: Key Formulas & Tables

1. Roughness and Shear Strength Estimation

• Peak shear strength (Ti6) is estimated from joint roughness coefficient (JRC) and joint compressive strength (JCS) as:

  [ T_{i6} = \tan \left( 5.10910 \times JCS + 30^\circ \right) \times \sigma_n ]

  where:

  • ( T_{i6} ) = peak shear strength (MPa)
  • ( JCS ) = joint compressive strength (MPa)
  • ( \sigma_n ) = normal stress (MPa)

• Fig. 5 illustrates shear strength curves for different JCS values, guiding JRC selection.

2. Roughness Profiles & JRC Classification (Fig. 4 & 6)

• Roughness divided into 3 intermediate scales: Stepped, Undulating, Planar.
• Small scale roughness: Rough, Smooth, Slickensided.
• Nine classes (I to IX) define combined roughness types with corresponding effective roughness angles (i).

• Shear strength hierarchy: (I > II > III > IV > V > VI > VII > VIII > IX).

3. SI Units & Definitions

• Stress/pressure unit: Pascal (Pa) = N/m²
• Force: Newton (N) = kg·m/s²
• Energy: Joule (J) = N·m
• Power: Watt (W) = J/s

flowchart LR
    A[Joint Roughness Coefficient (JRC)] --> B[Estimate

IS 11315 Part 4 (1987) - Scope: Key Formulas & Specifications

Scope Summary

• Defines joint roughness, shear strength estimation, and roughness classification for rock joints.
• Uses Joint Roughness Coefficient (JRC) and Joint-wall Compression Strength (JCS) for shear strength evaluation.
• Applies SI units (Pa, MPa, N, m, etc.) as standard.

Key Formulas

• Peak Shear Strength Estimation:

[ \tau = \sigma_n \tan \left( 5.10910 \cdot JCS + 30^\circ \right) ]

Where:

• (\tau) = shear stress (MPa)

• (\sigma_n) = normal stress (MPa)

• (JCS) = joint-wall compression strength (MPa)

• Joint Roughness Coefficient (JRC) relates to roughness profiles and shear strength.

Roughness Classification (Clause 5.4.2)

• Roughness profiles influence shear strength:
  (I > II > III), (IV > V > VI), (VII > VIII > IX) (approximate ranking)

Units (SI System)

Visual Summary of Roughness Profiles

graph TD
  A[Intermediate Roughness]
  A --> B[Stepped]
  A --> C[Undulating]
  A --> D[Planar]
  B --> I[Rough]
  B --> II[Smooth]
  B --> III[Slickensided]
  C --> IV[Rough]
  C --> V[Smooth]
  C --> VI[Slickensided]
  D --> VII[Rough]
  D --> VIII[Smooth]
  D --> IX[Slickensided

Key References and Formulas from IS 11315 Part 4 (1987)

1. Peak Shear Strength Estimation (Clause 5.10910)

[ \tau_i = \tan \left( 5.10910 \times JCS + 30^\circ \right) \sigma_n ]

• (\tau_i) = Peak shear strength (MPa)
• (JCS) = Joint-wall compression strength (MPa)
• (\sigma_n) = Normal stress (MPa)

This formula estimates peak shear strength from joint roughness and compression strength.

2. Joint Roughness Coefficient (JRC) and Roughness Profiles (Clause 5.4.2)

• Roughness is categorized into stepped, undulating, planar (intermediate scale) and rough, smooth, slickensided (small scale).
• Typical roughness profiles are classified into 9 types (I to IX), influencing shear strength hierarchy:
  • (I > II > III), (IV > V > VI), (VII > VIII > IX)
• Fig. 4 illustrates these profiles with equal vertical and horizontal scales (1 to 10 m length).

3. SI Units and Symbols

Refer to the standard for detailed unit definitions.

Summary Diagram of Roughness Profiles (Fig. 4)

graph TD
    A[Stepped] --> I[Rough (I)]
    A --> II[Smooth (II)]
    A --> III[Slickensided (III)]
    B[Undulating] --> IV[Rough (IV)]
    B --> V[Smooth (V)]
    B --> VI[Slickensided (VI)]
    C[Planar] --> VII[Rough (VII)]
    C --> VIII[Smooth (VIII)]
    C --> IX[Slickensided (IX)]

Note: For precise design, refer to IS 11358-1987 for definitions and IS 11315 Part 4 for detailed tables and figures.

IS 11315 Part 4: Terminology & Definitions - Key Points

1. Definitions

• Clause 2.1: Definitions follow IS 11358-1987 (rock mechanics terminology).

2. Roughness Classification (Clause 5.4 & 5.4.2)

• Roughness described on two scales:
  • Small scale (cm scale): Rough, Smooth, Slickensided
  • Intermediate scale (m scale): Stepped, Undulating, Planar
• Combined into 9 classes (Fig. 4):

• Shear strength ranking (assuming no mineral coatings):
  I > II > III, IV > V > VI, VII > VIII > IX

3. Shear Strength Estimation (Clause 5.10910)

• Peak shear strength (τ) estimated from Joint Roughness Coefficient (JRC) and Joint Compressive Strength (JCS):
  [ \tau = \tan(5.10910 \times JCS + 30^\circ) \times \sigma_n ] where
  • ( \tau ) = shear strength (MPa)
  • ( JCS ) = joint compressive strength (MPa)
  • ( \sigma_n ) = normal stress (MPa)

4. Units (SI Units)

Summary Diagram: Roughness Classification

graph TD
    A[Small Scale] -->|Rough| B[Stepped (I)]
    A -->|Smooth| C[Stepped (II)]
    A -->|Slickensided| D[Stepped (III)]

IS 11315 Part 4: Methods of Measuring Roughness

Key Methods & Equipment

• Photogrammetric Method (Clause 3.10 & 4.1.6):

  • Uses photographic images with a 1 m graduated ruler placed visibly.
  • Ruler tapered to a point for fine detail measurement (perpendicular distances, y).
  • Suitable for minimum, modal, and maximum roughness representation.
  • Automatic profilographs offer higher accuracy but generally unnecessary for rock mechanics.

• Linear Profiling Method (Clause 3.8):

  • Equipment:
    • Folding straight edge (≥ 2 m, graduated in mm)
    • Compass and clinometer
    • 10 m light wire/nylon with paint markings at 1 m (red) and 10 cm (blue) intervals
  • Wire tensioned between wooden blocks to form a straight reference line over undulating discontinuities.

Quantitative Description Notes (Clause 4.1.6)

• Measure perpendicular offsets (y) from the reference line or ruler.
• Profile offsets or steps indicating discontinuity persistence.
• Record roughness at multiple scales:
  • <1 cm, 1-10 cm, 10-100 cm, >1 m.
• Use clinometer on the straight edge placed at 1 m intervals down-dip to record dip variations.

Summary Table of Equipment

flowchart LR
    A[Start] --> B{Choose Method}
    B -->|Photogrammetric| C[Place 1m ruler on surface]
    C --> D[Take photographs]
    D --> E[Measure perpendicular offsets (y)]
    B -->|Linear Profiling| F[Set folding straight edge]
    F --> G[Tension wire with paint marks]
    G --> H[Measure offsets & dips using clinometer]
    E & H --> I[Quantitative roughness description]
    I --> J[Record &

IS 11315 Part 4 - Presentation of Results: Key Points

1. Presentation Format (Clauses 5.3 & 4.3)

• Profiles are preferred over contour diagrams for surface roughness.
• Profiles should be plotted with 1:1 vertical to horizontal scale (no exaggeration).
• Photogrammetric data can yield profiles or contour maps; typical contour intervals range from 1 mm to 5 cm depending on camera distance.
• Profiles should be aligned with the direction of potential sliding.

2. Roughness Classification (Clause 5.4.2 & Fig. 4)

• Roughness divided into:
  • Intermediate scale: Stepped, Undulating, Planar
  • Small scale: Rough (Irregular), Smooth, Slickensided
• Nine classes of roughness profiles combining these two scales:

• Shear strength order: I > II > III, IV > V > VI, VII > VIII, > IX (assuming no mineral coatings).

3. Additional Presentation Requirements (Clause 5.2.2)

• Include photographs showing minimum, modal, and maximum roughness.
• Present pole diagrams alongside roughness data.

Summary Table for Roughness Profiles

Estimation of Shear Strength from Roughness (IS 11315 Part 4)

Key Concepts:

• Shear strength depends on joint roughness coefficient (JRC) and joint wall compressive strength (JCS).
• Roughness is classified by scale and degree (stepped, undulating, planar; rough, smooth, slickensided).
• Roughness profiles influence the dilation angle (i), affecting shear strength.

Important Formula:

[ \tau_{\text{on}} = \tan \left( 20 \log_{10}(\text{JCS}) + 30^\circ \right) \sigma_n ]

• (\tau_{\text{on}}): Shear strength on the joint
• (\sigma_n): Normal stress
• JCS: Joint wall compressive strength (MPa)

Roughness Classification (Clause 5.4.2 & Fig.4):

• Roughness order of strength:
  (I > II > III > IV > V > VI > VII > VIII > IX)
• Roughness angles (i) from profiles are used to estimate dilation and shear strength.

Methods for JRC Estimation:

• Compass and disc-clinometer method: Measures roughness angles vs shear displacement.
• Photogrammetric method: Objective profile analysis.
• These methods generate a dilation curve (roughness angle vs displacement).

Summary:

• Use roughness profiles and JCS to estimate shear strength.
• Apply formula with JCS and normal stress.
• Classify roughness to understand relative shear strength.
• Use objective methods (clinometer, photogrammetry) for better JRC estimation.

flowchart LR
    A[Roughness Profile] --> B[JRC Estimation]
    B --> C[Dilation Angle (i)]
    C --> D[Shear Strength Calculation]
    D --> E[\tau_{on} = \tan(20 \log_{10}(JCS) + 30^\circ) \sigma_n]

This approach

IS 11315 Part 4: Notes on Equipment and Procedures - Key Points

Equipment for Roughness Sampling

• Compass and Disc-Clinometer Method (Clause 3.9):

  • Geological compass with horizontal leveling bubble.
  • Rotatable lid with graduated hinge for dip recording.
  • Four light alloy circular plates: 5 cm, 10 cm, 20 cm, 40 cm diameters.

• Photogrammetric Method (Clause 3.10):

  • Equipment details in Part 1 of IS 11315.

Procedure (Clause 4.2.2)

• Use plates of different diameters sequentially.
• Recommended number of measurements for accuracy:
  • 20 cm plate: 50 positions
  • 10 cm plate: 75 positions
  • 5 cm plate: 100 positions

Key Formula (Clause 5.10910)

Estimate peak shear strength from roughness profiles:

[ T_{i6} = \tan \left( 5.10910 \times JCS + 30^\circ \right) ]

• JCS: Joint wall compressive strength (MPa)
• This relates to shear stress estimation from roughness (JRC values 0 to 20).

Units (SI)

flowchart LR
  A[Start Sampling] --> B{Choose Plate Diameter}
  B --> C[40 cm Plate]
  B --> D[20 cm Plate: 50 positions]
  B --> E[10 cm Plate: 75 positions]
  B --> F[5 cm Plate: 100 positions]
  C --> G[Record Dip & Roughness]
  D --> G
  E --> G
  F --> G
  G --> H[Calculate Shear Strength using Ti6 formula]
  H --> I[Analyze & Report]

This ensures accurate roughness profiling and shear strength estimation per IS 11315 Part 4.

IS 11315 Part 4 (1987) — Typical Roughness Profiles & Classification

Roughness Classification (Clause 5.4.2)

• Intermediate scale roughness (3 degrees):

  • Stepped
  • Undulating
  • Planar

• Small scale roughness superimposed (3 degrees):

  • Rough (Irregular)
  • Smooth
  • Slickensided

Nine Roughness Classes (Fig. 4)

Shear Strength Order (assuming no mineral coatings)

• I > II > III > IV > V > VI > VII > VIII > IX
• Also, I > IV > VII, II > V > VIII, III > IX, VI > IX (some inequalities less certain).

Notes

• Profile length: 1 to 10 meters (vertical & horizontal scales equal).
• Direction of slickensides/striations must be noted (shear strength varies with direction).
• Profiles representing minimum, modal, and maximum roughness should be recorded and photographed (Clauses 4.1.3, 5.1.1, 5.3.2).

Summary Diagram of Roughness Classes

graph TD
    A[Intermediate Scale Roughness]
    A --> B[Stepped]
    A --> C[Undulating]
    A --> D[Planar]

    B --> I[Rough (I)]
    B --> II[Smooth (II)]
    B --> III[Slickensided (III)]

    C --> IV[Rough (IV)]
    C --> V[Smooth (V)]
    C --> VI[Slickensided (VI)]

    D --> VII[Rough (VII)]
   

Photogrammetric Method (IS 11315 Part 4) - Key Points

Purpose:

• Obtain coordinates of points on inaccessible discontinuity surfaces.
• Compute contour maps or profiles of surface roughness.
• Profiles preferred over contour diagrams for clarity.

Specifications & Procedures:

• Profiles: Presented at 1:1 vertical:horizontal scale (avoid exaggerated vertical scale).
• Contour intervals: Dependent on camera base distance; typically 1 cm to 5 cm; 1 mm possible in special cases.
• Data collection: Use stereoscopic plotting instruments or stereo comparators with automatic recording (e.g., punched tape).
• Surface roughness: Profiles computed in the direction of potential sliding (if known).
• Photographs: Include surfaces with minimum, modal, and maximum roughness with a 1 m scale visible.
• Base plate size effect:
  • Small plates → larger scatter & roughness angles.
  • Large plates → smaller scatter & roughness angles.

Equipment:

• Refer IS 11315 Part 1 for detailed photogrammetric equipment.

Roughness Analysis:

• Statistical analysis of coordinates estimates shear strength and dilation characteristics of unfilled joints.

Summary Table: Base Plate Size vs. Roughness Measurement Effect

flowchart LR
    A[Photogrammetric Method] --> B[Data Capture]
    B --> C[Stereoscopic Plotting]
    B --> D[Stereo Comparator]
    C & D --> E[Coordinate Recording]
    E --> F[Profile/Contour Computation]
    F --> G[Surface Roughness Profiles]
    G --> H[Shear Strength & Dilation Estimation]

References:

• IS 11315 Part 4: Clauses 3.10, 4.2.4, 4.3, 5.3
• Use profiles at 1:1 scale for reports
• Statistical methods for roughness analysis based on recorded coordinates

IS 11315 Part 4: Field Measurement Techniques - Key Points

1. Photogrammetric Method (Clause 4.3)

• Used for inaccessible discontinuity surfaces.
• Coordinates of surface points obtained via terrestrial photogrammetry.
• Minimum contour interval depends on camera distance; typical intervals: 1 mm to 5 cm.
• Coordinates recorded using stereoscopic plotting instruments or stereo comparators.
• Enables computation of roughness profiles and contour maps.
• Profiles should be aligned with the potential sliding direction.
• Statistical analysis of surface coordinates estimates shear strength and dilation characteristics.

2. Shear Strength Estimation (Clause 5.10910)

• Peak shear strength formula from roughness profiles:

[ \tau_{16} = \tan \left( 5.10910 \times JCS + 30^\circ \right) \times \sigma_n ]

Where:

• (\tau_{16}) = Peak shear strength (MPa)

• (JCS) = Joint wall compressive strength (MPa)

• (\sigma_n) = Normal stress (MPa)

• Roughness profiles correspond to Joint Roughness Coefficient (JRC) values: 0 (smooth) to 20 (rough).

3. Compass and Disc-Clinometer (Clause 5.2)

• Measures dip direction and dip.
• Data plotted as poles on equal area nets.
• Multiple discs combined into single contoured plots for clarity.

Summary Table: Units (SI)

flowchart TD
    A[Field Measurement] --> B[Photogrammetric Method]
    B --> C[Coordinate Acquisition]
    C --> D[Contour Maps & Profiles]
    D --> E[Shear Strength Estimation]
    A --> F[Compass & Disc-Clinometer]
    F --> G[Dip & Dip Direction]
    G --> H[Equal Area Net Plot]

For detailed equipment and procedures, refer to Part 1 of IS 11315.

IS 11315 Part 4: Interpretation of Roughness Data

Key Points from Clause 5.4.2 & Fig. 4

• Roughness scales:

  • Intermediate scale: 3 degrees — Stepped, Undulating, Planar
  • Small scale (superimposed): 3 degrees — Rough (Irregular), Smooth, Slickensided

• Nine roughness classes (combining scales):

• Shear strength ranking (assuming no mineral coatings):
  I > II > III, IV > V > VI, VII > VIII > IX
  Also: I > IV > VII, II > V > VIII, III > IX, VI > IX

• Note: Direction of striations/slickensides affects shear strength due to anisotropy.

Presentation of Results (Clause 5.1.1)

• Provide photographs showing minimum, modal, and maximum roughness.
• Present roughness profiles with equal vertical and horizontal scales (length: 1–10 m).

Application

• Use roughness classification to estimate shear strength and dilation of rock discontinuities.
• Consider stiffness of surrounding rock mass, which may inhibit dilation (e.g., underground excavations).

Summary Table for Roughness and Shear Strength Interpretation

Effect of Weathering on Discontinuity Strength (IS 11315 Part 4, Clause 6.2.2)

• Residual friction angle (φr) depends on weathering degree and rock type:

  • Unweathered rock: φr ≈ 25° to 35°, commonly ~30°
  • Strongly weathered rock: φr can reduce to ~15°, even without clay fillings

• Estimation method using Schmidt hammer rebound:

  [ \phi_r = \phi_{unweathered} \times \frac{r}{r + r_0} ]

  Where:

  • ( r ) = Schmidt hammer rebound on weathered surface
  • ( r_0 ) = Schmidt hammer rebound on unweathered surface

• Shear strength formula for discontinuities (Clause 6.2.5):

  [ \tau_{on} = \tan \left( 20 \cdot \log_{10}(JCS) + 30^\circ \right) \cdot \sigma_n ]

  Where:

  • ( \tau_{on} ) = shear strength on the discontinuity
  • ( JCS ) = Joint wall Compressive Strength (MPa)
  • ( \sigma_n ) = normal stress on discontinuity

Key Notes:

• Roughness parameters (JRC) affect shear strength and are measured via compass, disc-clinometer, or photogrammetric methods.
• Weathering reduces friction angle, thus lowering shear strength.
• Use rebound ratios for quick field estimation of weathering effect.

flowchart LR
    A[Unweathered Rock] -->|Schmidt rebound r0| B[Measure r0]
    C[Weathered Rock] -->|Schmidt rebound r| D[Measure r]
    B & D --> E[Calculate φr = φunweathered * (r / (r + r0))]
    E --> F[Estimate Reduced Shear Strength]

This concise approach helps quantify weathering impact on discontinuity strength for design and analysis.

IS 11315 Part 4 (1987) - Glossary of Terms and Symbols: Key Points

1. Basic Units and Symbols (SI Units)

Supplementary Units:

2. Derived Units

3. Roughness Classification for Shear Strength (Clause 5.4)

• Two scales of roughness:

  • Small scale (cm range)
  • Intermediate scale (m range)

• Descriptive terms:

IS 11315 Part 4 - Key Annexure Formulas & Tables

1. Peak Shear Strength Estimation

From Clause 5.10910:

[ T_{i6} = \tan \left( 5.10910 \times JCS + 30^\circ \right) \times \sigma_n ]

• (T_{i6}) = Peak shear strength (MPa)
• (JCS) = Joint wall compressive strength (MPa)
• (\sigma_n) = Normal stress (MPa)

This formula estimates peak shear strength based on joint roughness and compressive strength.

2. Joint Roughness Coefficient (JRC) Profiles

• Roughness profiles are categorized into 9 classes (Fig. 4):
  • Intermediate scale: Stepped, Undulating, Planar
  • Small scale: Rough, Smooth, Slickensided
• Roughness affects shear strength; higher JRC means higher shear strength.
• Typical JRC ranges are illustrated in Fig. 6.

3. SI Units Table

4. Roughness Influence Hierarchy

• Shear strength order:
  ( I > II > III, IV > V > VI, VII > VIII > IX )
• Roughness and striation direction affect strength.

graph TD
  A[JCS (MPa)] --> B[Calculate Peak Shear Strength]
  B --> C[T_i6 = tan(5.10910 * JCS + 30°) * σ_n]
  C --> D[Peak Shear Strength (MPa)]
  E[JRC Profiles] --> F[Classify Roughness]
  F --> G[Estimate Shear Strength Adjustment]

Summary: Use the tan-based formula with JCS and normal stress for peak shear strength. Refer to roughness profiles (JRC) for qualitative shear strength variation. SI units ensure consistency.