Method for the quantitative description of discontinuities in the rock mass, Part 4: Roughness
1987 Edition

IS 11315 Part 4 (1987) — Overview and Essential Formulas

1. Evaluation of Shear Strength Using Roughness

• The peak shear strength (T_i6) is calculated from the Joint Roughness Coefficient (JRC) and Joint Compressive Strength (JCS) by the relation:

  [ 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)

• Figure 5 depicts shear strength curves for varying JCS values to assist in selecting appropriate JRC values.

2. Roughness Profiles and Classification (Figures 4 & 6)

• Roughness is categorized into three intermediate scales: Stepped, Undulating, and Planar.
• Small scale roughness types include Rough, Smooth, and Slickensided surfaces.
• Nine distinct classes (I to IX) combine these scales with corresponding effective roughness angles (i).

• The shear strength ranking follows: ( I > II > III > IV > V > VI > VII > VIII > IX ).

3. SI Units and Terminology

• Stress and pressure measured in Pascals (Pa = N/m²)
• Force in Newtons (N = kg·m/s²)
• Energy expressed in Joules (J = N·m)
• Power in Watts (W = J/s)

flowchart LR
    A[Joint Roughness Coefficient (JRC)] --> B[Shear Strength Estimation]

IS 11315 Part 4 (1987) - Scope and Key Concepts

Scope Overview

• Establishes definitions and methodologies for assessing joint roughness, estimating shear strength, and classifying roughness in rock joints.
• Employs the Joint Roughness Coefficient (JRC) and Joint-wall Compressive Strength (JCS) in shear strength calculations.
• Adopts SI units for all measurements and calculations.

Fundamental Equations

• Peak Shear Strength Calculation:

[ \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 compressive strength (MPa)

• The Joint Roughness Coefficient (JRC) correlates roughness profiles with shear resistance.

Roughness Classification (Clause 5.4.2)

• Shear strength trends approximately as:
  ( I > II > III ), ( IV > V > VI ), ( VII > VIII > IX ).

SI Units Summary

Roughness Profile Visualization

graph TD
  A[Intermediate Roughness] --> 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]

Essential References and Equations in IS 11315 Part 4 (1987)

1. Peak Shear Strength Estimation (Clause 5.10910)

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

• ( \tau_i ): peak shear strength (MPa)
• ( JCS ): joint compressive strength (MPa)
• ( \sigma_n ): normal stress (MPa)

This formula links joint roughness and compressive strength to shear resistance.

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

• Roughness categorized into intermediate scales (stepped, undulating, planar) and small scales (rough, smooth, slickensided).
• Nine profile classes (I to IX) determine shear strength hierarchy: ( I > II > III ), ( IV > V > VI ), ( VII > VIII > IX ).
• Figure 4 shows profiles with equal vertical and horizontal scaling (1 to 10 meters).

3. SI Units Table

Refer to the full standard for detailed unit definitions.

Roughness Profile Diagram (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)]

IS 11315 Part 4: Key Terminology and Definitions

1. Fundamental Terms

• Defined as per IS 11358-1987 for consistency in rock mechanics vocabulary.

2. Roughness Classification (Clauses 5.4 & 5.4.2)

• Roughness described on two levels:
  • Small scale (cm range): Rough, Smooth, Slickensided
  • Intermediate scale (meter range): Stepped, Undulating, Planar
• Combined classification produces nine categories (Figure 4):

• Shear strength ordering (in absence of mineral coatings): ( I > II > III, IV > V > VI, VII > VIII > IX ).

3. Shear Strength Calculation (Clause 5.10910)

• Peak shear strength (( \tau )) is derived using JRC and 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 System)

Roughness Classification Diagram

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

IS 11315 Part 4: Techniques for Quantifying Roughness

Principal Methods and Instruments

• Photogrammetric Approach (Clauses 3.10 & 4.1.6):

  • Photographs taken with a 1-meter graduated ruler placed visibly on the surface.
  • The ruler tapers to a fine point to aid in measuring perpendicular offsets (y).
  • Suitable for capturing minimum, modal, and maximum roughness representations.
  • Although profilographs provide higher precision, they are often unnecessary for rock mechanics applications.

• Linear Profiling Technique (Clause 3.8):

  • Equipment includes:
    • Folding straight edge (minimum 2 meters, graduated in millimeters)
    • Compass and clinometer
    • 10-meter light wire or nylon cord marked in red at 1 m intervals and blue at 10 cm intervals
  • Wire is stretched taut between blocks to serve as a straight reference line over uneven rock joints.

Quantitative Measurement Notes (Clause 4.1.6)

• Perpendicular deviations (y) are measured from the reference straight edge or ruler.
• Offsets or steps in the profile indicate discontinuity persistence.
• Roughness is assessed at multiple scales: below 1 cm, 1–10 cm, 10–100 cm, and above 1 m.
• Clinometer readings taken along the straight edge at 1 m intervals record dip variations.

Equipment Summary Table

flowchart LR
    A[Start] --> B{Select Measurement Method}
    B -->|Photogrammetric| C[Position 1 m ruler]
    C --> D[Capture Images]
    D --> E[Measure Perpendicular Offsets (y)]
    B -->|Linear Profiling| F[Set Folding Straight Edge]
    F --> G[Tension Wire with Markings]
    G --> H[Record Offsets & Dip with Clinometer]
    E & H --> I[Quantitative Roughness Analysis]
    I --> J[Document and Report]

IS 11315 Part 4 - Guidelines for Reporting Results

1. Presentation Style (Clauses 5.3 & 4.3)

• Surface roughness is best represented through profiles instead of contour maps.
• Profiles must be plotted with equal vertical and horizontal scales (1:1 ratio) to avoid exaggeration.
• Photogrammetric data can be presented as profiles or contour plots; contour intervals vary between 1 mm and 5 cm depending on camera settings.
• Profiles should be aligned with the expected sliding direction.

2. Roughness Classification (Clauses 5.4.2 & Figure 4)

• Roughness is divided into:
  • Intermediate scale: Stepped, Undulating, Planar
  • Small scale: Rough (irregular), Smooth, Slickensided
• Nine combined roughness classes:

• Approximate shear strength order: I > II > III, IV > V > VI, VII > VIII > IX (assuming absence of mineral coatings).

3. Additional Reporting Requirements (Clause 5.2.2)

• Include photographs depicting minimum, modal, and maximum roughness states.
• Present pole diagrams along with roughness data for completeness.

Roughness Profile Summary Table

Determining Shear Strength from Rock Joint Roughness (IS 11315 Part 4)

Fundamental Principles:

• Shear strength is influenced by the Joint Roughness Coefficient (JRC) and the Joint Wall Compressive Strength (JCS).
• Roughness is categorized by scale (stepped, undulating, planar) and roughness type (rough, smooth, slickensided).
• Dilation angle (i), derived from roughness profiles, affects shear strength.

Key Formula:

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

Where:

• ( \tau_{on} ): shear strength along the joint
• ( \sigma_n ): normal stress
• JCS: joint wall compressive strength (MPa)

Roughness Classification (Clauses 5.4.2 & Figure 4):

• Roughness classes rank shear strength approximately as: ( I > II > III > IV > V > VI > VII > VIII > IX ).
• Roughness angles (i) from profiles quantify dilation and shear resistance.

JRC Estimation Techniques:

• Compass and disc-clinometer method: Measures roughness angles relative to shear displacement.
• Photogrammetric method: Provides objective profile data.
• Both methods produce dilation curves relating roughness angle to displacement.

Synopsis:

• Employ roughness profiles and JCS values to calculate shear strength.
• Use the provided tangent-based formula incorporating JCS and normal stress.
• Classify roughness to compare relative shear strengths.
• Utilize objective measurement methods (clinometer, photogrammetry) for improved JRC evaluation.

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

IS 11315 Part 4 - Notes on Instruments and Procedures

Tools for Roughness Measurement

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

  • Geological compass featuring a horizontal leveling bubble.
  • Rotatable lid attached via a graduated hinge for dip measurement.
  • Four lightweight circular plates of diameters: 5 cm, 10 cm, 20 cm, and 40 cm, used sequentially to sample roughness.

• Photogrammetric Method (Clause 3.10):

  • Equipment specifications detailed in Part 1 of IS 11315.

Measurement Procedure (Clause 4.2.2)

• Use circular plates of varying sizes in order.
• Recommended measurement counts for accuracy:
  • 20 cm plate: 50 sample points
  • 10 cm plate: 75 sample points
  • 5 cm plate: 100 sample points

Principal Formula (Clause 5.10910)

• Peak shear strength estimation from roughness profiles:

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

• JCS represents the joint wall compressive strength (MPa).
• This formula correlates shear stress to roughness (JRC values from 0 to 20).

SI Units Overview

flowchart LR
  A[Begin Sampling] --> B{Select 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 and Roughness]
  D --> G
  E --> G
  F --> G
  G --> H[Calculate Shear Strength using Ti6 formula]
  H --> I[Analyze and Document Results]

IS 11315 Part 4 (1987) - Common Roughness Profiles and Classification

Roughness Categories (Clause 5.4.2)

• Intermediate scale roughness types (three levels):

  • Stepped
  • Undulating
  • Planar

• Superimposed small scale roughness (three types):

  • Rough (irregular)
  • Smooth
  • Slickensided

Nine Roughness Classes (Figure 4)

Shear Strength Ranking (assuming absence of mineral coatings)

• ( I > II > III > IV > V > VI > VII > VIII > IX )
• Additional relations: ( I > IV > VII ), ( II > V > VIII ), ( III > IX ), ( VI > IX ) with some uncertainty.

Notes

• Profile lengths range from 1 to 10 meters with equal vertical and horizontal scale.
• The orientation of slickensides/striations is important as shear strength varies directionally.
• Profiles representing minimum, modal, and maximum roughness should be recorded and photographed (Clauses 4.1.3, 5.1.1, 5.3.2).

Roughness Classes Diagram

graph TD
    A[Intermediate Scale] --> 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)]
    D --> VIII[Smooth (VIII)]
    D --> IX[Slickensided (IX)]

Photogrammetric Technique per IS 11315 Part 4

Objective:

• To acquire coordinate data of points on rock discontinuity surfaces that are inaccessible.
• To generate contour maps or surface roughness profiles.
• Profiles are preferred over contours for clarity.

Methodology and Specifications:

• Profiles should be plotted to a 1:1 vertical-to-horizontal scale to avoid distortion.
• Contour intervals vary with camera base distance, typically between 1 cm and 5 cm, with 1 mm achievable under special conditions.
• Data is captured using stereoscopic plotting instruments or stereo comparators, often recorded automatically.
• Profiles are aligned with the potential sliding direction when known.
• Photographs of surfaces showing minimum, modal, and maximum roughness, including a visible 1 m scale, are required.
• The size of the base plate influences measurement scatter and roughness angle:
  • Smaller plates produce larger scatter and higher roughness angles.
  • Larger plates yield reduced scatter and smaller roughness angles.

Equipment Reference:

• Detailed photogrammetric equipment is described in IS 11315 Part 1.

Data Analysis:

• Statistical evaluation of coordinate data enables estimation of shear strength and dilation properties for unfilled joints.

Base Plate Size and Measurement Effects

flowchart LR
    A[Photogrammetric Method] --> B[Data Acquisition]
    B --> C[Stereoscopic Plotting]
    B --> D[Stereo Comparator]
    C & D --> E[Coordinate Recording]
    E --> F[Compute Profiles/Contours]
    F --> G[Derive Surface Roughness]
    G --> H[Estimate Shear Strength and Dilation]

IS 11315 Part 4 - Field Techniques Overview

1. Photogrammetric Approach (Clause 4.3)

• Suitable for evaluating roughness on surfaces that cannot be directly accessed.
• Coordinates of surface points are obtained via terrestrial photogrammetry.
• Contour intervals depend on camera distance, typically ranging from 1 mm to 5 cm.
• Coordinate data are collected with stereoscopic plotting devices or stereo comparators.
• Enables creation of roughness profiles and contour maps.
• Profiles should be oriented with respect to the expected sliding direction.
• Statistical analysis of these coordinates enables determination of shear strength and dilation characteristics.

2. Shear Strength Calculation (Clause 5.10910)

• Peak shear strength is calculated as:

[ \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 JRC values ranging from 0 (smooth) to 20 (very rough).

3. Compass and Disc-Clinometer Method (Clause 5.2)

• Used for measuring dip direction and dip angle.
• Data are plotted using equal area net projections.
• Multiple measurements are combined into contoured pole plots for clarity.

SI Units Summary

flowchart TD
    A[Field Data Collection] --> B[Photogrammetry]
    B --> C[Coordinate Acquisition]
    C --> D[Generate Contour Maps and Profiles]
    D --> E[Calculate Shear Strength]
    A --> F[Compass and Disc-Clinometer]
    F --> G[Measure Dip and Direction]
    G --> H[Plot on Equal Area Nets]

IS 11315 Part 4 - Roughness Data Interpretation

Highlights from Clause 5.4.2 and Figure 4

• Roughness is categorized on two scales:

  • Intermediate scale (meter level): Stepped, Undulating, Planar
  • Small scale (centimeter level): Rough (Irregular), Smooth, Slickensided

• Combination of these scales results in nine roughness classes:

• Shear strength ranking (assuming no mineral coatings): ( I > II > III, IV > V > VI, VII > VIII > IX ).
• Additional inequalities: ( I > IV > VII ), ( II > V > VIII ), ( III > IX ), ( VI > IX ).
• Directionality of slickensides affects strength due to anisotropy.

Presentation Recommendations (Clause 5.1.1)

• Include photographs illustrating minimum, modal, and maximum roughness.
• Present roughness profiles with a 1:1 vertical to horizontal scale over lengths from 1 to 10 meters.

Practical Use

• Use roughness classification to estimate shear strength and dilation behavior.
• Consider rock mass stiffness that may restrict dilation, especially in underground excavations.

Roughness and Shear Strength Summary

Impact of Weathering on Rock Joint Strength (IS 11315 Part 4, Clause 6.2.2)

• The residual friction angle (( \phi_r )) varies with the degree of weathering and rock type:

  • For unweathered rock, ( \phi_r ) generally lies between 25° and 35°, often around 30°.
  • For heavily weathered rock, ( \phi_r ) can drop to approximately 15°, even without clay infillings.

• Estimation using the Schmidt hammer rebound method:

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

  where:

  • ( r ) = rebound value on weathered surface
  • ( r_0 ) = rebound value on unweathered surface

• Shear strength of discontinuities is calculated as:

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

  where:

  • ( \tau_{on} ) = shear strength along the discontinuity
  • ( JCS ) = joint wall compressive strength (MPa)
  • ( \sigma_n ) = normal stress

Notes:

• Roughness parameters (JRC) influence shear strength and are determined via compass-disc clinometer or photogrammetric techniques.
• Weathering reduces friction angle and, consequently, shear strength.
• Schmidt hammer rebound ratios provide a practical field estimate of weathering effects.

flowchart LR
    A[Unweathered Surface] -->|Measure r0| B[Record Rebound]
    C[Weathered Surface] -->|Measure r| D[Record Rebound]
    B & D --> E[Calculate \( \phi_r = \phi_{unweathered} \times \frac{r}{r + r_0} \)]
    E --> F[Estimate Reduced Shear Strength]

IS 11315 Part 4 (1987) - Glossary and Unit Definitions

1. SI Base Units and Symbols

Supplementary Units:

2. Derived Units and Symbols

3. Roughness Classification for Shear Strength (Clause 5.4)

• Two roughness scales are recognized:

  • Small scale (centimeter range)
  • Intermediate scale (meter range)

• Descriptive categories include:

IS 11315 Part 4 - Important Annexure Formulas and Tables

1. Peak Shear Strength Computation

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 equation estimates peak shear strength based on roughness and compressive strength.

2. Joint Roughness Coefficient (JRC) Profile Classes

• Roughness profiles are divided into nine classes (Figure 4):
  • Intermediate scale: Stepped, Undulating, Planar
  • Small scale: Rough, Smooth, Slickensided
• Roughness directly influences shear resistance; higher JRC values indicate greater shear strength.
• Typical JRC ranges are shown in Figure 6.

3. SI Units Overview

4. Roughness Influence on Shear Strength

• Shear strength hierarchy: ( I > II > III, IV > V > VI, VII > VIII > IX )
• Surface roughness and striation orientation affect joint strength.

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

Summary: Employ the tangent-based equation with JCS and normal stress for peak shear strength determination. Refer to JRC profile classes for qualitative shear strength variation. SI units ensure measurement consistency.