Method for the quantitative description of discontinuities in rock masses, Part 1: Orientation
1987 Edition

Introduction and Scope of IS 11315 Part 1

1. Overview of Scope

• Pertains to rock mechanics challenges involving representation of structural data.
• Emphasis on slope stability evaluations using equatorial equal area nets.
• Facilitates graphical plotting of poles and great circles symbolizing joint planes and failure patterns.

2. Fundamental Concepts

• Poles of Joint Planes: Represent orientations perpendicular to discontinuities.
• Great Circles: Depict planes of discontinuities or failure modes.
• Common failure types:
  • Circular failures in heavily fractured rock masses.
  • Planar failures in well-ordered lithologies like slate.
  • Wedge failures resulting from intersecting joints.
  • Toppling failures due to steeply inclined joints.

3. SI Units Adopted

4. Structural Data Plotting (Fig. 9 Synopsis)

• Employ equatorial equal area nets for plotting poles and great circles.
• Enables visualization of three-dimensional orientations critical for stability assessments.

graph LR
A[Joint Planes] --> B[Poles on Projection Net]
C[Failure Modes] --> D[Great Circles on Net]
B & D --> E[Stability Evaluation]

Note: Terminology aligns with IS 11358-1986; rounding rules follow IS 2-1960.

IS 11315 Part 1 - Scope and Principal Concepts

Scope: This part addresses the depiction of structural geological data pertinent to rock mechanics challenges, concentrating on slope stability analysis using spherical projection tools such as equatorial equal-area nets.

Core Concepts and Specifications

• Representation of Structural Data:

  • Utilize poles and great circles on equal-area nets to interpret discontinuity orientations.
  • Characteristic failure modes include:
    • Circular failures in jointly fractured rock masses.
    • Planar failures typical in ordered rock fabrics (e.g., slates).
    • Wedge failures from intersecting joint sets.
    • Toppling failures associated with steeply dipping discontinuities.

• Measurement Instruments (Clause 5.2.1):

  • Optical square
  • Abney level
  • Alidade
  • Plane table with reconnaissance sketches

• Fundamental Units (SI System):

• Orientation of Geological Planes (Fig. 1):
  • Strike (a°)
  • Dip (B°)
  • Dip direction (a° - 90°)
  • Dip vector notation: (a/B)

Orientation Diagram

graph LR
    Strike --> Dip
    Dip --> DipDirection
    Strike["Strike (a°)"]
    Dip["Dip (B°)"]
    DipDirection["Dip Direction (a° - 90°)"]

Additional Notes

• Definitions conform to IS 11358-1986.
• Final measurements should be rounded as per IS 2-1960.
• Spherical projections assist in visualizing 3D orientations essential in stability evaluations.

This scope establishes foundational methods for assessing rock slope stability using consistent units, instruments, and graphical representations.

Significance of Discontinuity Orientation According to IS 11315 Part 1

• Orientation Parameters: Discontinuity orientation is detailed by its dip direction (azimuth) and dip angle, for example, 045°/30° (Clause 0.5).

• Influence on Stability: Orientation directly impacts the likelihood of instability or deformation in rock masses adjacent to engineered structures (Clause 3.1).

• Critical Influencing Factors: The effect of orientation becomes more pronounced when:

  • Discontinuities exhibit low shear strength.
  • Multiple discontinuity sets exist, facilitating slip.

• Comprehensive Discontinuity Parameters: Orientation is one among ten essential parameters, including spacing, persistence, roughness, aperture, infill material, seepage, number of sets, and block size (Clause 0.3).

Theoretical Relation of Orientation to Stability

Slip potential is governed by the resolved shear stress (τ) on a discontinuity:

[ \tau = \sigma_n \tan \phi + c ]

Where:

• (\sigma_n) is the normal stress on the discontinuity (dependent on orientation and in-situ stresses),
• (\phi) is the friction angle,
• (c) is cohesion.

Orientation affects (\sigma_n), thereby influencing slip probability.

Visualization of Orientation Impact

graph TD
A[In-situ Stress] --> B[Discontinuity Plane]
B --> C[Normal Stress (\sigma_n)]
B --> D[Shear Stress (\tau)]
D --> E[Slip Potential]
C --> E

Summary: Discontinuity orientation is a fundamental factor in evaluating rock mass stability, affecting stresses on joints and controlling potential slip or deformation near infrastructure.

Measurement of Discontinuity Orientation with Compass and Clinometer per IS 11315 Part 1

Key Measurement Parameters:

• Dip Direction (a): Azimuth measured clockwise from true north (0° to 360°).
• Dip (B): Angle of steepest incline from horizontal (0° to 90°).
• Results recorded as dip direction/dip angle, e.g., 010°/25° (Clause 4.4).

Measurement Steps:

• Level the compass using a spherical bubble.
• Use the integrated clinometer to determine dip angle along the maximum slope.
• Align clinometer parallel to the discontinuity surface before reading dip.
• For inaccessible dips, use an inclinable sighting device with a reflected bubble.
• In zones with magnetic disturbances, employ alternative tools such as clino-rules, measuring tapes, or theodolites.

Accuracy and Rounding:

• Dip direction rounded to the nearest 5°.
• Dip angle rounded to the nearest even degree or 1° when plotting poles.
• Use a 0-90° dip scale unless otherwise specified.

Field Data Collection Notes:

• Collect multiple orientation measurements to define joint sets.
• Apply three-point methods or borehole data for major discontinuities.
• Use downhole viewing techniques or integral sampling for minor joints.

Data Format Summary

Orientation Diagram

graph TD
A[True North (0°)] -->|Clockwise| B(Dip Direction a°)
B --> C(Dip Vector a°/B°)
C --> D(Dip Angle B° from horizontal)

References:

• Clauses 4.1, 4.4 and Notes from IS 11315 Part 1 (1987).
• Use tape or theodolite for magnetic anomaly areas.
• Employ three-point method for major discontinuities.
• Integral sampling for highly fractured rock masses.

This methodology ensures consistent and accurate field measurement of geological discontinuity orientations.

Photogrammetric Technique for Discontinuity Orientation (IS 11315 Part 1)

1. Input Data and Computation (Clause 5.6)

• Data Sources:
  • Control survey coordinates (c)
  • Photogrammetric measurements (f)
• Computational Steps:
  • Transform target points into ground coordinate system using a transformation matrix.
  • Fit planes to measured points applying the least squares technique.
  • Extract direction cosines from the symmetric coefficient matrix.
  • Convert direction cosines into dip direction and dip angle.
  • Calculate error metrics to evaluate measurement precision.

2. Required Equipment (Clause 5.2)

• Reconnaissance survey tools
• Phototheodolite mounted on tripod
• Control survey instruments
• Stereoscopic plotting devices or stereocomparators with automated recording features

3. Procedural Steps (Clauses 5.3 & 5.4)

• Conduct reconnaissance and control surveys.
• Capture overlapping stereo photographs using phototheodolite.
• Analyze overlapping images to identify joint planes or discontinuity zones.
• Use approximately ten points per discontinuity plane to define orientation precisely.

4. Sources of Error and Considerations (Clause 5.6 Notes)

• Potential inaccuracies stem from photographic film quality, camera calibration, plotting errors, control survey precision, earth curvature, atmospheric refraction, and operator proficiency.
• Operator-related errors are minimized by maintaining large base-to-distance ratios.
• Challenges arise in altered or weathered rock where features are indistinct.
• Photogrammetry additionally yields data on surface roughness, joint spacing, persistence, and rock surface conditions.

Plane Fitting Formula (Least Squares Method)

For points ((x_i, y_i, z_i)), fit plane equation:

[ Ax + By + Cz + D = 0 ]

Minimize the sum of squared distances from points to plane by solving the normal equations for (A, B, C, D).

Workflow Diagram

flowchart TD
    A[Reconnaissance Survey] --> B[Photography via Phototheodolite]
    B --> C[Control Survey Data Collection]
    C --> D[Data Processing]
    D --> E[Coordinate Transformation]
    E --> F[Plane Fitting with Least Squares]
    F --> G[Determine Dip & Dip Direction]
    G --> H[Error Evaluation]
    H --> I[Presentation of Results]

This method is essential for comprehensive orientation and stability analyses, especially in inaccessible or complex rock environments.

Data Visualization and Analysis in IS 11315 Part 1 (1987)

1. Spherical Projection for Data Display

• Employ equatorial equal area nets (Fig. 9) to plot:
  • Poles (normals) to joint planes.
  • Great circles representing discontinuity planes.
• Facilitates three-dimensional orientation analysis relative to free surfaces.
• Typical failure modes illustrated:
  • Circular failure in fractured rock.
  • Planar failure in organized lithologies.
  • Wedge failure due to intersecting joints.
  • Toppling failure from steeply dipping discontinuities.

2. SI Units and Symbols

3. Rounding Conventions

• Final results should be rounded following IS 2-1960 guidelines.

Data Representation Diagram

sphere
    title Equatorial Equal Area Net
    point poles "Poles of Joint Planes"
    circle great_circle "Great Circle (Plane)"
    poles --> great_circle
    note right of poles : Orientation of discontinuities
    note left of great_circle : Plane representation

Adoption of these graphical methods supports effective analysis of slope stability and rock mechanics challenges using 3D orientation data.

Strike and Dip Symbols per IS 11315 Part 1 (1987)

1. Definitions (Clause 3.3)

• Dip Direction (a): Clockwise azimuth from true north, 0° to 360°.
• Dip (B): Angle of steepest inclination, 0° to 90°.
• Notation format: a°/B°, e.g., 045°/30°.

2. Symbol Conventions (Clause 6.1)

• Strike represented by a line oriented along strike.
• Dip direction indicated by a short tick perpendicular to strike line.
• Dip angle noted adjacent to the dip tick.
• Examples:
  • Horizontal discontinuity: line without dip tick.
  • Vertical discontinuity: vertical strike line.
  • Inclined discontinuity: strike line with dip tick and angle.

3. Plotting on Equal Area Nets (Clause 6.4.3)

• Strike plus 90° plotted clockwise from north on net edge.
• Dip plotted inward at right angles to strike.
• Poles (normals) to planes also plotted for analysis.

4. Rounding Practices

• Strike and dip values rounded as per IS 11315 specifications.

5. Survey Instruments (Clause 5.2.1)

• Optical square, Abney level, alidade.
• Plane table with reconnaissance diagram.

Symbol Summary

flowchart LR
    A[Strike Line] --> B[Dip Tick at Right Angle]
    B --> C[Dip Angle Indicated]
    A --> D[Strike Direction]
    C --> E[Dip Direction by Tick]

Refer to Figures 1 and 7C in IS 11315 Part 1 for detailed symbol usage and plotting guidance.

Block Diagrams and Structural Depiction (IS 11315 Part 1, Clauses 6.2 - 6.2.2)

Overview:

• Purpose: Provide qualitative three-dimensional visualizations of rock mass structures and their interaction with engineering constructs such as tunnels, slopes, and dam abutments.

• Types of Diagrams:

  • Perspective Drawings (Fig. 5A): Show spatial relationships including principal stress ellipsoids if known.
  • Detailed Block Diagrams (Fig. 5B): Depict discontinuity orientation, spacing, and persistence at finer scales.
  • Excavated Corner Diagrams (Fig. 5C): Offer visual impressions of rock mass geometry where direct field views are limited.

• Applications: Useful for preliminary assessment and communication of field geological data, especially joint characteristics and spatial rock mass configuration.

Specifications and Usage

Conceptual Diagram

graph TD
  A[Engineering Structure] --> B[Rock Mass Geometry]
  B --> C[Orientation of Discontinuities]
  B --> D[Spacing and Persistence]
  A --> E[Principal Stress Ellipsoid]
  B --> F[Block Diagram Visualization]
  F --> G[Perspective Drawing]
  F --> H[Detailed Block Diagram]
  F --> I[Excavated Corner Sketch]

Summary:

• Employ block diagrams early to qualitatively understand rock mass and structure interactions.
• Include joint orientation, spacing, persistence, and stress data as available.
• Select diagram type based on required detail and data clarity.

This approach enhances design decisions and risk evaluation in rock engineering.

Joint Rosette Diagrams as per IS 11315 Part 1, Clause 6.3

• Objective: To present large orientation datasets quantitatively by grouping joint strikes in 10° sectors using a compass rose (0°–360° or 0–400g) with radial lines every 10°.

• Plotting Approach:

  • Aggregate observations into nearest 10° sectors.
  • Plot frequency as radial lengths using concentric circles (e.g., 5, 10, 15 counts).
  • Strike petals are symmetrical about the plot center.
  • Dip ranges indicated externally to the rosette circumference.

• Bias Consideration: Petal areas scale with the square of frequency, exaggerating dominant orientations and diminishing minor ones.

• Two Representation Methods (Fig. 6):

  1. Solid radial sectors proportional to frequency.
  2. Averaged strike values forming sharp petals—reduces bias but less reliable with dispersed data.

• Additional Applications: Radius may represent parameters like total discontinuity length.

Key Specifications

Conceptual Joint Rosette Plot

polar
    title Joint Rosette Diagram (Simplified)
    0: 10
    10: 5
    20: 12
    30: 8
    40: 15
    50: 7
    60: 10
    70: 5
    80: 3
    90: 12

Note: For detailed plotting, use equal area nets (Clause 6.4.1) to plot discontinuity poles on the lower hemisphere.

Summary of Spherical Projection and Contouring in IS 11315 Part 1

1. Projection Technique (Clause 6.4)

• Utilize Schmidt (polar) or Lambert equal area nets to plot poles of discontinuities.
• Provides accurate spatial representation of geological planes.
• Equal angle projections (Wulff nets) preserve angular relations but are not detailed here.

2. Contouring Methodology (Clause 6.4.5)

• Overlay a square grid on the equal area net.
• At each grid node, place a circle covering 1% of the net area.
• Count the number of poles within each circle to estimate pole density.
• Draw contour lines representing up to six density levels.

3. Interpretation of Pole Clusters (Clause 6.4.6)

• The peak pole density indicates the mean orientation of discontinuities.
• Orientation is inherently dispersed; probabilistic methods are preferred for detailed analysis.
• Note Schmidt method contouring can violate strict statistical rules due to multiple counts.

4. Practical Applications (Clause 6.4.7)

• Use equatorial equal area nets for plotting poles and great circles.
• Analyze rock slope stability and failure modes:
  • Circular
  • Planar
  • Wedge
  • Toppling

Important Parameters

Diagram: Pole and Great Circle Plotting

graph LR
A[Discontinuity Plane (K)] --> B[Pole P (Normal to K)]
B --> C[Plot on Polar Equal Area Net]
B --> D[Plot on Equatorial Equal Area Net]
C --> E[Count Poles in 1% Area Circles]
E --> F[Draw Contour Lines]

These techniques enable comprehensive spatial analysis of discontinuity orientations for geotechnical design and rock mass stability evaluations.