Quantitative classification systems of rock mass-Guidelines, Part 2: Rock mass quality for prediction of support pressure in underground openings

Scope Summary & Key Specifications from IS 13365 Part 2 (1992):

This part deals with rock mass classification, stress reduction, and water pressure factors affecting excavation stability.

1. Stress Reduction Factor (SRF) – Clause 3.1.5

Competent Rock Stress Classification:

2. Joint Water Reduction Factor (Jw) – Clause 3.1.4

IS 13365 Part 2 refers to IS 11315 Part 11 (1985) for Core Recovery and Rock Quality, focusing on Rock Quality Designation (RQD).

Key Formulas and Tables from IS 11315 Part 11:

1. Rock Quality Designation (RQD)

[ \boxed{ RQD = 115 - 3.3 \times J_v } ]

• (J_v) = Volumetric joint count (number of joints per cubic meter)
• If (RQD < 10%), use a nominal value of 10% for calculations.

2. RQD Classification Table

3. Rock Mass Classification Based on Q-value (from IS 13365 Part 2)

Summary:

• Use RQD as a key quantitative descriptor of rock mass quality.
• Calculate RQD from joint count using the formula.
• Classify rock quality using the RQD and Q-value tables for design and analysis.

flowchart LR
    A[Volumetric Joint Count (Jv)] -->

Determination of Rock Mass Quality (Q) - IS 13365 Part 2

Formula:

[ \boxed{ Q = \frac{RQD}{J_n} \times \frac{J_r}{J_a} \times \frac{J_w}{SRF} } ]

Where:

• RQD = Rock Quality Designation (from IS 11315 Part 11)
• Jn = Joint set number
• Jr = Joint roughness number
• Ja = Joint alteration number
• Jw = Joint water reduction factor
• SRF = Stress reduction factor

Rock Quality Designation (RQD) Calculation

[ RQD = 115 - 3.3 \times J_v ]

• (J_v) = Volumetric joint count (number of joints per cubic meter)
• If (RQD < 10%), use RQD = 10 as nominal for Q calculation.

Rock Mass Classification Based on Q

Notes

• Q relates directly to support pressure requirements for underground openings.
• Use RQD intervals of 5 for practical accuracy (e.g.,

Rock Quality Designation (RQD) — IS 13365 Part 2

Key Formula:

[ \boxed{ \text{RQD} = 115 - 3.3 \times J_v } ]

• (J_v) = volumetric joint count (total joints per cubic meter)

If RQD ≤ 10%, use a nominal value of 10 for rock mass quality evaluation.

Rock Quality Classification (Table 3.1.1):

Rock Mass Quality (Q) Formula (Clause 3.1):

[ Q = \frac{RQD}{J_n} \times \frac{J_r}{J_a} \times \frac{J_w}{SRF} ]

• (J_n) = joint set number
• (J_r) = joint roughness number
• (J_a) = joint alteration number
• (J_w) = joint water reduction factor
• (SRF) = stress reduction factor

Notes on Field Data Collection (Clause 3.3):

• Use 5-10 m core length for uniform rock.
• For variable zones, evaluate separately or use 10-50 m for overall quality.
• Calculate Q separately for roof, floor, and walls; use root mean square for mean Q.
• For power tunnels, reduce (J_w) considering seepage water pressure.

This system guides support design by quantifying rock mass quality based on jointing and alteration.

Joint Set Number (Jn) - IS 13365 Part 2

The Joint Set Number (Jn) quantifies the number of joint sets in rock mass, considering foliations, schistosity, slaty cleavage, or bedding planes as joint sets if strongly developed.

Key Points:

• Parallel discontinuities count as a full joint set.
• Few visible joints or occasional breaks → count as random joints.
• Multiply Jn by 2 for portals and 3 for intersections.

Table 2: Joint Set Number (Jn)

Usage Notes:

• For intersections:
  [ Jn_{intersection} = 3 \times Jn ]
• For portals:
  [ Jn_{portal} = 2 \times Jn ]

This parameter is critical in rock mass classification and stability analysis, influencing the Q-system rating and design decisions.

IS 13365 Part 2: Joint Roughness Number (Jr) and Joint Alteration Number (Ja)

1. Joint Roughness Number (Jr) — Table 3 (Clause 3.1.3)

• Add 1.0 if mean joint spacing > 3 m.
• Jr = 0.5 may be used for planar slickensided joints with favorable lineations.

2. Joint Alteration Number (Ja) — Table 4 (Clause 3.1.3)

Joint Water Reduction Factor (Jw) – IS 13365 Part 2

Jw quantifies the reduction in shear strength of rock joints due to water pressure, which lowers effective normal stress and may cause joint softening or outwash.

Table 5: Joint Water Reduction Factor (Jw)

Notes:

• Increase Jw if drainage measures are installed.
• Ice-related effects are not considered.
• Jw is used in rock mass quality calculations, e.g., Q = (RQD/Jn) × (Jr/Ja) × (Jw/SRF).

Usage in Shear Strength Reduction:

Effective normal stress on joints is reduced by water pressure:

[ \sigma' = \sigma - u ]

Where:

• (\sigma) = total normal stress
• (u) = pore water pressure related to Jw factor

Summary:

• Jw directly reduces joint shear strength.
• Select Jw based on water inflow and pressure conditions from Table 5.
• Use alongside Jr (roughness), Ja (alteration), and SRF (stress reduction factor) for rock mass quality.

flowchart LR
    Water_Pressure -->|Increases| Jw_Decrease[Decrease in Jw]
    Jw_Decrease -->|Reduces

Stress Reduction Factor (SRF) - IS 13365 Part 2

SRF quantifies loosening, rock stress, squeezing, and swelling pressures affecting tunnel stability.

Key Points from Clause 3.1.5 & Table 6:

Competent Rock Stress Categories (Gc/σ1 and SRF):

Additional Notes:

• Reduce SRF by 25-50% if shear zones only influence, not intersect excavation.
• For strongly anisotropic stress fields (σ1/σ3 > 10), reduce unconfined compression (σc) and tensile strength (σt) to 0.6 times.
• For shallow crown depth (less than span width), increase SRF from 2.5 to 5.

Rock Mass Quality (Q) Relation:

[ Q = \frac{RQD}{J_n} \times \frac{J_r}{J_a} \times \frac{J_w}{SRF} ]

Where:

• RQD = Rock Quality Designation

Classification of Rock Mass Based on Q (IS 13365 Part 2)

1. Rock Mass Quality (Q) Formula

[ \boxed{ Q = \frac{RQD}{J_n} \times \frac{J_r}{J_a} \times \frac{J_w}{SRF} } ]

• RQD = Rock Quality Designation (%)
• J_n = Joint set number
• J_r = Joint roughness number
• J_a = Joint alteration number
• J_w = Joint water reduction factor
• SRF = Stress reduction factor

2. Rock Mass Classification Table (Clause 3.4)

Summary:

• Higher Q → Better rock mass quality → Lower support needed.
• Lower Q → Poor rock mass → Higher support requirements.

flowchart TD
    A[RQD] --> C[Calculate Q]
    B[Jn, Jr, Ja, Jw, SRF] --> C
    C --> D{Q Value}
    D -->|>400| E[Exceptionally Good]
    D -->|100-400| F[Extremely Good]
    D -->|40-100| G[Very Good]
    D -->|10-40| H[Good]
    D -->|4-10| I[Fair]
    D -->|1-4| J[Poor]
    D -->|0.1-1| K[

Estimation of Support Pressures (IS 13365 Part 2: 1992)

Key Parameters:

• Q = Rock mass quality (post-excavation)
• Qwi, Qri = Short-term rock quality indices for wall and roof (related to Q)
• f = Overburden correction factor (Eq. 4)
• f' = Tunnel closure correction factor (Table 7, Fig. 2)

Rock Mass Quality Relations (Clause 2.5)

Support Pressure Formulas

• Short-term roof support pressure:

  [ P_{ri} = 120 \times (Q_{ri})^{1/3} \times f \times f' ]

• Short-term wall support pressure:

  [ P_{wi} = 20 \times (Q_{wi})^{-1/3} \times f \times f' ]

• Ultimate wall support pressure:

  [ P_{wu} = 120 \times (Q_{wu})^{-1/8} \times f \times f' ]

Important Notes:

• Tunnel closure > 6% of span is critical; immediate support needed.
• Steel ribs tolerate < 2% tunnel closure.
• For squeezing ground, keep tunnel span < 6 m.
• Use immediate shotcrete/rock bolts to minimize support pressure.
• Invert support is recommended only in poor/squeezing conditions.

Summary Diagram

flowchart TD
    A[Rock Mass Quality Q] --> B{Determine Qwi, Qri}
    B -->|Q > 10| C[Qwi=50Q, Qri=25Q]
    B -->|0.1 < Q < 10| D[Qwi=2.5Q, Qri=12.5Q]
    B -->|Q < 0.1| E[Q

IS 13365 Part 2: Ultimate Roof and Wall Support Pressure Correlations

1. Ultimate Roof Support Pressure (Pru)

[ P_{ru} = 1.0 \times (Q_{ru})^{-1/3} \times f \quad \text{(kg/cm}^2) ]

• (Q_{ru}) = Ultimate roof rock mass quality
• (f = 1 + \frac{H - 320}{800}) (Correction factor for overburden)
• (H) = Overburden depth in meters

2. Ultimate Wall Support Pressure (Pwu)

Wall rock quality (Q_{wu}) depends on rock group:

Ultimate wall support pressure:

[ P_{wu} = 120 \times (Q_{wu})^{-1/8} \times f \times f' \quad \text{(kg/cm}^2) ]

• (f') = Correction factor for tunnel closure (from Table 7, Fig. 2)
• (f) = Overburden correction (as above)

3. Short-term Support Pressures

• Roof:

[ P_{ri} = 120 \times (Q_{ri})^{-1/3} \times f \times f' ]

• (Q_{ri} = 5 Q_{ru}) (short-term roof rock quality)

• Wall:

[ P_{wi} = 201 \times (Q_{wi})^{-1/3} \times f \times f' ]

• (Q_{wi}) depends on rock quality (see clause 3.5.1.2)

4. Notes

• Tunnel closure should be limited to <6% span to avoid rapid pressure increase.
• Steel ribs absorb max 2% tunnel closure.

Short-term Support Pressure Calculations (IS 13365 Part 2)

Key Formulas:

1. Short-term Roof Support Pressure (Pri): [ P_{ri} = 120 \times Q_{ri}^{-1/3} \times f \times f' ]

   • (P_{ri}): short-term vertical roof support pressure (kg/cm²)
   • (Q_{ri} = 5Q): short-term roof rock quality
   • (f): correction factor for overburden (Eq. 4)
   • (f'): correction factor for tunnel closure (Table 7)

2. Short-term Wall Support Pressure (Pwi): [ P_{wi} = 102 \times Q_{wi}^{-1/3} \times f \times f' ]

   • (Q_{wi}): short-term wall rock quality (adjusted from Q by factors depending on Q magnitude)

3. Ultimate Wall Support Pressure (Pwu): [ P_{wu} = 120 \times Q_{wu}^{-1/8} \times f \times f' ]

Important Notes:

• Correction Factors:

  • (f): accounts for overburden depth.
  • (f'): accounts for tunnel closure; from Table 7 and Fig. 2.

• Tunnel Closure Limits:

  • Max 6% closure allowed; beyond this, support pressures rise rapidly.
  • Steel ribs absorb max 2% closure.

• Rock Mass Quality (Q):

  • Used as base parameter; multiplied by factors (e.g., 5 for roof) to get short-term qualities.

Summary Table

IS 13365 Part 2: Correction Factors for Tunnel Closure and Overburden

Key Formulas for Support Pressure (Clause 3.5.2.2)

• Short-term roof support pressure: [ P_{ru} = 20 \times (Q_{ru})^{-1/3} \times f \times f' ] where:

  • ( f ) = correction factor for overburden (Eq. 4)
  • ( f' ) = correction factor for tunnel closure (Table 7, Fig. 2)

• Ultimate wall support pressure: [ P_{wu} = 120 \times (Q_{wu})^{-1/8} \times f \times f' ]

• Short-term roof support pressure (alternative): [ P_{ri} = 120 \times (Q_{ri})^{1/3} \times f \times f' ]

• Short-term wall support pressure: [ P_{wi} = 201 \times (Q_{wi})^{-1/3} \times f \times f' ]

Correction Factors for Tunnel Closure ( f' ) (Table 7)

IS 13365 Part 2: Unsupported Span & Excavation Support Ratio (ESR)

1. Unsupported Span (Clause 3.6)

The equivalent unsupported dimension ( D_e ) (span, diameter, or height in meters) for self-supporting tunnels is:

[ \boxed{ D_e = 2 \times Q^{0.4} } ]

• (Q) = Rock mass quality (higher Q = better quality)
• Use span or diameter for roof support analysis.
• Use diameter or height for wall support analysis.

2. Excavation Support Ratio (ESR) (Table 8)

• For temporary support, multiply ESR by 1.5 and increase (Q) to (5Q).

3. General Conditions for Permanently Unsupported Openings

• (J_n < 9), (J_r > 1.0), (J_a < 10), (J_w = 1.0), SRF < 2.5
• Additional criteria based on RQD, joint set numbers, and SRF (see clauses for details).

4. Correction Factor for Tunnel Closure (f') (Table 7)

IS 13365 Part 2: Field Data Collection Guidelines (Clause 3.3)

Key Points for Field Data Collection:

• Core/Excavation Length:

  • For uniform rock mass: 5-10 m core/wall length is sufficient.
  • For closely jointed shear zones:
    • If shear zones > 1-2 m wide, evaluate parameters (RQD, Jn, Jr, Ja) separately.
    • If shear zones < 1-2 m and frequent, use an overall reduced Q value.
    • Core/wall length may extend to 10-50 m for overall rock mass quality.

• Rock Mass Quality (Q) Evaluation:

  • Obtain Q values separately for roof, floor, and two walls if rock mass is non-uniform.
  • Mean Q value = Root Mean Square (RMS) of max and min Q values:

  [ Q_{mean} = \sqrt{\frac{Q_{max}^2 + Q_{min}^2}{2}} ]

• Water Pressure (Jw) Adjustment:

  • For power tunnels, reduce Jw assuming seepage water pressure equals internal water pressure (refer Table 6 in IS 13365).

• Rounding Off:

  • Follow IS 2:1960 for rounding numerical values, retaining significant digits as per the standard.

Parameters to Collect:

flowchart TD
    A[Start: Field Data Collection] --> B{Rock Mass Uniformity?}
    B -- Uniform --> C[Core Length 5-10 m]
    B -- Non-uniform --> D{Shear Zone Width}
    D -- >2 m --> E[Evaluate parameters separately]
    D -- <2 m --> F[Use overall reduced Q]
    E --> G[Core Length 10-50 m]
    F --> G
    G --> H[Calculate Q