Chapter 3 — Shear Strength of Discontinuities¶
3.1 Mechanics of Shearing Along Joint Surfaces¶
In rock masses with persistent joint sets, structural failures (bench slides, wedge dropouts, toppling blocks) occur by sliding along pre-existing discontinuities rather than by fracturing through intact rock substance.
The shear resistance (\(\tau\)) along an unbonded rock joint is governed by three factors: 1. Normal Stress (\(\sigma_n'\)): Effective compressive stress clamping the joint lips together. 2. Basic Friction Angle (\(\phi_b\)): Inter-grain friction angle measured on smooth, planar, saw-cut surfaces of the same rock (typically \(25^\circ - 35^\circ\)). 3. Surface Roughness & Asperity Dilatancy: Geometric undulations (asperities) forcing the opposing joint walls to ride up over each other (dilate) during shearing, or shear through the asperities at high normal stresses.
3.2 Patton’s Bilinear Model¶
F.D. Patton (1966) showed that regular teeth-shaped asperities inclined at angle \(i\) produce a bilinear shear strength envelope:
Low Normal Stress (\(\sigma_n' < \sigma_T\)): Sliding Over Asperities¶
Shear displacement forces the blocks to dilate vertically over asperity teeth:
High Normal Stress (\(\sigma_n' \ge \sigma_T\)): Shearing Through Asperities¶
Normal stress suppresses dilation; the asperity teeth shear off across their roots:
Where \(c_j\) is apparent cohesion from asperity root shearing and \(\phi_r\) is residual friction angle.
3.3 The Barton-Bandis Non-Linear Shear Strength Criterion¶
Because real rock joints have irregular, multi-scale roughness rather than uniform teeth, Nick Barton and S. Bandis (1976, 1982, 1990) established the empirical non-linear criterion:
Where: - \(\text{JRC}\) = Joint Roughness Coefficient, varying from \(0\) (mirror smooth) to \(20\) (very rough, undulating). - \(\text{JCS}\) = Joint Wall Compressive Strength, determined using a Schmidt rebound hammer directly on the unweathered or weathered joint wall. - \(\phi_b\) = Basic friction angle of flat, unweathered rock surfaces. - \(\sigma_n'\) = Effective normal stress across the joint aperture.
Scale Correction for Field Joints¶
Laboratory shear box tests (\(L_0 = 100\text{ mm}\)) overestimate roughness compared to blocky field discontinuities (\(L_n = 1 - 5\text{ m}\)):
3.4 Infilled Joints & Gouge Fillings¶
When weathering or fault shearing deposits fine-grained infill (clay gouge, talc, chlorite) between joint walls, asperity interlock is lost.
- If infill thickness \(t < \text{asperity height } a\), rock-to-rock contact still contributes to shear resistance.
- If infill thickness \(t \ge 1.5 a\), shear strength drops to the drained or undrained shear strength of the gouge material alone (\(\phi' \approx 8^\circ - 18^\circ\) for smectite clays). This forms the critical slip planes responsible for historical landslides like the Vajont disaster.
3.5 Canonical Terminology¶
| English Term | Canonical Vietnamese Translation | Definition |
|---|---|---|
| Discontinuity shear strength | Sức kháng cắt của mặt bất liên tục | Shear resistance along joints, bedding, and faults |
| Basic friction angle \(\phi_b\) | Góc ma sát cơ bản \(\phi_b\) | Friction angle on smooth, planar saw-cut surfaces |
| Asperity | Mấu nhám | Micro- and macro-scale geometric undulation on a joint face |
| Joint Roughness Coefficient (JRC) | Hệ số độ nhám khe nứt (JRC) | Dimensionless index (0–20) quantifying joint surface profile |
| Joint Wall Compressive Strength (JCS) | Cường độ nén thành vách khe nứt (JCS) | Uniaxial compressive strength of the rock surface forming the joint wall |
| Fault gouge | Sét dập vỡ đứt gãy / Vữa đứt gãy | Soft, highly sheared clayey material filling a fault zone |