Slope stability analysis asseses the safety of natural slopes, embankments, cuttings, and tailings dams.
Slope stability is concerned with the resistance of an inclined soil/rock mass to sliding or collapse under gravitational and other loads.
Factor of Safety
$$ FS = \frac{\text{Sum of resisting forces (shear strength)}}{\text{Sum of driving forces (shear stress)}} $$| FS Value | Interpretation |
|---|---|
| FS < 1.0 | Failure — slope is unstable |
| FS = 1.0 | Limit equilibrium — on the verge of failure |
| FS = 1.0–1.3 | Marginally stable — may fail under adverse conditions |
| FS = 1.3–1.5 | Acceptable for temporary slopes |
| FS = 1.5–2.0 | Acceptable for permanent slopes |
| FS > 2.0 | Highly conservative |
Types of Slope Failure
| Failure Type | Description | Typical Soil/Rock |
|---|---|---|
| Rotational (circular) | Slip surface is curved | Homogeneous clay, fill embankments |
| Translational (planar) | Slip surface is approximately planar | Bedded rock, thin soil over rock |
| Wedge failure | Two intersecting discontinuities | Rock slopes |
| Toppling | Blocks rotate forward | Steep rock slopes with vertical joints |
| Flow | Soil behaves as viscous fluid | Loose saturated sands, debris |
| Compound | Combination of circular and planar | Layered soils, weak seam at base |
Factors Affecting Slope Stability
| Factor | Effect | Mechanism |
|---|---|---|
| Gravity | Driving force increases with slope height and angle | Increased shear stress |
| Water | Reduces effective stress, increases weight | Pore pressure reduces strength |
| Rainfall infiltration | Rapid increase in pore pressure | Transient positive pore pressure |
| Earthquake | Inertial forces, strength reduction | Cyclic loading, liquefaction |
| Excavation | Removes support at toe | Stress relief, unloading |
| Fill placement | Increases driving force | Additional weight |
| Weathering | Reduces shear strength over time | Loss of cohesion, increased permeability |
| Vegetation removal | Removes root reinforcement | Loss of apparent cohesion |
Slope Stability Analysis Methods
Infinite Slope Analysis
For shallow, planar failures where the failure surface is parallel to the ground surface:
Dry slope:
$$ FS = \frac{\tan\phi'}{\tan\beta} $$Seepage parallel to slope:
$$ FS = \frac{\gamma' \tan\phi'}{\gamma_{sat} \tan\beta} $$Where $\beta$ = slope angle.
Method of Slices (Ordinary / Fellenius)
The slope is divided into vertical slices. The factor of safety is:
$$ FS = \frac{\sum[c' l + (W\cos\alpha - ul)\tan\phi']}{\sum W\sin\alpha} $$Where:
- $W$ = weight of slice
- $\alpha$ = inclination of slice base
- $l$ = length of slice base
- $u$ = pore pressure at base of slice
Bishop's Simplified Method (Circular Failure)
$$ FS = \frac{\sum\frac{1}{m_\alpha}[c'b + (W - ub)\tan\phi']}{\sum W\sin\alpha} $$Where:
- $b$ = slice width
- $m_\alpha = \cos\alpha + \frac{\sin\alpha\tan\phi'}{FS}$
Since $FS$ appears on both sides, this method requires iteration (typically 3–6 cycles).
Bishop's method is the most commonly used limit equilibrium method in Australian practice and is widely accepted by regulatory authorities.
Janbu's Simplified Method (Non-Circular Failure)
For non-circular failure surfaces (often appropriate for layered soils):
$$ FS = f_0 \frac{\sum[c'b + (W - ub)\tan\phi']/\cos\alpha}{\sum W\tan\alpha} $$Where $f_0$ is a correction factor depending on the depth/length ratio of the slip surface.
Spencer's Method
Satisfies both force and moment equilibrium with inter-slice forces assumed parallel. Considered one of the most rigorous limit equilibrium methods.
Morgenstern-Price Method
The most rigorous limit equilibrium method — satisfies both force and moment equilibrium with a prescribed inter-slice force function.
Comparison of Methods
| Method | Force Equilibrium | Moment Equilibrium | Slip Surface | Accuracy |
|---|---|---|---|---|
| Ordinary (Fellenius) | No | Yes | Circular | Underestimates FS by 5–20% |
| Bishop's Simplified | No | Yes | Circular | Very good (±2–5%) |
| Janbu's Simplified | Yes | No | Any | ±5–10% (needs correction) |
| Spencer's | Yes | Yes | Any | Excellent |
| Morgenstern-Price | Yes | Yes | Any | Excellent |
Determination of Critical Failure Surface
Search Methods
| Method | Description | Use |
|---|---|---|
| Grid search | Systematic grid of centres | Simple circular surfaces |
| Pattern search | Derivative-based optimisation | Non-circular surfaces |
| Random search | Monte Carlo approach | Complex geology |
| Genetic algorithm | Evolutionary optimisation | Very complex conditions |
Critical Circle Location
For homogeneous clay slopes (Taylor's stability charts):
| Slope Angle $\beta$ | Critical Circle Location |
|---|---|
| < 53° (1:0.75) | Toe circle — passes through toe |
| > 53° | Base circle — deep-seated |
| Unlimited (vertical) | Face circle — passes above toe |
Influence of Water
Steady-State Seepage
Ru coefficient method:
$$ r_u = \frac{u}{\gamma H} $$Where $u$ = pore pressure and $H$ = height of slice above slip surface.
| Condition | Typical $r_u$ |
|---|---|
| Dry slope | 0 |
| Normal seepage | 0.25–0.50 |
| Heavy rainfall | 0.5–0.7 |
| Fully saturated | > 0.6 |
Rapid Drawdown
When water level drops quickly (reservoir, flood), the slope may become unstable:
- Upward seepage gradient reduces effective stress
- Saturated soil weight remains
- No strength gain from unloading
Rainfall-Induced Failure
Most slope failures in Australia occur during or after intense rainfall events:
- Within 24–48 hours of heavy rain (> 100 mm)
- Antecedent rainfall (7–14 days prior) weakens soil
- Positive pore pressure develops in the zone of infiltration
Stabilisation and Remedial Measures
Geometric Measures
| Measure | How It Works | Cost |
|---|---|---|
| Flatten slope | Reduces driving force | Moderate |
| Benching | Creates intermediate flat areas | Low-Moderate |
| Remove crest load | Reduces driving force | Low |
| Fill toe berm | Increases resisting force | Moderate |
| Relocate alignment | Avoids problem area | High |
Drainage Measures
| Measure | How It Works | Effectiveness |
|---|---|---|
| Surface drains | Prevent infiltration | Low-moderate |
| Horizontal drains | Lower phreatic surface | High |
| Trench drains / interceptor drains | Intercept groundwater flow | High |
| Vertical (relief) wells | Depressurise deep aquifers | High |
| Geotextile drainage layers | Internal drainage | Moderate |
| Gravity drainage adits | Deep drainage | Very high (expensive) |
Retaining Structures
| Structure | Application | Design |
|---|---|---|
| Gravity wall | Moderate heights, competent foundation | Sliding/overturning/bearing |
| Cantilever wall | Heights 3–8 m | Structural + geotechnical |
| Anchored wall | Tall slopes, limited space | Rock/soil anchors + wall |
| Pile wall / secant pile wall | Deep-seated failures | Passive resistance in stable stratum |
| Soil nailing | Stabilise existing slopes | Nail pullout + facing |
Ground Improvement
| Method | How It Works | Best For |
|---|---|---|
| Compaction | Increased shear strength | Fill slopes |
| Lime/cement stabilisation | Increased cohesion | Soft clays |
| Grouting | Fill voids, increase strength | All soils |
| Jet grouting | Create in-situ columns | Localised weak zones |
| Electro-osmosis | Drain soft clays | Very soft sensitive clays |
| Vegetation | Root reinforcement, drying | Shallow failures |
Landslides in Australia
Landslide-Prone Areas
| Region | Common Landslide Types | Triggers |
|---|---|---|
| Sydney Basin (Blue Mountains, Illawarra) | Rock falls, debris flows, translational slides | Rainfall, mining subsidence |
| NSW North Coast | Cut slope failures, deep seated slides | Heavy rainfall, cyclones |
| Victoria (Dandenongs, Yarra Ranges) | Debris flows, cut slope failures | Wet winters, bushfire aftermath |
| Queensland (Darling Downs, SEQ) | Slips on steep terrain | Rainfall, clearing |
| Tasmania | Deep-seated landslides | Wet periods, terrain |
| South Australia | Minor slides in cuttings | Rainfall |
| Western Australia (Darling Scarp) | Rock falls, shallow slides | Cleared slopes |
Australian Landslide Databases
| Database | Organisation | Coverage |
|---|---|---|
| National Landslide Risk Database | Geoscience Australia | National |
| NSW Landslide Inventory | NSW Department of Planning | NSW |
| VicLandslide | Geological Survey of Victoria | Victoria |
| QLD Landslide Susceptibility | Geological Survey of QLD | Queensland |
Seismic Slope Stability
Pseudostatic Analysis
$$ FS_{eq} = \frac{\sum[c'b + (W - ub)\tan\phi']}{\sum(W\sin\alpha + k_hW\cos\alpha)} $$Where $k_h$ is the horizontal seismic coefficient.
Typical $k_h$ values (Australia):
| Seismic Zone | PGA (g) | $k_h$ |
|---|---|---|
| Low (most of Australia) | < 0.08 | 0.04–0.06 |
| Moderate (Adelaide, Perth) | 0.08–0.15 | 0.06–0.10 |
| High (parts of WA, SA) | 0.15–0.22 | 0.10–0.15 |
Newmark Sliding Block Analysis
Estimates permanent displacement rather than FS:
$$ D \approx \frac{V^2}{2A} \times \left(\frac{A}{\text{CRR}}\right)^{-b} $$The approach is preferred for critical slopes where some deformation is acceptable.
Acceptable displacements:
| Slope Type | Acceptable Displacement |
|---|---|
| Critical slopes (dams, highways) | < 100 mm |
| Moderate slopes | 100–500 mm |
| Low-risk slopes | 500–1000 mm |
Monitoring and Instrumentation
| Instrument | Parameter | Application |
|---|---|---|
| Inclinometer | Lateral movement profile | Detect sliding surface location |
| Piezometer | Pore water pressure | Drainage effectiveness |
| Survey monuments | Surface movement | Visual monitoring |
| Tiltmeter | Rotation | Wall rotations |
| Crack gauge | Crack opening | Tensile cracks at crest |
| TDR (Time Domain Reflectometry) | Shear surface location | Deep-seated movements |
| LiDAR / drone survey | Surface deformation | Large-scale monitoring |
Monitoring frequency:
| Risk Level | During Construction | Routine Operation | During Heavy Rain |
|---|---|---|---|
| Low | Monthly | Quarterly | After events |
| Medium | Weekly | Monthly | Weekly |
| High | Daily | Weekly | Daily |
Australian Standards and Guidelines
| Standard/Guideline | Title | Application |
|---|---|---|
| AS 4678 | Earth Retaining Structures | Excavation slope stability |
| AGS Landslide Risk Management Series | Landslide Risk Management | Risk-based approach |
| ANCOLD | Guidelines on Tailings Dams | Dam slope stability |
| AS 5100 | Bridge Design | Abutment slope stability |
| TfNSW QA R10 | Earthworks | Embankment slopes |
| TfNSW QA B80 | Earth Retaining Structures | Cut slopes and walls |
Worked Example
Given: 10 m high clay slope, $\beta = 30°$, $\gamma = 19$ kN/m³, $c' = 10$ kPa, $\phi' = 25°$, no water table.
Searching for critical circle (using Bishop's simplified method):
Trial centre at coordinates producing a circular slip surface:
| Slice | $b$ (m) | $h$ (m) | $W$ (kN/m) | $\alpha$ (°) |
|---|---|---|---|---|
| 1 | 1.5 | 2.0 | 57.0 | -10 |
| 2 | 1.5 | 5.5 | 156.8 | 5 |
| 3 | 1.5 | 8.0 | 228.0 | 18 |
| 4 | 1.5 | 9.0 | 256.5 | 30 |
| 5 | 1.5 | 7.0 | 199.5 | 42 |
| 6 | 1.5 | 3.5 | 99.8 | 55 |
Assume FS = 1.4 as initial guess, iterate:
$$ FS = \frac{\sum[c'b + W\tan\phi']/m_\alpha}{\sum W\sin\alpha} $$After 4 iterations: FS = 1.78 (adequate for a permanent slope).