A limit equilibrium method for slope stability

A numerical finite element approach

🎓 Prepared by students from Boğaziçi University

What is Slope Stability Analysis?

Slope stability analysis assesses the risk of landslides and soil failure on inclined terrain. Using equilibrium methods or numerical models, engineers calculate the factor of safety to ensure slopes remain stable under current and future conditions.

Short answer

Slope stability analysis evaluates whether a slope will fail or remain stable using methods like limit equilibrium (Fellenius, Bishop) and finite element analysis. A factor of safety > 1.3 generally indicates stability.

Slope Failure Mechanics: Driving vs. Resisting Forces

Driving Forces

•Gravitational component down slope
•Water pressure in pores
•External loads on slope
•Weight of soil mass

Resisting Forces

•Soil cohesion
•Friction (φ angle)
•Shear strength
•Slope geometry (height, angle)

Step-by-step worked examples

A slope has 15 m height, 30° angle, cohesion 20 kPa, friction angle 35°, γ=18 kN/m³. Estimate stability.

Driving force component: W·sin(30°) ∝ load down slope
Resisting shear: τ = c + σ·tan(35°) = 20 + σ×0.7
If factor of safety (Resisting/Driving) > 1.3 → stable

After heavy rain, pore pressure increases. How does this affect slope stability?

Rising water reduces effective stress: σ' = σ − u
Lower effective stress → lower shear strength (τ = c + σ'·tan φ)
Factor of safety decreases → slope more prone to failure

Compare a 25° slope vs. a 40° slope in the same soil. Which is more stable?

Driving force = W·sin(angle)
At 25°: W·sin(25°) ≈ 0.42W
At 40°: W·sin(40°) ≈ 0.64W
40° slope has 52% more driving force → less stable

Flashcards

Quick quiz

Q1.Factor of safety (FS) = 1.5 means:

Correct answer: B. FS = Resisting/Driving. 1.5 means resisting forces are 1.5× stronger than driving forces—stable.

Q2.Which increases the risk of slope failure most?

Correct answer: B. Water pressure reduces effective stress, directly lowering shear strength.

Q3.Fellenius method is:

Correct answer: B. Fellenius is an equilibrium method; it divides slopes into slices and sums forces.

Q4.Critical slope angle (no cohesion, φ = 35°):

Correct answer: C. Critical angle ≈ φ. At φ = 35°, tan(35°) ≈ 0.7; equilibrium is FS=1 at θ ≈ 35°.

📄Download this topic as a printable worksheet (PDF)Summary + 10 questions + answer key — print it, share it in class.↓

Study better with Bounlu apps

Notek

The full card deck, worked steps and AI-tutor support for “What is Slope Stability Analysis?” are in Notek — study by hand before your exam.

Get it free

PromyNever miss an exam or homework deadline with Promy: AI turns the dates in your inbox into reminders automatically.

Common mistakes

✗

Ignoring pore pressure and assuming dry soil always. — Correct: Pore pressure from rain/seepage drastically reduces shear strength—must be included.

✗

Using the same FS value for all projects and conditions. — Correct: FS depends on risk tolerance: 1.3 for temporary cuts, 1.5+ for permanent slopes.

✗

Assuming a slope is safe just because it has stood for years. — Correct: Environmental changes (rain, excavation below) can destabilize old slopes suddenly.

✗

Only calculating FS at one critical surface. — Correct: Search for the most critical failure surface (often requires iteration or FEM).

FAQ

What is slope stability analysis?

The process of evaluating whether a sloped surface of soil or rock will fail or remain stable, using equilibrium or numerical models.

What is a safe factor of safety for slopes?

Typically 1.3 for temporary cuts, 1.5 or higher for permanent slopes. Values vary by design standard and risk.

How does rainfall affect slope stability?

Rainfall increases pore pressure, reducing effective stress and shear strength, making slopes more prone to failure.

What are the main slope failure methods?

Limit equilibrium (simplest), FEM (more accurate), and reliability analysis (probabilistic).