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Drainage Effect on FoS Estimator

Shows how much draining the water uplift from a rock or soil block improves its factor of safety against sliding on a single plane. It reports the wet factor of safety (with uplift) and the fully-drained factor of safety side by side, plus the percentage gain — the quickest way to justify a drainage adit or horizontal drains.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Enter the resolved per-metre forces on the sliding plane: cohesive resisting force C = c·A (kN/m), normal force N = W·cosψp (kN/m), and driving force T = W·sinψp (kN/m).
  2. Enter the friction angle φ (°) and the water uplift force U (kN/m) acting on the plane.
  3. Read the wet and drained factors of safety and the percentage improvement from removing the uplift.

How it works

For a rigid block on a single plane, limit equilibrium gives FoS = (C + (N − U)·tanφ) / T. Water uplift U reduces the effective normal force from N to (N − U), cutting the frictional resistance.

Draining the block sets U = 0, restoring the full N·tanφ friction and giving FoS_drained = (C + N·tanφ) / T. The reported percentage is (FoS_drained − FoS_wet)/FoS_wet × 100.

Worked example

Draining a block with 300 kN/m uplift. With C = 50, N = 1000, T = 500 kN/m, φ = 35° and U = 300 kN/m: wet FoS = 1.08; drained FoS = 1.50. Draining the block lifts the factor of safety from a marginal 1.08 to 1.50 — a 38.9 % improvement.

Common mistakes

  • Entering block weight W instead of its resolved components: N = W·cosψp and T = W·sinψp.
  • Forgetting the uplift force U — with U = 0 the wet and drained results are identical.
  • Applying this single-plane rigid-block method to a circular or multi-wedge soil slope, which needs a method of slices.

Frequently asked questions

How does drainage improve slope stability?

Water pressure on the sliding plane pushes the block off the surface (uplift U), reducing the effective normal force and the friction that resists sliding. Removing that water restores the full frictional resistance.

What is the uplift force U?

The resultant water pressure acting normal to (and pushing off) the sliding plane, per metre of slope width — the area under the pressure diagram along the plane.

Why doesn't drainage change the cohesion term?

Cohesion C = c·A depends on contact area and cohesive strength, not water pressure, so only the frictional (N·tanφ) term changes when you drain the block.

What if uplift exceeds the normal force?

If U > N the effective normal force is negative — the block is floated off the plane and the factor of safety collapses. The tool flags this as an error.

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