# Slope Stability Calculator

Resisting force over driving force for a single planar slip surface, checked against Fst.

- Page: https://jianzhujisuan.com/en/slope-stability
- Category: Construction (https://jianzhujisuan.com/en/c/construction)
- Chinese version: https://jianzhujisuan.com/zh/slope-stability.md
- Data checked: 2026-10-25

## Quick result

With the default inputs (Slope height 6 m, Slope safety class Class 2, Design case Permanent, normal, Slip surface angle 25 °, Unit weight 18 kN/m³, Friction angle 28 °, Cohesion 15 kPa): **Factor of safety 1.87**

## Inputs

| Parameter | Type | Default | Unit | Note |
|---|---|---|---|---|
| Slope height | number | 6 | m |  |
| Slope safety class | select | Class 2 | — | Per GB 50330-2013 Table 3.2.1, by consequence of failure |
| Design case | select | Permanent, normal | — |  |
| Slip surface angle | number | 25 | ° | Critical surface, near the slope angle for a rough check |
| Unit weight | number | 18 | kN/m³ |  |
| Friction angle | number | 28 | ° |  |
| Cohesion | number | 15 | kPa |  |

## Formula

- **Wedge weight**: W = ½·γ·H·(H/tanα)
- **Slip length**: L = H / sinα
- **Resisting**: R = W·cosα·tanφ + c·L
- **Driving**: T = W·sinα
- **Factor of safety**: Fs = R / T
- **State**: Fs≥Fst stable; 1.05≤Fs<Fst basically stable; 1.00≤Fs<1.05 marginally unstable; Fs<1.00 unstable

## Worked example

A 6 m slope, 25° slip, γ=18 kN/m³, φ=28°, c=15 kPa: slip length 14.2 m, wedge weight W=½×18×6×(6/tan25°) ≈ 695 kN/m, resisting ≈ 548 kN/m, driving ≈ 294 kN/m, Fs ≈ 1.87. Against Fst = 1.30 for a class 2 permanent slope under normal conditions, Fs ≥ Fst, stable.

## Questions

### What factor of safety is acceptable?

It depends on the safety class and the design case - there is no single number. GB 50330-2013 Table 5.3.2 gives: permanent slopes under normal conditions 1.35 / 1.30 / 1.25 for classes 1 / 2 / 3; seismic 1.15 / 1.10 / 1.05; temporary slopes 1.25 / 1.20 / 1.15. The computed Fs must reach the matching Fst. Table 5.3.1 also has two lower bands: 1.05 to Fst is basically stable, 1.00 to 1.05 is marginally unstable, and only below 1.00 is unstable. For very complex ground or severe consequences of failure, Fst is raised further (Table 5.3.2, note 2).

### Is planar sliding accurate enough?

Only for homogeneous soil and a single plane - a quick check or option comparison. Layered ground, weak seams and circular slips (common in clay) need a method of slices - Bishop, Janbu, Morgenstern-Price - run in software today. Treat this tool as an order-of-magnitude first pass; a real slope design needs a full calculation.

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