What does Eurocode 7 require for slope stability?

Eurocode 7 requires that slopes are verified using one of the Design Approaches (DA1, DA2 or DA3) with appropriate partial factors on actions, material properties and resistances. The design must show that the design value of the stabilising effect is greater than or equal to the design value of the destabilising effect. In practice this is often expressed as a factor of safety on shear strength or on actions, depending on the chosen approach and national annex.

What factor of safety is acceptable for slopes under Eurocode 7?

Eurocode 7 does not prescribe a single global factor of safety. Instead, it uses partial factors on actions and material properties. However, when back-calculated, typical design situations for long-term slopes often correspond to a global factor of safety in the range of 1.3–1.5 for drained conditions, depending on the design approach, consequence class and national annex requirements.

What is the difference between DA1 and DA2 for slope stability?

Design Approach 1 (DA1) uses two combinations: Combination 1 with partial factors mainly on actions, and Combination 2 with partial factors mainly on material properties. Design Approach 2 (DA2) applies partial factors simultaneously to actions and material properties. The choice of approach and the numerical values of the partial factors are given in the National Annex and can significantly influence the design factor of safety.

Can this calculator replace a full limit equilibrium or FEM analysis?

No. This calculator is an educational tool that implements a simplified limit equilibrium slice for planar or circular failure surfaces. It is useful for quick checks, sensitivity studies and teaching Eurocode 7 concepts, but it does not replace a full professional analysis using specialised software, detailed ground investigation data and engineering judgement.

Eurocode 7 Slope Stability Calculator

Quickly check slope stability according to Eurocode 7 using partial factors (DA1 / DA2 style) for drained or undrained conditions. Compute a global factor of safety and compare stabilising and destabilising design actions.

Educational tool – does not replace a full professional geotechnical design.

Geometry & Soil Parameters

Slope height H (m)

Slope angle β (deg)

Unit weight γ (kN/m³)

Effective cohesion c′ (kPa)

Effective friction angle φ′ (deg)

Average pore pressure u (kPa, optional)

Approximate average along slip surface. Set to 0 for dry slope.

Additional Actions on Slope Crest

Uniform surcharge q (kPa)

Permanent or variable load at crest (e.g. traffic, structure).

Horizontal seismic coefficient k_h (-)

Pseudo-static analysis: k_h·W acts downslope. Set 0 for static case.

Eurocode 7 Partial Factors

Defaults are typical illustrative values. Always check your National Annex.

γ_G – permanent actions

γ_Q – variable actions

γ_c – cohesion

γ_φ – tan φ′

Design approach style

Design Target

Target global factor of safety F_req

For comparison with computed F_s. Typical long-term slopes: 1.3–1.5.

How this Eurocode 7 slope stability calculator works

This tool implements a simplified limit equilibrium check for a planar slip surface through the toe of a homogeneous slope. It is intended for quick checks and teaching the concepts of Eurocode 7 partial factors, not for final design.

1. Geometry and slip surface

We idealise the slope as a triangular wedge of height \(H\) and slope angle \(\beta\). A planar slip surface is assumed to pass through the toe with length:

\( L \approx \dfrac{H}{\sin \beta} \)

The weight of the sliding wedge per metre out of plane is approximated as:

\( W \approx \dfrac{1}{2} \, \gamma \, \dfrac{H^2}{\sin \beta} \)

2. Shear strength along the slip surface

Effective stress Mohr–Coulomb parameters are used:

\( \tau_r = c' + (\sigma_n - u)\,\tan \varphi' \)

\(c'\) – effective cohesion
\(\varphi'\) – effective friction angle
\(\sigma_n\) – average total normal stress on the slip surface
\(u\) – average pore water pressure along the slip surface

The average normal stress is approximated from the component of the wedge weight normal to the slip surface:

\( \sigma_n \approx \dfrac{W \cos \beta}{L} \)

3. Driving shear stress and factor of safety

The driving shear stress combines the downslope component of weight, any pseudo-static seismic action and crest surcharge:

\( \tau_d = \dfrac{W \sin \beta + k_h W + q H}{L} \)

where \(k_h\) is the horizontal seismic coefficient and \(q\) is the uniform surcharge at the crest.

The global factor of safety against sliding is then:

\( F_s = \dfrac{\tau_r}{\tau_d} \)

4. Eurocode 7 design check

Eurocode 7 does not use a single global factor of safety, but partial factors on actions and material properties. In this simplified tool we compute:

Characteristic stabilising effect \(R_k = \tau_r L\)
Characteristic destabilising effect \(E_k = \tau_d L\)

Then we apply partial factors to obtain design values:

\( c_d = \dfrac{c'}{\gamma_c}, \quad \tan \varphi_d = \dfrac{\tan \varphi'}{\gamma_\varphi} \)

and:

\( R_d = c_d L + (\sigma_n - u)\tan \varphi_d \)
\( E_d = \gamma_G (W \sin \beta + k_h W) + \gamma_Q q H \)

The Eurocode 7 verification condition is:

\( R_d \geq E_d \quad \Rightarrow \quad \eta = \dfrac{R_d}{E_d} \geq 1.0 \)

The calculator reports the utilisation ratio \(\eta\) and whether the design check is passed or not.

Typical partial factors and design approaches

The numerical values of the partial factors and the choice of Design Approach (DA1, DA2 or DA3) are given in the National Annex. Common illustrative values (not binding) are:

Permanent actions: \( \gamma_G \approx 1.35 \)
Variable actions: \( \gamma_Q \approx 1.50 \)
Cohesion: \( \gamma_c \approx 1.25 \)
\(\tan \varphi'\): \( \gamma_\varphi \approx 1.25 \)

Design Approach 1 uses two separate combinations (actions factored vs materials factored), while Design Approach 2 applies factors to both actions and materials simultaneously. This tool mimics a DA2-style combination by default.

Interpreting the results

Global factor of safety \(F_s\) – useful for comparison with traditional methods and quick sensitivity checks.
Design ratio \(\eta = R_d / E_d\) – if \(\eta \ge 1.0\), the simplified Eurocode 7 check is satisfied.
Target factor of safety – you can set a required \(F_{req}\) to see whether the computed \(F_s\) is adequate.

For permanent slopes in drained conditions, many national practices aim for a back-calculated global factor of safety in the range 1.3–1.5, but you must always follow your local code and National Annex.

Limitations and good practice

Homogeneous soil and planar slip surface are assumed.
No multi-layered soils, complex pore pressure distributions or reinforcement are modelled.
Only a pseudo-static seismic coefficient is considered, not full dynamic analysis.
Results are per metre out of plane and are approximate.

For real projects, use specialised limit equilibrium or finite element software, detailed ground investigation data, and professional geotechnical engineering judgement. This calculator is best used for preliminary checks, teaching, and understanding the influence of Eurocode 7 partial factors.

Eurocode 7 slope stability – FAQ

Does Eurocode 7 specify a minimum factor of safety for slopes?

No. Eurocode 7 is based on partial factors rather than a single global factor of safety. The National Annex and project specifications govern the choice of partial factors and any implicit target safety level. When back-calculated, typical designs often correspond to global factors of safety around 1.3–1.5 for long-term slopes, but this is not a universal rule.

Can I use undrained shear strength (c_u) with this tool?

The current implementation is written in terms of effective stress parameters \(c'\) and \(\varphi'\). For purely undrained conditions you can approximate by setting \(\varphi' \approx 0\) and using an equivalent cohesion \(c' \approx c_u\), but this is a simplification. For rigorous undrained design, a dedicated undrained formulation should be used.

How should I choose the partial factors γ_G, γ_Q, γ_c, γ_φ?

Always follow your National Annex and project specifications. The default values in this calculator are illustrative only. Different countries adopt different sets of partial factors and may distinguish between persistent, transient and accidental design situations, as well as consequence classes.

Is a planar slip surface conservative compared to circular slips?

Not necessarily. The critical failure mechanism can be planar, circular or composite depending on soil stratigraphy, groundwater and geometry. Professional software typically searches for the most critical slip surface. This calculator uses a single idealised planar surface for simplicity, so it may be either conservative or unconservative compared to a full search.