What is geotechnical engineering and why is it important in the UK?

Geotechnical engineering assesses ground conditions to design safe foundations, slopes, and retaining structures. In the UK, variable geology and historical land use make thorough site investigation critical to avoid costly failures and ensure compliance with Eurocode 7.

What standards govern geotechnical work in the United Kingdom?

Geotechnical design in the UK follows Eurocode 7 (BS EN 1997) and its National Annex. Ground investigations comply with BS 5930, and SPT testing adheres to ASTM D1586. These standards ensure consistent, reliable results across the country.

How does your firm approach slope stability analysis?

Our firm uses limit equilibrium and finite element methods to evaluate slope stability, considering soil shear strength, groundwater, and surcharge loads. We apply partial factors per Eurocode 7 to deliver safe, economical designs for natural and engineered slopes.

Earth Pressure Calculator — Rankine Theory

Rankine's theory (1857) is the classic formulation for calculating the earth pressures that a soil exerts on retaining structures. This calculator provides the active (Ka) and passive (Kp) coefficients, the total thrust, and the moment at the base of the wall, considering the height of the backfill, the surface slope (β), cohesion (c), and the presence of a water table. It is the starting point for any retaining wall design in building construction, roadworks, and underground works.

What is it and when is it applied?

Rankine assumes the wall is vertical, the backfill has a planar surface inclined at β to the horizontal, there is no friction between the wall and the soil, and the failure state is reached by soil yielding. Under these assumptions, it provides Ka (active thrust, when the wall yields) and Kp (passive thrust, when the wall pushes against the soil). It is applied to gravity walls, cantilever walls with loose backfill, bridge abutments with uniform backfill, and basement walls with horizontal backfill. For wall inclination other than vertical or significant soil-wall friction, Coulomb is used.

Applied Formulas

Active thrust (horizontal backfill, cohesionless):

Ka = tan²(45° − φ/2) = (1 − sin φ) / (1 + sin φ)

Passive thrust: Kp = tan²(45° + φ/2) = 1/Ka

Rankine with slope β in the backfill:

Ka = cos β · (cos β − √(cos²β − cos²φ)) / (cos β + √(cos²β − cos²φ))

Total thrust (dry backfill, height H):

Pa = 0.5 · γ · H² · Ka; Pp = 0.5 · γ · H² · Kp

With cohesion: active thrust σa = γ·z·Ka − 2·c·√Ka (tension crack up to zc = 2c / (γ·√Ka))

With water table at depth d: below d, replace γ with γ' = γsat − γw and add hydrostatic pressure u = γw · (z − d)

Calculate online

Enter φ, γ and H to obtain Ka, Kp, active/passive thrusts and FS verification for overturning/sliding. The applied FS comply with the standard of the country selected on the right.

FS for overturning and sliding applied according to the standard of the selected country.

Calculation example

Input data — basement retaining wall, building in urban residential area
Parameter	Value
Wall height H	4.0 m
Unit weight γ	19 kN/m³
Friction angle φ	32°
Cohesion c	0
Surface slope β	0° (horizontal)
Water table	Not detected
Surcharge q at crest	10 kPa (pedestrian traffic)

With φ = 32°: Ka = (1 − sin 32°) / (1 + sin 32°) = (1 − 0.530) / (1 + 0.530) = 0.470 / 1.530 = 0.307. Kp = 1/0.307 = 3.26. Thrust from self-weight of backfill: Pa1 = 0.5 · 19 · 4² · 0.307 = 0.5 · 19 · 16 · 0.307 = 46.7 kN/m. Thrust from surcharge (equivalent to a uniform increase σ = q·Ka over the height): Pa2 = q · Ka · H = 10 · 0.307 · 4 = 12.3 kN/m. Total thrust Pa = 46.7 + 12.3 = 59.0 kN/m. Point of application: Pa1 acts at H/3 = 1.33 m from the base; Pa2 acts at H/2 = 2.0 m. Moment at the base M = 46.7 · 1.33 + 12.3 · 2.0 = 62.1 + 24.6 = 86.7 kN·m/m.

Result: Ka = 0.307 · Kp = 3.26 · Pa = 59.0 kN/m · M = 86.7 kN·m/m.

Interpretation of results

The wall must be designed to resist Pa = 59 kN/m in the horizontal direction and M = 87 kN·m/m of overturning, in addition to verifying sliding and bearing capacity. The passive thrust Kp is a reserve for sliding resistance but is usually limited to 1/2 or 1/3 of its theoretical value because it requires large displacements to be fully mobilised. In seismic zones (BS EN 1998-5), the Mononobe-Okabe component is added.

Reference standards

BS EN 1997-1 — Geotechnical design — Part 1: General rules
Rankine, W.J.M. (1857). On the stability of loose earth
BS EN 1997-1 (Eurocode 7) — Geotechnical design
BS EN 1997-1 — Geotechnical design — Part 1: General rules
BS EN 1998-5 — Design of structures for earthquake resistance — Part 5: Foundations, retaining structures and geotechnical aspects (for seismic thrust)

Frequently asked questions

When do I use Rankine and when Coulomb?

Rankine: vertical wall, inclined backfill β, no soil-wall friction. Coulomb: inclined wall, soil-wall friction δ ≠ 0, more general. In practice Coulomb is more realistic because wall-soil friction reduces active thrust by 5-15%. Rankine is conservative.

Can I use cohesion in active thrust?

Yes, but up to a depth zc the thrust is theoretically negative (tension). In practice this section is neglected because the soil cracks due to drying or seasonality. It is recommended to calculate thrust as if only γ·z·Ka from the surface, ignoring the relief from cohesion.

What about uniform surcharge at the crest?

A surcharge q is treated as a constant increase in vertical stress. Its contribution to thrust is q·Ka·H (linear with height) and acts at H/2 from the base. If the surcharge is strip or point, it is analysed with Boussinesq.

When are Ka and Kp fully mobilised?

Ka requires very small relative displacements of the order of 0.001·H. Kp requires much larger displacements (0.01-0.05·H) and therefore a reduction factor of 0.3-0.5 is used in wall design. In rigid structures (restrained basement walls at the top), design is with coefficient K0 (at rest) which is intermediate.