Active Earth Pressure

How to Use the Calculator

1. Enter the Retained soil height (H) — the vertical height of soil behind the wall — and select its unit (m or ft).
2. Enter the Soil unit weight (γ) of the backfill and choose kN/m³ or lb/ft³. Typical sands fall in 15–20 kN/m³, clays in 16–21 kN/m³.
3. Enter the Internal friction angle (φ) in degrees. Loose sand is roughly 28–32°, dense sand 35–42°, gravel 35–45°.
4. Read the Active earth-pressure coefficient (Ka) and the Resultant lateral force per unit wall length (Pa), together with the point of application and the base pressure.

What Is Active Earth Pressure?

Active earth pressure is the lateral push that a soil mass exerts on a retaining structure when the structure moves or rotates slightly away from the soil, allowing the soil to expand and mobilize its shear strength. This outward movement — typically only a few millimetres to a few hundredths of the wall height — is enough for a wedge of soil behind the wall to reach a limiting, "active" failure state. The word "active" refers to the soil actively pushing on the wall, and it is the smallest of the three classical lateral pressure states: active, at-rest and passive.

Rankine's theory derives the active pressure coefficient purely from the soil's friction angle, assuming the wall face is vertical and frictionless and the backfill surface is horizontal. Under these conditions the soil fails along a plane inclined at \(45^\circ + \varphi/2\) to the horizontal, and the ratio of horizontal to vertical stress at every depth equals \(K_a\). A lower friction angle gives a larger \(K_a\): at \(\varphi = 30^\circ\), \(K_a \approx 0.33\); at \(\varphi = 40^\circ\) it drops to about 0.22, which is why well-graded, freely draining granular backfill is strongly preferred behind walls.

The result \(P_a\) is a force per metre run of wall (kN/m), obtained by integrating the triangular pressure diagram over the height. It acts horizontally at one third of the wall height above the base — the centroid of the triangle. In stability checks this force drives sliding and overturning, so it is the key input for sizing the wall, its footing bearing pressure and any reinforcement. For the structural design of the wall stem as a bending member, the triangular pressure distribution can be treated like a linearly varying load on a cantilever; see the uniformly loaded beam calculator for the general bending relationships.

Assumptions, Limitations and Practical Tips

• Granular backfill only. Rankine's \(K_a\) assumes a cohesionless soil (\(c = 0\)). For cohesive soils, apparent cohesion temporarily reduces active pressure but can be unreliable long-term — use total-stress or more advanced analysis for clays.
• Vertical, frictionless wall and level backfill. Wall friction, a battered face or a sloping ground surface change \(K_a\); Coulomb's theory or the sloping-backfill form of Rankine's coefficient should be used instead.
• No water, no surcharge. Hydrostatic pressure behind the wall (e.g. from a blocked drain) adds \(\tfrac{1}{2}\gamma_w H^2\) and often governs the design — always provide drainage. Uniform surcharge \(q\) adds an extra \(K_a\, q\) to the pressure at every depth.
• Wall must be free to yield. Active pressure only develops if the wall can move outward a little. Rigid, braced or basement walls that cannot yield should be designed for the larger at-rest pressure.
• Check the base. The base pressure \(\gamma H K_a\) and the point of application \(H/3\) are what you need for overturning and sliding checks; the footing dimensions then determine the bearing pressure under the base.
• Seismic action. Under earthquake loading the lateral demand increases; the Mononobe–Okabe method extends this coefficient approach to pseudo-static conditions.

Once the wall geometry is fixed, reinforcement detailing follows: estimate the required steel area from the bending moment and check bar layout with the rebar spacing and count calculator and the rebar weight calculator.