Lateral Earth Pressure Calculator

What is lateral earth pressure?

Lateral earth pressure is the horizontal pressure that retained soil exerts on a structure such as a retaining wall, basement wall, sheet pile, or shoring system. It depends on the unit weight of the soil, its drained friction angle φ and cohesion c, the wall geometry (height, batter, wall friction), the slope of the backfill, the position of the groundwater table, and any surcharge loads applied at the surface.

What is the difference between active and at-rest pressure?

At-rest pressure is the in-situ horizontal stress before any wall movement; it is computed from the Jaky (1944) relationship K₀ = 1 − sin φ. Active pressure develops when the wall yields slightly away from the soil and the retained mass mobilizes its full shear strength — this is the smallest horizontal pressure the soil can sustain. Both are loadings on the back of the wall. The calculator reports active and at-rest values side by side so the engineer can choose the appropriate design load case (e.g. flexible vs. rigid wall).

When should I use Rankine vs. Coulomb?

Rankine (1857) assumes a vertical, frictionless wall and yields a closed-form solution in terms of φ and backfill slope β. It is the standard choice for near-vertical walls with no significant wall friction and is the basis for many code-prescribed simplifications. Coulomb (1776) accepts arbitrary wall batter α, wall friction δ, and backfill slope β, and is preferred when any of those are non-trivial (typical retaining-wall design with concrete-on-soil interface friction per AASHTO LRFD Table 3.11.5.3-1). Both methods are computed here against the same soil profile so you can compare.

How is groundwater handled?

The water-table elevation behind the wall is entered directly. Pore pressure u is computed hydrostatically from that water table; effective vertical stress σ'_v = σ_v − u governs the earth-pressure coefficient calculation. Below the water table, soil unit weight is taken from the saturated value γ_sat; above, the dry value γ_dry is used.

How are surcharge loads applied?

A uniform surcharge q is added to the vertical stress at the surface; its lateral effect on the wall is K × q in each layer. A strip surcharge uses the rigid-wall, doubled-Boussinesq form (NAVFAC DM-7.02 Figure 9; AASHTO LRFD C3.11.6.2-1): σ_h = (2q/π)(β − sin β cos 2α). The factor of 2 accounts for the assumed rigid, non-yielding wall boundary that prevents horizontal strain on the wall side.

How are c-φ (cohesive) soils treated?

Cohesion is included via the Bell (1915) correction for active pressure: σ_a = K_a σ'_v − 2c√K_a. The active diagram is truncated at the tension crack depth z_c = 2c/(γ√K_a). Coulomb theory was originally derived for cohesionless soils; for c-φ backfills Rankine is generally preferred.

Why is at-rest reported with no user override?

K₀ is computed from Jaky's (1944) relationship only. More elaborate K₀ formulations (e.g. Mayne & Kulhawy for over-consolidated soils) require an over-consolidation ratio that is not part of the calculator's input set. The reported K₀ is intentionally simple and conservative for drained, normally consolidated conditions; if your design requires an OCR-based K₀ it should be computed and applied separately.

Can I export a PDF report?

Yes — and the report is fully white-label. Every calculation produces a PDF report containing the inputs, governing assumptions and references, the full results tables, the surviving plots, and the engineering diagrams (geometry plus a combined pressure / resultant-force diagram). Supply your company name, your logo, and your project metadata and the report is generated under your own branding with no watermark and no charge.

Is this a substitute for a geotechnical investigation?

No. The calculator's output is a preliminary analysis based on the inputs you provide. Project-specific soil properties from a geotechnical investigation, slope-stability checks, sliding/overturning/bearing checks, structural design of the wall section, and seismic (Mononobe-Okabe) earth pressures are all outside the scope of this tool. Treat the output as a starting point for those analyses, not as the final design.

What are the limitations of this calculator?

The calculator computes static, drained, plane-strain (per linear foot or meter of wall) lateral earth pressures from classical theory. The following modeling assumptions and scope boundaries should be understood before relying on the output:

• Active and at-rest only. Passive resistance is not computed. If passive design is required (embedded sheet piles, toe keys, anchor blocks), it must be performed separately.
• Static loading. Seismic earth pressures (Mononobe-Okabe / pseudo-static), liquefaction, and dynamic loadings (vibration, blast, impact) are not modeled.
• Hydrostatic groundwater behind the wall only. Pore pressure is taken from the hydrostatic water-table elevation entered for the back of the wall. Seepage gradients, drainage details, perched water, capillary effects, and any water in front of the wall are not modeled.
• Drained effective-stress analysis. Inputs are drained φ and effective cohesion c. Undrained (φ = 0) analyses are not directly supported; an undrained shear strength can be entered as the cohesion field, but the result must be interpreted as total-stress and reviewed accordingly.
• Coulomb with cohesion is approximate. Coulomb wedge theory was originally derived for cohesionless soils; the Bell −2c√K_a correction is layered onto Coulomb here for convenience. For c–φ backfills Rankine is generally preferred.
• K₀ from Jaky only. Over-consolidation effects (e.g. Mayne & Kulhawy OCR-based formulations) are not modeled. The reported at-rest value is a normally-consolidated, drained-strength estimate.
• Strip surcharges assume a rigid, non-yielding wall. Lateral pressures from strip loads use the doubled-Boussinesq form (NAVFAC DM-7.02 Fig. 9; AASHTO LRFD C3.11.6.2-1). Flexible / yielding walls will see lower magnitudes; the calculator is conservative for that case.
• Layer idealization. Each layer is treated as homogeneous and isotropic with constant γ, φ, and c. Anisotropy, strain-softening, creep, swell, frost action, and spatial variability are not represented.
• Kinematic limits. When the backfill slope β meets or exceeds the layer friction angle φ, the active wedge is at or past failure. The calculator emits a warning and either clamps β to φ (Rankine) or zeros K_a (Coulomb); these edge cases require engineering judgment, not blind reliance on the reported number.
• Plane strain. Results are reported per linear foot (or meter) of wall. Three-dimensional effects (corners, finite wall length, transverse bracing, relieving shelves, tiebacks, soil nails) are not captured.