What does at-rest earth pressure mean?

At-rest earth pressure (K0) is the ratio of horizontal effective stress to vertical effective stress when the wall undergoes zero lateral strain or movement. It applies to rigid, restrained structures such as braced basement walls and unyielding abutments.

When is Jaky's formula valid?

Jaky (1944) formulated K0 ≈ 1 - sin(φ') for normally consolidated, level-ground cohesionless deposits. It provides an industry-standard estimate for free-draining granular backfill placed without excessive compaction energy.

How does overconsolidation alter K0?

Overconsolidated soils retain horizontal stress from previous overburden loads. Mayne & Kulhawy (1982) formulated K0 = (1 - sin φ') · OCR^sin(φ'). For heavily overconsolidated soils, K0 can exceed 1.0.

What is Equivalent Fluid Pressure (EFP)?

EFP equals K0 · γ (expressed in kN/m³ or pcf). It represents the equivalent unit weight of a fluid producing the same triangular pressure distribution as the soil self-weight component, facilitating comparison with prescriptive code minimums.

Does this calculation include groundwater or hydrostatic pressure?

No. This model assumes a fully drained backfill with no pore water pressure. If groundwater is present, effective vertical stress, buoyant soil unit weight, and hydrostatic water pressure (62.4 pcf or 9.81 kN/m³) must be evaluated separately.

Does this tool calculate global wall stability factors of safety?

No. Full stability evaluation requires wall foundation dimensions, concrete self-weight, toe/heel sizing, keyways, sliding interface friction, and factored load combinations per design codes.

At-Rest Earth Pressure Calculator

Compute K0 via Jaky or Mayne-Kulhawy OCR formulations, lateral stress distribution, total horizontal thrust, base moment, and equivalent fluid pressure.

Soil & Wall Parameters

K0 Method

K0 = 1 − sin(φ′) — normally consolidated backfill.

Units:

Effective Friction Angle φ′ (degrees)

Valid range: 1.0° to 89.0° (typical granular soils: 28°–40°).

Soil Unit Weight γ (kN/m³)

Moist/total unit weight of backfill soil.

Wall Height H (m)

Uniform Surcharge q (kPa) (optional)

Uniform surcharge applied at ground surface.

Coefficient K0

—

dimensionless

Total Thrust (P_total)

—

kN/m

Base Moment (M_base)

—

kN·m/m

Equiv. Fluid Pressure

—

kN/m³ (EFP)

Lateral Pressure Profile

Lateral stress (kPa)

Depth Station	Soil Stress (σ_s)	Surcharge Stress (σ_q)	Total Stress (σ_h)

Thrust & Base Moment Breakdown (per unit width)

Soil Self-Weight Component (P_soil) ½ · K0 · γ · H² acting at H/3 from base

— —

Surcharge Component (P_q) K0 · q · H acting at H/2 from base

— —

Total Resultant Lateral Thrust (P_total) Base Overturning Moment (M_base = ∑ P_i × y_i)

— —

Soil thrust acts at — from wall base (y = H/3).

Surcharge thrust acts at — from wall base (y = H/2).

Combined resultant acts at — from wall base (ȳ).

Engineering Model Scope & Limitations

Rigid At-Rest Assumption: Applies strictly to unyielding walls with zero horizontal strain. Yielding cantilever walls develop lower active pressures (Ka).
Drained Soil Only: Assumes a homogeneous, level backfill, a vertical wall, and no groundwater table. Saturated backfills require submerged unit weight (γ′ = γ_sat − γ_w) and hydrostatic water pressure added separately.
Compaction Induced Stresses: Heavy vibratory rolling equipment behind rigid walls can induce residual lateral pressures exceeding theoretical K0, particularly in upper backfill zones.
EFP Benchmark: Equivalent Fluid Pressure (EFP = K0 × γ) is displayed for comparison with building code minimum equivalent fluid densities (e.g. IBC Table 1610.1). It does not by itself establish full structural code compliance.

Engineering references: FHWA GEC 6, FHWA NHI-06-089, and USACE EM 1110-2-2502.

Summary

Compute K0 via Jaky or Mayne-Kulhawy OCR formulations, lateral stress distribution, total horizontal thrust, base moment, and equivalent fluid pressure.

How it works

Select the calculation method: Jaky (normally consolidated) or Mayne & Kulhawy (overconsolidated).
Enter the soil effective internal friction angle (φ') in degrees.
If using the overconsolidated method, enter the overconsolidation ratio (OCR ≥ 1.0).
Enter the moist/total soil unit weight (γ) and wall height (H) in SI or Imperial units.
Optionally specify a uniform surcharge pressure (q) on the level ground surface.
The calculator updates K0, resultant horizontal thrust, base moment, equivalent fluid pressure, and the depth station schedule.

Use cases

Designing basement retaining walls and restrained bridge abutments with no lateral yield.
Evaluating horizontal thrust and stem base moments for cantilever or propped retaining elements.
Comparing calculated at-rest equivalent fluid pressure against code minimum fluid density benchmarks.
Assessing overconsolidation ratio (OCR) impact on lateral earth pressure in preloaded deposits.
Coursework and professional geotechnical verification checks before detailed finite-element analysis.

Frequently Asked Questions

Last updated: 2026-09-22 · Reviewed by Nham Vu