What is the at-rest earth pressure coefficient K0?

K0 is the ratio of horizontal to vertical effective stress, σ′h / σ′v, in soil that has not been allowed to strain sideways. It applies to rigid, restrained walls. By Jaky's formula, sands with φ′ = 30–40° give K0 ≈ 0.36–0.50; normally consolidated clays are typically 0.5–0.7, and heavily overconsolidated clays can exceed 1.

How do you calculate K0 with Jaky's formula?

K0 = 1 − sin φ′. For φ′ = 30°, K0 = 1 − 0.5 = 0.50; for φ′ = 35°, K0 = 1 − 0.574 = 0.426. Jaky (1944) is the simplified form of his original expression and applies to normally consolidated soil with a level ground surface.

How does overconsolidation change K0?

Mayne & Kulhawy (1982) give K0 = (1 − sin φ′)·OCR^sin φ′ for soil that has been unloaded. For φ′ = 30° and OCR = 4, K0 = 0.5 × 4^0.5 = 1.00. K0 cannot exceed the passive coefficient Kp = tan²(45° + φ′/2), because the soil would fail in passive shear first, so the calculator caps it there.

How is groundwater included in at-rest pressure?

Below the water table, use the buoyant unit weight γ′ = γsat − γw for the effective vertical stress, then add the full hydrostatic pressure u = γw·(z − zw). Example: H = 5 m, water at 2 m, γ = 18, γsat = 20 kN/m³, φ′ = 30° (K0 = 0.5). At the base, σ′v = 18 × 2 + 10.19 × 3 = 66.57 kPa, so σ′h = 33.29 kPa, u = 29.43 kPa and σh = 62.72 kPa. Fully drained, the base pressure would be 45 kPa, so the water adds about 40%, which is why wall drains matter.

Where does the resultant act on the wall?

For a triangular soil diagram the thrust ½·K0·γ·H² acts at H/3 above the base. A uniform surcharge adds K0·q·H at H/2. With a water table the diagram has a kink, so the tool integrates each segment and reports the combined line of action ȳ = ΣM / ΣP.

What is equivalent fluid pressure (EFP)?

EFP = K0·γ, the unit weight of a fluid that produces the same triangular pressure as the soil. Below a water table the equivalent value is K0·γ′ + γw. For φ′ = 30° and γ = 120 pcf, EFP = 60 pcf, a common at-rest value for basement walls in granular backfill.

When should I use at-rest instead of active pressure?

Use at-rest (K0) when the wall cannot rotate or slide enough to mobilise active pressure. A cantilever wall reaches active pressure after a top movement of roughly 0.001–0.004 H in sand. Basement walls tied to floor slabs, braced walls and stiff abutments stay near K0. Heavy compaction behind a rigid wall can push pressure above K0 near the top.

Does this tool check wall stability?

No. It gives the lateral load only. Sliding, overturning, bearing, wall bending and seismic increments (for example Mononobe–Okabe) need the full wall geometry and the governing design code's load factors.

At-Rest Earth Pressure Calculator

Get K0 = 1 − sin φ′ (Jaky) or (1 − sin φ′)·OCR^sin φ′ (Mayne & Kulhawy), then the lateral pressure diagram with surcharge and groundwater, total thrust, its line of action, base moment, EFP and a Ka / K0 / Kp comparison.

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.

Groundwater behind wall

Coefficient K0

—

dimensionless

Total Thrust (P_total)

—

kN/m

Base Moment (M_base)

—

kN·m/m

Equiv. Fluid Pressure

—

kN/m³ (EFP)

K0 compared with Rankine active and passive (level backfill, vertical wall)

Ka = tan²(45° − φ′/2)

—

K0 (this wall)

—

Kp = tan²(45° + φ′/2)

—

Lateral Pressure Profile

Lateral stress (kPa)

Depth Station	Soil Stress (σ_s)	Surcharge Stress (σ_q)	Water (u)	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).
Level, Homogeneous Backfill: Assumes one soil layer, a level ground surface, a vertical wall and hydrostatic (non-flowing) groundwater. Seepage, sloping backfill or layered soils need a separate analysis.
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.

K0 by friction angle and OCR, with Rankine Ka and Kp

K0 = (1 − sin φ′)·OCR^sin φ′ (OCR = 1 is Jaky). Ka = tan²(45° − φ′/2), Kp = tan²(45° + φ′/2) for a level backfill and a smooth vertical wall.

φ′	Ka	K0 (OCR 1)	OCR 2	OCR 4	OCR 8	Kp
25°	0.406	0.577	0.774	1.037	1.390	2.464
28°	0.361	0.531	0.735	1.017	1.408	2.770
30°	0.333	0.500	0.707	1.000	1.414	3.000
32°	0.307	0.470	0.679	0.980	1.415	3.255
34°	0.283	0.441	0.650	0.957	1.410	3.537
36°	0.260	0.412	0.620	0.931	1.399	3.852
38°	0.238	0.384	0.589	0.902	1.383	4.204
40°	0.217	0.357	0.558	0.871	1.360	4.599

Summary

This tool computes the at-rest lateral earth pressure coefficient K0 for walls that cannot move, such as basement walls, braced excavations and restrained abutments. It uses Jaky's formula K0 = 1 − sin φ′ for normally consolidated soil and the Mayne & Kulhawy (1982) relationship K0 = (1 − sin φ′)·OCR^sin φ′ for overconsolidated soil, capped at the Rankine passive coefficient Kp. The lateral stress at each depth is σh = K0·σ′v + u. σ′v uses the moist unit weight above the water table and the buoyant unit weight γsat − γw below it, and u = γw·(z − zw) is the hydrostatic water pressure, which acts in full on the wall. The tool integrates the diagram to give the soil, surcharge and water thrusts, the line of action, the base moment and the equivalent fluid pressure, and compares K0 with the Rankine active and passive coefficients.

How it works

Choose Jaky (normally consolidated) or Mayne & Kulhawy (overconsolidated, enter OCR ≥ 1).
Enter the effective friction angle φ′, the moist unit weight γ, the wall height H and any uniform surcharge q.
Tick "Groundwater behind wall" to enter the depth to the water table zw and the saturated unit weight γsat (γw = 9.81 kN/m³ or 62.4 pcf).
Vertical effective stress: σ′v = q + γ·z above the water table and q + γ·zw + (γsat − γw)·(z − zw) below it.
Lateral stress: σh = K0·σ′v + u, where u = γw·(z − zw) is the pore water pressure. The coefficient K0 applies only to effective stress, never to water pressure.
Each linear segment of the diagram is integrated to give thrust and moment about the base, reported per unit length of wall.

Use cases

Designing basement and foundation walls that are braced by floor slabs.
Checking restrained bridge abutments, culverts and integral-abutment walls.
Estimating extra lateral load when the groundwater table rises behind an undrained wall.
Showing how overconsolidation (OCR) raises K0 in preloaded or glacially overridden soils.
Comparing at-rest pressure with active and passive pressure for the same soil.
Coursework checks of lateral pressure diagrams, resultants and points of application.

Frequently Asked Questions

Last updated: 2026-10-10 · Reviewed by Nham Vu