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GEO-09

Jáky at-rest coefficient

K0 = 1 − sin φ' for normally consolidated sand and clay.

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Earth pressureJáky 1944Eurocode 7

Governing equation

K0=1−sin⁡φ′,σh′=K0σv′K_0 = 1-\sin\varphi',\quad \sigma'_h = K_0\sigma'_v

φ′∈[10,45]\varphi' \in \left[10, 45\right]

where

\varphi'
Effective friction (°)
\sigma'_v
Vertical effective stress (kPa)
K_0
At-rest coefficient (—)
\sigma'_h
Horizontal effective stress (kPa)

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①

Governing law — red

K0=1−sin⁡φ′,σh′=K0σv′K_0 = 1-\sin\varphi',\quad \sigma'_h = K_0\sigma'_v

φ′∈[10,45]\varphi' \in \left[10, 45\right]

φ′=10\varphi' = 10K0=0.826K_0 = 0.826

②

Domain of the variable — blue

φmin⁡′=10,φmax⁡′=45\varphi'_{\min} = 10,\quad \varphi'_{\max} = 45

φ′∈[10,45]\varphi' \in \left[10, 45\right]

φ′=10\varphi' = 10φ′=10\varphi' = 10

③

Response curve — green

K0=1−sin⁡φ′,σh′=K0σv′K_0 = 1-\sin\varphi',\quad \sigma'_h = K_0\sigma'_v

φ′∈[10,45]\varphi' \in \left[10, 45\right]

φ′=10\varphi' = 10K0=0.826K_0 = 0.826

④

Rate of change — amber

dK0dφ′\frac{\mathrm{d}K_0}{\mathrm{d}\varphi'}

φ′∈[10,45]\varphi' \in \left[10, 45\right]

φ′=10.22\varphi' = 10.22K0′=−0.017K_0^{\prime} = -0.017

Lecture brief

Historical brief

Soil mechanics became a quantitative laboratory after Karl von Terzaghi’s 1925–1943 work on effective stress, consolidation and bearing. These sheets still size shallow foundations, retaining walls, piles and drainage in SI. This sheet (GEO-09 — Jáky at-rest coefficient) is the form associated with Jáky 1944 · Eurocode 7. Working symbols: φ′\varphi', σv′\sigma'_v →\rightarrow K0K_0, σh′\sigma'_h. Jáky derived K0 from the stress state in a wedge-shaped sand pile; the compact field form 1−sinφ' is used worldwide for NC soils.

Purpose

Purpose: compute K0K_0, σh′\sigma'_h from φ′\varphi', σv′\sigma'_v in Geotechnical engineering via K0=1−sin⁡φ′,σh′=K0σv′K_0 = 1-\sin\varphi',\quad \sigma'_h = K_0\sigma'_v K0 = 1 − sin φ' for normally consolidated sand and clay. Use it when a real geotechnical engineering question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given φ′=32.000 ∘\varphi' = 32.000\,\mathrm{^{\circ}}, σv′=100.000 kPa\sigma'_v = 100.000\,\mathrm{kPa}, the governing relation K0=1−sin⁡φ′,σh′=K0σv′K_0 = 1-\sin\varphi',\quad \sigma'_h = K_0\sigma'_v yields K0=0.470 —K_0 = 0.470\,\mathrm{—}, σh′=47.008 kPa\sigma'_h = 47.008\,\mathrm{kPa}. Normally consolidated, no overconsolidation OCR correction. Move a slider: the numbers are this situation, not a canned story.

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Inputs

Outputs

  • At-rest coefficient K_00.470 —
  • Horizontal effective stress \sigma'_h47.008 kPa
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Narration of this film

Normally consolidated, no overconsolidation OCR correction.

Jáky derived K0 from the stress state in a wedge-shaped sand pile; the compact field form 1−sinφ' is used worldwide for NC soils.

Reading speed

Watch on YouTube