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GEO-24

Jaky at-rest K0

K0 = (1 − sin φ′) OCR^{sin φ′}. Jaky for NC sand, Brooker–Ireland OCR lift.

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Earth pressureJaky 1944

Governing equation

K0=(1−sin⁡φ′) OCRsin⁡φ′K_0=(1-\sin\varphi')\,\mathrm{OCR}^{\sin\varphi'}

OCR∈[1,16]OCR \in \left[1, 16\right]

where

\varphi'
Friction angle (°)
OCR
OCR (—)
K_0
At-rest coefficient (—)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

GEO-24 · bearing
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①

Governing law — red

K0=(1−sin⁡φ′) OCRsin⁡φ′K_0=(1-\sin\varphi')\,\mathrm{OCR}^{\sin\varphi'}

OCR∈[1,16]OCR \in \left[1, 16\right]

OCR=1OCR = 1K0=0.47K_0 = 0.47

②

Domain of the variable — blue

OCRmin⁡=1,OCRmax⁡=16OCR_{\min} = 1,\quad OCR_{\max} = 16

OCR∈[1,16]OCR \in \left[1, 16\right]

OCR=1OCR = 1OCR=1OCR = 1

③

Response curve — green

K0=(1−sin⁡φ′) OCRsin⁡φ′K_0=(1-\sin\varphi')\,\mathrm{OCR}^{\sin\varphi'}

OCR∈[1,16]OCR \in \left[1, 16\right]

OCR=1OCR = 1K0=0.47K_0 = 0.47

④

Rate of change — amber

dK0dOCR\frac{\mathrm{d}K_0}{\mathrm{d}OCR}

OCR∈[1,16]OCR \in \left[1, 16\right]

OCR=1.094OCR = 1.094K0′=0.239K_0^{\prime} = 0.239

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-24 — Jaky at-rest K0) is the form associated with Jaky 1944. Working symbols: φ′\varphi', OCROCR →\rightarrow K0K_0. A normally consolidated sediment remembers the one-dimensional strain path. Overconsolidation raises K0.

Purpose

Purpose: compute K0K_0 from φ′\varphi', OCROCR in Geotechnical engineering via K0=(1−sin⁡φ′) OCRsin⁡φ′K_0=(1-\sin\varphi')\,\mathrm{OCR}^{\sin\varphi'} K0 = (1 − sin φ′) OCR^{sin φ′}. Jaky for NC sand, Brooker–Ireland OCR lift. 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}}, OCR=1.000 —OCR = 1.000\,\mathrm{—}, the governing relation K0=(1−sin⁡φ′) OCRsin⁡φ′K_0=(1-\sin\varphi')\,\mathrm{OCR}^{\sin\varphi'} yields K0=0.470 —K_0 = 0.470\,\mathrm{—}. A level ground, a K0 arrow between Ka and Kp. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • At-rest coefficient K_00.470 —
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GEO-24 · bearing
00:0 / 00:08

Narration of this film

A level ground, a K0 arrow between Ka and Kp.

A normally consolidated sediment remembers the one-dimensional strain path. Overconsolidation raises K0.

Reading speed

Watch on YouTube