GEO-31

Overconsolidation ratio

OCR = σ′p / σ′v0. Preconsolidation over present effective overburden.

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ConsolidationCasagrande

Governing equation

\mathrm{OCR}=\sigma'_p/\sigma'_{v0}

$\sigma'_{v0} \in \left[10, 400\right]$

where

\sigma'_p: Preconsolidation (kPa)
\sigma'_{v0}: Present effective (kPa)
OCR: OCR (—)

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.

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①

Governing law — red

\mathrm{OCR}=\sigma'_p/\sigma'_{v0}

$\sigma'_{v0} \in \left[10, 400\right]$

$\sigma'_{v0} = 10$ $OCR = 18$

Along the curve

②

Domain of the variable — blue

\sigma'_{v0}_{\min} = 10,\quad \sigma'_{v0}_{\max} = 400

$\sigma'_{v0} \in \left[10, 400\right]$

$\sigma'_{v0} = 10$ $\sigma'_{v0} = 10$

Along the curve

③

Response curve — green

\mathrm{OCR}=\sigma'_p/\sigma'_{v0}

$\sigma'_{v0} \in \left[10, 400\right]$

$\sigma'_{v0} = 10$ $OCR = 18$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}OCR}{\mathrm{d}\sigma'_{v0}}

$\sigma'_{v0} \in \left[10, 400\right]$

$\sigma'_{v0} = 12.45$ $OCR^{\prime} = -1.208$

Along the curve

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-31 — Overconsolidation ratio) is the form associated with Casagrande. Working symbols: $\sigma'_p$ , $\sigma'_{v0}$ $\rightarrow$ $OCR$ . Casagrande's construction on the e–log σ′ curve picks σ′p. OCR > 1 means the clay remembers a heavier past.

Purpose

Purpose: compute

OCR

from

\sigma'_p

\sigma'_{v0}

in Geotechnical engineering via

\mathrm{OCR}=\sigma'_p/\sigma'_{v0}

OCR = σ′p / σ′v0. Preconsolidation over present effective overburden. 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

\sigma'_p = 180.000\,\mathrm{kPa}

\sigma'_{v0} = 80.000\,\mathrm{kPa}

, the governing relation

\mathrm{OCR}=\sigma'_p/\sigma'_{v0}

yields

OCR = 2.25\,\mathrm{—}

. A yield point on a compression curve, a ratio. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Preconsolidation \sigma'_p180 kPaPresent effective \sigma'_{v0}80 kPa

Outputs

OCR OCR2.25 —

Reading speed

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Narration of this film

A yield point on a compression curve, a ratio.

Casagrande's construction on the e–log σ′ curve picks σ′p. OCR > 1 means the clay remembers a heavier past.

Reading speed

Watch on YouTube