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Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
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Write the Density index formula.
(emax−emin)/(emin−emax)
(emax−e)/(emin−e)
(emax−e)/(emax−emin)
(emax−emin)/(emax−e)
(emax−e)/(emax−emin)
The Density Index (ID), also known as the Relative Density (Dr), is a measure used to quantify the degree of compactness of cohesionless (granular) soils. It expresses the current void ratio of the soil relative to its loosest and densest possible states.
The Density Index (ID), also known as the Relative Density (Dr), is a measure used to quantify the degree of compactness of cohesionless (granular) soils. It expresses the current void ratio of the soil relative to its loosest and densest possible states.
ID=emax−eminemax−e — Calculation of Density Index
ID=γdmax−γdminγd−γdmin×γdγdmax — Alternate formula using dry unit weights
In cohesionless soils, the stability and shear strength depend on the arrangement of particles. ID compares the existing void ratio (e) with the minimum (emin) and maximum (emax) void ratios. A value of 0 implies the soil is at its loosest state, while a value of 1 (or 100%) implies the soil is at its densest state.
Used specifically for cohesionless, granular soils (sands, gravels).
Range of ID: 0≤ID≤1.
Classifies soil as very loose (<15%), loose (15−35%), medium (35−65%), dense (65−85%), or very dense (>85%).
Provides a reliable indicator of the strength and compressibility of granular deposits.
Essential for evaluating the liquefaction potential of sands under seismic loading.
Not applicable to cohesive (clayey) soils.
Difficulty in accurately determining emin and emax in laboratory settings.
Foundation engineering design for granular soil sites.
Assessing stability of slopes and embankments composed of granular materials.
In terms of unit weights, ID can be expressed via dry density γd, where γdmax and γdmin are the maximum and minimum dry unit weights respectively.
Option A is inverted, Option B uses incorrect variables in the denominator, and Option D is the reciprocal.
C is correct — The density index is defined as the ratio of the difference between the maximum void ratio and the natural void ratio to the range of void ratios (difference between maximum and minimum).
Always verify if the question asks for void ratio (e) or dry unit weight (γd); they have inverse relationships in the ID formula structure.