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Examoogle • User • info@examoogle.com • EE-2024-8821
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The sum liquidity index + Consistency index is always equal to
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1
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1
The sum of the liquidity index (IL) and the consistency index (IC) of a soil is always equal to 1. This relationship arises from the mathematical definitions of these indices relative to the Atterberg limits.
The sum of the liquidity index (IL) and the consistency index (IC) of a soil is always equal to 1. This relationship arises from the mathematical definitions of these indices relative to the Atterberg limits.
IL=Ipwn−wp — Liquidity Index formula
IC=IpwL−wn — Consistency Index formula
IL+IC=1 — Fundamental identity
Consistency index (IC) is defined as IPwL−wn, where wL is the liquid limit, wn is the natural moisture content, and IP is the plasticity index. Liquidity index (IL) is defined as IPwn−wp, where wp is the plastic limit. Adding these two expressions: IPwL−wn+IPwn−wp=IPwL−wp. Since IP=wL−wp, the sum simplifies to wL−wpwL−wp=1.
Both indices quantify the state of cohesive soil based on its natural water content.
When wn=wL, IL=1 and IC=0.
When wn=wp, IL=0 and IC=1.
These indices are only applicable to fine-grained (cohesive) soils.
Provides immediate insight into the physical state of soil relative to its limits.
Standardized index system used globally for geotechnical site characterization.
Does not account for non-cohesive or granular soils where plasticity is absent.
Highly dependent on the accuracy of liquid and plastic limit laboratory testing.
Predicting soil strength, compressibility, and sensitivity.
Used in highway and foundation engineering for classifying clays.
The indices reflect the range of consistency from liquid state (IL>1) to solid state (IC>1).
Option B is correct because the algebraic sum of the numerators (wn−wp+wL−wn) exactly equals the denominator (wL−wp).
B is correct — The sum of the liquidity index and the consistency index is always equal to 1, derived from the identity (wL−wn+wn−wp)/(wL−wp)=1.
Always verify if the soil is plastic before applying these indices; these concepts are irrelevant for sands (where Ip=0).