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The sum liquidity index + Consistency index is always equal to
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The sum of the liquidity index (ILтАЛ) and the consistency index (ICтАЛ) 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 (ILтАЛ) and the consistency index (ICтАЛ) of a soil is always equal to 1. This relationship arises from the mathematical definitions of these indices relative to the Atterberg limits.
ILтАЛ=IpтАЛwnтАЛтИТwpтАЛтАЛ тАФ Liquidity Index formula
ICтАЛ=IpтАЛwLтАЛтИТwnтАЛтАЛ тАФ Consistency Index formula
ILтАЛ+ICтАЛ=1 тАФ Fundamental identity
Consistency index (ICтАЛ) is defined as IPтАЛwLтАЛтИТwnтАЛтАЛ, where wLтАЛ is the liquid limit, wnтАЛ is the natural moisture content, and IPтАЛ is the plasticity index. Liquidity index (ILтАЛ) is defined as IPтАЛwnтАЛтИТwpтАЛтАЛ, where wpтАЛ is the plastic limit. Adding these two expressions: IPтАЛwLтАЛтИТwnтАЛтАЛ+IPтАЛwnтАЛтИТwpтАЛтАЛ=IPтАЛwLтАЛтИТwpтАЛтАЛ. Since IPтАЛ=wLтАЛтИТwpтАЛ, the sum simplifies to wLтАЛтИТwpтАЛwLтАЛтИТwpтАЛтАЛ=1.
Both indices quantify the state of cohesive soil based on its natural water content.
When wnтАЛ=wLтАЛ, ILтАЛ=1 and ICтАЛ=0.
When wnтАЛ=wpтАЛ, ILтАЛ=0 and ICтАЛ=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 (ILтАЛ>1) to solid state (ICтАЛ>1).
Option B is correct because the algebraic sum of the numerators (wnтАЛтИТwpтАЛ+wLтАЛтИТwnтАЛ) exactly equals the denominator (wLтАЛтИТwpтАЛ).
B is correct тАФ The sum of the liquidity index and the consistency index is always equal to 1, derived from the identity (wLтАЛтИТwnтАЛ+wnтАЛтИТwpтАЛ)/(wLтАЛтИТwpтАЛ)=1.
Always verify if the soil is plastic before applying these indices; these concepts are irrelevant for sands (where IpтАЛ=0).
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