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Plasticity, Liquidity and Consistency Indexes
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1. Plasticity Index:-

Plasticity Index (PI, OR $I_p$) is equal to difference between the liquid ($W_l$) nad plastic limiy ($W_p$)

Thus, $I_p=W_l-W_p$

Note:- When either $W_l$ or $W_p$ cannot be determined, then soil is non plastic (NP)

When $P.L.\gt L.L. \rightarrow$ Plasticity index is reported as a zero (or non negative)

2. Liquidity Index:-

The liquidity index ($I_L$ or LI ) of soil indicates the nearness of its water content to liquid limit ($L_l$)

Water content of the soil in natural condition.

$I_l=\frac{W-W_p}{I_p}\times 100$

• When soil is at plastic limit, the liquidity index is 0.
• It is also called as water plasticity ratio.

3. Consistency Index:-($I_c,CI$)

• Soil indicates nearness of water content of soil to its plastic limit.

• $I_c$ is zero at liquid limit

• $I_c$ is 100% $\rightarrow$ When soil is relatively strong as it is in a semi-solid stage

• It is also known as relative consistency.

$I_c=\frac{W_L-W}{I_p}\times 100$

4. Flow index:-

It is the slope of the flow curve obtained between the number of blows and the water content in Casagrande's method of determination of the liquid limit.

Thus, $I_f\frac{W_1-W_2}{log_{10}(\frac{N_2}{N_1})}$

where,

$N_1$:- No. of blows required at water content of $W_1$

$N_2$:-No. of blows required at water content of $W_2$

It is also written as in general formula,

$W=-I_f log_{10}(N)+C$  • Flat flow curve has relatively more (S.S.) shear strength compared to a steep flow curve ($n_1\lt n_2\lt n_3$)

Shear strength $\propto \frac{1}{I_f}$

Toughness Index:-

• Toughness Index $(I_t)$ is defined as ratio of the pasticity index $(I_p)$ to the flow Index $(I_f)$

Thus, $I_t=\frac{I_p}{I_f}$

• Toughness index of a soil is measure of shearing strength of soil at the plastic limit. This can be provided under.
• Let's assume the flow curve is straight line (L.L.) & (P.L.). As the shearing resistance of the soil is directly proportional to the number of blows in Casagrande's device,

$K S_l=N_l$----------------- (1)

$K S_p=N_p$----------------- (2)

where,

$N_l=$No. of blows at the liquid when shear strength is $S_l$

$N_p=$No. of blows at the plastic limit when shear strength is $S_p$

$K=$constant

• The value of toughness index is lies between 0 to 3.

Sensitivity and Thixotropy

Thixotropy:- Thixo (Touch) + Tropy (Change)

It means change which is occurs due to touch.

• Thixotropy of soil is of great practical importance in soil engineering

• Example,

When a pile is driven into the ground, the loss of strength occur due to disturbance caused. Thixotropy indicates the how much shear strength will be regained after pile has been driven and left in place for some time.

Sensitivity:- It measure loss of strength of soil like consistency

Water content $\rightarrow$ to check shear strength $\text{Compressive Stress}=\frac{load}{As}(\frac{N}{mm^2/km^2})$

$\text{Sensitivity}=q'_u\lt q_u$

$\text{Sensitivity of Soil}=\frac{\text{Compressive strength of soil in natural/undisturbed state }(q_u)}{\text{Compressive state of remoulded soil }(q'_u)}$

Use of Consistency Limit:-

The consistency limits are determined for remould soil. Since the actual behavior of soil can be depend on natural structure, the consistency limit do not give actual information about in site soil. They give at best a rough estimate & the behavior of in-site soil.

1. It has been observed that both plastic and liquid limits depend upon the type and amount of clay in a soil. However the plasticity index depends upon the amount of clay.
2. As the particle size decreases, both P.L. & L.L. increases. Therefore plasticity index increases at a rapid rate.
3. When silt is added to clay it become learner. It is L.L. & P.L. both decreases, but the former at a faster rate but the net effect is that the plasticity index decreases.
4. The plastic limit of soil increases if organic matter is added, without any significant increase in the liquid limit. Therefore, soil with high organic content have a low plasticity index.
5. The shrinkage index is directly proportional to the % of clay-size friction present in the soil.
6. The toughness index is a measure of the shearing strength of the soil at the plastic limit.
7. Sandy soil changes from the liquid state to semi-solid rather abruptly. These soil do not posses plasticity and are classified.

Reason for $q'_u$

1. This soil solid orientation alters $\rightarrow$ cohesion there is breakage of bonding between solids of soil.
2. Due to alteration in arrangement no force in orientation of water molecules absorbed layer.

Sensitivity:

• The breakage of bond between solid molecules of soil.
• Permenant loss
• Suppose, $q_u=100, q'_u=20$

$S_t=\frac{100}{20}=5$

loss of compression strength recorded=100-20=80

$60 N/mm^2$, $20 N/mm^2$

• Due to re-orientation of water molecules present in the adsorbed layer of soil.

• Temporary loss

• Completely recover with time

Sensitiity Soil Condition in sensitivity
1 less/normal/medium sensitive
2-4 sensitive soil
4-8 Highly sensitive
8-16 Quick soil(excavation soil become loss)
$\gt$16 16 times strength loose

Thixotropy:-

Over a period of time soil regains a part of its lossed strength on the account of rehabilitation of water molecules in adsorbed layer of soil solid. But, the strength loss on the account of permanent destruction of soil is not regained by soil. Example: If soil is high sensitive

1. $S_t=8 (\frac{16}{2})$ 14=10(Permannat)+4(temporary)
2. $S_t=6 (\frac{12}{2})$ 10=8(Permannat)+2(temporary)

High sensitive soils are always reflection high thixotropy value

Sensitivity$\rightarrow$Strength loss$\rightarrow$Temporary loss$\rightarrow$Regained strength$\rightarrow$Thixotropy strength