1. PLASTICITY INDEX :- Plasticity index (PI or Ip) is equal the difference between the liquid (Wc) and plastic limit (Wp)

Thus,
Ip=W1-Wp

NOTE:- When either w1or wp cannot be determined,then soil is non-plastic (NP) When P.L > L.L -> Plasticity index is reported as zero (on non- negative)

1. LIQUIDITY INDEX :- The liquidity index of soil is indicated the nearness of its water content to liquid limit (IL) (iL or Li) $IL =\frac{W-Wp}{Ip} *100$

   Where W=Water content of the soil in natural condition.

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

3.CONSISTENCY INDEX :- (Ic,CI) - Soil indicate hearness of water control of soil to its plastic limit. - Ic is zero at liquid limit. - Ic is 100% When soil is relatively strong, as it is in semi solid stage. - It is also known as relative consistency.
$I_c$= $\frac{WL-W}{I_p}*100$

1. FLOW INDEX :- It is the slope of the flow curve obtained between the number of flow and the water content in casagrande's method of determination the liquid limit.

Thus , $ IF =\frac{ W1-W2}{log_1{}_0(N2/N1)}$
Where N1- no. of blows required of water content of $W_1$
N2- no. of blow required of water content of $W_2$.

It is also written in general formula, $W= -IFlog_1{}_0(N)+C$

• Flat flow curve has more relatively (S.S)
  Shear strength compared to a steep flow curve.
  ($n_1 \lt n_2 \lt n_3$)
  Sher strength x $\frac{1}{If}$

TOUGHNESS INDEX:-

• Toughness index (It) is defined as ration of the plasticity index (Ip) to the floe index (Ef). Thus, $It=\frac{Ip}{If}$

• Toughness index of the 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 a shearing resistance od soil is directly proportional to the number of blorosin Casagrande's device.
  $KS_l=N_l$ ------(1)
  $KS_p=N_p$ -----(2)
  Where ,
  $N_l$= No. of blow at the liquid when shear strength is $S_l$
  $N_p$= No. of blow at plastics limit when shear strength is $S_p$.
  $k$= Constant - The value of toughness index lies between 0 to 3 Sensitivity and Thixotropy-----(1) Thixotropy :- Thixo + Tropy Where Thixo means Touch and Trophy means Change Means change which is occur due to touch. - Thixotropy of soils is of great impedance in soil engineering. - Example : When a pile is driven into the ground, the loss of strength occurs due to disturbance caused,Thixotropy indicated how much shear strength is regained of the pile has been driven and left in place for same time. SENSITIVITY:- Its measure loss of strength of soil like consistency. ![enter image description here][2] (1) A soil has a liquid limit of 25% and flow index of 12.5%. If the plastic limit is 50%. then determine the plasticity index and toughness index. If water content of the soils in its natural condition in the field is 20%. find the liquidity index and relative consistency. Given data :- $I_L$=25% , $I_f$=12.5% $W_p$=25% Natural water content W=20% P.I or $I_p=W_l-W_p$ =25-15 =10% $I_t$=$\frac{I_P}{I_f}$=$\frac{10}{12.5}$
  =0.8(80%)
  $I_l$=$\frac{W-W_p}{I_p}*100$ =0.20-0.15/0.10100 =50%
  $I_c=\frac{W_l-w}{Ip}*100$ =0.25-20/0.10100 =50%

Use of consistency limit: The consistency limit are determined for Remould soils.Since the actual behaviour of the soil can be depend on natural structure, the consistency limit do not give actual information about the site soils.They give at best a rough estimate of the behaviour of the site soils.

1. It has been observe that both plastic and liquid limit depends upon the type and the amountof clay in a soil.However the plasticity index depend upon the the amount of clay.

2. As the particle size decrease, bot P.L&L.L increase.Therefore plasticity index increase at rapid rate.

3. When site is added to clay it become leaner. Its L.L & P.L both decrease, But the former at a faster rate.But the net effect is that the plasticity index is decreases.

4. The plastic limit of soils is increase 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 soils changes from liquid state to semi-solid rather abruptly. These soil do not passes plasticity and area classified.