Chapter 3, Problem 3.1P

(a)

To determine

Mention whether the given statement is true or false.

Answer to Problem 3.1P

The given statement, “Moisture content must be always less than 100%” is $\underset{\_}{\text{false}}$.

Explanation of Solution

Calculation:

The moisture content (w) is the ratio of weight of water $\left(W_w\right)$ to the weight of solids $\left(W_s\right)$ in a soil sample. It is expressed as follows:

$\begin{array}{l}w=\frac{W_w}{W_s}\\ w\ge 0\end{array}$

If the water content in the soil exceeds 100%, the weight of water $\left(W_w\right)$ is greater than the weight of solids. It is possible only the soil must be in the form of mud or slurry.

Hence, the moisture content may be greater than 100%.

Therefore, the given statement, “Moisture content must be always less than 100%” is $\underset{\_}{\text{false}}$.

(b)

To determine

Mention whether the given statement is true or false.

Answer to Problem 3.1P

The given statement, “Plastic limit is always less than plasticity index” is $\underset{\_}{\text{false}}$.

Explanation of Solution

Calculation:

Write the equation for the relationship between the plasticity index (PI), liquid limit (LL), and the plastic limit (PL) as follows:

$PI=LL-PL$

When the plastic limit is equal or greater than the liquid limit, the plasticity index is considered as zero. In this case the plastic limit is greater than the plasticity index.

The given statement is not satisfying the condition.

Therefore, the given statement “Plastic limit is always less than plasticity index” is $\underset{\_}{\text{false}}$.

(c)

To determine

Mention whether the given statement is true or false.

Answer to Problem 3.1P

The given statement, “Liquidity index cannot be negative” is $\underset{\_}{\text{false}}$.

Explanation of Solution

Calculation:

Write the equation for liquidity index (LI) as follows:

$LI=\frac{w-PL}{LL-PL}$

Here, the in situ moisture content of the soil is w, plastic limit is PL, and liquid limit is LL.

For sensitive clays, the in situ moisture content is greater than the liquid limit $w>LL$.

In this condition liquidity index is greater than 1 $LI>1$.

For soils that are heavily over consolidated, the in situ moisture content is less than the plastic limit $w<PL$. In this condition liquidity index is less than 0.

The liquidity index can be less than zero.

Therefore, the given statement “Liquidity index cannot be negative” is $\underset{\_}{\text{false}}$.

(d)

To determine

Mention whether the given statement is true or false.

Answer to Problem 3.1P

The given statement, “The dry unit weight is always less than the moist unit weight” is $\underset{\_}{\text{true}}$.

Explanation of Solution

Calculation:

Find the moist unit weight $\left(\gamma \right)$ using the relation:

$\begin{array}{c}\gamma =\frac{\text{Total}\text{weight}}{\text{Total}\text{volume}\text{of}\text{soil}}\\ =\frac{W_w+W_s}{V}\end{array}$

Find the dry unit weight $\left({\gamma }_d\right)$ using the relation:

$\begin{array}{c}{\gamma }_d=\frac{\text{weight}\text{of}\text{solids}}{\text{total}\text{volume}\text{of}\text{soil}}\\ =\frac{W_s}{V}\end{array}$

From the equations of moist unit weight and the dry unit weight, the dry unit weight will be less than the moist unit weight.

Therefore, the given statement “The dry unit weight is always less than the moist unit weight” is $\underset{\_}{\text{true}}$.

(e)

To determine

Mention whether the given statement is true or false.

Answer to Problem 3.1P

The given statement, “Relative density increases with void ratio” is $\underset{\_}{\text{false}}$.

Explanation of Solution

Calculation:

Write the equation for relative density $\left(D_r\right)$ as follows:

$D_r=\frac{e_{\max }-e}{e_{\max }-e_{\min }}$

Here, in situ void ratio of the soil is e, void ratio of the soil in the loosest condition is $e_{\max }$, and the void ratio of the soil in the densest condition is $e_{\min }$.

Refer to the relative density equation, the relative density is inversely proportional to the void ratio.

When the void ratio increases, the relative density decreases.

Therefore, the given statement “Relative density increases with void ratio” is $\underset{\_}{\text{false}}$.