Chapter 10, Problem 10.1P

(a)

To determine

Find whether the statement “For normally consolidated clays $c^{\prime }=0$” is true or false.

Answer to Problem 10.1P

The statement, “For normally consolidated clays $c^{\prime }=0$” is true.

Explanation of Solution

According to Mohr-Coulomb failure criteria, the value of effective stress cohesion $\left(c^{\prime }\right)$ for gravel, sand, and inorganic silt is 0.

The effective stress cohesion is approximated as 0 for normally consolidated clay.

$c^{\prime }=0$.

Therefore, the statement, “For normally consolidated clays $c^{\prime }=0$” is true.

(b)

To determine

Find whether the statement “Peak friction angle cannot be less than the ultimate friction angle” is true or false.

Answer to Problem 10.1P

The statement, “Peak friction angle cannot be less than the ultimate friction angle” is true.

Explanation of Solution

When the load is applying on a dense sand, the resisting shear stress increases with shear displacement until it attains a failure stress of ${\tau }_f$. This ${\tau }_f$ is called peak shear strength.

The shear stress gradually decreases with increases of shear displacement after reaches the failure stress. The continuous increase of shear displacement finally attains a constant value, then it is called ultimate shear strength.

Express the peak shear strength as follows:

${\tau }_f={\sigma }^{\prime }\tan {\varphi }^{\prime }$

Find the peak friction angle $\left({\varphi }^{\prime }\right)$ from the above Equation as follows:

${\varphi }^{\prime }={\tan }^{-1}\left(\frac{{\tau }_f}{{\sigma }^{\prime }}\right)$ (1)

Express the ultimate shear strength as follows:

${\tau }_{\text{ult}}={\sigma }^{\prime }\tan {{\varphi }^{\prime }}_{\text{ult}}$

Find the ultimate friction angle $\left({{\varphi }^{\prime }}_{\text{ult}}\right)$ from the above Equation as follows:

${{\varphi }^{\prime }}_{\text{ult}}={\tan }^{-1}\left(\frac{{\tau }_{\text{ult}}}{{\sigma }^{\prime }}\right)$ (2)

Refer to Figure 10.6, “Determination of shear strength parameters for a dry sand using the results of direct shear stress” in the textbook.

From the Figure 10.6, the peak friction angle $\left({\varphi }^{\prime }\right)$ is always greater or equal to the ultimate friction angle $\left({{\varphi }^{\prime }}_{\text{ult}}\right)$.

The statement, “Peak friction angle cannot be less than the ultimate friction angle” is true.

(c)

To determine

Find whether the statement “The stress strain plot of a dense sand is similar in shape to that of a normally consolidated clay” is true or false.

Answer to Problem 10.1P

The statement, “The stress strain plot of a dense sand is similar in shape to that of a normally consolidated clay” is false.

Explanation of Solution

Sketch the stress-strain relationship for loose and dense sand as shown in Figure 1.

Refer to figure 1

The stress-strain curve for the loose sand is same as that of the normally consolidated clay.

The stress-strain curve for the dense sand is same as that of the over consolidated clay.

The statement, “The stress strain plot of a dense sand is similar in shape to that of a normally consolidated clay” is false.

(d)

To determine

Find whether the statement “Sensitivity of a clay can be less than one” is true or false.

Answer to Problem 10.1P

The statement, “Sensitivity of a clay can be less than one” is false.

Explanation of Solution

The sensitivity of clays is defined as the ratio of the unconfined compressive strength of clay in undisturbed to remoulded state.

The sensitivity of clay varies from 1 or $>1$.

The statement, “Sensitivity of a clay can be less than one” is false.

(e)

To determine

Find whether the statement “$c^{\prime }$ and ${\varphi }^{\prime }$ cannot be determined from an unconsolidated undrained triaxial test” is true or false.

Answer to Problem 10.1P

The statement, “$c^{\prime }$ and ${\varphi }^{\prime }$ cannot be determined from an unconsolidated undrained triaxial test” is true.

Explanation of Solution

In consolidated undrained test, the shear strength parameters for over consolidated clay based on effective stress c and $\varphi$ can be obtained by plotting the effective-stress Mohr’s circle and then draw a failure envelope for the total stress.

In an unconsolidated undrained test, the failure envelope for the total stress lies on the horizontal line.

Hence, $c^{\prime }$ and ${\varphi }^{\prime }$ cannot be determined from an unconsolidated undrained triaxial test.

The statement, “$c^{\prime }$ and ${\varphi }^{\prime }$ cannot be determined from an unconsolidated undrained triaxial test” is true.