Chapter 16, Problem 16.1P

(a)

To determine

Whether the statement “In loose sands, foundations fail in general shear failure mode” is true or false.

Answer to Problem 16.1P

The given statement is $\underset{\_}{\text{false}}$.

Explanation of Solution

• The general shear failure is the bearing capacity failure that occurs when the shear stress exceeds the shear strength of the soil.
• The local shear failure is the sliding or jerking failure (excessive movements) that occurs at the time when the structure is supported by the soil.
• The dense sand initially supports the structure, and then fails due to settlement. Hence, the foundations in dense sand fail due to general shear failure.
• The foundations in loose sand fail due to sudden jerks. Hence, the foundations in loose sand fail due to local shear failure.

Therefore, the statement is $\underset{\_}{\text{false}}$.

(b)

To determine

Whether the statement “The larger the relative density of a sand, the larger the bearing capacity factors $N_q$ and $N_{\gamma }$” is true or false.

Answer to Problem 16.1P

The given statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

Write the equation of relative density (R.D).

$R.D=\frac{e_{\max }-e}{e_{\max }-e_{\min }}$ (1)

Here, $e_{\max }$ is the maximum void ratio, e is the natural void ratio, and $e_{\min }$ is the minimum void ratio.

Write the equation of bearing capacity factors $N_q$ and $N_{\gamma }$ according to modified Terzaghi’s bearing capacity theory.

$N_q={\tan }^2\left(45+\frac{{\varphi }^{\prime }}{2}\right)e^{\pi \tan {\varphi }^{\prime }}$ (2)

$N_{\gamma }=2\left(N_q+1\right)\tan {\varphi }^{\prime }$ (3)

• From Equations (1), (2), and (3), the relative density and bearing capacity factors are the functions of void ratio, and the larger void ratio indicates larger relative density and larger bearing capacity factors.
• Therefore, the larger relative density of a soil sample clearly explains that the soil sample has the larger bearing capacity factors $N_q$ and $N_{\gamma }$.

Therefore, the given statement is $\underset{\_}{\text{true}}$.

(c)

To determine

Whether the statement “Eccentricity increases the ultimate bearing capacity” is true or false.

Answer to Problem 16.1P

The given statement is $\underset{\_}{\text{false}}$.

Explanation of Solution

• When the eccentricity exceeds the limit of eccentricity, the foundation is ineffective to withstand the tensile stresses.
• Hence, the higher eccentricity reduces the bearing capacity of the foundation.

Therefore, the given statement is $\underset{\_}{\text{false}}$.

(d)

To determine

Whether the statement “In calculating the ultimate bearing capacity of eccentrically loaded foundations, depth factors are computed using B and not $B^{\prime }$” is true or false.

Answer to Problem 16.1P

The given statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

• After the loading, the effective width $\left(B^{\prime }\right)$ would be considered for the design of foundation.
• The depth factor is computed before the eccentric loading because the bearing capacity of the soil depends on soil properties. Hence, use B instead of $B^{\prime }$ for depth factor calculation.

Therefore, the statement is $\underset{\_}{\text{true}}$.

(e)

To determine

Whether the statement “The three shape factors for a continuous foundation are one” is true or false.

Answer to Problem 16.1P

The given statement is $\underset{\_}{\text{true}}$.

Explanation of Solution

Write the equation of shape factors $F_{cs},F_{qs},\text{and}{F}_{\gamma s}$.

$F_{cs}=1+\frac{B}{L}\frac{N_q}{N_c}$

$F_{qs}=1+\frac{B}{L}\tan {\varphi }^{\prime }$

$F_{\gamma s}=1-0.4\frac{B}{L}$

Here, B is the breadth of the footing, L is the length of the footing, $N_q$ and $N_c$ are the bearing capacity factors, and ${\varphi }^{\prime }$ is the friction angle.

• For the continuous foundation, the length of footing is infinite. The reciprocal of infinity can be zero. Therefore, the terms $\frac{B}{L}\frac{N_q}{N_c}$, $\frac{B}{L}\tan {\varphi }^{\prime }$, and $0.4\frac{B}{L}$ are zero
• Hence, the shape factors $F_{cs},F_{qs},\text{and}{F}_{\gamma s}$ are 1 for continuous foundation.

Therefore, the given statement is $\underset{\_}{\text{true}}$.