Chapter 17, Subsoil Exploration Video Solutions, Principles of Geotechnical Engineering

Problem 1

During a soil exploration program, the following choices were available for soil sampling:
$\bullet$ Shelby tube A: outside diameter, $D_n=76.2 \mathrm{~mm}$; inside diameter, $D_{\mathrm{r}}=73 \mathrm{~mm}$
$\bullet$ Shelby tube $B$ : outside diameter, $D_0=3.5$ inch; inside diameter, $D_2=3.375$ inch
$\bullet$ Split spoon sampler: outside diameter, $D_e=50.8 \mathrm{~mm}$; inside diameter.
$$
D_i=35 \mathrm{~mm}
$$

Calculate the area ratio for each case and determine which sampler would be appropriate for the following soil characterization tests: grain-size distribution, Atterberg limits, consolidation, and unconfined compression.

Hast Aggarwal

Numerade Educator

Problem 2

The following are the results of a standard penetration test in sand. Determine the corrected standard penetration numbers, $\left(N_1\right)_{60}$, at the various depths given. Note that the water table was not found within $12 \mathrm{~m}$ below the ground surface. Assume that the average unit weight of sand is $17 \mathrm{kN} / \mathrm{m}^3$. Use Liao and Whitman's relationship $[\mathrm{Eq} .(17.10)]$. Assume $p_a=100 \mathrm{kN} / \mathrm{m}^2$.
$$
\begin{array}{cr}
\hline \text { Depth }(\mathrm{m}) & \boldsymbol{N}_{\mathrm{sa}} \\
\hline 2 & 7 \\
4 & 10 \\
6 & 11 \\
8 & 14 \\
10 & 9 \\
\hline
\end{array}
$$

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Problem 3

For the soil profile given in Problem 17.2, estimate the average soil friction angle, $\phi^{\prime}$, using the Kulhawy and Mayne correlation [Eq. (17.20)]. Assume $p_a=100 \mathrm{kN} / \mathrm{m}^2$.

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Problem 4

Following are the results of a standard penetration test in dry sand.
$$
\begin{array}{cr}
\hline \text { Depth }(\mathrm{m}) & \boldsymbol{N}_{e 0} \\
\hline 1.5 & 9 \\
3 & 10 \\
4.5 & 14 \\
6 & 18 \\
7.5 & 20 \\
\hline
\end{array}
$$
For the sand deposit, assume the mean grain size, $D_{50}$ to be $0.3 \mathrm{~mm}$, and the unit weight of sand to be $15.7 \mathrm{kN} / \mathrm{m}^3$. Estimate the variation of relative density with depth using the correlation developed by Cubrinovski and Ishihara [Eq. (17.18)]-

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Problem 5

Refer to the boring log shown in Figure 17.15. Estimate the average drained friction angle, $\phi^{\prime}$, based on corrected standard penetration number, $\left(N_1\right)_{60}$. Use Eqs. (17.10) and (17.24).

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Problem 6

Refer to Problem 17.5 and Figure 17.15. Suppose a footing ( $2 \mathrm{~m} \times 2 \mathrm{~m}$ ) is constructed at a depth of $1.5 \mathrm{~m}$.
a. Estimate the design values for $N_{60}$ and $\phi^{\prime}$.
b. What is the net allowable load that the footing can carry? The maximum allowable settlement is $25 \mathrm{~mm}$.

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Problem 7

Refer to Figure 17.15. Estimate the variation of cone penetration resistance, $q_c$ with depth using Eq. (17.39). Assume $D_{50}=0.28 \mathrm{~mm}$.

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Problem 8

Refer to the footing in Problem 17.6. For calculating elastic settlement under the footing, it is necessary to estimate the elastic modulus of the foundation soil. Using $q_c$ from Problem 17.7 and Eq. (17.33), estimate the variation of elastic modulus with depth for the soil profile shown in Figure 17.15.

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Problem 9

A cone penetration test was conducted in a layer of saturated clay. The cone tip resistance, $q_c$ at $22 \mathrm{ft}$ below the ground surface was found to be $26,000 \mathrm{lb} / \mathrm{ft}^2$. If the unit weight of the saturated clay is $118 \mathrm{lb} / \mathrm{ft}^3$, estimate the undrained shear strength of the clay.

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Problem 10

During a field exploration program, rock was cored for a length of $8 \mathrm{ft}$ and the length of the rock core recovered was $4.5 \mathrm{ft}$. Determine the recovery ratio.

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