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solve the problem step by step with calculation
3 At a site in the Christchurch CBD, the standard penetration test (SPT) was performed for the design of shallow foundations. The SPT blow counts are in Table 1 below. The split spoon samples collected from these investigations suggest a relatively uniform layer of clean sand down to a depth of $8 \mathrm{~m}$. The energy efficiency of the SPT hammer was measured to be $75 \%$ and the water table was found to be $1 \mathrm{~m}$ below the ground surface. Using the Hatanaka and Uchida (1996) SPT-to-friction angle correlation, provided in the lecture notes and in Figure 1 below, compute the average friction angle for the sand layer. Use this average friction angle to estimate the ultimate bearing capacity of a square $2 \times 2 \mathrm{~m}$ footing embedded to a depth of $1 \mathrm{~m}$. Assume the unit weight of soil above $8 \mathrm{~m}$ is $20 \mathrm{kN} / \mathrm{m}^{3}$. Using a strength reduction factor of 0.5 , calculate the allowable bearing pressure that can be used for design. ( 50 marks)
Table 1: Raw SPT N values from borehole BH-1.
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|}
\hline Depth $(\mathrm{m})$ & 0.5 & 1.0 & 2.0 & 3.0 & 4.0 & 5.0 & 6.0 & 7.0 & 8.0 \\
\hline SPT blow count, N & 8 & 9 & 12 & 12 & 14 & 13 & 15 & 15 & 16 \\
\hline
\end{tabular}
Figure 1: SPT to friction angle correlation by Hatanaka and Uchida (1996)
ENCN353-24S1 Assignment 2 - In-Situ Testing.docx
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Answer from Sia

Posted 4 months ago

Solution by Steps

step 1

Calculate the friction angle for each SPT blow count using the given formula $\phi' = \sqrt{15.4 \cdot N_{60}} + 20$ where $N_{60}$ is the normalized SPT blow count (corrected for energy efficiency)

step 2

For the SPT blow counts given in Table 1, apply the energy efficiency correction by multiplying each count by 0.75

step 3

Use the corrected SPT blow counts to calculate the friction angle for each depth using the formula from step 1

step 4

Compute the mean of the friction angles obtained in step 3 to get the average friction angle for the sand layer

step 5

Use the average friction angle to estimate the ultimate bearing capacity (q_u) for a square footing using the formula $q_u = 1.3 \cdot \gamma' \cdot B' \cdot N_q$ where $\gamma'$ is the effective unit weight of soil, $B'$ is the width of the footing, and $N_q$ is the bearing capacity factor related to the friction angle

step 6

Calculate the allowable bearing pressure (q_a) using a strength reduction factor of 0.5, so $q_a = 0.5 \cdot q_u$

[question number] Answer

The steps provided above outline the process to calculate the average friction angle and the allowable bearing pressure for the design of a square footing.

Key Concept

Friction angle estimation from SPT blow counts and bearing capacity calculation for footing design

Explanation

The friction angle is estimated using the Hatanaka and Uchida correlation, which is then used to calculate the ultimate bearing capacity for a square footing. The allowable bearing pressure is determined by applying a strength reduction factor to the ultimate bearing capacity.

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