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solve the problem with step by step calculation
3 At c tel: $9 \% 2012 \% 2012 \% 2014 \% 2013 \% 2015 \% 2015 \% 2016$ st (SPT) was performed for the 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 - 1 -
ENCN353-24S1 Assignment 2 - In-Situ Testing.docx
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Answer from Sia

Posted 6 months ago

Solution

a

Calculate the average SPT blow count, N, from the given data in Table 1

b

Normalize the SPT blow count, N, to a 60% energy efficiency using the formula: $(N1)_{60} = N \left(\frac{E_{\text{measured}}}{60\%}\right)$ where $E_{\text{measured}}$ is the energy efficiency of the SPT hammer

c

Use the Hatanaka and Uchida (1996) correlation formula to calculate the average friction angle, Φ': $\Phi' = [15.4(N1)_{60}]^{0.5} + 20°$

d

Calculate the ultimate bearing capacity, $q_u$, for the square footing using Terzaghi's bearing capacity equation for square footing: $q_u = 1.3C_{\text{nc}}N_{\text{c}} + \sigma'_{\text{z}}N_{\text{q}} + 0.4\gamma B N_{\text{γ}}$ where $C_{\text{nc}}$ is the cohesion, $N_{\text{c}}$, $N_{\text{q}}$, and $N_{\text{γ}}$ are bearing capacity factors, $\sigma'_{\text{z}}$ is the effective overburden pressure, $\gamma$ is the unit weight of soil, and $B$ is the width of the footing

e

Calculate the allowable bearing pressure, $q_a$, using the strength reduction factor, $F_s$: $q_a = \frac{q_u}{F_s}$

Answer

[Insert final answer here after calculations]

Key Concept

Bearing capacity is a critical concept in geotechnical engineering, determining the maximum load a soil can support without failure. Terzaghi's bearing capacity theory provides a method to calculate the ultimate bearing capacity of shallow foundations.

Explanation⋮ The solution involves normalizing the SPT blow counts to account for the hammer efficiency, using the provided correlation to find the friction angle, and then applying Terzaghi's equation to find the ultimate and allowable bearing pressures for the footing. ⚹

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