Respuesta :
Explanation:
Determine the weight of footing
[tex]W_{f}=\gamma(L)(B)(D)[/tex]
Where [tex]W_{f}[/tex] is the weight of footing, γ is the unit weight of concrete, L is the length of footing is the width of footing, and D is the depth of footing
Substitute [tex]2 m \text { for } L, 1.5 m \text { for } B, 0.5 m \text { for } D \text { and } 23.6 kN / m ^{3}[/tex] for γ in the equation
[tex]\begin{aligned}W_{f} &=\left(23.6 kN / m ^{3}\right)(2 m )(1.5 m )(0.5 m ) \\&=35.4 kN\end{aligned}[/tex]
Therefore, the weight of the footing is 35.4 kN
Determine the initial vertical effective stress.
[tex]\sigma_{z p}^{\prime}=\gamma(D+B)-u[/tex]
Here, [tex]\sigma_{z^{p}}^{\prime}[/tex] is initial vertical stress at a depth below ground surface γ is the unit weight of soil, D is depth and u is pore water pressure.
Substitute [tex]18 kN / m ^{3} \text { for } \gamma, 1.5 m \text { for } B, 0.5 m \text { for } D \text { and } 0[/tex] for u in the equation
[tex]\begin{aligned}\sigma_{z p}^{\prime} &=\left(18 kN / m ^{3}\right)(1.5+0.5) m -0 \\&=36 kPa\end{aligned}[/tex]
Therefore, the initial vertical stress is 36 kPa
Determine the vertical effective stress.
[tex]\sigma_{z D}^{\prime}=\gamma D[/tex]
Here, [tex]\sigma_{z^{p}}^{\prime}[/tex] is initial vertical stress at a depth below ground surface γ is the unit weight of soil, D is depth and u is pore water pressure.
Substitute [tex]\(18 kN / m ^{3}\) for \(\gamma, 0.5 m\) for \(D\) and 0 for \(u\)[/tex] in the equation.
[tex]\begin{aligned}\sigma_{z b}^{\prime} &=\left(18 kN / m ^{3}\right)(0.5 m )-0 \\&=9 kPa\end{aligned}[/tex]
Therefore, the vertical stress at a depth below the ground surface is
9 kPa
Determine the influence factor at the midpoint of soil layer,
[tex]I_{e p}=0.5+0.1 \sqrt{\frac{q-\sigma_{s 0}^{\prime}}{\sigma_{z p}^{\prime}}}[/tex]
Here [tex]I_{e p}[/tex] is the influence factor at the midpoint of soil layer [tex]\sigma_{z^{p}}^{\prime}[/tex] is initial vertical stress, [tex]\sigma_{z^{p}}^{\prime}[/tex] is vertical effective stress, and [tex]Q[/tex] is bearing pressure
Substitute [tex]36 kPa for \(\sigma_{z p}^{\prime}, 228.47\) kPa for \(q,\) and 9 kPa for \(\sigma_{z D}^{\prime}\)[/tex] in the equation[tex]\begin{aligned}I_{\epsilon P} &=0.5+0.1 \sqrt{\frac{228.47 kPa -9 kPa }{36 kPa }} \\&=0.75\end{aligned}[/tex]
Therefore the influence factor at the midpoint of the soil layer is 0.693
