<u>Explanation:</u>
Determine the weight of footing
![W_{f}=\gamma(L)(B)(D)](https://tex.z-dn.net/?f=W_%7Bf%7D%3D%5Cgamma%28L%29%28B%29%28D%29)
Where
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
for γ in the equation
![\begin{aligned}W_{f} &=\left(23.6 kN / m ^{3}\right)(2 m )(1.5 m )(0.5 m ) \\&=35.4 kN\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DW_%7Bf%7D%20%26%3D%5Cleft%2823.6%20kN%20%2F%20m%20%5E%7B3%7D%5Cright%29%282%20m%20%29%281.5%20m%20%29%280.5%20m%20%29%20%5C%5C%26%3D35.4%20kN%5Cend%7Baligned%7D)
Therefore, the weight of the footing is 35.4 kN
Determine the initial vertical effective stress.
![\sigma_{z p}^{\prime}=\gamma(D+B)-u](https://tex.z-dn.net/?f=%5Csigma_%7Bz%20p%7D%5E%7B%5Cprime%7D%3D%5Cgamma%28D%2BB%29-u)
Here,
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
for u in the equation
![\begin{aligned}\sigma_{z p}^{\prime} &=\left(18 kN / m ^{3}\right)(1.5+0.5) m -0 \\&=36 kPa\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csigma_%7Bz%20p%7D%5E%7B%5Cprime%7D%20%26%3D%5Cleft%2818%20kN%20%2F%20m%20%5E%7B3%7D%5Cright%29%281.5%2B0.5%29%20m%20-0%20%5C%5C%26%3D36%20kPa%5Cend%7Baligned%7D)
Therefore, the initial vertical stress is 36 kPa
Determine the vertical effective stress.
![\sigma_{z D}^{\prime}=\gamma D](https://tex.z-dn.net/?f=%5Csigma_%7Bz%20D%7D%5E%7B%5Cprime%7D%3D%5Cgamma%20D)
Here,
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
in the equation.
![\begin{aligned}\sigma_{z b}^{\prime} &=\left(18 kN / m ^{3}\right)(0.5 m )-0 \\&=9 kPa\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Csigma_%7Bz%20b%7D%5E%7B%5Cprime%7D%20%26%3D%5Cleft%2818%20kN%20%2F%20m%20%5E%7B3%7D%5Cright%29%280.5%20m%20%29-0%20%5C%5C%26%3D9%20kPa%5Cend%7Baligned%7D)
Therefore, the vertical stress at a depth below the ground surface is
9 kPa
Determine the influence factor at the midpoint of soil layer,
![I_{e p}=0.5+0.1 \sqrt{\frac{q-\sigma_{s 0}^{\prime}}{\sigma_{z p}^{\prime}}}](https://tex.z-dn.net/?f=I_%7Be%20p%7D%3D0.5%2B0.1%20%5Csqrt%7B%5Cfrac%7Bq-%5Csigma_%7Bs%200%7D%5E%7B%5Cprime%7D%7D%7B%5Csigma_%7Bz%20p%7D%5E%7B%5Cprime%7D%7D%7D)
Here
is the influence factor at the midpoint of soil layer
is initial vertical stress,
is vertical effective stress, and
is bearing pressure
Substitute
in the equation![\begin{aligned}I_{\epsilon P} &=0.5+0.1 \sqrt{\frac{228.47 kPa -9 kPa }{36 kPa }} \\&=0.75\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7DI_%7B%5Cepsilon%20P%7D%20%26%3D0.5%2B0.1%20%5Csqrt%7B%5Cfrac%7B228.47%20kPa%20-9%20kPa%20%7D%7B36%20kPa%20%7D%7D%20%5C%5C%26%3D0.75%5Cend%7Baligned%7D)
Therefore the influence factor at the midpoint of the soil layer is 0.693