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Question 6.1: A concentrated load of 1000 kN is applied at the ground surf...

A concentrated load of 1000 kN is applied at the ground surface. Compute the vertical pressure (i) at a depth of 4 m below the load, (ii) at a distance of 3 m at the same depth. Use Boussinesq’s equation.

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The equation is

 

\sigma_{z}=\frac{Q}{z^{2}} I_{B}, \text { where } I_{B}=\frac{3 / 2 \pi}{\left[1+(r / z)^{2}\right]^{5 / 2}}

 

(i) When r / z=0, I_{B}=3 / 2 \pi=0.48, \sigma_{z}=0.48 \frac{Q}{z^{2}}=0.48 \times \frac{1000}{4 \times 4}=30 kN / m ^{2}

 

(ii) When r / z=3 / 4=0.75

 

I_{B}=\frac{3 / 2 \pi}{\left[1+(0.75)^{2}\right]^{5 / 2}}=0.156, \sigma_{z}=\frac{0.156 \times 1000}{4 \times 4}=9.8 kN / m ^{2}

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