An engineer has designed the foundation for column system (20 columns) of a 5 story residential building. Preliminary excavation showed level of water below 3.5 m from ground level. The column loads were equal in all columns. Each column carried 2500 kN of axial load. The design engineer came up with the foundation size of 3.0 m  2.0 m for all columns. The assumed depth of footing was 1.5 m below the ground. Please calculate the appropriate boring depth from ground level for detail site investigation. Use ASCE procedure for your calculation.

Boring depth = 6.76m

Explanation:

Given Data:

No. of columns = 30

No. of storeys = 5

Water level =3.5m below ground level

Axial load = 2500kN

Foundation size = 3mx2m

Depth of footing = 1.5m = Df

Solution:

First we need to calculate estimated net stress on footing

As we know that: q₀ = P/A

By putting values we get

q₀ = 2500/(3*2) = 416.677 kN/m³

Now for the depth of bedrock from the bottom surface of footing,

D₃ = total depth of bedrock - Df = 100 -1.5 = 98.5m

Now for the calculation of D1, here D1 is the distance from bottom surface of footing to depth where change in vertical stress = Δσ¹ = (1/10)q₀ ---------equation (1)

Now, second diagram attached below is drawn according to stress distribution of 2V:1H

Δσ¹ = P/A¹ = (2500)/(3+z)(2+z) ---------equation (2)

From equation 1 and 2 we get

0.1*416.677 = 2500/(3+D1)(2+D1)

D1²+5D1 = 54

D1 = 5.2621 m

Now we will calculate D2 where we have Δσ¹ /σ₀¹ = 0.05

Now,

we will check this ratio for bottom most layer first(i.e. clay layer, ρsat=16.9kN/m³), if it is satisfied then O.K other wise we will continue procedure for top layers.

We have, Δσ¹ = σ₀¹(0.05)

First we need to find vertical stress σ₀¹ at depth z

σ₀¹ = (3.5*17) + 1.5*(ρsat-ρw)sand + (ρsat-ρw)clay*(D2-3.5)

By putting values we get

σ₀¹ = 59.5 + 13.035 _ 7.09D2 - 28.815

Putting it in equation 2 , we get

σ₀¹ = 2500/(3+D2)(2+D2) = 0.05 * (7.09D2 + 47.72)

By simplification, we get

7.09D₂³+83.167D₂²282.147D₂-49714 = 0

D₂ = 15.35 m

So from this calculation it is evident that Δσ¹ /σ₀¹ = 0.05 is at depth of 15.35m which is in clay layer, so no need to check in upper layers.

Now, for the calculation of boring depth depth,

Boring depth = D +Df

1st case = 5.26 + 1.5 = 6.76m

2nd case = 15.35 + 1.5 = 16.85m

13rd case = 98.5 + 1.5 = 100m

Boring depth = 6.76m

option number c is the right answer.