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Terzaghi, Theoretical Soil Mechanics, Article 70 question

Terzaghi, Theoretical Soil Mechanics, Article 70 question

Terzaghi, Theoretical Soil Mechanics, Article 70 question

(OP)
I read Article 70 this morning, and an equation is presented for the pressure on a tunnel crown "at a great depth below the surface."

σv = [(γ*B1)/(Ktanф)] * [1-e^(-Ktanф(D1/B1))] + [γ*D2] * e^(-Ktanф(D1/B1))

In the paragraph below, Terzaghi writes "As soon as the height D1 becomes equal to about 20 per cent of the total depth D1+D2 the second term on the right-hand side of the preceeding equation becomes negligible."

This second term would be: [γ*D2] * e^(-Ktanф(D1/B1))

I'm not able to make the term become negligible at this 20% point. An example I am running right now has the following parameters:

γ=125pcf
ф=30deg
Tunnel dimensions = 20'x20', therefore B1=21.55' based upon Terzaghi equation 70.1
total height above tunnel = 50', check with D1=1', 2', 3', etc. and the corresponding D2=49', 48', 47', etc.

At 20%, D1=10' & D2=40', I have the first term coming out to 1096.56 and the second term coming out to 3630.67, which is not negligible.

Am I missing something? Would appreciate any insight. Thanks in advance, and my apologies if this a silly math error I'm overlooking.

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