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  3. 34 a civil engineer is going to excavate a trench...

Question: 34 a civil engineer is going to excavate a trench...

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3.4 A civil engineer is going to excavate a trench in clay. He/she wants to know how deep the trench can be, and still be stable and stand for a short time without support. The trench will be square in cross-section. The relevant variable describing the strength of the clay is a stress, a force per unit area, called by geotechnical engineers the undrained shear strength: undrained means that there is not enough time for water to move about within the clay. The clay density is important, and so is the gravitational acceleration, because if there were no gravity the clay would have no weight. The variables and their dimensions are trench depth H clay density p clay shear strength c gravitational acceleration g LT1 ILI [ML-3] [force/area] [MLT2/L [ML-1T-21 Form a dimensionless group out of these four variables. Show that you get the same result if you decide that you will take the fundamental dimensions as force [FI and length [L].

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