Question

A geotechnical engineer has to decide between two foundation designs at a site which is believed to contain a lens of soft clay, whose size can be discretized into large, medium or small. Design A assumes a large lens of soft clay, while design B assumes the size of soft clay lens, if any, is insignificant The expected cost-which includes initial and expected failure costs-for each design and lens size combination is given below (in million dollars): Size of Soft Clay Lens Design A 4.03.8 3.6 B| 4.8 | 3.8 | 3.0 Suppose the lens size is equally likely among L, M and S based on prior information. (a) Which is the better design based on the maxium EMV (Expected Monetary Value) criterion? (b) Suppose four borings can be driven on site to reveal the existence of soft clay lens. Due to the large spacing between borings, which exceeds the width of size L lens, the probabilities of such soil exploration tests encountering a weak spot are 0.99, 0.44 and 0.02 for lens sizes L, M and S, respectively. If the boring test costs $0.15 million, draw the decision tree and decide if such borings should be driven before adopting the foundation design. Hint: start the decision tree with boring program and a chance node; work assuming a free test, find all EMVs; finally check if savings compared to (a) justify the cost of $0.15M Respective probabilities of L, M, S given a weak spot is hit/not hit by the borings will be needed. No need to include the tree from (a). for verifying the size of soft clay lens? Hint: determine the value of a perfect test that would reveal LM/S with certainty, the decision tree starts with a chance node with three outcomes.

Answer 1