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A 30m deep quarry pit is to be constructed in a jointed basalt rock mass. The quarry management wants to maximise the side wall inclination to 70° for economic reasons. The geological survey revealed that the two joint sets inclined at a dip of 60° directly towards the East and the other almost horizontal are present. The near horizontal joints are spaced at 5.5m intervals while the steeply inclined joints are spaced at approximately 4m intervals throughout the quarry. The laboratory tests indicate that the basalt rock density is approximately 2.75g/cm3, both joint sets are smooth, wet and infilled with weak clay deposits of low cohesion. Cable bolting can be used.
The pit boundary corner locations calculated by a registered surveyor and the rock properties are given in Table 1 below. Note that the excavation edge must be at least 5m from the surveyed boundary.
What are the no-arbitrage lower bound, and the no-arbitrage upper bound, of the vertical spread c(k1)-c(k2)?
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