A Relativist's Toolkit - The Math of Black Hole Mechanics by E. Poisson

By E. Poisson

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G. g. 84. Estimate the unit weight of the soil in its loosest state. 24). 84. 4 An engineer wishes to investigate the bulk permeability of a layered soil comprising alternating bands of fine sand (5 mm thick) and silt (3 mm thick). The engineer makes a special constant head permeameter of square cross section (internal dimensions 112 mm × 112 mm) and carries out two tests on undisturbed samples. In one test, the flow is parallel to the laminations: in the other test, the flow is perpendicular to the laminations.

Consider the flowrate q through an annular ring around the well, concentric with the well and having a general radius r. The flow area at a general radius r is 2πrD, where D is the thickness of the aquifer. The hydraulic gradient i = -dh/dr where h is the head measured above some convenient datum. 12, because we are interested in the flow towards the well, which is in the r negative direction. (h-hw)] We need to think about the relationships between heads and drawdowns. Taking the datum for the measurement of head h at the bottom of the aquifer, 24 m below ground level, the initial groundwater level (at a depth of 2 m below the ground surface) corresponds to a head of 24 m – 2 m = 22 m.

18, the settlement after a period of 18 months. Take the unit weight of water γw=10 kN/m3. 7 Solution Calculate the initial and final stresses at the top and bottom of each layer: Level, m above σv, SD kPa 105 0 98 126 94 210 84 420 70 714 u initial, σ'v kPa kPa 0 0 0 126 40 170 95 325 235 479 final, σ'v initial, u kPa kPa 0 0 0 126 40 170 0 420 200 514 final, ∆σ'v, kPa 0 0 0 +95 +35 i) Initial settlement is due to compression of the Thanet Sands, which will occur very quickly owing to their relatively high permeability and stiffness.

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