Technical Report 129, c4e-Preprint Series, Cambridge

Authors: Kok Foong Lee, John F. Davidson, Jethro Akroyd, and Markus Kraft*

Reference: Technical Report 129, c4e-Preprint Series, Cambridge, 2013

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A theory is given to predict the upward force, F, to lift an object buried at depth H in granular material. The object is either (1) a horizontal disc of diameter D or (2) a horizontal plate of width B and length L, where L >> B. In case (1), the lifted disc is assumed to cause axi-symmetric upward particle motion, reverse hopper flow, within an inverted cone. Active failure is assumed: the vertical stress, σ₂, is K x (horizontal stress σ₁); here K = (1 + sin φ)/(1 - sin φ), φ being the angle of friction for the granular material. This gives the vertical stress, σ₂₀, on the disc. An additional lift force is needed to overcome the frictional stress, Ï„, at the conical interface between stationary and upward moving particles: it is assumed that Ï„ = μ σ₁, μ being the internal friction coefficient. For consolidated granules, μ = tan φ, but for the sheared material, μ < tan φ. The total lift force F is the sum of (i) the effect of σ₂₀ plus (ii) the effect of Ï„; this sum gives an equation to predict the breakout factor N_qf = F/(γ^′AH), where γ^′ = bulk weight density and A = Ï€ D²/4. For case (2), relevant to the uplift of a long buried pipe, the theory is similar: the two failure surfaces are flat, inclined at angles +α and -α to the vertical. Similar assumptions as to the stress distribution, i.e. two-dimensional active failure, give an equation for N_qf. The two predictive equations for cases (1) and (2) agree well with relevant published measurements of N_qf.

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