## Lifting a buried object: Reverse hopper theory

A theory is given to predict the upward force, *F*, to lift an object buried at depth *H* in granular material. Explicit formulae give *F* in terms of the material friction coefficient of the granular material and the geometric parameters.
The lifted 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, Ïƒ_{2}, is *K* x (horizontal stress Ïƒ_{1}); here *K* = (1 + sin Ï†)/(1 - sin Ï†), Ï† being the angle of friction for the granular material. This gives the vertical stress, Ïƒ_{20}, 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„ = Î¼ Ïƒ_{1}, Î¼ being the internal friction coefficient. For consolidated granules, Î¼ = tan Ï†, but for the sheared material, Î¼ < tan Ï†. The total lift force *F* is the sum of (i) the effect of Ïƒ_{20} plus (ii) the effect of Ï„; this sum gives an equation to predict the *breakout factor* *N*_{qf} = F/(Î³^{â€²}*AH*), where Î³^{â€²} = bulk weight density and *A* = Ï€ *D*^{2}/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 +Î± and -Î± 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}.

- This paper draws from preprint 129: Lifting a buried object: reverse hopper theory
- Access the article at the publisher: DOI: 10.1016/j.ces.2013.11.002