33.1: Introduction
- Page ID
- 33021
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)For a wide range of engineering materials, their processing requires that they are in powder form or granular form at some stage. For example, recycled plastics are routinely pelletised and nickel ore in granular form is routinely transported by ship containers across the Pacific Ocean from the Philippines, the largest exporting country of nickel ore, to China, where it is used in the manufacture of stainless steel. Soils are routinely piled into heaps during the construction of new roads and bridges and to conceal industrial plants.
Pelletised recycled plastic (image from: http://www.plasgranltd.co.uk/how-is-plastic-recycled/)
It is vitally important to understand the conditions under which soil and heaps of material in granular form remain stable because the conditions under which they are no longer stable can have devastating consequences.
For example, under suitably adverse conditions in the transport of bulk cargo such as nickel ore and iron ore in ship containers, the cargo can transform abruptly from a solid state to an almost fluid state, i.e., it can liquefy. If this occurs, the stability of the vessel transporting the cargo will be affected. The consequences of this can be dramatic – the ship’s structure can be damaged and, under severe conditions, the ship can capsize with the loss of life. Fortunately, there are now operational guidelines for the transport of mineral ores which will make the incidence of such catastrophic events much less in the future.
Many countries around the world are susceptible to landslides and mudslides where, as a consequence of severe rainfall, the pore pressure in the soil rises so that the soil is unable to bear both an equal-all-round compressive spherical stress and any shear stress – the soil becomes a slippery mess. The consequences can be catastrophic to local communities with loss of life, unless areas at risk of mudslides and landslides can be evacuated beforehand.
A third example is that of the stability of piles of granular material. It is not unusual to find such stockpiles failing suddenly, such as in the example below.
Failure of a pellet feed stockpile at the port of Vitoria in south-east Brazil (courtesy Evandro Moraes da Gama, Matheus Henrique de Castro, Carlos Gomes, Felipe Abbas da Gama, Geomaterials, 4, 18-26 (2014))
Coal waste is also routinely piled into heaps. Again, under adverse circumstances, water can build up in the heap so that it is unable to bear both an equal-all-round compressive spherical stress and any shear stress. The Aberfan disaster in Wales (https://en.Wikipedia.org/wiki/Aberfan_disaster) occurred after a prolonged period of heavy rain in October 1966, so that liquefaction occurred in the material in a coal heap adjacent to the village of Aberfan. 144 people died as a consequence of the collapse of this coal heap.
Another way in which the flow behaviour of granular material is relevant in everyday life is when considering the nature of quicksand (https://en.Wikipedia.org/wiki/Quicksand). The two essential components of quicksand are a fluid, such as water, and fine particles, such as clay or fine sand. Central to its behaviour is its ability to liquefy, so that materials on top of it can sink into it without being fully submerged.
Clearly, therefore, understanding the mechanical behaviour of granular material is of intense practical interest, as well as being of interest in its own right.