33.10: Summary
- Page ID
- 34923
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)After working through this teaching and learning package, you should:
- Understand the concept of dilatation
- Have a feeling for 'typical' angles of repose for granular materials
- Recognise how friction, cohesive forces and the shapes of grains all affect the angle of repose of a pile of granular material
- Be able to appreciate the various ways in which soil can fail in compression and how the choice of failure mode is a function of the water content of the soil
- Be able to recognise the factors which cause soil to fail catastrophically and flow like a liquid – the phenomenon of liquefaction
- Recognise that quicksand is dangerous, but that if you ever happen to fall into quicksand, you can reassure yourself that you will not be sucked beneath the surface.
Going Further
Books
- A. Mehta, Granular Physics, CUP, 2007.
- A. Schofield, Disturbed Soil Properties and Geotechnical Design, Thomas Telford Ltd., London, 2005.
- A. Schofield and C.P. Wroth, Critical State Soil Mechanics, McGraw-Hill, Maidenhead, 1968.
- D.M. Wood, Soil Behaviour and Critical State Soil Mechanics, CUP, 1990.
Websites
- and
- en.Wikipedia.org/wiki/Soil_liquefaction
are both useful web sites to help to go further into the subject of granular flow and to cover aspects of granular materials not covered in detail in this TLP, such as how forces are transmitted between particles in granular media.
Other resources
For those interested in going much deeper into the subject of granular flow, these research references should be useful:
R. Albert, I. Albert, D. Hornbaker, P. Schiffer and A. Barabási, ‘Maximum angle of stability in wet and dry spherical granular media’, Phys. Rev. E 56, R6271-R6274 (1997).
A. Barabási, R. Albert, and P. Schiffer, ‘The physics of sand castles: maximum angle of stability in wet and dry granular media’, Physica A 266, 366-371 (1999).
M.D. Bolton, ‘The strength and dilatancy of sands’, Géotechnique 36, 65-78 (1986).
H.W. Chandler and D.E. Macphee, ‘A model for the flow of cement pastes’, Cem. Conr. Res. 33, 265-270 (2003).
B.-P. Dai, J. Yang and C.-Y. Zhou, ‘Micromechanical origin of angle of repose in grnular materials’, Granular Matter 19: art. 24 (2017).
P.A. Arias García, R.O. Uñac, A.M. Vidales and A. Lizcano, ‘Critical parameters for measuring angles of stability in natural granular materials’, Physica A 390, 4095-4104 (2011).
T.C. Halsey and A.J. Levine, ‘How sandcastles fall’, Phys. Rev. Lett. 80, 3141-3144 (1998).
B.C. Johnson, C.S. Campbell and H.J. Melosh, ‘The reduction of friction in long runout landslides as an emergent phenomenon’, J. Geophys. Res.: Earth Surf. 121, 881-889 (2016).
A. Khaldoun, E. Eiser, G.H. Wegdam and D. Bonn, ‘Liquefaction of quicksand under stress’, Nature 437, 635 (2005).
A. Mehta and G.C. Barker, ‘The dynamics of sand’, Rep. Prog. Phys. 57, 384-416 (1994).
C.N.P. Mackenzie, Traditional Timbering in Soft Ground Tunnelling: A Historical Review, British Tunnelling Society, 2014.
G.R. McDowell and M.D. Bolton, ‘On the micromechanics of crushable aggregates’, Géotechnique 48, 667-679 (1998).
G.R. McDowell, M.D. Bolton and D. Robertson, ‘The fractal crushing of granular materials’, J. Mech. Phys. Solids 44, 2079-2102 (1996).
S. Nowak, A. Samadan and A. Kudrolli, ‘Maximum angle of stability of a wet granular pile’, Nature Physics 1, 50-52 (2005).
D.A. Robinson and S.P. Friedman, ‘Observations of the effects of particle shape and particles size distribution on avalanching of granular media’, Physica A 311, 97-110 (2002).
C.M. Sands, A.R. Brown and H.W. Chandler, ‘The application of principles of soil mechanics to the modelling of pastes’, Granular Matter 13, 573-584 (2011).
Z.Y. Zhou, R.P. Zou, D. Pinson and A.B. Yu, ‘Angle of repose and stress distrbution of dandpiles formed with ellipsoidal particles’, Granular Matter 16, 695-709 (2014).