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33.11: Questions

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    You should be able to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

    Which of these factors do not influence the angle of repose taken up by a pile of granular particles?

    a Shape
    b Friction
    c Density
    d Cohesion

    C. Density. Shape is important - the more 'angular' the particles, the more likely the angle of repose will be higher. Conversely, the more rounded the particles, the lower the angle of repose, all other factors remaining unchanged. Friction is vitally important - without friction, even a simple arrangement such as a regular tetrahedron on a flat surface is unstable. Cohesion is also important, and is particularly important if there is a steep angle to be maintained by a pile of granular particles, e.g., when building a sandcastle.

    Which of the following systems of granular materials exhibit dilatancy?

    a Soil which when picked up from the ground is dry to the touch
    b Tomato ketchup
    c Sparkly nail polish
    d Soil which when picked up from the ground is wet to the touch

    D. Soil which when picked up is dry to the touch has too low a water content to be able to dilate. When packed together, this type of soil will take in water to fill the pores between the grains of soil. Shearing this soil will enable grains to move relative to one another so that the packing efficiency is improved and so there is a decrease in the overall porosity of the soil aggregate. Tomato ketchup is a suspension of edible solids within water at a level typically of 25% by volume. It is a shear-thinning fluid, meaning that its viscosity decreases as it is sheared, in contrast to shear-thickening fluids such as dense wet sand, the viscosity of which increases as it is sheared. Sparkly nail polish has a suspension of particles such as mica, BiOCl (bismuth oxychloride) and aluminium powder, but the amount of solids per unit volume in the fluid is too low to cause the phenomenon of dilatancy - nail polish is in essence a liquid containing small granular particles, rather than being a wet assembly of granular material.

    Inspired by this TLP, you purchase some corn starch and mix it with water in the ratio by volume of 1 part water to 2 parts corn starch to make a thick paste of corn starch which you pour into a large plastic container. The surface of the corn starch is then hit quickly with a rubber mallet so that the time of contact with the surface is 100 milliseconds or so. What happens to the surface of the corn starch?

    a The rubber mallet bounces back from the surface. Everything happens too quickly to work out what is going on!
    b Water retreats from where the impact is made by the rubber mallet because of the phenomenon of dilatancy, so that in this region the surface goes from shiny to matt after the hammer has struck. The rubber mallet causes a small impression in the corn starch which over time gradually disappears as water returns. Eventually, the surface returns to being shiny and it is difficult to determine where the rubber mallet had struck.
    c The rubber mallet causes a mess everywhere because it has gone deep into the paste initially, causing paste to be ejected from the surface into the surrounding environment, and has then been forcibly removed.
    d The surface of the cornstarch is lowered where the rubber mallet has struck, but it returns to its initial state quickly. There is no change to the shininess of the surface anywhere.

    B. However, this answer will be heavily dependent on making a sufficiently dense paste of corn starch. If the paste is not dense enough, so that the density of corn starch particles per unit volume is not high enough, the rubber mallet will be able to go deep into the paste and it will splash (answer (c)). Answers (a) and (d) would suggest that you have not paid enough attention when undertaking the experiment!

    Deeper questions

    The following questions require some thought and reaching the answer may require you to think beyond the contents of this TLP.

    Ginkaku-ji ('The Silver Pavilion') is a Zen temple in Kyoto, Japan renowned for its meticulously maintained raked dry sand garden called Ginshadan known as the 'sea of silver sand' next to which there is a massive 1.8 m high sand cone platform called Kogetsudai said to symbolise Mount Fuji.

    The 'angle of repose' of Kogetsudai is impressively high, as are the angles of repose in Ginshadan. Which of the following are the most likely explanations for how these angles of repose are maintained?

    • a The sand is highly angular, very cohesive and has a high coefficient of friction because it is unusually rough to enable the sand particles to form such steep structures.
    • b Moisture, e.g., water, is added to the dry sand daily to enable the structures to be maintained, just like the shapes of sandcastles can be maintained by adhesive forces generated by capillarity between grains.
    • c The dry sand contains some cementitious binding agent such as cement, gypsum mortar or lime mortar cunningly disguised in the white sand.
    • d The custodians of such dry sand gardens have secrets handed down to them by their predecessors over the years which science has yet to establish.

    All of the above, apart from (d). A variety of special rakes are used by custodians of dry sand gardens and is it evident that water is used in the process of designing and maintaining these gardens - see and, so that areas which require raking need only be raked on a weekly basis. Therefore, the term 'dry sand garden' is somewhat of a misnomer. Where there are steep sides to dry sand garden features such as at Ginkaku-ji and at the sand mounds at Honen-in, it would make sense not to have to alter the underlying shape of the features, so that the underlying shape is a rigid assembly of sand and cement, i.e., concrete, on the surface of which there is a relatively thin dusting of moistened sand raked into shape. Custodians of these dry sand gardens clearly have expertise in maintaining them which can take time to learn, but which is explicable in terms of the science behind the art.

    Soil in an embankment is made progressively more wet by unusually heavy rain. What measures should be in place during the construction of the embankment and its subsequent maintenance to reduce the risk of possible failure of this embankment?


    This is a question which is of direct relevance to the construction of the levees which broke when Hurricane Katrina struck New Orleans in August 2005. In constructing and maintaining a soil embankment a number of engineering problems require attention: the foundations, the nature of the material used to construct the embankment and the degree of compaction, the need for adequate drainage, the monitoring of erosion and the monitoring of pore water pressure. A relevant research paper on the levees which failed in New Orleans is G. L. Sills, N. D. Vroman, R. E. Wahl and N. T. Schwanz, Overview of New Orleans levee failures: lessons learned and their impact on national levee design and assessment, J. Geotech. Geoenv. Engng. 134, 556-565 (2008).

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