Dilatancy (granular material)

Last updated
Typical curves of stress-difference as a function of strain in dense sands. MasonSandDryTriaxialCompressionStressDiffStrain.png
Typical curves of stress-difference as a function of strain in dense sands.

In soil mechanics, dilatancy or shear dilatancy [1] is the volume change observed in granular materials when they are subjected to shear deformations. [2] [3] This effect was first described scientifically by Osborne Reynolds in 1885/1886 [4] [5] and is also known as Reynolds dilatancy. It was brought into the field of geotechnical engineering by Peter Walter Rowe  [ de ]. [6]

Contents

Unlike most other solid materials, the tendency of a compacted dense granular material is to dilate (expand in volume) as it is sheared. This occurs because the grains in a compacted state are interlocking and therefore do not have the freedom to move around one another. When stressed, a lever motion occurs between neighboring grains, which produces a bulk expansion of the material. On the other hand, when a granular material starts in a very loose state it may continuously compact instead of dilating under shear. A sample of a material is called dilative if its volume increases with increasing shear and contractive if the volume decreases with increasing shear. [7] [8]

Dilatancy is a common feature of soils and sands. Its effect can be seen when the wet sand around the foot of a person walking on beach appears to dry up. The deformation caused by the foot expands the sand under it and the water in the sand moves to fill the new space between the grains.

Phenomenon

Dilatancy of a sample of dense sand in simple shear. SoilDilatancySimpleShear plain.svg
Dilatancy of a sample of dense sand in simple shear.

The phenomenon of dilatancy can be observed in a drained simple shear test on a sample of dense sand. In the initial stage of deformation, the volumetric strain decreases as the shear strain increases. But as the stress approaches its peak value, the volumetric strain starts to increase. After some more shear, the soil sample has a larger volume than when the test was started.

The amount of dilation depends strongly on the initial density of the soil. In general, the denser the soil, the greater the amount of volume expansion under shear. It has also been observed that the angle of internal friction decreases as the effective normal stress is decreased. [9]

The relationship between dilation and internal friction is typically illustrated by the sawtooth model of dilatancy where the angle of dilation is analogous to the angle made by the teeth to the horizontal. Such a model can be used to infer that the observed friction angle is equal to the dilation angle plus the friction angle for zero dilation.[ citation needed ]

Why is dilatancy important?

Because of dilatancy, the angle of friction increases as the confinement increases until it reaches a peak value. After the peak strength of the soil is mobilized the angle of friction abruptly decreases. As a result, geotechnical engineering of slopes, footings, tunnels, and piles in such soils have to consider the potential decrease in strength after the soil strength reaches this peak value.

Poorly / uniformly graded silt with trace sand to sandy that is non-plastic can be associated with challenges during construction, even when they are hard. These materials often appear to be granular because the silt is so coarse and thus may be described as dense to very dense. Vertical excavations below the water table in these soil types exhibit short term stability, similar to many dense sandy soil deposits, in part due to matric suction. However, as shearing of the soil occurs in the active wedge due to gravity forces, strength is lost and the rate of failure accelerates. This can be exacerbated by hydrostatic forces developing at the location(s) where water (drains to and) collects in tension cracks in or near the back of the active wedge. Generally retrogressive spalling manifests, often accompanied by piping / internal erosion. The use of appropriate filters is critical to managing these materials; a preferred filter might be a #4 sized clear gravel / coarse-grained sand as a commercial aggregate which is generally readily available. Some non- woven filter fabrics are also suitable. As with all filters, D15 and D50 compatibility criteria should be checked.

Dilatancy cut-off

After extensive shearing, dilating materials arrive in a state of critical density where dilatancy has come to an end. This phenomenon of soil behaviour can be included in the Hardening Soil model by means of a dilatancy cut-off. In order to specify this behaviour, the initial void ratio, , and the maximum void ratio, , of the material must be entered as general parameters. As soon as the volume change results in a state of maximum void, the mobilised dilatancy angle, , is automatically set back to zero. [10]

See also

Related Research Articles

<span class="mw-page-title-main">Geotechnical engineering</span> Scientific study of earth materials in engineering problems

Geotechnical engineering, also known as geotechnics, is the branch of civil engineering concerned with the engineering behavior of earth materials. It uses the principles of soil mechanics and rock mechanics to solve its engineering problems. It also relies on knowledge of geology, hydrology, geophysics, and other related sciences.

Rheology is the study of the flow of matter, primarily in a fluid state but also as "soft solids" or solids under conditions in which they respond with plastic flow rather than deforming elastically in response to an applied force. Rheology is the branch of physics that deals with the deformation and flow of materials, both solids and liquids.

<span class="mw-page-title-main">Plasticity (physics)</span> Non-reversible deformation of a solid material in response to applied forces

In physics and materials science, plasticity is the ability of a solid material to undergo permanent deformation, a non-reversible change of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the material itself. In engineering, the transition from elastic behavior to plastic behavior is known as yielding.

<span class="mw-page-title-main">Quicksand</span> Mixture of sand, silt or clay with water, which creates a liquefied soil when agitated

Quicksand is a colloid consisting of fine granular material and water. It forms in saturated loose sand when the sand is suddenly agitated. When water in the sand cannot escape, it creates a liquefied soil that loses strength and cannot support weight. Quicksand can form in standing water or in upward flowing water. In the case of upward flowing water, forces oppose the force of gravity and suspend the soil particle.

<span class="mw-page-title-main">Angle of repose</span> Steepest angle at which granular materials can be piled before slumping

The angle of repose, or critical angle of repose, of a granular material is the steepest angle of descent or dip relative to the horizontal plane on which the material can be piled without slumping. At this angle, the material on the slope face is on the verge of sliding. The angle of repose can range from 0° to 90°. The morphology of the material affects the angle of repose; smooth, rounded sand grains cannot be piled as steeply as can rough, interlocking sands. The angle of repose can also be affected by additions of solvents. If a small amount of water is able to bridge the gaps between particles, electrostatic attraction of the water to mineral surfaces increases the angle of repose, and related quantities such as the soil strength.

<span class="mw-page-title-main">Soil liquefaction</span> Soil material that is ordinarily a solid behaving like a liquid

Soil liquefaction occurs when a cohesionless saturated or partially saturated soil substantially loses strength and stiffness in response to an applied stress such as shaking during an earthquake or other sudden change in stress condition, in which material that is ordinarily a solid behaves like a liquid. In soil mechanics, the term "liquefied" was first used by Allen Hazen in reference to the 1918 failure of the Calaveras Dam in California. He described the mechanism of flow liquefaction of the embankment dam as:

If the pressure of the water in the pores is great enough to carry all the load, it will have the effect of holding the particles apart and of producing a condition that is practically equivalent to that of quicksand... the initial movement of some part of the material might result in accumulating pressure, first on one point, and then on another, successively, as the early points of concentration were liquefied.

<span class="mw-page-title-main">Granular material</span> Conglomeration of discrete solid, macroscopic particles

A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact. The constituents that compose granular material are large enough such that they are not subject to thermal motion fluctuations. Thus, the lower size limit for grains in granular material is about 1 μm. On the upper size limit, the physics of granular materials may be applied to ice floes where the individual grains are icebergs and to asteroid belts of the Solar System with individual grains being asteroids.

<span class="mw-page-title-main">Soil mechanics</span> Branch of soil physics and applied mechanics that describes the behavior of soils

Soil mechanics is a branch of soil physics and applied mechanics that describes the behavior of soils. It differs from fluid mechanics and solid mechanics in the sense that soils consist of a heterogeneous mixture of fluids and particles but soil may also contain organic solids and other matter. Along with rock mechanics, soil mechanics provides the theoretical basis for analysis in geotechnical engineering, a subdiscipline of civil engineering, and engineering geology, a subdiscipline of geology. Soil mechanics is used to analyze the deformations of and flow of fluids within natural and man-made structures that are supported on or made of soil, or structures that are buried in soils. Example applications are building and bridge foundations, retaining walls, dams, and buried pipeline systems. Principles of soil mechanics are also used in related disciplines such as geophysical engineering, coastal engineering, agricultural engineering, hydrology and soil physics.

<span class="mw-page-title-main">Effective stress</span>

The effective stress can be defined as the stress, depending on the applied tension and pore pressure , which controls the strain or strength behaviour of soil and rock for whatever pore pressure value or, in other terms, the stress which applied over a dry porous body provides the same strain or strength behaviour which is observed at ≠ 0. In the case of granular media it can be viewed as a force that keeps a collection of particles rigid. Usually this applies to sand, soil, or gravel, as well as every kind of rock and several other porous materials such as concrete, metal powders, biological tissues etc. The usefulness of an appropriate ESP formulation consists in allowing to assess the behaviour of a porous body for whatever pore pressure value on the basis of experiments involving dry samples.

A direct shear test is a laboratory or field test used by geotechnical engineers to measure the shear strength properties of soil or rock material, or of discontinuities in soil or rock masses.

<span class="mw-page-title-main">Soil compaction</span> Process in geotechnical engineering to increase soil density

In geotechnical engineering, soil compaction is the process in which stress applied to a soil causes densification as air is displaced from the pores between the soil grains. When stress is applied that causes densification due to water being displaced from between the soil grains, then consolidation, not compaction, has occurred. Normally, compaction is the result of heavy machinery compressing the soil, but it can also occur due to the passage of, for example, animal feet.

<span class="mw-page-title-main">Triaxial shear test</span>

A triaxial shear test is a common method to measure the mechanical properties of many deformable solids, especially soil and rock, and other granular materials or powders. There are several variations on the test.

<span class="mw-page-title-main">Shearing (physics)</span> Deformation due to shear stress

In continuum mechanics, shearing refers to the occurrence of a shear strain, which is a deformation of a material substance in which parallel internal surfaces slide past one another. It is induced by a shear stress in the material. Shear strain is distinguished from volumetric strain. The change in a material's volume in response to stress and change of angle is called the angle of shear.

<span class="mw-page-title-main">Shear strength (soil)</span> Magnitude of the shear stress that a soil can sustain

Shear strength is a term used in soil mechanics to describe the magnitude of the shear stress that a soil can sustain. The shear resistance of soil is a result of friction and interlocking of particles, and possibly cementation or bonding of particle contacts. Due to interlocking, particulate material may expand or contract in volume as it is subject to shear strains. If soil expands its volume, the density of particles will decrease and the strength will decrease; in this case, the peak strength would be followed by a reduction of shear stress. The stress-strain relationship levels off when the material stops expanding or contracting, and when interparticle bonds are broken. The theoretical state at which the shear stress and density remain constant while the shear strain increases may be called the critical state, steady state, or residual strength.

In geology, a deformation mechanism is a process occurring at a microscopic scale that is responsible for changes in a material's internal structure, shape and volume. The process involves planar discontinuity and/or displacement of atoms from their original position within a crystal lattice structure. These small changes are preserved in various microstructures of materials such as rocks, metals and plastics, and can be studied in depth using optical or digital microscopy.

Methods have been devised to modify the yield strength, ductility, and toughness of both crystalline and amorphous materials. These strengthening mechanisms give engineers the ability to tailor the mechanical properties of materials to suit a variety of different applications. For example, the favorable properties of steel result from interstitial incorporation of carbon into the iron lattice. Brass, a binary alloy of copper and zinc, has superior mechanical properties compared to its constituent metals due to solution strengthening. Work hardening has also been used for centuries by blacksmiths to introduce dislocations into materials, increasing their yield strengths.

<span class="mw-page-title-main">Cellular confinement</span> Confinement system used in construction and geotechnical engineering

Cellular confinement systems (CCS)—also known as geocells—are widely used in construction for erosion control, soil stabilization on flat ground and steep slopes, channel protection, and structural reinforcement for load support and earth retention. Typical cellular confinement systems are geosynthetics made with ultrasonically welded high-density polyethylene (HDPE) strips or novel polymeric alloy (NPA)—and expanded on-site to form a honeycomb-like structure—and filled with sand, soil, rock, gravel or concrete.

In structural geology, strain partitioning is the distribution of the total strain experienced on a rock, area, or region, in terms of different strain intensity and strain type. This process is observed on a range of scales spanning from the grain – crystal scale to the plate – lithospheric scale, and occurs in both the brittle and plastic deformation regimes. The manner and intensity by which strain is distributed are controlled by a number of factors listed below.

In granular mechanics, the μ(I) rheology is one model of the rheology of a granular flow.

<span class="mw-page-title-main">Powder</span> Dry, bulk solid composed of fine, free-flowing particles

A powder is a dry, bulk solid composed of many very fine particles that may flow freely when shaken or tilted. Powders are a special sub-class of granular materials, although the terms powder and granular are sometimes used to distinguish separate classes of material. In particular, powders refer to those granular materials that have the finer grain sizes, and that therefore have a greater tendency to form clumps when flowing. Granulars refer to the coarser granular materials that do not tend to form clumps except when wet.

References

  1. Tighe, Brian P. (April 2014). "Shear dilatancy in marginal solids". Granular Matter. 16 (2): 203–208. doi:10.1007/s10035-013-0436-6.
  2. Nedderman, R. M. (1992). Statics and Kinematics of Granular Materials. doi:10.1017/CBO9780511600043. ISBN   978-0-521-40435-8.[ page needed ]
  3. Andreotti, Bruno; Forterre, Yoël; Pouliquen, Olivier (2013). Granular Media: Between Fluid and Solid. Cambridge University Press. ISBN   978-1-107-03479-2.[ page needed ]
  4. Reynolds, Osborne (December 1885). "LVII. On the dilatancy of media composed of rigid particles in contact. With experimental illustrations". The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science. 20 (127): 469–481. doi:10.1080/14786448508627791.
  5. Reynolds, Osborne (12 February 1886). Experiments showing dilatancy, a property of granular material, possibly connected with gravitation. Royal Institution of Great Britain. Weekly evening meeting. OCLC   1440246508.
  6. Rowe, P. W. (9 October 1962). "The stress-dilatancy relation for static equilibrium of an assembly of particles in contact". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 269 (1339): 500–527. Bibcode:1962RSPSA.269..500R. doi:10.1098/rspa.1962.0193.
  7. Casagrande, A., Hirschfeld, R. C., & Poulos, S. J. (1964). Fourth Report: Investigation of Stress-Deformation and Strength Characteristics of Compacted Clays. HARVARD UNIV CAMBRIDGE MA SOIL MECHANICS LAB.
  8. Poulos, S. J. (1971). The stress-strain curves of soils. Geotechnical Engineers Incorporated. Chicago.
  9. Houlsby, G. T. (28 May 1991). How the dilatancy of soils affects their behaviour (PDF). 10th European Conference on Soil Mechanics and Foundation Engineering. Florence, Italy. Bibcode:1991smfe.conf.....H.
  10. PLAXIS 2D CE V20.02: 3 - Material Models Manual.pdf page 78 [ full citation needed ]