![MasonSandDryTriaxialCompressionStressDiffStrain](https://upload.wikimedia.org/wikipedia/commons/9/9e/MasonSandDryTriaxialCompressionStressDiffStrain.png)
Dilatancy is the volume change observed in
granular materials
A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose gra ...
when they are subjected to
shear deformations. This effect was first described scientifically by
Osborne Reynolds
Osborne Reynolds (23 August 1842 – 21 February 1912) was an Irish-born innovator in the understanding of fluid dynamics. Separately, his studies of heat transfer between solids and fluids brought improvements in boiler and condenser design. ...
in 1885/1886
[Reynolds, O., "Experiments showing dilatancy, a property of granular material, possibly connected with gravitation," Proc. Royal Institution of Great Britain, Read, February 12, 1886.] and is also known as Reynolds dilatancy.
Unlike most other solid materials, the tendency of a compacted dense
granular material
A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose gra ...
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
A lever is a simple machine consisting of a beam or rigid rod pivoted at a fixed hinge, or ''fulcrum''. A lever is a rigid body capable of rotating on a point on itself. On the basis of the locations of fulcrum, load and effort, the lever is div ...
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
Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to:
* Interstate compact
* Blood compact, an ancient ritual of the Philippines
* Compact government, a type of colonial rule utilized in British ...
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.
[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.][Poulos, S. J. (1971). The stress-strain curves of soils. Geotechnical Engineers Incorporated. Chicago.]
Dilatancy is a common feature of
soil
Soil, also commonly referred to as earth or dirt, is a mixture of organic matter, minerals, gases, liquids, and organisms that together support life. Some scientific definitions distinguish ''dirt'' from ''soil'' by restricting the former te ...
s and
sand
Sand is a granular material composed of finely divided mineral particles. Sand has various compositions but is defined by its grain size. Sand grains are smaller than gravel and coarser than silt. Sand can also refer to a textural class of s ...
s. 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.
Reynolds dilatancy concept has been brought into the field of
geotechnical engineers
Geotechnical engineering is the branch of civil engineering concerned with the engineering behavior of earth materials. It uses the principles of soil mechanics and rock mechanics for the solution of its respective engineering problems. It als ...
by ,
[Rowe, P. W., "The stress-dilatancy relation for static equilibrium of an assembly of particles in contact," Proceedings of the Royal Society A, 1962.] and is a part of the broader topic of
soil mechanics
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 (usually air and wat ...
.
Phenomenon
![SoilDilatancySimpleShear plain](https://upload.wikimedia.org/wikipedia/commons/b/b9/SoilDilatancySimpleShear_plain.svg)
The phenomenon of dilatancy can be observed in a drained
simple shear
Simple shear is a deformation in which parallel planes in a material remain parallel and maintain a constant distance, while translating relative to each other.
In fluid mechanics
In fluid mechanics, simple shear is a special case of deformati ...
test on a sample of dense sand. In the initial stage of deformation, the
volumetric strain
In continuum mechanics, the infinitesimal strain theory is a mathematical approach to the description of the deformation of a solid body in which the displacements of the material particles are assumed to be much smaller (indeed, infinitesimal ...
decreases as the
shear strain
In physics, deformation is the continuum mechanics transformation of a body from a ''reference'' configuration to a ''current'' configuration. A configuration is a set containing the positions of all particles of the body.
A deformation can ...
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
Effectiveness is the capability of producing a desired result or the ability to produce desired output. When something is deemed effective, it means it has an intended or expected outcome, or produces a deep, vivid impression.
Etymology
The ori ...
normal stress
In continuum mechanics, stress is a physical quantity. It is a quantity that describes the magnitude of forces that cause deformation. Stress is defined as ''force per unit area''. When an object is pulled apart by a force it will cause elonga ...
is decreased.
[Houlsby, G. T. How the dilatancy of soils affects their behaviour. University of Oxford, Department of Engineering Science, 1991.http://www.eng.ox.ac.uk/civil/publications/reports-1/ouel_1888_91.pdf]
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.
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.
PLAXIS 2D CE V20.02: 3 - Material Models Manual.pdf page 78
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See also
* Triaxial shear tests
A triaxial shear test is a common method to measure the mechanical properties of many deformable solids, especially soil (e.g., sand, clay) and rock, and other granular materials or powders. There are several variations on the test.
In a triaxial ...
References
{{Geotechnical engineering
Soil mechanics