Terzaghi's Principle states that when stress is applied to a porous material, it is opposed by the fluid pressure filling the pores in the material.
Karl von Terzaghi
Karl von Terzaghi (October 2, 1883 – October 25, 1963) was an Austrians, Austrian Mechanical Engineer, mechanical engineer, geotechnical engineer, and geologist known as the "father of soil mechanics and geotechnical engineering".
Early life
I ...
introduced the idea in a series of papers in the 1920s based on his examination of building
consolidation on soil. The principle states that all quantifiable changes in
stress to a
porous medium
In materials science, a porous medium or a porous material is a material containing pores (voids). The skeletal portion of the material is often called the "matrix" or "frame". The pores are typically filled with a fluid (liquid or gas). The sk ...
are a direct result of a change in
effective stress
Effective stress is a fundamental concept in soil mechanics and geotechnical engineering that describes the portion of total stress in a soil mass that is carried by the solid soil skeleton, rather than the pore water. It is crucial for understan ...
. The ''effective stress,''
, is related to ''total stress,''
, and the ''pore pressure,''
, by
:
,
where
is the
identity matrix
In linear algebra, the identity matrix of size n is the n\times n square matrix with ones on the main diagonal and zeros elsewhere. It has unique properties, for example when the identity matrix represents a geometric transformation, the obje ...
. The negative sign is there because the pore pressure serves to lessen the volume-changing stress; physically this is because there is fluid in the pores which bears a part of the total stress, so partially unloading the solid matrix from normal stresses.
Terzaghi's principle applies well to porous materials whose solid constituents are incompressible - soil, for example, is composed of grains of incompressible silica so that the volume change in soil during consolidation is due solely to the rearrangement of these constituents with respect to one another. Generalizing Terzaghi's principle to include compressible solid constituents was accomplished by
Maurice Anthony Biot in the 1940s, giving birth to the theory of
poroelasticity and
poromechanics.
[Biot, M. A. "The general three—dimensjona1 consolidation theory." ''Journal ofAppfied Physics'' 12.2 (1941): 155-164.]
Assumptions of Terzaghi's Principle
# The soil is homogenous (uniform in composition throughout) and isotropic (show same physical property in each direction).
# The soil is fully saturated (zero air voids due to water content being so high).
# The solid particles are incompressible.
# Compression and flow are one-dimensional (vertical axis being the one of interest).
#
Strains in the soil are relatively small.
#
Darcy's Law is valid for all hydraulic gradients.
# The coefficient of
permeability and the coefficient of
volume compressibility remain constant throughout the process.
# There is a unique relationship, independent of time, between the
void ratio and effective stress
Validity
Though the first 5 assumptions are either likely to hold, or deviation will have no discernible effect, experimental results contradict the final 3. Darcy's Law does not seem to hold at high hydraulic gradients, and both the coefficients of permeability and volume compressibility decrease during consolidation. This is due to the non-linearity of the relationship between void ratio and effective stress, although for small stress increments assumption 7 is reasonable. Finally, the relationship between void ratio and effective stress is not independent of time, again proven by experimental results.
Over the past century several formulations have been proposed for the effective stress according to several work hypotheses (e.g. compressibility of grains, their brittle or plastic behavior, high confining stress etc.).
By way of example, at high pressures (e.g. in the Earth crust, at depth of some km, where the lithostatic load can reach values of several hundreds of MPa), Terzaghi’s formulation shows relevant deviation from experimental data and the formulation provided by
Alec Skempton should be utilized, in order to achieve more accurate results. Substantially, the effective stress definition is conventional and related to the problem being treated.
Among various effective stress formulations, Terzaghi's one seems particularly appropriate, for its simplicity and as it describes with excellent approximation a wide variety of real cases.
See also
*
Karl von Terzaghi
Karl von Terzaghi (October 2, 1883 – October 25, 1963) was an Austrians, Austrian Mechanical Engineer, mechanical engineer, geotechnical engineer, and geologist known as the "father of soil mechanics and geotechnical engineering".
Early life
I ...
References
{{reflist
External links
Amazon.com link
Soil mechanics