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Uniform effective stress equation for soil mechanics
Équation aux contraintes effectives uniformes pour la Mécanique des Sols
Shao L.-T., Liu G., Guo X.-X.
Dalian University of Technology, Dalian, P. R. China
ABSTRACT: The internal force of soil skeleton may, according to its different effect, be seperated into two groups of different
balance system, including one by external load, and the pore fluid pressure and the skeleton internal force by it. In this paper we
define the soil skeleton stress as the soil skeleton internal force by the external load excluding the pore fluid pressure. Then taking the
soil skeleton, pore water and pore air as independent analysis object, we educe the soil differential equation of equilibrium from the
balance analysis of infinitesimal. By comparing with the soil differential equation of equilibrium of total stress after adding up the soil
differential equation of equilibrium of each phase of the soil, we can obtain the relationship expression of total soil stress, skeleton
stress and pore fluid pressure, which is considered as the soil skeleton stress equation, equivalent to the effective stress equation by
Terzaghi in the saturated condition. Therefore, the uniform soil mechanics effective stress equation is obtained, indicating the physical
property of the effective stress equation is the interaction of inter-phase forces. The effective stress expression on the basis of the
shearing strength equivalent or volume deformation equivalent can be expressed with the soil skeleton stress or pore fluid pressure as
well.
RÉSUMÉ : Les efforts subis par le squelette solide d’un sol peuvent se diviser en deux parties en équilibres qui sont celles dues à le
pression du fluide interstitiel et celle due au chargement externe. Dans cet article, dans l’analyse des efforts sur le squelette les effets
de la pression interstitielle ne sont pas pris en compte dans un premier temps. Ensuite, on écrit les équations d’équilibre global sur un
élément de volume infinitésimal en introduisant les effets des pressions de fluide et de gaz interstitiels. On analyse successivement
l’équilibre de chaque phase et on additionne ensuite les équations ce qui permet de relier entre eux les efforts total, effective et de
pression de fluide. L’équation des efforts du squelette représente, dans le cas saturé, l’équation sur les contraintes effectives de Karl
Terzaghi. On trouve ainsi une équation unifiant des contraintes effectives en Mécanique des Sols. On l’utilise pour prouver que la
nature physique de l’équation des contraintes effectives est de représenter l’interaction entre les différentes phases. On peut aussi
établir de manière équivalente une expression de la contrainte effective basée sur la contrainte de cisaillement ou la déformation
volumique.
KEYWORDS: Soil mechanics ; Effective stress equation ; Soil skeleton stress ; Saturated soil ; Unsaturated soil ; Equivalent stress
1 INTRODUCTION
The soil is the multiple-phase body of the soil skeleton and
pore fluid, of which the former forms the soil structure The soil
deformation and shearing strength is considered as the soil
skeleton deformation and shearing strength.
The analysis shall, according to the present soil mechanics
study method, be made on the soil internal force, with the whole
soil including the pore fluid as the object and obtain the
effective stress controlling the soil deformation and strength
with the introduction of the effective stress principle. In terms
of effective stress, some scholars consider it as the equivalent
stress educed from the soil strength or deformation equivalent
while some others regard it as the soil skeleton stress. However,
the effective stress principle has no sufficient theoretical basis.
Therefore, the principle has been in debate since it was put
forward, with focus on the amendment and applicability of the
effective stress equation for the saturated soil and whether there
is the effective stress equation and its form for the unsaturated
soil.
This thesis, taking the soil skeleton and pore water as
independent analysis object, divided the force on the soil
skeleton into two groups of balance system according to
different effects. The thesis educes the internal force differential
equation of equilibrium of the saturated and unsaturated soil
with the interaction principle of inter-phase force, thus
obtaining the soil skeleton stress equation, which indicates the
soil skeleton stress equation is the soil effective stress equation.
The thesis makes further discussion on the effective stress
principle, indicating the effective stress equation by Terzaghi is
unnecessary to be amended for it’s accurately tenable for the
saturated soil. The effective stress expression on the basis of the
shearing strength equivalent or volume deformation equivalent
may be expressed with the soil skeleton stress or pore fluid
pressure as well. The study in the thesis may provide foundation
for establishing the uniform soil mechanics theory of the
saturated and unsaturated soil.
2 TWO BALANCE FORCE SYSTEMS ACTING ON SOIL
SKELETON
To be definite, we consider the stress of the soil mixture as
the total soil stress and the stress with the skeleton as the
independent analysis object as the soil skeleton stress. In the
internal force analysis on infinitesimal free body with the soil
skeleton as the independent object, the acting forces shall be
divided into two balance force systems, namely, the external
load (excluding pore fluid pressure) and arising interaction
forces between skeleton grains and the pore fluid pressure and
arising interaction force between grains .
To place an isolated waterproof soil grain (as sand) in the
water statically, if the pressure difference of different depth of
the water is ignored, each point of the grain surface will bear the
