394
30 Complex Strain of Soils
As we said in Sect. 12.7, due to the complexity of building the general mathematical plasticity theory, currently it can be universally deemed that it is impossible
to create a single, universal, and sufficiently full plasticity theory by using either
classical methods of solid body mechanics or philosophical synergetic methods.
Therefore, we believe (see also p. 158) that much attention in the upcoming decades
will be paid to simplified settings and solutions of problems of non-elastic strains
reproducing the primary and most important properties of real bodies.
30.2 Simple Strain Model of Hardening Dense Soils
The studies show [1, 5] that low-moistened clay and loamy soils have a relatively
high strength. Ultimate compressive strength when compressing loamy gray soil
at a moisture of 0.61% reaches the strength of a grade 100 brick or even exceeds
it ([5], p. 276). Permanent strains (especially during elongation tests) are almost as
elastic strains. Such bodies are often called [12] semi-brittle.
During the non-elastic strain of a semi-brittle body [8], loosening or compaction
of the material structure occurs that is caused by the formation and growth or closure
of micro- and macro-fractures. This process manifests itself in a residual change in
volume.
Let us represent the full strain of such body as a sum of elastic, purely plastic
strain, as well as the strain of compaction (loosening). Let us write elastic strain
components in the principal axes (1, 2, 3) as
ε
y
j =
p
K
+
σ j − p
2G o
, (j = 1, 2, 3),
(30.1)
where K/3 is an elastic modulus of volumetric expansion, G o is the elastic shear
modulus, and the average stress p is defined by the formula as before:
p =
1
3
(σ 1 + σ 2 + σ 3 ).
(30.2)
Let us represent purely plastic strain as
ε
p
j = (σ j − p)
1
2G
−
1
2G o
, (j = 1, 2, 3),
(30.3)
whereas G is a still unknown function.
Let us represent the components of compaction (loosening) strain as
ε
p
j = f (σ n , σ m , p)|σ j − p|
1
G
−
1
G o
,
(30.4)
30 Complex Strain of Soils
As we said in Sect. 12.7, due to the complexity of building the general mathematical plasticity theory, currently it can be universally deemed that it is impossible
to create a single, universal, and sufficiently full plasticity theory by using either
classical methods of solid body mechanics or philosophical synergetic methods.
Therefore, we believe (see also p. 158) that much attention in the upcoming decades
will be paid to simplified settings and solutions of problems of non-elastic strains
reproducing the primary and most important properties of real bodies.
30.2 Simple Strain Model of Hardening Dense Soils
The studies show [1, 5] that low-moistened clay and loamy soils have a relatively
high strength. Ultimate compressive strength when compressing loamy gray soil
at a moisture of 0.61% reaches the strength of a grade 100 brick or even exceeds
it ([5], p. 276). Permanent strains (especially during elongation tests) are almost as
elastic strains. Such bodies are often called [12] semi-brittle.
During the non-elastic strain of a semi-brittle body [8], loosening or compaction
of the material structure occurs that is caused by the formation and growth or closure
of micro- and macro-fractures. This process manifests itself in a residual change in
volume.
Let us represent the full strain of such body as a sum of elastic, purely plastic
strain, as well as the strain of compaction (loosening). Let us write elastic strain
components in the principal axes (1, 2, 3) as
ε
y
j =
p
K
+
σ j − p
2G o
, (j = 1, 2, 3),
(30.1)
where K/3 is an elastic modulus of volumetric expansion, G o is the elastic shear
modulus, and the average stress p is defined by the formula as before:
p =
1
3
(σ 1 + σ 2 + σ 3 ).
(30.2)
Let us represent purely plastic strain as
ε
p
j = (σ j − p)
1
2G
−
1
2G o
, (j = 1, 2, 3),
(30.3)
whereas G is a still unknown function.
Let us represent the components of compaction (loosening) strain as
ε
p
j = f (σ n , σ m , p)|σ j − p|
1
G
−
1
G o
,
(30.4)