Chapter 31
Simple Loadings of Geomaterials
31.1 Uniaxial Compression
In this case, σ 1 = σ 2 = 0, σ 3 < 0; σ n < 0, SG(σ n ) = −1. Let us designate
σ = |σ 3 | and ε = |ε 3 |. Then σ m = σ and
p = −
1
3
σ ; τ o =
√
2
3
σ ; = c =
2
3 + c
; u = c τ o .
(31.1)
Taking into account formulas (31.1) from (30.6) in the considered case, it follows
that:
ε 1 = ε 2 =
σ
3
−
1
K
+
1
2G
−
3
4
η
1
G
+
1
G o
;
ε = |ε 3 | =
σ
3
1
K
+
1
2G
+
3
2
η
1
G
+
1
G o
.
(31.2)
In this manner, a link between stresses and strains is given by formulas (31.2),
where G is defined according to (30.13) or (30.17).
31.2 Creep in Uniaxial Compression
Assume that the stress σ (t ∗ ) = σ ∗ is recorded at some point in time t ∗ during
uniaxial compression. By designating
u
∗
= u(τ
∗
o ) = c
σ ∗
3
√
2,
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
V. Molotnikov, A. Molotnikova, Theory of Elasticity and Plasticity,
https://doi.org/10.1007/978-3-030-66622-4_31
401