One-dimensional compression

Virgin load: The load, that is larger than maximum previous load.

Unloading and reloading are quite important terminals in soil mechanics.

Linear elastic material

Compression modulus: K=E/(3*(1-2*v))

Shear modulus: G=E/(2*(1+v))

E is Young modulus and v is Passion’s coefficient.

Real soil

Actually, soil is non-linear and also non-elastic material. K and G are considered as tangent modulus of the curve “stress-strain”. But if the increasing of stress is small (in comparison with maximum sustained stress ), and the strain is as a result small, we can consider soil as linear material, or delta stress/delta strain = constant. On the other hand, the plasticity is neglected, irreversible deformation is disregarded. We can say, compression modulus and shear modulus K and G are  functions of initial stresses.

One-dimensional compression

εvol=εzz, εxx=εyy=εxy=εxz=εyz=0;

Constrained modulus D=3*(1-v)/(1+v)*K=E*(1-v)/(1+v)/(1-2*v) (As linear elastic material)

lnσ-lnσ0=-C*ε → dσ/dε=-C*σ → D=C*σ. Apparently, the constrained modulus (stiffness) is increasing linearly with stress. It give chance to estimate (originally) of stiffness of soil layer in some depth.