The elastic modulus of soil particles are much more than the elastic modulus of soil. So, the deformation due to compression of soil particle is neglected (very small in comparison with other deformations) [Of course soil particles cannot impose tension]. The deformation of soil is the result of rearrangement of soil particle, in fact, they roll and slide with respect to each other.
The deformation can be classified into two types: pure compression and shear deformation.
Pure compression: the shape is same meanwhile the volume increases. The condition of external loads is homogeneous in all directions (hydro-static external loads – for a cube, in 3 directions). Obviously, soil is not absolutely homogeneous material, so in pure compression, there is also shear, but local. The relation between stress (sigma) and strain (epsilon) is:
Why volume strain – epsilonvol? Because, we have epsilonV=epsilonXX+epsilonYY+epsilonYY. In pure compression, the shear strains IJ are zeros. The deformation is compression, so the positive direction of the horizontal axis is -epsilonV. As we expect, when the load is applied, the stiffness of soil is E1, it means: sigma1=E1*epsilonV1. In progress, the volume of soil is increasing, meanwhile, the number of soil particles is unchanged, consequently, the porous of soil is increasing. As a result, the stiffness of soil is increasing. It means: after some time stiffness of soil becomes E2>E1. The stiffness, mathematically, is tangent of the curve sigma-epsilon, is increasing. In this tendency, when stress becomes infinite large, the stiffness also become infinite large too. Mathematically, stiffness=derivative of curve sigma-epsilon.
The pure shear is: the volume is the same, but the shape changes. When shear load increases, the compression load is unchanged, soil particles are expected to slide and roll with respect to each other. Why? As we know, at each contact point of particles, the relation between shear and normal stress is restricted less then a certain value (internal friction fint). The normal stress remains unchanged due to the constant of compression load. The shear stress increases, and, when it is large enough, particle will roll and slide. It contacts with neighbor ones and make them roll and slide, as well. The deformation due to pure shear is comparatively large in comparison with deformation of pure compression. Let’s consider to relation between epsilon and tau/sigma. Why tau/sigma but not tau? The reason is that failure shear stress depends on normal stress by constant – value of internal friction. When sigma increases, the shear stress increases, as well. But when shear stress (tau) increases, stiffness in distortion of soil decreases. It’s suitable to logic. Increasing of shear stress, soil particles are seemly to roll and slide more. The stiffness in distortion, mathematically, as a derivative of the curve (tau/sigma -epsilon), decreases. Expecting, when shear stress become infinite large, stiffness in distortion becomes zeros and shear deformation will infinitely large.
The key: Compression makes soil stiffer, distortion makes soil softer.
Unloading and Reloading
Deformation of soil is due to rearrangement of soil particles. Especially, deformation mainly created by shear deformation, that is irreversible. So in unloading, there is irreversible deformation. In reloading, when the value of stress is under maximum previous load, deformation is considered as elastic. Why?
Let’s have a look at the figure: When stress in reloading in under maximum sustained stress, the soil (stiffer than in virgin loading) is responded as elastic material, although there is some plastic deformation.
Over-consolidation is when the load on reloading process is larger than maximum sustained load. Pre-consolidation is oppositely, in reloading process, the load is under the maximum previous value. In over-consolidation, the soil is become softer quickly.
Dilatation and contraction
Dilatancy and contractancy.
Imagining soil particles are as circles. Their relative position make soil become very dense or very loose. In densest condition: porous space is minimum. In shear deformation, particles roll and slide with respect to each other. It makes porous space increase, as a result the volume increases. For saturated soil, the phenomenon has significant role. Under shear loads, the soil sustains shear deformation. Dilatancy is occurred when the volume increases. The porous space increases. Water is required to fill pore. This lead at just moment, the pore pressure ( pore stress) is increasing. The total stress remain unchanged due to the same external load. As a result, the effective stress increases, the soil is stiffer (until water fills out porous space).
Oppositely, contractancy is for loosest soil, makes soil volume increase. It make saturated soil become softer. In some cases, the effective stress is become zeros, and soil becomes liquid → liquefaction.
Circle loads
After each circle load, soil seems to be contract. It means after a circle load, some particles find new positions to make the volume become smaller. The phenomenon seemly lasts forever.
