Primary Consolidation Parameters
The primary consolidation settlement of the soil (settlement that occurs along path AB in Figure can be expressed through the slopes of the curves in Figure 9.3. We are going to defi ne two slopes for primary consolidation. One is called the coeffi cient of compression or compression index, Cc, and is obtained from the plot of e versus log s9z.
where the subscripts 1 and 2 denote two arbitrarily selected points on the NCL. The other is called the modulus of volume compressibility, mv, and is obtained from the plot of εz versus s9z (Figure as
where the subscripts 1 and 2 denote two arbitrarily selected points on the NCL.
Similarly, we can defi ne the slope BC in Figure 9.3b as the recompression index, Cr, which we can express as
where the subscripts 1 and 2 denote two arbitrarily selected points on the URL. The slope BC in Figure 9.3c is called the modulus of volume recompressibility, mvr, and is expressed as
where the subscripts 1 and 2 denote two arbitrarily selected points on the URL.
From Hooke’s law, we know that Young’s modulus of elasticity is
where the subscript c denotes constrained because we are constraining the soil to settle only in one direction (one-dimensional consolidation), E9 is Young’s modulus based on effective stresses, and n9 is Poisson’s ratio. We can rewrite Equation as
The slopes Cc, Cr, mv, and mvr are positive values to satisfy our sign convention of compression or recompression as positive.
Effects of Loading History:
In our experiment, we found that during reloading the soil follows the normal consolidation line when the past maximum vertical effective stress is exceeded. The history of loading of a soil is locked in its fabric, and the soil maintains a memory of the past maximum effective stress. To understand how the soil will respond to loads, we have to unlock its memory. If a soil were to be consolidated to stresses below its past maximum vertical effective stress, then settlement would be small because the soil fabric was permanently changed by a higher stress in the past.
However, if the soil were to be consolidated beyond its past maximum effective stress, settlement would be large for stresses beyond its past maximum effective stress because the soil fabric would now undergo further change from a current loading that is higher than its past maximum effective stress. The practical signifi cance of this soil behavior is that if the loading imposed on the soil by a structure is such that the vertical effective stress in the soil does not exceed its past maximum vertical effective stress, the settlement of the structure would be small, otherwise signifi cant permanent settlement would occur. The past maximum vertical effective stress defi nes the limit of elastic behavior. For stresses that are lower than the past maximum vertical effective stress, the soil will follow the URL and we can reasonably assume that the soil will behave like an elastic material. For stresses greater than the past maximum vertical effective stress, the soil would behave like an elastoplastic material.