Assumptions in Terzaghi's Consolidation Equation

Understanding consolidation is essential to soil mechanics, particularly in the design of foundations or structures that rest on soft soil. 

Terzaghi's consolidation equation outlines how soil gradually expels excess water as an applied load is introduced into the soil. However, like any mathematical model, Terzaghi's equation-based assumptions. Let's break it down into simple words:

 Assumptions in Terzaghi's Consolidation Equation:

1. Homogenous Mass of Soil

The soil is considered to be homogeneous in all respects such as density, permeability, compressibility, etc. While this does not hold true across each depth and location of soil, for our interest in simply assuming, we assume it to be homogeneous.

2. Fully Saturated Void Spaces with Water

This assumption means the soil is saturated. There is no air or space left; all of the voids-between the soil particles-are filled with water. This is normally the case for soils beneath the water table.

3. Soil Solids and Water Are Incompressible

Neither the soil particles nor the water that fills the voids is compressible. This makes the analysis somewhat easier because then consolidation will only be due to the flow of water out of the soil, not compression of the individual soil particles or water.

4. Darcy's Law Is Applicable

It relates the flow of the water in the soil to the differential pressure and the permeability of the soil. The assumptions involved in Darcy's law are that the flow of the water shall be slow and steady and relative permeability shall be considerable, allowing water to move through it in a predictable and systematic manner.

5. One-Dimensional Seepage and Deformation

Because flow and deformation happen only in one direction—along a vertical axis, for example—it is assumed. This simplifies the mathematics because, in reality, flow and deformation might happen in more than one direction.

6. Strains Are Small

The variations in the size or shape of the soil mass are much less compared to the overall dimensions of the soil. This assumption is crucial so that calculations remain under control and, therefore, the mathematical relations are valid.

7. Constant Permeability with Respect to Effective Stress

Permeability, the ability of the soil to let water pass through, does not vary with the effective stress, which is the load carried by the soil particles after excess water is expelled. Actually, permeability may vary with changing stress level, but this assumption simplifies the equation.

8. Specific Pressure-Void Ratio Relationship

The relation between the applied pressure to the oil and compression (void ratio) is unique and consistent throughout the process. That is, the soil would compress in a predictable manner as it undergoes a change in pressure.

9. Time Lag Due to Low Permeability

The consolidation process is delayed only by the low permeability of the soil, which needs some time to leak out the water. This is why consolidation does not occur overnight under load but rather over time.

Why These Assumptions Matter

Under these assumptions, Terzaghi was able to develop a workable equation predicting how much and how fast the soil would compress under a load. None of the above assumptions presented by Terzaghi will exactly present true-field conditions, but they do represent an approximation useful enough for engineers when designing structures.

Known by the said assumptions, we discuss the limitations and applicability of Terzaghi's consolidation theory when applied to civil engineering designs in a safe and effective way here.