The theory for the time rate of one-dimensional consolidation is NOT based on which of the following assumptions?
Try it first: pick an option, then read the explanation.
Asked in SSC JE 14/11/2022
Detailed Explanation
Terzaghi's one-dimensional consolidation theory (1925) describes how excess pore water pressure in a clay layer dissipates with time. It leads to the equation
\[ \frac{\partial u}{\partial t} = c_v\,\frac{\partial^2 u}{\partial z^2} \]
To arrive at this simple equation, Terzaghi made a set of assumptions about the soil and the loading.
Why “The clay layer is not saturated” Is Correct
The theory relates the volume change of the layer directly to the volume of water flowing out. That only works if the voids are completely full of water, with no compressible air. So the theory assumes the clay is fully saturated. A ‘not saturated’ clay layer contradicts the theory, which makes option (b) the answer.
| Assumption of Terzaghi's 1-D consolidation theory | Why it matters |
|---|---|
| Soil is homogeneous | Properties (k, mv, cv) are the same throughout the layer. |
| Soil is fully saturated | Volume change equals the volume of water squeezed out; no air to compress. |
| Soil grains and water are incompressible | All compression comes from a change in void volume. |
| Darcy's law is valid | Flow of pore water is laminar and proportional to the hydraulic gradient. |
| Flow and compression are one-dimensional (vertical) | Lateral strain is zero, as in an oedometer ring. |
| k and mv (hence cv) stay constant | Allows a single linear differential equation to be solved. |
| Load is applied instantly and stays constant | The initial excess pore pressure u0 equals the applied stress increment. |
Why the Other Options Are Wrong
- A. Darcy's law is valid: Darcy's law is a key assumption; it is used to express the flow of water out of the layer.
- C. The compression of the soil layer is due to the change in volume only: The theory does assume compression is only by change in volume (of voids), with grains and water incompressible.
- D. The clay layer is homogeneous: Homogeneity is assumed so that k, mv and cv have single values for the whole layer.
Key Point
Terzaghi's theory: homogeneous, fully saturated, incompressible grains and water, Darcy's law, 1-D flow and strain, constant cv.
Key Concepts for Students
- The theory ignores secondary compression, so it only predicts primary consolidation.
- In reality k and mv decrease as the clay consolidates, so cv is not strictly constant.
- Lab oedometer conditions (laterally confined ring) match the 1-D assumption closely.
Practice more: this is question 6 in Soil Consolidation MCQs – Part 1. Try the whole set and check every answer instantly.