Which one of the following is the part of assumptions made by Terzaghi while developing the mathematical statement of the consolidation process?
- AThe soil is non-homogeneous
- BThe soil particles and water are incompressibleCorrect
- CThe partial deformation of soil is due to partial change in volume
- DCo-efficient of permeability is variable during consolidation
Solution
Concept
Terzaghi assumed the soil is homogeneous and fully saturated, the soil grains and water are incompressible, flow and compression are one-dimensional, Darcy's law is valid, and k and mv stay constant.
Formula
∂u/∂t = cv × ∂^2u/∂z2, cv = k / (mv × γw)
Step-by-step solution
1. Recall Terzaghi's assumptions: the soil is homogeneous and fully saturated. 2. Soil particles and pore water are incompressible. 3. All deformation comes only from a change in volume (expulsion of water). 4. The coefficient of permeability k is constant during consolidation. 5. Only option B matches these assumptions. Answer: (B).
Explanation
Terzaghi assumed that the soil grains and water cannot be compressed. Volume change happens only because water flows out of the voids. So option B is a correct assumption.
Why the other options are wrong
A: The soil is assumed homogeneous, not non-homogeneous. C: Deformation is assumed to come entirely from volume change, not partly. D: k is assumed constant, not variable.
Shortcut
Terzaghi's theory has everything 'simple': homogeneous, saturated, incompressible, constant k, 1-D.
Common mistake
Choosing D because k really does change in the field. Terzaghi's theory assumes it is constant.
Correct answer: B) The soil particles and water are incompressible