Terzaghi’s one-dimensional consolidation theory assumes that (i) Darcy’s law is valid (ii) Soil is partially saturated (iii) Load is applied incrementally (iv) Water and soil solids are compressible
- AOnly (i)Correct
- B(i) and (ii)
- C(iii) and (iv)
- D(i), (ii), (iii) and (iv)
Solution
Concept
Classical assumptions of Terzaghies one dimensional consolidation
Formula
partial u / partial t = cv × (partial2 u / partial z2)
Step-by-step solution
1. Statement (i) is correct: Terzaghi assumed flow of pore water follows Darcy’s law throughout consolidation. 2. Statement (ii) is incorrect: Terzaghi assumed the soil mass is 100% completely saturated. 3. Statement (iii) is not a constitutive assumption of the 1D differential equation formulation. 4. Statement (iv) is incorrect: Terzaghi assumed both soil mineral grains and pore water are completely incompressible. 5. Hence, only statement (i) represents an authentic Terzaghi assumption. Answer: A
Explanation
Terzaghi's 1D consolidation theory is based on several classical assumptions: Darcy's law is valid (statement i is correct); the soil is 100% fully saturated (statement ii is false); the soil solids and pore water are incompressible (statement iv is false); and drainage and compression occur strictly in one dimension.
Why the other options are wrong
B) Soil is assumed 100% saturated, so statement (ii) is false. C) Solids and water are strictly incompressible, so statement (iv) is false. D) Statements (ii) and (iv) directly contradict Terzaghi's explicit assumptions.
Shortcut
Terzaghi 1D consolidation = Darcy's law valid + Fully saturated + Incompressible water and solids.
Common mistake
Assuming soil is partially saturated or that soil solids/water are compressible.
Correct answer: A) Only (i)