Which of the following statements is/are correct? 1. Isochrones are curves of equal pore water pressure. 2. Isochrones depict the variation of the pore water pressure along the depth of the soil sample. 3. Isochrones vary with time.
Try it first: pick an option, then read the explanation.
Asked in SSC JE 30/10/2020 (Morning)
Detailed Explanation
The word isochrone means ‘equal time’. Solving Terzaghi's equation gives the excess pore water pressure u at every depth z and time t. If we freeze time at one value (one value of the time factor Tv) and plot u against depth, the curve we get is an isochrone.
\[ \frac{\partial u}{\partial t} = c_v\,\frac{\partial^2 u}{\partial z^2} \]
Why “2 and 3 only” Is Correct
Statement 2 is correct: each isochrone shows how excess pore pressure varies with depth through the layer.
Statement 3 is correct: there is a different isochrone for every instant. As time passes the curves move towards zero pore pressure.
Statement 1 is wrong: along an isochrone the pore pressure changes with depth. What is equal along one curve is the time, not the pore pressure. Hence ‘2 and 3 only’.
Why the Other Options Are Wrong
- A. 1 and 2 only: Statement 1 is wrong: pore pressure is not constant along an isochrone, the time is.
- B. 1, 2 and 3: Includes statement 1, which is incorrect.
- C. 1 only: Statement 1 alone is the incorrect one.
Key Point
Isochrone = u versus depth at one instant. Its slope at any depth gives the hydraulic gradient, i = (1/γw)·∂u/∂z.
Key Concepts for Students
- With double drainage, u is zero at the top and bottom and largest at mid-depth.
- With single drainage (impervious base), u is largest at the impervious boundary.
- The area between the initial and current isochrone, divided by the initial area, gives the average degree of consolidation U.
Practice more: this is question 9 in Soil Consolidation MCQs – Part 1. Try the whole set and check every answer instantly.