As per IS 1893:2016, what is the value of constant ‘A’ in the equation mentioned below for determining cyclic stress ratio (CSR) ? CSR = A (amax / g) (σvo / σ′vo) rd where, amax = Peak ground acceleration (PGA) preferably in terms of g, g = acceleration due to gravity, rd = stress reduction factor.
- A0·5
- B0·15
- C0·36
- D0·65Correct
Solution
Concept
Seed and Idriss simplified procedure for liquefaction
Formula
CSR = 0.65 (amax/g) (σvo / σ′vo) rd
Step-by-step solution
1. The cyclic shear stress due to an earthquake is taken as 65% of the peak shear stress: τavg = 0.65 (amax/g) σvo rd. 2. Dividing by σ′vo gives CSR with the constant A = 0.65.
Explanation
The factor 0.65 converts the peak cyclic shear stress to an equivalent average (uniform) cyclic stress for a magnitude 7.5 event. It is used in the Seed–Idriss simplified liquefaction method adopted in IS 1893.
Why the other options are wrong
0.5, 0.15 and 0.36 are not the factor used in the simplified procedure.
Shortcut
CSR = 0.65 (amax/g)(σ/σ′) rd.
Common mistake
Using 0.5.
Correct answer: D) 0·65