Q: How is the Cyclic Stress Ratio (CSR) calculated?

CSR = 0.65 × (σ_v / σ_v') × (a_max / g) × r_d, where σ_v is total vertical stress, σ_v' is effective vertical stress, a_max is the peak ground acceleration, and r_d is the stress reduction coefficient that accounts for flexibility of the soil column. For depths z ≤ 9.15 m, r_d = 1.0 − 0.00765z; for 9.15 < z ≤ 23 m, r_d = 1.174 − 0.0267z.

Q: What are common liquefaction mitigation techniques?

Main mitigation methods are: (1) densification (sand compaction piles, vibroflotation) to increase N and CRR; (2) drainage (gravel drains) to dissipate excess pore pressure quickly; (3) solidification (deep soil mixing, chemical grouting) to stiffen the ground; (4) grid-pattern ground improvement to restrain shear deformation. Selection depends on site constraints, cost, and acceptable residual settlement.

Question 1

What is the Tokimatsu-Seed method for post-liquefaction settlement?

Accepted Answer

The Tokimatsu & Seed (1987) method estimates post-liquefaction volumetric strain ε_v (%) from the cyclic stress ratio (CSR), SPT blow count N, and liquefaction safety factor FL using empirical charts and formulas. Settlement is then Sv = Σ(ε_v × Δz) summed over the liquefiable layer thickness. The method is widely used in seismic design codes worldwide.

Question 2

What is the liquefaction safety factor FL, and what threshold triggers liquefaction?

Accepted Answer

The liquefaction safety factor is FL = CRR / CSR (Cyclic Resistance Ratio divided by Cyclic Stress Ratio). FL < 1.0 indicates liquefaction is expected. Many codes (e.g., AASHTO, Japanese RRS) use FL = 1.5 as the threshold below which liquefaction-induced settlement should be assessed in detail.

Question 3

How is the Cyclic Stress Ratio (CSR) calculated?

Accepted Answer

CSR = 0.65 × (σ_v / σ_v') × (a_max / g) × r_d, where σ_v is total vertical stress, σ_v' is effective vertical stress, a_max is the peak ground acceleration, and r_d is the stress reduction coefficient that accounts for flexibility of the soil column. For depths z ≤ 9.15 m, r_d = 1.0 − 0.00765z; for 9.15 < z ≤ 23 m, r_d = 1.174 − 0.0267z.

Question 4

What are common liquefaction mitigation techniques?

Accepted Answer

Main mitigation methods are: (1) densification (sand compaction piles, vibroflotation) to increase N and CRR; (2) drainage (gravel drains) to dissipate excess pore pressure quickly; (3) solidification (deep soil mixing, chemical grouting) to stiffen the ground; (4) grid-pattern ground improvement to restrain shear deformation. Selection depends on site constraints, cost, and acceptable residual settlement.

Earthquake-Induced Liquefaction Settlement Calculator

Tokimatsu-Seed Method Summary