The Procedure and Formulations for Liquefaction Calculations
The calculation tool given above for calculating factor of safety against soil liquefaction follows the procedure given in the Turkish Earthquake Code (2019) - Chapter 16B. The details of this procedure is given below.
SPT Corrections
Measured SPT values in the field (N) at each depth (z) will be corrected to N1,60 values using the equation below.
$$N_{1,60} = N \times C_{N} \times C_{R} \times C_{S} \times C_{B} \times C_{E}$$
Where;
CN: Overburden Pressure Correction Factor
Overburden correction factor will be calculated using the equation below. The vertical effective pressure, σ'(kN/m2) should be calculated for the ground conditions when the Standard Penetration Test (SPT) is performed. Any
excavation, fill or foundation loads after the test will be ignored.
$$C_{N} = {9.78 \sqrt{1 \over σ'}} \le 1.70 $$
CR: Rod Length Correction Factor
Rod length correction factor will be selected from the table below.
| Correction Factor |
Rod Length(m) |
Value |
| CR |
3-4 |
0.75 |
| 4-6 |
0.85 |
| 6-10 |
0.95 |
| >10 |
1.00 |
CS: Sampler Type Correction Factor
Sampler type correction factor will be selected from the table below.
| Correction Factor |
Sampler Type |
Value |
| CS |
Standard Liner (With liner) |
1.00 |
| Without Liner |
1.10 - 1.30 |
CB: Borehole Diameter Correction Factor
Borehole diameter correction factor will be selected from the table below.
| Correction Factor |
Borehole Diameter (mm) |
Value |
| CB |
65 - 115 |
1.00 |
| 150 |
1.05 |
| 200 |
1.15 |
CE: Energy Correction Factor
Energy correction factor will be selected from the table below.
| Correction Factor |
Hammer Type |
Value |
| CE |
Safety |
0.60 - 1.17 |
| Donut |
0.45 - 1.00 |
| Auto |
0.90 - 1.60 |
SPT Corrections for Fine Content
N1,60 values will be corrected to N1,60f values considering the fine content (FC%) of the samples using the equation below.
$$ N_{1,60f} = \alpha + \beta N_{1,60} $$
Where;
$$ \alpha = 0; \quad \beta =1 \qquad \qquad(FC\leq \%5) $$
$$ \alpha = e^{[1.76-(190/FC^2)]}; \quad \beta = 0.99+FC^{1.5}/1000 \qquad \qquad(\%5 \lt FC \leq \%35) $$
$$ \alpha = 5; \quad \beta =1.2 \qquad \qquad(FC \gt \%35) $$
Liquefaction Resistance of Soil
τR (Liquefaction resistance of the soil) will be calculated by multiplying CRRM7.5 (cyclic resistance ratio for a magnetide 7.5 earthquake), CM (Earthquake magnitude correction factor) and effective
stress (σ') as follows:
$$ \tau_R = CRR_{M7.5} \times C_M \times \sigma' $$
Where;
$$ CRR_{M7.5} = {1 \over 34-N_{1,60f}} + {N_{1,60f} \over 135} + {50 \over ({10N_{1,60f}+45})^2} - {1 \over 200}$$
$$ C_M = {{10^{2.24}} \over {M_w^{(2.56)}}}$$
Average Cyclic Shear Stress
τeq (Average cyclic shear stress) will be calculated by multiplying σ' (effective stress at calculation depth) SDS (Design spectral response acceleration parameter at short periods), rd (Stress
reduction factor) as follows:
$$ \tau_{eq} = 0.65 \times \sigma' \times (0.4 S_{DS}) \times r_d $$
Where;
$$ r_d = 1- 0.00765z \qquad \qquad \qquad (z\leq 9.15m) $$
$$ r_d = 1.174- 0.0267z \qquad \qquad(9.15m \lt z \leq 23m) $$
$$ r_d = 0.744- 0.008z \qquad \qquad(23m \lt z \leq 30m) $$
$$ r_d = 0.5 \qquad \qquad \qquad \qquad \quad (z \gt 30m) $$
Factor of Safety Against Liquefaction
$$ FS = {\tau_R \over \tau_{eq}} $$