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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

$$FS = {\tau_R \over \tau_{eq}}$$