Liquefaction Assessment

Method: Idriss & Boulanger (2008); Youd et al. (2001)

1. Introduction

Liquefaction assessment is performed by comparing the seismic demand imposed on soil with its resistance to cyclic loading.

\[ FS = \frac{CRR}{CSR} \]

The procedure involves:

  1. Computation of stresses
  2. Evaluation of CSR
  3. SPT normalization
  4. Fines correction
  5. CRR estimation
  6. Magnitude adjustment
  7. Factor of safety
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2. Cyclic Stress Ratio (CSR)

\[ CSR = 0.65 \cdot \frac{\sigma_v}{\sigma'_v} \cdot a_{max} \cdot r_d \]

CSR represents the seismic shear stress induced in soil.

CSR is not evaluated at very low effective stresses (typically \( \sigma'_v \lesssim 5 \) kPa), as empirical correlations are not valid in this range.
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3. Stress Reduction Factor (rd)

\[ r_d = \exp(\alpha + \beta M_w) \]
\[ \alpha = -1.012 - 1.126 \sin\left(\frac{z}{11.73} + 5.133\right) \]
\[ \beta = 0.106 + 0.118 \sin\left(\frac{z}{11.73} + 5.133\right) \]
Typical bounds: \(0.3 \le r_d \le 1.0\). Applicable for depths up to ~30 m.
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4. SPT Corrections

\[ N_{60} = N \cdot C_E \cdot C_B \cdot C_R \cdot C_S \]
\[ C_N = \sqrt{\frac{P_a}{\sigma'_v}} \]
\[ (N_1)_{60} = N_{60} \cdot C_N \]
A lower bound of \( \sigma'_v = 10 \) kPa is adopted to avoid instability in normalization.
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Fines Content Correction

\[ (N_1)_{60cs} = \alpha + \beta (N_1)_{60} \]
\[ \alpha = 0,\quad \beta = 1 \quad (FC \le 5\%) \]
\[ \alpha = e^{\left(1.76 - \frac{190}{FC^2}\right)}, \quad \beta = 0.99 + \frac{FC^{1.5}}{1000} \quad (5\% < FC \le 35\%) \]
\[ \alpha = 5,\quad \beta = 1.2 \quad (FC > 35\%) \]
Applicable primarily for sandy soils with low plasticity.
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5. Cyclic Resistance Ratio (CRR)

\[ CRR_{7.5} = \frac{1}{34 - (N_1)_{60cs}} + \frac{(N_1)_{60cs}}{135} + \frac{50}{[10(N_1)_{60cs} + 45]^2} - \frac{1}{200} \]
Valid for \( (N_1)_{60cs} \lesssim 30 \).
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6. Magnitude Scaling Factor

\[ MSF = 6.9 e^{-M_w/4} - 0.058 \]
\[ CRR = CRR_{7.5} \cdot MSF \]
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7. Factor of Safety

\[ FS = \frac{CRR}{CSR} \]

FS < 1 → Liquefaction likely
FS ≈ 1 → Marginal
FS > 1 → Liquefaction unlikely

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8. Cohesive Soil Assessment

\[ FS = \frac{0.8 S_u}{CSR \cdot \sigma'_v} \]
Cohesive soils do not liquefy but may undergo cyclic softening.
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9. Limitations

• Empirical method based on case histories
• Applicable mainly to sandy soils
• Not valid for high-plasticity soils (PI > 20)
• Assumes level ground conditions
• Results require engineering judgment