CEEN 545 - Lecture 24 - Soil Liquefaction (Part 2)

Summary

The lecture explains how to assess whether soil is likely to liquefy during an earthquake using the simplified cyclic-stress approach. It moves from the physical definition of liquefaction initiation to practical calculations based on earthquake loading and in-situ soil test data.

Liquefaction Initiation and Pore Pressure

• Liquefaction initiation is commonly defined as the point at which excess pore-water pressure equals the soil’s effective confining stress.
• The pore-pressure ratio, (r_u), is the excess pore pressure divided by effective stress. When (r_u = 1), effective stress has fallen to zero and initial liquefaction has occurred.
• The lecture reiterates the distinction between:
  • Flow liquefaction, which begins when the soil stress path reaches the flow-liquefaction surface; failure is then considered inevitable.
  • Cyclic mobility, which is associated with the stress path reaching the failure envelope and cyclically approaching a state of zero effective stress.

Factor of Safety: Resistance Versus Demand

Rather than requiring costly laboratory tests for every project, engineers can express liquefaction potential as a factor of safety:

[ \text{Factor of safety against liquefaction} = \frac{\text{CRR}}{\text{CSR}} ]

• CRR (cyclic resistance ratio) represents the soil’s capacity to resist liquefaction.
• CSR (cyclic stress ratio) represents the seismic demand placed on the soil.
• Both ratios relate cyclic shear stress to effective vertical stress.
• The number of loading cycles matters: the cyclic stress needed to trigger liquefaction depends on the number of cycles, as well as soil density and confining stress.

Estimating Cyclic Stress Ratio (CSR)

Two approaches are described:

1. Soil-response analysis

   • Use equivalent-linear or nonlinear effective-stress analysis to estimate cyclic shear stresses through the soil profile.
   • Average the relevant stresses and normalize them by effective stress to obtain CSR.

2. Simplified empirical method

   • The simplified Seed–Idriss method estimates earthquake-induced cyclic stress from surface acceleration and soil stresses.
   • Its assumptions and adjustments include:
     • The initial model treats the soil as a rigid block.
     • A correction accounts for the transient loading of an earthquake compared with harmonic laboratory loading.
     • A depth-reduction factor, (r_d), accounts for soil flexibility. It is approximately 1 at the ground surface and generally decreases with depth.
   • In the conventional formulation, CSR depends on peak ground acceleration, total and effective vertical stress, and (r_d).

Estimating Cyclic Resistance Ratio (CRR)

Seed and Idriss developed an in-situ empirical approach partly because obtaining undisturbed samples of saturated sand for laboratory testing is difficult and expensive.

Their approach compared earthquake case histories in which liquefaction did and did not occur with field penetration resistance measurements and estimated seismic demand. A boundary between liquefied and non-liquefied cases represents the soil’s resistance; a case plotting on the liquefaction side of the boundary indicates predicted triggering.

The method accounts for factors that affect resistance:

• Magnitude scaling factor (MSF): Adjusts for earthquake duration and the number of significant cycles relative to a magnitude 7.5 reference event. The reference factor is 1.0. Larger earthquakes generally reduce the adjusted resistance, while smaller events increase it.
• Overburden correction: Adjusts SPT resistance to a reference confining pressure, since measured blow counts tend to rise with confining stress.
• Initial static shear-stress correction, (K_\alpha): Accounts for pre-existing static shear stress. The lecturer notes that available case histories provide limited support for this correction, so practitioners often omit it in routine calculations.

Limits and Alternatives

• The simplified cyclic-stress method does not directly calculate pore-pressure generation.
• A cyclic-strain approach may be more directly related to pore-pressure development, but it requires reliable prediction of cyclic soil deformation. Large deformations in liquefied soil are especially difficult to model, and the approach depends on high-quality nonlinear effective-stress analysis and constitutive models.
• Several simplified procedures are used in practice, including the NCEER/Youd et al. approach, the Cetin et al. approach, and the Idriss–Boulanger method. The course will use Idriss and Boulanger.

Idriss–Boulanger Triggering-Analysis Workflow

1. Obtain earthquake inputs

   • Determine the estimated earthquake magnitude and peak ground acceleration at the ground surface.
   • If the hazard analysis provides rock acceleration, adjust it using an appropriate site-amplification factor, such as one derived from soil-response analysis or applicable code provisions.

2. Develop the soil profile

   • Divide the profile into layers and sublayers. The lecturer generally recommends sublayers no thicker than about 5 ft.
   • Assign SPT resistance and fines content to each sublayer.
   • Screen each layer for liquefaction susceptibility using composition criteria and, where appropriate, other susceptibility criteria. Exclude layers judged not susceptible from triggering calculations.

3. Correct the SPT resistance

   • Calculate the normalized SPT blow count, commonly written ((N_1)_{60}), correcting for hammer energy, rod length, and overburden pressure.
   • Adjust for fines content to obtain the clean-sand-equivalent value, commonly written ((N_1)_{60cs}).
   • Idriss–Boulanger calculations may require spreadsheet iteration because of cyclic dependencies in the equations.

4. Calculate soil stresses

   • Determine total and effective vertical stress at the same depth used for the clean-sand-equivalent SPT value. This need not be the midpoint of the sublayer.

5. Calculate earthquake and resistance corrections

   • For each susceptible sublayer, calculate the depth-reduction factor, (r_d).
   • Calculate the magnitude scaling factor; this is the same for all sublayers for a given earthquake.
   • Calculate the shear-stress correction factor if it is being used.

6. Calculate CSR and CRR

   • Calculate CSR using the simplified cyclic-stress equation and the relevant stresses, surface acceleration, and (r_d).
   • Calculate CRR using the corrected SPT resistance and the method’s correction factors.

7. Determine the factor of safety

   • For each susceptible sublayer, calculate (FS_{\text{liq}} = \text{CRR}/\text{CSR}).
   • A value below 1 indicates that the estimated seismic demand exceeds the estimated cyclic resistance, so liquefaction triggering is predicted at that loading level.

The lecturer emphasizes that this analysis involves several linked calculations and recommends starting the work early.

Speakers and Sources Featured

Speaker

• One unnamed lecturer, speaking throughout the video.

Researchers, methods, and sources mentioned

• Harry B. Seed and I. M. Idriss, including the Seed–Idriss simplified method.
• Idriss and Boulanger, particularly their 2010 method/report.
• Youd et al. and the 2001 NCEER method.
• Cetin and colleagues, and the method discussed as developed in 2004.
• Ricardo Dobry, in connection with the cyclic-strain approach.
• The lecture also refers to Japanese laboratory practice, ASCE publication, and seismic-hazard/code-based inputs.