LIQUEFACTION ANALYSIS

Soil liquefaction is a phenomenon that occurs mostly in medium to fine-grained sands wherein a mass of soil loses a large percentage of its shear resistance when subjected to monotonic, cyclic or shock loading, and flows in a manner resembling a liquid. Much of the damage on substructures and foundation during earthquake is attributed to this phenomenon. A loose saturated sand deposit, when subjected to vibration, tends to compact and decrease in volume. If drainage is unable to occur, the pore water pressure increases. If the pore water pressure in the sand deposit is allowed to build up by continuous vibration, a condition will be reached at some time where the overburden pressure will be equal to the pore water pressure. Based on the effective stress principle,

υσσ −='

where 'σ is the effective stress, σ is the total overburden pressure, and υ is the pore water pressure. If σ is equal to υ , 'σ is zero. Under this condition, the sand does not possess any shear strength, and it develops into a liquefied state.

Recent studies indicate, however, that effective stress 'σ need not equal to zero. Liquefaction may also occur when the shear stresses acting on the soil is as low as the residual shear strength. Loading that could induce liquefaction may also be cyclic, shock loading or monotonic.

Liquefaction analysis considering SPT data was undertaken using LiquefyPro software. This is based on the most recent methods recommended by the National Center for Earthquake Engineering Research (NCEER) Workshop on Liquefaction and Special Publication 117 (Guidelines in Analyzing and Mitigating Liquefaction in California). The results are appended to this report. The Factor of Safety (FS) for liquefaction potential is calculated as the ratio of the Cyclic Resistance Ratio (CRR) to the Cyclic Stress Ratio (CSR).

𝐹𝐹𝐹𝐹 =𝐶𝐶𝐶𝐶𝐶𝐶𝑀𝑀𝐶𝐶𝐹𝐹𝐶𝐶𝑓𝑓𝑓𝑓

The CRR liquefaction curves are developed for an earthquake magnitude of 7.5 and is hereafter called CRR7.5. To take different magnitudes into account, the factor of safety against liquefaction is multiplied with a magnitude scaling factor (MSF). CRR7.5 is determined using the formula below (Blake, 1997):

𝐶𝐶𝐶𝐶𝐶𝐶7.5 = 𝑎𝑎 + 𝑐𝑐𝑐𝑐 + 𝑒𝑒𝑐𝑐2 + 𝑔𝑔𝑐𝑐3

1 + 𝑏𝑏𝑐𝑐 + 𝑑𝑑𝑐𝑐2 + 𝑓𝑓𝑐𝑐3 + ℎ𝑐𝑐4

where:

x = N60,cf e = 0.0006136 a = 0.048 f = -0.0003285 b = -0.1248 g = -1.673x10-5

c = -0.004721 h = 3.714x10-6 d = 0.009578

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Additional vertical overburden stress correction of CRR7.5 is suggested as:

𝐶𝐶𝐶𝐶𝐶𝐶𝑣𝑣 = 𝐶𝐶𝐶𝐶𝐶𝐶7.5𝐾𝐾𝛼𝛼𝐾𝐾𝜎𝜎

where: CRRV is corrected CRR7.5 (Magnitude=7.5) Kα is the correction factor for initial shear stress and is set to 1 Kσ is the correction factor for overburden stress

Figure 1. SPT Overburden correction for CRR7.5

In the chart, the effective confining pressure, σ'm, is in tsf, which can be calculated as:

𝜎𝜎′𝑚𝑚 = 1 + 2𝐾𝐾0

3= 0.65 ∙ 𝜎𝜎′0

Ko is the coefficient of lateral earth pressure and by default set to 0.47. σ'o and σ'm are the effective vertical overburden pressure in tsf, based on water table during the in-the testing and fill does not affect them. CRRV is based on earthquake with magnitude of 7.5. For a given earthquake with different magnitude, CRRV need to be corrected. MSF is applied to the CRRV to obtain CRRM, which is the magnitude-corrected cyclic stress ratio.

𝐶𝐶𝐶𝐶𝐶𝐶𝑀𝑀 = 𝐶𝐶𝐶𝐶𝐶𝐶𝑣𝑣 ∙ 𝑀𝑀𝐹𝐹𝐹𝐹 MSF is a magnitude-scaling factor given by:

𝑀𝑀𝐹𝐹𝐹𝐹 = 102.24

𝑀𝑀2.56

On the other hand, CSR is calculated using the Seed & Idriss method (1971).

𝐶𝐶𝐹𝐹𝐶𝐶 = 0.65

𝜎𝜎𝑜𝑜𝜎𝜎′𝑜𝑜

𝑎𝑎𝑚𝑚𝑚𝑚𝑚𝑚𝑟𝑟𝑑𝑑

where:

amax = peak ground acceleration (in g) σo = total vertical stress σ'o = effective vertical stress rd = stress reduction factor, for soil flexibility rd = 1.0 - 0.00765z (for z≤9.15m) rd = 1.174 - 0.0267z (for 9.15m<z≤23m) rd = 0.744 - 0.008z (for 23m<z≤30m) rd = 0.5 (for z>30m)

0

0.2

0.4

0.6

0.8

1

1.2

0 1 2 3 4 5 6 7 8 9 10

Kσ

Effective Confining Pressure (tsf)

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Liquefaction-induced settlements are based on the Ishihara and Yoshimine (1990). The volumetric strain is charted against the factor of safety against liquefaction.

Figure 2.Post-liquefaction volumetric strain charts

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REFERENCES

NCEER-97-022 Proceedings of the NCEER Workshop on Evaluation of Liquefaction Resistance of Soils (1997)

EERC 3003-06 Recent Advances in Soil Liquefaction Engineering: A Unified and Consistent Framework (2003)

LiquefyPro Liquefaction and Settlement Analysis Software Manual Version 5 and Later (2010)

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