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  • Settle3D Liquefaction Theory Manual

    Liquefaction Analysis Theory Manual

    2014 Rocscience Inc.

  • 1

    Table of Contents 1 Introduction ....................................................................................................................................... 2

    2 Theory ................................................................................................................................................ 2

    3 Standard Penetration Test (SPT) Based Calculations ................................................................... 3

    3.1 Cyclic Stress Ratio (CSR) ........................................................................................................ 3

    3.2 Stress Reduction Factor, rd ..................................................................................................... 4

    3.3 SPT-N Value Correction Factors ............................................................................................ 7

    3.3.1 Overburden Correction Factor, CN ..................................................................................... 7

    3.3.2 Hammer Energy Efficiency Correction Factor, CE ............................................................ 9

    3.3.3 Borehole Diameter Correction Factor, CB .............................................................................. 9

    3.3.4 Rod Length Correction Factor, CR .................................................................................... 10

    3.3.5 Sampler Correction Factor, CS .......................................................................................... 11

    3.4 Cyclic Resistance Ratio (CRR) .............................................................................................. 11

    3.5 Relative Density, DR .............................................................................................................. 16

    3.6 Fines Content Correction ...................................................................................................... 17

    3.7 Magnitude Scaling Factor, MSF ........................................................................................... 18

    3.8 Overburden Correction Factor, K ........................................................................................ 19

    3.9 Shear Stress Correction Factor, K ...................................................................................... 22

    4 Cone Penetration Test (CPT) Based Calculations ........................................................................ 23

    5 Velocity (Vs) Measurement Based Calculations............................................................................ 30

    6 Post-Liquefaction Lateral Displacement ....................................................................................... 32

    7 Post-Liquefaction Settlement......................................................................................................... 38

    References ............................................................................................................................................... 42

    Table of Symbols .................................................................................................................................... 45

  • 2

    1 Introduction

    Liquefaction of soils is a major cause of both damage and loss of life in earthquakes (e.g.; the 1964

    Alaska and Niigata, 1983 Nihonakai-Chubu, 1987 Elmore Ranch and Superstition Hills, 1989 Loma

    Prieta, 1993 Kushiro-Oki, 1994 Northridge, 1995 Hyogoken-Nambu (Kobe), 1999 Izmit earthquakes).

    Researchers have tried to quantify seismic soil liquefaction initiation risk through the use of both

    deterministic and probabilistic techniques based on laboratory test results and/or correlations of

    insitu index tests with field case history performance data.

    Settle3D offers different methods of calculating the factor of safety associated with liquefaction

    resistance, probability of liquefaction, and the input parameters required for those calculations. This

    manual also describes a simplified method for calculating the lateral spreading displacement as well

    as the vertical settlement due to liquefaction.

    2 Theory

    The use of in situ index testing is the dominant approach for assessment of the likelihood of

    triggering or initiation of liquefaction. There in-situ test methods have now reached a level of

    sufficient maturity as to represent viable tools for this purpose. The following tests are often used:

    Standard Penetration Test (SPT)

    Cone Penetration Test (CPT)

    Shear Wave Velocity (VST)

    The potential for liquefaction can be evaluated by comparing the earthquake loading (CSR) with the

    liquefaction resistance (CRR) - this is usually expressed as a factor of safety against

    Liquefaction:

    =7.5

    where

    7.5 = cyclic resistance ratio for an earthquake with magnitude 7.5 = magnitude scaling factor = overburden stress correction factor = ground slope correction factor

  • 3

    3 Standard Penetration Test (SPT) Based Calculations

    This section summarizes the methods available for calculating liquefaction resistance based on SPT

    data. The following are presented:

    Cyclic Stress Ratio (CSR)

    Stress Reduction Factor (rd)

    SPT N-Value Correction Factors

    Cyclic Resistance Ratio (CRR)

    Relative Density (DR)

    Fines Content Correction

    Magnitude Scaling Factor (MSF)

    Overburden Correction Factor

    Shear Stress Reduction Factor

    3.1 Cyclic Stress Ratio (CSR)

    The cyclic stress ratio, CSR, as proposed by Seed and Idriss (1971), is defined as the average cyclic

    shear stress, , developed on the horizontal surface of soil layers due to vertically propagating shear waves normalized by the initial vertical effective stress,

    , to incorporate the increase in shear

    strength due to increase in effective stress. By appropriately weighting the individual stress cycles

    based on laboratory test data, it has been found that a reasonable amplitude to use for the average

    or equivalent uniform stress, , is about 65% of the maximum shear stress.

    =

    = 0.65 (

    ) (

    )

    where

    = maximum horizontal ground surface acceleration (g)

    = gravitational acceleration

    = total overburden pressure at depth z

    = effective overburden pressure at depth z

    = stress reduction factor

  • 4

    3.2 Stress Reduction Factor, rd

    The stress reduction factor, rd, is used to determine the maximum shear stress at different depths in

    the soil. Values generally range from 1 at the ground surface to lower values at larger depths.

    The following formulations are provided in Settle3D:

    NCEER (1997)

    Idriss (1999)

    Kayen (1992)

    Cetin et al. (2004)

    Liao and Whitman (1986a)

    NCEER (1997)

    = 1.0 0.00765 9.15

    = 1.174 0.0267 9.15 < 23

    = 0.744 0.008 23 < 30

    = 0.50 > 30

    where

    = depth in meters

    Idriss (1999)

    ln() = () + ()

    () = 1.012 1.126 sin (

    11.73+ 5.133)

    () = 0.106 + 0.118 sin (

    11.28+ 5.142)

    where

    = depth in meters 34

  • 5

    = earthquake magnitude

    Kayen (1992)

    = 1 0.012

    where

    = depth in meters

    Cetin et al. (2004)

    (, , , ,12 ) =

    [1 +23.013 2.949 + 0.999 + 0.0525,12

    16.258 + 0.2010.341(+0.0785,12 +7.586)

    ]

    [1 +23.013 2.949 + 0.999 + 0.0525,12

    16.258 + 0.2010.341(0.0785,12 +7.586)

    ]

    for z

  • 6

    Notes:

    - If the site stiffness estimation is difficult, take ,12 150-200m/s.

    - For very soft sites with ,12 less than 120m/s, use a limiting stiffness of 120m/s in

    calculations.

    - For very stiff sites, ,12 with stiffness greater than 250m/s, use 250m/s as the limiting value

    in calculations.

    Liao and Whitman (1986a)

    = 1.0 0.00765 for z9.15m

    = 1.174 0.0267 for 9.15 m

  • 7

    3.3 SPT-N Value Correction Factors

    Before the CRR can be calculated, the N values obtained from the SPT must be corrected for the

    following factors: overburden, rod length, non-standard sampler, borehole diameter, and hammer

    energy efficiency, resulting in a(1)60 value. The equation below illustrates the correction.

    60 =

    (1)60 = 60

    The equations used to calculate the correction factors are summarized below.

    Table 1.1: Summary of Correction Factors for Field SPT-N Values

    Factor Equipment Variable Term Correction

    Overburden Pressure CN Section 3.3.1

    Energy Ratio

    Donut hammer

    CE

    0.5-1.0

    Safety hammer 0.7-1.2

    Automatic hammer 0.8-1.3

    Borehole Diameter

    65 mm -115 mm

    CB

    1.0

    150 mm 1.05

    200 mm 1.12

    Rod Length

  • 8

    Liao and Whitman (1986)

    = (1

    0 )

    0.5

    1.7

    = (

    )0.5

    Bazaraa (1967)

    =4

    1 + 20 0

    1.5

    =4

    3.25 + 0.50 0

    > 1.5

    2.0

    Idriss and Boulanger (2004)

    = (

    )0.7840.0768(1)60

    1.7

    (1)60 46

    Peck, Hansen, and Thorburn (1974)

    = 0.77 log (2000

    0 ) 0

    282

    Kayen et al. (1992)

    =2.2

    1.2 +

    1.7

  • 9

    3.3.2 Hammer Energy Efficiency Correction Factor, CE

    The energy efficiency correc