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4.4.2 Lateral Ground Displacement from Regression Analysis
Recent work has been conducted using a multiple linear regression (MLR) analysis to take into
account a great number of variables in a predictive equation for horizontal displacements
(Bartlett and Youd 1995; Youd et. al. 1999). This analysis examined 43 detailed factors from
eight earthquakes in order to account for seismological, topographical, geological, and
geotechnical effects on permanent ground displacement. The database comprised 467 horizontal
displacement vectors, SPT blow counts, soil descriptions, grain-size analyses from 267
boreholes, and 19 observations selected from Ambraseys (1988). Youd and others (1999)
updated the MLR analysis with the addition of data from 4 recent earthquakes, and addressed
inconsistencies in the data and regression analysis.
Observations from Japanese and U.S. case studies demonstrated that there were generally two
types of lateral spreading: (1) lateral spread towards a free face (e.g., incised river channel or
some other abrupt topographical depression), and (2) lateral spread down gentle ground slopes
where a free face was absent. Analyses showed that each of these would need separate predictive
equations. The final analysis resulted in two equations based on six geotechnical and seismologic
parameters. The lateral spread displacement is estimated for free-face and uniformly sloping
ground conditions by Equations 4-6 and 4-7, respectively.
log D h = -18.084 + 1.581 M – 1.518 log R* - 0.011 R + 0.551 log W
+ 0.547 log T 15 + 3.976 log (100 - F 15 ) - 0.923 log (D50 15 + 0.1 mm) (4-6)
log D h = -17.614 + 1.581 M – 1.518 log R* - 0.011 R + 0.343 log S
+ 0.547 log T 15 + 3.976 log (100 - F 15 ) - 0.923 log (D50 15 + 0.1 mm) (4-7)
where
D h is the estimated lateral ground displacement (m),
M is the earthquake moment magnitude,
R is the epicentral (horizontal) distance to earthquake (km),
R* = R + 10 (0.89 M - 5.664) ,
W is the ratio of free face height to distance to the free face (%),
S is ground slope (%),
T 15 is cumulative thickness of saturated sandy layers with (N 1 ) 60 ≤ 15 (m),
F 15 is average fines content of saturated granular layers included in T 15 (%), and
D50 15 is the average mean grain size of layers included in T 15 (mm).
To demonstrate the uncertainty associated with Equations 4-6 and 4-7, the displacements
computed using the regression equations are plotted against the measured displacements from the
compiled case histories. These are shown in Figure 4.7. The arrows represent the change in
prediction between the method as proposed by Bartlett and Youd (1995), and the updated
method proposed by Youd et al. (1999). The middle diagonal line in this plot represents a perfect
prediction line, while the lower and upper diagonal lines represent a 100% over-prediction and a
50% under-prediction bound, respectively. The results suggest that the equations are generally
accurate within plus or minus a factor of two. The predicted response from MLR models may be
strongly nonlinear outside the range of the data used to derive the regression coefficients, and
caution is warranted when extrapolating beyond the intended range of parameters. Table 4.3 is
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