4.1. Liquefaction and Landslide models#
4.1.1. Liquefaction models#
Several liquefaction models are implemented in the OpenQuake engine. One of them is the method developed for the HAZUS software by the US Federal Emergency Management Agency. This model involves categoriza- tion of sites into liquefaction susceptibility classes based on geo- technical characteristics, and a quanitative probability model for each susceptibility class. The remaining models are the academic geospatial models, i.e., statistical models that uses globally avai- lable input variables as first-order proxies to characterise satura- tion and density properties of the soil. The shaking component is expressed either in terms of Peak Ground Acceleration (PGA) or Peak Ground Velocity (PGV).
4.1.1.1. HAZUS#
The HAZUS model classifies each site into a liquefaction susceptibility class (LSC) based on the geologic and geotechnical characteristics of the site, such as the sedimentological type and the deposition age of the unit. In addition to the LSC and the local ground acceleration at each site, the depth to groundwater at the site and the magnitude of the causative earthquake will affect the probability that a given site will experience liquefaction.
The equation that describes this probability is:
LSC |
PGA min |
PGA slope |
PGA int |
|
---|---|---|---|---|
very high |
0.09 |
9.09 |
0.82 |
0.25 |
high |
0.12 |
7.67 |
0.92 |
0.2 |
moderate |
0.15 |
6.67 |
1.0 |
0.1 |
low |
0.21 |
5.57 |
1.18 |
0.05 |
very low |
0.26 |
4.16 |
1.08 |
0.02 |
none |
0.0 |
0.0 |
0.0 |
Table 1: Liquefaction values for different liquefaction susceptibility
categories (LSC). PGA min is the minimum ground acceleration required
to initiate liquefaction. PGA slope is the slope of the liquefaction
probability curve as a function of PGA, and PGA int is the y-intercept
of that curve.
4.1.1.2. Geospatial models#
4.1.1.2.1. Zhu et al. (2015)#
The model by Zhu et al. (2015) is a logistic regression model requiring
specification of the
The model is quite simple. An explanatory variable
and the final probability is the logistic function
The term
Both the
The CTI (Moore et al., 1991) is a proxy for soil wetness that relates the topographic slope of a point to the upstream drainage area of that point, through the relation
where
Model’s prediction can be transformed into binary class (liquefaction occurrence or nonoccurrence) via probability threshold value. The authors proposed a threshold of 0.2.
4.1.1.2.2. Bozzoni et al. (2021)#
The parametric model developed by Bozzoni et al. (2021), keeps the same
input variables (i.e.,
and the probability of liquefaction in calculated using equation (3).
The adopted probability threshold of 0.57 converts the probability of liquefaction into binary outcome.
4.1.1.2.3. Zhu et al. (2017)#
Two parametric models are proposed by Zhu and others (2017), a coastal
model (Model 1), and a more general model (Model 2). A coastal event is
defined as one where the liquefaction occurrences are, on average, within
20 km of the coast; or, for earthquakes with insignificant or no liquefaction,
epicentral distances less than 50 km.The implemented geospatial models
are for global use. An extended set of input parameters is used to
describe soil properties (its density and wetness). The ground shaking
is characterised by
The explanatory varibale
Model 1: .. math:: X = 12.435 + 0.301, ln, PGV - 2.615, ln, Vs30 + 0.0005556, precip .. math:: -0.0287, sqrt{d_{c}} + 0.0666,d_{r} - 0.0369, sqrt{d_{c}} cdot d_{r} (6)
Model 2: .. math:: X = 8.801 + 0.334, ln, PGV - 1.918, ln, Vs30 + 0.0005408, precip .. math:: -0.2054, d_{w} -0.0333, wtd (7)
and the probability of liquefaction is calculated using equation (3).
Zero probability is heuristically assigned if
The proposed probability threshold to convert to class outcome is 0.4.
Another model’s outcome is liquefaction spatial extent (LSE). After an earthquake LSE is the spatial area covered by surface manifestations of liquefaction reported as a percentage of liquefied material within that pixel. Logistic regression with the same form was fit for the two models, with only difference in squaring the denominator to improve the fit. The regression coefficients are given in Table 2.
Parameters |
Model 1 |
Model 2 |
---|---|---|
a |
42.08 |
49.15 |
b |
62.59 |
42.40 |
c |
11.43 |
9.165 |
Table 2: Parameters for relating proba- bilities to areal liquefaction percent.
4.1.1.2.4. Rashidian et al. (2020)#
The model proposed by Rashidian et al. (2020) keeps the same functional form
as the general model (Model 2) proposed by Zhu et al. (2017); however, introdu-
cing two constraints to address the overestimation of liquefaction extent. The
mean annual precipitation has been capped to 1700 mm. No liquefaction is heuri-
stically assign when
The explanatory variable
The proposed probability threshold to convert to class outcome is 0.4.
4.1.1.2.5. Akhlagi et al. (2021)#
Expanding the liquefaction inventory to include 51 earthquake, Akhlagi et al.
(2021) proposed two candidate models to predict probability of liquefaction.
Shaking is expressed in terms of
Model 1: .. math:: X = 4.925 + 0.694, ln, PGV - 0.459, sqrt{TRI} - 0.403, ln, d_{c}+1 .. math:: -0.309, ln, d_{r}+1 - 0.164, sqrt{Z_{wb}} (10)
Model 2: .. math:: X = 9.504 + 0.706, ln, PGV - 0.994, ln, Vs30 - 0.389, ln, d_{c}+1 .. math:: -0.291, ln, d_{r}+1 - 0.205, sqrt{Z_{wb}} (11)
and the probability of liquefaction is calculated using equation (3).
Zero probability is heuristically assigned if
The proposed probability threshold to convert to class outcome is 0.4.
4.1.1.2.6. Allstadth et al. (2022)#
The model proposed by Allstadth et al. (2022) uses the model proposed by
Rashidian et al. (2020) as a base with slight changes to limit unrealistic
extrapolations. The authors proposed capping the mean annual precipitation
at 2500 mm, and PGV at 150 cm/s. The magnitude scaling factor
4.1.1.2.7. Todorovic et al. (2022)#
A non-parametric model was proposed to predict liquefaction occurrence and
the associated probabilities. The general model was trained on the dataset
including inventories from over 40 events. A set of candidate variables
were considered and the ones that correlate the best with liquefaction
occurrence are identified as: strain proxy, a ratio between
4.1.1.3. Permanent ground displacements due to liquefaction#
Evaluation of the liquefaction induced permanent ground deformation is conducted using the methodology developed for the HAZUS software by the US Federal Emergency Management Agency. Lateral spreading and vertical settlements can have detrimental effects on the built environement.
4.1.1.3.1. Lateral spreading (Hazus)#
The expected permanent displacement due to lateral spreading given the susceptibility category can be determined as:
Where:
4.1.1.3.2. Vertical settlements (Hazus)#
Ground settlements are assumed to be related to the area’s susceptibility category. The ground settlement amplitudes are given in Table 3 for the portion of a soil deposit estimated to experience liquefaction at a given ground motion level. The expected settlements at the site is the product of the probability of liquefaction (equation 1) and the characteristic settlement amplitude corresponding to the liquefaction susceptibility category (LSC).
LSC |
Settlements (inches) |
---|---|
very high |
12 |
high |
6 |
moderate |
2 |
low |
1 |
very low |
0 |
none |
0 |
Table 3: Ground settlements amplitudes for liquefaction susceptibility categories.
4.1.2. Landslide models#
Landslides are considered as one of the most damaging secondary perils
associated with earthquakes. Earthquake-induced landslides occurs when
the static and inertia forces within the sliding mass reduces the factor
of safety below 1. Factors contributing to a slope failure are rather
complex. The permanent-displacement analysis developed by Newmark (1965)
is used to model the dynamic performance of slopes (Jibson 2020, 2007).
It considers a slope as a rigid block resting on an inclined plane at
an angle
The lower bound of
where:
Note that the units of the input parameters reported in this document corresponds to the format required by the Engine to produce correct results. The first and second term of the the equation (15) corresponds to the cohesive and frictional components of the strength, while the third component accounts for the strength reduction due to pore pressure.
A variety of regression equations can be used to estimate the Newmark displacements, and within the engine, Newmark displacement as a function of critical acceleration ratio and moment magnitude is implemented. The displacement is in units of meters.
The computed displacements do not necessarily correspond directly to measurable slope movements in the field, but the modeled displacements provide an index to correlate with field performance. Jibson (2000) compared the predicted displacements with observations from 1994 Northridge earthquake and fit the data with Weilbull curve. The following equation can be used to estimate the probability of slope failure as a function of Newmark displacement.
The rock-slope failures are the other common effect observed in earthquakes. The methodology proposed by Grant et al., (2016) captures the brittle behavior associated with rock-slope failures and discontinuities common in rock masses. The static factor of safety is computed as:
where:
The critical acceleration is computed similarly to equation (14). For rock-
slope failures, the
Finaly, the coseismic displacements are estimated using Jibson’s (2007) sliding block displacement regression equation:
4.1.3. Reference#
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Fee, J., Schovanec, H., Slosky, D., & Haynie, K. L. (2022). The US Geological Survey ground failure product: Near-real-time estimates of earthquake-triggered landslides and liquefaction. Earthquake Spectra, 38(1), 5–36. https://doi.org/10.1177/87552930211032685
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