Liquefaction and Landslide#
Landslides and liquefaction are well-known perils that accompany earthquakes. Basic models to describe their occurrence have been around for decades and are constantly improving. However, these models have rarely been incorporated into PSHA.
The tools presented here are implementations of some of the more common and appropriate secondary perils models. The intention is seamless incorporation of these models into PSH(R)A calculations done through the OpenQuake Engine, though the incorporation is a work in progress.
In what follows, we provide a brief overview of the implemented models, preceded by general considerations on the spatial resolution at which these analyses are typically conducted. For more in-depth information on the geospatial models, we recommend referring to the original studies. Additionally, we offer corresponding demonstration analyses, which can be found in the demos section) of our GitHub repository. We encourage users to check them out and and familiarize themselves with the required inputs for performing liquefaction or landslide assessment. We also provide tools to extract relevant information from digital elevation data and its derivatives, which are often given as rasters.
General considerations#
Spatial resolution and accuracy of data and site characterization#
Much like traditional seismic hazard analysis, liquefaction analysis may range from low-resolution analysis over broad regions to very high resolution analysis of smaller areas. With advances in computing power, it is possible to run calculations for tens or hundreds of thousands of earthquakes at tens or hundreds of thousands of sites in a short amount of time on a personal computer, giving us the ability to work at a high resolution over a broad area, and considering a very comprehensive suite of earthquake sources. In principle, the methods should be reasonably scale-independent but in practice this isn’t always the case.
Two of the major issues that can arise are the limited spatial resolutions of key datasets and the spatial misalignments of different datasets.
Some datasets, particularly those derived from digital elevation models, must be of a specific resolution or source to
be used accurately in these calculations. As we will see in the coming sections of this document, a common proxy to
most of the geospatial models is shear wave velocity in the top
In and of itself, this is not necessarily a problem. The issues can arise when the average spacing of the sites is much lower than the resolution of the data, or the characteristics of the sites vary over spatial distances much less than the data, so that important variability between sites is lost.
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 categorization of sites into liquefaction
susceptibility classes based on geotechnical 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 available input variables as first-order proxies to characterise saturation and density properties of the
soil. The shaking component is expressed either in terms of Peak Ground Acceleration ,
HAZUS#
The HAZUS model (see HAZUS manual) classifies each site into a liquefaction
susceptibility class,
The equation that describes this probability is:
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,
Geospatial models#
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
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.
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.
Zhu et al. (2017)#
Two parametric models, a coastal model (Model 1), and a more general model (Model 2) are proposed by
Zhu et al. (2017).
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:
Model 2:
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,
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 probabilities to areal liquefaction percent.
Rashidian and Baise (2020)#
The model proposed by Rashidian and Baise (2020) keeps the same functional form as the general model (Model 2) proposed by Zhu et al. (2017);
however, introducing two constraints to address the overestimation of liquefaction extent. The mean annual
precipitation has been capped to
The explanatory variable
The proposed probability threshold to convert to class outcome is 0.4.
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:
Model 2:
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.
Allstadt 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
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
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.
Lateral spreading (Hazus)#
The expected permanent displacement due to lateral spreading given the susceptibility category can be determined as:
Where:
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 |
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.
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 et al., 2000,
Jibson 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 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 et al. (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 (17). For rock- slope failures, the
Finally, the coseismic displacements are estimated using the sliding block displacement regression equation proposed by Jibson (2007).
Nowicki Jessee et al. (2018)#
A geospatial model used to predict probability of landsliding using globally available geospatial variables was proposed by
Nowicki Jessee et al. (2018). The level of shaking is
characterised by Peak Ground Velocity ,
Explanatory variable
Coefficients alpha and beta values are estimated for several rock and landcover classes. The reader is reffered to the original study by Nowicki Jessee et al. (2018), where the coefficient values are reported in Table 3.
Probability of landsliding is then evaluated using logistic regression.
These probabilities are converted to areal percentages to unbias the predictions.
Furthermore, we introduced modifications by the USGS, capping the peak ground velocity at
Reference#
[1] HAZUS-MH MR5 Earthquake Model Technical Manual (https://www.hsdl.org/?view&did=12760)
[2] Youd, T. L., & Idriss, I. M. (2001). Liquefaction Resistance of Soils: Summary Report from the 1996 NCEER and 1998 NCEER/NSF Workshops on Evaluation of Liquefaction Resistance of Soils. Journal of Geotechnical and Geoenvironmental Engineering, 127(4), 297–313. https://doi.org/10.1061/(asce)1090-0241(2001)127:4(297)
[3] I. D. Moore, R. B. Grayson & A. R. Ladson (1991). Digital terrain modelling: A review of hydrological, geomorphological, and biological applications. Journal of Hydrological Processes, 5(1), 3-30. https://doi.org/10.1002/hyp.3360050103
[4] Wald, D.J., Allen, T.I., (2007). Topographic Slope as a Proxy for Seismic Site Conditions and Amplification. Bull. Seism. Soc. Am. 97 (5), 1379–1395.
[5] Zhu et al., 2015, ‘A Geospatial Liquefaction Model for Rapid Response and Loss Estimation’, Earthquake Spectra, 31(3), 1813-1837.
[6] Bozzoni, F., Bonì, R., Conca, D., Lai, C. G., Zuccolo, E., & Meisina, C. (2021). Megazonation of earthquake-induced soil liquefaction hazard in continental Europe. Bulletin of Earthquake Engineering, 19(10), 4059–4082. https://doi.org/10.1007/s10518-020-01008-6
[7] Zhu, J., Baise, L. G., & Thompson, E. M. (2017). An updated geospatial liquefaction model for global application. Bulletin of the Seismological Society of America, 107(3), 1365–1385. https://doi.org/10.1785/0120160198
[8] Rashidian, V., & Baise, L. G. (2020). Regional efficacy of a global geospatial liquefaction model. Engineering Geology, 272, 105644. https://doi.org/10.1016/j.enggeo.2020.105644
[9] Allstadt, K. E., Thompson, E. M., Jibson, R. W., Wald, D. J., Hearne, M., Hunter, E. J., 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
[10] Baise, L. G., Akhlaghi, A., Chansky, A., Meyer, M., & Moeveni, B. (2021). USGS Award #G20AP00029. Updating the Geospatial Liquefaction Database and Model. Tufts University. Medford, Massachusetts, United States.
[11] Todorovic, L., Silva, V. (2022). A liquefaction occurrence model for regional analysis. Soil Dynamics and Earthquake Engineering, 161, 1–12. https://doi.org/10.1016/j.soildyn.2022.107430
[12] Newmark, N.M., 1965. Effects of earthquakes on dams and embankments. Geotechnique 15, 139–159.
[13] Jibson, R.W., Harp, E.L., & Michael, J.A. (2000). A method for producing digital probabilistic seismic landslide hazard maps. Engineering Geology, 58(3-4), 271-289. https://doi.org/10.1016/S0013-7952(00)00039-9
[14] Jibson, R.W. (2007). Regression models for estimating coseismic landslide displacement. Engineering Geology, 91(2-4), 209-218. https://doi.org/10.1016/j.enggeo.2007.01.013
[15] Grant, A., Wartman, J., & Grace, A.J. (2016). Multimodal method for coseismic landslide hazard assessment. Engineering Geology, 212, 146-160. https://doi.org/10.1016/j.enggeo.2016.08.005
[16] Nowicki Jessee, M. A., Hamburger, M. W., Allstadt, K., Wald, D. J., Robeson, S. M., Tanyas, H., et al. (2018). A global empirical model for near-real-time assessment of seismically induced landslides. Journal of Geophysical Research: Earth Surface, 123, 1835–1859. https://doi.org/10.1029/2017JF004494
[17] Danielson, J.J., and Gesch, D.B., 2011, Global multi-resolution terrain elevation data 2010 (GMTED2010): U.S. Geological Survey Open-File Report 2011–1073, 26 p.
[18] Hartmann, J., and N. Moosdorf (2012), The new global lithological map database GLiM: A representation of rock properties atthe Earth surface, Geochem. Geophys. Geosyst., 13, Q12004, doi:10.1029/2012GC004370.
[19] Arino, O., Ramos Perez, J.J., Kalogirou, V., Bontemps, S., Defourny, P., Van Bogaert, E. (2012): Global Land Cover Map for 2009 (GlobCover 2009), https://doi.org/10.1594/PANGAEA.787668