# Liquefaction#

## Site characterization for probabilistic liquefaction analysis#

There are many methods to calculate the probabilities and displacements that result from liquefaction. In OpenQuake, we have several models, the methods developed by the US Federal Emergency Management Agency through their HAZUS project, and geospatial methods recently developed by Zhu et al. (2015), Zhu et al. (2017), Rashidian et al. (2020), Akhlagi et al. (2021), Bozzoni et al. (2021), Allstadt et al. (2022), Todorovic and Silva (2022).

These methods require different input datasets. The HAZUS methods are simplified from older, more comprehensive liquefaction evaluations that would be made at a single site following in-depth geotechnical analysis; the HAZUS methods retain their reliance upon geotechnical parameters that may be measured or inferred at the study sites. The methods by Zhu et al. (2015) were developed to only use data that can be derived from a digital elevation model (DEM), but in practice, the datasets must be chosen carefully for the statistical relations to hold. Furthermore, Zhu’s methods do not predict displacements from liquefaction, so the HAZUS site characterizations must be used for displacement calculations regardless of the methods used to calculate the probabilities of liquefaction.

## 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. For example, if Vs30 is calculated from slope following methods developed by Wald and Allen (2007), the slope should be calculated from a DEM with a resolution of around 1 km. Higher resolution DEMs tend to have higher slopes at a given point because the slope is averaged over smaller areas. The mathematical correspondance between slope and Vs30 was developed for DEMs of about 1 km resolution, so if modern DEMs with resolutions of 90 m or less are used, the resulting Vs30 values will be too high.

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.

The misalignment of datasets is another issue. Datasets derived from geologic mapping or other vector-type geospatial data may be made at spatial resolutions much higher or lower than those derived from digital elevation data or other raster geospatial datasets (particularly for 1 km raster data as discussed above). This can cause a situation where irregular geographic or geologic features such as rivers may be in different locations in two datasets, which can

## HAZUS#

### Liquefaction probabilities#

The HAZUS methods require several variables to characterize the ground shaking and the site response:

Earthquake magnitude

Peak Ground Acceleration (PGA)

Liquefaction susceptibility category

Groundwater depth

The magnitude of the earthquake and the resulting PGA may be calculated by OpenQuake during a scenario or event-based PSHA, or alternatively from ShakeMap data or similar for real earthquakes, or through other methods. The earthquake magnitude should be given as the moment magnitude or work magnitude (M or MW). PGA should be provided for each site in units of g (i.e., 9.81 m/s2).

#### Liquefaction suscepibility category#

The HAZUS methods require that each site be assigned into a liquefaction susceptibility category. These categories are ordinal variables ranging from ‘no susceptibility’ to ‘very high susceptibility’. The categorization is based on geologic and geotechnical characteristics of the site, including the age, grain size and strength of the deposits or rock units.

For a regional probabilistic liquefaction analysis, the categorization will be based on a geologic map focusing on Quaternary geologic units. The analyst will typically associate each geologic unit with a liquefaction susceptibility class, based on the description or characteristics of the unit. (Please note that there will typically be far fewer geologic units than individual unit polygons or contiguous regions on a geologic map; the associations described here should generally work for each unit rather than each polygon.)

Please see the HAZUS manual, Section 4-21, for more information on associating geologic units with susceptibility classes. The descriptions of the susceptibility classes may not align perfectly with the descriptions of the geologic units, and therefore the association may have some uncertainty. Consulting a local or regional geotechnical engineer or geologist may be helpful. Furthermore, may be prudent to run analyses multiple times, changing the associations to quantify the effects on the final results, and perhaps creating a final weighted average of the results.

Once each geologic map unit has been associated with a liquefaction susceptibility class, each site must be associated with a geologic unit. This is most readily done through a spatial join operation in a GIS program.

#### Groundwater depth#

The groundwater depth parameter is the mean depth from the surface of the soil to the water table, in meters. Estimation of this parameter from remote sensing data is quite challenging. It may range from less than a meter near major water bodies in humid regions to tens of meters in dry, rugged areas. Furthermore, this value may fluctuate with recent or seasonal rainfall. Sensitivity testing of this parameter throughout reasonable ranges of uncertainty for each site is recommended. For large scale application (e.g., in geospatial models), the ground water depth database compiled by Fan et al. (2013) can be used.

### Lateral spreading#

The horizontal displacements from lateral spreading may be calculated through HAZUS methods as well. These calculations do not require additional data or site characterization. However, if methods are used for calculating liquefaction probabilities that do not use the HAZUS site classifications (such as Zhu et al. (2015)), then these classifications will have to be done in order to calculate the displacements.

### Geospatial models#

The geospatial liquefaction models (e.g, Zhu et al. (2015), Zhu et al. (2017)) calculates the probability of liquefaction via logistic regression of a few variables that are, in principle, easily derived from digital elevation data. In practice, there are strict requirements on the spatial resolution and sources of these data derivations, and deviations from this will yield values at each site that may be quite discrepant from those calculated ‘correctly’. This may produce very inaccurate liquefaction probabilities, as the logistic coefficients will no longer be calibrated correctly.

#### Getting raster values at sites#

Digital elevation data and its derivatives are often given as rasters. However, in the case of probabilistic analysis of secondary perils (particularly for risk analysis) the analyist may need to deal with sites that are not distributed according to a raster grid.

Raster values may be extracted at sites using a GIS program to perform a spatial join, but following inconvenient historical precedent, this operation often produces new data files instead of simply appending the raster values to the point data file.

Therefore we have implemented a simple function, [`openquake.sep.utils.sample_raster_at_points`

] srap,
to get the raster values. This function requires the filename of the raster, and the longitudes and latitudes of the
sites, and returns a Numpy array with the raster values at each point. This function can be easily incorporated into a
Python script or workflow in this manner.

#### Probability of liquefaction#

Calculating liquefaction probabilities requires values for Vs30 and the Compound Topographic Index, which is a proxy for soil wetness.

**Vs30**

Zhu et al (2015) calibrated their model on Vs30 data derived from DEMs using the methods of Wald and Allen (2007).

This method is implemented in the engine here.
It requires that the slope is calculated as the gradient (dy/dx) rather than an angular unit, and the study area is
categorized as tectonically `active`

or `stable`

.

A more general wrapper function has also been written here. This function can calculate gradient from the slope in degrees (a more common formulation), and will be able to use different formulas or relations between slope and Vs30 if and when those are implemented (we have no current plans for doing so).

**Soil wetness proxies**

A set of candidate proxies are globally available to characterise the soil wetness. The general model by Zhu et al. (2015) and Bozzoni et al. (2021) used the compound topographic index, a proxy for soil wetness that relates the topographic slope of a point to the upstream drainage area of that point. This index can be obtained from dataset that has a global range of 0-20 Marthews et al. (2015). In more recent models, additional proxies were introduced such as distance to the nearest coast available here, distance to the nearest river network available here, and precipitation available here.