Empirical relationships between magnitude and liquefaction distance using the Philippine dataset

• The Philippine liquefaction database includes 1,386 accounts from 130 earthquakes. • The MS – Remax equation applies to 5.1 ≤ MS ≤ 7.8. • The MS – Rfmax equation applies to 5.1 ≤ MS ≤ 7.6. • Two equations relating Mw to Remax and Rfmax are valid for 4.70 ≤ MW ≤ 7.88. • The equations can be used to rapidly determine the extent of areas that may liquefy. Earthquake-triggered liquefaction can cause ground failure and damage to built-up structures. It is therefore necessary to determine the possible extent of the hazard during earthquakes. A common approach in predicting liquefaction occurrence is to relate the earthquake magnitude with its maximum liquefaction distance. However, while several empirical equations based on global datasets already exist, they contain sparse accounts from the Philippines. In this study, a total of 1,386 liquefaction observation sites from 130 earthquakes that occurred from 1619 to 2023 were reviewed and analyzed to determine empirical equations that may relate liquefaction occurrence with the distance to the epicenter and seismic source. Using the Linear Least Squares (LLS) method on liquefaction case histories, four bounding equations relating earthquake magnitude to the maximum liquefaction distance from the epicenter ( R emax ) and causative fault ( R fmax ) were generated. The equation relating surface-wave magnitude ( M S ) to R emax is valid for 5.1 ≤ M S ≤ 7.8, while the equation relating M S to R fmax is valid for 5.1 ≤ M S ≤ 7.6. The two equations relating moment magnitude ( M W ) to R emax and R fmax are valid for 4.70 ≤ M W ≤ 7.88. These equations are applicable for the Philippine setting and can be used to rapidly determine the possible extent of liquefaction for any given earthquake, especially in the absence of detailed geological or geotechnical data.