Liquefaction Potential Index Calculator

Liquefaction analysis compares seismic demand with soil capacity. Demand is the cyclic stress ratio, CSR = 0.65 * (sigma_v / sigma_v_prime) * (a_max / g) * rd, in which the factor 0.65 converts an irregular acceleration record into an equivalent uniform cyclic series, the stress ratio accounts for buoyancy below the water table, and rd reduces the demand with depth because the soil column is not perfectly rigid. Capacity is the cyclic resistance ratio CRR, obtained from the penetration resistance corrected for overburden, hammer energy, rod length, borehole diameter, and fines content to give N1-60. Both are referenced to a magnitude 7.5 event through a magnitude scaling factor, since larger earthquakes deliver more equivalent loading cycles. The factor of safety is CRR divided by CSR, and the Liquefaction Potential Index weights the shortfall F = 1 - FS by a depth function w = 10 - 0.5z and integrates it over the upper 20 meters, so shallow layers count far more toward surface damage than deep ones. Interpretation follows the bands proposed with the original index: LPI of zero indicates no liquefaction, values up to 5 low severity, 5 to 15 high, and above 15 very high, with field studies finding sand boils typically appearing near LPI of about 5 and severe ground disruption above roughly 12 to 15. Susceptibility itself is restricted to loose, saturated, cohesionless deposits, chiefly Holocene fine to medium sands, silty sands, and non-plastic silts with a shallow water table; clean sands with N1-60 above about 30 are generally treated as non-liquefiable, and fines with a plasticity index above roughly 7 add substantial resistance. The main limitations are that the empirical CRR curves are calibrated to case histories from level ground below about 15 meters depth and roughly one atmosphere of effective stress, that they say nothing directly about the amount of settlement or lateral spread, and that a single-depth evaluation such as this one approximates a profile integral that properly requires borehole data through the full 20 meters.

Liquefaction became an engineering priority after two 1964 earthquakes. The magnitude 7.6 Niigata event in Japan tilted and toppled apartment blocks at Kawagishi-cho while the buildings themselves stayed intact, and the magnitude 9.2 Great Alaska earthquake produced the Turnagain Heights landslide in Anchorage. Both were caused by saturated sand losing strength under shaking rather than by structural failure. H. Bolton Seed and Izzat Idriss at the University of California, Berkeley responded with the simplified procedure published in 1971, which replaced expensive site-response analysis with the cyclic stress ratio expression and the penetration-based resistance curves that remain the backbone of practice. The index built on top of it came from Japan. Toshio Iwasaki and coworkers at the Public Works Research Institute proposed the Liquefaction Potential Index in 1978, refining it in 1982 by calibrating the severity bands against sites in Japan that had and had not shown surface manifestation, and the depth weighting function reflected the observation that liquefaction below about 20 meters rarely damages the ground surface. The framework was consolidated at the 1996 and 1998 workshops convened by the National Center for Earthquake Engineering Research and the National Science Foundation, whose consensus recommendations were published by T. Leslie Youd, Idriss, and 19 coauthors in the ASCE Journal of Geotechnical and Geoenvironmental Engineering in 2001. Selim Toprak and Thomas Holzer of the United States Geological Survey correlated LPI with observed surface effects in 2003. Idriss and Ross Boulanger issued substantially revised correlations in 2008 and 2014, and the dense case-history record from the 2010 and 2011 Canterbury earthquakes in Christchurch, New Zealand has since been used to test and recalibrate the index.