<p>This paper reviews recent work on energy-based methodologies for estimating pore water pressure rise and the timing of initial soil liquefaction. Unlike stress-based methods, energy-based approaches use a scalar, cumulative parameter—making them well suited to modeling pore pressure buildup and the timing of liquefaction onset. The rise in pore pressure and onset of liquefaction can be estimated by summing cumulative dissipated hysteretic strain energy normalized by effective stress, which correlates strongly with the pore-pressure ratio <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({r}_{u}\)</EquationSource> </InlineEquation>. As such,, normalized energy is a complex parameter that combines the demand and capacity sides of the liquefaction problem into one term. Energy dissipated beyond the liquefaction boundary maintains <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({r}_{u}=1.0\)</EquationSource> </InlineEquation>, and likely is correlated with the potentially large shear and volumetric strains associated with liquefaction damage. However, one practical challenge of applying the method is that it requires empirical hysteretic relationships between normalized cumulative energy and excess pore pressure ratio, that are difficult to obtain in the laboratory and almost never available in the field. Proxy models for dissipated work—using Arias Intensity, Cumulative Absolute Velocity (CAV), and soil parameters, relative density or the state parameter of Been and Jeffries (1985)—appear to be the most practical path forward. However, these parameters are hampered by their elevated predictive uncertainties. The key benefit of the scalar and cumulative nature of energy-based methods are that they lead to improved estimation of liquefaction timing. Therefore, we can use just the the post-initial liquefaction time history to correlate with shear and volumetric strains. Three independent methods are currently used: the hysteretic strain-energy method, the Spectral Energy Ratio (SER) method, and Arias Intensity timing. These approaches aim to link total energy demand (Arias Intensity) to partial absorbed work (hysteretic strain energy). Parallel research investigates shear and volumetric strains before, during, and after <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({r}_{u}=1.0\)</EquationSource> </InlineEquation>. Liquefaction timing estimates based on Arias Intensity and SER can recalibrate soil models for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(G/{G}_{max}\)</EquationSource> </InlineEquation>, energy absorption, and pore pressure rise. Future work will establish relationships between hysteretic strain energy, Arias Intensity, and CAV with field penetration resistance, relative density, and initial shear stress. If successful, simplified energy demand parameters could assess liquefaction potential and act as proxies for dissipated work. Ultimately, well-documented case histories and robust proxy models will provide the foundation for energy-based, performance-oriented liquefaction assessment methods.</p>

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Energy-Based Methods for Seismic Soil Liquefaction: Past, Present, and Future

  • Robert E. Kayen,
  • Kil-Wan Ko

摘要

This paper reviews recent work on energy-based methodologies for estimating pore water pressure rise and the timing of initial soil liquefaction. Unlike stress-based methods, energy-based approaches use a scalar, cumulative parameter—making them well suited to modeling pore pressure buildup and the timing of liquefaction onset. The rise in pore pressure and onset of liquefaction can be estimated by summing cumulative dissipated hysteretic strain energy normalized by effective stress, which correlates strongly with the pore-pressure ratio \({r}_{u}\) . As such,, normalized energy is a complex parameter that combines the demand and capacity sides of the liquefaction problem into one term. Energy dissipated beyond the liquefaction boundary maintains \({r}_{u}=1.0\) , and likely is correlated with the potentially large shear and volumetric strains associated with liquefaction damage. However, one practical challenge of applying the method is that it requires empirical hysteretic relationships between normalized cumulative energy and excess pore pressure ratio, that are difficult to obtain in the laboratory and almost never available in the field. Proxy models for dissipated work—using Arias Intensity, Cumulative Absolute Velocity (CAV), and soil parameters, relative density or the state parameter of Been and Jeffries (1985)—appear to be the most practical path forward. However, these parameters are hampered by their elevated predictive uncertainties. The key benefit of the scalar and cumulative nature of energy-based methods are that they lead to improved estimation of liquefaction timing. Therefore, we can use just the the post-initial liquefaction time history to correlate with shear and volumetric strains. Three independent methods are currently used: the hysteretic strain-energy method, the Spectral Energy Ratio (SER) method, and Arias Intensity timing. These approaches aim to link total energy demand (Arias Intensity) to partial absorbed work (hysteretic strain energy). Parallel research investigates shear and volumetric strains before, during, and after \({r}_{u}=1.0\) . Liquefaction timing estimates based on Arias Intensity and SER can recalibrate soil models for \(G/{G}_{max}\) , energy absorption, and pore pressure rise. Future work will establish relationships between hysteretic strain energy, Arias Intensity, and CAV with field penetration resistance, relative density, and initial shear stress. If successful, simplified energy demand parameters could assess liquefaction potential and act as proxies for dissipated work. Ultimately, well-documented case histories and robust proxy models will provide the foundation for energy-based, performance-oriented liquefaction assessment methods.