Energy-Based Liquefaction Potential Evaluation and its Application to a Case History

Triaxial undrained cyclic loading tests show that the strain amplitude or pore-pressure buildup during harmonic as well as irregular cyclic loadings is uniquely correlated not only to energy dissipated in soil specimens but also to strain energy imposed during earthquakes. Similar tests using torsional simple shear apparatus also demonstrate the uniqueness between the energy and pressure-buildup. Then, a procedure of an energy-based method (EBM) is explained in which liquefaction potential can be evaluated by comparing energy capacity for liquefaction in a sand layer with upcoming seismic energy with no regard to differences in seismic motions. As an example, the EBM evaluation is applied to a liquefaction case triggered by a weak shaking during far-field M8.0 earthquake to demonstrate a better applicability than the current stress-based method (SBM) . Introduction The energy-based liquefaction potential evaluation method (EBM) was first proposed by Davis and Berrill (1982) following the assumption that the pore-pressure buildup is directly related to the amount of seismic energy dissipated in the unit volume of soil. Undrained cyclic loading tests focusing on the dissipated energy in soil specimens were conducted and a unique relationship was found between the dissipated energy and excess pore-pressure or induced strain independent of shear stress history by several researchers. For example, Figure 1(a) shows a typical cyclic stress-strain relationship for Dr=51% and Fc=0% in a triaxial test (Kokusho 2013). The dissipated energy per unit volume in a test specimen is calculated for a k-th loading cycle from a hysteretic area ABCD illustrated in the figure with a dashed curve and summed up for individual cycles from the start to a certain cycle. In Figure 1(b), the values thus calculated are normalized by the effective confining stress c σ ′ =98 kPa as c W σ ′ ∆ in the horizontal axis and correlated with pore-pressure buildup ratio, c u σ ′ ∆ , and double amplitude axial amplitude, DA ε , in the vertical axes for Dr-values 30, 50 and 70%. It is remarkable that the difference in the c u σ ′ ∆ ~ c W σ ′ ∆ correlations is marginal and c u σ ′ ∆ =1.0 at around c W σ ′ ∆ =0.02 for sands with different Dr. In the same figure, induced strain amplitude can be correlated consistently with dissipated energy depending on individual Dr-values up to the initial liquefaction ( DA ε =5%) and thereafter, and serves as an indicator for the severity of Professor, emeritus, Civil & Environment Department, Chuo University, Tokyo, Japan, koktak@ad.email. ne.jp Ex-graduate student, Civil & Environment Department, Chuo University, Tokyo, Japan. Ex-graduate student, Civil & Environment Department, Chuo University, Tokyo, Japan. liquefaction. Figure 2(a) shows a similar cyclic loading test result using a torsional simple shear apparatus for an irregular seismic motion recorded during 2011 Tohoku earthquake (Kokusho & Kaneko 2014). The dissipated energy W ∆ calculated in the same way as in Figure 1(a) is shown at the top in Figure 2(a) and correlated with the associated excess pore-pressure shown at the bottom to produce the c W σ ′ ∆ ~ c u σ ′ ∆ plots in Figure 2(b). Here, the plots of irregular motions for sands with Dr= 50% (solid symbols) are superposed on those for harmonic motions (open symbols) by the same torsional shear tests for sands with Dr=30% and 50%, which coincide well with those obtained in cyclic triaxial tests shown in Figure 1(b). In Fig. (b), it seems difficult to recognize a systematic difference in the plots between irregular and harmonic loadings, demonstrating that the energy principle holds for earthquake loadings, too. Thus, the superiority of energy-based liquefaction evaluation has been recognized in many previous researches. Nevertheless, its application in engineering practice has been very limited so far in contrast to the stress-based method (SBM) mainly due to difficulties in comparing the dissipated energy with seismic wave energy. In this paper, a simplified EBM previously proposed by Kokusho (2013) is addressed again to explain a procedure including how to evaluate the seismic energy and compare it with the dissipated energy. Then the EBM procedure is applied, together with SBM, to a liquefaction case triggered by a weak seismic motion during a far-field M8.0 earthquake in Hokkaido to compare with actual performance. Figure 1. Dissipated energy △W and strain energy W in stress-strain curves (a), and normalized energy △W/σ’c versus normalized pore-pressure c u σ ′ ∆ and axial strain DA ε (b) -0.08 -0.04 0.00 0.04 -30 -20 -10 0 10 20 30