Prediction of time of liquefaction using kinetic and strain energy

Abstract

The time of liquefaction triggering during a strong ground motion can have a large influence on the expected level of foundation and superstructure damage. To enable simple, yet accurate estimates of the triggering time, the build-up of pore pressure needs to be understood in terms of cumulative measures of ground motion intensity. This paper develops a theoretical framework and simple procedure to predict the build-up of excess pore pressure based on the principles of conservation of energy. The liquefaction resistance is first quantified in terms of cumulative absolute change in strain energy, which is shown through the evaluation of experimental cyclic simple shear tests to be insensitive to loading amplitude. A ground motion intensity measure is presented that uniquely calculates the cumulative absolute change in kinetic energy. This intensity measure is then used to provide an exact analytical solution for the cumulative absolute change in strain energy at any depth in a homogenous linear elastic soil deposit using the novel, nodal surface energy spectrum (NSES). A simple reduction to the NSES is proposed for viscous and nonlinear soil deposits, as well as a correction for changes in stiffness between layers of soil. The estimation of strain energy and build-up of pore pressure using the simple NSES method was applied to 500 randomly generated soil deposits using a range of different ground motions and validated against nonlinear total stress and nonlinear effective stress time-history analyses, with the NSES method providing a high level of accuracy. The proposed spectrum based solution provides an efficient and physically consistent procedure for the prediction of excess pore pressure build-up.

Macromechanism Approach for Vulnerability Assessment of Buildings on Shallow Foundations in Liquefied Soils

“…Some of them only provide the factor of safety against liquefaction triggering, but others provide the whole pore pressure evolution during the earthquake duration including the time of liquefaction triggering. In this work, the strain energy-based model proposed by Millen et al (2020) was used, but other simplified models that provide the pore pressure time series could be used instead (see Seed et al 1975;Green et al 2000;Kokusho 2013;Rios et al 2019). In the method developed by Millen et al (2020), liquefaction resistance is measured in terms of normalized cumulative absolute strain energy (NCASE), which was shown to be insensitive to loading amplitude but sensitive to soil properties.…”

“…In this work, the strain energy-based model proposed by Millen et al (2020) was used, but other simplified models that provide the pore pressure time series could be used instead (see Seed et al 1975;Green et al 2000;Kokusho 2013;Rios et al 2019). In the method developed by Millen et al (2020), liquefaction resistance is measured in terms of normalized cumulative absolute strain energy (NCASE), which was shown to be insensitive to loading amplitude but sensitive to soil properties. NCASE is defined as the cumulative change in absolute elastic strain energy divided by the initial vertical effective stress, σ 0 vo , [Eqs.…”

Cyclic and Dynamic Behavior of Sand–Rubber and Clay–Rubber Mixtures

“…The energy absorbed by the material may be evaluated based on the strain energy density, as used by Indraratna et al (2017) for monotonic shearing. Millen et al (2019) applied this concept to cyclic tests and suggested normalization by the effective confining stress σ'c, calling the obtained parameter NCASE (normalized accumulated absolute strain energy). The NCASE can be calculated with the following expression:…”

Site classification using equivalent soil profiles for building-liquefaction interaction

“…The contraction rate parameter ( h p0 ) was determined using the fitting expression, Eq. 3, from Millen et al (2020), where the target cyclic resistance ratio for 15 cycles ( CRR n15,target ) was determined using Eq. 4 from Boulanger and Idriss (2016), which is an empirical expression for the cyclic resistance for a magnitude 7.5 event.…”