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The two types of numerical techniques related to the Material Point Method (MPM) are reported; one is the alternative interpolation function called Arbitrary Particle Domain Interpolation (APDI), and the other is the particle-element coupled method. APDI interpolation function is one of the domain integration methods, which can consider the arbitrary shape of particle domain in MPM. The numerical domain integration employed in APDI method has realized the simpler algorithm in both 2- or 3-dimensional implementation. Especially in 3-dimensional formulation, the simple formulation and implementation is inevitable for the integrity of the numerical method. On the other hand, the particle-element coupled method is the numerical framework to reduce the computational cost such as memory, storage and computational time. The basic idea of the particle-element method is to divide the target domain physically into subdomains, and they are combined together numerically by using the numerical grid. This technique enables us to apply the different interpolation function to the different parts of the target domain, realizing the complex calculation using both particle and element in the same procedure. In this paper, the formulations and the demonstrations of both APDI method and the particle-element coupled method are reported, and the applicability and effectiveness of the methods to geomaterial are clarified.

This paper presents a summary of the element test simulations (calibration simulations) submitted by 11 numerical simulation (prediction) teams that participated in the LEAP-2017 prediction exercise. A significant number of monotonic and cyclic triaxial (Vasko, An investigation into the behavior of Ottawa sand through monotonic and cyclic shear tests. Masters Thesis, The George Washington University, 2015; Vasko et al., LEAP-GWU-2015 Laboratory Tests. DesignSafe-CI, Dataset, 2018; El Ghoraiby et al., LEAP 2017: Soil characterization and element tests for Ottawa F65 sand. The George Washington University, Washington, DC, 2017; El Ghoraiby et al., LEAP-2017 GWU Laboratory Tests. DesignSafe-CI, Dataset, 2018; El Ghoraiby et al., Physical and mechanical properties of Ottawa F65 Sand. In B. Kutter et al. (Eds.), Model tests and numerical simulations of liquefaction and lateral spreading: LEAP-UCD-2017. New York: Springer, 2019) and direct simple shear tests (Bastidas, Ottawa F-65 Sand Characterization. PhD Dissertation, University of California, Davis, 2016) are available for Ottawa F-65 sand. The focus of this element test simulation exercise is to assess the performance of the constitutive models used by participating team in simulating the results of undrained stress-controlled cyclic triaxial tests on Ottawa F-65 sand for three different void ratios (El Ghoraiby et al., LEAP 2017: Soil characterization and element tests for Ottawa F65 sand. The George Washington University, Washington, DC, 2017; El Ghoraiby et al., LEAP-2017 GWU Laboratory Tests. DesignSafe-CI, Dataset, 2018; El Ghoraiby et al., Physical and mechanical properties of Ottawa F65 Sand. In B. Kutter et al. (Eds.), Model tests and numerical simulations of liquefaction and lateral spreading: LEAP-UCD-2017. New York: Springer, 2019). The simulated stress paths, stress strain responses, and liquefaction strength curves show that majority of the models used in this exercise are able to provide a reasonably good match to liquefaction strength curves for the highest void ratio (0.585) but the differences between the simulations and experiments become larger for the lower void ratios (0.542 and 0.515).