Spatiotemporal analysis of strain localization in dense granular materials

  • Gang Ma
  • Richard A. Regueiro
  • Wei Zhou
  • Jiaying Liu
Research Paper


Predicting localized failure in granular materials is a problem of great interest from both the scientific and technological perspectives. The initiation and growth of strain localization have been studied using laboratory experiments and particle-based numerical simulations, and their findings have been preliminarily implemented into continuum constitutive models. In this study, we revisit strain localization in granular materials using the spatiotemporal data analysis technique, which has been extensively employed in data mining science and social science for the sake of different applications. A dense packing of granular material subjected to biaxial compression was simulated using the combined finite and discrete element method. The large amount of particle-level kinematical data, including the translational and rotational particle motion, fluctuating velocity, granular temperature, and local strain, are collected for subsequent spatiotemporal data analysis. The spatiotemporal data analysis provides a new perspective on the strain localization in dense granular materials and a rich body of new insights are presented for the first time. The spatial autocorrelation analysis results in Moran’s I values close to 1, and positive Z scores and statistically significant p values, which indicate that a dense granular system features clustered patterns during shearing. This finding proves yet again that dense granular materials have an inherent short range order. Eventually, correspondence between localized modes with different particle kinematics and spatial distributions of local Moran statistics and quadrant location map are investigated. By assuming shearing of dense granular materials is a first-order Markov chain process, the convergence and time homogeneity of this process are analyzed. Both the maximum likelihood and Pearson test statistics clearly demonstrate that shearing of dense granular materials is a time-homogenous Markov chain process.


Granular materials Markov chain Moran’s I Spatiotemporal data analysis Strain localization 



The authors thank the anonymous reviewers for their careful review and constructive comments, which significantly improved the manuscript. This work has been supported by National Key R&D Program of China (Grant No. 2017YFC0404801), National Science Foundation of China under Grant No. 51509190, and China Postdoctoral Science Foundation (No. 2016T907272).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Water Resources and Hydropower Engineering ScienceWuhan UniversityWuhanChina
  2. 2.Department of Civil, Environmental, and Architectural EngineeringUniversity of Colorado BoulderBoulderUSA

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