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Determination of shape parameters of sands: a deep learning approach

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Abstract

The shape parameters of sand particles can be determined by either a Krumbein-Sloss chart or mathematical computation based on the particle image. However, these approaches are limited by user-dependent uncertainty and complicated algorithms with computational issues. This study explores the feasibility of predicting the shape parameters of sand particles via a well-trained deep learning model. Over 7000 sand particle images from six different sand types were used, and the corresponding shape parameters such as sphericity, roundness, slenderness, and circularity were computed. Inception-ResNet-v2 whose performance has been widely validated, as one of convolutional neural network-based model, used the pair dataset (i.e., image and each computed shape parameter) and comprised a pre-trained network for feature extraction and a regression output layer. Strategic data augmentation helped in increasing the number of training data to reduce the test loss efficiently. Several hyperparameters were carefully tuned to accomplish model optimization, while the generalization ability of the model was evaluated during training by using a validation dataset. The prediction results showed that the trained model yielded a highly accurate and precise prediction of the shape parameters, regardless of the image types. The predicted roundness had relatively scattered values in comparison with other parameters, presumably because of its indeterminate definition of the ground-truth. Thus, the proposed trained model enables accurate prediction of the shape parameters of sand particles solely based on an image containing the complete shape of the particle, without mathematical computation.

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References

  1. Alqahtani N, Alzubaidi F, Armstrong RT et al (2020) Machine learning for predicting properties of porous media from 2d X-ray images. J Pet Sci Eng 184:106514. https://doi.org/10.1016/j.petrol.2019.106514

    Article  Google Scholar 

  2. Badrinarayanan V, Kendall A, Cipolla R (2017) SegNet: a deep convolutional encoder-decoder architecture for image segmentation. IEEE Trans Pattern Anal Mach Intell 39:2481–2495. https://doi.org/10.1109/TPAMI.2016.2644615

    Article  Google Scholar 

  3. Bergstra J, Bengio Y (2012) Random search for hyper-parameter optimization. J Mach Learn Res 13:281–305

    MathSciNet  MATH  Google Scholar 

  4. Chen LC, Papandreou G, Kokkinos I et al (2017) DeepLab: semantic image segmentation with deep convolutional nets, atrous convolution, and fully connected CRFs. IEEE Trans Pattern Anal Mach Intell 40:834–848

    Article  Google Scholar 

  5. Cho GC, Dodds J, Santamarina JC (2006) Particle shape effects on packing density

  6. Claesen M, De Moor B (2015) Hyperparameter search in machine learning. arXiv Preprint. arXiv:1502.02127

  7. Cui X, Goel V, Kingsbury B (2015) Data augmentation for deep convolutional neural network acoustic modeling. IEEE/ACM Trans Audio Speech Lang Process 23:1469–1477. https://doi.org/10.1109/ICASSP.2015.7178831

    Article  Google Scholar 

  8. Girshick R, Donahue J, Darrell T et al (2014) Rich feature hierarchies for accurate object detection and semantic segmentation. Proc IEEE Conf Comput Vis pattern Recognit. https://doi.org/10.1109/CVPR.2014.81

    Article  Google Scholar 

  9. He K, Zhang X, Ren S, Sun J (2016) Deep residual learning for image recognition. In: IEEE conference on computer vision and pattern recognition (CVPR), pp 770–778

  10. Hinton GE (2012) A practical guide to training restricted Boltzmann machines. Springer, Berlin

    Book  Google Scholar 

  11. Hryciw RD, Zheng J, Shetler K (2016) Particle roundness and sphericity from images of assemblies by chart estimates and computer methods. J Geotech Geoenvironmental Eng 142:04016038. https://doi.org/10.1061/(ASCE)GT.1943-5606.0001485

    Article  Google Scholar 

  12. Huang H, Luo J, Tutumluer E et al (2020) Size and shape determination of riprap and large-sized aggregates using field imaging. Illinois Center for Transportation/Illinois Department of Transportation.

  13. Ioffe S, Szegedy C (2015) Batch normalization: accelerating deep network training by reducing internal covariate shift. In: International conference on machine learning. PMLR, pp 448–456

  14. Kim Y, Yun TS (2021) How to classify sand types: a deep learning approach. Eng Geol 288:106142. https://doi.org/10.1016/j.enggeo.2021.106142

    Article  Google Scholar 

  15. Kim KY, Suh HS, Yun TS et al (2016) Effect of particle shape on the shear strength of fault gouge. Geosci J 20:351–359. https://doi.org/10.1007/s12303-015-0051-0

    Article  Google Scholar 

  16. Kim Y, Suh HS, Yun TS (2019) Reliability and applicability of the Krumbein-Sloss chart for estimating geomechanical properties in sands. Eng Geol 248:117–123. https://doi.org/10.1016/j.enggeo.2018.11.001

    Article  Google Scholar 

  17. Krizhevsky A, Sutskever I, Hinton GE (2012) Imagenet classification with deep convolutional neural networks. Adv Neural Inf Process Syst 25:1097–1105

    Google Scholar 

  18. Krumbein WC, Sloss LL (1951) Stratigraphy and sedimentation. W. H. Freeman and Company, San Francisco

  19. Larochelle H, Erhan D, Courville A et al (2007) An empirical evaluation of deep architectures on problems with many factors of variation. Int Conf Mach Learn PMLR. https://doi.org/10.1145/1273496.1273556

    Article  Google Scholar 

  20. LeCun YA, Bottou L, Orr GB, Müller KR (2012) Efficient backprop. Springer, Berlin

    Book  Google Scholar 

  21. Lee C, Suh HS, Yoon B, Yun TS (2017) Particle shape effect on thermal conductivity and shear wave velocity in sands. Acta Geotech 12:615–625. https://doi.org/10.1007/s11440-017-0524-6

    Article  Google Scholar 

  22. Li M, Soltanolkotabi M, Oymak S (2020) Gradient descent with early stopping is provably robust to label noise for overparameterized neural networks. In: International conference on artificial intelligence and statistics. PMLR, pp 4313–4324

  23. Li J, Shao S, Hong J (2021) Machine learning shadowgraph for particle size and shape characterization. Meas Sci Technol 32:015406. https://doi.org/10.1088/1361-6501/abae90

    Article  Google Scholar 

  24. Lin M, Chen Q, Yan S (2013) Network in network. arXiv Preprint. arXiv:1312.4400

  25. Long J, Shelhamer E, Darrell T (2015) Fully convolutional networks for semantic segmentation. In: IEEE conference on computer vision and pattern recognition (CVPR), pp 3431–3440

  26. Mikołajczyk A, Grochowski M (2018) Data augmentation for improving deep learning in image classification problem. In: 2018 International interdisciplinary PhD workshop (IIPhDW). IEEE, pp 117–122

  27. Niu Y, Mostaghimi P, Shabaninejad M et al (2020) Digital rock segmentation for petrophysical analysis with reduced user bias using convolutional neural networks. Water Resour Res. https://doi.org/10.1029/2019WR026597

    Article  Google Scholar 

  28. Otsu N (1979) A threshold selection method from gray-level histograms. IEEE Trans Syst Man Cybern 9:62–66

    Article  Google Scholar 

  29. Prechelt L (1998) Early stopping-but when? Springer, Berlin

    Book  Google Scholar 

  30. Ren S, He K, Girshick R, Sun J (2015) Faster r-cnn: towards real-time object detection with region proposal networks. Adv Neural Inf Process Syst 28:91–99

    Google Scholar 

  31. Riley NA (1941) Projection sphericity. J Sediment Res 11:94–95

    Google Scholar 

  32. Shin H, Santamarina JC (2013) Role of particle angularity on the mechanical behavior of granular mixtures. J Geotech Geoenvironmental Eng 139:353–355. https://doi.org/10.1061/(ASCE)GT.1943-5606.0000768

    Article  Google Scholar 

  33. Shorten C, Khoshgoftaar TM (2019) A survey on image data augmentation for deep learning. J Big Data 6:1–48. https://doi.org/10.1186/s40537-019-0197-0

    Article  Google Scholar 

  34. Simonyan K, Zisserman A (2014) Very deep convolutional networks for large-scale image recognition. arXiv Preprint

  35. Suh HS, Kim KY, Lee J, Yun TS (2017) Quantification of bulk form and angularity of particle with correlation of shear strength and packing density in sands. Eng Geol 220:256–265. https://doi.org/10.1016/j.enggeo.2017.02.015

    Article  Google Scholar 

  36. Sun Q, Zheng J (2020) Clone granular soils with mixed particle morphological characteristics by integrating spherical harmonics with Gaussian mixture model, expectation–maximization, and Dirichlet process. Acta Geotech 15:2779–2796

    Article  Google Scholar 

  37. Szegedy C, Liu W, Jia Y et al (2015) Going deeper with convolutions. In: IEEE conference on computer vision and pattern recognition (CVPR), pp 1–9

  38. Szegedy C, Ioffe S, Vanhoucke V, Alemi AA (2017) Inception-v4, inception-resnet and the impact of residual connections on learning. In: AAAI Conf Artif Intell

  39. Tang S, Wang J, Tang C (2021) Identification of microseismic events in rock engineering by a convolutional neural network combined with an attention mechanism. Rock Mech Rock Eng 54:47–69. https://doi.org/10.1007/s00603-020-02259-0

    Article  Google Scholar 

  40. Wadell H (1933) Sphericity and roundness of rock particles. J Geol 41:310–331. https://doi.org/10.1086/624040

    Article  Google Scholar 

  41. Wang J, Perez L (2017) The effectiveness of data augmentation in image classification using deep learning. Convolutional Neural Netw Vis Recognit 11:1–8

    Google Scholar 

  42. Yang J, Luo XD (2015) Exploring the relationship between critical state and particle shape for granular materials. J Mech Phys Solids 84:196–213. https://doi.org/10.1016/j.jmps.2015.08.001

    Article  Google Scholar 

  43. Yang D, Wang X, Zhang H et al (2021) A mask R-CNN based particle identification for quantitative shape evaluation of granular materials. Powder Technol 392:296–305. https://doi.org/10.1016/j.powtec.2021.07.005

    Article  Google Scholar 

  44. Zheng J, Hryciw RD (2015) Traditional soil particle sphericity, roundness and surface roughness by computational geometry. Géotechnique 65:494–506. https://doi.org/10.1680/geot.14.P.192

    Article  Google Scholar 

  45. Zheng J, Hryciw RD (2016) Roundness and sphericity of soil particles in assemblies by computational geometry. J Comput Civ Eng 30:04016021. https://doi.org/10.1061/(asce)cp.1943-5487.0000578

    Article  Google Scholar 

  46. Zheng J, He H, Alimohammadi H (2021) Three-dimensional Wadell roundness for particle angularity characterization of granular soils. Acta Geotech 16:133–149. https://doi.org/10.1007/s11440-020-01004-9

    Article  Google Scholar 

  47. Zheng J, Zhang Z, Li C et al (2021) Laboratory-on-a-smartphone for estimating angularity of granular soils. Acta Geotech. https://doi.org/10.1007/s11440-021-01259-w

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Land and Housing Institute (LHI) grant funded by the Korea Land and Housing Corporation, and the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIT) (Nos. 2020R1A2C1014815, NRF-2021R1A5A1032433).

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Yejin Kim: Conceptualization, Methodology, Software, Validation, Investigation, Data curation, Writing—Original draft preparation. Jeehoon Ma: Data curation, Methodology. Seok Yong Lim: Data curation, Methodology. Jun Young Song: Data curation, Methodology, Writing—Original draft preparation. Tae Sup Yun: Conceptualization, Formal analysis, Validation, Writing—Reviewing and Editing, Supervision, Project administration.

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Correspondence to Tae Sup Yun.

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Kim, Y., Ma, J., Lim, S.Y. et al. Determination of shape parameters of sands: a deep learning approach. Acta Geotech. 17, 1521–1531 (2022). https://doi.org/10.1007/s11440-022-01464-1

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  • DOI: https://doi.org/10.1007/s11440-022-01464-1

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