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Quan sát và đánh giá sự thay đổi về tính dị hướng của vật liệu dạng hạt dưới tải trọng cắt thông qua phương pháp phần tử rời rạc

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Trong bài viết "Quan sát và đánh giá sự thay đổi về tính dị hướng của vật liệu dạng hạt dưới tải trọng cắt thông qua phương pháp phần tử rời rạc" các mô phỏng cắt mẫu vật liệu dạng hạt ở trạng thái rời được thực hiện thông qua phương pháp phần tử rời rạc (DEM) nhằm đánh giá ứng xử của các chúng về sức kháng cắt và sự thay đổi về cấu trúc liên kết của các phần tử bên trong mẫu vật liệu.

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Nội dung Text: Quan sát và đánh giá sự thay đổi về tính dị hướng của vật liệu dạng hạt dưới tải trọng cắt thông qua phương pháp phần tử rời rạc

  1. Hội nghị Khoa học trẻ lần 4 năm 2022 (YSC2022) – IUH Ngày 14/10/2022 ISBN: 978-604-920-156-1 YSC4F.303 QUAN SÁT VÀ ĐÁNH GIÁ SỰ THAY ĐỔI VỀ TÍNH DỊ HƯỚNG CỦA VẬT LIỆU DẠNG HẠT DƯỚI TẢI TRỌNG CẮT THÔNG QUA PHƯƠNG PHÁP PHẦN TỬ RỜI RẠC TRUNG-TRI LE*, BA-PHU NGUYEN, NHAT-PHI DOAN, VAN-NAM NGUYEN Department of Civil Engineering, Industrial University of Ho Chi Minh City * letrungtri@iuh.edu.vn Abstract. Trong bài bào này, các mô phỏng cắt mẫu vật liệu dạng hạt ở trạng thái rời được thực hiện thông qua phương pháp phần tử rời rạc (DEM) nhằm đánh giá ứng xử của các chúng về sức kháng cắt và sự thay đổi về cấu trúc liên kết của các phần tử bên trong mẫu vật liệu. Trước tiên, các mẫu được nén cố kết đẳng hướng, sau đó biến dạng cưỡng bức được áp dụng ở phương 1-3 nhằm mô phỏng điều kiện cắt không thoát nước (bảo toàn thể tích). Các kết quả chỉ ra rằng có sự tương quan chặt chẽ giữa sức kháng cắt, sự thay đổi trong tính dị hướng của cấu trúc mẫu và số lượng các liên kết trung bình của phần tử hạt trong tập hợp khi chịu tải trọng. Sau khi chạm tới trạng thái mất ổn định, sức kháng cắt giảm dần khi tiếp tục xảy ra biến dạng thì số liên kết trung bình không có sự thay đổi đáng kể. Ngoài ra, các thành phần ứng suất cố kết là một trong những nhân tố chính ảnh hưởng tới sức kháng cắt và tính dị hướng của mẫu vật liệu trong quá trình chịu tải trọng cắt. Keywords. Sức kháng cắt, tính dị hướng, phương pháp phần tử rời rạc. INVESTIGATION ON FABRIC EVOLUTION OF GRANULAR MATERIAL UNDER DIRECT SIMPLE SHEAR LOADING USING DISCRETE ELEMENT METHOD Abstract. In this study, a numerical direct simple shear test was performed using the discrete element method (DEM) to investigate the particle behaviors in terms of monotonic shear strength and the evolution of fabric of sample under shear loading. The granular samples were subjected to an isotropic compression phase at various confining stress values and then a shearing phase under constant volume conditions. The results indicated that there was a close correlation between shear strength, the change in fabric anisotropy, and coordination number during the shearing phase. After reaching an instability point, while shear strength gradually decreased, the coordination number remained relatively constant when the shear deformation increased continually. Additionally, confining pressure was the predominant effect on the shear strength and fabric anisotropy characteristics during the shearing phase. Keywords. Shear strength, fabric anisotropy, discrete element method. 1. INTRODUCTION In soil mechanics, various laboratory tests which aims to mimic the in-situ conditions of sample in laboratory have been performed to study the characteristics and behaviors of soil in terms of stress and strain observation. These include oedometric compression, uniaxial compression, monotonic/cyclic shear test, and monotonic/cyclic triaxial tests [1] - [3]. However, these ordinary stress-train test devices make it impossible to investigate the micro parameters including fabric anisotropy, rearrangement of particles and effects of shape and state of particle assemblies in terms of microstructure observation. Recently, discrete element method has been used extensively as a numerical technique to solve aforementioned difficulties and has been shown to be a strong technique used in studies to connect macro results from laboratory tests 32  2022 Trường Đại học Công nghiệp Thành phố Hồ Chí Minh
  2. Hội nghị Khoa học trẻ lần 4 năm 2022 (YSC2022) – IUH Ngày 14/10/2022 ISBN: 978-604-920-156-1 with micro characteristics of granular materials. Therefore, in this study, discrete the element method was used to get a deeper understanding of the behavior of the sample under undrained simple shear loading and the effects of evolution of fabric anisotropy on shear strength of granular materials. 2. DISCRETE ELEMENT MODELING In this study, open-source DEM Yade [4] was used to investigate the behavior and the change in microstructure of granular material under simple shear test (undrained conditions). Cubical assemblies of spheres were generated within a periodic boundary (10cm ×10 cm×10 cm) and then subjected to isotropic consolidation at 50 kPa or 100 kPa to obtain the fabric isotropy before shearing. After isotropic compression, the sample was subjected to a shearing phase to shearing velocity of 0.1 applied on the 3-1 plane. Under undrained simple shear condition, the volume of the sample was kept constant and the shear stress in 3-1 direction equals to the 31 (refers to Fig. 1 and Fig. 2). All particles were assigned a normal contact stiffness of 1e9 (N/m2), a ratio of shear (tangential) to normal stiffness of 0.25, a frictional angle of 29 degrees and the density of 1000 (kg/m3). Figure 1: Stress condition of sample under isotropic consolation (left) and simple shear (undrained) condition (right). Figure 2: Shape of granular assemblies under isotropic consolidation (left) and simple shear condition (right) by DEM modeling. 3. RESULTS AND DISCUSSIONS The typical behavior of granular samples under undrained simple shear loading is illustrated in Fig 3. After being isotropically consolidated to a target confining pressure, shear stress of all samples increased to a  2022 Trường Đại học Công nghiệp Thành phố Hồ Chí Minh 33
  3. Hội nghị Khoa học trẻ lần 4 năm 2022 (YSC2022) – IUH Ngày 14/10/2022 ISBN: 978-604-920-156-1 peak value (instability point) with a gradually decreased in normal pressure 33 (see Fig. 3). After that, the sample showed a flow behavior when shear strain continued to increase while shear stress remained constant or decreased. This contractive behavior of these samples could be observed clearly through the stress-path in Fig. 3-a, when the instability point was triggered, the shear stress and normal stress declined in thepotential instability zone (cyan color zone) and then aligned in the critical state line (CSL). Figure 3: (a) Stress-strain response and (b) stress-path of granular material under undrained simple shear loading. In DEM modeling, the coordination number Zc indicates the average interactions per particle. This number is defined as Zc = 2C/N, where C is the number of total contacts and N is the total of particles. As shown in Fig. 4, granular particles increased their connections with others in the consolidation phase. Also, there is a difference in Zc values between n samples subjected to confining pressure of 50 kPa and 100 kPa, in which the sample confined at higher pressure (100kPa) has about 6 contacts higher than that of the samples confined at 50kPa (5.5 contacts). This point could be obviously explained since the samples, which had higher confining pressure, were in denser state compared to the other samples. During the shearing phase, all samples showed a gradual decrease in the Zc values. This means that particles tended to rearrange and move far away from each other during applying shear deformation on the 3-1 plane. Interestingly, after reaching to the critical state line, while shear stress continued to decrease, the Zc still remained relatively constant. This point reveals that when the stress path was in the potential stability zone the rearrangement of granular particles, rather than the change in number of contacts, played a dominant factor resulting in the decrease in shear strength or the collapse of samples after that in a metastable granular structure [5]. 34  2022 Trường Đại học Công nghiệp Thành phố Hồ Chí Minh
  4. Hội nghị Khoa học trẻ lần 4 năm 2022 (YSC2022) – IUH Ngày 14/10/2022 ISBN: 978-604-920-156-1 Figure 4: Change in coordination number during isotropic consolidation and undrained simple shear. Figure 5: Evolution of force chains (fabric anisotropy) of sample after isotropic consolidation and during undrained shearing phase. The evolution of fabric anisotropy was observed clearly in Fig. 5 through the change in the intensity (diameter of force chains) and direction of force chains: (i) after isotropic consolidation and (ii) during undrained shearing phase. Firstly, the structure of samples is relatively isotropic after consolidation, regardless of confining pressure. The difference between samples subjected to confining pressure of 50 kPa and 100 kPa, however, was the intensity of the force chains. A typical change in direction of force chain was observed clearly when starting applied shear deformation. The direction of these force chains tended to rotate and were mainly distributed in the diagonal direction compared to its direction after isotropic consolidation (see Fig. 5). In the potential instability zone (at  = 45%), the intensity of force chains was smaller than that after consolidation or before shearing. This intensity continued to decrease as the sample continued to deform. The number of force chains also decreased (see sample subjected to confining pressure of 50kPa in Fig.5) as a result of rearrangement of particles causing a decrease in the shear strength (refers to Fig. 3).The effects of confining pressures were clearly observed in Fig. 5.The sample had higher confining pressure and showed a higher shear resistance to collapse than that of the sample that had lower confining pressure. To be more specific, at large shear strain of 15%, the sample subjected to 50kPa in the consolidation phase seemed to fail or flow with no existence of connections or forces chains between particles. In contrast, the samples subjected to 100 kPa in the consolidation phase were able to work against the shearing phase at  = 15% that was shown via the number and intensity force chains in samples.  2022 Trường Đại học Công nghiệp Thành phố Hồ Chí Minh 35
  5. Hội nghị Khoa học trẻ lần 4 năm 2022 (YSC2022) – IUH Ngày 14/10/2022 ISBN: 978-604-920-156-1 4. CONCLUSIONS This work studied the behavior of granular samples under undrained simple shear test using the discrete element method. The result indicated that microstructure characteristics related to the fabric anisotropy and the rearrangement of particles within samples significantly influenced the shear strength and behavior of the samples during subjected shear loading. From that, more extensive studies need to be performed to get a deeper understanding about the roles of micro parameters on the strength of granular materials. REFERENCES [1] S.-S. Park, T.-T. Le, Z. Nong, H.-D. Moon, and D.-E. Lee, “Chemically Induced Calcium Carbonate Precipitation for Improving Strength of Sand,” Journal of Materials in Civil Engineering, vol. 32, no. 9, p. 04020238, Sep. 2020, doi: 10.1061/(ASCE)MT.1943-5533.0003318. [2] T. Le, S. Park, J. Lee, and D. Lee, “Strength characteristics of spent coffee grounds and oyster shells cemented with GGBS-based alkaline-activated materials,” Construction and Building Materials, no. xxxx, p. 120986, 2020, doi: 10.1016/j.conbuildmat.2020.120986. [3] T. T. Le, S. S. Park, S. W. Woo, and L. Tran, “Cyclic Response and Post-cyclic Settlement of Sand Experiencing Repeated Earthquakes,” in Lecture Notes in Civil Engineering, 2022, vol. 203. doi: 10.1007/978-981- 16-7160-9_103. [4] V. Šmilauer and B. Chareyre, “Yade DEM Formulation,” Yade Documentation, vol. 2011, 2010. [5] M. M. Rahman, H. B. K. Nguyen, A. B. Fourie, and M. R. Kuhn, “Critical State Soil Mechanics for Cyclic Liquefaction and Postliquefaction Behavior: DEM study,” Journal of Geotechnical and Geoenvironmental Engineering, vol. 147, no. 2, 2021, doi: 10.1061/(asce)gt.1943-5606.0002453. 36  2022 Trường Đại học Công nghiệp Thành phố Hồ Chí Minh
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