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研究生： 周柏先
Po-Hsien Chou
論文名稱： 顆粒物質受束制壓力負載之力學分析
Mechanical Response of Granular Solid under Confined Compression
指導教授： 林志光
Chih-Kuang Lin
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
畢業學年度： 100
語文別： 英文
論文頁數： 98
中文關鍵詞： 應力 、束制壓力負載實驗 、顆粒體
外文關鍵詞： stress, confined compression test, granular material
相關次數： 點閱：15  下載：0 
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    • 本研究主旨在探討聚苯乙烯顆粒物質在壓克力容器中受頂部束制壓力負載之力學行為，並探討不同顆粒大小以及顆粒堆高度對於相關力學行為之影響。透過不同高度位置應變之量測及廣義虎克定律，探討顆粒堆之應力隨高度變化之情形。實驗用聚苯乙烯顆粒之直徑大小分別為 4.5 mm及6 mm，填充高度分別為100 mm及200 mm，藉以分析顆粒堆高度及顆粒大小對顆粒體受束制壓力負載力學響應之影響。另以商業用離散元素法分析軟體模擬6 mm直徑之顆粒填充於壓克力容器內200 mm 之高度所得到的計算結果與實驗數據相比對。
    實驗結果顯示，在束制壓力負載過程中，不論顆粒大小以及顆粒填充之高度，隨著頂部力量值增加，顆粒體與壓克力容器之間之摩擦力也隨之增加。於過程中顆粒受壁面摩擦力之影響，顆粒堆內相關應力值由高處往低處遞減。在具有相同顆粒大小分別填充不同高度進行束制壓力負載下，較高填充高度的顆粒堆，其應力在頂部與底部之差距較大。將兩種不同顆粒大小分別填充相同高度，小顆粒於束制壓力負載時，顆粒堆上層部分之應力差距較大顆粒為明顯；而小顆粒於顆粒堆下層部分之應力差距相較於大顆粒為小。離散元素法模擬求得之顆粒體垂直應力與水平應力、壓克力壁面與顆粒體間之剪應力、側壓力係數以及整體壁面與顆粒摩擦係數皆與實驗之趨勢相符，因而證明模擬之結果之有效性。

    The purpose of this study is to investigate the mechanical responses of polystyrene particles stored in acrylic cylinders with different particle sizes and heights of the granular solid during confined compression test. Variations of wall strains are measured using strain gages at three axial positions and used to calculate the relevant stresses through a generalized Hooke’s law. Two diameters of the polystyrene spheres, 4.5 mm and 6 mm, and two heights of the granular solid, 100 mm and 200 mm, are selected to study the effects of particle size and granular solid height on the confined compression test results. The experimental data of a 200-mm-height granular solid of 6-mm-diameter polystyrene spheres are compared with the simulations calculated by a commercial code of discrete element method (DEM).
    Experimental results show that frictional force between the granular solid and the cylinder wall increases with the top force during the confined compression. The frictional force between the particles and the cylinder wall makes the stresses decrease with increasing depth in the granular solid. Given a particle size, the differences of the stresses between the higher position and the lower position in a higher granular solid are greater than those in a shorter granular solid. Given a height of granular solid stored in an acrylic cylinder, variation of the stresses at the upper position for smaller particles is larger than that for larger particles while variation of the stresses at the lower position for a smaller particle size is smaller than that of a larger particle size. DEM solutions show a good agreement with the experimental data of vertical stress, horizontal stress, shear stress, lateral pressure ratio, and bulk wall friction in a confined compression test.

    TABLE OF CONTENTS Page LIST OF TABLES V LIST OF FIGURES VI 1. INTRODUCTION 1 1.1 Storage of Granular Materials 1 1.2 Discrete Element Method (DEM) 2 1.3 Linkage of DEM and FEM 3 1.4 Confined Compression Test 4 1.5 Purpose and Scope 5 2. EXPERIMENTAL PROCEDURES 7 2.1 Confined Compression Test 7 2.2 Mechanical Properties and Experimental Procedure 8 2.3 DEM-FEM Implementation and Model Parameters 13 3. RESULTS AND DISCUSSION 15 3.1 Mechanical Response of Granular Solid 15 3.2 Effect of Cylinder Length and Height of Granular Solid 18 3.3 Effect of Particle Size 20 3.4 Comparison of Experimental Results and DEM-FEM Simulation 24 4. CONCLUSIONS 30 REFERENCES 32 TABLES 35 FIGUURES 36 LIST OF TABLES Page Table 1 Material properties of acrylic cylinder [23,24] 35 Table 2 Material properties of 6-mm-polystyrene particles [25] 35 Table 3 DEM input parameters for 6-mm-diameter spherical polystyrene particles 35 Table 4 Material properties of 4.5-mm-polystyrene particles 35 LIST OF FIGURES Page Fig. 1 A confined compression test apparatus for bulk solid. [20] 36 Fig. 2 Schematic of an experimental setup of confined compression test. 37 Fig. 3 Photograph of the experimental setup. 38 Fig. 4 Top and side views of a 160-mm-long acrylic cylinder. 39 Fig. 5 Top and side views of a 260-mm-long acrylic cylinder. 40 Fig. 6 A Hertz-Mindlin contact force model between two particles. [28] 41 Fig. 7 Vertical forces at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 42 Fig. 8 Average vertical stresses at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 43 Fig. 9 Average horizontal stresses at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 44 Fig. 10 Average shear stresses at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 45 Fig. 11 Lateral pressure ratios at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 46 Fig. 12 Bulk wall friction at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 47 Fig. 13 Vertical forces at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 48 Fig. 14 Average vertical stresses at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 49 Fig. 15 Average horizontal stresses at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 50 Fig. 16 Average shear stresses at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 51 Fig. 17 Lateral pressure ratios at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 52 Fig. 18 Bulk wall friction at different positions of the granular solid during confined compression for 6-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 53 Fig. 19 Vertical forces at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 54 Fig. 20 Average vertical stresses at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 55 Fig. 21 Average horizontal stresses at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 56 Fig. 22 Average shear stresses at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 57 Fig. 23 Lateral pressure ratios at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 58 Fig. 24 Bulk wall friction at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 260-mm-long cylinder. 59 Fig. 25 Vertical forces at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 60 Fig. 26 Average vertical stresses at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 61 Fig. 27 Average horizontal stresses at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 62 Fig. 28 Average shaer stresses at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 63 Fig. 29 Lateral pressure ratios at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 64 Fig. 30 Bulk wall friction at different positions of the granular solid during confined compression for 4.5-mm-diameter polystyrene spheres in a 160-mm-long cylinder. 65 Fig. 31 Load-displacement responses of the granular solid in an acrylic cylinder during confined compression. 66 Fig. 32 Load-displacement responses of the granular solid in a stainless steel cylinder during confined compression. 67 Fig. 33 Variations of vertical stress with axial position in the granular solid under different top forces: (a) 500 N; (b) 1,000 N; (c) 1,500 N; (d) 2,000 N. 68 Fig. 34 Variations of horizontal stress with axial position in the granular solid under different top forces: (a) 500 N; (b) 1,000 N; (c) 1,500 N; (d) 2,000 N. 70 Fig. 35 Variations of shear stress with axial position in the granular solid under different top forces: (a) 500 N; (b) 1,000 N; (c) 1,500 N; (d) 2,000 N. 72 Fig. 36 Lateral pressure ratio versus top force at various positions of the granular solid: (a) 8/10 height; (b) 5/10 height; (c) 2/10 height. 74 Fig. 37 DEM predictions of lateral pressure ratio versus axial position of granular solid during confined compression. 76 Fig. 38 Bulk wall friction versus top force at various positions of the granular solid: (a) 8/10 height; (b) 5/10 height; (c) 2/10 height. 77 Fig. 39 DEM predictions of bulk wall friction versus axial position of granular solid during confined compression. 79 Fig. 40 Axial stress versus top force at various positions of the acrylic cylinder: (a) top; (b) middle; (c) bottom. 80 Fig. 41 Hoop stress versus top force at various positions of the acrylic cylinder: (a) top; (b) middle; (c) bottom. 82 Fig. 42 FEM predictions of average axial stress versus axial position of acrylic cylinder during confined compression. 84 Fig. 43 FEM predictions of average hoop stress versus axial position of acrylic cylinder during confined compression. 85

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