FINITE ELEMENT MODELING OF STEEL CONTAINMENT STRUCTURES UNDER LATERAL LOADS

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1 Ain Shams University Faculty of Engineering Structural Engineering Department Abstract of the M.Sc. Thesis submitted by: Al-Hussein Ibrahim Hilal Ibrahim Title of Thesis: Finite Element Modeling of Steel Containment Structures under Lateral Loads. Supervisors: Prof. Dr. Adel Helmy Salem Ass. Prof. Dr. Hesham Ahmed El-Arabaty Prof. Dr. Abdel Monem Yassin Sanad Registration date: 9/ 11/ 2009 Examination date: ABSTRACT The research presents a 3-D finite element modeling for simulating the progressive filling process of flat-bottomed square and rectangular steel silos filled with granular materials (wheat) using ABAQUS software. The material, silo, and base are discretized by finite elements of type hexahedron with 8 nodes (cubic brick element) with 3 degrees of freedom per node. An axisymmetric finite-element model is used to represent both the stored granular material and the structure. The granular materials are modeled using an elastic-plastic model, while the steel silo is modeled using a linear elastic model. In this research, the granular material was simulated by Mohr-Coulomb model to define the yield surface and flow potential parameters for elastic-plastic model. Surface-to surface interface contact is used between the steel silo wall and the granular materials to admit laws of behavior of the granular materials and boundary conditions with the walls. (no contact elements I

2 are used). Contact pair is used for simulating the interaction between the stored granular material and the silo wall. This interaction is between the outer surface of granular material and the inner surface of silo wall which applies friction properties into a mechanical surface interaction model governing the interaction of contact pair. The influence of mechanical properties of granular materials on the lateral wall pressure is studied. The influence of silo dimensions on the lateral wall pressure is investigated. The distribution of the lateral wall pressure in the horizontal section along the silo height is studied. A progressive filling process is conducted to fulfill actual filling process of the silo and analyzes the static lateral wall pressure at the end of filling which is compared to one time filling process. Keywords: Finite-element modeling, Three dimensional steel silos, Square silos, Silo filling, Lateral wall pressure, Silo Dimensions, Mechanical properties of stored material. II

3 APPROVAL SHEET Name of Author: Al-Hussein Ibrahim Hilal Ibrahim Title of Thesis: Finite Element Modeling of Steel Containment Structures under Lateral Loads Degree: Master of Science in Civil Engineering (Structural Engineering) EXAMINERS COMMITTEE Name, Title & Affiliation: (Signature) Prof. Dr. Mohamed Ebrahim El-Nagar Prof. of Structural Engineering Faculty of Engineering, Alexandria University Prof. Dr. Abdel-Rahim Khalil Dessouki Prof. of Steel Structures Faculty of Engineering, Ain Shams University Prof. Dr. Adel Helmy Salem Prof. of Structural Engineering Faculty of Engineering, Ain Shams University Ass. Prof. Dr. Hesham Mahmoud El-Arabaty Ass. Prof. of Structural Engineering Faculty of Engineering, Ain Shams University Date: / / 2015 III

4 STATEMENT This dissertation is submitted to Ain Shams University for the degree of M. Sc. in Civil Engineering. The work included in this thesis was carried out by the author in the Department of structural Engineering, Ain Shams University from 2009 to No part of this thesis has been submitted for a degree or for qualification at any other University or Institution. Name : Al-Hussein Ibrahim Hilal Ibrahim Signature : Date : / / 2015 IV

5 ACKNOWLEDGEMENTS First and foremost thanks to GOD the most merciful The author dedicates this book to people who have always supported me, in life in general and in the realization of this work in particular, with all my love and my respect... The author is greatly indebted to my Professor Dr. Moustafa Khalifa to him; wish to express my profound gratitude and deep thanks for his constructive guidance and general help which were the paramount axes in the ignition and completion of this work and for his reviewing of manuscript. Great gratitude and honest appreciation go to Professor Dr. Adel Helmy Salem for his supervision, great advice and support, and encouraging me to finish this work. Special thanks go to my supervisor Professor Dr. Abdel-Moneam Sanad for his sincere help, his guidance and for his reviewing of manuscript. The author would like to express my true indebtedness to Assistant Professor Hesham Al-Arabaty for his help and valuable advice. The author would like to thank my friends and colleagues Mostafa Yossef, Mohamed Morsy, Mohamed Al-Sayyad, Abdel-Rahman Gamal for their continuous help and encouraging me. Finally, The author would like to express my thanks to my family for their continuous encouragement and support to finish this work. Al-Hussein Ibrahim February, 2015 V

6 TABLE OF CONTENTS AIN SHAMS UNIVERSITY... I FACULTY OF ENGINEERING... I ABSTRACT... I APPROVAL SHEET... III STATEMENT... IV ACKNOWLEDGEMENTS... VI TABLE OF CONTENTS... V LIST OF FIGURES... IX LIST OF TABLES...XII NOTATIONS & SYMBOLS... XIII CHAPTER (1): INTRODUCTION Introduction Pressure in Silos Eccentric Discharge Objectives of the Study Thesis Organization...6 CHAPTER (2): LITERATURE REVIEW Introduction Review of Previous Research Classical Theories Experimental Studies...24 VI

7 2.2.3 Regulatory Policies and Codes French Regulations German Regulations Numerical Modeling in Silos Two Dimensional Numerical Models American Model Swedish Model Three Dimensional Numerical Models Conclusions CHAPTER (3): DEVELOPMENT OF THREE-DIMENSIONAL MODEL Introduction Discretization Problem Automatic Mesh Module Boundary Conditions Surface Interaction Mechanical and Physical Properties of Granular Material and Steel Silo Output Model Results Validation of the Model Numerical Model Properties Analytical Solution Finite Element Model Influence of Elements Number on Results Capabilities of the 3D model VII

8 3.6 Conclusions...64 CHAPTER (4): PARAMETRIC STUDY Introduction Lateral Wall Pressure Mechanical and Physical Properties Effects of the Granular Material Young's Modulus, E of Granular Material Poisson's ratio, ν of Granular Material Density of Grains, ρ of Granular Material Grain-wall Frictional coefficient, µ of Granular Material Cohesion of granular materials, c of Granular Material Internal friction angle, φ of Granular Material Dilatation angle, φ r of Granular Material Silo Dimensions Effect of cross section dimensions Effect of silo proportions Rectangularity Ratio Lateral Pressure Distribution Progressive Filling Process Conclusions...90 CHAPTER (5): CONCLUSIONS & PERSPECTIVES Summary Conclusions...92 VIII

9 5.1 Recommended for Future Studies REFERENCES APPENDIX A IX

10 LIST OF FIGURES Figure 1-1: Circular steel silo with Flat-Bottom (resting on ground)...3 Figure 1-2: Rectangular steel silo with conical hopper...3 Figure 2-1: Horizontal slice model showing an average value of vertical pressure established by Janssen...10 Figure 2-2: Horizontal Square cross-section of the Silo showing that the Pressure Distribution is not Uniform based on Janssen Measurements.12 Figure 2-3: Schematic drawing of material showing the fracture plane based on Airy method...13 Figure 2-4: Model established by Ketchum showing that vertical and horizontal pressure could be constant at any point...15 Figure 2-5: Flow Patterns...17 Figure 2-6: Possibility of Mass Flow...18 Figure 2-7: Bounds between Mass Flows and Funnel Flow hoppers (Eurocode 1 Part 4)...18 Figure 2-8: Mohr's-circle of limit state (active and passive)...21 Figure 2-9: Lateral wall pressure of silos with cylindrical hopper during filling and emptying processes...22 Figure 2-10: Flow Patterns in Silos (French Standards)...28 Figure 2-11a: Flow mode for conical hoppers (Circular Silos) (DIN)..33 Figure 2-11b: Flow mode for flat hoppers (Rectangular Silos) (DIN)...33 Figure 2-12: Normal stresses in the wall during emptying (German 3D Model)...37 Figure 2-13: Normal stress at the wall (Eccentric Emptying) plane deformation calculations...38 Figure 3-1a: Axisymmetric finite-element model using ABAQUS software...43 Figure 3-1b: Silo and base elements using ABAQUS software...43 Figure 3-1c: Grain elements using ABAQUS software...43 X

11 Figure 3-2: Finite elements of hexahedron type with 8 nodes (cubic brick element C3D8R) Figure 3-2a: Axis-symmetry Silo Model Figure 3-3: Various possibilities of the mesh Figure 3-4: Pressure distribution along X-Axis for the grains elements using F.E software (ABAQUS), Silo 8 x 8 x 15 ms Figure 3-5: Vertical displacement for whole structure, Silo 8 x 8 x 15 ms Figure 3-6: Pressure distribution along X-Axis for grains elements using F.E software (ABAQUS), Silo 4 x 4 x 15 ms Figure 3-7: Vertical displacement for whole structure, Silo 4 x 4 x 15 ms Figure 3-8: Comparison between the finite element model, the numerical model and analytical solution results, Silo 8 x 8 x 15 ms Figure 3-9: Comparison between the finite element model, the numerical model and analytical solution results, Silo 4 x 4 x 15 ms (Slender Silo) 60 Figure 3-10: Influence of the vertical elements number on results (Plane Strain) Figure 3-11: Influence of the horizontal elements number on results (Plane Strain) Figure 4-1: Square silo cross-section showing results at sec. A-A Figure 4-2: Influence of Young's modulus, E, on the lateral wall pressure Figure 4-3: Influence of Poisson's ratio, ν, on the lateral wall pressure 68 Figure 4-4: Influence of density, ρ, on the lateral wall pressure Figure 4-5: Influence of grain-wall frictional coefficient, µ, on the lateral wall pressure Figure 4-6: Influence of cohesion, c, on the lateral wall pressure Figure 4-7: Influence of internal friction angle, φ, on the lateral wall pressure XI

12 Figure 4-8: Influence of repose angle, φ r, on the lateral wall pressure..71 Figure 4-9a: Different square cross section silos...72 Figure 4-9b: Different silo dimensions...73 Figure 4-9c: Lateral wall pressure for different silo dimensions with constant height (h=15 m.)...75 Figure 4-9d: Lateral wall pressure limit of plane deformation (Plane Strain) compared with Squat Silo Pressure (Height= 15 m.)...76 Figure 4-10: Different lateral pressures for different square silo dimensions...79 Figure 4-11a: Rectangular finite element Model using ABAQUS software...80 Figure 4-11b: Lateral wall pressure for different rectangularity ratios of silos with constant height (h= 15m.)...81 Figure 4-12a: Three column elements illustrated for square silo (middle, quarter, and corner) using ABAQUS software...82 Figure 4-12b: 3-D lateral static wall pressure along silo height...83 Figure 4-12c: Lateral wall pressure distribution along silo height, Silo 8 x 8 x 15 ms...84 Figure 4-12d: Lateral wall pressure distribution along silo height, Silo 4 x 4 x 15 m. (Slender Silo)...85 Figure 4-13: Progressive filling process for two square silos...86 Figure 4-14: One-Time filling process for two square silos...86 Figure 4-15: Lateral wall pressure along silo height for two methods of filling process, Silo 8 x 8 x 15 m...87 Figure 4-16: Lateral wall pressure along silo height for two methods of filling process, Silo 4 x 4 x 15 m. (Slender Silo)...88 Figure 4-17: Alternative Conical Filling Process...89 XII

13 LIST OF TABLES Table 3-1: Mechanical and physical properties for stored granular material Table 3-2: Parameters of silo 8 x 8 x 15 ms height Table 3-3: Parameters of Silo 4 x 4 x 15 ms height Table 3-2a: Comparison of Lateral static pressure between analytical solution, finite element model, and Numerical model of Sanad. (for Silo 8 x 8 x 15 ms height) Table 3-3b: Comparison of Lateral static pressure between analytical solution, finite element model, and Numerical model of Sanad. (for Silo 4 x 4 x 15 ms height, slender silo) Table 4-1: Silos with different dimension ratios XIII

14 NOTATIONS & SYMBOLS A : Area of the horizontal section of the silo. U : Perimeter of the rectangular section. D : Diameter of circular silo. h 0 : Height of the vertical part of the silo. h t : Height of the hopper. h c : Height of the flow cone during draining. dz : Horizontal layer thickness. P y : Vertical pressure. P x, S 11 : Horizontal pressure along the x axis. P z : Horizontal pressure along the Z axis. P n : Normal pressure at the wall. z : Section depth from the free surface of the silage material. z t : Depth of the section from the junction of vertical hopper part. : Coefficient of friction to the wall. : Specific gravity of the ensiled material. K : Ratio between horizontal stress and vertical stress, multiplied by friction Coefficient of the wall. K= x XIV

15 λ : Ratio between horizontal stress and vertical stress, Rankine's coefficient of active earth pressure. : The internal friction angle of the material. r : The dilatation angle of the material. r : The angle of friction between the wall and the material for filling. : Young's modulus of the material. : Poisson's ratio of the material. : The angle of inclination of the hopper with the vertical. a : Bigger side of rectangle. b : Smaller side of rectangle. a / b : Rectangularity Ratio. XV

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