RHEOLOGICAL FLOW MODELLING OF SNOW AVALANCHES
Amod Kumar
DEPARTMENT OF CIVIL ENGINEERING
In fulfilment of the requirements for the degree of DOCTOR OF PHILOSOPHY
to the
INDIAN INSTITUTE OF TECHNOLOGY, DELHI
July 2010
RHEOLOGICAL FLOW MODELLING OF SNOW AVALANCHES
AMOD KUMAR
O
DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY, DELHI
July 2010
Dedicated
my parents
Shri Vishwanath Singh and
Smt Sharmista
CERTIFICATE
This is to certify that the thesis entitled "Rheological Flow Modelling of Snow Avalanches"
being submitted by Amod Kumar to the Indian Institute of Technology, Delhi for the degree of Doctor of Philosophy is a bonafide record of research work carried out by him under our supervision and guidance. The thesis work, in our opinion, has reached the requisite standard, fulfilling the requirements of the said degree. The results contained in the thesis have not been submitted, in part or full, to any other university or Institute for the award of any degree or diploma.
Dr. A. K. Keshari Professor
Dept. of Civil Engineering I.I.T. Delhi
Hauz Khas, New Delhi, India
Dr. H. S. Gupta
Senior Scientific Officer Dept. of Civil Engineering I.I.T. Delhi
Hauz Khas, New Delhi, India
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ACKNOWLEDGEMENTS
I express my whole hearted gratitude to my thesis supervisors Prof A. K. Keshari and Dr. H. S. Gupta, Department of Civil Engineering, Indian Institute of Technology, Delhi, for their valuable guidance, constant encouragement and support at every stage in successful completion of my research work.
I am also thankful to the Snow and Avalanche Study Establishment (SASE), a premier Institute working in Indian Himalaya under Defence Research and Development Organisation (DRDO) for providing support to carry out snow chute experiments, field study and research work. I express my sincere thanks to Shri Ashwagosha Ganju, Director Snow and Avalanche Study Establishment for their encouragement and moral support during my research work.
I am grateful to Dr. R. N. Sarwade, Former Director of Snow and Avalanche Study Establishment, RDC, Chandigarh for extending help and sparing me to pursue Ph. D program.
I am thankful to my colleagues Shri Arun Chaudhary, Shri Ganesh Kumar and Shri Sunil Bhardwaj for their help during my research work. I express my special thanks to Shri Agraj Upadyay and Shri Mithlesh Sahu for their help while conducting snow chute experiments and field study.
I am also thankful to co-research scholar Shri R. Maheswaran, Shri Ashwini Soni and Shri Deba Prakash Satapathy and M Tech student Shri Raktim Haldar with whom I have many fruitful technical discussions about my research work. My special thanks to Mr Narendar who has helped me during my stay at IIT Delhi.
I am also thankful to Dr. V.D. Mishra for giving me encouragement during my research work.
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Finally, I deserve deepest appreciation to my wife Smt Seema, my son Shivam and my daughter Tusita for getting source of inspiration. The research work is dedicated to my source of inspiration my beloved parents Shri Vishwanath Singh and Smt Sharmista.
Amod Kumar
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ABSTRACT
The snow avalanche is one of natural hazards in snow bound mountainous regions which is drawing significant attentions by worldwide researchers. In India, Jammu and Kashmir (Higher reaches of Kashmir and Gurez valleys, Kargil and Ladakh), Himachal Pradesh (Chamba, Kullu- Spiti and Kinnaur) and Uttrakhand (Tehri, Garhwal and Chamoli) have snow bound avalanche prone regions. The people living in these areas are directly or indirectly affected by snow and avalanche problems and they remain cut off from the rest part of the world as highways in these regions remain closed during winter due to snow and avalanche problem. Many infrastructural projects, namely highway, railways, transmission lines, hydel powers and winter tourism are coming in avalanche prone regions which need better understanding of avalanche dynamics and interaction between avalanches and protecting structures. This helps significantly in hazard assessment and designing control structures. The avalanche flow depends on terrain parameters, quantity of released and entrained snow mass from the formation zone and the middle zone, respectively, and the snow rheology. The granular and rheological properties of moving snow are dependent on terrain roughness, channel geometry and mechanical properties of snow including density variation.
The currently used avalanche dynamics models lack in the actual description of rheological properties of moving snow mass. In this study, an improved one dimensional avalanche dynamics model is presented by incorporating rheological properties of moving snow mass. The developed model consists of a set of partial differential equations describing mass and momentum conservation, and are obtained by making use of Criminale-Ericksen- Filbey-Fluid (CEFF) and granular mass theories for the snow rheology. The model incorporates the density variation, velocity distribution and pressure distributions, which facilitates to account variation in the snow and flow properties during the initiation of
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avalanche occurrence as well as during its movement along the flow path, because of associated physical processes. The rheological behaviour of moving snow mass is introduced in the density varying model by incorporating mass flux distribution factor and momentum distribution factor. These factors depend on slip velocity, fluidization layer thickness, channel shape and density gradient in avalanche mass. The granular effect is incorporated by introducing the term active earth pressure coefficient in acceleration phase and passive earth pressure in deceleration phase. The solution is obtained numerically using McCormack Finite Difference Method. The experiments were also carried out in a snow chute at Dhundhi, Manali to validate the developed numerical model and to understand the effect of channel transition on the avalanche flow with different contraction and divergence angles.
Analytical solution is also obtained for the studying the interaction between avalanche flow and diversionary protecting structures. The processes involved in dissipating energy at supercritical flow transition is studied. The results obtained from the numerical model are in good agreement with the experimental observations and also with the published results in literature for some cases.
A number of computational run were taken to investigate the variation of velocity and flow depth along the avalanche path. The sensitivity analysis is carried out to investigate the sensitivity of various model parameters consisting of friction and pressure coefficients and distribution factors on results in term of velocity, flow depth, runout distance. Results were also obtained to estimate the run up heights of oblique jump for different deflection angle of supercritical flow transition resulting from the presence of protecting structure in avalanche path.
The developed model has been also applied to real avalanche site, MSP-7, called Phindri Nallah near Manali, India.
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CONTENT
Page
• CERTIFICATE i
• ACKNOWLEDGEMENT ii
• ABSTRACT iv
• CONTENT
• LIST OF FIGURES x
• LIST OF TABLES xv
• LIST OF SYMBOLS xvi
INTRODUCTION 1
1.1 Background 1
1.2 Basics of Avalanche Dynamics 5
1.2.1 Avalanche path in India 14
1.3 Scope of Research 19
1.4 Objectives 23
1.5 Organisation of Thesis 23
2 LITERATURE REVIEW 25
2.1 Avalanche Dynamics Models 26
2.2 Rheology of Moving Snow 35
2.3 Diversionary and Retarding Structures 39
3 MODEL DEVELOPMENT 41
3.1 Avalanche Dynamics Model 41
3.1.1 Governing Equations 41
3.1.2 Estimation of Solid Friction 43
3.1.3 Mass Flux and Momentum Flux Distribution Factors 43
3.1.4 Granular Pressure Coefficient 50
3.1.5 Modelling of Snow Density 52
3.2 Numerical Solution 53
3.2.1 MacCormack Method 53
3.2.2 Boundary Conditions 55
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3.2.3 Convergence and stability 56
3.3 Avalanche-Structure Interaction 57
3.3.1 Oblique Jump Equations
4. EXPERIMENTAL SETUP AND MEASURING TECHNIQUES 66
4.1 Description of Experimental System 66
4.1.1 Snow Chute Section-1 68
4.1.2 Snow Chute Section-2 69
4.1.3 Snow Chute Section-3 70
4.1.4 Snow Chute Section-4 70
4.1.5 Snow Chute Section-5 71
4.1.6 Snow Chute Section-6 72
4.1.7 Control Room 72
4.1.8 Hydraulic System 73
4.1.8.1 Feeding Platform 73
4.1.8.2 Testing Platform 73
4.1.9 Electric Work 73
4.1.10 Polycarbonate Sheet 74
4.1.11 Supporting Structure for Snow Chute 75
4.2 Measuring Velocity and its Profile 75
4.2.1 CCD Camera and Video Recorder 76
4.2.2 Optical Velocity Measuring Sensor 76 4.2.2.1 Measurement Principle of Optical Velocity Sensors 77 4.2.3 Velocity Profile Measuring System 79 4.3 Measuring Mass Distribution in Run-out Zone 80
4.4 Parameters Measured 83
4.5 Measured Velocity Profile in Snow Chute 83
5. RESULTS AND DISCUSSIONS 86
5.1 Model Validation 86
5.2 Variation of Velocity and Flow Depth 91
5.3 Sensitivity of Flow Variable with Model Parameters 94 5.4 Effect of Confinement on Distribution Factors 100
5.4.1 Mass Flux Distribution Factor 100
5.4.2 Momentum Distribution Factor 101
5.4.3 Significance of Distribution Factors 102 vii
5.5 Study of oblique Jump in Transition 105 5.5.1 Characteristics of Granular Shock Wave Equation 105 5.5.2 Effect of granular pressure coefficient on Shock Wave Height109 5.6 Avalanche Flow Calculation for Natural Path 114
5.7 Effect of grid size 114
6. CONCLUSIONS AND RECOMMENDATION 121
6.1 Scope for future research 123
6.2 Limitations of avalanche flow model 123
REFERENCES
Appendix I: Experimental data
Appendix II: photographs of Experiments
