Dynamics of structure and foundation: a unified approach. I, Fundamentals

Dynamics of Structure and Foundation – A Unified Approach: 2. Applications......Page 2
Contents......Page 4
Preface......Page 11
Table of Contents......Page 0
1.1.1 The marriage of soil and structure......Page 13
1.1.2 What does the interaction mean?......Page 14
1.1.3 It is an expensive analysis do we need to do it?......Page 16
1.2.1 Lagrangian formulation for 2D frames or stick-models......Page 18
1.2.2.1 Calculation of spring constant for rigid raft......Page 26
1.2.2.2 Calculation of spring constant for flexible raft......Page 27
1.2.2.3 What sin thou make in treating foundation & the structure separately?......Page 28
1.3.1 Dynamic response of a structure with multi degree of freedom considering the underlying soil stiffness......Page 40
1.3.2 Extension of the above theory to system with multi degree of freedom......Page 41
1.3.3 Estimation of damping ratio for the soil structure system......Page 42
1.3.4 Formulation of damping ratio for single degree of freedom......Page 43
1.3.5 Extension of the above theory to systems with multi-degree freedom......Page 44
1.3.6 Some fallacies in coupling of soil and structure (Chowdhury 2008)......Page 52
1.3.7 What makes the structural response attenuate or amplify?......Page 53
1.4.1 Some modelling techniques......Page 54
Finally a word on the soil.......Page 56
1.5 GEOTECHNICAL CONSIDERATIONS FOR DYNAMIC SOIL STRUCTURE INTERACTION......Page 58
1.5.1 What parameters do I look for in the soil report?......Page 59
1.6.1 Block vibration test......Page 61
1.6.2 Seismic cross hole test......Page 62
1.6.3 How do I co-relate dynamic shear modulus when I do not have data from the dynamic soil tests?......Page 63
1.7.1.1 Hardin and Richart’s Formula......Page 64
1.7.1.2 Seed and Idriss Formula......Page 65
1.7.1.3 Corrections to SPT value......Page 66
1.7.1.4 Ohsaki and Iwasaki’s formula......Page 67
1.7.2.1 Hardin and Drnevich formula......Page 70
1.8.1 Whitman’s formula......Page 73
1.8.2 Hardin’ formula......Page 74
1.8.3 Ishibashi and Zhang’s formula......Page 75
1.9.1 Estimation of strain in soil for machine foundation......Page 77
1.9.2 Estimation of soil strain for earthquake analysis......Page 82
1.9.3 What do we do if the soil is layered with varying soil property?......Page 89
1.9.4.1 Field test......Page 91
1.10 EPILOGUE......Page 92
SUGGESTED READING......Page 93
2.1.1 Case history #1......Page 94
2.1.2 Case history #2......Page 95
2.2.1 Block foundations resting on soil/piles......Page 96
2.2.2 How does a block foundation supporting rotating machines differ from a normal foundation?......Page 97
2.2.2.2 Amplitude check......Page 98
2.2.3.1 Tschebotarioff’s (1953) method......Page 99
2.2.3.3 Newcomb’s (1951) method......Page 100
2.2.4.1 Hsieh’s (1962) method......Page 101
2.2.4.2.1 Vertical direction......Page 103
2.2.4.2.3 For horizontal force, H......Page 104
2.2.4.2.4 Torsional mode......Page 105
2.2.4.2.5 The Limitations......Page 106
2.2.4.3 Richart and Lysmer’s model......Page 107
2.2.4.3.1 Vertical motion considering damping of the soil......Page 108
2.2.4.3.2 Coupled horizontal and rocking motion considering damping soil......Page 109
2.2.5 Approximate analysis to de-couple equations with non-proportional damping......Page 110
2.2.6 Alternative formulation of coupled equation of motion for sliding and rocking mode......Page 116
2.3 TRICK TO BY PASS DAMPING – MAGNIFICATION FACTOR, THE KEY TO THE PROBLEM…......Page 124
2.4 EFFECT OF EMBEDMENT ON FOUNDATION......Page 128
2.5 FOUNDATION SUPPORTED ON PILES......Page 130
2.5.1 Pile and soil modelled as finite element......Page 132
2.5.2 Piles modelled as beams supported on elastic springs......Page 134
2.5.3 Novak’s (1974) model for equivalent spring stiffness for piles......Page 135
2.5.4 Equivalent pile springs in vertical direction......Page 136
2.5.5 The group effect on the vertical spring and damping value of the piles......Page 138
2.5.6 Effect of pile cap on the spring and damping stiffness......Page 139
2.5.7 Equivalent pile springs and damping in the horizontal direction......Page 140
2.5.8 Equivalent pile springs and damping in rocking motion......Page 141
2.5.9 Group effect for rotational motion......Page 142
2.5.10 Model for dynamic response of pile......Page 149
2.5.10.2 Vibration of friction piles......Page 150
2.5.10.2.1 Mass of the pile......Page 156
2.5.10.2.2 Damping of the pile......Page 157
2.5.10.3 Vibration of bearing piles......Page 159
2.5.10.5 Vertical vibration of partially embedded piles......Page 160
2.5.10.5.1 Stiffness of the pile for soils with varying elastic property......Page 161
2.5.10.5.2 Shear modulus having a linear variation......Page 162
2.5.10.7 Effect of pile cap on pile stiffness......Page 163
2.5.10.8 Solutions for higher modes......Page 166
2.5.10.10 Design steps......Page 172
2.5.11.1 Piles under dynamic lateral loading......Page 173
2.5.11.2 Radiation damping for pile under lateral load......Page 180
2.5.11.5 Partially embedded piles......Page 182
2.5.11.6 Pile embedded in soils with varying elastic property......Page 184
2.5.11.7 Computation of bending moment and shear force......Page 185
2.5.11.8 Dynamic response of short piles in the horizontal mode......Page 186
2.5.11.8.1 Comparison of results......Page 192
2.5.11.8.2 Computer run steps for short pile based on field observed data......Page 194
2.5.11.9 Dynamic analysis of piles under rocking or rotational mode......Page 196
2.5.11.9.1 Estimation of mass contribution of pile......Page 201
2.5.11.9.2 Radiation damping factor for pile under rocking mode......Page 202
2.5.11.9.3 Consideration of material damping of pile......Page 203
2.5.12 Partially embedded piles under rocking mode......Page 204
2.5.12.1 Stiffness of the pile for soils with varying elastic property......Page 205
2.5.12.1.1 Calculation of dynamic bending moment and shear force in pile......Page 206
2.5.12.2 Dynamic response of short piles under rotational mode......Page 207
2.5.13.1 Effect of pile cap on pile stiffness......Page 212
2.5.14 Comparison of results......Page 214
2.5.15.1 Environmental and economic impact......Page 216
2.5.15.2 Machine data......Page 217
2.5.15.3 My Machine is perfectly balanced. you don’t need to worry about the dynamic force!......Page 218
2.5.15.3.2 For Centrifugal compressors......Page 219
2.5.15.4 Soil data......Page 220
2.5.15.5 Trial sizing of the block foundation......Page 221
2.5.15.6 Centre of gravity of the machine foundation......Page 222
2.6.2 Frequency separation......Page 224
2.6.6 Reinforcements......Page 225
2.6.7 Cover to concrete......Page 226
2.7.1.1 How does the behavior of a mechanical system under impact differ from externally applied harmonic loads?......Page 242
2.7.1.2 How do the planks behave under these two conditions?......Page 244
2.7.2 Mathematical model of a hammer foundation......Page 249
2.7.2.1 of foundationMathematicalmodel resting inside a trough......Page 250
2.7.2.2 Un-damped Response of a system under impact loading having multi-degree of freedom......Page 252
2.7.2.3 Damped response of a system under impact loading having multi-degree of freedom......Page 256
2.8.1 Design criteria for hammer foundation......Page 259
2.8.1.3 Minimum weight of foundation......Page 260
2.8.1.7 Velocity of anvil after of impact......Page 261
2.8.1.10 Stability of pad between anvil and block......Page 262
2.8.2 Discussion on the IS-code method of analysis......Page 263
2.8.4.1 Selection of elements......Page 264
2.8.4.5 Method of analysis......Page 266
2.9.1 Mathematical formulation of anvil placed eccentrically on a foundation......Page 279
2.9.2 withDampedequationofmotion eccentric anvil......Page 281
2.10.2 Construction procedure......Page 282
2.11.3 Vibration pick-ups......Page 283
2.11.3.1 Displacement transducer......Page 284
2.11.3.2 Instrument with low natural frequency......Page 285
2.11.3.3 Instrument with high natural frequency......Page 286
2.11.3.4 Velocity transducers......Page 287
2.11.3.5 Acceleration transducers......Page 288
2.11.3.5.1 Phase angles......Page 289
2.11.3.7 Phase distortion......Page 291
2.12 EVALUATION OF FRICTION DAMPING FROM ENERGY CONSIDERATION......Page 294
2.13 VIBRATION ISOLATION......Page 295
2.13.1 Active isolation......Page 296
2.13.2 Passive isolation......Page 298
2.13.3 Isolation by trench......Page 299
2.14.1 Introduction......Page 300
2.14.2 Different types of turbines and the generation process.......Page 301
2.14.3 Layout planning......Page 303
2.14.4.1 Rausch’s method......Page 304
2.14.4.2 Amplitude or Barkan’s method......Page 307
2.14.4.3 Combined or Major’s method of analysis......Page 311
2.15 DYNAMIC SOIL-STRUCTURE INTERACTION MODEL FOR VIBRATION ANALYSIS OF TURBINE FOUNDATION......Page 316
2.16 COMPUTER ANALYSIS OF TURBINE FOUNDATION BASED ON MULTI DEGREE OF FREEDOM......Page 323
2.17.1 The analysis......Page 330
2.17.2 Calculation of the eigen values......Page 331
2.17.5 Calculation of moments, shears and torsion......Page 332
2.18.1 Check list for turbine foundation design......Page 333
2.18.2 Spring mounted turbine foundation......Page 341
2.18.2.1 Theory of vibration isolation......Page 342
2.18.2.2 Effect of damping on the transmissibility factor......Page 345
2.18.2.3 How springs affect turbine foundation?......Page 346
2.18.2.4 Mathematical modelling of spring mounted turbines......Page 347
2.18.2.5 Turbine foundations concrete versus steel structure......Page 348
2.18.2.6 Design of RCC sections......Page 350
Discussion on the results......Page 397
We also furnish some selected papers which we feel would further ameliorate your insight to the problem......Page 398
3.1 INTRODUCTION......Page 400
3.1.1 Why do earthquakes happen in nature?......Page 401
3.1.2 Essential difference between systems subjected to earthquake and vibration from machine......Page 402
3.1.3 Some history of major earthquakes around the world......Page 403
3.1.4 Intensity......Page 405
3.1.6.1 What is liquefaction?......Page 406
3.1.6.2 Co-Relation between CRR and SPT value......Page 408
3.1.6.4 Effect of earthquake magnitude on liquefaction resistance......Page 410
3.1.6.5 Correlation between CRR and CPT value......Page 413
3.1.6.7 Settlement of foundation due to liquefaction failure......Page 414
3.1.6.9 Punching shear failure of soil......Page 416
3.1.6.10 General shear failure capacity reduction due to liquefaction......Page 418
For sloped terrain condition......Page 420
3.1.6.12 Effect of earthquake on structures......Page 422
3.2.1 Seismic coefficient method......Page 423
3.2.2 Response spectrum method......Page 428
3.2.2.1 Response spectrum method as per 1984 version......Page 429
3.2.2.2 Response spectrum method as per IS-1893 2002......Page 431
3.2.3 Dynamic analysis under earthquake loading......Page 435
3.2.4 How do we evaluate the earthquake force?......Page 436
3.2.5.1 Analysis based on assumed shape function......Page 442
3.2.5.2 Dynamic analysis of systems having multi-degree of freedom under earthquake forces......Page 447
3.2.6.1 The absolute sum method (ABSSUM)......Page 455
3.2.6.3 The complete quadratic combination method (CQC)......Page 456
3.3 TIME HISTORY ANALYSIS UNDER EARTHQUAKE FORCE......Page 459
Steps for Newmark-beta method for earthquake analysis......Page 460
3.3.1 Earthquake analysis of tall chimneys and stack like structure......Page 467
3.3.1.1 Analysis as proposed in IS-code......Page 468
3.3.1.2 Dynamic analysis of tall chimneys......Page 469
3.3.1.3 Transformation to the format of IS-code......Page 475
3.3.1.4 Analysis of single flue tapered chimney......Page 481
3.3.1.7 Do we consider soil structure interaction for dynamic analysis of chimney?......Page 490
3.3.1.8 Thus to sum it up…......Page 491
3.4.1.1 The IS-code method......Page 492
3.4.1.2 Hydrodynamic pressure on dam from the reservoir......Page 494
3.4.1.3 Some comments and review of the IS-code method......Page 495
3.4.2.1 Calculation of time period of the dam having variable cross section......Page 496
3.4.2.1.1 Comparison of natural frequency (rad/sec) proposed and exact analysis......Page 501
3.4.2.3 Dynamic Bending Moment and Shear force for the fundamental mode......Page 502
3.4.2.4 Free field time period of the reservoir and the hydrodynamic pressure from reservoir......Page 503
3.4.2.6 Determination of the fluid spring and mass......Page 506
3.4.2.7 A semi-analytic model for fluid structure interaction......Page 508
3.4.2.8 Lumped mass and stiffness approach for Fluid-Structure interaction......Page 513
3.4.2.9 Model for fluid-structure interaction of the dam and reservoir......Page 514
3.4.2.10 Consideration of fluid- structure-foundation interaction......Page 516
3.4.2.12 Finite element analysis of concrete dam......Page 517
3.5.2 Mononobe’s method for analysis of earth dam......Page 530
3.5.3 Gazetas’ method for earth dam analysis......Page 533
3.5.4 Makadisi and Seed’s method for analysis of earth dam......Page 534
3.6.1 Earthquake analysis of earth retaining structures......Page 537
3.6.2 Mononobe’s method of analysis of retaining wall......Page 538
3.6.4 Arango’s method......Page 541
3.6.5 Steedman and Zeng’s method......Page 543
3.6.7 Dynamic analysis of cantilever and counterfort retaining wall......Page 544
3.6.9 Extension to the generic case of soil at a slope i behind the wall......Page 555
3.6.10 Dynamic analysis of counterfort retaining wall......Page 558
3.6.10.2 Derivation of stiffness coefficient......Page 561
3.6.10.4 The integration constants......Page 564
3.6.10.5 Calculation of nodal forces under dynamic load......Page 565
3.6.10.6 Calculation of dynamic amplitude......Page 567
3.6.10.7 Calculation of dynamic moments and shear......Page 569
3.6.11 Soil sloped at an angle i with horizontal......Page 571
3.6.11.1 Design moments and shear coefficients......Page 572
3.7.1 Earthquake Analysis of rigid walls when the soil does not yield......Page 582
3.7.2 Ostadan’s method......Page 586
3.8.1 Analysis of water tanks under earthquake force......Page 588
3.8.2 Impulsive time period for non rigid walls......Page 592
3.8.4 Calculation of horizontal seismic force for tank resting on ground......Page 594
3.8.6 Calculation of bending moment on the tank wall resting on the ground......Page 595
3.8.7 Calculation of sloshing height......Page 596
3.9.1 Earthquake Analysis for overhead tanks......Page 599
3.9.3 Hydrodynamic pressure for circular tank......Page 603
3.9.6 Pressure due to inertia of the wall......Page 604
3.9.7 Maximum design dynamic pressure......Page 605
3.10 PRACTICAL ASPECTS OF EARTHQUAKE ENGINEERING......Page 609
3.10.1 Epilogue......Page 614
References......Page 615