Mitigation of Train-Induced Floor Vibrations in Multi-Story Buildings Using a Blocking Floor

Transcription

1 Mitigation of Train-Induced Floor Vibrations in Multi-Story Buildings Using a Blocking Floor Ningyu Zhao, Doctoral student, Tufts University Masoud Sanayei, Professor, Tufts University, Dept. of Civil & Env. Engineering James A. Moore, Supervisory Consultant, Acentech Inc. Jeffrey A. Zapfe, Senior Consultant, Acentech Inc. Eric M. Hines, Professor of Practice, Tufts University, Dept. of Civil & Env. Engineering; Associate, LeMessurier Consultants Structures Congress 21 Saturday May 15 th, 11 1

2 Importance of this Research Vibrations Considerations Human Comfort Sensitive Equipment Air-rights development Sources of Measured Excitation Running Trains / Subways Vehicular Traffic Simple predictive model for vertical vibration transmission and mitigation 675 Massachusetts Avenue, Cambridge, Massachusetts. 2

3 Background Sanayei et al. (28) developed a predictive model and compared it with measurements in collaborations with Acentech Inc. and LeMessurier Consultants Vibration excitation is from the subway and train stations below Vibration transmission is from ground into the foundation Columns are modeled with axial wave propagation (not bending) Floors slabs are modeled with transverse bending deformations TD Banknorth Garden, Boston, Massachusetts Courtesy of TD Banknorth Garden 3

4 Scale Model Testing Hughes et al. (28) confirmed the mathematical model by testing a scale model building at Tufts University Testing & modeling of structural components such as finite beams, columns and thin plates. Scale model testing & verification between 1 and 5 Hz (corresponding to full-scale frequencies of 1 to 5 Hz). The vibration transmission model was verified with measurements on the scale model 4

5 Current Research Evaluate feasibility of using blocking floor for vibration transmission mitigation to upper floors A blocking floor is referred to increasing the thickness of the first floor to reduce vibration transmission to upper floors. It is a cost-effective solution to vibration mitigation The scale model building is used to evaluate the effectiveness of the blocking floor hypothesis Consider the shear softening of thicker blocking floor(s) at higher frequencies 5

6 Assumptions: System modeled as a vibration propagating column and bending floor slabs Axial vibration of column excites bending deformation of the slab at each floor E = E 1 +η i c 2 [ Kcol ω Meff ]{ U} = { F} System Modeling Complex modulus to represent damping Dynamic Equilibrium (Harmonic excitation and response at frequency ω) 6

7 Column Modeling Modeled as a wave propagating rod Dynamic stiffness matrix (2 x 2) where wave number is λ is the wave length. c L cos( βl) sin( βl) 1 EAβ [ ] = k col π ω ρ β = 2 = = ω λ E c L is the axial wave speed. 1 cos( β L) 7

8 Impedance (Z) Impedance Modeling Measure of applied force to resulting velocity F Z = V Finite and infinite system impedances: Resonances & Anti-resonances Z= iωm+ c ik ω Stiffness controlled at low ω and mass controlled at high ω Effective mass used in modeling F u m c k meff = m+ + ( iω ) ( iω ) 2 k c 8

9 Bending Deformation Model of Floor Slabs Kirchoff plate theory for modeling of thin plates Only bending deformation considered No transverse shear and rotary inertia Input impedance at connection to columns: m eff Floor impedance is proportional to t 2 : infinite plate theory Z = 8 D ρt = 8t Slab 2 ρe v 2 12(1 ) Mindlin plate theory for modeling thick plates (blocking floor) Accounts for shear deformation and rotary inertia Shear softening reduces the impedance of slab at the column 9

10 Blocking Floor Impedance of Scale Model Building Impedance (db re:1 N.S/m) Z = 2 log 1 Z 1 db is 3 fold increase in impedance 2 db is 1 fold increase in impedance Kirchhoff Plate.75" Kirchhoff Plate 1.5" Kirchhoff Plate 2.25" Mindlin Plate.75" Mindlin Plate 1.5" Mindlin Plate 2.25" 1"x1" Aluminum Column Analytical impedances of slabs and columns used in scale model building 1

11 Blocking Floor in a 4-story Scale Model Building Only the first floor blocking slab thickness has increased. Upper 3 floors are unchanged at (a) (c) (d).75" MDF 1.5" MDF 2.25" MDF Predicted Velocity Ratios relative to Base Vibration at the shaker using Kirchoff slab model (a) 1 st fl., (b) 2 nd fl., (c) 3 rd fl., (d) 4 th fl (b) υi VdB = 2 log1 υ B 11

12 Design of Scale Model Building Slab-to-column ratios are matched between scale model and typical full-scale buildings with steel columns (W14x9) and concrete slabs (4.75 ) Scale-Model Column: 8/2 Aluminum Model Slab: Medium Density Fiberboard (various thicknesses) Connection: 8 L-shape brackets (4 above & 4 below) to ensure moment connection between slab and column (modeled as lumped masses) Material properties of MDF were verified by Hughes (28) & Zhao (29) 12

13 Scale Model Building 13

14 Instrumentation Brüel & Kjær Permanent Magnetic Vibration Exciter Type 488 Connected to the base of center column Drives axially into the column Force Gauge model B&K-823 Acceleration measurements: PCB Accelerometer model 352C65 Measure vertical vibration at each floor 14

15 Velocity Ratios with.75 MDF on 1 st Floor (a) (c) (b) (d) Classical Kirchoff model with 5% damping Good match between model and data Model slightly overpredicted vibration attenuation on all floors Measured Prediction (Infinite) Prediction (Finite) (a) 1 st Floor; (b) 2 nd Floor; (c) 3 rd Floor; (d) 4 th Floor 15

16 Velocity Ratios with 1.5 MDF on 1 st Floor (a) (c) (b) (d) Measured Prediction (Infinite) Prediction (Finite) Classical Kirchoff model with 5% damping Model is accurate on floors 2 to 4 Model accurately predicted column resonances. (a) 1 st Floor; (b) 2 nd Floor; (c) 3 rd Floor; (d) 4 th Floor 16

17 Measured Results with Doubled Thickness of Blocking Floor (a) (c) (d) 5.75" Floor 1.5" Blocking Floor (b) Frequency smoothing used for ease of visualization 2 to 5 db reduction of slab vibration form 1-3 khz Thicker blocking floors required to achieve greater reductions (a) 1 st Floor; (b) 2 nd Floor; (c) 3 rd Floor; (d) 4 th Floor 17

18 Shear Behavior of Blocking Floor (a) (c) (b) (d) Kirchhoff Plate.75" Mindlin Plate.75" Kirchhoff Plate 2.25" Mindlin Plate 2.25" Predicted Velocity Ratios Using Kirchhoff/Mindlin Theory for Various Slabs on 1 st Floor: (a) 1 st fl., (b) 2 nd fl., (c) 3 rd fl., (d) 4 th fl. 18

19 Conclusions The system mathematical model was successful in predicting vibration levels Adding a blocking floor at the first floor is potentially an effective method for vibration mitigation at all floors 19

20 Future Work Full-scale testing Verify the mathematical model for a full-scale building Estimate the effects of additional structural components and foundations on vibration propagation Measurements of blocking floor behavior Shear softening for thicker blocking floor(s) 2

21 Acknowledgements Acentech, Inc. LeMessurier Consultants Stephen Fratto, CEE lab coordinator Former Graduate Students: Mike Hughes Kaitlyn Conroy 21

22 Thanks for Listening! Questions? 22