Test Plan

REPORT NO. XXXXXXXXX

CENTER FOR GEOTECHNICAL MODELING

COMPATIBLE SOIL AND STRUCTURE YIELDING TO IMPROVE SYSTEM PERFORMANCE: CENTRIFUGE DATA REPORT FOR MAH01

BY M. HAKHAMANESHI B. L. KUTTER W. LIU T. C. HUTCHINSON

DEPARTMENT OF CIVIL & ENVIRONMENTAL ENGINEERING COLLEGE OF ENGINEERING UNIVERSITY OF CALIFORNIA AT DAVIS

July, 2011

COMPATIBLE SOIL AND STRUCTURE YIELDING TO IMPROVE SYSTEM PERFORMANCE: Centrifuge Data Report for MAH01 M. Hakhamaneshi, B.L. Kutter, T. C. Hutchinson, W. Liu Center for Geotechnical Modeling Data Report UCD/CGMDR – XX/XX Date:

July, 2011

Date of testing:

Oct 1 – Dec 2, 2010

Project:

Compatible Soil and Structure Yielding to Improve System Performance (CoSSY)

Sponsor:

National Science Foundation

Related Reports:

Soil-Foundation-Structure Interaction: Shallow Foundations (Centrifuge Data Reports for, KRR01, KRR02, LJD01, LJD02, and LJD03, SGG02, SGG03 and SGG04).

ACKNOWLEDGEMENTS This work was supported primarily by the National Science Foundation (NSF) under a project titled Compatible Soil and Structure Yielding to Improve System Performance. The contents of this report are not necessarily endorsed by the sponsors. The authors would like to acknowledge the suggestions and assistance of Dan Wilson, Chad Justice, Ray Gerhard, Peter Rojas, Lars Pedersen, and Anatoliy Ganchenko, of the UC Davis CGM, and UC Davis graduate students Lijun Deng, and Jackee Allmond. Development of the large centrifuge at UC Davis was supported primarily by the Network of Earthquake Engineering Simulation (NEES), National Science Foundation, NASA, and the University of California.

CONDITIONS AND LIMITATIONS Permission is granted for the use of these data for publications in the open literature, provided that the authors and sponsors are properly acknowledged. It is essential that the authors be consulted prior to publication to discuss errors or limitations in the data not known at the time of release of this report. In particular, these may be later releases of this report. Questions about this report may be directed by e-mail to [email protected].

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TABLE OF CONTENTS ACKNOWLEDGEMENTS ............................................................................................................ 1 CONDITIONS AND LIMITATIONS............................................................................................ 1 LIST OF FIGURES ........................................................................................................................ 3 LIST OF TABLES .......................................................................................................................... 4 PURPOSE AND CONFIGURATION ........................................................................................... 5 SOIL PROPERTIES ....................................................................................................................... 8 1D-CONSOLIDATION TEST ..................................................................................................... 12 UNDRAINED SHEAR STRENGTH OF THE CLAY SPECIMEN ........................................... 14 STRUCTURE PROPERTIES IN SLOW CYCLIC TEST ........................................................... 17 DESIGN OF A ROCKING SHALLOW FOUNDATION ........................................................... 21 SDOF MODEL COLUMNS......................................................................................................... 23 SDOF MODEL FOOTINGS ........................................................................................................ 24 SDOF MODEL MASS ................................................................................................................. 24 SDOF MODEL ASSEMBLY ....................................................................................................... 24 SCALE FACTORS ....................................................................................................................... 27 INSTRUMENTATION AND MEASUREMENTS ..................................................................... 28 Sensors ...................................................................................................................................... 28 Video ......................................................................................................................................... 33 KNOWN LIMITATIONS............................................................................................................. 34 ORGANIZATION OF DATA FILES AND PLOTS ................................................................... 35 REFERENCES ............................................................................................................................. 37 APPENDIX A: CENTRIFUGE TEST CHRONOLOGY AND CALENDER ........................ 39 APPENDIX B: INSTRUMENTATION LIST ......................................................................... 48 APPENDIX C: SPIN LOCATIONS AND DRAWINGS ........................................................ 58 APPENDIX D: SHOP DRAWINGS & STRUCTURAL PROPERTIES ................................ 63 APPENDIX E: SDOF MATHCAD DESIGN SHEETS .......................................................... 70 SD STRUCTURE ................................................................................................................. 70 LD STRUCTURE ................................................................................................................. 74 APPENDIX F: SC & LC MATHCAD DESIGN SHEETS ...................................................... 78 SC STRUCTURE ................................................................................................................. 78 LC STRUCTURE ................................................................................................................. 79 APPENDIX G: CRITICAL PLOTS OF THE DYNAMIC SHAKES ...................................... 80 APPENDIX H: MATHCAD SHEET FOR DYNAMIC ANALYSIS ................................... 111

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LIST OF FIGURES Figure 1. Schematic of a rocking footing ........................................................................................ 5 Figure 2. Gap created during rocking of foundations ..................................................................... 5 Figure 3. Detailed plan view of the test matrix of MAH01 (unit: mm, model scale)...................... 6 Figure 4. Schematic summary of different test series in MAH01 experiment (unit: mm, model scale) ............................................................................................................................................... 7 Figure 5. Hydrometer test results on the Yolo Loam, Park (2011) ................................................. 8 Figure 6. Layout of the soil in the rigid container ........................................................................... 9 Figure 7. Soil specimen preparation ............................................................................................. 11 Figure 8. 1D consolidation test on Yolo Loam .............................................................................. 12 Figure 9. Schematic of a 1D consolidometer ................................................................................ 12 Figure 10. Compression curve of void ratio versus Log of vertical effective stress ..................... 14 Figure 11. Hand shear vane apparatus ......................................................................................... 14 Figure 12.. Hand shear vane test results throughout the experiment ......................................... 15 Figure 13. Bearing Failure test results for a centrifugal acceleration of 60 g & 30 g ................... 16 Figure 14. Instrumented aluminum plate used for slow cyclic test ............................................. 18 Figure 15. Steel structure used during the SC_Steel experiment................................................. 18 Figure 16. Displacement-Time history of the actuator used for the slow cyclic test series......... 19 Figure 17. Outline of the displacement controlled slow cyclic structure ..................................... 20 Figure 18. SC_Al test results under 30 g, 60 g and 15 g................................................................ 20 Figure 19. SC_Al and SC-St results under 30 g and 60 g ............................................................... 21 Figure 20. 2 SDOFs being instrumented for dynamic shakes ....................................................... 22 Figure 21. 2 SDOF structures used in the dynamic shaking (units: inch, model scale) ................ 23 Figure 22. Instrumentation Rack and the buried sensors into the clay........................................ 29 Figure 23. Outline of all the buried sensors in the soil profile and on the container .................. 29 Figure 24. Instrumented slow cyclic structures, connected to the actuator ................................ 30 Figure 25. Instrumentation of the SD structure ........................................................................... 31 Figure 26. Instrumentation of the LD structure ............................................................................ 32 Figure 27. Different type of sensors and cameras typically used in a centrifuge model ............. 33 Figure 28. Outline of the location of the high speed and analog cameras used during the dynamic shaking............................................................................................................................ 34 Figure 29. Footing rotation from vertical accelerometer integration versus LP readings ........... 35 Figure 30. Plan view of all the trials tested in MAH01.................................................................. 58 Figure 31. Side view drawings of spin #1, SC1_Alum ................................................................... 58 Figure 32. Side view drawings of spin #2, LC_Alum...................................................................... 59 Figure 33. Side view drawings of spin #3, BF1 .............................................................................. 59 Figure 34. Side view drawings of spin #4, SD & LD ....................................................................... 60 Figure 35. Side view drawings of spin #5, BF2 .............................................................................. 60 Figure 36. Side view drawings of spin #6, SC2_Alum ................................................................... 61 Figure 37. Side view drawings of spin #7, SC_Steel ...................................................................... 61 Figure 38. Side view drawings of spin #8, BF3 .............................................................................. 61 Figure 39. Side view drawings of spin #9, BF4 .............................................................................. 62

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Figure 40. SD and LD structures columns, plan and side view ..................................................... 63 Figure 41. Two mild steel plates used as a part of the total mass on the SD structure ............... 64 Figure 42. The two aluminum masses used as a part of the total mass on the SD and LD structures ...................................................................................................................................... 65 Figure 43. Two mild steel plates used as a part of the total mass on the LD structure ............... 66 Figure 44. Two aluminum plates used as the footings of the SD and LD structures .................... 66 Figure 45. Aluminum plate used as the footing of the LC structure ............................................ 67 Figure 46. Aluminum plate used as the footing of the SC structure ............................................ 68 Figure 47. The masses bolted to the sides of the SC structure .................................................... 69 Figure 48. Assembly of the slow cyclic structures ........................................................................ 69

LIST OF TABLES Table 1. Atterberg limit test results on Yolo Loam (Ogul 2008 and Park 2011) ............................. 8 Table 2. Nevada sand properties, as reported by Rosebrook (2001) and CGM File Server ........... 9 Table 3. 1D consolidation test results on Yolo Loam.................................................................... 13 Table 4. Properties of the structures used in the slow cyclic test series...................................... 18 Table 5. Variation of the L/L c ratio and the shear strengths with the centrifugal acceleration... 19 Table 6. Natural Frequency and Period of the Fixed Base models............................................... 25 Table 7. 2 SDOF structures characteristics ................................................................................... 25 Table 8. Shake chronology in model scale. Note that the raw data file name indicates the date, starting time of slow data recordings, start time of fast data recording and RPM of the event. For example, shake 1 occurred on November 10, 2010, the slow data reading started at 10:29:49 AM and fast data recording was started at 11:49:29 AM at 55.2 RPM. ....................... 26 Table 9. Scale factors for different quantities .............................................................................. 27 Table 10. Instrumentation Nomenclature .................................................................................... 28 Table 11. Test calendar ................................................................................................................. 39 Table 12. Test chronology ............................................................................................................. 47 Table 13. Spin number 4, Dynamic SD and LD shaking................................................................. 50 Table 14. Spin number 5, BF2 ....................................................................................................... 52 Table 15. Spin number 6, SC2_Alum............................................................................................. 53 Table 16. Spin number 7, SC_Steel ............................................................................................... 54 Table 17. Spin number 8, BF3 ....................................................................................................... 56 Table 18. Spin number 9, BF4 ....................................................................................................... 57

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PURPOSE AND CONFIGURATION Rocking foundations have shown the advantages that may benefit the seismic performance of structures. Previous centrifuge tests have characterized the behavior of rocking foundations on sand, but fewer results are available for clayey ground. In this study a series of centrifuge model tests of shear walls and single-degree-of- freedom (SDOF) structures with rocking foundations supported on clay of medium strength are conducted. Test preparation, construction, and results from the model tests will be presented and discussed in this report. As the footing rocks, a gap is created between the footing and the soil surface (Figure 1), and the center of the footing will uplift a distance of -s (opposite direction of settlement). When the structure is unloaded, the gravity causes gap closure and thus provides a natural re-centering mechanism. The minimum value of Lc represents the minimum length of the footing required to support the vertical load when the soil bearing capacity is fully mobilized on the contact area. We can obtain Lc, using the conventional equations for limit bearing capacity (qult), where Lc=V/( qult* Bf). Figure 2 shows the gaps created at the edges of the rocking footing.

Figure 1. Schematic of a rocking footing

MAH01 test results provide us knowledge about this behavior and help us design our future experiments on clay more accurately.

Figure 2. Gap created during rocking of foundations

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In this report we will review the design, experiment and data analysis of the MAH01 test series. The test was completed at the Center for Geotechnical Modeling at the University of California at Davis, on the 9 meter radius centrifuge. The test series included 22 shaking events, 4 slow cyclic loading tests and 4 bearing failure tests at different centrifugal accelerations of 30 g, 60 g and 15 g. A plan view of the rigid container is presented in Figure 3. Figure 4 shows the schematic of the different trials ran in this experiment. All dimensions referenced in this report are in model scale units unless noted otherwise.

Figure 3. Detailed plan view of the test matrix of M AH01 (unit: mm, model scale)

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Figure 4. Schematic summary of different test series in M AH01 experiment (unit: mm, model scale)

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SOIL PROPERTIES Yolo Loam was obtained from a mound stored outside at the Center for Geotechnical Modeling. The weeds were cleared with a hand shovel from the surface and the ground was dug with a wheel loader. The soil was spread out on the pavement and left for a couple of days to dry out. The soil was processed by discarding the portion that was retained on a number 40 sieve and the finer fraction was stored in 55 gallon drums. 870 kg of processed soil was prepared to enable construction of models for both the MAH01 and MAH02 test series. Previous hydrometer test results by Park (2011) on Yolo Loam show that the processed Yolo Loam had 62% of the material finer than the 200 sieve (Figure 5).

Figure 5. Hydrometer test results on the Yolo Loam, Park (2011)

Atterberg limit tests were also performed on Yolo Loam and results are compared with previous results, obtained by other researchers in Table 1. Index Property LL (%) PL (%) PI (%)

MAH01 29.1 20.8 8.3

DongSoon Park 29 19 10

Doygun Ogul 30 18 12

Table 1. Atterberg limit test results on Yolo Loam (O gul 2008 and Park 2011)

Figure 7 summarizes the process of soil preparation. First a 20 mm thick layer of dense (Dr = 80 to 85%) Nevada Sand (properties shown in Table 2) was placed as a drainage layer on

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the bottom of the container. After this stage, we covered the sand surface with filter paper and saturated the sand. As shown in Figure 6 below, the sides of the container were also lined with Nevada Sand to create a drainage path. Then we were ready to add the mixed clay slurry into the container.

Figure 6. Layout of the soil in the rigid container

Soil Supplier/Manufacturer Classification Specific Gravity Mean Grain Size, D50 Coefficient of Uniformity, C u Maximum Void Ratio, emax Minimum Void Ratio, emin Dry Unit Weights, δd (kN/m3 )

Nevada Sand Gordon Sand Co., Compton, CA Uniform, Fine Sand; SP 2.67 2.67 0.17mm 0.15mm 2.0 2.07 < 0.887 0.887 < 0.511 < 0.511 < + 15.96 15.93 +

Table 2. Nevada sand properties, as reported by Rosebrook (2001) and CGM File Server

The water content of the slurry before consolidation was about 38%, which is approximately 1.3 times its liquid limit. The slurry used for the first lift consisted of 200 kg of Yolo Loam and 76 kg of water. The mix was then transferred to the container which gave us a 121 mm thick layer of slurry. The slurry was covered with a geofabric and then the steel consolidation plate of the hydraulic press was laid on the fabric. The clay specimen was consolidated in about 5 days and it experienced a total settlement of about 50 mm. For the 2nd lift, we mixed a total 235 kg of soil and 89 kg of water, resulting in a 135 mm thick slurry. The consolidation took about 7 days and the clay specimen experienced a settlement of 65 mm. The maximum consolidation pressure was 290.6 kPa, and the final thickness of the consolidated Yolo Loam was 141 mm. The pre-consolidation pressure comes from the hydraulic

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press load capacity (100,000 pounds), applied to the soil in the 1693 x 904 mm model container. The load is being transferred through a steel plate. Its weight is being neglected from the calculation of the applied load, as it is much smaller than the press capacity. It is important to characterize the strength of the consolidated Yolo Loam both under gravity and different centrifugal accelerations. As discussed and shown later, this is done using Bearing Failure tests for different centrifugal accelerations and using a Hand Shear Vane apparatus for gravity loading. After consolidation, we place the buried sensors into the soil. This was done by cutting the space required to dig the sensors in the model, using a cutting knife. Next, a very thin (3 mm) layer of Nevada sand was placed on top of the Yolo Loam to ensure that the surface is smooth and is ready for the foundations to be placed on top of it. The entire surface was then covered with additional 10 mm of Monterey 0/30 sand. The purpose of the surfacial sand layer was to limit the evaporation and desiccation of the clay, especially while it is exposed to the high winds in the centrifuge.

(a) Large hopper for dense sand

(b) Saturating the sand on the bottom

(c) Pouring mixed clay slowly into container (d) Smoothed surface

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(e) Filter paper on top of clay for drainage

(f) Geotech cloth on top of filter papers

(g) Consolidation under hydraulic press

(h) Consolidation under hydraulic press

(i) Consolidated model

(j) Buried sensors

(j) Shear vane test on the consolidated sample

(k) Finished buried sensors Figure 7. Soil specimen preparation

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1D-CONSOLIDATION TEST A 1D-consolidation test was performed to estimate the permeability, coefficient of consolidation and compression and recompression indices of the Yolo Loam. The basic setup of the 1D consolidation test is shown in Figures 8 and 9. The soil specimen is inside a stiff ring which is designed to resist its lateral expansion. On the top and the bottom of the soil specimen, we have two porous stone disks. Table 3 summarizes the results of the 1D consolidation test performed in the lab.

Figure 8. 1D consolidation test on Yolo Loam

Figure 9. Schematic of a 1D consolidometer

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Increment 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Seating Load Load Load Load Load Load Load Load Unload Unload Reload Reload Load

σ'vo

EOP Strain

(kPa) 3 6 12 24 48 80 140 200 280 140 48 140 280 400

(%) 0 1.6224 3.3244 5.4992 7.7479 9.4381 11.4924 12.7764 14.0146 13.8313 13.4682 13.7783 14.1708 15.4654

EOP e

0.786 0.754 0.721 0.678 0.634 0.601 0.561 0.536 0.512 0.515 0.522 0.516 0.509 0.483

Average Stress

mv

cm /s

(kPa)

(m /kN)

(cm/s)

0.0004 0.0016 0.0021 0.0033 0.0042 0.0013 0.0027 0.0009

4.5 9.0 18.0 36.0 64.0 110.0 170.0 240.0

0.0054 0.0028 0.0018 0.0009 0.0005 0.0003 0.0002 0.0002

2.1E-07 4.51E-07 3.8E-07 3.02E-07 2.19E-07 4.47E-08 5.57E-08 1.36E-08

0.0058

340.0

0.0001 6.16E-08

√t90

cv

(√min) 6.3 6.8 3.3 2.8 2.2 1.9 3.3 2.3 3.9

1.5

2

2

k

Table 3. 1D consolidation test results on Yolo Loam

Figure 10 below shows the compression curves obtained from

+

consolidation of the

specimen. The slope of the virgin compression curve is called the compression index and can be calculated as: C c 

 de dLog

'

 v

0.678  0.561  0.15 . The recompression index is the average 24 Log ( ) 140

slope of the unloading/reloading part of the e versus log σ 'v curve and can be calculated as: Cr  

0.522  0.509  0.0179 . These values compare reasonably to C c = 0.137 and Cr = 0.014 48 Log ( ) 280

for Yolo Loam reported by Park (2011).

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0.80 0.75

Void ratio, e

0.70 0.65 0.60 0.55 0.50 0.45 0.40 1

10

100 σ' vo (kPa)

1000

Figure 10. Compression curve of void ratio versus Log of vertical effective stress

UNDRAINED SHEAR STRENGTH OF THE CLAY SPECIMEN A hand operated laboratory shear vane was used to determine the strength of the clay at 1g, immediately after every spin of the centrifuge (Figure 11). The device was manufactured by Geotechnics Ltd. and the corresponding specimen manual was prepared by the New Zealand Geotechnical Society (2001). A summary of all the strengths can be found in Figure 12; measured strengths varied between 42 and 65 kPa.

Figure 11. Hand shear vane apparatus

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Su (kPa)

70 60 50 40 30 20 10 0

30 mm depth 50 mm depth 0

10

20

30

40

Elapsed Days after Consolidation (days) Figure 12.. Hand shear vane test results throughout the experiment

The undrained shear strength varies as we change the centrifugal acceleration and it is important to characterize this change. It is especially important to know the strength at shallower depths since our footing is sitting on the top surface of the clay layer. The most reliable measure of the undrained shear strength was obtained by performing a plate bearing test where a plate is pushed by an actuator into the clay to measure the bearing capacity while the sample was spinning. The length of the plate (111 mm) averaged the length of the footings (111 mm and 107 mm). The width of the designed plate had approximately the same size as length of contact during rocking of the foundations (20 mm). The loading protocol included pushes and pulls of the plate in intervals of 3 mm. This test was done under 30 g and 60 g in order to give us good estimates of the strength at the centrifugal accelerations used during shaking. Figure 13 below shows the results of the plate bearing tests (BF3 & BF4) under centrifugal accelerations of 30 g and 60 g, where the x-axis is the force measured by the load cell of the actuator and the y-axis is the vertical displacement of the plate measured by the feedback sensor in the actuator. In order to obtain the undrained shear strength at any desired depth, we can read the corresponding force required to push the plate to that depth and divide it by the area of the plate and by N c=π+2, the theoretical bearing capacity factor for strip footings. Therefore,

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Force Su 

 2 Plate Area

At the surface of the clay (zero settlement), the bearing loads of 792 N and 670 N were obtained, which corresponds to a bearing pressure of 360 kPa and 304 kPa. Therefore, Su = 70 kPa at 60 g and 59 kPa at 30 g.

Figure 13. Bearing Failure test results for a centrifugal acceleration of 60 g & 30 g

As will be shown in the next chapter, a centrifugal acceleration of 15 g was also tested during lateral slow cyclic and dynamic shaking trials. However, we did not perform any bearing failure tests under this centrifugal acceleration to have an estimate of the undrained shear strength. Instead, we will use the SHANSEP model to get this estimate. We start by calculating the OCR for the 60 g scenario, at a depth of 1cm. Since we have a shallow footing, we need to calculate the undrained shear strength at the shallower depths. For calculating the OCR, we consider a depth of 1 cm from the surface of the clay (1 cm on top of the water table). Therefore,

 v' .60g  [(1 cm *1900 OCR60 g

kg m kg m * 9.81 2 )  (1 cm *1000 3 * 9.81 2 )] * 60  17.1 kPa 3 m s m s

10 70 kPa ( ) ( ) 8  43.5 0.2* 'v.60 g 0.2*17.1 kPa

Su.1cm.60 g

10 8

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For the 60 g scenario, the pre-consolidation pressure is the pressure applied by the hydraulic pressure during the consolidation (290.6 kPa), while the current pressure remains to be the pressure from the centrifugal acceleration. As we move from 60 g to 15 g, the preconsolidation pressure remains to be 290.6 kPa while the current pressure at any desired depth comes from the centrifugal acceleration of 15 g. Therefore , the OCR of 15 g scenario should be four times the OCR of the 60 g case. Therefore,

OCR15g  OCR60g * 4  174



' v.15g



 v' .60g 4

 4.28 kPa

S u.15g  0.2 *  v' .15g * (OCR15g ) 0.8  53 kPa Therefore, Su = 53 kPa when the centrifugal acceleration is 15 g. The same procedure is repeated moving from 30 g to 15 g and it is found that the final undrained shear strength is in reasonable agreement with 53 kPa.

STRUCTURE PROPERTIES IN SLOW CYCLIC TEST The first 2 setups for slow cyclic tests did not provide useful data because of the problems with the data acquisition system. Only the results of the other two trials will be shown in this report. Within Tables 4 and 5 , the structure code qualitatively describes the experiment as follows: The first two letters specify the type of experiment (Slow Cyclic) being done on the footing (SC), Alum or Steel indicates that the structure was made of aluminum or steel. The full test chronology of the spins and loading events can be found in the Appendix A and the corresponding drawings can be found in Appendix D. An aluminum and a steel plate were used to simulate rigid columns in the slow cyclic tests as indicated in Figures 14 and 15 and their properties are summarized in Tables 4 and 5. The lateral loading was applied at the height indicated in Table 4. Steel blocks were bolted to the wall to increase the weight of the structure. Details of this design can be found in the Appendix F.

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Figure 14. Instrumented aluminum plate used for slow cyclic test

Tables 4 and 5 summarize the properties of all the structures tested during the slow cyclic test series.

Figure 15. Steel structure used during the SC_Steel experiment

Properties Footing Length (mm) Footing Width (mm) Footing Thickness (mm) Embedment (mm) Total Structure Mass (kg) Loading Height (mm) Structure Height (mm)

SC_Steel LC_Alum 111 107 111 176 9.525 9.525 0 0 6.375 3.11 205 200 476

476

Table 4. Properties of the structures used in the slow cyclic test series

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Derivation of L/Lc Ratios

N=30

SC_Alum N=60

N=15

SC_Steel N=30 N=60

Shear Strength Su (kPa)

60

70

53

60

70

Total Load Q (kN) = N * Mass * g

0.92

1.83

0.46

1.88

3.75

Bearing Capacity qul t (kPa) = (π+2) * Su

308.4

359.8

277.56

308.4

359.8

Contact Length L c (cm) = Q / (qul t * Width)

2.67

4.58

1.48

5.48

9.39

L / Lc

4.2

2.5

7.5

2.0

1.2

Table 5. Variation of the L/Lc ratio and the shear strengths with the centrifugal acceleration

The loading included 3 cycle packets of sinusoidal motions with gradually increasing amplitude as shown in Figure 16. Figure 17 shows the schematic of the forces and displacements where H represents the height of the actuator and the input displacement time history to the actuator was constructed as: D(t )  d * Sin (

2 t ) where d  H *  T

Figure 16. Displacement-Time history of the actuator used for the slow cyclic test series

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Figure 17. Outline of the displacement controlled slow cyclic structure

Tests were performed under different centrifugal accelerations. Figures 18 & 19 below summarize the Moment-Rotation and Settlement-Rotation behavior of the scenarios shown in Table 4. The rocking moment is normalized by VL/2 which represents the moment capacity on rigid base as the L/Lc ratio goes to infinity. Settlement has been normalized by the length of the footing (L) in the plane of shaking. For each plot, the calculated rocking moment capacity is shown as straight lines.

0

 0.5

 0.05

 0.5

0.05

 0.05

0

0

 0.02

 0.05

0

Rotation (Rad.)

0.05

0.5

0

 0.5

 0.05

0

0.05

0

0.05

0.02

0

 0.02

 0.04

1

1

0.05

0.02

Normalized Settlement (s/L)


0

1

0

0.02

 0.04

0.5


1

1

Normalized Moment [M/(V.L/2)]

Normalized Moment [(M/(V.L/2)]

Normalized Moment [(M/(V.L/2)]

0.5

SC_Alum, N=15, L/Lc = 7.5


SC_Alum, N=30, L/Lc = 4.2 1

 0.05

0

0.05

0

 0.02

 0.04

 0.05

Rotation (Rad.)

Rotation (rad.)

Figure 18. SC_Al test results under 30 g, 60 g and 15 g

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0

 0.5

 0.05

0.5

0

 0.5

1

0

1

1




0.5

1

SC_Steel, N=60, L/Lc = 1.2

SC_Steel, N=30, L/Lc = 2

1

0.05

 0.05

0

0.5

0

 0.5

1

0.05

 0.05

0

0.05

 0.05

0

0.05

0

 0.02

 0.04

 0.05

0

0.05




0.02 0

 0.05

 0.1

 0.05

0

0.05

0

 0.05

 0.1

Rotation (rad.)

Rotation (rad.)

Rotation (rad.)

Figure 19. SC_Al and SC-St results under 30 g and 60 g

DESIGN OF A ROCKING SHALLOW FOUNDATION Two Single Degree of Freedom (SDOF) structures were designed to have factors of safety, L/Lc, of 4 and 9 (based on an estimated undrained shear strength of 50 kPa). Each model was labeled with two letters. The first letter designates the footing size (S: small, L: Large), while the second designates the type of the test (D: Dynamic). Therefore, the footings are labeled as follows: SD Small footing, Dynamic test

LD Large footing, Dynamic test

The design included several trials where the input parameters were size of the footing, total load on the footing, height of the column and size of the cross-section of the column. The trial output parameters are the period of structure, base shear coefficient and the factor of safety of the structure (

L ). In order for the structure to rock, we had to design for a base shear Lc

coefficient of not greater than 0.4. The MathCAD sheets used to design the two SDOF systems are available in Appendix E. The struggle in the design comes from the fact that increasing the length of the footing will affect the factor of safety as well as the base shear coefficient. Also the height of the column will affect the period of the structure and the base shear coefficient. Due to

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the limitations of the rigid container, we only had a limited range to design the height of the column and length of the footing. The estimate of the undrained shear strength also played an important role in the design. Each structure was constructed of footing, aluminum rectangular tubing (column), and aluminum and steel square blocks to be used as a mass on top of the column. The shop drawings for each of these parts are provided in Figures 40 to 47.

Figure 20. 2 SDOFs being instrumented for dynamic shakes

Figures 20 and 21 show the assembly of the SDOF structures used during the dynamic shaking tests.

22

Figure 21. 2 SDOF structures used in the dynamic shaking (units: inch, model scale)

SDOF MODEL COLUMNS The column used for the smaller footing structure (SD) was constructed of 6063-Al tubing with outer dimensions of 50.8 mm (2”) by 50.8 mm (2”) and 3.175 mm (0.125”) thickness in model scale as shown in Error! Reference source not found. The total length of the column measured 155 mm (6.11”) to obtain a 149 mm (5.86“) height of center of gravity of the deck when fully constructed, measured from the bottom of the footing. The column for the larger footing structure was constructed of 6063-Al tubing with outer dimensions of 38.1 mm (1.5”) by 38.1 mm (1.5”) and 3.175 mm (0.125”) thickness in model scale as shown in Figure 40. The total length of the column measured 197 mm (7.76”) to obtain a 155 mm (6.1“) height of center of gravity of the deck when fully constructed, measured from the bottom of the footing.

23

SDOF MODEL FOOTINGS The smaller footing was designed in a square of length and width equal to 111 mm. The larger footing was designed with a length of 107 mm (4.21"), a width of 176 mm (6.93"). Both of the footings were made out of 6061-Al.

SDOF MODEL MASS A lumped mass of one 6061-Al square plate and two mild steel pieces were bolted to the top of the columns. For the smaller footing structure, we used a deck mass of 2.3 kg. The aluminum plate measured a square of length 92.9 mm (3.66") and a thickness of 25.4 mm (1"). The steel plates measured a square of 92.9 mm (3.66") with thicknesses of 15.87 mm (0.625") and 9.525 mm (0.375"). The aluminum piece was notched and fastened to the top of the column in the same fashion as the column/footing connection. The larger footing structure was designed with a smaller mass of 1.42 kg. The aluminum plate measured a square of length 72.9 mm (2.87") and a thickness of 25.4 mm (1"). The steel plates (2 plates) measured a square of 72.9 mm (2.87") with thicknesses of 15.87 mm (0.625") and 9.525 mm (0.375"). The aluminum piece was notched and fastened to the top of the column in the same fashion as the column/footing connection.

SDOF MODEL ASSEMBLY The base of the column was welded into a 6.35 mm (0.250”) deep slot in the footing, as shown in Figure 21 while the top of the column was welded into a 6.35 mm (0.250”) slot of the aluminum deck. The steel mass was then placed on top of the aluminum mass and finally the top steel plate was placed on the very top and secured at four locations with 5/16” bolts. Before testing these models, it was desirable to determine some structural properties of the constructed models. An assembled model was anchored to a rigid table and fitted with a ccelerometers at the deck’s center of gravity location. The deck was then hit gently with a hammer and the acceleration response was recorded. Table 6 summarizes the resulting fixed natural frequenc ies of the models.

24

SD S tructure Longitudinal Direction (Shaking Direction) Natural Frequency

Model Scale Prototype Scale

LD S tructure Longitudinal Direction (Shaking Direction) Natural Frequency

(Hz)

(Hz)

80.645 2.667

89.286 2.976

Table 6. Natural Frequency and Period of the Fixed Base models

Table 7 summarizes the structural properties of the two SDOF structures tested dynamically with the footings clamped to a heavy steel table.

Element

Properties

Deck

Mass (kg) Height (mm) Width (mm) Length (mm) Center of gravity from footing base (mm) Footing Length (mm) Footing Width (mm) Thickness (mm) Mass (kg) Embedment (mm) Total Height (mm) Height (mm) : Top of Footing to Base of Deck Thickness (mm) Width (mm) Length (mm) Mass (kg) Effective Icolumn_trans(mm4 ) Effective Icolumn_long(mm4 ) Transverse Stiffness, Kct (kN/m)

Footing

Column

Long Stiffness, Kcl(kN/m) Yield Moment, My_trans(N*m)

SD 2.3 50.8 92.9 92.9

LD 1.42 50.8 92.9 92.9

170.9

155

111.1 111.1 9.525 0.317 0 155.2

107 176 9.525 0.484 0 197.1

136

178

3.175 50.8 50.8 0.253 229658.94 229658.94

3.175 38.1 38.1 0.236 90915.13 90915.13

19172.82

3385.29

3EAl IT rans/H3

19172.82 Elastic

3385.29 Elastic

3EAl Ilong/H3

[wL3 /12] - [(w-2t)(L-2t)3 /12] [Lw3 /12] - [(L-2t)(w-2t)3 /12]

Table 7. 2 SDOF structures characteristics

The summary of the shakes along with their characteristics in model scale is summarized in Table 8. This table can be updated to prototype scale using the scaling laws (Kutter 1995).

25

Model Scale Event

Cent. Accel.

Motion and Amplification Peak-toFactor Peak - Base

(g)

PGA Base

PGV Base

Model Scale Peak-toPGA PGV Peak - Free Free Field Free Field Field

Raw Data File Name

(g)

(g)

(m/sec)

(g)

(g)

(m/sec)

1.273

0.688

0.023

1.966

1.008

0.031

11102010@102949@[email protected]

Shake 1

30

Step Wave - AF = 2.0

Shake 2

30


1.27

0.675

0.024

2.135

1.137

0.032


Shake 3

30


0.617

0.332

0.01

1.001

0.526

0.015


Shake 4

30

Morgan - AF = 0.2

7.164

3.645

0.106

14.209

7.186

0.157


Shake 5

30

Sfern - AF = 0.2

15.13

8.172

0.193

20.849

11.267

0.252


Shake 6

30

TCU - AF = 0.2

7.132

3.819

0.121

15.788

8.735

0.17


Shake 7

30


1.076

0.574

0.012

0.982

0.52

0.014


Shake 8

30

Gazli-0.2

7.065

3.962

0.095

12.432

6.872

0.123


Shake 9

30

Sfern-0.4

34.539

17.524

0.380

34.890

19.443

0.508


Shake 10

30

Gazli-0.6

33.436

17.418

0.315

48.878

25.881

0.549


Shake 11

60

Gazli-1.5

70.152

38.428

0.683

72.009

36.533

0.985


Shake 12

60

Sfern-1.0

65.140

36.188

0.762

68.714

36.902

0.985


Shake 13

15


0.677

0.375

0.002

0.097

0.052

0.002


Shake 14

15

Sfern-0.2

13.393

6.979

0.210

18.445

10.449

0.301


Shake 15

15

Gazli-0.3,

14.531

7.971

0.163

24.273

12.632

0.290


Shake 16

15

Sfern-0.4

33.152

16.734

0.403

36.940

21.243

0.650


Shake 17

15

Gazli-0.6

37.925

19.250

0.336

37.680

19.939

0.534


Shake 18

30

Sine Wave-1.1, freq=71Hz

2.242

1.149

0.026

3.803

2.104

0.042


Shake 19

30

Sine Wave-1.0, freq =175Hz

1.172

0.644

0.016

2.143

1.171

0.023


Shake 20

30

Gazli-0.4

21.246

11.436

0.207

28.060

15.135

0.354


Shake 21

30

Sfern-0.4

33.432

16.737

0.368

39.592

21.085

0.599


Shake 22

30

Gazli-0.6

33.375

17.516

0.308

41.820

21.173

0.504


Table 8. Shake chronology in model scale. Note that the raw data file name indicates the date, starting time of slow data recordings, start time of fast data recording and RPM of the event. For example, shake 1 occurred on November 10, 2010, the slow data reading started at 10:29:49 AM and fast data recording was started at 11:49:29 AM at 55.2 RPM .

26

SCALE FACTORS Imagine a 1 m soil profile which is being subjected to a centrifugal acceleration of 30g. The pressure and stresses are increase by a factor of 30 and as a result, the vertical stresses at the bottom of the container matches the vertical stress at a depth of 30 m below the ground surface, or in other words the 1m soil in model scale, matches 30 m of soil in prototype scale. The purpose of a centrifuge test is to subject the model structures to the stresses they feel in prototype scale, or in other words:

* 

 mod el  1 where the asterisk on the quantity means the scaling factor for that quantity.  Pr ototype As we increase the gravity in a centrifuge by a scaling factor of N, we scale down the

length of our model by a factor of N, or:

a* 

a mod el L 1  N and L*  mod el  a Pr ototype LPr ototype N The same procedure can be followed to obtain the scaling factors of different quantities

such as velocity, force, mass and any other quantity. Table 9 summarizes the scaling factors for some of the important quantities measured in a centrifuge experiment. MAH01, were performed at the 9- m-radius centrifuge at various centrifugal accelerations. The scaling laws for centrifuge tests were described by Kutter (1995). Centrifuge g- level Time Displacement, Length Acceleration, Gravity Moment SCALE Moment of area Velocity Pressure, Stress Pore Fluid Viscosity

N 1/N 1/N N 1/N 3 1/N 4 1 1 10/N

Table 9. Scale factors for different quantities

27

INSTRUMENTATION AND MEASUREMENTS Sensors The following table summarizes the instrumentation nomenclature used throughout testing and analysis (Table 10). By implementing this system, each instrument is given a specific alphanumeric cluster which defines the element measured, sub-element measured, global orientation, type of measurement, global/local location, and position in an instrument array. The Sub-Element, Global Orientation, Global Location, and Tag Number categories are optional and only used when needed to differentiate between certain instruments. Element & Test G = Ground B= Base/Container SC = Small Cyclic LC: Large Cyclic SD: Small Dynamic LD: Large Dynamic

1) 2) 3) 4) 5) 6)

Sub-Element

D = Deck F = Footing G= + Footing/Soil Interface (Ground)

Global Orientation

V = Vertical + H= Horizontal

Measurement Type

+

LP = Displacement Ac = Accelerat ion (PCBs) MM = Accelerat ion (MEMs) LC = Load Cell LVDT: Feedback

Global/Local XY-Location

N = No rth S = South + E = East W = West

Tag No. 1 2 3 + . . . etc.

Element (G, B, SC, LC, SD, LD) Sub-Element (D, F, G) Global Orientation (H, V) Measurement (Ac, LP, MM) Global/Local XY-Location (N, S, E, W) Tag Number (1, 2, 3,…, etc.) Table 10. Instrumentation Nomenclature

Linear Potentiometers (LPs) were used to measure displacements of the deck and footing of each structure, as well as free field settlement of the soil. An instrument rack was designed to hold the body of the LP during testing. Piezoelectric accelerometers (supplied by PCB) were bolted to factory- made metal discs, which were then glued to the structures. The soil was also instrumented with arrays of vertical and horizontal accelerometers to capture dynamic soil accelerations at variable depths. Two PCBs were placed on the NE and NW outside corner of the container (measuring in the shaking direction) to determine the base motion for each shake. A second type of accelerometer (MEMS, MicroElectroMechanical System) was used on the footings measures dynamic and DC signals. The difference between the initial and final constant acceleration measured by the MEMS accelerometers can be interpreted to provide 28

information regarding the residual tilt of the structure in the g- field; it acts as an inclinometer. The soil was also instrumented with Pore Pressure Transducers (PPT) at variable depths. Figure 22 shows the buried accelerometers in to the soil and the instrume nted SDOF models. Figure 23 summarizes all the sensors buried into the soil profile and their corresponding locations. Figure 24 shows the outline of the instrumented slow cyclic structures and Figures 25 & 26 summarize the instrumentation of the 2 SDOFs used for dynamic shaking part of our experiment.

(a)

(b) Figure 22. Instrumentation Rack and the buried sensors into the clay

Figure 23. Outline of all the buried sensors in the soil profile and on the container

29

Figure 24. Instrumented slow cyclic structures, connected to the actuator

30

Figure 25. Instrumentation of the SD structure

31

Figure 26. Instrumentation of the LD structure

In total, 28 LPs, 28 PCBs, 8 MEMs and 5 PPTs were used for various measurements in the dynamic shaking test. Pictures of these instruments are shown in Figure 27, the sensor placement for each SDOF structure is shown in Figures 25 and 26, and a summary of the type, measurement, and orientation of instruments used for each specimen is summarized in Tables 13 to 18.

PCB Accelerometer

MEMs Accelerometer

Linear Potentiometer

32

Analog Camera

High-Speed Video Camera Figure 27. Different type of sensors and cameras typically used in a centrifuge model

Video During the dynamic shakes a total of two High Speed (HS) and four Analog (AG) cameras were used. For the slow cyclic tests, four analog cameras were used to capture the behavior of the structure and footing during the rocking of the foundation. Video from selected events is archived at NEEShub (Kutter et al. 2011) The high speed video used during dynamic shaking events recorded a maximum of 20 seconds at 200 frames/second (fps), capturing video of the LD and SD structures. Additionally, three analog cameras were placed to inspect the entire container, consisting of a North end view, South end view, and Plan view. Since the analog cameras capture frames as such a low speed (1 fps), this data was most useful for monitoring residual positions of models, sensors, and water levels after each event. Figure 28 shows the analog and digital cameras used during the testing of the SDOF structures. The green lines (labeled as cross-beam) show the configuration of the beams supporting these cameras.

33

Figure 28. Outline of the location of the high speed and analog cameras used during the dynamic shaking

KNOWN LIMITATIONS The integrated displacement and measured displacement sometimes do not match each other very well. Figure 29 shows the comparison of two footing rotation time histories. One history is from the double integration of vertical accelerometers on the footing, and the other is directly from the vertical displacement transducers on the footing. LP records predict the permanent displacement reasonably well. However they do not provide us with accurate readings during the high frequency part of the motion. They also go out of range sometimes and are not able to match the accelerometer data on the peaks. Figure 29 also shows that at a time about 1.36 and at 1.43 seconds, the LP data do not follow the accelerometer. A likely explanation for the difference is that the LP rods sometimes bounce around and lose contact with the object they are supposed to measure. Also there seems to be a small phase lag in the LP records which were delayed by approximately 0.002 seconds in model scale, or 0.06 seconds in prototype scale.

34

Ftg Rotation (rad)

0.01 3

510

0 3

 510

Accelerometer LP

 0.01 1.3

1.35

1.4

1.45

Time (sec) Figure 29. Footing rotation from vertical accelerometer integration versus LP readings

ORGANIZATION OF DATA F ILES AND PLOTS All the data files recorded during the testing have been archived in the NEEShub website at neeshub.org under a project named "Design of soil and structure compatible yielding to improve system performance". Table 11 presents the test calendar based on the spin name, date and the centrifugal accelerations for each spin. Table 11 presents the event description, sample rate, amplitude of earthquake motions, raw data files and comments pertaining to each event. The column labeled "Raw Data File" lists all the ResDAQ data files stored in the date archive. A ResDAQ data file is usually named in a standard format “date @ initialization time @ recording time @ rpm reading.txt". Tables 13-18 present all the sensor channel gain lists (CGLs) used for the static, dynamic and bearing failure test events. They specify which instruments’ outputs, and in what order, would be recorded for a particular event. The meaning of the column headings in the SensorChannel-Gain lists deserve some explanation. “Group” describes the location of the sensor with respect to the container. For example “Soil” means that the sensor is buried into the ground, or “LD” means that the sensor is attached to the LD structure. “Label” provides us a simplified version of the location and quantity of the sensor. Table 10 provides a detailed explanation of the instrumentation nomenclature. “Instrument Type” describes the type of the sensor. For example “acc” refers to accelerometer or “ppt” refers to pore pressure transducer. “Location description” gives a detailed explanation of the location of the sensor. “Range” and “Unit” describe the maximum capacity of the sensor. The “X”, “Y” and “Z” describe the coordinates of the sensor. For buried accelerometers, the global reference is used which is the Bottom North East of the

35

box. For all the other accelerometers (connected to structures), local coordinate system is used which its origin is the Bottom North East of the structure's corresponding footing. “Calibration” provides us with the factor which converts the raw data recorded by the DAQ (in voltage) to engineering units. “Unit” describes the orientation of the sensor with respect to the global coordinate system. For example, a horizontal accelerometer with a unit vector of +1 means that the sensor was placed in the orientation of the positive x-axis, or in other words, the tip of the accelerometer aims in the positive direction. For PPTs, a unit vector of +1 means that the plastic tip of the sensor is aiming to the positive direction. “Channel” specifies the amplifier bank and the channel name used by the DAQ to store the data for each sensor. For example PCB1- 2 is the second channel of the first PCB amplifier bank. The slow cyclic raw data files used for analysis and uploaded to the project's web site are being down-sampled by 10 times since the sampling frequency was set very small which would make the data processing slow. sensor. Nine appendices are attached to the report. Appendix A is the test calendar and the detailed test chronology which summarizes the details of each spin. Appendix B shows the detailed instrumentation list for all the spins. Appendix C shows the detailed location of the structures used in each spin and provides us with plan and profile view of the structures in the container for each spin. Appendix D presents all the shop drawings provided to the manufact urer (Langill's General Machine, Inc.) and the structural properties. Appendix E provides us the MathCAD sheet used to design the two SDOF structures tested in this experiment (SD and LD structures). Appendix F summarizes the design for the masses that were bolted to the slow cyclic structures to make them equal weight with the SDOF structures. Appendix G plots the critical plots for the important shakes and Appendix H presents the MathCAD sheet used to process all the sensor data and gives us plots of all the sensors used in a selected shaking event. This data report presents processed plots of data from selected sensors for every significant event. For one of the large shaking events, data is presented from all of the sensors. The data presented in Appendix G includes the plots from the accelerometers capturing the container acceleration and the propagation of the input acceleration through the soil profile. It also includes the Moment-Rotation and Settlement-Rotation behavior of the SDOF structures. These plots have been obtained by combining the data from the accelerometers and linear potentiometers (LP). Displacement of the footing is being calculated using both the

36

accelerometers and linear potentiometers mounted on the footing. Double integration of the accelerometer data provides us the high frequency response of the structure while the LP data gives us the residual and low frequency response.

REFERENCES Centrifuge Modeling Center (CGM) filer server, http://cgmfileserver.ucdavis.edu/binders/ Deng, L., Kutter, B. L., and Kunnath, S. (2011). “Centrifuge modeling of bridge systems designed for rocking foundations.” J. Geotech. Geoenviron. Engrg., 10.1061/(ASCE)GT.1943-5606.0000605 (25 July 2011). Deng, L., Kutter, B. L. (2010b), “Seismic Performance of Bridge Systems with Rocking Foundations: Centrifgue Data Report for LJD03”, UCD/CGMDR-10/01. Davis, CA: University of California. Deng, L., Algie, T., Kutter, B. L. (2009a), “Innovative Economical Foundations with Improved Performance that is Less Sensitive to Site Conditions: Centrifuge Data Report for LJD01”, UCD/CGMDR-09/01. Davis, CA: University of California. http://webshare.cgm.ucdavis.edu/LJD01. Deng, L., Algie, T., Kutter, B. L. (2009b), “Seismic Performance of Bridge Systems with Rocking Foundations: Centrifuge Data Report for LJD02”, UCD/CGMDR-09/02. Davis, CA: University of California. http://webshare.cgm.ucdavis.edu/LJD02. Doygun, O. (2009). “Monotonic and cyclic undrained loading behavior of intermediate soils. ” MS Thesis, University of California, Davis. Gajan S, Kutter BL, Phalen JD, Hutchinson TC, Martin GR. (2005), “Centrifuge modeling of load-deformation behavior of rocking shallow foundations,” Soil Dynamics and Earthquake Engineering 2005; 25: 773–783. DOI: 10.1016/j.soildyn.2004.11.019. Gajan, S., Phalen, J.D. and Kutter, B.L. (2003). “Soil-Foundation-Structure Interaction: Shallow Foundations Centrifuge Data Report for SSG02,” University of California, Davis, Center for Geotechnical Modeling, Report No. UCD/CGMDR-03/01. Gajan, S. (2006). “Physical and Numerical Modeling of Nonlinear Cyclic Load - Deformation Behavior of Shallow Foundations Supporting Rocking Shear Walls”, Ph.D. dissertation, University of California, Davis. Hakhamaneshi, M., Kutter, B.L., Deng, L., Hutchinson, T.C., Liu, W. (2011) “New findings from centrifuge modeling of rocking shallow foundations in clayey ground.” ASCE 2012 Geo-Congress (submitted for publication)

37

Kutter et al. (2011). “NEES-CR Design of soil and structure compatible yielding to improve system performance” , NEES Consortium Data Archives, http://nees.org/warehouse/project/732 Kutter, B.L (1995). “Recent advances in centrifuge modeling of seismic shaking.” Proc. 3rd Intl. Conf. on Recent Advances in Geotech. Earthq. Engrg. Soil Dyn ., University of Missouri, Rolla, MO, Vol.2, 927-942. New Zealand Geotechnical Society Guidelines for Hand Held Shear Vane Test August 2011. http://www.nzgs.org/wp-content/uploads/shear_vane_guidelines.pdf Park, D.S. (2011). “Strength loss and softening of sensitive clay slopes.” Ph.D Thesis, University of California, Davis. (In Review) Rosebrook, K.R. (2001), “Moment Loading on Shallow Foundations: Centrifuge Test Data Archives,” MS Thesis, University of California, Davis. Rosebrook, K.R. and Kutter, B.L. (2001a). “Soil-Foundation-Structure Interaction: Shallow Foundations Centrifuge Data Report for KRR01,” University of California, Davis, Center for Geotechnical Modeling, Report No. UCD/CGMDR-01/09. Rosebrook, K.R. Shallow California, 01/10.

and Kutter, B.L. (2001b). “Soil-Foundation-Structure Interaction: Foundations Centrifuge Data Report for KRR02,” University of Davis, Center for Geotechnical Modeling, Report No. UCD/CGMDR-

Rosebrook, K.R. and Kutter, B.L. (2001c). “Soil-Foundation-Structure Interaction: Shallow Foundations Centrifuge Data Report for KRR03,” University of California, Davis, Center for Geotechnical Modeling, Report No. UCD/CGMDR-01/11.

38

APPENDIX A: CENTRIFUGE TEST CHRONOLOGY AND CALENDER

Spin No.

Label

1

SC_Al_1

2

LC_Al

3

BF1

4

SD, LD

5

BF2

6

SC_Al_2

7

SC_St_1

8 9

BF3 BF4

Events Slow Cyclic Test, DAQ problem, NO DATA, Small Footing Slow Cyclic Test, DAQ problem, NO DATA, Large Footing Bearing Failure 1 SDOF Dynamic Tests on Small and Large Footings Bearing Failure 2 Slow Cyclic Test on Aluminum Structure, Small Footing Slow Cyclic Test on Steel Structure, Small Footing Bearing Failure 3 Bearing Failure 4

Label Description

Initial glevel

Up to

Down to

Final glevel

Date

Small Cyclic_Aluminum

30

60

15

30

11/1/2010

Large Cyclic_Aluminum

30

60

15

30

11/4/2010

Bearing Failure 1 Small Dynamic, Large Dynamic Bearing Failure 2

30 30

11/5/2010 60

15

30

30

11/10/2010 11/22/2010

Small Cyclic_Aluminum

30

60

15

30

11/24/2010

Small Cyclic_Steel

30

60

--

--

12/1/2010

Bearing Failure 3 Bearing Failure 4

30 60

---

---

---

12/2/2010 12/2/2010

Table 11. Test calendar

39

Motion or S ine Wave Amplitude

S ample Rate (Hz)

Raw Data File

CGL File

Spin-up

11012010@113016

SC_1_Alum

11:39AM

Reach 30g

11012010@113016

4:09PM

SC1_30-01

4:11PM

SC1_30-02

4:12PM

SC1_30-03

4:14PM

SC1_30-04

4:17PM

SC1_30-05

4:18PM

SC1_30-06

4:25PM

Spin Down

5:18PM

11012010@113016

11:21AM

Stop Slow Data Spin-up

11:37AM

Reach 60g

11022010@112122

1:43PM

SC1_60-01

0.009 / 3 Cycles


1:48PM

SC1_60-02

0.0225 / 3 Cycles


1:49PM

SC1_60-03

0.045 / 3 Cycles


1:51PM

SC1_60-04

1:53PM

SC1_60-05

1:55PM

SC60-06

1:58PM

SC60-07

2:01PM 2:17PM

Spin Down to 15g Reach 15g

2:18PM

SC1_15-01

2:20PM

SC1_15-02

2:21PM

SC1_15-03

2:23PM

SC1_15-04

2:24PM 2:26PM

0.0225 / 3 Cycles


0.045 / 3 Cycles


0.09


/ 3 Cycles

0.175 / 3 Cycles

4096

glevel

30

S tation

Spin 1, North East Corner


0.35

/ 3 Cycles


0.50

/ 3 Cycles

11012010@113016@[email protected] 11012010@113016

11022010@112122

0.09 / 3 Cycles


0.175 / 3 Cycles


0.35 / 3 Cycles


0.5 / 3 Cycles


4096

60

11:30AM

S tructure

Spin 1, North East Corner

Event

SC_Aluminum_Weight = 3.11kg

Time

SC_Aluminum_Weigh t = 3.11kg

SC_1_Alum

11022010@112122 11022010@112122

0.009 / 3 Cycles


0.0225 / 3 Cycles


0.045 / 3 Cycles


0.09 / 3 Cycles


SC1_15-05

0.175 / 3 Cycles


SC1_15-06

0.35 / 3 Cycles


15

MAH-01

Test

MAH-01

11/2/2010

11/1/2010

Date

40

2:27PM

SC1_15-07

2:28PM

Spin Up to 30g Reach 30g

2:33PM 2:35PM 2:36PM 2:38PM 2:39PM 2:40PM 2:42PM 2:48PM

Stop Slow Data

Time

Event

3:10PM

0.009 / 3 Cycles


0.0225 / 3 Cycles


0.045 / 3 Cycles


0.09 / 3 Cycles


0.175 / 3 Cycles


0.35 / 3 Cycles


0.5 / 3 Cycles

11022010@112122@[email protected] 11022010@112122 11022010@112122

CGL File

Spin-up

11042010@145420

LC_1-Alum

3:22PM

Reach 30g

11042010@145420

4:29PM

LC1_30-01

4:39PM

LC1_30-02

4:49PM

LC1_30-03

4:52PM

LC1_30-04

4:54PM

LC1_30-05

4:57PM

LC1_30-06

5:06PM

LC1_30-07

5:08PM



S ample Rate (Hz)

0.009 / 3 Cycles


0.0225 / 3 Cycles


0.045 / 3 Cycles


0.09 / 3 Cycles


0.175 / 3 Cycles

4096

30

glevel


0.35 / 3 Cycles


0.5 / 3 Cycles

11042010@145420@[email protected] 11042010@145420

60

S tation

Spin 2, North West Corner

Raw Data File

5:20PM

S tructure

LC_Aluminum_Weight = 3.11kg

Test

MAH-01

11/4/2010

Date

11022010@112122

SC1_30_201 SC1_30_202 SC1_30_203 SC1_30_204 SC1_30_205 SC1_30_206 SC1_30_207 Spin-Down

3:29PM

11022010@112122@[email protected] 11022010@112122

30

2:31PM

0.5 / 3 Cycles

11042010@145420

41

5:23PM

LC1_60-01

0.009 / 3 Cycles


5:24PM

LC1_60-02

0.0225 / 3 Cycles


5:25PM

LC1_60-03

0.045 / 3 Cycles


5:27PM

LC1_60-04

0.09 / 3 Cycles


5:29PM

LC1_60-05

0.175 / 3 Cycles


5:30PM

LC1_60-06

0.35 / 3 Cycles


5:31PM

LC1_60-07

0.5 / 3 Cycles


5:33PM 5:47PM


5:50PM

LC1_15-01

0.009 / 3 Cycles


5:52PM

LC1_15-02

0.0225 / 3 Cycles


5:53PM

LC1_15-03

0.045 / 3 Cycles


5:54PM

LC1_15-04

0.09 / 3 Cycles


6:23PM

LC1_15-05

0.175 / 3 Cycles


6:25PM

LC1_15-06

0.35 / 3 Cycles


6:26PM

LC1_15-07

0.5 / 3 Cycles


6:29PM


6:37PM 6:39PM 6:42PM 6:44PM 6:47PM 6:49PM 6:51PM 6:53PM

LC_30_201 LC_30_202 LC_30_203 LC_30_204 LC_30_205 LC_30_206 LC_30_207 Spin-Down

15

11042010@145420

11042010@145420 11042010@145420

30

6:34PM

11042010@145420

0.009 / 3 Cycles


0.0225 / 3 Cycles


0.045 / 3 Cycles


0.09 / 3 Cycles


0.175 / 3 Cycles


0.35 / 3 Cycles


0.5 / 3 Cycles

11042010@145420@[email protected] 11042010@145420

42

Spin Up

1:57PM

Reach 30g

3:03PM

Push & Pull

4:05PM

Spin-Down

4:52PM

Stop Slow Data

Time

Event

8:43AM

S tructure

S tation

S tation

glevel


S ample Rate (Hz)

Raw Data File

CGL File

4096

11052010@133059

BF_Final

11052010@133059 30

1:45PM

S tructure

Spin 3, Mid North Corner

Event

BF 1

Time

11042010@145420

3mm Increments

11052010@143353@[email protected] 11052010@133059 11052010@133059

Raw Data File

CGL File

Pre-Shake


Dynamic_Final

10:40AM

Start Spin

11102010@102949

10:52AM

Reach 30g

11102010@102949

11:49AM

Shake1

12:42PM

Shake2

1:20PM

Spin Down

Spin 4, Middle East and West Corner

glevel


S ample Rate

Step wave AF=2.0


Step wave AF=2.0

11102010@102949@[email protected] 11102010@102949

Start Spin

2:40PM

Reach 30g

11162010@142732

3:32PM

Shake3

4:30PM

Shake4

5:06PM

Shake5

6:15PM

Shake6

6:20PM

Spin-Down

11:38AM

Start Spin

11172010@113712

11:50AM

Reach 30g

11172010@113712

12:21PM

Shake7

Step wave AF=1.0

4096

2:27PM

30

MAH01 Trial 3 30g

11.16.2010 11.17.2010

Stop Slow Data

SD, LD

Test

11/10.2010

Date

Test

MAH01

11/5/2010

Date

7:35PM

11162010@142732 11162010@142732@[email protected]

M organ AF=0.2


Sfern AF=0.2


TCU AF=0.2

11162010@142732@[email protected] 11162010@142732

Step Wave


43

Gazli AF=0.2


Shake9

Sfern AF=0.4


1:37PM

Shake10

Gazli AF=0.6


1:48PM

Spin-Down

11172010@113712

2:47PM

11172010@113712

3:08PM

Stop Slow Data Start Spin

11172010@150844

3:24PM

Reach 60g

11172010@150844

3:50PM 4:20PM 4:25PM

Shake11 Shake12 Spin-Down

5:15PM

2:08PM

Stop Slow Data Spin Up to 15g Reach 15g

2:39PM 3:04PM 3:16PM 3:27PM

Shake13 Shake14 Shake15 Shake16

3:41PM 3:52PM

11172010@150844@[email protected] 11172010@150844@[email protected] 11172010@150844 11172010@150844 [email protected] [email protected] 11182010@135259@[email protected] 11182010@135259@[email protected] 11182010@135259@[email protected] 11182010@135259@[email protected]

Gazli AF=0.6

11182010@135259@[email protected] [email protected]

4:15PM 4:25PM

Shake17 Spin Up to 30g Shake18 Shake19

Sine Wave Sine Wave

11182010@135259@[email protected] 11182010@135259@[email protected]

4:35PM

Shake20

Gazli AF=0.4


4:45PM

Shake21

Sfern AF=0.4


4:57PM 5:00PM

Shake22 Spin-Down

Gazli AF=0.6

11182010@135259@[email protected] [email protected]

Time

Event

2:16PM 2:25PM 2:33PM

Spin Up Reach 30g Push & Pull

S tructure

S tation

glevel


3mm Increments

S ample Rate (Hz) 4096

15

Step Wave =0.5AF Sfern AF=0.2 Gazli AF=0.3 Sfern AF=0.4

30

MAH01 Test

Gazli AF=1.5 Sfern AF=1.0

30

11/22/201 0

Date

MAH01

11/18/2010

2:02PM

60

Shake8

1:10PM

BF2

MAH01

11.17.2010

12:37PM

Raw Data File

CGL File

11222010@141040 11222010@141040 11222010@141040@[email protected]

BF_Final

44

Spin-Down Stop Slow Data

11222010@141040 11222010@141040

Time

Event

8:36AM

Spin-up

8:58AM

SC2_30-01

0.0225 / 3 Cycles


9:01AM

SC2_30-02

0.045 / 3 Cycles


9:05AM

SC2_30-03

0.09 / 3 Cycles


9:08AM

SC2_30-04

0.175 / 3 Cycles


9:24AM

SC2_30-05

0.35 / 3 Cycles


9:26AM

SC2_30-06

0.5 / 3 Cycles


9:27AM 9:33AM

Spin U to 60g Reach 60g

9:40AM

SC2_60-01

9:41AM

SC2_60-02

9:43AM

SC2_60-03

9:45AM

SC2_60-04

9:47AM

SC2_60-05

9:50AM

SC2_60-06

9:53AM 10:00AM


10:02AM

SC2_15-01

0.0225 / 3 Cycles


10:04AM

SC2_15-02

0.045 / 3 Cycles


10:08AM

SC2_15-03

0.09 / 3 Cycles


10:10AM

SC2_15-04

0.175 / 3 Cycles


10:12AM

SC2_15-05

0.35 / 3 Cycles


10:14AM

SC2_15-06

0.5 / 3 Cycles


10:15AM

Spin Up to

S tation

glevel

30

S tructure


S ample Rate (Hz)

Raw Data File

CGL File

[email protected]

SC_2_Alum

[email protected]

0.0225 / 3 Cycles


0.045 / 3 Cycles


0.09 / 3 Cycles


0.175 / 3 Cycles

4096

60

[email protected]


0.35 / 3 Cycles


0.5 / 3 Cycles

11242010@082432@[email protected] [email protected] [email protected]

15

Spin 6, Middle East Corner

SC_Aluminum_Weight = 3.11 kg

Test

MAH-01

11/24/2010

Date

2:58PM 3:46PM

[email protected]

45

30g Reach 30g

10:32AM

SC2_30_201 SC2_30_202 SC2_30_203 SC2_30_204 SC2_30_205 SC2_30_206 Spin-Down

10:33AM 10:35AM 10:37AM 10:45AM 10:47AM 10:51AM

Stop Slow Data

Time

Event

2:08PM

0.0225 / 3 Cycles


0.045 / 3 Cycles


0.09 / 3 Cycles


0.175 / 3 Cycles


0.35 / 3 Cycles


0.5 / 3 Cycles

11242010@082432@[email protected] [email protected] [email protected]

12012010@140246

SC_Steel_Final

2:22PM

Reach 30g

12012010@140246

2:41PM

SC3_30-01

0.0225 / 3 Cycles


2:44PM

SC3_30-02

0.045 / 3 Cycles


2:46PM

SC3_30-03

0.09 / 3 Cycles


2:48PM

SC3_30-04

0.175 / 3 Cycles


2:51PM

SC3_30-05

0.35 / 3 Cycles


2:54PM

SC3_30-06

0.5 / 3 Cycles


2:56PM

Spin Down

3:34PM

Stop Slow Data Start Spin

4:35PM

SC3_60_02

S ample Rate (Hz)

12012010@140246 12012010@140246 [email protected] [email protected]

60

Reach 60g SC3_60_01


4096

Start Spin

4:34PM

glevel

30

CGL File

4:23PM

S tation

Spin 7, Mid South East Corner

Raw Data File

4:14PM

S tructure

SC_Steel_Weight = 6.375 kg

Test

MAH-01

12/1/2010

Date

11:38AM

[email protected]

30

10:20AM

0.0225 / 3 Cycles


0.045 / 3 Cycles


46

SC3_60_03

0.09 / 3 Cycles


4:38PM

SC3_60_04

0.175 / 3 Cycles


4:39PM

SC3_60_05

0.35 / 3 Cycles


4:40PM

SC3_60_06

0.5 / 3 Cycles


4:43PM

Spin-Down

[email protected]

5:22PM

Stop Slow Data

[email protected]

Time

Event

1:25PM

Spin Up

1:38PM

Reach 30g

2:22PM

Push & Pull

2:35PM

Spin-Down

3:18PM 3:40PM

Stop Slow Data Spin Up

3:51PM

Reach 60g

4:06PM

Push & Pull

4:14PM

Spin-Down

4:56PM

Stop Slow Data

glevel


S ample Rate (Hz)

Raw Data File

CGL File

12022010@132058

BF_Final

30

12022010@132058 3mm Increments

12022010@132058@[email protected] 12022010@132058 4096

12022010@132058 12022010@154035

BF_Final

12022010@154035 60

Spin 8, South West Corner

S tation

Spin 9, South East Corner

BF3

S tructure

BF4

Test

MAH01

12/2/2010

Date

4:36PM

3mm Increments

12022010@154035@[email protected] 12022010@154035 12022010@154035

Table 12. Test chronology

47

APPENDIX B: INSTRUMENTATION LIST 1. Spin 1 CGL File (SC_1_Alum Structure) The CGL file is not being shown since the DAQ did not function properly and the data recorded is invalid. 2. Spin 2 CGL File (LC1). The CGL file is not being shown since the DAQ did not function properly and the data recorded is invalid. 3. Spin 3 CGL File (BF_Final) The CGL file is not being shown since the DAQ did not function properly and the data recorded is invalid. 4. Spin 4 CGL File (Dynamic Shaking) Group

Label

Sensor Type

Location Description

Rang e

Unit

X(m)

Y(m)

Z(m)

Gain

Exc. Voltage

BASE

BE

acc

NE side of box, X horizontal

100

g

0

0.78

0

1

1

19.08

BASE

BW

acc

NW side of box, X horizontal

100

g

0

0

0

1

1

100

g

-0.011

0.085

0

1

100

g

-0.011

0

0

50

g

0.2

0.452

100

g

0.2

100

g

100

Frame

FBE

acc

Frame

FBW

acc

Soil

GAV1

acc

Soil

GAH3

acc

Soil

GAH4

acc

Soil

GAH5

acc

Soil

GAH6

acc

Soil

GAH7

acc

NE side of frame, X horizontal NW side of frame, X horizontal North M iddle, Free Field, Just at the surface of top of the clay North M iddle, Free Field, Just at the top surface of top of clay W-E W M iddle, X horizontal, M id. Top of the 2nd Clay Layer E M iddle, X Horizontal, M id. Top of 2nd Clay Layer M iddle, Free field, X horizontal, M id Top of 2nd Clay Layer M iddle, Free field, X horizontal,M id of 2nd Clay Layer

Calibration

Unit

Channel

g/V

1

PCB1-1

19.16

g/V

1

PCB1-2

1

19.88

g/V

1

PCB1-3

1

1

19.27

g/V

1

PCB1-4

0.145

1

1

20.00

g/V

1

PCB1-5

0.452

0.145

1

1

20.33

g/V

1

PCB1-6

0.8

0.75

0.1414

1

1

20.20

g/V

1

PCB1-7

g

0.8

0.15

0.1314

1

1

19.53

g/V

1

PCB1-8

100

g

1.15

0.452

0.1274

1

1

20.16

g/V

1

PCB1-9

100

g

1.15

0.452

0.0974 2

1

1

19.80

g/V

1

PCB1-10

48

Soil

GAH8

acc

Soil

GAV9

acc

Soil

GAH10

acc

LD

LDFVAC2

PCB

LD

LDFVAC1

PCB

LD

LDFHAC1

PCB

LD LD

LDDVAC1 LDDVAC2

PCB PCB

LD

LDDHAC1

PCB

SD

SDFVAC2

PCB

SD

SDFVAC1

SD SD

M iddle, Free field, X horizontal,M id of 1st Clay Layer W end, 1st Lift, Y Vertical, M iddle of 1st Clay Layer M iddle, Free field, W-E horizontal, M id Top of 2nd Clay Layer

100

g

1.15

0.452

0.0674

1

1

19.96

g/V

1

PCB1-11

50

g

1.559

0.452

0.1394

1

1

9.53

g/V

1

PCB1-12

100

g

1.559

0.452

0.1394

1

1

19.92

g/V

1

PCB1-13

Footing_vertical_accel_South

50

g

0.102

0.085

0.0095

1

1

9.18

g/V

1

PCB1-14

Footing_vertical_accel_North

50

g

0.06

0.085

0.0095

1

1

9.79

g/V

1

PCB1-15

100

g

0.05

0.085

0.0095

1

1

19.96

g/V

1

PCB1-16

50 50

g g

0.017 0.09

0.086 0.086

0.238 0.238

1 1

1 1

9.54 9.40

g/V g/V

-1 1

PCB2-1 PCB2-2

100

g

0.093

0.085

0.21

1

1

20.20

g/V

-1

PCB2-3

Footing_vertical_accel_South

50

g

0.108

0.057

0.0095

1

1

9.39

g/V

1

PCB2-4

PCB

Footing_vertical_accel_North

50

g

0.009

0.057

0.0095

1

1

10.24

g/V

1

PCB2-5

SDDVAC1 SDDVAC2

PCB PCB

Deck_vertical_accel_North Deck_vertical_accel_South

50 50

g g

0.009 0.1

0.055 0.055

0.198 0.198

1 1

1 1

9.50 9.38

g/V g/V

1 1

PCB2-7 PCB2-8

SD

SDDHAC1

PCB

Deck_horizontal_accel_South

100

g

0.1

0.055

0.17

1

1

20.45

g/V

-1

PCB2-9

LD

LDCHAC1

PCB

Column-Horiz_accel_South

100

g

0.09

0.095

0.055

1

1

20.24

g/V

1

PCB2-10

LD

LDDHAC2

PCB

100

g

0.04

0.075

0.23

1

1

21.28

g/V

1

PCB2-11

SD

SDCHAC1

PCB

100

g

0.04

0.085

0.038

1

1

19.80

g/V

1

PCB2-12

SD

SDFHAC1

PCB

100

g

0.108

0.057

0.0095

1

1

18.48

g/V

-1

PCB3-1

LD

LDFVLP1

LP

4

in

0.0127

0.15

0

1

1

0.0016

m/V

-1

PT1-0

SD

SDFHLP3

LP

1

in

0.04

0.055

0.038

1

1

0.0025

m/V

-1

PT1-1

LD

LDFHLP3

LP

Footing_horizontal_displacem ent_North Footing Horiz Disp North

1

in

0.04

0.105

0.04

1

1

0.0004

m/V

1

PT1-2

LP

Footing_vertical_displacemen t_Northwest

2

in

0.024

0.01

0

1

1

0.0051

m/V

-1

PT1-3

SD

SDFVLP1

Footing_horizontal_accel_Nor th (NS) Deck_vertical_accel_North Deck_vertical_accel_South Deck_horizontal_accel_South (SN)

Top Col Horiz Accel North (NS) Unit Vector -1 Column Horiz Accel North (NS) Footing_Horizontal_accel_So uth Footing_vertical_displacemen t_Northeast

49

LD

LDDLP

LP

M ass Horizontal_North Footing_vertical_displacemen t_Southwest M ass Horizontal North Footing_vertical_displacemen t_Southeast

2

in

0.04

0.12

0.205

1

1

0.0012

m/V

1

PT1-4

2

in

0.1

0.01

0

1

1

0.0051

m/V

-1

PT1-5

2

in

0.03

0.055

0.19

1

1

0.0051

m/V

1

PT1-6

4

in

0.095

0.15

0

1

1

0.0016

m/V

-1

PT1-7

SD

SDFVLP2

LP

SD

SDDLP

LP

LD

LDFVLP2

LP

N/A

N/A

N/A

N/A

1

0

0

0

0

1

1

0.00

0

0

PROGB1-0

Soil

PPT1

ppt

N W end, SAND LAYER

100

psi

0.032

0.011

0.03

10

5

12.48

psi/V

1

PROGA1-0

Soil

PPT2

ppt

N E end, SAND LAYER

100

psi

0.032

0.7

0.025

10

5

12.19

psi/V

1

PROGA1-1

50

psi

0.55

0.452

0.1294

10

5

5.47

psi/V

1

PROGA1-2

50

psi

1.4

0.452

0.1224

10

5

5.44

psi/V

1

PROGA1-3

100

psi

0.55

0.452

0.0604

10

5

14.59

psi/V

1

PROGA1-4

100

g

0.054

0.105

0.21

1

1

25.00

g/V

1

PROGA2-0

100

g

0.095

0.06

0.035

1

1

25.00

g/V

1

PROGA2-1

1

1

25.00

g/V

1

PROGA2-2

1

1

25.00

g/V

-1

PROGA2-3

1

1

25.00

g/V

1

PROGA2-4

1

1

50.00

g/V

1

PROGA2-5

1

1

25.00

g/V

1

PROGA2-6

1

1

50.00

g/V

-1

PROGA2-7

Unit

Channel

Soil

PPT3

ppt

N end, 2nd Lift, M iddle of 2nd Layer of Clay

Soil

PPT4

ppt

S end, 2nd Lift, M iddle of 2nd Layer of Clay

Soil

PPT5

ppt

LD

LDDHMM 5

M EM

LD

LDFHMM 3

M EM

LD LD SD SD SD SD 5.

S end, 1nd Lift, M iddle of 1st Layer of Clay Deck_horizontal_accel_EW_ East Footing_horizontal_accel_NS _South Ftg

Footing_horizontal_accel_EW 100 g 0.105 0.07 0.035 _South Ftg Deck_horizontal_accel_NS_N LDDHMM 4 M EM 100 g 0.017 0.085 0.21 orth Footing_horizontal_accel_EW SDFHMM 2 M EM 100 g 0.1 0.04 0.038 _SouthWest Ftg Deck_horizontal_accel_EW_ SDDHMM 5 M EM 200 g 0.055 0.1 0.17 East Footing_horizontal_accel_NS SDFHMM 3 M EM 100 g 0.103 0.035 0.038 _South Ftg Deck_horizontal_accel_NS_N SDDHMM 4 M EM 200 g 0.009 0.055 0.178 orth Table 13. Spin number 4, Dynamic SD and LD shaking Spin 5 CGL File (Bearing Failure Test) LDFHMM 2

M EM

Group

Label

Sensor Type

BASE

BE

acc

BASE

BW

acc


Range

Unit

X(m)

Y(m)

Z(m)

Gain

Exc. Voltage

NE side of box, X horizontal NW side of box, X horizontal

100

g

0

0

0

1

1

19.08

g/V

1

PCB1-1

100

g

0

0

0

1

1

19.16

g/V

1

PCB1-2

Calibration

50

Frame

BE

acc

Frame

BW

acc

Soil

GAV1

acc

Soil

GAH3

acc

Soil

GAH4

acc

Soil

GAH5

acc

Soil

GAH6

acc

Soil

GAH7

acc

Soil

GAH8

acc

Soil

GAV9

acc

Soil

GAH10

acc

Soil Soil

PPT 1 PPT 2

ppt ppt

Soil

PPT 3

ppt

Soil

PPT 4

ppt

Soil

PPT 5

ppt

Actuator

LoadCell

LC81363

Actuator

Feedback

LP

NE side of box, X horizontal NW side of box, X horizontal North M iddle, Free Field, Just at the surface of top of the clay North M iddle, Free Field, Just at the top surface of top of the clay W-E W M iddle, X horizontal, M id. Top of the 2nd Clay Layer E M iddle, X Horizontal, M id. Top of 2nd Clay Layer M iddle, Free field, X horizontal, M id Top of 2nd Clay Layer M iddle, Free field, X horizontal,M id of 2nd Clay Layer M iddle, Free field, X horizontal,M id of 1st Clay Layer W end, 1st Lift, Y Vertical, M iddle of 1st Clay Layer M iddle, Free field, W-E horizontal, M id Top of 2nd Clay Layer N W end, SAND LAYER N E end, SAND LAYER N end, 2nd Lift, M iddle of 2nd Layer of Clay S end, 2nd Lift, M iddle of 2nd Layer of Clay S end, 1nd Lift, M iddle of 1st Layer of Clay M easure vertical force to bearing plate -M odel No. SN-1000 horizontal displacement of the rod

100

g

-0.011

0.085

0

1

1

19.88

g/V

1

PCB1-3

100

g

-0.011

0

0

1

1

19.27

g/V

1

PCB1-4

50

g

0.2

0.452

0.145

1

1

20.00

g/V

1

PCB1-5

100

g

0.2

0.452

0.145

1

1

20.33

g/V

1

PCB1-6

100

g

0.8

0.75

0.1414

1

1

20.20

g/V

1

PCB1-7

100

g

0.8

0.15

0.1314

1

1

19.53

g/V

1

PCB1-8

100

g

1.15

0.452

0.1274

1

1

20.16

g/V

1

PCB1-9

100

g

1.15

0.452

0.09742

1

1

19.80

g/V

1

PCB1-10

100

g

1.15

0.452

0.0674

1

1

19.96

g/V

1

PCB1-11

50

g

1.559

0.452

0.1394

1

1

9.53

g/V

1

PCB1-12

100

g

1.559

0.452

0.1394

1

1

19.92

g/V

1

PCB1-13

100 100

psi psi

0.032 0.032

0.011 0.7

0.03 0.025

10 10

5 5

12.48 12.19

psi/V psi/V

1 1

PROGA1-0 PROGA1-1

50

psi

0.55

0.452

0.1294

10

5

5.47

psi/V

1

PROGA1-2

50

psi

1.4

0.452

0.1224

10

5

5.44

psi/V

1

PROGA1-3

100

psi

0.55

0.452

0.0604

10

5

14.59

psi/V

1

PROGA1-4

1000

lbf

0.00125

0

0.205

1000

5

2471.2

N/V

1

PROGA1-5

2

in

0.05555

0.2

0.205

1

1

0.015

m/V

1

PTb4b-7

51

Table 14. Spin number 5, BF2 6.

Spin 6 CGL File (SC_Aluminum Structure)

Group

Label

Sensor Type


Range

Unit

X(m)

Y(m)

Z(m)

Gain

Exc. Voltage

BASE

BE

acc


100

g

0

0.78

0

1

1

19.08

100

g

0

0

0

1

1

100

g

-0.011

0.085

0

1

100

g

-0.011

0

0

50

g

0.2

0.452

100

g

0.2

100

g

100

NW side of box, X horizontal NE side of frame, X horizontal

BASE

BW

acc

Frame

BE

acc

Frame

BW

acc

Soil

GAV1

acc

Soil

GAH3

acc

Soil

GAH4

acc

Soil

GAH5

acc

Soil

GAH6

acc

Soil

GAH7

acc

Soil

GAH8

acc

Soil

GAV9

acc

Soil

GAH10

acc

Soil

PPT 1

ppt

North M iddle, Free Field, Just at the surface of top of the clay North M iddle, Free Field, Just at the top surface of top of the clay W-E W M iddle, X horizontal, M id. Top of the 2nd Clay Layer E M iddle, X Horizontal, M id. Top of 2nd Clay Layer M iddle, Free field, X horizontal, M id Top of 2nd Clay Layer M iddle, Free field, X horizontal,M id of 2nd Clay Layer M iddle, Free field, X horizontal,M id of 1st Clay Layer W end, 1st Lift, Y Vertical, M iddle of 1st Clay Layer M iddle, Free field, W-E horizontal, M id Top of 2nd Clay Layer N W end, SAND LAYER

Soil

PPT 2

ppt

N E end, SAND LAYER

NW side of frame, X horizontal

Calibration

Unit

Channel

g/V

1

PCB1-1

19.16

g/V

1

PCB1-2

1

19.88

g/V

1

PCB1-3

1

1

19.27

g/V

1

PCB1-4

0.145

1

1

20.00

g/V

1

PCB1-5

0.452

0.145

1

1

20.33

g/V

1

PCB1-6

0.8

0.75

0.1414

1

1

20.20

g/V

1

PCB1-7

g

0.8

0.15

0.1314

1

1

19.53

g/V

1

PCB1-8

100

g

1.15

0.452

0.1274

1

1

20.16

g/V

1

PCB1-9

100

g

1.15

0.452

0.0974

1

1

19.80

g/V

1

PCB1-10

100

g

1.15

0.452

0.0674

1

1

19.96

g/V

1

PCB1-11

50

g

1.559

0.452

0.1394

1

1

9.53

g/V

1

PCB1-12

100

g

1.559

0.452

0.1394

1

1

19.92

g/V

1

PCB1-13

100

psi

0.032

0.011

0.03

10

5

12.48

psi/V

1

PROGA1-0

100

psi

0.032

0.7

0.025

10

5

12.19

psi/V

1

PROGA1-1

52

Soil

PPT 3

ppt


50

psi

0.55

0.452

0.1294

10

5

5.47

psi/V

1

PROGA1-2

Soil

PPT 4

ppt


50

psi

1.4

0.452

0.1224

10

5

5.44

psi/V

1

PROGA1-3

Soil

PPT 5

ppt

Actuator

LoadCell

LC81363

Actuator

Feedback

LP

SC

SCS1

SC

S end, 1nd Lift, M iddle of 1st Layer of Clay M easure cyclic horizontal force to structures -Model No. sn-1000 cyclic horizontal displacement of structures

100

psi

0.55

0.452

0.0604

10

5

14.59

psi/V

1

PROGA1-4

1000

lbf

0.1

0.05

0.205

1000

5

2471.2 0

N/V

1

PROGA1-5

2

in

0.0556

0.2

0.205

1

1

0.0038

m/V

1

PTb4-6

LP

Horizontal of higher loc of Structure SC

2

in

0.02

0.055

0.2

1

1

0.0051

m/V

1

PT1-2

SCS2

LP

Horizontal of lower loc of Structure SC

2

in

0.02

0.055

0.13

1

1

0.0051

m/V

1

PT1-4

SC

SCF1

LP

Vertical of N side of Structure SC-M iddle

3

in

0.02

0.125

0

1

1

0.0075

m/V

1

PT1-0

SC

SCF2

LP

Vertical of S side of Structure SC-M iddle

3

in

0.09

0.125

0

1

1

0.0076

m/V

1

PT1-1

Unit

Channel

Table 15. Spin number 6, SC2_Alum 7.

Spin 7 CGL File (SC_Steel Structure)

Group

Label

Sensor Type


Range

Unit

X(m)

Y(m)

Z(m)

Gain

Exc. Voltage

BASE

BE

acc


100

g

0

0.78

0

1

1

19.08

g/V

1

PCB1-1

BASE

BW

acc

100

g

0

0

0

1

1

19.16

g/V

1

PCB1-2

Frame

BE

acc

100

g

-0.011

0.085

0

1

1

19.88

g/V

1

PCB1-3

Frame

BW

acc

100

g

-0.011

0

0

1

1

19.27

g/V

1

PCB1-4

Soil

GAV1

acc

50

g

0.2

0.452

0.145

1

1

20.00

g/V

1

PCB1-5

Soil

GAH3

acc

100

g

0.2

0.452

0.145

1

1

20.33

g/V

1

PCB1-6

Soil

GAH4

acc

100

g

0.8

0.75

0.1414

1

1

20.20

g/V

1

PCB1-7

NW side of box, X horizontal NE side of frame, X horizontal NW side of frame, X horizontal North M iddle, Free Field, Just at the surface of top of the clay North M iddle, Free Field, Just at the top surface of top of the clay W-E W M iddle, X horizontal, M id. Top of the 2nd Clay Layer

Calibration

53

Soil

GAH5

acc

Soil

GAH6

acc

Soil

GAH7

acc

Soil

GAH8

acc

Soil

GAV9

acc

Soil

GAH10

acc

Soil

PPT 1

ppt

Soil

PPT 2

E M iddle, X Horizontal, M id. Top of 2nd Clay Layer M iddle, Free field, X horizontal, M id Top of 2nd Clay Layer M iddle, Free field, X horizontal,M id of 2nd Clay Layer M iddle, Free field, X horizontal,M id of 1st Clay Layer W end, 1st Lift, Y Vertical, M iddle of 1st Clay Layer M iddle, Free field, W-E horizontal, M id Top of 2nd Clay Layer

100

g

0.8

0.15

0.1314

1

1

19.53

g/V

1

PCB1-8

100

g

1.15

0.452

0.1274

1

1

20.16

g/V

1

PCB1-9

100

g

1.15

0.452

0.0974

1

1

19.80

g/V

1

PCB1-10

100

g

1.15

0.452

0.0674

1

1

19.96

g/V

1

PCB1-11

50

g

1.559

0.452

0.1394

1

1

9.53

g/V

1

PCB1-12

100

g

1.559

0.452

0.1394

1

1

19.92

g/V

1

PCB1-13

N W end, SAND LAYER

100

psi

0.032

0.011

0.03

10

5

12.48

psi/V

1

PROGA1-0

ppt

N E end, SAND LAYER

100

psi

0.032

0.7

0.025

10

5

12.19

psi/V

1

PROGA1-1

50

psi

0.55

0.452

0.1294

10

5

5.47

psi/V

1

PROGA1-2

50

psi

1.4

0.452

0.1224

10

5

5.44

psi/V

1

PROGA1-3

100

psi

0.55

0.452

0.0604

10

5

14.59

psi/V

1

PROGA1-4

1000

lbf

0.1

0.05

0.205

1000

5

2471.2

N/V

1

PROGA1-5

2

in

0.0556

0.2

0.205

1

1

0.0038

m/V

1

PTb4-6

3

in

0.015

0.055

0.39

1

1

0.0076

m/V

1

PT1-4

2

in

0.015

0.055

0.2

1

1

0.0051

m/V

1

PT1-0

2

in

0.015

0.055

0.13

1

1

0.0051

m/V

1

PT1-1

3

in

0.025

0.013

0

1

1

0.0075

m/V

1

PT1-5

3

in

0.105

0.013

0

1

1

0.0076

m/V

1

PT1-2

Soil

PPT 3

ppt


Soil

PPT 4

ppt


Soil

PPT 5

ppt

Actuator

LoadCell

LC81363

Actuator

Feedback

LP

SC_Steel

SCS1

LP

SC_Steel

SCS2

LP

SC_Steel

SCS3

LP

SC_Steel

SCF1

LP

SC_Steel

SCF2

LP

S end, 1nd Lift, M iddle of 1st Layer of Clay M easure cyclic horizontal force to structures -Model No. SN-1000 cyclic horizontal displacement of structures Horizontal of higher loc of Structure SC Horizontal of lower loc of Structure SC Horizontal of middle lower of structure Vertical of N side of Structure SC Vertical of S side of Structure SC

Table 16. Spin number 7, SC_Steel

54

8.

Spin 8 (Bearing Failure Test)

Group

Label

Sensor Type

BASE

BE

acc

BASE

BW

acc

Frame

BE

acc


Range

Unit

X(m)

Y(m)

Z(m)

Gain

Exc. Voltage

NE side of box, X horizontal NW side of box, X horizontal NE side of box, X horizontal

100

g

0

0

0

1

1

19.08

100

g

0

0

0

1

1

100

g

-0.011

0.085

0

1

100

g

-0.011

0

0

50

g

0.2

0.452

100

g

0.2

100

g

100

NW side of box, X horizontal North M iddle, Free Field, Just at the surface of top of the clay North M iddle, Free Field, Just at the top surface of top of the clay W-E

Calibration

Unit

Channel

g/V

1

PCB1-1

19.16

g/V

1

PCB1-2

1

19.88

g/V

1

PCB1-3

1

1

19.27

g/V

1

PCB1-4

0.145

1

1

20.00

g/V

1

PCB1-5

0.452

0.145

1

1

20.33

g/V

1

PCB1-6

0.8

0.75

0.1414

1

1

20.20

g/V

1

PCB1-7

g

0.8

0.15

0.1314

1

1

19.53

g/V

1

PCB1-8

100

g

1.15

0.452

0.1274

1

1

20.16

g/V

1

PCB1-9

100

g

1.15

0.452

0.09742

1

1

19.80

g/V

1

PCB1-10

100

g

1.15

0.452

0.0674

1

1

19.96

g/V

1

PCB1-11

50

g

1.559

0.452

0.1394

1

1

9.53

g/V

1

PCB1-12

Frame

BW

acc

Soil

GAV1

acc

Soil

GAH3

acc

Soil

GAH4

acc

Soil

GAH5

acc

Soil

GAH6

acc

Soil

GAH7

acc

Soil

GAH8

acc

Soil

GAV9

acc

Soil

GAH10

acc

M iddle, Free field, W-E horizontal, M id Top of 2nd Clay Layer

100

g

1.559

0.452

0.1394

1

1

19.92

g/V

1

PCB1-13

Soil Soil

PPT 1 PPT 2

ppt ppt

N W end, SAND LAYER N E end, SAND LAYER

100 100

psi psi

0.032 0.032

0.011 0.7

0.03 0.025

10 10

5 5

12.48 12.19

psi/V psi/V

1 1

PROGA1-0 PROGA1-1

Soil

PPT 3

ppt


50

psi

0.55

0.452

0.1294

10

5

5.47

psi/V

1

PROGA1-2

Soil

PPT 4

ppt


50

psi

1.4

0.452

0.1224

10

5

5.44

psi/V

1

PROGA1-3

W M iddle, X horizontal, M id. Top of the 2nd Clay Layer E M iddle, X Horizontal, M id. Top of 2nd Clay Layer M iddle, Free field, X horizontal, M id Top of 2nd Clay Layer M iddle, Free field, X horizontal,M id of 2nd Clay Layer M iddle, Free field, X horizontal,M id of 1st Clay Layer W end, 1st Lift, Y Vertical, M iddle of 1st Clay Layer

55

Soil

PPT 5

ppt

Actuator

LoadCell

LC81363

Actuator

Feedback

LP

S end, 1nd Lift, M iddle of 1st Layer of Clay M easure vertical force to bearing plate -M odel No. SN-1000 horizontal displacement of the rod

100

psi

0.55

0.452

0.0604

10

5

14.59

psi/V

1

PROGA1-4

1000

lbf

0.00125

0

0.205

1000

5

2471.2

N/V

1

PROGA1-5

2

in

0.05555

0.2

0.205

1

1

0.015

m/V

1

PTb4b-7

Unit

Channel

Table 17. Spin number 8, BF3

9.

Spin 9 (Bearing Failure Test)

Group

Label

Sensor Type

BASE

BE

acc

BASE

BW

acc

Frame

BE

acc

Frame

BW

acc

Soil

GAV1

acc

Soil

GAH3

acc

Soil

GAH4

acc

Soil

GAH5

acc

Soil

GAH6

acc

Soil

GAH7

acc

Soil

GAH8

acc

Soil

GAV9

acc


Range

Unit

X(m)

Y(m)

Z(m)

Gain

Exc. Voltage

NE side of box, X horizontal NW side of box, X horizontal NE side of box, X horizontal NW side of box, X horizontal North M iddle, Free Field, Just at the surface of top of the clay North M iddle, Free Field, Just at the top surface of top of the clay W-E

100

g

0

0

0

1

1

19.08

g/V

1

PCB1-1

100

g

0

0

0

1

1

19.16

g/V

1

PCB1-2

100

g

-0.011

0.085

0

1

1

19.88

g/V

1

PCB1-3

100

g

-0.011

0

0

1

1

19.27

g/V

1

PCB1-4

50

g

0.2

0.452

0.145

1

1

20.00

g/V

1

PCB1-5

100

g

0.2

0.452

0.145

1

1

20.33

g/V

1

PCB1-6

100

g

0.8

0.75

0.1414

1

1

20.20

g/V

1

PCB1-7

100

g

0.8

0.15

0.1314

1

1

19.53

g/V

1

PCB1-8

100

g

1.15

0.452

0.1274

1

1

20.16

g/V

1

PCB1-9

100

g

1.15

0.452

0.09742

1

1

19.80

g/V

1

PCB1-10

100

g

1.15

0.452

0.0674

1

1

19.96

g/V

1

PCB1-11

50

g

1.559

0.452

0.1394

1

1

9.53

g/V

1

PCB1-12

W M iddle, X horizontal, M id. Top of the 2nd Clay Layer E M iddle, X Horizontal, M id. Top of 2nd Clay Layer M iddle, Free field, X horizontal, M id Top of 2nd Clay Layer M iddle, Free field, X horizontal,M id of 2nd Clay Layer M iddle, Free field, X horizontal,M id of 1st Clay Layer W end, 1st Lift, Y Vertical, M iddle of 1st Clay Layer

Calibration

56

Soil

GAH10

acc

M iddle, Free field, W-E horizontal, M id Top of 2nd Clay Layer

100

g

1.559

0.452

0.1394

1

1

19.92

g/V

1

PCB1-13

Soil Soil

PPT 1 PPT 2

ppt ppt

N W end, SAND LAYER N E end, SAND LAYER

100 100

psi psi

0.032 0.032

0.011 0.7

0.03 0.025

10 10

5 5

12.48 12.19

psi/V psi/V

1 1

PROGA1-0 PROGA1-1

Soil

PPT 3

ppt


50

psi

0.55

0.452

0.1294

10

5

5.47

psi/V

1

PROGA1-2

Soil

PPT 4

ppt


50

psi

1.4

0.452

0.1224

10

5

5.44

psi/V

1

PROGA1-3

Soil

PPT 5

ppt

100

psi

0.55

0.452

0.0604

10

5

14.59

psi/V

1

PROGA1-4

Actuator

LoadCell

LC81363

1000

lbf

0.00125

0

0.205

1000

5

2471.2

N/V

1

PROGA1-5

Actuator

Feedback

LP

2

in

0.05555

0.2

0.205

1

1

0.015

m/V

1

PTb4b-7

S end, 1nd Lift, M iddle of 1st Layer of Clay M easure vertical force to bearing plate -M odel No. SN-1000 horizontal displacement of the rod

Table 18. Spin number 9, BF4

57

APPENDIX C: SPIN LOCATIONS AND DRAWINGS

Figure 30. Plan view of all the trials tested in MAH01

Figure 31. Side view drawings of spin #1, SC1_Alum

58

Figure 32. Side view drawings of spin #2, LC_Alum

Figure 33. Side view drawings of spin #3, BF1

59

Figure 34. Side view drawings of spin #4, SD & LD


60

Figure 36. Side view drawings of spin #6, SC2_Alum

Figure 37. Side view drawings of spin #7, SC_Steel


61


62

APPENDIX D: SHOP DRAWINGS & STRUCTURAL PROPERTIES

Figure 40. SD and LD structures columns, plan and side view

63

Figure 41. Two mild steel plates used as a part of the total mass on the SD structure

64

Figure 42. The two aluminum masses used as a part of the total mass on the SD and LD structures

65

Figure 43. Two mild steel plates used as a part of the total mass on the LD structure

Figure 44. Two aluminum plates used as the footings of the SD and LD structures

66

Figure 45. Aluminum plate used as the footing of the LC structure

67

Figure 46. Aluminum plate used as the footing of the SC structure

68

Figure 47. The masses bolted to the sides of the SC structure

Figure 48. Assembly of the slow cyclic structures

69

APPENDIX E: SDOF MATHCAD DESIGN SHEETS SD STRUCTURE COM PATIBLE SOIL STRUCTURE YIELDING TO IM PROVE SYS TE M PERFORM ANCE

Tit le : SDOF De s ig n

GREE NS A RE INPUT

IN T HIS M A T HCAD S HEE T WE CHANGE T HE FOOT ING SIZE S IN ORDER T O OBT AIN A L/LC FACT OR OF APPROX IM AT E LY 4.

Foo ting Inpu ts BFtg  0.111m 

wdi th of footi ng

LFtg  0.111m 

l ength of footi ng

t Ftg  0.375in  0.952cm 

thi ckness of footi ng

lb Al  0.0975 3 in

al um i num densi ty

Mas s Ftg  BFtg LFtg t Ftg Al 3

a 

BFtg LFtg 3

Radi us of equi val ent Ci rcul ar Ftg

So il Inpu ts   0.5

Undrai n P oi sson Rati o

HClay  0.14 m

Hei ght of Cl ay

Nc  ( 2   ) HSand  0.01m

Hei ght of sand on top of bottom of footi ng

HCol  17.1cm

T otal Hei ght of Col um n

PI  8

Pl asti i ty Index of cl ay obtai ned from l i qui d l i m i t tests kg

soil  1900

Densi ty of soi l under 1g

3

m w  1000

kg

Densi ty of water under 1g

3

m

Cont aine r Inp uts LCont  1.759m  BCont  0.904m  Pres s Force  100000lbf

M axi m um force appl i ed by the press to the soi l duri ng consol i dati on

70

Press Force MaxLoad   279.738kPa  LCont BCont

M axim um Consolidation P ressure

De ck Inp uts & Desig n Mass Deck  2.3kg We need total of 2300g. we design for com bin ation of Alum inum & S teel. kg Aluminum 2700 3 m kg STEEL 7800 3 m Solve the equation below:



3

 (2700)   a a 5   2.543 (7800)   a a 3   2.543 (7800)  2.3kg

( a a 1)  2.54 



6

10 Therefore

a  3.66in

8



6

10

8

6

10

Therefore we need to order a 1" square of alum inum along with a 0.375" square of alum inum and a 0.625" squa re of alum inum . Therefore the total height of the deck would be equal to: 1"+0.375" +0.625" = 2"

HDeck  2in

Colum n In put s



HCol_Exposed   HCol  t Ftg 



HDeck  2

M easured from top of the footing to the bottom of the deck.

 

Mass Col  0.25 kg HC  t Ftg 

 HDeck     HCol_Exposed  17.1 cm  2 

M easured from bottom of the footing to the center of the m ass.

Pr elim inar y Outp uts n_cent  30  Clay  n_cent  19

kN

Specific Gravity of clay, under 30g

3

m ng  n_cent  g

Centrifugal A cceleration

q 0   Clay HSand  5.7 kPa

Overburden P ressure

71





Q   Mass Col  Mass Deck  ng  

Total Force acting on the footing

Su  59kPa

Undrained S hear Strength of Clay estimated fro m Bearing Failure T est results under 30g

Gs  200 Su

Shear Modolus of soil

q ult  Nc  Su

Ultimate B earing Capacity





M 0  soil  HSand  t Ftg  LFtg BFtg  0.011kg    Lc  LFtg Lc

Q q ult BFtg

Overburden Mass

 2.228cm 

Required Contact Length

 4.982

This satisfies our design L/Lc

Compute the Column Stiffness and Period of Model and Prototype Bc1  50.8mm

Outside width of the column

t c  3.175mm

Thickness of the column

Lc1  50.8mm

Outside length of the column

7

EAl  10 psi

Aluminum's Y oung's Modolus

 

Inside width of the column



Intside length of the column

Bc2  Bc1  2t c  4.445cm 



Lc2  Lc1  2 t c  4.445cm 

1 3 3 7 4 Ic       Bc1  Lc1  Bc2  Lc2   2.297 10 m 12   Kc 

3 EAl  Ic

8 Gs  a

 1.273 10 

3

m

Lateral Stiffness of the column 0.5 inches embedment of column into the mass and 0.25 inches of embedment into the footing. These embedments will be welded

4

k   1.6  10  N  m 3 ( 1  )

T  2

PLA N VIE W COLUMN

Moment of Inertia of the column

7 N

3 2  H   Col_Exposed  0.5in  in  8  

1 represents outside 2 represents inside

Mass Deck Kc



Rocking S tiffness

 2

Mass Deck  HC k

 0.013s

Period of the structure in model scale

72

T.prot  T n_cent  0.395s

Period of the structure in prototype scale

Tot_HCol  HCol_Exposed  ( 0.5in)  ( 0.25in)  15.512cm 







Total height of the column including the embedments in the deck and footing

Mass Column  Al Tot_HCol  Bc1  Lc1  Bc2  Lc2  0.253kg This design is compatible with MC_MAST ER_CARR, since tubes come in 1/8" and in squares of 2" * 2" also. CHECK ROCKING VERSUS SLIDING Calculate the base shear coefficient to confirm that rocking happens instead of sliding (Cr