Determination of impedance functions and soil-structure interaction analysis for wind turbines in a centrifuge model

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(1)Determination of Impedance Functions and SoilStructure Interaction Analysis for Wind Turbines in a Centrifuge Model. A thesis submitted for the Degree of Master in Civil Engineering. by. Miguel Angel Cabrera Cabrera Adviser. Prof. Phd. Bernardo Caicedo Hormanza Juries. Mce. Phd. Carol Andrea Murillo Mce. Phd. Juan Carlos Reyes. University of Los Andes Faculty of Engineering Department of Civil and Environmental Engineering May 2011.

(2) Contents Abstract ................................................................................................................................................ i Acknowledgements ............................................................................................................................. ii 1.. Introduction ................................................................................................................................. 1. 2.. Dynamic Actuator ....................................................................................................................... 3. 3.. 4.. 5.. 2.1. Dynamic Piezoelectric Actuator.......................................................................................... 4. 2.2. Response Tests .................................................................................................................... 6. 2.3. Suggested Reading .............................................................................................................. 7. Scale Model ................................................................................................................................. 8 3.1. Scale Model Properties........................................................................................................ 9. 3.2. Suggested Reading ............................................................................................................ 11. Centrifuge Model ...................................................................................................................... 12 4.1. Soil Model ......................................................................................................................... 12. 4.2. Soil and Scale Model Instrumentation .............................................................................. 13. 4.3. Centrifuge Test Routine .................................................................................................... 16. 4.4. Data Analysis .................................................................................................................... 16. 4.5. Suggested Reading ............................................................................................................ 19. Final Remarks and Future Recommendations........................................................................... 20. Appendix 1 ........................................................................................................................................ 21 Appendix 2 ........................................................................................................................................ 39 Appendix 3 ........................................................................................................................................ 59.

(3) MIC 2011-I0-5B. List of Figures Fig. 1, Development of wind turbine size and nominal capacity from 1980 to 2005 (Faber & Steck, 2005). 1 Fig. 2. Layout of the APA 120 ML actuator, Cedrat (2005). 5 Fig. 3. Layout of the Dynamic Actuator. 5 Fig. 4, Response tests assembly. 6 Fig. 5. Layout and photography of the reduced scale model of wind turbine at three levels of height. 9 Fig. 6. Finite element model of scaled structure of 200 mm of height (developed in SAP2000). 10 Fig. 7, Density verification procedure: a) filling of standard cylinders during the pluviation, and b) mass measure of the soil inside the standard cylinder. 13 Fig. 8, Soil accelerometer: a) bidirectional inside soil accelerometers, and b) superficial soil accelerometers.14 Fig. 9, Side distribution of soil accelerometers, the arrows inside the squares denote the direction recorded by the accelerometers. 14 Fig. 10, Schematic centrifuge testing control and dispositive. 16 Fig. 11, Comparison between the measured accelerations in the physical model against the response of the FEM model for impedance functions estimated experimentally and via CONAN (Wolf & Deeks, 2004), for 2.0V of input amplitude at: a) 200 Hz, b) 300 Hz, and c) 400 Hz of input frequency. 18. ii.

(4) MIC 2011-I0-5B. List of Tables Table 1, Characteristics of common dynamic actuators employed in centrifuge modeling. Table 2. Model and prototype dimensions Table 3, First and second mode of vibration estimated with the FEM developed. Table 4, Fontainebleau sand properties (Geolabo, 2003) Table 5, Resume chart for soil and structure instrumentation. Table 6, Subspace alforithm input properties.. iii. 4 8 10 13 15 17.

(5) MIC 2011-I0-5B. Abstract The present research thesis is divided in two main papers, with the common aim of study the SoilStructure Interaction of wind turbines in a centrifuge model. Although, the thesis document is intended to introduce, describe and give extra information of the experimental procedures and set up the topics treated inside the papers. In the first paper is presented a new dynamic actuator developed for centrifuge testing. This device is based on an “Amplified Piezo Actuator” with which allows to impose mechanic vibrations of different frequencies and amplitudes. The principle of the dynamic actuator consists in a set of masses in a single degree of freedom system, where a piezoelectric actuator and a piezoelectric load cell are adapted to measure the dynamic load. A description of the dynamic actuator with an its application to dynamic soil structure interaction of Wind turbines is presented; and the calibration of the dynamic actuator and some results of centrifuge tests for shallow and embedded foundations are presented. In the second paper is presented an experimental analysis of the Soil-Structure Interaction for wind turbines. The term of trapped mass is experimentally analysed, relating the peak accelerations inside the soil model. System identification method was implemented for the measures made during the centrifuge test, showing that the natural frequency of the soil-structure system varies as a function of the input excitation frequency, and is not affected by the height of the structure and level of foundation. The estimation of the dynamic-stiffness coefficients of the soil model is presented and a trend analysis was made.. i.

(6) MIC 2011-I0-5B. Acknowledgements Esta investigación fue posible gracias a la financiación ofrecida por la Universidad de Los Andes (ULa), al Laboratoire Central des Ponts et Chaussées (LCPC) por permitirme realizar los ensayos en sus instalaciones y contar con toda la asesoría técnica y científica, en especial a Luc Thorel, Alain Neel, Claude Favraud, Patrick Gadechau, Jean-Louis Chazelas, Meriam Khemankhem, y Nawel Chenaf; al cuerpo técnico del Laboratorio de Modelos Geotécnicos de la ULA por toda la colaboración y asesoría prestada, en especial a Liliana Garcia y Julieth Monroy; al profesor Bernardo Caicedo por su gran apoyo y colaboración con el cual fue posible desarrollar el presente trabajo; y a todas las grandes personas que han sido un gran apoyo: Camila Acero, Sergio Pachón, Natalia Pachón, Juan José Cabrera, Eliana Amaya, Felipe Cortés, Mateo Gutierrez, Juan Tapia, Juan Carlos Reyes, y en especial a mis padres Elda y Alberto Cabrera por su incondicional apoyo y amor.. Cette recherche a été possible grâce au financement de la part de l’Université de Los Andes (ULA) et du Laboratoire Central des Ponts et Chaussées (LCPC) qui a permis de faire les essais dans leurs installations et ont apporte l’encadrement technique et scientifique. Je voudrais remercier en particulier à Mr. Luc Thorel, Alain Neel, Claude Favraud, Patrick Gadechau, Jean-Louis Chazelas, Meriam Khemankhem, et Nawel Chenaf; et au personnel du le Laboratoire du Modèles Géotechniques du ULA pour toute la collaboration et conseilles, on particulier a Liliana Garcia et Julieth Monroy; au le professeur Bernardo Caicedo pour leur grand assistance et sans leur collaboration cette recherché il ne aurait pas été possible, et a toutes les personnes importantes pour moi pour leur grande coopération: Camila Acero, Sergio Pachón, Natalia Pachón, Juan José Cabrera, Eliana Amaya, Felipe Cortés, Mateo Gutierrez, Juan Tapia, Juan Carlos Reyes, et un remerciement spécial à mes parents Elda et Alberto Cabrera pour leur amour.. This research was possible by the economical support made by the University of Los Andes (ULA), and by the Laboratoire Central des Ponts et Chaussées (LCPC) for giving me the possibility to carry the tests in their laboratory and count with all the technical and scientific support, special thanks to Luc Thorel, Alain Neel, Claude Favraud, Patrick Gadechau, Jean-Louis Chazelas, Meriam Khemankhem, and Nawel Chenaf; to the Geotechnical Models Laboratory staff of the ULA for all the collaboration and technical support, special thanks to Liliana Garcia and Julieth Monroy; to the professor Bernardo Caicedo for its huge support and collaboration without whom this research wasn’t feasible, and to all these people that been always a great support: Camila Acero, Sergio Pachón, Natalia Pachón, Juan José Cabrera, Eliana Amaya, Felipe Cortés, Mateo Gutierrez, Juan Tapia, Juan Carlos Reyes, and special to my parents Elda and Alberto Cabrera for its unconditional support and love.. ii.

(7) MIC 2011-I0-5B. Chapter 1 1. Introduction The increasing interest in the use of wind renewable energy has heightened the need for new methods suitable to examine Soil-Structure Interaction (SSI) associated with wind loads. Reason why in recent years is a common subject of research (Zaaijer, 2006, Ibsen, 2008, and Bhattacharya & S.Adhikari, 2011). Also, the size and nominal capacity has increased (Fig. 1), regarding to huger loads and particular technical-design aspects.. Fig. 1, Development of wind turbine size and nominal capacity from 1980 to 2005 (Faber & Steck, 2005).. Nowadays, the design of foundations with dynamic solicitations is based on theoretical impedance functions (Veletsos & Wei, 1971, Luco & Westmanm, 1971, Veletsos & Verbic, 1973, and Gazetas, 1991), and industrial charts for foundations design. Another possibility of analysis rely on the use of. 1.

(8) MIC 2011-I0-5B numerical modeling taking in consideration most of the complexities of soil behavior, however this approach requires experimental data coming from instrumented sites or reduced scale models. The importance of foundation design and its proper stability makes part of a considerable portion of the total costs of a wind turbines project, for example, an offshore wind turbines project the foundation costs reaches up to 34% of the total project’s costs (Bhattacharya & S.Adhikari, 2011). Reason why, the understanding of the dynamic phenomena due to the wind loading over the structure, will lead to optimize the design and extend the working life of wind turbine projects.. 1.1 Objectives of Study With the intention of study the dynamic Soil-Structure Interaction in wind turbines, a centrifuge controlled parametric model test was conducted, with the next main objectives: . Develop a dynamic actuator able to reproduce harmonic wind actions over a wind turbine scaled structure.. . Make a parametric characterization of the dynamic Soil-Structure Interaction for wind turbines in a centrifuge model.. . Estimate the impedance functions in centrifuge for a wind turbine´s scaled structure.. 1.2 Scope of Thesis The present thesis document is divided into three chapters and two main appendixes. In Chapter 2 a brief description of the dynamic actuator developed is presented, enunciating the characteristics of the ¨Amplified Piezo Actuator¨ used, its implications in the scale model developed, and presenting the response tests conducted in order to compare the capabilities of the dynamic actuator on a fixedstatic condition, describing the test routine and its implications in the centrifuge tests developed. Chapter 3 focuses in the characterization of the scale model developed and a compute the properties of the scale model with a Finite Element Model. Chapter 4 exhibits the features of the centrifuge model, the soil model characteristics and instrumentation, the test routine employed and the considerations employed in the data analysis developed. In Appendixes 1 and 2 are listed the main information developed in the present thesis, divided into two main papers: “dynamic actuator for modeling soil-structure interaction in centrifuge” and “SoilStructure Interaction analysis for wind turbines in a centrifuge model” respectively.. 2.

(9) MIC 2011-I0-5B. Chapter 2 2. Dynamic Actuator In order to reproduce this dynamic phenomenon in a controlled parametric test, the dynamic loading must act directly over the structure, induce harmonic loads, and cover a proper range of frequency and load-amplitude properly controlled. For these reasons, the main issue of the scale model is the dynamic actuator. Previous researches made by Pak (1995) and Pak et al. (2011) develop a scaled foundation exited by an electromagnetic actuator and Arulanandan (1977), Arulanandan et al. (1983) and Canclini & Henderson (1979) worked with piezoelectric actuators, both researches carried out in centrifuge models showing the accuracy and applicability of this kind of actuators for geotechnical purposes. The early works concerning piezoelectric actuators in centrifuge began with the development of a scaled shaking table at the Ames Research Center (Canclini & Henderson, 1979); also dynamic tests in centrifuge models with piezoelectric actuators was developed to study the excess pore water pressures during earthquakes at the University of California at Davis, Arulanandan et al (1983). These early works gave important guidelines to use dynamic piezoelectric actuators in geotechnical centrifuges and made the baseline of the present research. Other kinds of dynamic actuators employed in centrifuge modeling works with mechanic or hydraulic mechanisms, but its size and weight are not suitable for the modeling purposes of present research. In Table 1 is presented a brief comparison of the main characteristics of common dynamic actuators employed in centrifuge modeling, showing that piezoelectric actuators are more suitable for the scale model characteristics.. 3.

(10) MIC 2011-I0-5B Table 1, Characteristics of common dynamic actuators employed in centrifuge modeling.. Actuator. Frequency. Peak stroke. Size/Weight. Electro-magnetic. High. Low. Low. Mechanic. Low. High. High. Hydraulic. Low. Medium. High. Low to high. Low to medium. Low. Piezoelectric. 2.1. Dynamic Piezoelectric Actuator. The development of piezoelectric materials began in 1880 from the researches of Curie brothers on crystal materials that were able of changing its dimensions under applied electrical charges. In the late 1960’s the discovery of piezoelectricity in PZT materials (Lead Zirconate Titanate) began the industrial applications of piezoelectric actuators. The PZT are ferroelectric materials under the Curie temperature (typically between -40°C to 80°C), composed by asymmetric structures that can create an “electric dipole moment in the crystal lattice, which is sensitive to both elastic strain and applied electrical field”, (Cedrat Technologies, 2005). One of the multiple applications with PZT materials are the dynamic actuators initially developed for the French and European Space Agency (CNES, ESA) and now used in many fields, from mechanical engineering to optics, working on positioning of tools to laser cavity tuning. One of these dynamic actuators is the Amplified Piezo Actuators (APA®) built by Cedrat Technologies SA. The APA 120 ML® works with a stack of low voltage multilayer piezoelectric ceramics (PZT), placed in the long axis of a rhombus shell (Fig. 2). This shell induces a pre-stress to the stack that amplifies the displacements on the actuator in the short axis. The operation of the Amplified Piezoelectric Actuators (APA®) is as follows, Claeyssen et al (2007): when the piezoelectric stack in the APA®, is supplied to expand the shell long axis, the shell undergo a flexo-tensional deformation and consequently its short axis contracts.. 4.

(11) MIC 2011-I0-5B. Fig. 2. Layout of the APA 120 ML actuator, Cedrat (2005).. The APA 120 ML in the dynamic actuator developed works in a blocked-free mode. At the blocked side the actuator is fixed to a piezoelectric load cell attached to a rigid support, and at the free side the actuator is attached to a sliding base (linear bearing) on which different masses can be attached (Fig. 3), the dimensions of each mass used was 36.9 × 39.7 × 10 mm. The maximum dynamic force applied by the APA actuator depends on the pre-stress or blocked condition, for a fixed-free configuration the peak force equal is 500 N (Cedrat, 2005). It must be taking into account that all connections between the APA actuator in the blocked and free side is made by screws. The masses placed over the sliding base (SKF-LLMHS 7) are screwed all together and connected with 1cm stainless steel cubes glued to the sliding base (for more details see Appendix 3).. Fig. 3. Layout of the Dynamic Actuator.. The operation of APA 120ML actuator must be made by an Amplifier (LA 75C). The LA 75C is a Linear Amplifier that makes a bridge between the Function Generator and the APA actuator. 5.

(12) MIC 2011-I0-5B producing a gain of 20; these means that a signal with an input amplitude of 1.0 V arrives to the APA 120ML actuator at 20.0V preserving the induced frequency.. 2.2. Response Tests. A series of tests with fixed foundation were carried out to evaluate the performance of the actuator, checking the effect of the excitation frequencies, input voltage and masses over the sliding support in a fixed foundation. For each input frequency, input voltage, and masses over the sliding support the measure on the dynamic load cell (DLC 101 5k) and on the mono-axis piezoelectric accelerometer (Brüel & Kjær 4517) was recorded. The fixed condition was obtained by screwing the foundation on an iron mass of 126 kg. Taking into account that the total mass of the assemblage is 3.72 kg (for one level of height), hence it could be assumed that the overweight of the supporting-mass absorbs, in a proper way, all the displacements generated by the assemblage vibrations (Fig. 4) and is able to reproduce a fixed condition for the scale model.. Iron mass (126 kg). Fig. 4, Response tests assembly.. The response tests were carried out for a sinusoidal signal, scanning frequencies between 50 to 500 Hz every 50 Hz, input amplitudes between 0.5 and 3.0 V every 0.5 V, and two conditions over the sliding support, one without masses and other with three masses of steel (total masses of 321.29 g).. 6.

(13) MIC 2011-I0-5B According to the results obtained in the response tests (Appendix 1) the ensuing conclusions could be made. The actuator is able to induce harmonic loads, with a proper control of induced frequency and amplitude. The response tests gave the possibility of set up a range between 1.0 and 2.0 V of input amplitudes and the masses over the sliding support increases the peak load of the actuator, setting the initial characteristics of centrifuge test routine.. 2.3. Suggested Reading. Arulanandan K., 1977, “Centrifuge Testing in Geotechnical Engineering”, University of California, Davis, Department of Civil Engineering, Technical Report. Arulanandan K., Canclini J. & Anadrajah A., 1982, “Simulation of earthquake motions in the centrifuge”, Journal of Geotechnical Engineering, ASCE, Vol. 8, pp. 730-742. Arulanandan K., Anandarajah A. and Abghari A., 1983, “Centrifugal Modeling of Soil Liquefaction Susceptibility”, Journal of Geotechnical Engineering, ASCE, Vol. 109, No. 3. Canclini J. & Henderson J. M., 1979, “Design of a Piezoelectric Shaker for Centrifuge Testing”, NASA, Ames Research Center. Cedrat Technologies SA., 2005, “Piezo Actuators & Electronics© 2005”. Claeyssen F., Barillot F., Le Letty R., Sosnicki O., 2007, “Amplified Piezoelectric Actuators: Static & Dynamic Applications”, Ferroelectrics, pp. 351:3-14. Claeyssen F., Ducamp A., Barillot F., Le Letty R., Porchez T., Sosnicki O., Belly C., 2008, Cedrat Technologies S.A., “Stepping Piezoelectric Actuators Based on APAs”, ACTUATOR 2008, 11th International Conferences on New Atuators, Germany. Pak R., Guzina B., 1995. “Dynamic characterization of vertically loaded foundations on granular soils”, Journal of Geotechnical Engineering, Vol. 121, No. 3, pp 274 – 286. Pak R.Y.S, Ashlock J.C., Kurahashi S. & Soudkhah M., 2011. “Physical characteristics of dynamic vertical–horizontal-rocking response of surface foundations on cohesionless soils” Géotechnique, doi:10.1680/geot.8.P.072.. 7.

(14) MIC 2011-I0-5B. Chapter 3 3. Scale Model In order to reproduce the SSI phenomena in a wind turbine foundation, it was built a scale assemblage in stainless steel. Composed by a circular rigid base, three cylindrical modules representing the body of the tower (letting test different heights), able to adjust the dynamic actuator in the top of the model (Fig. 5). The base is weld with the first cylindrical module, and the two extension modules are connected by screws and a cone coupling in the interface (for more details see Appendix 3). The main characteristics of the scale model are shown in Table 2. Table 2. Model and prototype dimensions. Parameter Model Prototype Tower height Height 1 0.2 m 20 m Height 2 0.4 m 40 m Height 3 0.6 m 60 m Foundation diameter 0.2 m 20 m Mass of actuator 1.29 kg 1.29 106 kg Mass of tower Height 1 1.13 kg 1.13 106 kg Height 2 1.49 kg 1.49 106 kg Height 3 1.48 kg 1.48 106 kg Mass of foundation 2.09 kg 2.09 106 kg Excitation frequencies 50 – 500 Hz 0.05 – 5.0 Hz Maximum dynamic load** 362.6 N 3626 kN * For embedded condition ** Maximum load for embedded base with masses and 3.0 V. 8.

(15) MIC 2011-I0-5B of input amplitude. Fig. 5. Layout and photography of the reduced scale model of wind turbine at three levels of height.. 3.1. Scale Model Properties. The scale model properties are understood as the dynamic characteristics of the structure, like the stiffness and mass matrix. These matrixes vary only with the height of the model, and its determination is explained in Chopra (2004) referring to the substructure method and in also explained in Appendix 2. In order to represent in a proper way the scale model and estimate the dynamic characteristics of the structure, it was developed a finite element model (FEM) in SAP2000 (Fig. 6). The scale model developed was made with the intention that the footing and the top section behaves as a rigid body, for this reason the flexural properties are increased. The materials assigned in the FEM are related with the stainless steel properties.. 9.

(16) MIC 2011-I0-5B The analysis executed, reduce the structure at three main degrees of freedom (one horizontal in the top of the model, and one horizontal and one rotational at the base of the model); where at each degree of freedom a unit displacement was applied when the others degrees remains restricted. For example, when the unit horizontal displacement is applied in the top section of the model, the base of the model is restricted in all joint degrees of freedom, allowing to obtain the reactions in the node and the deformed shape produced by the unit horizontal displacement, and hence obtain the mass and stiffness matrixes.. Fig. 6. Finite element model of scaled structure of 200 mm of height (developed in SAP2000).. As a result of the procedure explained, the fundamental modes of vibration of the scale model are enounced in table 3, where at 200 mm of height of the model the 1st mode of vibration is presented at 156.75 Hz staying a possible resonance when the system is excited at 150 Hz, but in experimental analysis this phenomena is not seen. Table 3, First and second mode of vibration estimated with the FEM developed.. Height of the model 200 mm 400 mm 600 mm. 1st mode 156.75 Hz 67.97 Hz 36.09 Hz. 2nd mode 364.77 Hz 183.20 Hz 106.87 Hz. With the dynamic characteristics of the structure calculated it is possible to focus the response of the model in soil dynamic behavior and hence obtain the impedance functions in centrifuge for a wind turbine scale model. Also with the FEM model developed, is possible to reduce the SSI into a spring-dashpot model and compare the response of the computational model with the measured centrifuge test.. 10.

(17) MIC 2011-I0-5B. 3.2. Suggested Reading. Chopra A.K., 2007, “Dynamics of structures, theory and applications to earthquake engineering”, ISBN 0-13-1516174-X. Pearson Prentice Hall, Upper Saddle River, N.J. Veletsos & Wei, 1971, “Lateral and Rocking Vibration of Footings”, Journal of the Soil Mechanics and Foundations Division ASCE, pp. 1227-1248. Veletsos & Verbic, 1973, “Vibration of Viscoelastic Foundations”, Earthquake Engineering and Structural Dynamics, Vol. 2, pp. 87-102. Wolf J. P., 1994, “Foundation Vibration Analysis Using Simple Physical Models”, ISBN 0-13010711-5, Prentice-Hall, Inc, Englewood Cloffs, N.J. Wolf, J.P. & Deeks, A.J., 2004, “Foundation vibration analysis: a strength-of-materials approach”, Elsevier, Linacre House, Jordan Hill, Oxford OX2 8DP.. 11.

(18) MIC 2011-I0-5B. Chapter 4 4. Centrifuge Model The main characteristic of the present research are the centrifuge tests, which have as key advantages that: centrifuge models are able to simulate gravity-induced stresses on foundations at a reduced geometric scale, for these reason large structures that incurs in high testing costs (time/money) can be modeled at lower costs, and centrifuge modeling is potentially a more accurate testing method, and therefore can be used to verify and improve present finite element analysis techniques and theoretical presumptions (Canclini et al., 1979). In these order of ideas, the development of a dynamic actuator and a scale model able to represent the dynamic SSI of a wind turbine are linked with a proper development and planning of the centrifuge model, reason why in the next subsections it will be presented some extra details of the preparation of the soil model, details of the soil and scale model instrumentation, details of the centrifuge test routine, and remarkable information of the subsequent data analysis.. 4.1. Soil Model. The tests were carried over dry Fontainebleau well graded silica sand (NE34) due to its low variability in its properties and huge investigation on France, comparable to sands from Otawa and from El Guamo-Tolima in Colombia. On table 4 are presented the main properties of the Fontainebleau sand. The preparation of the model was made by the pluviation method, were a hopper let fall the sand across a slot in movement, maintaining a constant falling height and horizontal frequency of. 12.

(19) MIC 2011-I0-5B displacement. The height of the hopper was adjusted every round trip, and before the location of the soil instrumentation, the density of the pluviated sand was verified by standard cylinders placed strategically inside the strongbox (Fig. 7). Table 4, Fontainebleau sand properties (Geolabo, 2003). Density of solid particles. ρs. 2.64. density. γ. 1630. Maximum void ratio. emax 0.833. Minimum void ratio. emin 0.553. Coefficient of uniformity CU 1.778 Mean particle diameter. a). D50. 0.3. b). Fig. 7, Density verification procedure: a) filling of standard cylinders during the pluviation, and b) mass measure of the soil inside the standard cylinder.. With the intention of made the centrifuge tests over dense soil, the pluviation method was made with a 4mm slot, at a constant falling height of 75 mm and horizontal frequency of displacement of 22 Hz; reaching a relative density of 79.7%.. 4.2. Soil and Scale Model Instrumentation. Due to the dynamic nature of the tests proposed, the dynamic motion must be measure, for this reason, a series of inside soil accelerometers was located. The inside soil accelerometers are spaced by 10 cm in depth, and measure in the horizontal and vertical direction, this accelerometers are glued to an thin plastic paper and orientated in the line of. 13.

(20) MIC 2011-I0-5B action of the actuator. The superficial accelerometers only measure in the vertical direction. For more details of the accelerometers and its location inside the strongbox see Figs. 8 and 9 respectively, and on Table 5.. a). b) Fig. 8, Soil accelerometer: a) bidirectional inside soil accelerometers, and b) superficial soil accelerometers.. Fig. 9, Side distribution of soil accelerometers, the arrows inside the squares denote the direction recorded by the accelerometers.. 14.

(21) MIC 2011-I0-5B On the scale structure were located two vertical accelerometers in the edges of the footing, and one horizontal accelerometer in the footing, and one horizontal accelerometer in the sliding support at the top on the scale model. Table 5, Resume chart for soil and structure instrumentation.. Deeper Sensors B&K B&K B&K B&K B&K B&K B&K B&K B&K B&K. Serial Num. Orientation Distrib.ChanReal coord. at setup [cm] 56646 56642 56651 58111 58112 58113 58114 58115 58116 58117. 80 78 83 84 85 86 87 88 89 90. Horizontal Vertical Vertical Horizontal Vertical Horizontal Vertical Horizontal Vertical Horizontal. 58118 59400 59442 59443 59313 59340 59255 59256 59254 59341. 91 94 96 97 99 103 105 106 107 105R. Vertical Horizontal Vertical Horizontal Vertical Horizontal Vertical Horizontal Vertical Horizontal. 55506 56650 56629 56647 59337 59338 59342. 75 76 77 79 100 101 104. Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal Horizontal. 59441 59444 59339 56648. 95 98 102 82. Horizontal Vertical Vertical Horiz-Top. 1 2 3 4 5. 3 4 5 6 7 8 9 10 11 12. 40.0. 19.6. 20.0. 40.0. 40.3. 20.5. 39.0. 61.0. 20.3. 39.3. 79.5. 20.0. 39.3. 99.5. 20.8. 40.2. 20.0. 10.2. Mid deep sensors B&K B&K B&K B&K B&K B&K B&K B&K B&K B&K. 13 14 15 16 17 18 19 20 21 22. 39.9. 41.0. 11.4. 39.5. 60.6. 10.1. 40.0. 80.0. 11.2. 39.5. 99.0. 11.6. 11 12 13 14 15 16 17. 23 24 25 26 27 28 29. 40.0 40.0 40.5 40.0 40.3 40.0 40.0. 20.0 39.2 50.0 60.0 69.8 80.0 99.8. 2.0 3.4 2.5 2.5 2.6 3.1 2.5. 18 19 20 21. 30 31 32 33. -. -. -. 6 7 8 9 10. Surface sensors B&K B&K B&K B&K B&K B&K B&K. Scale Model sensors B&K B&K B&K B&K. Additional to the accelerometers recently enounced, it were also placed two vertical laser displacement sensors over a structure placed in the strongbox, but its accuracy wasn’t trustfully.. 15.

(22) MIC 2011-I0-5B. 4.3. Centrifuge Test Routine. According to the response tests made, the centrifuge test routine was planned to cover input frequencies between 50 to 500 Hz every 50 Hz, at input amplitudes of 1.0 to 2.0 V every 0.5 V. In Fig. 10 is presented an schematic distribution of the control devices placed inside the control room, where the centrifuge acceleration is controlled, and the input signal is transmitted via a fiber optic connection to the centrifuge chamber to the actuator amplifier which transmit the signal amplified to the actuator and release the motion, during the motion of the actuator all the instrumentation placed in soil model and in the scale model is measure and recorded in the data acquisition system. Transmitted to the centrifuge inside control and then via the fiber optic connection to the control room and visualized in real time. This procedure is repeated for each signal covering the centrifuge test routine plan.. Fig. 10, Schematic centrifuge testing control and dispositive.. 4.4. Data Analysis. The data analysis made in the estimation of the transfer/frequency-response functions (FRF) was made with the peak picking method. Where for each signal recorded the fast-Fourier transform (fft). 16.

(23) MIC 2011-I0-5B function in MatLab was implemented and for the peak fft frequency recorded in the dynamic load cell, the peak fft values in the accelerometers was estimated. The filtering of the vertical accelerations in the footing was made with MatLab’s zero-phase digital filtering, using a ten point averaging filter with constant values (filtfilt function). Also, in the analysis of the inside soil accelerometers was applied the peak picking method, using the Kriging gridding method for the contour generation. This analysis gives an experimental visualization of the soil mass that is hugely affected by the structure’s vibration and could be related to an experimental trapped mass. Reason why more research could be made in this topic in order to validate or elaborate a centrifugal vibration theory. In the analysis of forced vibration the system identification method (Van Overschee & De Moor, 1996) with a subspace algorithm developed by Van Overschee & De Moor (1996) and Giraldo et al. (2009) was applied (stating the initial properties enounced in Table 6). The subspace algorithm takes the input signal recorded in the dynamic load cell at the top of the scale model and relates to the output signals recorded in the scaled model’s accelerometers, dividing all signals in subspace signals of 100 points-length (signal window); during this relation the algorithm solves an eigenvalue problem finding the eigen–values and –vectors of the Input-Output system. In simple words, for all signal window eigen–values and –vectors calculated, another algorithm classifies the information and made a statically analysis and stays which values and vectors are predominant in the signals analyzed, and in this way the characteristics of the system are founded. Table 6, Subspace alforithm input properties.. Sampling Frequency Resampling Frequency Number of outputs Order of the system Number of points MAC tolerance Frequency tolerance Maximum damping ratio. 12800 Hz 1000 Hz 8 3 100 0.9 0.1 Hz 20 %. The procedure developed for the solution of the equations of motion presented in Appendix 2, begins with the statement of all structure properties (stiffness and mass matrixes), then the peak values of horizontal displacement, rotation and load registered at a particular excitation frequency and amplitude are computed in order to obtain the peak horizontal displacement at the top of the. 17.

(24) MIC 2011-I0-5B model. With the three motions known in each degree of freedom (top-horizontal, base-horizontal, and base-rotational) the estimation of the impedance functions regarding the soil interaction in the dynamic response of the system, requires two different assumptions: •. For shallow case, the coupling between the horizontal and rocking motion in the soil response functions is neglected as in Veletsos & Wei (1974), Wolf (1994), and Wolf & Deeks (2004).. •. For embedded case, the coupling could be understood by a relation of the horizontal motion with the rotational motion, as is stated in Wolf (1994) and shown in Appendix 2.. For the impedance functions estimated and with the FEM developed, it was adapted a springdashpot system at the base of the model, excited with the signal recorded in the load cell at the same point as in the physical model, and comparing the accelerations in the base with the accelerations measured. The details of the results obtained at this stage are presented in Appendix 2, and on Fig, 11 is shown the comparison some of the results obtained with the FEM calibrated with the experimental impedance functions, and the results obtained for an impedance functions obtained via CONAN (Cone theory developed by Wolf & Deeks, 2004), against the experimental measures.. Acc h [m/s2]. Acc v [m/s2]. 40. a). 20. 60. b). 40 20. 0. 120 40. 0. 0. -20. -20. -40. -40. -40. -80. 10. 20. 20. 10. 0. 0. 0. -10. -10. -20. -20. -20. -40. 0.06. 0.064. Exp. FEM CONAN Experimental. 0.068 0.072 Time [s]. 0.076. c). 80. 0.06. 0.064. 0.068 0.072 Time [s]. 0.076. 0.06. 0.064. 0.068 0.072 Time [s]. 0.076. Fig. 11, Comparison between the measured accelerations in the physical model against the response of the FEM model for impedance functions estimated experimentally and via CONAN (Wolf & Deeks, 2004), for 2.0V of input amplitude at: a) 200 Hz, b) 300 Hz, and c) 400 Hz of input frequency.. 18.

(25) MIC 2011-I0-5B. 4.5. Suggested Reading. Bhattacharya S. & Adhikari S., 2011, “Experimental validation of soil-structure interaction of offshore wind turbines” Soil Dynamics and Earthquake Engineering, Vol. 31, pp. 805 – 816. Cremona C., 2005. “Qu’est-ce qu’une évaluation dynamique? Principes et méthodes”, Evaluation dynamique des ouvrages, REGC-9. Ibsen, L.B., 2008, “Implementation of a new foundations concept for Offshore Wind farms”, NGM 15th, Keynote: NGM 2008. Giraldo, D. Song, W. Dyke, S.J., & Caicedo, J.M., 2009, “Modal Identification through Ambient Vibration: Comparative Study”, ASCE, Journal of Engineering Mechanics, Vol. 135, No. 8. Prowell I., Elgamal A., Lu J., & Luco J. E., 2009, “Modal Properties of a Modern Wind Turbine Including SSI, 17th International Conference on Soil Mechanics and Geotechnical Engineering.” Alexandria. Semblat J.F. & Pecker A., 2009. “Waves and vibrations in soils: earthquakes, traffic, shocks, construction works”, IUSS press. Van Overchee, P. & De Moor, B., 1996,”Subspace identification for linear systems: Theory, implementation and applications”, Kluwer Academic, Dordrecht, The Netherlands. Zaaijer M.B., 2006, “Foundation modeling to assess dynamic behavior of offshore wind turbines”, Applied Ocean Research, Vol. 28, pp45 – 57.. 19.

(26) MIC 2011-I0-5B. 5. Final Remarks and Future Recommendations As a result of the present research it was possible to develop a dynamic actuator able to induce harmonic loads, varying the amplitude and frequency of the induced load. This dynamic actuator was adapted to a scale wind turbine structure and tested in a parametric centrifugal test scanning frequencies between 50 to 500 Hz and input amplitudes of 1.0 to 2.0 V of the induced excitation. The signals induced preserve the main input frequency (monochromatic mechanical wave), the ratio between load and frequency is not proportional and describes a peak behavior of the actuator, and the ratio between load and input amplitude is proportional. The effect of vary the amplitude of the signal induced is not as significant as vary the height of the structure in the response of the system. The term of trapped mass could be extended and refined with experimental data, as seen in the present research. And a probable vibration analysis in soil dynamics could be developed based in centrifugal tests, reason why more experimental researches are needed. More work and effort is needed to solve the uncertainties and model in a proper way the experimental results in a FEM, nevertheless with the analysis developed, the trend of the soil response states the variability of the dynamic problem. Hence future researches in this field should take into account the next recommendations in order to enhance the experimental results obtained: • Place more accelerometers in the structure, covering at least the main degrees of freedom. • In the response tests, place more accelerometers in the structure and measure the decay of the induced accelerations, in order to deduce the experimental structure’s properties as the natural frequency of the assemblage and the structural damping ratio. • Cover a wide range of frequencies, in order to observe the experimental resonance frequency of the soil-structure system.. 20.

(27) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. MIC 2011-I0-5B. Appendix 1 Dynamic Actuator for Interaction in Centrifuge. Modeling. Soil-Structure. Miguel Angel Cabrera1, Bernardo Caicedo2, Luc Thorel3. ABSTRACT: This paper presents a method to study Soil Structure Interaction in centrifuge. A new dynamic device was developed for centrifuge testing. This device is based on an “Amplified Piezoelectric Actuator” with which is possible to impose vibrations of different frequencies and amplitudes. The principle of the dynamic actuator consists in a set of masses in a single degree of freedom system, a piezoelectric actuator and a piezoelectric load cell to measure the dynamic load. A description of the dynamic actuator with application to dynamic soil structure interaction of Wind turbines is presented. The calibration of the dynamic actuator and some results of centrifuge tests for shallow and embedded foundations are presented. KEYWORDS: Piezoelectric Actuator, Soil-Structure Interaction, Centrifuge Modeling, Wind Turbines Foundations. 1. Department of Civil and Environmental Engineering University of Los Andes, Carrera 1 N° 18 A 10 Bogota, Colombia, [email protected] 2 Department of Civil and Environmental Engineering University of Los Andes, Carrera 1 N° 18 A 10 Bogota, Colombia, [email protected] 3 Nantes Angers Le Mans, IFSTTAR, Centre de Nantes, Département GER, Physical Modelling in Geotechnics Group, Route de Bouaye F-44344 Bouguenais, France, [email protected]. 21.

(28) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. 1.. MIC 2011-I0-5B. INTRODUCTION. The increasing interest in the use of renewable energy based on wind has heightened the need for new methods suitable to examine soil-structure interaction (SSI) associated with wind loads. Characterization of the SSI is particularly relevant for shallow and embedded foundations on sands or unbound granular materials. The lack of bonding between grains and consequently the incapacity to sustain tension stresses, the occurrence of plastic strains for very low stresses, and the anisotropic soil behavior illustrate some of the constraints met when the SSI need to be known. As a result of wind loads, the fundamental modes of vibration of wind turbines in operation are in the range of frequencies from 0.7 to 4.0 Hz (Prowell et al., 2009). Nowadays, the design of foundations with dynamic solicitations is based on theoretical impedance functions, industrial charts for foundations design and theoretical transfer functions (Veletsos and Wei 1971, Veletsos and Verbic 1973, Luco and Mita 1987, Gazetas 1991a, Gazetas 1991b, Sieffert and Cevaer 1992); most of these approaches consider isotropic linear elastic behavior of the materials involved. These abstractions could be so restrictive for example in the case of foundations on sand. Another possibility of analysis rely on the use of numerical modeling taking in consideration most of the complexities of soil behavior, however this approach requires experimental data coming from instrumented sites or reduced scale models. This paper presents a dynamic actuator conceived to reproduce the dynamic soil structure interaction in a centrifuge model. Previous researches made by Pak (1995 and 2011) develop a scaled foundation exited by an electromagnetic actuator, and Arulanandan (1977), Arulanandan et al. (1983) and Canclini & Henderson (1979) worked with piezoelectric actuators in centrifuge models showing the accuracy and applicability of this kind of actuators for geotechnical purposes. The early works concerning piezoelectric actuators in centrifuge began with the development of a scaled shaking table at the Ames Research Center, Canclini & Henderson (1979); also dynamic tests in centrifuge models with piezoelectric actuators to study the excess pore water pressures during earthquakes have been carried out at the University of California at Davis, Arulanandan et al (1983). These early works gave important guidelines to use dynamic piezoelectric actuators in geotechnical centrifuges. As the dynamic actuator presented in this paper is conceived to work on a reduced scale model of a wind turbine, the actuator is designed to reproduce harmonic loads with variable frequencies and amplitudes. The principles of piezoelectric actuators are described and the reduced scale model of a structure similar to a wind turbine is presented, then the experimental set-up, developed at the University of Los Andes (ULA), Bogotá (Colombia), has been validated in the centrifuge of the Laboratoire Central des Ponts et Chaussées (LCPC), Nantes (France) through a set of tests on a reduced scale model of a wind turbine. 2.. PRINCIPLES OF PIEZOELECTRIC ACTUATORS. The development of piezoelectric materials began in 1880 from the researches of Curie brothers on crystal materials that were able of changing its dimensions under applied electrical charges. In the late 1960’s the discovery of piezoelectricity in PZT (Lead Zirconate Titanate) began the industrial applications of piezoelectric actuators. The PZT are ferroelectric materials under the Curie temperature (typically between -40°C to 80°C), composed by asymmetric structures that can create an “electric dipole moment in the crystal lattice, which is sensitive to both elastic strain and applied electrical field”, (Cedrat Technologies, 2005).. 22.

(29) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. MIC 2011-I0-5B. According to the piezoceramics behavior, compressive stresses in piezoelectric actuators have good reliability and attain high compressive stresses (generally more than 200 MPa, cf. Claeyssen et al 2007, and Claeyssen et al., 2008); in addition, to achieve high displacements the ceramics are superposed in stacks. On the other hand the behavior of piezoelectric actuators is totally different under tensile forces. In fact, tensile stresses could reduce the contact between the ceramics and disband the stack behavior. One alternative to prevent this limitation is to induce a pre-stress, carrying a limited tensile force to the stack. However pre-stressing the piezoelectric actuator reduces its performance; a clear effect of this condition is the loss of amplification efficiency of the actuator due to the stiffness of the pre-stressing device. The amplification efficiency η is defined in equation 1, Cleyssen et al (2007):. η=. u a Fa u p Fp. (1). Where ua is the actuator free displacement, Fa is the maximum blocked force, up the free stroke, and Fp the respective blocked force. One of the multiple applications with PZT materials are the dynamic actuators initially developed for the French and European Space Agency (CNES, ESA) and now used in many fields, from mechanical engineering to optics, working on positioning of tools to laser cavity tuning. One of these dynamic actuators is the Amplified Piezo Actuators (APA®) built by Cedrat Technologies SA. APA® works with a stack of low voltage multilayer piezoelectric ceramics (PZT), placed in the long axis of a rhombus shell (Fig. 1). This shell induces a pre-stress to the stack that amplifies the displacements on the actuator in the short axis. The operation of the Amplified Piezoelectric Actuators (APA®) is as follows: when the piezoelectric stack in the APA®, is supplied to expand the shell long axis, the shell undergo a flexotensional deformation and consequently its short axis contracts, Claeyssen et al (2007).. FIG. 1– Layout of the APA 120 ML actuator, Cedrat (2005).. Some requirements for a dynamic actuator reproducing wind loads in centrifuge models are: the actuator must be as small and light as possible, be able to adapt to the structure with the minimum of extra accessories, produce a dynamic loading in agreement with the wind loads in a wind turbine in operation,. 23.

(30) MIC 2011-I0-5B. APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. and working in a wide range of frequencies (covering the fundamental modes of vibration). Table 1 presents the characteristics of the Amplified Piezoelectric Actuator APA 120 choose for to fulfill the previous requirements. Table 1, Characteristics of the APA 120 ML (Cedrat Technologies S.A, 2005). Actuator data Free displacement Max Blocked force Stiffness Actuator Height Actuator free strain Active material data Length of piezo stack Actuator Width Section No-load strain Blocked stress No-load displacement Blocked force Amplification analysis Displacement amplification factor Strain amplification factor Force disamplification factor Actuator mechanical efficiency. µm N N/µm cm % mm mm mm2 ppm MPa µm N. ua Fa K h Sa. 130 1400 10.8 4.5 0.29. Sp. 60 45 100 1000 40 60 4000. up Fp Au As. %. η. 2.2 2.9 2.9 76. The dynamic behavior of piezoelectric actuators (which is of special interest in the present research) could be described at first by the resonant frequency fr (Eq. 2), where K is the actuator stiffness, m is the effective mass of the piezoelectric stack, and M is an additional load that could be connected to the actuator. This frequency could be related to the response time tr as shown in Eq. 3.. fr =. tr =. 1 2π. K m+M. (2). 1 2 fr. (3). The range of displacements that are feasible using the piezoelectric actuator depend on the dynamic conditions: fixture conditions (blocked, blocked-free, or free-free), moving mass, frequency, and excitation charge in the piezoelectric stack. Usually a mechanical quality factor Qm is used to obtain the dynamic behavior from the pseudo-static condition. This quality factor relates the input voltage V, the force factor N of the actuator, and the stiffness K of the actuator with the displacement Du (Eq. 4).. ∆ u = Qm. NV K. (4). 24.

(31) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. MIC 2011-I0-5B. The APA 120 ML included in the dynamic actuator works in a blocked-free mode: at the blocked side the actuator is fixed to a piezoelectric load cell attached to a rigid support, and at the free side the actuator is attached to a sliding base (linear bearing) on which different masses can be attached (Fig. 2); the dimensions of each mass is 36.9 mm of width 39.7 mm of length and 10 mm of thickness. According with the technical data, the stiffness K of the APA actuator is 10.77 N/µm, and the actuator mass m is 160 g, hence using Eq. 2 the resonant frequency fr is 0.75 kHz for a mass M=321.29 g. The maximum dynamic force applied by the APA actuator depends on the pre-stress, for a fixed-free configuration the peak force equal is 500 N.. FIG. 2– Layout of the Dynamic Actuator.. Under dynamic mode, the operation of the actuator is characterized by a coupled piezoelectric problem typified by an interrelationship between mechanical and electrical state variables. In fact in piezoelectric materials, an electric potential gradient causes deformation (inverse effect), while a mechanical stress induces electrical charges (direct effect). Obtaining the dynamic force applied by the actuator requires solving the coupled problem involving mechanical strains and electric fields, Poizat and Benjeddou (2006). The software Compact developed by Cedrat (2007) solve this coupled problem and allows to obtain the dynamic response of the piezoelectric actuator for different dynamic configurations, Fig. 3 shows the dynamic load of the APA 120 ML obtained using this software in a fixed free configuration and having different masses at the free side.. FIG. 3– Dynamic response of the piezoelectric actuator APA 120 ML.. 25.

(32) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. 3.. MIC 2011-I0-5B. DYNAMIC ACTUATOR FOR CENTRIFUGE. In centrifuge modeling, the similarity of the conditions between the model (reduced scale) and the prototype (full scale) is guaranteed by using scaling factors. These scaling laws are presented in Table 2, (Philips, 1869; Mandel, 1962; Corté, 1989, Garnier et al., 2007, Murillo et al., 2009b, 2009c). Two scaling factors are possible in dynamic problems depending on the coupling with fluid transport (ie. liquefaction problems), in the case presented in this paper the foundation is over dry sand, therefore it is a classic dynamic problem where the time scaling factor is 1/N. Table 2, Centrifuge Scaling Laws. Parameter Pressure, stress Density Length Gravity Time (diffusion) Time (dynamics) Force Velocity Frequency Acceleration Stiffness. Model/Prototype 1 1 1/N N 1/N2 1/N 1/N2 1 N N 1/N. Table 3, Model and prototype dimensions Parameter Model Prototype Tower height Height 1 0.2 m 20 m Height 2 0.4 m 40 m Height 3 0.6 m 60 m Foundation diameter 0.2 m 20 m Mass of actuator 1.29 kg 1.29 106 kg Mass of tower Height 1 1.13 kg 1.13 106 kg Height 2 1.49 kg 1.49 106 kg Height 3 1.48 kg 1.48 106 kg Mass of foundation 2.09 kg 2.09 106 kg * Fundamental frequencies Height 1 1750 Hz 17.5 Hz Height 2 537 Hz 5.4 Hz Height 3 262 Hz 2.6 Hz Excitation 50 – 500 0.05 – 5.0 frequencies Hz Hz Maximum dynamic 362.6 N 3626 kN load** * For embedded condition ** Maximum load for embedded base with masses and 3.0 V of input amplitude. 26.

(33) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. MIC 2011-I0-5B. FIG. 4– Layout of the reduced scale model of wind turbine.. 3.1. Operation of the Dynamic Actuator. The instrumentation of the actuator includes a dynamic load cell Omega DLC101 5k, attached on the rigid support of the piezoelectric actuator (Fig. 4), measuring the load transmitted by the actuator to the top of the assembly, and an accelerometer, Brüel & Kjær 4517, is attached to the sliding support. The control of the piezoelectric actuator is performed by a Linear Amplifier LA75, Cedrat (LA75C) this amplifier provides high power at low and high frequencies, the harmonic signal is applied to the actuator using a Function Generator linked to the amplifier. The data acquisition is performed automatically by a SCADAS Mobile data acquisition system developed by LMS (SCM05), at a rate of 12800 samples per second (12.8 kHz) in 72 simultaneous channels. An optic fiber connection allows controlling the actuator and the acquisition system from the centrifuge control room.. 27.

(34) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. MIC 2011-I0-5B. FIG. 5– Details of the dynamic actuator and model a) top section, b) assemblage for first height.. 3.2. Response tests with fixed base. A series of tests with fixed foundation were carried out to evaluate the performance of the actuator. The response of the system over a fixed foundation was evaluated recording the signal of the dynamic load cell and the mono-axis piezoelectric accelerometer for different excitation frequencies, input voltage and masses over the sliding support. The fixed condition was obtained by screwing the foundation on a mass of 126 kg, taking into account that the total mass of the assemblage (for one level of height) is 3.72 kg, it could be assumed that the over weight of the supporting-mass absorbs, in a proper way, all the displacements generated by the assemblage vibrations. The response tests were made using a sinusoidal signal, scanning frequencies between 50 to 500 Hz every 50 Hz, input amplitudes between 0.5 and 3.0 V every 0.5 V, and two conditions over the sliding support: one without masses and the other one with three masses of steel (total masses of 321.29 g). Figs. 6 and 7 show the load signal recorded on tests having masses over the sliding support, it is observed on these figures that the ratio between load and frequency is not proportional and describes a peak. 28.

(35) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. MIC 2011-I0-5B. behavior of the actuator, these peak behavior as will be seen next, is function of the forced conditions induced on the actuator. On the other hand, the ratio between load and input amplitude is proportional (Fig. 8), showing that for bigger input amplitudes the actuator generates bigger loads over the assemblage. The results obtained show that the signal recorded in the load cell present the same dominant frequency than the input signal applied to the actuator; the fast Fourier transform FFT (Fig. 7) gives an idea of the clear monochromatic mechanical wave generated by the actuator. 300. a). Load (N). 200 100 0 -100 -200 300. b). Load (N). 200 100 0 -100 -200 300. c). Load (N). 200 100 0 -100 -200 -300 0. 0.01. 0.02. 0.03. 0.04. 0.05. Time (s) FIG. 6– Recorded load signals for 2.0V of input amplitude at a) 200Hz, b) 300Hz and c) 400Hz.. Also the tests show the clear influence of the masses in the actuator behavior, finding that the actuator increase the dynamic load transmitted to the assemblage in a proportion of the masses over the sliding support (Figs. 9a and 9b), and that actuator is able to perform a maximum dynamic load close to 400 N. Reason why the centrifuge tests will be carried out with the three masses of steel over the sliding support.. 29.

(36) MIC 2011-I0-5B. APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. 800. a). 2.0V - 200Hz. 30. Load (N). Load [N]. 40. 20 10. -400. b). 2.0V - 300Hz. 120 80 40. 400 0 -400 800. 0. 2.0V - 400Hz Load (N). 40. Load [N]. 0. 800. Load (N). Load [N]. 0. 400. 30 20. 400 0. 10. -400. 0. -800 0. 100. 200. 300. 400. 500. c). 600. 0. 0.01. Frequency [Hz]. 0.04. 400. a). 0.5 V 1.0 V 1.5 V 2.0 V 2.5 V 3.0 V. 0. 0.5 V 1.0 V 1.5 V 2.0 V 2.5 V 3.0 V. 300 200 100. b). 0 0. 100. 200 300 Frequency [Hz]. 0.05. FIG. 8– Recorded load signals for 300Hz at a) 1.0V, b) 2.0V and c) 3.0V of input amplitude.. Peak Load [N]. Peak Load [N]. 60. 20. 0.03. Time (s). FIG. 7– Fourier spectra of the recorded load signals at 2.0V of input amplitude.. 40. 0.02. 400. 500. 0. 100. 200 300 Frequency [Hz]. 400. 500. FIG. 9– Actuator response a) without masses and b) with three steel masses, recorded in the dynamic load cell.. 30.

(37) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. 4. MIC 2011-I0-5B. MODEL RESULTS. A scale factor of 1/100 was chose to model the SSI phenomena taking place at the foundation of a wind turbine. The physical model have the following components (Figs. 4 and 5): a circular rigid foundation having a diameter of 200 mm, three modules of 200 mm height and 129 mm of diameter making the body of the tower (allowing tests with different tower heights), and an adjustable top section where the dynamic actuator reproduce the wind solicitations Fig. 5a. The modules of the assemblage are interconnected by a conical coupling providing good adjustment and transmitting the dynamic-load generated by the actuator (Fig. 4). Centrifuge modeling is based in some practical scaling laws, where a prototype (full scale phenomena) is scaled N times the earth’s gravity, making a reduced scale model. These scaling laws are presented in Table 2 (Mandel, 1962, Corté, 1989, Semblat, 1998, Derkx et al., 2006). The characteristics of the model and the prototype following the scaling laws are presented in Table 3. The scale model was tested in the LCPC’s 200g-ton centrifuge (Corté and Garnier, 1986). The tests were carried over dry Fontainebleau well graded silica sand (NE34) with 340 mm of thickness. The properties of Fontainebleau sand are shown in table 4 and according to Murillo et al (2009a) the sand has a Shear wave velocity Vs of 230 m/s. The tests were carried in this sand because of its long history in centrifugetests showing a low variability of its properties. Table 4, Fontainebleau sand properties (Geolabo, 2003). Density of solid particles. ρs. 2.64. density. γ. 1630. Maximum void ratio. emax 0.833. Minimum void ratio. emin 0.553. Coefficient of uniformity CU 1.778 Mean particle diameter 4.1. D50. 0.3. Centrifuge instrumentation. For the centrifuge tests the instrumentation is composed by: one dynamic load cell DLC101 5k, one mono-axis piezoelectric accelerometer located in the top section and three mono-axis piezoelectric accelerometers in the foundation covering the vertical and horizontal vibrations in the action axis of the system. Inside the soil model were located three lines of accelerometers spaced by 10 cm in depth, the two deepest lines were composed each one for five pairs of accelerometers covering the vertical and horizontal directions, and the superficial line were composed by seven accelerometers recording the surface vertical vibrations. All these sensors are aligned in the action axis of the actuator and with the long side of the centrifuge container (Fig. 10). The present paper will focus only in the foundation’s behavior, reason why the data recorded within the soil mass accelerometers will not take into account in the analysis.. 31.

(38) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. MIC 2011-I0-5B. FIG. 10– Side distribution of soil accelerometers, the arrows inside the squares denote the direction recorded by the accelerometers.. 4.2. Preparation of the model. The soil model was prepared using the “pluviation” or “sand raining” method, were a hopper let fall the sand across a 4 mm slot in movement, maintaining a constant falling height of 75 mm and horizontal frequency of displacement of 22 Hz. The sand “pluviated” falls into a strongbox of 1200 mm of length, 800 mm of width, and 360 mm of depth. This specific method gives a uniform soil model, with a relative density of 79.7%. During the pluviation process it was also made the positioning of the soil sensors, divided in the lines described earlier (Fig. 10). 4.3. Centrifuge Test Routine. The centrifuge models was performed at a centrifuge acceleration of 100 g, scanning frequencies between 50 to 500 Hz every 50 Hz, three input amplitudes of 1.0, 1.5, and 2.0 V, tree heights of the tower (200, 400, 600 mm), and for a shallow case and a embedded case (50 mm below the surface). Every signal induced was a series of 200 sinuses, recording 2 seconds before the trigger of the signal and tree seconds during the signal. 4.4. Results of the SSI phenomena. The SSI phenomena is analyzed here taking into account the signals recorded by the dynamic load cell, the horizontal accelerometer placed on the foundation, the vertical accelerometer placed under the foundation’s center, and the pair of accelerometers placed over each side of the foundation; these last sensors allows calculating the rocking motion in the load direction. The recorded signals in all sensors preserve the sinusoidal behavior induced by the actuator (Fig. 11) just as it was seen in the response tests, also the signal maintain the monochromatic mechanical wave as observed in the Fourier spectra of each signal (Fig. 12). As described, the pair of accelerometers placed over the foundation and orientated in the line of action of the actuator gives the proper information of the rocking motion. The full acceleration recorded in both sides divided by the distance between each sensor (diameter d) gives the rotational acceleration θ&& (Eq.. 32.

(39) MIC 2011-I0-5B. APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. 5). Due to a noise recorded in the accelerators, the calculation of θ&& needs a previous filter maintaining the main frequency (Fig. 13). In Fig. 14a is shown the rotational acceleration obtained with the filtered signals with the Zero-phase filtering (Mitra, 2001), and in Fig. 14b is the Fourier spectra, showing that the monochromatic mechanical wave behavior is preserved.. θ&& =. u&&1 (t i ) − u&&2 (t i ) d. (5). 300. a). a). 200. Load (N). Load (N). 400. 0 -200. 25. b). 20 0 -20. b). 20 15 10 5. -40 80. 40. c). c) Acc (m/s 2). Acc (m/s2). 100. Acc (m/s2). Acc (m/s2). 40. 200. 40 0. 30 20 10. -40. 0 0.6. 0.61. 0.62. 0.63. 0.64. 0.65. 0. 200. 400. 600. Frequency (Hz). Time (s) FIG. 11– Recorded signals for shallow test at 600mm of height, 2.0V of input amplitude and 400Hz in a) the load cell, b) horizontal accelerometer, and c) vertical accelerometer under the foundation’s center. FIG. 12– Fourier spectra for shallow test at 600mm of height, 2.0V of input amplitude and 400Hz in a) the load cell, b) horizontal accelerometer, and c) vertical accelerometer under the foundation’s center. 33.

(40) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. MIC 2011-I0-5B. Acc (1/s2). 80 40 0 -40 -80 0.6. 0.604. 0.608. 0.612. Time (s) FIG. 13– Recorded and filtered signal (dashed and continues line) for sensors located over the foundation, at 600 mm, 2.0 V of input amplitude, and 400 Hz.. Acc (1/s2). 40. a). 20 0 -20 -40 0.6. 0.61. 0.62. 0.63. 0.64. 0.65. Time (s). 400. Acc (1/s2). b) 300 200 100 0 0. 200. 400. 600. Frequency (Hz) FIG. 14– a) Filtered rotational acceleration signal for shallow test at 600mm of height, 2.0V of input amplitude and 400Hz, b) Fourier spectra of rotational acceleration.. A first approach of the Transfer Function of the model is obtained by using a transfer/frequency-response functions (FRF) for the horizontal and rocking vibration (Eqs. 6 and 7). These functions are obtained using the accelerations in the model’s foundation and the peak load F registered in the Fourier spectra of the dynamic load cell.. FRF H =. v&& F. (6). 34.

(41) MIC 2011-I0-5B. APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. FRF R =. θ&& F×H. (7). && and θ&& are the horizontal and rotational accelerations in the model’s foundation, F is the peak Where v load in the Fourier spectra of the dynamic load cell, and H is the height of the assemblage.. FRF Horizontal, v/F (m s-2 N-1). 0.16 a). 1.0 V 1.5 V 2.0 V. 0.08. a). 200 mm 400 mm 600 mm. 0.03. 12 b). 10. ... 1.0 V 1.5 V 2.0 V. 8. 0.02 0.01. FRF Rocking, θ/(F*H) s-2(m N)-1. ... FRF Rocking, θ/(F*H) s-2(m N)-1. 0.04. 6 4 2. 10 b). 200 mm 400 mm 600 mm. 8 6 4 2 0. 0 0. 100. 200 300 400 Frequency [Hz]. 500. 0. 600. FIG. 15–a) Horizontal and b) Rocking transfer/frequency-response functions for the shallow test at 600 mm of height.. 4.4.1. 0.04. ... 0.12. ... FRF Horizontal, v/F (m s-2 N-1). Fig. 15 shows the horizontal and rocking FRF functions for a test on shallow foundation, height of the tower of 600 mm and different level of input signals. As observed the response of the foundation is linear between 150 and 350 Hz since all the values of the FRF function are almost the same for the different input loads. On the other hand for frequencies higher than 400 Hz and lower than 150 Hz a non linear behavior appears, in fact the response of the foundation that is characterized by its FRF function increase as the input level increases; this trend was observed in all the tests.. 100. 200 300 400 Frequency [Hz]. 500. 600. FIG. 16–a) Horizontal and b) Rocking transfer/frequency-response functions for the embedded tests at 2.0 V of input amplitude.. Height and embedded influence. According to the FRFs developed, it is possible to relate the influence of the tower height and the embedded foundation in the dynamic response of the system. Fig. 16 shows the FRF for the embedded case and 2.0 V of input amplitude; in this case the response of the system is affected by the height of the dynamic source. In fact, the FRF function that relate the SSI of the system presents a peak at 300 Hz for 200 mm height.. 35.

(42) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. 250 Sha 200 mm Sha 600 mm Emb 200 mm Emb 400 mm Emb 600 mm. ... 0.12 0.08 0.04 25 20 15. a). 200. 200 mm 400 mm 600 mm. 150 100 50 6. Sha 200 mm Sha 600 mm Emb 200 mm Emb 400 mm Emb 600 mm. b). FRF Rocking, θ/(F*H) s-2(m N)-1 (x108). FRF Rocking, θ/(F*H) s-2 (m N)-1. ... a). FRF Rocking , θ/(F*H) m s-2 N-1 (x108). FRF Horizontal, v/F (m s-2 N-1). 0.16. MIC 2011-I0-5B. 10 5. b) 200 mm 400 mm 600 mm. 4. 2. 0 0. 100. 200 300 400 Frequency [Hz]. 500. 0. 600. 0. FIG. 17– a) Horizontal and b) Rocking transfer/frequency-response functions for the embedded and shallow tests at 2.0 V of input amplitude.. 100. 200 300 400 Frequency [Hz]. 500. 600. FIG. 18 – Horizontal and Rocking transfer/frequencyresponse functions for a) shallow test and b) embedded test at 2.0 V of input amplitude.. In Wind turbine design process is common to work with the rotation of the tower, reason why in Fig. 18 is shown the FRF obtained with the rotation q (Eq. 8), the rotation is calculated by the double integration of the rotational acceleration signal by the Newmark’s method (Chopra, 1995). The relation obtained is similar to the FRF presented in Fig. 16, but with the difference that the difference between the higher and lower values of FRF is higher in the rotation case.. FRF R = 5.. θ F×H. (8). CONCLUSIONS. The main purpose of this study is to develop a dynamic actuator able to reproduce wind action over a structure and study the SSI phenomena of wind turbines in a scale model for centrifuge testing. The actuator developed is composed by an Amplified Piezoelectric Actuator APA able to transform electric input harmonic-signals into dynamic harmonic-strains, which remains to dynamic loads in a scaled structure (Wind turbine). The actuator and the whole model are tested in a fixed-base condition (response test) measuring the load transmitted by the actuator to the structure, scanning frequencies between 50 to 500 Hz and input amplitudes of 0.5 to 3.0 V. The response test gives the next results: the signals induced preserve the main input frequency (monochromatic mechanical wave), the ratio between load and frequency is not. 36.

(43) APPENDIX 1 – Dynamic Actuator for Modeling Soil-Structure Interaction in Centrifuge. MIC 2011-I0-5B. proportional and describes a peak behavior of the actuator, and the ratio between load and input amplitude is proportional. The centrifuge models of shallow and embedded foundations were carried out for three different heights of the structure, scanning frequencies between 50 to 500 Hz and input amplitudes of 1.0 to 2.0 V. The response of the foundation was measured in each case and a transfer/frequency-response functions FRF was calculated. The results show a linear response of the model between 150 and 350 Hz for all input amplitudes, and for the shallow and embedded cases the response of the system is related with the height of the dynamic source. The actuator presented in this paper offer a possibility to analyze the impedance functions based on the response of a reduce scale models in centrifuge and its application to wind turbine cases.. 6.. ACKNOWLEDGMENTS. This research has been supported by the ULA in Bogota, Colombia, and conducted in collaboration with the IFSTTAR (formerly LCPC) in Nantes, France. Their collaboration and contributions were really helpful. Special thanks to C. Favraud, P. Gaudicheau, and A. Neel (IFSTTAR) and J. Monroy (ULA) without whom some results would not have been achieved.. REFERENCES Arulanandan K., 1977, “Centrifuge Testing in Geotechnical Engineering”, University of California, Davis, Department of Civil Engineering, Technical Report. Arulanandan K., Canclini J. & Anadrajah A., 1982, “Simulation of earthquake motions in the centrifuge”, Journal of Geotechnical Engineering, ASCE, Vol. 8, pp. 730-742. Arulanandan K., Anandarajah A. and Abghari A., 1983, “Centrifugal Modeling of Soil Liquefaction Susceptibility”, Journal of Geotechnical Engineering, ASCE, Vol. 109, No. 3. Canclini J. & Henderson J. M., 1979, “Design of a Piezoelectric Shaker for Centrifuge Testing”, NASA, Ames Research Center. Cedrat Technologies SA., 2005, “Piezo Actuators & Electronics© 2005”. Chopra A., 1995, “Dynamics of structures: theory and applications to earthquake engineering”, ISBN 013-855214-2, Prentice-Hall, Inc, Englewood Cloffs, N.J. Claeyssen F., Barillot F., Le Letty R., Sosnicki O., 2007, “Amplified Piezoelectric Actuators: Static & Dynamic Applications”, Ferroelectrics, pp. 351:3-14. Claeyssen F., Ducamp A., Barillot F., Le Letty R., Porchez T., Sosnicki O., Belly C., 2008, Cedrat Technologies S.A., “Stepping Piezoelectric Actuators Based on APAs”, ACTUATOR 2008, 11th International Conferences on New Atuators, Germany. Corté J.-F., Garnier J., 1986. “Une centrifugeuse pour la recherchée en géotechnique”, Bulletin de liaison des Laboratoire des Ponts et Chaussées 146, pp. 5-28. Corté, J.-F., 1989, “Model Testing. Geotechnical Model Tests”, Proceedings of the 12th ICSMFE, Rio, Balkema, Rotterdam, The Netherlands, pp. 2553-2571.. 37.