Fatigue Assessment of Concrete Foundations for Wind Power Plants

Transcription

1 Fatgue Assessment of Concrete Foundatons for Wnd Power Plants Master of Scence Thess n the Master s Programme Structural Engneerng and Buldng Performance Desgn FRIDA GÖRANSSON, ANNA NORDENMARK Department of Cvl and Envronmental Engneerng Dvson of Structural Engneerng Concrete Structures CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 011 Master s Thess 011:119

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3 MASTER S THESIS 011:119 Fatgue Assessment of Concrete Foundatons for Wnd Power Plants Master of Scence Thess n the Master s Programme Structural Engneerng and Buldng Performance Desgn FRIDA GÖRANSSON, ANNA NORDENMARK Department of Cvl and Envronmental Engneerng Dvson of Structural Engneerng Concrete Structures CHALMERS UNIVERSITY OF TECHNOLOGY Göteborg, Sweden 011

4 Fatgue Assessment of Concrete Foundatons for Wnd Power Plants Master of Scence Thess n the Master s Programme Structural Engneerng and Buldng Performance Desgn FRIDA GÖRANSSON, ANNA NORDENMARK FRIDA GÖRANSSON, ANNA NORDENMARK, 011 Examensarbete / Insttutonen för bygg- och mljöteknk, Chalmers teknska högskola 011:119 Department of Cvl and Envronmental Engneerng Dvson of Concrete Structures Chalmers Unversty of Technology SE Göteborg Sweden Telephone: + 46 (0) Chalmers Reproservce / Department of Cvl and Envronmental Engneerng Göteborg, Sweden 011

5 Fatgue Assessment of Concrete Foundatons for Wnd Power Plants Master of Scence Thess n the Master s Programme Structural Engneerng and Buldng Performance Desgn FRIDA GÖRANSSON, ANNA NORDENMARK Department of Cvl and Envronmental Engneerng Dvson of Concrete Structures Chalmers Unversty of Technology ABSTRACT The demands on cleaner and renewable energy have ncreased wth the depleton of natural resources and a way to meet these demands s to use wnd power. Wth an ncreasng amount of wnd power plants the desgn of foundaton slabs for these are of nterest. The foundaton slab for a wnd power plant s subjected to cyclc loadng from the wnd and there have been uncertantes concernng the effect of fatgue. From the begnnng of 011 all new structures n Sweden should be desgned accordng to Eurocode and as a result of ths a new approach to calculate the nfluence of fatgue s to be consdered. The am of ths project s to gve recommendatons for desgnng concrete foundaton slabs wth regard to fatgue. Ths s done by clarfyng the ssues of fatgue for a foundaton slab for a wnd power plant, comparng methods for fatgue assessment accordng to Eurocode and fb Model Code 010 as well as performng parametrc studes of the fatgue desgn of a foundaton slab and dentfyng parameters that have sgnfcant mpact on fatgue of a foundaton slab for a wnd power plant. When performng a fatgue assessment the choce of assessment method s mportant. In ths project two fatgue assessment methods regardng renforcement, accordng to Eurocode, have been ncluded. One of the methods takes the frequency of the load nto account and uses the Palmgren-Mner damage summaton to estmate the fatgue damage, whle the other method uses an equvalent value for the fatgue load and a reference number of cycles. For fatgue assessment of compressed concrete two methods accordng to Eurocode have been used, as well as a method accordng to fb Model Code 010. One of the Eurocode methods and the fb Model Code method are damage calculaton methods, whle the second Eurocode method just checks for an adequate fatgue lfe by usng the maxmum and mnmum compressve stress under the frequent load combnaton. The fatgue assessment and parametrc study performed shows that the dmensons of the slab have an mpact on fatgue of the foundaton slab. It s concluded that the damage calculaton methods are preferable when performng a fatgue assessment based on a spectrum load, lke the wnd actng on a wnd power plant. The fatgue assessment methods that do not take the frequency of the load nto account has been seen to not be vald for such a complex load used n ths project. Key words: Fatgue, fatgue assessment method, wnd power plant, concrete foundaton slab, Eurocode, fb Model Code 010 I

6 Utmattnngsbedömnng av Betongfundament för Vndkraftverk Examensarbete nom Structural Engneerng and Buldng Performance Desgn FRIDA GÖRANSSON, ANNA NORDENMARK Insttutonen för bygg- och mljöteknk Avdelnngen för Konstruktonsteknk Betongbyggnad Chalmers teknska högskola SAMMANFATTNING Kraven på renare och förnybar energ har ökat med snande naturresurser och ett sätt att möta dessa krav är att använda vndkraft. Med ett ökande antal vndkraftverk har desgnen av fundament för dessa blvt mer av ntresse. Ett vndkraftverks fundament är utsatt för cyklsk last från vnden och det har vart osäkerheter angående effekten av utmattnng. Från början av 011 ska alla nya byggnader Sverge desgnas enlgt Eurocode och och med detta ska nya metoder för beräknng av utmattnng användas. Syftet med det här projektet är att ge rekommendatoner för desgn av betongfundament med avseende på utmattnng. Detta görs genom att klargöra utmattnngsproblematken för ett fundament för ett vndkraftverk, jämföra metoder för utmattnngsverferng enlgt Eurocode och fb Model Code 010 samt att utföra parameterstuder avseende utmattnngsdesgn av ett fundament och att dentfera parametrar som har en betydande nverkan på utmattnng av ett fundament för ett vndkraftverk. Vd utmattnngsverferng är valet av metod vktgt. I det här projektet har två metoder enlgt Eurocode avseende armerngsutmattnng använts. En av metoderna tar hänsyn tll lastfrekvens och använder Palmgren-Mners delskadesummerng för att uppskatta utmattnngsskadan, medan den andra metoden använder ett ekvvalent värde för utmattnngslasten och ett referensvärde för antalet lastcykler. För utmattnngsverferng av tryckt betong har två metoder enlgt Eurocode använts, samt en metod enlgt fb Model Code 010. En av Eurocode-metoderna och metoden från fb Model Code använder delskadesummerngen, medan den andra Eurocodemetoden kontrollerar att lvslängden med avseende på utmattnng är tllräcklg genom att använda den maxmala och mnmala tryckspännngen under den frekventa lastkombnatonen. Utmattnngsverferngen och parameterstuden som har utförts vsar att fundamentets dmensoner har en nverkan på utmattnng av fundamentet. En slutsats som har dragts är att metoderna som använder delskadesummerng är att föredra när en utmattnngsverferng av en spektrumlast utförs. De metoder som nte tar hänsyn tll lastfrekvens har vsat sg vara otllfredsställande för den komplexa last som använts detta projekt. Nyckelord: Utmattnng, utmattnngsverferng, vndkraftverk, betongfundament, Eurocode, fb Model Code 010 II

7 Contents ABSTRACT SAMMANFATTNING CONTENTS PREFACE NOTATIONS I II III V VI 1 INTRODUCTION Background 1 1. Am and objectves 1.3 Method 1.4 Lmtatons 3 FOUNDATION SLABS FOR WIND POWER PLANTS 4.1 Ground condtons 4. Loadng condtons 4.3 Typcal foundaton slab desgns 5 3 FATIGUE OF REINFORCED CONCRETE General 7 3. Concrete Renforcng steel Fatgue of renforced concrete members 10 4 FATIGUE VERIFICATION ACCORDING TO EUROCODE AND FIB MODEL CODE Fatgue verfcaton of concrete accordng to Eurocode 1 4. Fatgue verfcaton of concrete accordng to fb Model Code Fatgue verfcaton of renforcng steel accordng to Eurocode 16 5 STATIC DESIGN PROCEDURE OF FOUNDATION SLABS FOR WIND POWER PLANTS Propertes and geometry Loads Desgn of the foundaton slab n the ultmate lmt state Stablty and szng 5.3. Force dstrbuton Strut and te model and desgn of compresson-compresson node 5 III

8 5.3.4 Flexural resstance Shear capacty Remarks and conclusons from the statc desgn 7 6 FATIGUE VERIFICATION OF FOUNDATION SLAB FOR WIND POWER PLANT Fatgue load calculatons 9 6. Strut and te models to fnd fatgue stresses Crtcal sectons for fatgue assessment Fatgue stresses n the crtcal sectons Fatgue verfcaton of foundaton slab Fatgue verfcaton regardng compresson of the concrete Fatgue verfcaton regardng tensle renforcement Fatgue verfcaton regardng shear 39 7 PARAMETRIC STUDY OF FOUNDATION SLAB SUBJECTED TO FATIGUE Parameters studed Varaton of wdth of slab Study of damage development n top and shear renforcement Varaton of heght of slab Study of damage development n top and shear renforcement Analyss of the results from the parametrc study Analyss of the results regardng renforcement Analyss of the results regardng concrete 70 8 CONCLUSIONS AND RECOMMENDATIONS Fatgue desgn of foundaton slabs 7 8. Suggested future research 73 9 REFERENCES 74 APPENDIX IV

9 Preface Ths study was ntated by Ramböll due to uncertantes regardng the effect of fatgue on a foundaton slab for a wnd power plant. The project was carred out between January and August 011 n cooperaton wth Ramböll and the Department of Structural Engneerng, Concrete Structures, Chalmers Unversty of Technology, Sweden. We would lke to thank Ramböll Byggteknk, Göteborg, for the opportunty to work wth ths thess and especally our supervsor, Per Lndberg, for hs support and for provdng us wth nformaton durng our work. Next, we would lke to show our grattude to our supervsor at Chalmers, Rasmus Remplng, for helpng us wth all our questons and thoughts, especally regardng fatgue. We would also lke to thank our examner, Björn Engström, for hs partcpaton, comments and nvaluable knowledge. Wthout the help of Karl Lundstedt at Skanska Teknk, Malmö, ths project would not have turned out as t dd and we deeply apprecate hs commtment and tme. We are also grateful to Pekko Sverge AB and Semens for provdng us wth materal durng the work wth ths project. Last but not least, we would lke to show are apprecatons to our opponents Maln Johansson and Terese Löfberg for always beng there for us wth comments and coffee breaks. Göteborg August 011 Frda Göransson & Anna Nordenmark V

10 Notatons Roman upper case letters A c0 A A A A s s s A' sv s max s the area the horzontal compressve force s actng on s the renforcement amount s the requred renforcement amount s the amount of bottom renforcement s the amount of shear renforcement s the amount of top renforcement C s the maxmum compressve concrete force n a cycle C mn s the mnmum compressve concrete force n a cycle D s the bendng dameter of a bent bar D s the fatgue damage D s the damage caused by the stress range E Ed cd max, equ Ecd max Ecd mn, equ F C, s the maxmum compressve stress level, s the maxmum compressve stress level, s the mnmum compressve stress level s the compressve force n the force couple F T s the tensle force n the force couple F s the horzontal force res F z s the normal force transferred from the tower to the slab G s the self weght of the foundaton slab M. s the peak to peak fatgue moment fat ampltude M res s the overturnng moment M z s the torson moment N s the number of load cycles untl fatgue falure N( σ ) s the ultmate number of cycles for stress range σ * N s a reference value for number of cycles untl fatgue falure dependng on renforcement type P s the horzontal sol pressure R s the stress rato eq R equ s the stress rato R res s the reacton force from the ground S s the maxmum compressve stress level c,max S c,mn s the mnmum compressve stress level T s the tensle force estmated n the strut and te model T s the maxmum tensle force n the renforcement n a cycle max T s the mnmum tensle force n the renforcement n a cycle mn VI

11 Roman lower case letters b s the dstance from the edge of the slab to the gravty centre of the reacton force f s the desgn compressve concrete strength n [MPa] cd f, s the desgn fatgue resstance for concrete cd fat f ck s the characterstc compressve strength n [MPa] f, s the reference fatgue compressve strength ck fat f ctk 0 s 10 MPa f s the desgn yeld strength of the renforcement k 4 yd s a parameter nfluencng the desgn strength for concrete struts k 1 s a coeffcent affectng the fatgue strength k 1 s the exponent that defnes the slope of the frst part of the S-N curve k s the exponent that defnes the slope of the second part of the S-N curve n R s the number of cycles causng falure at the same stress level and stress range s the number of actng stress cycles at a gven stress level and stress range n S n( σ ) s the number of cycles for stress range σ s s a coeffcent dependng on the type of cement t 0 s the concrete age n days when frst subjected to fatgue loadng Greek upper case letters M s half the ampltude of the fatgue moment s the stress range S c σ Rsk s the reference fatgue stress range after * ( N ) s the reference resstng fatgue stress range at σ Rsk σ S,max s the maxmum steel stress range * N cycles * N cycles Greek lower case letters β ( t 0 ) s a coeffcent for concrete compressve strength at frst load applcaton cc ( t ) β s a coeffcent that takes the effect of hgh mean stresses durng loadng φ γ C c, sus,t 0 f nto account s the dameter of the renforcement bar s a partal factor for concrete γ s a partal factor for loads, accordng to IEC γ F, fat s a partal factor for fatgue loadng γ G s a partal factor for permanent loads γ s a partal factor for materals, accordng to IEC m VII

12 γ n s a partal factor for consequence of falure, accordng to IEC γ s a partal factor for varable loads Q γ S S, fat s a partal factor for steel γ s a partal factor for fatgue that takes the materal uncertantes nto account ν s a parameter nfluencng the desgn strength for concrete struts σ s the maxmum compressve concrete stress n a cycle c0,max σ c0,mn s the mnmum compressve concrete stress n a cycle σ cd, max,equ s the maxmum equvalent compressve stress for 10 6 cycles σ cd, mn,equ s the mnmum equvalent compressve stress for 10 6 cycles σ c,max s the maxmum compressve stress n a cycle σ c,max s the maxmum concrete compressve stress under the frequent load combnaton σ s the mnmum compressve stress n a cycle c,mn σ c,mn s the mnmum concrete compressve stress n the secton where σ c, max found σ Rd.max s the largest stress that can be appled at the edge of compresson node n strut and te models σ s the maxmum tensle steel stress n a cycle s,max σ s,mn s the mnmum tensle steel stress n a cycle ξ s a reducton factor for the reference fatgue stress range for bent bars s VIII

13 1 Introducton 1.1 Background The demands on cleaner and renewable energy have ncreased wth the depleton of natural resources and a way to meet these demands s to use wnd power. Between 1999 and 010 the energy producton from wnd power plants n Sweden ncreased extensvely as a result of ths, Energmyndgheten (011). Year 010 the energy producton from wnd power plants was 3,0 TWh and the Swedsh government has set a goal of an ncrease of the energy producton from wnd power to 30,0 TWh year 00. Ths would result n a need for wnd power plants nstead of today s 1500, see Fgure Development of wnd power plants n Sweden Energy producton [MWh] Number of wnd power plants Year Fgure 1.1 The energy producton from wnd power and number of wnd power plants n Sweden and the plannng goal for 00. Based on tables from Energmyndgheten. The technology for wnd power plants s developng fast and plants become bgger and more effectve. Ths leads to that the lfetme of a wnd power plant s short, but the foundatons can be gven a longer lfe span. The foundaton slab for a wnd power plant s subjected to cyclc loadng from the wnd. In earler desgn there have been uncertantes concernng the effect of fatgue and ths has n many cases been assumed gnorable. Now wth desgn accordng to Eurocode and larger wnd power plants the nfluence of fatgue has become more of nterest. CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119 1

14 From the begnnng of 011 all new structures n Sweden should be desgned accordng to Eurocode. Ths European Standard s a desgn code wth purpose to smplfy the cooperaton between engneers from dfferent European countres and to functon as a legal document for the engneer to relate to. As a result of ths code a new approach to calculate the nfluence of fatgue s to be consdered. 1. Am and objectves The am of ths project s to gve recommendatons for desgnng concrete foundaton slabs wth regard to fatgue. Objectves of ths project are to: Clarfy the ssues of fatgue for a foundaton slab for a wnd power plant n relaton to the general desgn problems. Compare methods for fatgue assessment accordng to Eurocode and fb Model Code 010, as well as ther backgrounds. Perform parametrc studes of the fatgue desgn of a foundaton slab. Identfy parameters that have sgnfcant mpact on the fatgue of a foundaton slab for a wnd power plant. Formulate recommendatons for fatgue desgn of foundaton slabs. 1.3 Method To ncrease the knowledge of fatgue a lterature study was done. Ths study ncluded fatgue of renforced concrete as well as concrete and renforcement behavour under fatgue loadng. The approaches of fatgue accordng to Eurocode and fb Model Code 010 was also part of ths study. Further a lterature study concernng the desgn of foundaton slabs for wnd power plants has been carred out. A foundaton slab was desgned for ntal condtons dsregardng the fatgue loads. Ths slab was then nvestgated wth regard to fatgue usng both Eurocode and fb Model Code 010 to see how and f fatgue nfluences the desgn. A comparson between the approaches was done. When the desgn of the slab was made, the wdth and heght of the slab was vared wthn reasonable lmts. To do ths each parameter was altered to see the nfluence t has on the foundaton slab wth regard to fatgue. Durng the change of parameters the statc desgn was always verfed. After the study of the behavour of the foundaton slab wth respect to fatgue, an analyss of the results from the desgn of the slab and the fatgue assessment was done. CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119

15 1.4 Lmtatons Prmarly the foundaton slab for a wnd power plant was nvestgated but the results should be possble to apply on slabs n machne rooms. However the calculatons were only performed for foundaton slabs for wnd power plants. The project was lmted to nvestgatng onshore foundatons that are square and wth a constant heght. The most common type of foundatons for onshore wnd power plants are gravty foundatons, whle ths s the type studed. The transfer of loads between the tower and the slab s done by an nserted anchor rng n the concrete. The loads taken nto consderaton n the study were the self weght of the slab and the loads transferred from the tower to the slab. These loads consst of normal and horzontal force, and overturnng and torson moment. The fatgue assessment regardng concrete only ncluded a verfcaton of the concrete fatgue compressve strength snce ths enabled a comparson between the methods n fb Model Code 010 and Eurocode. For the fatgue verfcaton of renforcement the methods used was accordng to Eurocode and wll only verfy the fatgue tensle strength of the renforcement. CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119 3

16 Foundaton Slabs for Wnd Power Plants.1 Ground condtons Wnd power plants are used at locatons that fulfl requrements for wnd condtons. Every locaton s dfferent wth regard to the ground condtons and may requre dfferent types of foundatons. If a wnd power plant s bult on rock, a specal concrete rock adapter can be used for anchorage. For clay there s often a need to use pled foundatons due to the low bearng capacty of clay. The most common foundaton type for wnd power plants s gravty foundatons whch are sutable for sol types from sand and clay to hard rock. When decdng on the geometry of the slab the ground condtons are an nfluencng factor snce t s crucal that the ground can resst the pressure under the slab. The foundaton and sol must also have a suffcent rotatonal stffness whch s estmated as a combned stffness for foundaton and sol.. Loadng condtons A wnd power plant s subjected to a range of dfferent actons. Many of the loads are transferred from the wnd power plant tower to the foundaton slab. The loads can be dvded nto two categores, statc loads and fatgue loads. The loads consst for example of the self weght of the plant, the wnd load actng on the turbne at hubheght and a sectonal overturnng moment on the foundaton slab that the wnd load gves rse to. Fgure.1 shows the dfferent parts of a wnd power plant. Hub Rotor blades Tower Foundaton Fgure.1 The dfferent parts of a wnd power plant. 4 CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119

17 The slab s also subjected to other varable actons lke snow and temperature. These actons are though small n comparson to the others. The self weght of the whole structure, the wnd power plant and the foundaton slab, s ressted by the resultng earth pressure actng on the foundaton slab. The foundaton slab s subjected to a fatgue load caused by the wnd actng on the tower and the movement of the turbne. Ths fatgue load s more complex and dffers from the fatgue load caused by traffc on a brdge for example. The wnd s actng on the tower wth varyng speed and drecton. When desgnng the foundaton slab the fatgue loads are often gven by the suppler of the wnd power plant and may dffer between dfferent supplers. The heght and sze of the tower are also nfluencng factors for the fatgue load actng on the slab. Fatgue loads specfed by the suppler are often gven n form of tables from whch fatgue damage can be calculated..3 Typcal foundaton slab desgns The foundaton slab for a wnd power plant s usually square, crcular or octagonal. The top of the slab s ether flat or wth a small slope of maxmum 1:5. Ths slope s a way of makng the slab more economcally benefcal due to the fact that less concrete s needed. It also ensures that water s led away from the slab. The maxmum slope s chosen so that no upper formwork has to be used when castng the concrete and the maxmum slab thckness s provded where the hghest shear force and moment are actng. The concrete strength class for foundaton slabs of wnd power plants normally ranges from C30/37 to C35/45. The sze of the foundaton slab s determned by the demand on foundaton stffness, set by the manufacturer of the wnd power plant. Ths s to avod self-oscllaton and lmt the rsk of settlements. Due to ths demand the foundaton slabs normally have a wdth of 15 to 0 meters and a thckness of 1.5 to.5 meters. The manufacturer also provdes nformaton about an anchor rng that s used to anchor the tower n the foundaton slab. For a prncpal drawng of an anchor rng see Fgure.. Fgure. Square foundaton slab of a wnd power plant wth anchor rng, Pekko Sverge AB. CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119 5

18 Dfferent foundaton slab shapes result n dfferences n the resultng earth pressure and dfferent renforcement layouts. For square and octagonal slabs the bottom renforcement s placed n two drectons, perpendcular, whle the top renforcement s radal through the anchor rng and smlar to the bottom renforcement outsde the rng, see Fgure.3. For crcular slabs both the top and bottom renforcement can be radal. a) b) c) Fgure.3 Renforcement layouts for a square foundaton slab of a wnd power plant: (a) Bottom renforcement (b) Radal top renforcement through the anchor rng (c) Top renforcement outsde the anchor rng. 6 CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119

19 3 Fatgue of Renforced Concrete 3.1 General When a structure s subjected to a cyclc load, falure can occur before the statc loadng strength of the materal s reached. Ths type of falure s known as a fatgue falure. Typcal cyclc loads are wnd, waves, traffc loads and vbratons from machnes. These affect structures lke brdges, tall buldngs, offshore structures and wnd power plants. The fatgue capacty of the materal s nfluenced by several dfferent parameters such as load frequency, maxmum load level, stress ampltude and materal composton. Cyclc load, or fatgue loadng, s dvded nto three dfferent categores: low-cycle, hgh-cycle and super-hgh-cycle fatgue. The number of load cycles determnes the type of fatgue. Few load cycles, up to 10 3 cycles, gve low-cycle fatgue. If the number of cycles s between t s referred to as hgh-cycle fatgue. The last category s super-hgh-cycle fatgue and t s wth more than 10 7 cycles. See Fgure 3.1 for examples of structures subjected to the dfferent types of fatgue loadng. LOW-CYCLE FATIGUE HIGH-CYCLE FATIGUE SUPER- HIGH-CYCLE FATIGUE Structures subjected to earthquakes Structures subjected to storm Brdges Wnd power plants Arport pavement Mass rapd transt structures Sea structures NUMBER OF CYCLES Fgure 3.1 Spectra of fatgue load categores and examples of structures subjected to the fatgue loads. When performng a fatgue lfe assessment of structural elements there are two basc approaches that can be used. One consders an analyss of crack propagaton at the pont under consderaton and s based on lnear elastc fracture mechancs. The second approach, whch s more commonly appled, uses a curve that shows the relaton between cyclc stress range and number of cycles to fatgue falure n logarthmc scales. Ths s known as a Wöhler or an S N curve where S s the stress range and N s the number of cycles. CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119 7

20 The S N curves are derved usng expermental data obtaned from fatgue tests. The curve s presented by the best ft lne wth constant slope. In practce the curve used s parallel to that obtaned from the fatgue tests, but wth a devaton to acheve a safety margn, see Fgure 3.. log S Curve obtaned from test data Curve used n practce Fgure 3. Prncpal S N curve. log N Fatgue falure s dvded nto three dfferent stages: crack ntaton, crack propagaton and falure. However concrete and steel behave dfferently wth regard to fatgue and renforced concrete s treated as two separate materals when desgnng for ths, Johansson (004). Investgatons have been made about how concrete behave and how renforcement react, but only a few studes have been made of renforced concrete members. Due to the fact that the self weght of concrete s normally a large part of the total load, ths counteracts the affect of fatgue. Wth the work towards more optmsed structures the self weght s reduced and the utlzaton of the concrete strength s ncreased. Ths could lead to that fatgue wll have a larger sgnfcance when desgnng n concrete. 3. Concrete Concrete s not a homogenous materal and durng hardenng of concrete pores and mcro cracks are formed. It s also common that macro cracks are formed before any load s appled, ths due to shrnkage and temperature dfferences. Because of the cracks and the nhomogenety concrete can be regarded as a stran-softenng materal.e. wth large strans the stffness decreases, see Fgure CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119

21 Stress, σ Stran 7,81cm softenng f c Stran, ε Fgure 3.3 Stress-stran relaton for concrete showng the decreasng stffness due to stran softenng. When the concrete s subjected to a cyclc load there wll be no clear crack ntaton process, snce cracks already exst. Instead these cracks wll grow, slowly at frst and then qucker, untl falure n the remanng part of the concrete secton, Svensk Byggtjänst (1994). Unlke steel, fatgue cracks n concrete have no dentfable surface topography and due to ths fatgue falure n concrete structures s dffcult to dentfy. 3.3 Renforcng steel In contrast to concrete steel s a stran-hardenng materal, whch means that wth large strans above yeldng the strength ncreases, see Fgure 3.4. Ths gves steel a fatgue stress lmt and below ths lmt no fatgue falure wll occur, Thun (006). Stress, σ Stran hardenng 3,5cm f y Stran, ε Fgure 3.4 Stress-stran relaton for steel showng the ncreasng strength due to stran hardenng. For renforcng steel cracks are ntated by dscontnutes or stress concentratons n the bar; these cracks grow untl they cause a brttle falure n the remanng uncracked part of the bar. It has been seen that the strength of renforcement subjected to fatgue loadng s reduced to about 44 % of the yeld strength, CEB (1988). CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119 9

22 The most mportant factor nfluencng the fatgue lfe of renforcement s the stress ampltude. Other nfluencng factors are geometry (whch affects stress concentratons n the bar) and envronment (.e. corroson). Wth ncreasng bar dameter the fatgue strength of the renforcement decreases. Ths s due to the ncreased rsk of flaws n the surface because of the larger dameter/area. Accordng to CEB (1988) bent bars, mechancal and welded connectons and corroson of the bars also result n a lowered fatgue performance of the renforcement. 3.4 Fatgue of renforced concrete members If a renforced concrete beam or slab s subjected to cyclc bendng loadng, cracks wll appear and ntal cracks wll grow. Wth the crack propagaton the tensle stresses n the concrete wll redstrbute to the renforcement. Deformaton of the member ncreases due to cyclc loadng, whch leads to that the mportance of deformatons, s generally greater than the actual fatgue lfe of the element. Fatgue falure n renforced concrete can occur n the concrete, renforcement or n the connecton between them. The falures are charactersed as bendng, whch results n compresson falure of the concrete or tensle falure of the renforcement, shear or punchng and bond falure. Bendng falure depends on how the concrete s renforced. For under-renforced sectons the fatgue resstance s manly determned by the fatgue propertes of the renforcement. Fatgue falure of the renforcement due to tensle forces, caused by bendng, occur wthout notceable stran and s therefore dffcult to predct. If the secton s over-renforced fatgue falure wll occur n the compresson zone n the concrete as a compresson falure, CEB (1988). Shear falure s dependng on whether the beam or slab has shear renforcement. For beams wthout shear renforcement a crtcal shear crack may develop after only a few loadng cycles. Ths shear crack appears when the tensle strength of the concrete s reached and the fatgue falure s determned by the propagaton of ths crack, CEB (1988). Two dfferent fatgue falure modes for beams wthout shear renforcement exst and are shown n Fgure 3.5. The frst mode s formaton of a dagonal crack and the second s compresson of the concrete at the top of the shear crack. Fgure 3.5 Possble shear fatgue falure modes n a beam wthout shear renforcement: (a) dagonal crackng (b) compresson of the concrete at the top of the shear crack 10 CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119

23 The fatgue behavour of beams wth shear renforcement s dependng on the fatgue propertes of the renforcement. In Fgure 3.6 four fatgue falure modes are shown. The frst two show when fatgue falure occur n the renforcement, ether n the strrups or n the longtudnal renforcement. The last two s when the concrete fals n compresson, ether at the top of the shear crack or n the mddle of the beam between cracks. Fgure 3.6 Possble shear fatgue falure modes n a beam wth shear renforcement: (a) fatgue of shear renforcement (b) fatgue of longtudnal renforcement crossng the shear crack (c) fatgue of the concrete n compresson at the top of the shear crack (d) fatgue of the concrete n compresson n the mddle of the beam. Bond falure s falure between the concrete and the renforcement. There are three dfferent types of bond falures; splttng of the surroundng concrete, concrete falng n shear along the permeter of the renforcement bar and break down of the shear strength of chemcal bonds between the renforcement bar and the concrete. These falures are affected by e.g. load level, frequency of load, strength of concrete and confnng effects, fb (000). Splttng of the surroundng concrete occur when the shear strength of the bond s suffcent and s caused by the radal pressure from the anchored renforcng bar. Ths pressure develops when the prncpal tensle stress cracks the concrete and causes the bond forces to be drected outward from the bar. The effect of cyclc load on ths type of falure s that under cyclc load the stress pattern changes due to stress redstrbuton. The repeated loadng opens up longtudnal cracks and cyclc creep of concrete causes the stress pattern at ultmate falure to emerge earler. When the concrete has suffcent splttng resstance the fatgue bond falure wll occur as shear falure of the concrete. Ths s the hghest bond resstance and s determned by the shear strength of confned concrete. Bond falure of chemcal type of bonds has rarely been studed wth regard to fatgue snce chemcal bonds are seldom used. However, when the concrete determnes the strength of the chemcal bond a reducton of the bond strength due to fatgue can be assumed, CEB (1988). CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119 11

24 4 Fatgue Verfcaton Accordng to Eurocode and fb Model Code Fatgue verfcaton of concrete accordng to Eurocode The fatgue verfcaton methods for concrete n compresson, accordng to Eurocode, are presented n EN , SIS (005). In Eurocode there are two methods for fatgue verfcaton of compressed concrete that can be appled on foundaton slabs. These methods only take the compressve stresses n the concrete nto consderaton and not the number of load cycles untl fatgue falure occurs. Instead a reference value of 10 6 load cycles s appled. The methodology used s that a comparson s done for the stresses caused by the cyclc load and a reference concrete strength for statc load f,. Ths reference concrete strength s defned by equaton (4.5). cd fat Accordng to the frst fatgue verfcaton method the compressed concrete has a suffcent fatgue resstance f the followng condton s fulflled: Where: E 0,43 1 R 1 (4.1) cd, max, equ + equ R equ Ecd,mn, equ (4.) E cd,max, equ E E cd,mn, equ cd,max, equ σ cd,mn, equ (4.3) f cd, fat σ cd,max, equ (4.4) f cd, fat Where: R equ s the stress rato Ecd, mn, equ s the mnmum compressve stress level Ecd, max, equ s the maxmum compressve stress level f, s the desgn fatgue resstance for the concrete accordng to equaton cd fat (4.5) σ cd, max,equ s the maxmum equvalent compressve stress for 10 6 cycles σ cd, mn,equ s the mnmum equvalent compressve stress for 10 6 cycles 1 CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119

25 The desgn fatgue resstance of concrete accordng to Eurocode s determned by: Where: k 1 ( ) f ( ) ck fcd, fat k1 β cc t0 fcd 1 (4.5) 50 s a coeffcent dependng on the reference number of cycles tll falure. Accordng to EN :005-NA, ths coeffcent should be set to 1.0 β cc t 0 s a coeffcent for the concrete compressve strength at a certan age accordng to equaton (4.6) t 0 s the concrete age n days when frst subjected to the fatgue loadng f cd s the desgn compressve concrete strength n [MPa] f ck s the characterstc compressve concrete strength n [MPa] The coeffcent for estmaton of the concrete compressve strength for a certan age s calculated accordng to: Where: ( t ) s 1 8 t 0 β e (4.6) cc 0 s s a coeffcent dependng on the type of cement The second method n Eurocode checks the stresses n the concrete under the frequent load combnaton. It states that f the followng condton s fulflled the compressed concrete has adequate fatgue strength: σ σ c 0,5 + 0,45 f cd c,max,mn f cd, fat, fat 0,9 for f ck 50MPa 0,8 for f ck > 50MPa (4.7) CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119 13

26 Where: σ c,max s the maxmum concrete compressve stress under the frequent load combnaton σ c,mn s the mnmum concrete compressve stress n the secton where σ c,max s found In ths project the frst Eurocode concrete method wll be referred to as EC:1 and the second method as EC:. 4. Fatgue verfcaton of concrete accordng to fb Model Code 010 Fatgue verfcaton of plan concrete accordng to fb Model Code 010 s found n Model Code 010, frst complete draft, fb (010). In ths method the number of load cycles untl fatgue falure s estmated for constant ampltude stress, n contrast to the approaches n Eurocode that only consders the stresses n the concrete. As well as n Eurocode a reference concrete strength for statc load,, s estmated and f ck, fat compared to the concrete stresses. The fatgue verfcaton n fb Model Code 010 can be used to check pure compresson, compresson-tenson and pure tenson falure of the concrete. Here the fatgue assessment wll only nclude a verfcaton of the concrete compressve strength snce ths can be compared to the methods n Eurocode. The maxmum and mnmum compressve stress levels caused by fatgue loadng are defned as: S c,max σ c,max (4.8) f ck, fat S c,mn σ c,mn (4.9) f ck, fat S S S (4.10) c c, max c,mn Where: S c,max s the maxmum compressve stress level S c,mn s the mnmum compressve stress level S c s the stress range σ c,max s the maxmum compressve stress n a cycle 14 CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119

27 σ c,mn s the mnmum compressve stress n a cycle For compresson of the concrete the condton below should be fulflled, and then the followng equatons apply: For S 0. 8 assume S 0. 8 c, mn > For S c, 0. 8 log N 0 mn c, mn (1 + 16S + 8S ) (1 S ) (4.11) 1 c,mn c,mn c, max log N 0. log N1 (log N1 1) (4.1) 1 ( ) log N 3 log N Sc, mn (4.13) Sc If log N 6 (4.14) 1 then log N log N1 If log 1 > 6 N and S ( S ) then log N log N (4.15) c 0 c,mn Where: If log 1 > 6 N and S < ( S ) then log N log N 3 (4.16) c 0 c,mn N s the number of load cycles untl fatgue falure The fatgue reference compressve concrete strength can be determned by: f ck, fat f β (4.17) ( ) ( ) ck t 0 β c, sus t, t0 f ck 1 5 f ctk cc 0 CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119 15

28 Where: f ck s the characterstc compressve strength n [MPa] f, s the reference fatgue compressve strength ck fat f ctk 0 s 10 MPa ( ) t 0 β cc s a coeffcent dependng on the age of the concrete at the frst applcaton of fatgue loadng ( t ) β s a coeffcent that takes the effect of hgh mean stresses durng c, sus,t 0 loadng nto account. May be assumed to 0.85 for fatgue loadng When the number of load cycles untl fatgue falure s known the Palmgren-Mner damage summaton may be appled to estmate the fatgue lfe. Where: ns D < 1 (4.18) n R D n S s the fatgue damage s the number of actng stress cycles at a gven stress level and stress range n R s the number of cycles causng falure at the same stress level and stress range 4.3 Fatgue verfcaton of renforcng steel accordng to Eurocode Fatgue verfcaton of renforcng steel, accordng to Eurocode, s presented n EN , SIS (005). Two dfferent approaches for fatgue assessment of the renforcement are gven. In the frst method the Palmgren-Mner damage summaton s used to estmate the damage. n( σ ) DEd < 1 N( σ ) (4.19) 16 CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119

29 Where: n( σ ) s the number of cycles for stress range σ N( σ ) s the ultmate number of cycles for stress range σ From the characterstc fatgue strength curve ( S N relaton) of renforcng and prestressng steel the ultmate number of cycles, N( σ ), can be estmated. As can be seen n Fgure 4.1 the S N relaton s a curve wth two dfferent slopes. The condtons stated n equatons (4.0) and (4.1) have been estmated from the S N relaton and gve the ultmate number of cycles for the slope vald for a certan stress range σ. log σ Rsk f yd k 1 1 k 1 N* log N Fgure 4.1 S N relatons for renforcng and prestressng steel. N( σ Rsk k1 * S, fat σ ) N f γ F, fat σ γ γ σ Rsk F, fat σ (4.0) γ S, fat N( σ Rsk k * S, fat σ ) N f γ F, fat σ γ γ σ Rsk F, fat σ < (4.1) γ S, fat Where: * N s a reference value for number of cycles untl fatgue falure dependng on renforcement type, Table 6.3N n EN :005 * σ Rsk s the reference fatgue stress range after N cycles, Table 6.3N n EN :005 CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119 17

30 γ S, fat s a partal factor for fatgue that takes the materal uncertantes nto account, Table.1N n EN : γ F, fat s a partal factor for fatgue loadng wth recommended value 1.0, EN : (1) k 1 k s the exponent that defnes the slope of the frst part of the S-N curve, Table 6.3N n EN :005 s the exponent that defnes the slope of the second part of the S-N curve, Table 6.3N n EN :005 The second method for fatgue verfcaton of the renforcement uses a damage equvalent stress range. Ths method can be appled on standard cases wth known loads, most commonly brdges. When usng t for buldngs the damage equvalent stress range can be approxmated wth the maxmum steel stress range under the exstng load combnaton. Accordng to ths method the renforcement has suffcent fatgue resstance f the followng condton s fulflled: γ σ ( N ) * Rsk F, fat σ S,max (4.) γ S, fat Where: σ S,max s the maxmum steel stress range * ( N ) s the reference resstng fatgue stress range at σ Rsk * N cycles The two methods for fatgue verfcaton of the renforcement wll n ths project be referred to as EC:1 and EC:. For shear renforcement the methods descrbed above can be used, however the value of σ Rsk s only vald for straght bars and therefore needs to be reduced for the bent bars n the shear renforcement. Ths s done accordng to the followng equaton: Where: D ξ (4.3) φ ξ D φ s a reducton factor for the reference fatgue stress range for bent bars s the bendng dameter of a bent bar s the dameter of the renforcement bar 18 CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119

31 5 Statc Desgn Procedure of Foundaton Slabs for Wnd Power Plants 5.1 Propertes and geometry When makng a prelmnary desgn of a foundaton slab for a wnd power plant, ntal condtons need to be determned. The condtons for the locaton of the wnd power plant are often gven by the suppler of the plant wth help from a geotechncal ste study. The type of sol, the depth to sold ground and the groundwater level are some of these condtons. There are also requrements on the foundaton slab and sol for mnmum rotatonal stffness around the horzontal axs and mnmum stffness for horzontal translaton. These demands are set by the suppler of the plant. For the desgn of the foundaton slab n ths project, the condtons were based on nformaton receved from Semens for a plant located near Tuggarp, Gränna n Sweden. Some of the condtons were based on what s common for buldng stes of wnd power plants. The condtons for the foundaton slab are; frcton sol, the groundwater level s below the foundaton slab, the mnmum demand for combned stffness of sol and foundaton s 1500MNm/deg wth regard to rotatonal stffness and the mnmum stffness wth regard to horzontal translaton s 500MN/m. The placement above the ground water level means that the pore pressure n the sol was dsregarded. The desgned slab s a gravty foundaton, snce ths s the most common type of foundaton for wnd power plants. The shape of the slab was assumed to be square and wth a constant heght,.e. no slope at the top of the slab. Concrete class C30/37 and renforcement type B500B was chosen. The anchor rng s placed n the centre of the slab, 1.7 meters down n the concrete. It has a heght of.45 meters, an outer dameter of 4. meters and an nner dameter of 3.6 meters. 5. Loads Statc loads actng on the slab are loads from the tower, snow and temperature actons, see Chapter, n partcular Secton.. The varable loads actng drectly on the foundaton are small n comparson and was dsregarded n ths analyss. The specfc wnd power plant has a hub-heght of 99.5 meters and the desgn wnd speed at the heght of the hub s 8.5 m/s. Ths has been used to fnd the loads actng on the foundaton slab. The desgn loads for the foundaton slab are calculated by Semens accordng to the standard for wnd power plants, IEC Ths standard descrbes several dfferent desgn load cases, for 8 desgn stuatons, that should be consdered n desgn of members of wnd power plants. From these load cases the most crtcal cases should be found, and the desgn of the member should be based on these. For each of the desgn load cases the approprate type of analyss s specfed, wth U for analyss of ultmate loads used to ensure structural stablty and materal strength, or wth F for load cases used n fatgue assessment of the member. The desgn load cases for CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119 19

32 ultmate loads are dvded nto normal, abnormal and transport and erecton load cases. The normal load cases are expected to occur frequently and the turbne s then n a normal state or sufferng mnor faults. The abnormal load cases are less lkely to occur and often result n severe faults. Semens provde nformaton about fve desgn load cases and state that two of these should be used for the desgn of the foundaton slab. These two load cases are maxmum desgn loads under normal power producton and maxmum desgn loads under extreme condtons and they are ncludng partal safety factors from IEC In ths standard t s stated that partal safety factors from other desgn codes can be used together wth partal safety factors from IEC Ths s vald as long as the combned value of the partal safety factors for loads, materals and consequence of falure s not less than the combnaton of the partal safety factors that are stated n IEC In ths project the desgn loads provded by Semens were used ncludng the partal safety factors from IEC The partal safety factors for the materals, the self weght of the slab and the horzontal sol pressure were accordng to Eurocode. It was ensured that the combned value of the safety factors was at least what s stated n IEC Table 5.1 shows the partal safety factors accordng to IEC and Eurocode. Table 5.1 Partal safety factors accordng to IEC and partal safety factors n the ultmate lmt state accordng to Eurocode. IEC Eurocode Loads Normal γ 1, 0 f or 1, 35 Permanent γ G 1,0 or 1, 35 Abnormal γ 1, 1 Varable γ 1, 50 Transport γ 1, 5 Materal γ 1, 1 Concrete γ 1, 50 m f f Steel γ 1, 15 Q C S Consequence of falure Class 1 γ 0, 9 0,9 n Class γ 1, 0 1,0 n Class 3 γ 1, 3 1,1 n The foundaton desgn loads provded by Semens are gven as sectonal forces for the normal load case based on normal operaton and the abnormal load case whch s the load case wth the hghest overturnng moment. From the tower to the foundaton slab the followng sectonal forces due to loadng are transferred; normal force, horzontal force, overturnng and torson moment. The foundaton slab desgn n the ultmate lmt state was based on the desgn load case whch resulted n the hghest sectonal 0 CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119

33 forces and ths s the one wth the hghest overturnng moment, see Table 5.. For desgn of the slab n servceablty lmt state the desgn load case for normal operaton was used. Table 5. Foundaton desgn loads, ncludng partal safety factors accordng to IEC , for normal operaton and desgn load case wth hghest overturnng moment. Normal operaton Hghest overturnng moment Normal force, Horzontal force, Overturnng moment, Torson moment, F kn kn z F 800 kn kn res M knm knm res M knm knm z 5.3 Desgn of the foundaton slab n the ultmate lmt state For the statc desgn of the foundaton slab there are several aspects that need to be consdered. The stablty of the slab has to be verfed for resstance aganst overturnng moment and requred rotatonal stffness. The slab must also have a suffcent flexural resstance wth regard to postve and negatve bendng moments. Further the shear capacty of the slab must be adequate, and f necessary shear renforcement has to be desgned. For a foundaton slab for a wnd power plant the anchor rng transfers forces from the tower to the concrete slab by embedded anchor bolts. The lower part of the anchor rng, that s embedded n the concrete slab, provdes the anchorage of the tensle forces from the tower. The connecton wth the concrete s done by geometrcal lockng at the lower part of the anchor rng. The choce wth embedded bolts enables post-tensonng of the nterface between the tower and the foundaton slab and ths s preferable snce t s ncreasng the fatgue lfe of the structure. The compressve forces from the tower can be assumed to be transferred drectly from the upper part of the anchor rng, whch s not embedded n the concrete slab, to the top of the foundaton slab, see Fgure 5.1. Due to these compressve forces punchng shear needs to be checked under the loaded area of the rng. CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119 1

34 Secton where the compressve load from the tower s transferred to the slab Secton where the tensle load from the tower s anchored n the slab Fgure 5.1 Sectons where the compressve and tensle loads from the tower are transferred. Compresson of the concrete under the loaded area of the anchor rng also needs to be checked snce t can be consdered as a concentrated compresson node n a strut and te model. All of these verfcatons were performed accordng to Eurocode Stablty and szng The demands on stablty of the foundaton slab wll determne the sze of t. In order to check stablty, the slab sze was assumed and the reacton force from the ground was checked to be actng under the slab. If the reacton force s actng outsde the slab ths would mply that the stablty aganst overturnng moment s not suffcent. The locaton of the reacton force, R res, was found by moment equlbrum for the self weght of the wnd power plant and the slab, and the sectonal forces as well as the horzontal sol pressure, see Fgure 5.. Ths resulted n an estmaton of b, whch s the dstance from the edge of the foundaton slab to the gravty centre of the reacton force. The reacton force s unformly dstrbuted over the length b. The compressed area under the slab was then found to verfy that the ground could resst the sol pressure caused by the slab. F z F res M res G h b R res D/ P Fgure 5. Model of the loads actng on the slab and the reacton force from the ground. CHALMERS, Cvl and Envronmental Engneerng, Master s Thess 011:119