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        整體式橋臺(tái)橋梁極限長(zhǎng)度

        2014-08-08 19:08:14BRISEGHELLABruno薛俊青蘭成ZORDANTobia陳寶春
        關(guān)鍵詞:有限元模型

        BRISEGHELLA+Bruno+薛俊青蘭成+ZORDAN+Tobia+陳寶春

        建筑科學(xué)與工程學(xué)報(bào)2014年文章編號(hào):16732049(2014)01010407

        收稿日期:20140123

        基金項(xiàng)目:海外高層次人才引進(jìn)計(jì)劃(“千人計(jì)劃”)項(xiàng)目(TM201227);福州大學(xué)人才引進(jìn)科研啟動(dòng)基金項(xiàng)目(XRC1369)

        作者簡(jiǎn)介:BRISEGHELLA Bruno(1971),男,意大利人,教授,博士研究生導(dǎo)師,工學(xué)博士

        摘要:以目前世界上最長(zhǎng)的整體式橋臺(tái)橋梁Isola della Scala橋?yàn)閷?shí)例建立有限元模型,通過(guò)實(shí)橋動(dòng)力測(cè)試對(duì)模型進(jìn)行校正;提出整體式橋臺(tái)橋梁極限長(zhǎng)度的簡(jiǎn)化計(jì)算公式,并通過(guò)有限元模型驗(yàn)證其精確性;利用該簡(jiǎn)化計(jì)算公式預(yù)測(cè)不同限制條件下整體式橋臺(tái)橋梁的極限長(zhǎng)度。結(jié)果表明:考慮橋墩的轉(zhuǎn)動(dòng)能力和橋臺(tái)的承載能力時(shí),極限長(zhǎng)度可以達(dá)到540 m;考慮溫度位移產(chǎn)生的疲勞影響時(shí),極限長(zhǎng)度可以達(dá)到450 m;考慮橋頭搭板的耐久性時(shí),極限長(zhǎng)度可以達(dá)到430 m。

        關(guān)鍵詞:整體式橋臺(tái)橋梁;極限長(zhǎng)度;有限元模型;動(dòng)力測(cè)試;溫度荷載;土結(jié)構(gòu)相互作用

        中圖分類號(hào):U443文獻(xiàn)標(biāo)志碼:A

        Maximum Length of Integral Abutment BridgesBRISEGHELLA Bruno1, XUE Junqing1, LAN Cheng2, ZORDAN Tobia2, CHEN Baochun1

        (1. School of Civil Engineering, Fuzhou University, Fuzhou 350108, Fujian, China;

        2. Bolina Ingegneria s.r.l., Venice 30174, Veneto, Italy)Abstract: Taking “Isola della Scala” Bridge in Verona (Italy), the longest integral abutment bridge ever built, as case, an accurate finite element model was built. The finite element model was updated using the results of static and dynamic tests. Then, a simplified formula which can be used to predict the maximum length of integral abutment bridge was proposed, and the validity was verified by the finite element model. Finally, using the simplified formula, the maximum length of integral abutment bridge considering different limiting conditions was predicted. The results show that: when considering the pier rotation and abutment capacities, the maximum length can reach 540 m; when considering the fatigue effects due to thermalinduced displacement, the maximum length can reach 450 m; when considering the durability of approach slab, the maximum length can reach 430 m.

        Key words: integral abutment bridge; maximum length; finite element model; dynamic test; thermal load; soilstructure interaction

        0引言

        隨著中國(guó)經(jīng)濟(jì)的發(fā)展,社會(huì)對(duì)交通運(yùn)輸能力的要求不斷提高,荷載等級(jí)、交通流量、行車速度等也必然提高,再加上中國(guó)超載車輛的問題長(zhǎng)期沒有得到解決,如何保證橋梁的安全、耐久、全壽命服務(wù)品質(zhì)這些可持續(xù)發(fā)展問題,都是當(dāng)前需要解決的重要問題。目前,中國(guó)擁有大量的有伸縮縫橋(有縫橋),有縫橋通過(guò)伸縮縫和支座來(lái)吸收溫度升降所引起的主梁膨脹和收縮、混凝土收縮和徐變以及基礎(chǔ)的不均勻沉降。隨著橋齡增長(zhǎng),在氣候、環(huán)境等自然因素的作用以及一些不可預(yù)測(cè)的自然破壞力作用下,絕大多數(shù)有縫橋在使用過(guò)程中均出現(xiàn)耐久性問題。

        通過(guò)對(duì)大量橋梁使用情況的調(diào)查可以發(fā)現(xiàn),伸縮縫和支座損壞最為常見且影響最大[12]。同時(shí)伸縮縫和支座損壞還會(huì)產(chǎn)生其他一系列橋梁病害,如伸縮縫損壞漏水造成主梁端部、臺(tái)帽或墩帽混凝土和支座的腐蝕以及跳車、顛簸等不舒適的行車感受,甚至高速情況下造成事故。此外,由于伸縮縫和支座損壞所引起的頻繁更換或維修會(huì)耗費(fèi)大量的時(shí)間和費(fèi)用,造成嚴(yán)重負(fù)面社會(huì)影響[3]。

        1超長(zhǎng)整體式橋臺(tái)橋梁

        為了從根本上解決橋梁伸縮縫和支座的耐久性和易損性問題,許多工程師提出了“沒有伸縮縫就是最好的伸縮縫”概念[4]。對(duì)于多跨橋梁,采用連續(xù)梁、連續(xù)剛構(gòu)等橋型,橋墩上的伸縮縫或支座就可以被取消。針對(duì)橋臺(tái)處無(wú)縫化的做法主要有3種,包括全整體式橋臺(tái)、半整體式橋臺(tái)和延伸橋面板[1]。

        整體式橋臺(tái)橋梁(整體橋)最早于20世紀(jì)30年代出現(xiàn)在美國(guó)。然而整體橋在初期并沒有得到很好的發(fā)展,主要是因?yàn)楦郊赢a(chǎn)生的溫度影響、土結(jié)構(gòu)的相互作用等問題沒有得到很好解決。整體橋的上部結(jié)構(gòu)、下部結(jié)構(gòu)、臺(tái)后填土及樁周土將一起承受荷載作用,特別是原先由伸縮縫和支座吸收的由于溫度升降所引起的主梁膨脹和收縮將通過(guò)下部結(jié)構(gòu)傳遞到臺(tái)后填土和樁周土中[56]。隨著國(guó)際上高速公路建造興旺時(shí)期的到來(lái),近幾年整體橋發(fā)展迅速,目前已在美國(guó)、加拿大、意大利、英國(guó)、德國(guó)和日本等發(fā)達(dá)國(guó)家得到了大量的應(yīng)用。然而,關(guān)于整體橋極限長(zhǎng)度目前并沒有一個(gè)統(tǒng)一的標(biāo)準(zhǔn),不同地質(zhì)情況、溫度變化和施工經(jīng)驗(yàn),導(dǎo)致不同國(guó)家和地區(qū)對(duì)于整體橋總長(zhǎng)度的限值也不盡相同,且主要依靠主梁的溫度變形值和已建整體橋的經(jīng)驗(yàn)數(shù)據(jù)來(lái)確定。目前,世界各國(guó)規(guī)范的建議值通常小于或等于100 m,因此整體橋的應(yīng)用主要集中于中小跨徑橋梁中。

        部分學(xué)者針對(duì)整體橋極限長(zhǎng)度開展了相應(yīng)的研究,以期擴(kuò)展整體橋的使用范圍。有學(xué)者以總長(zhǎng)度305,381,457 m的整體橋有限元模型為基礎(chǔ),開展了大量參數(shù)分析。結(jié)果表明,當(dāng)整體橋總長(zhǎng)度超過(guò)305 m時(shí),樁、橋臺(tái)樁連接處和主梁橋臺(tái)背墻連接處的應(yīng)力很高,因此這些參數(shù)可以被看作是限制整體橋長(zhǎng)度的主要因素。較高的橋臺(tái)、適中的橋臺(tái)背墻施工節(jié)點(diǎn)剛度、較低的土壤剛度和樁繞強(qiáng)軸彎曲可以降低整體橋的應(yīng)力和位移,有利于增加整體橋的總長(zhǎng)度,最后提出整體橋的極限長(zhǎng)度可以達(dá)到457 m[7]。瑞士洛桑聯(lián)邦理工大學(xué)的學(xué)者也開展了相應(yīng)的研究,并認(rèn)為將瑞士聯(lián)邦公路署對(duì)整體橋的總長(zhǎng)度限制從60 m提高到數(shù)百米是可能的[8]。還有學(xué)者根據(jù)美國(guó)AASHTO規(guī)范,預(yù)測(cè)了位于中等密度粘土且采用H型鋼樁的整體橋極限長(zhǎng)度。采用不同H型鋼樁,位于寒帶的混凝土整體橋極限長(zhǎng)度從150 m變化到265 m,而鋼整體橋極限長(zhǎng)度從80 m變化到145 m;位于溫帶的混凝土整體橋極限長(zhǎng)度從180 m變化到320 m,而鋼整體橋極限長(zhǎng)度從125 m變化到220 m[910]。

        endprint

        本文中將總長(zhǎng)度超過(guò)200 m的整體橋稱為超長(zhǎng)整體橋。通過(guò)對(duì)多篇文獻(xiàn)[11]~[16]的總結(jié)和歸納,得到世界上已建設(shè)超長(zhǎng)整體橋的國(guó)家以及對(duì)應(yīng)的極限長(zhǎng)度,見表1。從表1可以看出,將整體橋的概念應(yīng)用于總長(zhǎng)度超長(zhǎng)的橋梁中是可行的。

        表1超長(zhǎng)整體橋的極限長(zhǎng)度

        Tab.1Maximum Lengths of Superlong

        Integral Abutment Bridges地區(qū)極限長(zhǎng)度/m意大利維羅納400.8美國(guó)田納西358.4美國(guó)科羅拉多339.2美國(guó)俄勒岡335.5美國(guó)路易斯安那304.8美國(guó)印第安納302.0美國(guó)維吉尼亞235.5美國(guó)南達(dá)科他213.4以目前世界上總長(zhǎng)度最長(zhǎng)的整體橋,位于意大利維羅納的Isola della Scala橋?yàn)閷?shí)例,建立有限元模型,并通過(guò)實(shí)橋動(dòng)力測(cè)試結(jié)果校正模型。提出整體橋極限長(zhǎng)度的簡(jiǎn)化計(jì)算公式,通過(guò)有限元模型驗(yàn)證其精確性。最后利用該簡(jiǎn)化公式,估算在不同限制條件下整體橋的極限長(zhǎng)度。2實(shí)例分析

        2.1Isola della Scala橋

        意大利的Isola della Scala橋共13跨,跨度為29.9 m+11×31 m+29.9 m,總長(zhǎng)為400.8 m。該橋主要參數(shù)見表 2,其立面見圖 1。該橋通過(guò)在相鄰跨的主梁之間和主梁與橋臺(tái)背墻之間現(xiàn)澆混凝土,從而取消伸縮縫。下部結(jié)構(gòu)與上部結(jié)構(gòu)之間通過(guò)鋼棒連接,其節(jié)點(diǎn)剛度介于鉸接和剛接之間。該橋從2007年建成通車直到現(xiàn)在,并沒有發(fā)現(xiàn)任何問題,只在橋臺(tái)搭板處出現(xiàn)了一些尚在容許范圍內(nèi)的裂縫[5]。

        表2Isola della Scala橋主要參數(shù)

        Tab.2Main Parameters of Isola della Scala Bridge結(jié)構(gòu)參數(shù)參數(shù)值橋面系寬度/m13.5橋面系高度/m1.50+0.30墩橫截面直徑/m3墩帽高度/m1.80墩身高度/m3.775~5.385樁帽高度/m2.50樁基礎(chǔ)類型鋼筋混凝土摩擦樁樁橫截面直徑/m1.2樁長(zhǎng)/m15~20樁數(shù)每個(gè)橋墩或橋臺(tái)6根圖1Isola della Scala橋立面(單位:m)

        Fig.1Elevation Layout of Isola della

        Scala Bridge (Unit:m)2.2有限元模型

        本文以Isola della Scala橋?yàn)楸尘肮こ?,采用ANSYS有限元軟件建立二維有限元模型,見圖2。主梁、橋墩、橋臺(tái)和樁基礎(chǔ)均采用梁?jiǎn)卧M(jìn)行模擬。對(duì)于主梁與橋臺(tái)之間的連接,采用共用節(jié)點(diǎn)模擬剛性連接;而對(duì)于主梁與橋墩的連接,則采用轉(zhuǎn)動(dòng)彈簧單元模擬鉸接。對(duì)于結(jié)構(gòu)的塑性鉸,模型采用轉(zhuǎn)動(dòng)彈簧進(jìn)行模擬,塑性鉸布置在主梁和橋臺(tái)連接處及樁的頂部和橋墩底部。

        圖2Isola della Scala橋有限元模型

        Fig.2Finite Element Model of Isola della Scala Bridge與傳統(tǒng)的有縫橋梁不同,整體橋取消了伸縮縫和支座,因此有限元模擬必須考慮結(jié)構(gòu)與土的相互作用,本文中采用縱向彈簧單元進(jìn)行模擬。對(duì)于橋臺(tái)土相互作用的模擬,模型選用美國(guó)橋梁基礎(chǔ)設(shè)計(jì)手冊(cè)NCHRP343[17]中建議的非線性臺(tái)后土壓力橋臺(tái)位移關(guān)系曲線。對(duì)于樁土相互作用的模擬,模型選用美國(guó)API設(shè)計(jì)手冊(cè)[18]中推薦的非線性土壓力樁身位移關(guān)系曲線。模型的材料特性、荷載工況、邊界條件等信息參見文獻(xiàn)[5]。

        2.3環(huán)境振動(dòng)試驗(yàn)及模型驗(yàn)證

        為了評(píng)價(jià)Isola della Scala橋的性能,本文中通過(guò)定期進(jìn)行環(huán)境振動(dòng)試驗(yàn)來(lái)獲得該橋的頻率、周期等模態(tài)參數(shù)以及關(guān)鍵節(jié)點(diǎn)的等效剛度。第1批的2次試驗(yàn)已經(jīng)在2010年9月和2011年2月完成。

        利用實(shí)測(cè)的試驗(yàn)數(shù)據(jù),本文中選用絕對(duì)頻率差異法和模態(tài)置信度法來(lái)驗(yàn)證有限元模型的正確性。絕對(duì)頻率差異法是將環(huán)境振動(dòng)試驗(yàn)實(shí)測(cè)的橋梁頻率與有限元模型計(jì)算得到的頻率代入公式(1)計(jì)算得到絕對(duì)頻率差異DF,即

        DF=|fTEST-fFEM|fTEST(1)

        式中:fTEST為試驗(yàn)實(shí)測(cè)的橋梁頻率;fFEM為有限元模型計(jì)算的橋梁頻率。

        模態(tài)置信度是一個(gè)統(tǒng)計(jì)學(xué)上的相關(guān)系數(shù),取值為0~1。將實(shí)測(cè)結(jié)果與有限元模型計(jì)算結(jié)果進(jìn)行對(duì)比,若環(huán)境振動(dòng)試驗(yàn)所測(cè)的振型與有限元模型計(jì)算的振型相關(guān)較好,則模態(tài)置信度取值大于0.85[19]。模態(tài)置信度CMAC的具體計(jì)算方法為

        CMAC(φA,i,φB,j)=(φTA,iφB,j)2(φTA,iφA,i)(φTB,jφB,j)(2)

        式中:φA,i為數(shù)據(jù)組A的第i階模態(tài);φB,j為數(shù)據(jù)組B的第j階模態(tài)。

        由于篇幅限制,選取前3階橫向振型進(jìn)行絕對(duì)頻率差異法和模態(tài)置信度法(MAC)分析,其計(jì)算結(jié)果分別見表3和表4。從比較結(jié)果可以發(fā)現(xiàn),有限元模型能較好地模擬實(shí)橋的性能。

        表3絕對(duì)頻率差異的對(duì)比

        Tab.3Comparisons of Absolute Frequency Discrepancy模態(tài)有限元模型計(jì)算

        的頻率/Hz第1次試驗(yàn)第2次試驗(yàn)頻率/HzDF/%頻率/HzDF/%12.8932.8322.22.9301.323.0283.1182.93.1223.033.2063.4446.93.4607.3利用有限元模型,本文中針對(duì)模型的不同部位進(jìn)行深入分析,發(fā)現(xiàn)主梁橋墩節(jié)點(diǎn)的剛度是一個(gè)重要的影響因素。對(duì)于Isola della Scala橋,主梁橋墩節(jié)點(diǎn)的實(shí)際轉(zhuǎn)動(dòng)剛度是介于鉸接與剛接之間?,F(xiàn)有模型采用純鉸接進(jìn)行模擬會(huì)導(dǎo)致有限元計(jì)算結(jié)果與環(huán)境振動(dòng)試驗(yàn)結(jié)果稍有偏差。因此本文中以試驗(yàn)結(jié)果為基礎(chǔ),利用最小二乘法推導(dǎo)出實(shí)橋中主梁橋

        表4模態(tài)置信度的對(duì)比

        Tab.4Comparisons of Modal Assurance Criterion模態(tài)有限元模型模態(tài)置信度第1次試驗(yàn)第2次試驗(yàn)10.9100.89920.7330.90630.7820.737墩節(jié)點(diǎn)的轉(zhuǎn)動(dòng)剛度(表5),從而對(duì)有限元模型進(jìn)行修正。

        表5主梁橋墩節(jié)點(diǎn)修正后的轉(zhuǎn)動(dòng)剛度

        Tab.5Modified Rotation Stiffness of

        Girderpier Connection旋轉(zhuǎn)軸方向轉(zhuǎn)動(dòng)剛度/[(MN·m)·rad-1]x縱橋向4.8×103y豎橋向0z橫橋向1.0×1053整體式橋臺(tái)橋梁極限長(zhǎng)度計(jì)算

        3.1極限長(zhǎng)度簡(jiǎn)化計(jì)算公式

        根據(jù)大量分析發(fā)現(xiàn),溫度升降所產(chǎn)生的土結(jié)構(gòu)相互作用是限制整體橋總長(zhǎng)度的主要因素。本文中首先根據(jù)所有跨的變形情況和靜力平衡關(guān)系,提出當(dāng)橋跨總數(shù)量分別為奇數(shù)和偶數(shù)2種不同情況時(shí),橋梁在溫度變化作用下的位移計(jì)算公式為:

        當(dāng)橋跨總數(shù)量為奇數(shù)時(shí)

        ΔLi=ΔL1i=1

        (3+K1LEA)ΔL1i=2

        (2+Ki-1LEA)ΔLi-1-ΔLi-23≤i≤n(3)

        當(dāng)橋跨總數(shù)量為偶數(shù)時(shí)

        ΔLi=ΔL1i=1

        (2+K1LEA)ΔL1i=2

        (2+Ki-1LEA)ΔLi-1-ΔLi-23≤i≤n(4)

        式中:ΔLi為第i跨的位移;E為混凝土彈性模量;A為主梁橫截面積;L為橋梁總長(zhǎng);Ki為第i跨橋墩側(cè)向剛度。

        聯(lián)立公式(3)和公式(4),可以獲得公式(5),即

        ΔLi=ciΔL1(5)

        式中:ci為第i跨的位移,是與Ki-1,L,EA均有關(guān)的參數(shù),ci=fi(Ki-1L/EA),對(duì)于混凝土的開裂和收縮徐變,通過(guò)改變其彈性模量E進(jìn)行考慮。

        endprint

        根據(jù)第n跨的變形協(xié)調(diào)條件和公式(5),可以推導(dǎo)出公式(6),即

        Nn=EA[αΔT-(cn-cn-1)ΔL1/L](6)

        式中:Nn為第n跨水平力;ΔT為溫度變化量。

        橋臺(tái)受力如圖3所示,其中,M為彎矩,V為剪力,hD為主梁高度,d為橋臺(tái)厚度,np為樁的數(shù)量,Vp為樁的最大抗剪能力,Pb為橋臺(tái)后土層的壓力,γ為臺(tái)后填土單位質(zhì)量,Hb為橋臺(tái)高度,Ks為橋臺(tái)后土壓力系數(shù)[17]。假設(shè)當(dāng)橋臺(tái)達(dá)到最大剪力和彎矩時(shí),樁基礎(chǔ)頂部達(dá)到最大的塑性彎矩和承載力,則第n跨水平力可以采用公式(7)進(jìn)行保守計(jì)算,即

        Nn=Pb+npVp(7)

        圖3橋臺(tái)受力

        Fig.3Forces on Abutment橋臺(tái)后土層的壓力可以簡(jiǎn)化為三角形分布,采用公式(8)進(jìn)行計(jì)算,即

        Pb=12KsγH2bwb(8)

        式中:wb為橋臺(tái)寬度。

        當(dāng)只考慮升溫影響時(shí),公式(8)變?yōu)楣剑?),即

        Pb=12(K0+kpΔLnHb)γH2bwb(9)

        式中:K0為靜止土的壓力系數(shù);kp為被動(dòng)土的壓力系數(shù)。

        聯(lián)立公式(6),(7),則可以獲得ΔL1的計(jì)算公式(10),即

        ΔL1=EAαΔT-npVp-K0γH2bwb/2EA(cn-cn-1)+kpcnγHbLwb/2L(10)

        對(duì)于第n跨的位移ΔLn,可以通過(guò)公式(11)計(jì)算獲得,即

        ΔLn=EAαΔT-npVp-K0γH2bwb/2EA(cn-cn-1)+kpcnγHbLwb/2cnL(11)

        3.2極限長(zhǎng)度計(jì)算公式的非線性修正

        筆者所提出的整體橋的極限長(zhǎng)度計(jì)算公式只能考慮結(jié)構(gòu)的線彈性響應(yīng)。為了更準(zhǔn)確地預(yù)測(cè)整體橋極限長(zhǎng)度,考慮結(jié)構(gòu)的非線性響應(yīng)十分必要,其主要有以下3種不同的方法:

        (1)根據(jù)跨數(shù)和不同溫度荷載修改每一跨的抗壓剛度。

        (2)根據(jù)不同位移所產(chǎn)生的橋墩轉(zhuǎn)動(dòng)值修改沿縱向橋的橋墩側(cè)向剛度。

        (3)考慮臺(tái)后土抗力和樁側(cè)土抗力與位移的非線性關(guān)系。

        從上述分析可知,主梁橋墩節(jié)點(diǎn)的剛度是影響橋梁性能的一個(gè)重要因素。因此,本文中選擇修改沿縱向橋的橋墩側(cè)向剛度對(duì)公式(11)進(jìn)行非線性修正,通過(guò)試算可以得到橋墩側(cè)向剛度系數(shù)的修正公式,即

        Ki,m=Kii3/2(12)

        式中:Ki為未修正的橋墩側(cè)向剛度;Ki,m為非線性修正后的橋墩側(cè)向剛度。

        將非線性修正后的公式計(jì)算結(jié)果與有限元模型結(jié)果進(jìn)行對(duì)比,結(jié)果如圖4所示。從圖4可以看出,非線性修正后的公式計(jì)算結(jié)果與考慮塑性鉸的理想化模型以及實(shí)橋模型吻合較好,可用于預(yù)估整體橋的極限長(zhǎng)度。

        圖4簡(jiǎn)化計(jì)算公式與有限元模型位移對(duì)比

        Fig.4Displacement Comparisons Between Simplified

        Formula and Finite Element Model3.3極限長(zhǎng)度計(jì)算

        整體橋極限長(zhǎng)度受到多個(gè)因素的綜合影響,包括橋墩的極限轉(zhuǎn)動(dòng)能力、橋臺(tái)的極限強(qiáng)度、溫度位移產(chǎn)生的疲勞影響、橋頭搭板的耐久性等。

        3.3.1橋墩轉(zhuǎn)動(dòng)能力和橋臺(tái)強(qiáng)度

        考慮橋墩的極限轉(zhuǎn)動(dòng)能力,即第1跨的位移必須滿足橋墩的轉(zhuǎn)動(dòng)性能,則第n跨的位移需要滿足公式(13)

        ΔLn≤cncn-1θprHpr(13)

        式中:θpr為橋墩的轉(zhuǎn)動(dòng)能力;Hpr為橋墩高度。

        考慮橋臺(tái)的極限強(qiáng)度時(shí),可以假設(shè)橋臺(tái)位移很大時(shí),其樁基礎(chǔ)在早期就達(dá)到塑性鉸,但其仍然可以承受一定的荷載,因此在某些情況下,橋臺(tái)的剪力和彎矩有可能比橋墩更早達(dá)到極限狀態(tài)[20]。根據(jù)受力平衡原理,假設(shè)橋臺(tái)極限剪力和彎矩出現(xiàn)的位置如圖3所示,可以推導(dǎo)出臨界剪力和彎矩的計(jì)算公式[21]。考慮升溫的作用,則第n跨的位移需要滿足公式(14),(15)

        ΔLn≤2(Va,cr-npVp)Hbkpγ[H2b-(hD+d)2]wb-K0Hbkp(14)

        ΔLn≤Ma,crHb-npHb[Mp+Vp(Hb-hD)]kpγ[(Hb-hD)3/3+hD(Hb-hD)2/2]wb-

        K0Hbkp(15)

        式中:Va.cr為橋臺(tái)處的臨界剪力;Ma.cr為橋臺(tái)處的臨界彎矩。

        綜上所述,通過(guò)控制第n跨的位移ΔLn,即公式(13)~(15)的較小值,從而控制整體橋的最大跨數(shù)ns,進(jìn)而估算全橋極限長(zhǎng)度Ls,Ls=nsL。以Isola della Scala橋?yàn)閷?shí)例,考慮升溫20 ℃情況下,不同跨數(shù)對(duì)應(yīng)的熱膨脹位移見圖5。從圖5可以看出,橋墩的轉(zhuǎn)動(dòng)能力是限制整體橋跨數(shù)的關(guān)鍵因素。本例中單跨30 m,最大跨數(shù)可以達(dá)到18跨,因此整體橋總長(zhǎng)預(yù)估可達(dá)到540 m。

        圖5不同跨數(shù)的熱膨脹位移

        Fig.5Thermal Displacements of Different Span Numbers3.3.2溫度位移產(chǎn)生的疲勞影響

        由于整體橋取消了伸縮縫和支座,因此溫度變化產(chǎn)生的橫向荷載被認(rèn)為是限制整體橋極限長(zhǎng)度的重要因素之一。整體橋中樁的溫度位移是由每年隨季節(jié)溫度變化所產(chǎn)生的一個(gè)主要的往復(fù)位移和每天溫度變化所產(chǎn)生的大量小往復(fù)位移所組成[9,10,22]。因此在估算整體橋的極限長(zhǎng)度時(shí),需要考慮這些由于溫度荷載所產(chǎn)生的往復(fù)位移對(duì)橋梁結(jié)構(gòu)的疲勞影響。本文中以Isola della Scala橋?yàn)閷?shí)例,采用一個(gè)簡(jiǎn)單且保守的方式來(lái)考慮溫度位移產(chǎn)生的疲勞影響,即溫度變化(20 ℃)和橋梁的材料強(qiáng)度均考慮折減系數(shù)0.5,其余參數(shù)不變。利用修正后的簡(jiǎn)化計(jì)算公式,考慮疲勞影響的不同跨數(shù)對(duì)應(yīng)的熱膨脹位移見圖6。本例中單跨30 m,最大跨數(shù)可達(dá)15跨,故考慮疲勞影響時(shí),整體橋總長(zhǎng)預(yù)估可達(dá)到450 m。

        圖6考慮疲勞影響的不同跨數(shù)的熱膨脹位移

        Fig.6Thermal Displacements of Different Span

        Numbers with Considering of Fatigue Effect3.3.3橋頭搭板的耐久性

        隨著整體橋長(zhǎng)度增大,橋梁端部的位移同樣增大,同時(shí)傳遞到橋頭搭板以及接線道路的位移也相應(yīng)增大,因此橋頭搭板的耐久性也成為影響整體橋極限長(zhǎng)度的重要因素之一。很多學(xué)者都認(rèn)為對(duì)于整體橋,必須要選擇合適的橋頭搭板,從而避免橋頭跳車、臺(tái)后路面開裂或沉降等病害[2324]。瑞士學(xué)者針對(duì)整體橋中溫度荷載所產(chǎn)生的位移對(duì)橋頭搭板性能影響進(jìn)行了試驗(yàn)和數(shù)值分析,并設(shè)計(jì)出一種搭板形式可適用于橋梁端部水平位移不超過(guò)43 mm的整體橋[25]。因此假設(shè)升溫20 ℃,考慮橋頭搭板的耐久性,整體橋總長(zhǎng)預(yù)估可達(dá)到430 m。4結(jié)語(yǔ)

        整體式橋臺(tái)橋梁作為一種從橋梁全壽命方面考慮最為經(jīng)濟(jì)的方案,不僅適用于中短長(zhǎng)度的橋梁,還適用于超長(zhǎng)橋梁。本文中介紹了超長(zhǎng)整體橋的發(fā)展現(xiàn)狀,以目前世界上最長(zhǎng)的整體式橋臺(tái)橋梁Isola della Scala橋?yàn)閷?shí)例,建立有限元模型并提出極限長(zhǎng)度修正計(jì)算公式。利用該簡(jiǎn)化計(jì)算公式,可以預(yù)估不同限制條件下整體式橋臺(tái)橋梁的極限長(zhǎng)度。當(dāng)考慮橋墩的轉(zhuǎn)動(dòng)能力和橋臺(tái)的承載能力時(shí),極限長(zhǎng)度可以達(dá)到540 m;當(dāng)考慮溫度位移產(chǎn)生的疲勞影響時(shí),極限長(zhǎng)度可以達(dá)到450 m;當(dāng)考慮橋頭搭板的耐久性時(shí),極限長(zhǎng)度可以達(dá)到430 m。參考文獻(xiàn):

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        [3]BRISEGHELLA B,ZORDAN T.Integral Abutment Bridge Concept Applied to the Rehabilitation of a Simply Supported Prestressed Conventional Concrete Superstructure[J].Structural Concrete,2006,8(1):2533.

        [4]BURDETTE E G,HOWARD S C,INGRAM E E,et al.Behavior of Pile Supported Integral Abutments[C]//Constructed Facilities Center.Integral Abutment and Jointless Bridges (IAJB 2005).Baltimore:Constructed Facilities Center,2005:222232.

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        [12]KUNIN J,ALAMPALLI S.Integral Abutment Bridges:Current Practice in United States and Canada[J].Journal of Performance of Constructed Facilities,2000,14(3):104111.

        [13]PARASCHOS A,AMDE A M.Integral Abutment Bridge:a Survey on the Status of Use,Problems,and Costs Associated with Integral Abutment Bridges[R].Tuscaloosa:Tina Grady Barbaccia,2011.

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        [15]OLSON S M,LONG J H,HANSEN J R,et al.Modification of IDOT Integral Abutment Design Limitations and Details[R].Urbana:University of Illinois at UrbanaChampaign,2009.

        [16]LIU D,MAGLIOLA R A,DUNKER K F.Integral Abutment Bridges—Iowa and Colorado Experience[C]//Constructed Facilities Center.Integral Abutment and Jointless Bridges(IAJB2005).Baltimore:Constructed Facilities Center,2005:136147.

        [17]BARKER R M,DUNCAN J M,ROJIANI K B,et al.Manuals for the Design of Bridge Foundations:Shallow Foundations,Driven Piles,Retaining Walls and Abutments,Drilled Shafts,Estimating Tolerable Movements,and Load Factor Design Specifications and Commentary[R].Washington DC:Transportation Research Board,1991.

        [18]API 2000,Recommended Practice for Planning,Designing and Constructing Fixed Offshore Platforms—Working Stress Design[S].

        [19]ALLEMANG R J.The Modal Assurance Criteriontwenty Years of Use and Abuse[J].Sound and Vibration,2003,37(8):1423.

        [20]BOZORGZADEH A.Effect of Structure Backfill on Stiffness and Capacity of Bridge Abutments[D].San Diego:University of California,2007.

        [21]ERHAN S,DICLELI M.Live Load Distribution Equations for Integral Bridge Substructures[J].Engineering Structures,2009,31(5):12501264.

        [22]ENGLAND G L,TSANG N C M,BUSH D I.Integral Bridges:a Fundamental Approach to the Timetemperature Loading Problem[M].London:Thomas Telford,2000.

        [23]BURKE M P.Integral and Semiintegral Bridges[M].Oxford:WileyBlackwell,2009.

        [24]ARSOY S,BARKER R M,DUNCAN J M.The Behavior of Integral Abutment Bridges[R].Virginia:Virginia Transportation Research Council,1999.

        [25]DREIER D,BURDET O,MUTTONI A.Transition Slabs of Integral Abutment Bridges[J].Structural Engineering International,2011,21(2):144150.

        endprint

        [2]XUE J Q.Retrofit of Existing Bridges with Concept of Integral Abutment Bridge:Static and Dynamic Parametric Analyses[D].Trento:University of Trento,2013.

        [3]BRISEGHELLA B,ZORDAN T.Integral Abutment Bridge Concept Applied to the Rehabilitation of a Simply Supported Prestressed Conventional Concrete Superstructure[J].Structural Concrete,2006,8(1):2533.

        [4]BURDETTE E G,HOWARD S C,INGRAM E E,et al.Behavior of Pile Supported Integral Abutments[C]//Constructed Facilities Center.Integral Abutment and Jointless Bridges (IAJB 2005).Baltimore:Constructed Facilities Center,2005:222232.

        [5]ZORDAN T,BRISEGHELLA B,LAN C.Parametric and Pushover Analyses on Integral Abutment Bridge[J].Engineering Structures,2011,33(2):502515.

        [6]ZORDAN T,BRISEGHELLA B.Attainment of an Integral Abutment Bridge Through the Refurbishment of a Simply Supported Structure[J].Structural Engineering International,2007,17(3):228234.

        [7]BAPTISTE K T,KIM W,LAMAN J A.Parametric Study and Length Limitations for Prestressed Concrete Girder Integral Abutment Bridges[J].Structural Engineering International,2011,21(2):151156.

        [8]EVANGELISTA S.200meterlong Bridges Without Expansion Joints:Is It Possible?[R].Lausanne:EPFL,2011.

        [9]DICLELI M,ALBHAISI S M.Effect of Cyclic Thermal Loading on the Performance of Steel Hpiles in Integral Bridges with Stubabutments[J].Journal of Constructional Steel Research,2004,60(2):161182.

        [10]DICLELI M,ALBHAISI S M.Estimation of Length Limits for Integral Bridges Built on Clay[J].Journal of Bridge Engineering,2004,9(6):572581.

        [11]BAKEER R M,MATTEI N J,ALMALIK B K,et al.Evaluation of DOTD Semiintegral Bridge and Abutment System[R].Baton Rouge:Louisiana Transportation Research Center,2005.

        [12]KUNIN J,ALAMPALLI S.Integral Abutment Bridges:Current Practice in United States and Canada[J].Journal of Performance of Constructed Facilities,2000,14(3):104111.

        [13]PARASCHOS A,AMDE A M.Integral Abutment Bridge:a Survey on the Status of Use,Problems,and Costs Associated with Integral Abutment Bridges[R].Tuscaloosa:Tina Grady Barbaccia,2011.

        [14]HUSAIN I,BAGNARIOL D.Integral Abutment Bridges[R].Ontario:Ontario Ministry of Transportation,1996.

        [15]OLSON S M,LONG J H,HANSEN J R,et al.Modification of IDOT Integral Abutment Design Limitations and Details[R].Urbana:University of Illinois at UrbanaChampaign,2009.

        [16]LIU D,MAGLIOLA R A,DUNKER K F.Integral Abutment Bridges—Iowa and Colorado Experience[C]//Constructed Facilities Center.Integral Abutment and Jointless Bridges(IAJB2005).Baltimore:Constructed Facilities Center,2005:136147.

        [17]BARKER R M,DUNCAN J M,ROJIANI K B,et al.Manuals for the Design of Bridge Foundations:Shallow Foundations,Driven Piles,Retaining Walls and Abutments,Drilled Shafts,Estimating Tolerable Movements,and Load Factor Design Specifications and Commentary[R].Washington DC:Transportation Research Board,1991.

        [18]API 2000,Recommended Practice for Planning,Designing and Constructing Fixed Offshore Platforms—Working Stress Design[S].

        [19]ALLEMANG R J.The Modal Assurance Criteriontwenty Years of Use and Abuse[J].Sound and Vibration,2003,37(8):1423.

        [20]BOZORGZADEH A.Effect of Structure Backfill on Stiffness and Capacity of Bridge Abutments[D].San Diego:University of California,2007.

        [21]ERHAN S,DICLELI M.Live Load Distribution Equations for Integral Bridge Substructures[J].Engineering Structures,2009,31(5):12501264.

        [22]ENGLAND G L,TSANG N C M,BUSH D I.Integral Bridges:a Fundamental Approach to the Timetemperature Loading Problem[M].London:Thomas Telford,2000.

        [23]BURKE M P.Integral and Semiintegral Bridges[M].Oxford:WileyBlackwell,2009.

        [24]ARSOY S,BARKER R M,DUNCAN J M.The Behavior of Integral Abutment Bridges[R].Virginia:Virginia Transportation Research Council,1999.

        [25]DREIER D,BURDET O,MUTTONI A.Transition Slabs of Integral Abutment Bridges[J].Structural Engineering International,2011,21(2):144150.

        endprint

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