液化場(chǎng)地橋梁群樁-土耦合體系強(qiáng)震反應(yīng)分析

唐 浩, 石秀峰, 唐 亮, 蔡德鉤, 凌賢長(zhǎng), 王東洋

(1.華中科技大學(xué)機(jī)械科學(xué)與工程學(xué)院,湖北 武漢 430074; 2.哈爾濱工業(yè)大學(xué)土木工程學(xué)院,黑龍江 哈爾濱 150090;2.中國(guó)鐵道科學(xué)研究院,北京 100081)

液化場(chǎng)地橋梁群樁-土耦合體系強(qiáng)震反應(yīng)分析

唐 浩1, 石秀峰2, 唐 亮2, 蔡德鉤3, 凌賢長(zhǎng)2, 王東洋2

(1.華中科技大學(xué)機(jī)械科學(xué)與工程學(xué)院,湖北 武漢 430074; 2.哈爾濱工業(yè)大學(xué)土木工程學(xué)院,黑龍江 哈爾濱 150090;2.中國(guó)鐵道科學(xué)研究院,北京 100081)

針對(duì)振動(dòng)臺(tái)試驗(yàn),采用u-p形式控制方程表述飽和砂土的動(dòng)力屬性,選用土的多屈服面塑性本構(gòu)模型刻畫(huà)飽和砂土和黏土的力學(xué)特性,引入非線性梁-柱單元模擬樁,建立試驗(yàn)受控條件下液化場(chǎng)地群樁-土強(qiáng)震相互作用分析的三維有限元模型,并通過(guò)試驗(yàn)結(jié)果驗(yàn)證數(shù)值建模途徑與模擬方法的正確性。以實(shí)際工程中常用的2×2群樁為例,建立樁-土-橋梁結(jié)構(gòu)強(qiáng)震反應(yīng)分析三維有限元模型?；诖?針對(duì)不同群樁基礎(chǔ)配置對(duì)液化場(chǎng)地群樁-土強(qiáng)震相互作用影響展開(kāi)具體分析。對(duì)比發(fā)現(xiàn),樁的數(shù)量相同時(shí),樁排列方向與地震波輸入方向平行時(shí)比垂直時(shí)樁基受力減小5%～10%,而對(duì)場(chǎng)地液化情況無(wú)明顯影響;相同排列形式下,三樁模型中土體出現(xiàn)液化的時(shí)間約比雙樁模型延緩5 s,樁上彎矩和剪力減小33%～38%。由此可見(jiàn),樁基數(shù)量增加,樁-土體系整體剛度更大,場(chǎng)地抗液化性能顯著,樁基對(duì)上部橋梁結(jié)構(gòu)的承載性能明顯增強(qiáng),其安全性與可靠性更高。這對(duì)實(shí)際橋梁工程抗震設(shè)計(jì)具有一定的借鑒意義。

液化場(chǎng)地; 群樁基礎(chǔ); 強(qiáng)震反應(yīng); 樁-土相互作用; 三維非線性有限元法

0 引言

諸多震害調(diào)查顯示:地震土體液化是導(dǎo)致樁基橋梁結(jié)構(gòu)破壞的重要原因之一[1]。近年來(lái)我國(guó)橋梁事業(yè)蓬勃發(fā)展,實(shí)際工程中多采用群樁基礎(chǔ),加之我國(guó)地震分布廣且多發(fā),一般建橋地區(qū)多為極易液化場(chǎng)地,故而地震中土體液化是否導(dǎo)致群樁基橋梁結(jié)構(gòu)的破壞便成為我國(guó)橋梁工程抗震中需要認(rèn)真考慮且妥善處理的問(wèn)題之一[2]。液化場(chǎng)地樁-土-橋梁結(jié)構(gòu)動(dòng)力相互作用分析對(duì)于橋梁樁基抗震研究具有重要作用,已受到諸多學(xué)者的關(guān)注[3-4]。國(guó)外,Klar等[5]、Zhou等[6]及Lu等[7]探討了液化場(chǎng)地群樁效應(yīng)問(wèn)題,并對(duì)樁間距等因素對(duì)群樁響應(yīng)的影響進(jìn)行了研究。Wang等[8]、Jayasinghe等[9]采用非線性有限元方法,針對(duì)爆炸荷載對(duì)樁-土相互作用及上部結(jié)構(gòu)的影響進(jìn)行了研究。國(guó)內(nèi),王睿等[10]給出了液化土側(cè)向大變形下彈性單樁和群樁地震響應(yīng)的解析解。李雨潤(rùn)等[11]、王志華等[12]調(diào)查了液化土對(duì)樁的力學(xué)行為的影響情況。唐亮等[13]、Tang等[14]、Tang和Ling[15]研究了液化場(chǎng)地橋梁各類群樁的地震反應(yīng)特征與地震失穩(wěn)機(jī)理。

目前,研究液化場(chǎng)地樁基橋梁結(jié)構(gòu)抗震問(wèn)題的手段主要包括試驗(yàn)方法和理論與數(shù)值分析方法。動(dòng)力模型試驗(yàn)存在較大的局限性,如耗時(shí)、費(fèi)錢(qián)且考慮的影響因素有限;數(shù)值分析方法因其技術(shù)優(yōu)勢(shì),能夠較好地模擬土體的液化效應(yīng)及樁-土動(dòng)力相互作用等,國(guó)際上已將其廣泛用于液化場(chǎng)地樁基橋梁結(jié)構(gòu)地震反應(yīng)分析中,但其更多集中于液化場(chǎng)地單樁地震反應(yīng)的模擬與分析的研究中,對(duì)于群樁及群樁配置形式對(duì)樁-土動(dòng)力相互作用的研究尚少。本文針對(duì)液化場(chǎng)地樁-土強(qiáng)震相互作用問(wèn)題,借助OpenSees有限元計(jì)算平臺(tái)建立液化場(chǎng)地樁基動(dòng)力反應(yīng)三維非線性有限元數(shù)值模型,開(kāi)展液化場(chǎng)地橋梁群樁基強(qiáng)震反應(yīng)與影響因素研究工作,分析群樁配置對(duì)樁-土耦合體系動(dòng)力性能的影響效應(yīng)。

1 振動(dòng)臺(tái)試驗(yàn)數(shù)值模型

1.1 振動(dòng)臺(tái)試驗(yàn)

試驗(yàn)傳感器布置見(jiàn)圖1[15]。試驗(yàn)中,樁徑0.08 m,樁長(zhǎng)2.0 m,入土深度1.7 m,樁底距土箱底部0.2 m,樁間距0.3 m;承臺(tái)長(zhǎng)0.46 m×寬0.46 m×高0.15 m;柱墩直徑0.16 m,長(zhǎng)0.82 m。模型樁、柱墩為微粒混凝土且配鍍鋅鐵絲,微?；炷烈暂^大粒徑的砂礫為粗骨料、較小粒徑的砂礫為細(xì)骨料,鍍鋅鐵絲規(guī)格為φ1.9 mm;承臺(tái)制作材料采用C30混凝土;上部配重120 kg以模擬橋梁結(jié)構(gòu)。地基總厚度1.9 m,下伏1.6 m厚砂土層,上覆0.3 m厚人工重塑黏土(分層碾壓、夯實(shí),形成地震作用下典型的不排水場(chǎng)地條件)。地下水位處于上下土層分界處,飽和砂層采用水沉法形成,以保證地基砂土層充分飽和且均勻。箱底輸入0.633gEI Centro波。

圖1 振動(dòng)臺(tái)試驗(yàn)傳感器布置Fig.1 Layout of sensors in test

1.2 有限元模型

針對(duì)振動(dòng)臺(tái)試驗(yàn),建立液化場(chǎng)地群樁-土-橋梁結(jié)構(gòu)動(dòng)力相互作用分析的三維有限元模型(圖2),采用有限元公式u-p表示飽和砂土的動(dòng)力水土耦合作用機(jī)制(u為土顆粒位移,p為砂土的孔壓)。為了保證數(shù)值計(jì)算的收斂性,引入瑞利阻尼(C=αM+βK,α為質(zhì)量比例系數(shù),β為剛度比例系數(shù))考慮體系的阻尼效應(yīng)。通過(guò)對(duì)體系白噪聲掃頻,得到α=0.063 76和β=0.006 34。借助體系線性辨識(shí)理論,針對(duì)液化問(wèn)題,將α調(diào)整為0、β設(shè)置為0.002。砂層采用土-水完全耦合(u-p) 20-8節(jié)點(diǎn)六面體等參單元模擬。為了模擬黏土剪切彈塑性特征,采用具有多屈服面運(yùn)動(dòng)特征的塑性本構(gòu)模型:假定土體只在偏應(yīng)力-應(yīng)變反應(yīng)中出現(xiàn)塑性變形,體應(yīng)力-應(yīng)變反應(yīng)為線彈性而與偏分量無(wú)關(guān),通過(guò)嵌套面概念與相關(guān)聯(lián)流動(dòng)法則表示土的塑性,且采用雙曲線關(guān)系定義剪應(yīng)力-應(yīng)變骨干曲線。計(jì)算參數(shù)見(jiàn)表1[14]。砂土采用多屈服面塑性本構(gòu)模型,可描述循環(huán)動(dòng)荷載下大變形砂土的動(dòng)力特性。基于Prevost模型理論框架,利用多屈服面的方法描述砂土的循環(huán)滯回特性,引入合理的加載-卸載流動(dòng)法則,刻畫(huà)循環(huán)動(dòng)載作用下砂土的收縮、理想塑性和剪脹特性等偏體應(yīng)變動(dòng)力耦合效應(yīng)。為使數(shù)值計(jì)算穩(wěn)定,模型特別融入了修正的Mroz偏硬化準(zhǔn)則。計(jì)算參數(shù)見(jiàn)表2[14]。

圖2 液化場(chǎng)地群樁-土-橋梁結(jié)構(gòu)地震相互作用模型Fig.2 Interaction model of pilegroup-soil-bridge structure in liquefied ground

表1 黏土的本構(gòu)模型參數(shù)

表2 砂土的本構(gòu)模型計(jì)算參數(shù)

有限元模型中,樁頂施加集中質(zhì)量點(diǎn)用于模擬橋梁結(jié)構(gòu)。樁模擬為非線性梁?jiǎn)卧?并采用非線性彎矩-曲率關(guān)系表述樁的屬性,計(jì)算參數(shù)見(jiàn)表3[16]。通過(guò)徑向輻射狀桿單元,連結(jié)梁?jiǎn)卧?jié)點(diǎn)和樁周土單元節(jié)點(diǎn)以模擬樁-土相互作用;模型基底為剛性邊界。模型側(cè)邊界采用一致耗能阻尼邊界(即通過(guò)在模型邊界處設(shè)置阻尼器吸收地震波能量,減小邊界影響)。模型基底直接施加實(shí)測(cè)的地震時(shí)程，合理考慮樁-土體系受到的作用效應(yīng)。計(jì)算中選用位移增量準(zhǔn)則作為收斂判據(jù)。

1.3 數(shù)值建模技術(shù)途徑與可靠性檢驗(yàn)

土體加速度計(jì)算值與試驗(yàn)值對(duì)比見(jiàn)圖3。由圖可知,無(wú)論是地表處還是埋深0.7 、1.05 m處,土體加速度的計(jì)算值與試驗(yàn)值步調(diào)均保持一致。在10～15 s內(nèi)近場(chǎng)土體加速度計(jì)算值幅值要比試驗(yàn)值略小,但在不同埋深處其變化規(guī)律一致,且僅在該時(shí)段內(nèi)出現(xiàn)較大波動(dòng)。圖4展示砂層超孔隙水壓力計(jì)算值與試驗(yàn)值對(duì)比情況。由圖可知,模型孔壓二者之值吻合較好,且在振動(dòng)初期均較小;隨后隨基底激勵(lì)的增大二者均出現(xiàn)較大增幅,振動(dòng)繼續(xù)進(jìn)行,孔壓逐漸消散且圖像中出現(xiàn)毛刺現(xiàn)象;在振動(dòng)末期孔壓趨于穩(wěn)定,計(jì)算值略大于試驗(yàn)值,可能是土箱水流出所致。樁的應(yīng)變計(jì)算值與試驗(yàn)值的對(duì)比見(jiàn)圖5。由圖可知,在振動(dòng)初期樁的應(yīng)變二者之值吻合較好;隨后試驗(yàn)值率先出現(xiàn)波動(dòng)且幅值大于計(jì)算值,但整體二者變化趨勢(shì)并無(wú)較大差異;在15～30 s內(nèi),埋深0.3 m處樁的應(yīng)變計(jì)算值與試驗(yàn)值出現(xiàn)較大差異,原因是埋深0.3m處為土層分界面,試驗(yàn)過(guò)程中樁基發(fā)生破壞完全折斷;振動(dòng)末期,樁的應(yīng)變趨于穩(wěn)定且計(jì)算值略大于試驗(yàn)值。

表3 鋼筋混凝土樁的物理參數(shù)

圖3 土體加速度試驗(yàn)值與計(jì)算值的時(shí)程比較Fig.3 Comparison between experimental and calculated values of acceleration time-history of soil

2 液化場(chǎng)地群樁配置影響效應(yīng)分析

基于上述驗(yàn)證的數(shù)值建模途徑與模擬方法,將研究直接拓展到實(shí)際橋梁工程中,系統(tǒng)研究雙樁與三樁排列形式下液化場(chǎng)地群樁-土強(qiáng)震相互作用問(wèn)題。由于振動(dòng)臺(tái)實(shí)驗(yàn)尺寸較小,為了模擬真實(shí)場(chǎng)地,改變模型尺寸,土體分為上、下兩層,上覆10 m厚中砂,下伏10 m厚密砂,計(jì)算參數(shù)見(jiàn)表4、表5[16],地下水位位于地表處。群樁基長(zhǎng)15 m,地上1.5 m,地下13.5 m,計(jì)算參數(shù)見(jiàn)表3[16]?；纵斎?.633gEI Centro波。以2×2群樁為基礎(chǔ)進(jìn)行分析。在保證樁間距均為3倍樁徑時(shí)分別考慮2根樁在一行(2PR,即與地震動(dòng)輸入方向平行)、2根樁在一列(2PP,即與地震動(dòng)輸入方向垂直)的情況,并擴(kuò)展到3×3、3PR和3PP群樁形式(圖6)。

圖4 砂層超孔隙水壓力試驗(yàn)值與計(jì)算值對(duì)比Fig.4 Comparison between experimental and calculated values of excess pore water pressure of sand layer

圖5 樁應(yīng)變?cè)囼?yàn)值與計(jì)算值對(duì)比Fig.5 Comparison between experimental and calculated values of the strain of pile

表4 中砂的本構(gòu)模型計(jì)算參數(shù)

表5 密砂的本構(gòu)模型計(jì)算參數(shù)

2.1 雙樁排列形式

圖7給出了雙樁排列形式下土體Δu/σ′(超孔隙水壓力/土體有效應(yīng)力)的變化。地震時(shí),三種群樁配置的上部中砂層均發(fā)生液化,但2PR和2PP的群樁模型土體液化時(shí)間要早于2×2群樁模型。究其原因,2×2群樁對(duì)樁周土體加固更顯著,樁-土體系整體剛度更大,地震下土體可更久地保持原有的強(qiáng)度和剛度,因此其抗液化性能更優(yōu),從而提高了樁基的安全性和可靠性。雙樁排列形式下樁的彎矩和剪力的變化見(jiàn)圖8。2×2群樁模型比2PR和2PP群樁模型樁的彎矩分別減小16%和20%,樁的剪力分別減小17%和27%。可見(jiàn),2×2群樁模型中土體對(duì)樁的支撐作用更明顯,地震過(guò)程中樁受到外荷載較小,樁基抗震性能更優(yōu),這與場(chǎng)地孔壓反應(yīng)分析得出的結(jié)論一致。對(duì)于2PR模型與2PP模型,當(dāng)樁排列方向與地震動(dòng)方向平行時(shí)樁-土體系整體剛度更大,樁受到的荷載更小。對(duì)比上下土層,上部中砂層發(fā)生液化,而下部密砂層的Δu/σ′峰值僅為0.4。樁的峰值彎矩出現(xiàn)在土層分界面處,而其峰值剪力位于土層分界面上方約1.5～1.7 m。

圖6 群樁形式Fig.6 Pile-group configurations

2.2 三樁排列形式

圖9給出了三樁排列形式下土體Δu/σ′的變化。由圖可知3PR和3PP的群樁模型土體液化時(shí)間早于3×3群樁模型,這與單排雙樁條件下的結(jié)果一致。對(duì)比圖7和圖9,發(fā)現(xiàn)相同排列形式下,群樁數(shù)量越多孔壓增長(zhǎng)越緩慢,3×3群樁模型中土體出現(xiàn)液化的時(shí)間約比2×2群樁模型延緩5 s。其他兩種樁基排列形式也可得出類似的規(guī)律。三樁排列形式下樁的彎矩和剪力的變化見(jiàn)圖10。樁的彎矩分別減小20%和25%,剪力分別減小33%和38%,其變化規(guī)律與雙樁排列形式一致。對(duì)比圖8和圖10,發(fā)現(xiàn)單排三樁模型的樁的彎矩和剪力比單排雙樁約減小21%～25%,可見(jiàn)單排三樁群樁基礎(chǔ)的抗震性能更優(yōu)良。

圖7 單排雙樁配置對(duì)Δu/σ′影響Fig.7 Influence of configurations with single row and two piles on the Δu/σ′

圖8 單排雙樁配置對(duì)樁的彎矩和剪力影響Fig.8 Influence of configurations with single row and two piles on bending moment and shear force of pile

圖9 單排三樁配置對(duì)Δu/σ′影響Fig.9 Influence of configurations with single row and three piles on the Δu/σ′

3 結(jié)論

針對(duì)振動(dòng)臺(tái)試驗(yàn),建立試驗(yàn)受控條件下液化場(chǎng)地群樁-土動(dòng)力相互作用三維非線性有限元分析模型。將試驗(yàn)測(cè)得的土體和樁的響應(yīng)與數(shù)值計(jì)算結(jié)果進(jìn)行對(duì)比,對(duì)數(shù)值模型的可靠性進(jìn)行驗(yàn)證,并將試驗(yàn)?zāi)Ｐ屯卣沟綄?shí)際工程中,分析不同形式的群樁基礎(chǔ)地震性能與場(chǎng)地反應(yīng),并得到如下基本認(rèn)識(shí):

(1) 場(chǎng)地液化情況與群樁數(shù)量有關(guān);樁的峰值彎矩和剪力與土層土性、群樁數(shù)量、樁基排列形式等因素密切相關(guān)。場(chǎng)地液化過(guò)程中,土層分界處樁出現(xiàn)峰值彎矩,在其上部1.5～1.7 m處出現(xiàn)峰值剪力。揭示了地震液化區(qū)橋梁產(chǎn)生傾斜、傾倒震害的根本原因之一。

(2) 2×2群樁模型的土體液化時(shí)間晚于2PR和2PP群樁模型,樁的彎矩分別減小16%和20%,剪力分別減小17%和27%。2×2群樁模型中土體對(duì)樁的支撐作用更明顯,樁在地震過(guò)程中受到的外荷載較小,樁基抗震性能更優(yōu)。

圖10 單排三樁配置對(duì)樁的彎矩和剪力影響Fig.10 Influence of configurations with single row and three piles on bending moment and shear force of pile

(3) 3×3群樁模型的土體液化時(shí)間晚于3PR和3PP群樁模型,樁的彎矩分別減小25%和33%,剪力分別減小20%和25%。這與雙樁分析結(jié)果一致。

(4) 樁的數(shù)量相同時(shí),樁排列方向與地震波輸入方向平行時(shí)(2PR,3PR)比與地震波輸入方向垂直時(shí)(2PP,3PP)樁基受力減小5%～10%,而對(duì)場(chǎng)地液化情況則無(wú)明顯影響。

(5) 相同排列形式下,三樁模型中土體出現(xiàn)液化的時(shí)間約比雙樁模型延緩5 s,樁的彎矩和剪力減小33%～38%。由此可見(jiàn),地震條件下,樁基數(shù)量增加,樁-土體系整體剛度更大,場(chǎng)地抗液化性能越顯著,樁基對(duì)上部橋梁結(jié)構(gòu)的承載性能增強(qiáng)越明顯,其安全性與可靠性則更高。

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Strong Seismic Response of Pile Group-soil Coupling System in Liquefied Ground

TANG Hao1, SHI Xiu-feng2, TANG Liang2, CAI De-gou3, LING Xian-zhang2, WANG Dong-yang2

(1.SchoolofMechanicalScience&Engineering,HuazhongUniversityofScienceandTechnology,Wuhan430074,Hubei,China; 2.SchoolofCivilEngineering,HarbinInstituteofTechnology,Harbin150090,Heilongjiang,China; 3.ChinaAcademyofRailwaySciences,Beijing100081,China)

A three-dimensional finite element model was established for a shaking table test of dynamic pile group-soil interaction. Governing equations ofu-pformulation were used to describe the dynamic properties of saturated sand. We choose a plastic multi-yield surface constitutive model to describe the dynamic properties of saturated sand, and a nonlinear beam-column element was used to simulate the pile in this model. The results of the test verify the validity and effectiveness of the numerical model. In an experiment using a 2×2 pile group, a three-dimensional nonlinear finite element model of soil-pile-bridge structure interaction was established. Based on this 2×2 pile group model, with a 2 piles in row pile group model (2PR) and a 2 piles in parallel pile group model (2PP), a 3×3 pile group model (with a 3PR pile group model and a 3PP pile group model) have been expended. Based on different configurations of pile group foundations, an analysis of soil-pile group interaction in liquefied ground was made. When using the same number of piles and a pile array direction parallel to the direction of seismic wave, stress is reduced by 5%～10%. However, there are few obvious effects on site liquefaction conditions. Under the same parallel array of piles, in comparison to the two-pile model, the three-pile model ground-liquefaction time results in delays of 5 s, and pile bending moment and shear force decreases 33%～38%. With an increase in the number of piles, the ground-liquefaction time is delayed, and the stress of pile body decreases. The results of this study will be of significant use for bridge engineering design.

liquefied ground; pile group foundation; strong seismic response; pile-soil interaction; three-dimensional nonlinear finite element method

2016-10-21 基金項(xiàng)目:國(guó)家自然科學(xué)基金項(xiàng)目(51578195，51378161和51308547)；國(guó)家重點(diǎn)基礎(chǔ)研究發(fā)展973計(jì)劃項(xiàng)目(2012CB026104) 作者簡(jiǎn)介:唐 浩(1992-)，男，工程師，主要從事土木工程機(jī)械動(dòng)力學(xué)等方面研究。E-mail：tanghao2358@163.com。 通信作者:唐 亮(1981-)，男，博士，副教授,博士生導(dǎo)師,主要從事巖土地震工程與土動(dòng)力學(xué)、路基動(dòng)力學(xué)等方面教學(xué)和研究。 E-mail：hit_tl@163.com。

TU4

A

1000-0844(2016)06-0869-08

10.3969/j.issn.1000-0844.2016.06.0869