馬福恒 葉偉 建劍波
摘要:針對(duì)高面板堆石壩的結(jié)構(gòu)特性,采用三維非線性有限元技術(shù),對(duì)大壩的地震反應(yīng)特性及抗震安全性進(jìn)行計(jì)算分析。動(dòng)力計(jì)算中壩體材料及覆蓋層按照等效線性黏彈性模型考慮圍壓效應(yīng)進(jìn)行模擬,混凝土面板動(dòng)力計(jì)算分析采用線性彈性模型,并依據(jù)考慮圍壓效應(yīng)的殘余體應(yīng)變及殘余軸應(yīng)變的動(dòng)應(yīng)力殘余應(yīng)變模型對(duì)某高面板堆石壩進(jìn)行壩體地震工況下永久變形計(jì)算。計(jì)算結(jié)果顯示:順河向最大永久變形為15 cm,豎直向最大永久變形為49 cm,均發(fā)生壩頂位置,地震引起的豎向變形為壩高的04%;三維動(dòng)力參數(shù)敏感性分析表明,堆石體的水平絕對(duì)加速度反應(yīng)極值為9 m/s2,最大放大系數(shù)為42,堆石體、面板最大地震反應(yīng)位于壩頂局部位置,存在明顯的鞭稍效應(yīng),但壩體地震反應(yīng)的分布規(guī)律一致,壩體及面板抗震安全性較好。
關(guān)鍵詞:高面板堆石壩;地震反應(yīng);敏感性分析;有限元法
中圖分類號(hào):TV641 文獻(xiàn)標(biāo)志碼:A 文章編號(hào):
16721683(2018)05015207
Analysis of earthquake response characteristics of a high face rockfill dam
MA Fuheng1,2,YE Wei2,JIAN Jianbo3
(
1.State Key Laboratory of HydrologyWater Resources and Hydraulic Engineering,Nanjing 210029,China;2.Nanjing Hydraulic Research Institute,Nanjing 210029,China;3.Management Bureau of Hekoucun Reservoir,Jiyuan 454661,China)
Abstract:
In view of the structural characteristics of the high face rockfill dam,we calculated and analyzed the dynamic response characteristics and the seismic safety of the dam by the threedimensional nonlinear finite element method.In the dynamic calculation,the dam material and overburden layer were simulated according to the equivalent linear viscoelastic model with consideration to the confining pressure effect.A linear elastic model was used for the calculation of concrete dynamics.The permanent deformation of the dam was calculated based on the dynamic stressresidual strain model,which could be used to calculate the residual body strain and residual axial strain.The results showed that the maximum permanent deformation along the river was 15cm and the maximum permanent deformation in the vertical direction was 49 cm;both at the dam crest.In the threedimensional analysis,the horizontal absolute acceleration response of the rockfill was 9 m/s2,and the maximum amplification factor was 42.The maximum earthquake response of the rockfill and the panel occurred at the top of the dam,showing an obvious whiplash effect.
Key words:
high face rockfill dam;earthquake response;sensitivity analysis;finite element method
近年來,隨著土體理論的發(fā)展以及筑壩技術(shù)的不斷提高,涌現(xiàn)出一批200 m級(jí)甚至300 m的高土石壩[14],這類高土石壩大多建于高地震烈度帶,這樣的高壩一旦失事后果將造成巨大的生命財(cái)產(chǎn)損失,地震中的大壩表現(xiàn)出的動(dòng)力反應(yīng)是大壩抗震安全研究的關(guān)鍵問題,因此對(duì)高地震烈度區(qū)的高土石壩進(jìn)行動(dòng)反應(yīng)分析研究十分重要[57]。
對(duì)于地震高烈度區(qū)的高土石壩的動(dòng)力反應(yīng)特性通常采用試驗(yàn)?zāi)P秃陀?jì)算分析方法研究。最早在1936年,Mononobe[8]就提出采用剪切梁法分析地震反應(yīng)。隨后Gazetas[9]依據(jù)此方法進(jìn)行了地震中豎向震動(dòng)的影響分析。Oner[10]分析了壩肩約束以及剪切模型的不均勻性對(duì)地震動(dòng)反應(yīng)的影響程度。Dakoulas等[1112]在傳統(tǒng)剪切梁法的基礎(chǔ)上考慮剪切模量與壩高關(guān)系,進(jìn)一步推導(dǎo)出表現(xiàn)大壩動(dòng)反應(yīng)特性的剪切梁公式。后來,隨著有限元法的推廣,土石壩動(dòng)力反應(yīng)分析取得較大發(fā)展。在強(qiáng)度較低的地震荷載下,土體的動(dòng)應(yīng)變相對(duì)較小,此時(shí)有限元法能科學(xué)地反應(yīng)靜動(dòng)力應(yīng)力應(yīng)變關(guān)系。對(duì)于修建在深厚覆蓋層地基上的高土石壩,沈慧[13]等依據(jù)有限元方法分析了材料的動(dòng)強(qiáng)度及壩體動(dòng)反應(yīng)強(qiáng)烈部位。在三維非線性地震反[HJ2.14mm]應(yīng)分析的基礎(chǔ)上,趙劍明等[1415]以某心墻堆石壩為背景,獲悉地震中大壩的動(dòng)反應(yīng)特性,繼而提出了用于研究高土石壩極限抗震能力的分析方法。采用有限元法分析地震中高土石壩動(dòng)力反應(yīng)特性時(shí),可根據(jù)筑壩材料本構(gòu)模型的選用類型不同而分為兩類:一類方法采用基于等價(jià)黏彈性模型的本構(gòu)模型;另一類為基于(黏)彈塑性本構(gòu)模型分析方法[1620]。本文采用有限元方法,依據(jù)等效線性法建立大壩動(dòng)力計(jì)算方程,結(jié)合具體高面板堆石壩進(jìn)行地震反應(yīng)特性分析。
1 模型構(gòu)建及計(jì)算參數(shù)
1.1 某工程概況
某水庫(kù)大壩為面板堆石壩,最大壩高1225 m(河床段趾板修建在深覆蓋層上)。大壩典型剖面圖見圖1。壩址場(chǎng)地地震動(dòng)反應(yīng)譜特征周期為040 s,地震動(dòng)峰值加速度01 g,相應(yīng)地震烈度為VII度。由于最大壩高超過100 m,按規(guī)定抗震等級(jí)提高一級(jí)設(shè)計(jì),確定大壩按VIII度地震進(jìn)行抗震設(shè)防,地震動(dòng)峰值加速度02 g。
1.2 計(jì)算方法
本文計(jì)算采用等效線性法,該方法的基本假定為將筑壩土石料與地基土層視為為黏彈性體。通過等效剪切模量Gd和等效阻尼比λd來反映地震中土的動(dòng)應(yīng)力應(yīng)變關(guān)系的非線性和滯后性,將其表示為剪切模量和阻尼比與動(dòng)剪應(yīng)變幅的關(guān)系。引入地震中土體動(dòng)剪切應(yīng)變?chǔ)?10-6左右時(shí)的最大動(dòng)剪切模量Gmax,以G/Gmax-γ和λ-γ曲線來描述動(dòng)應(yīng)力應(yīng)變關(guān)系。
1.3 模型構(gòu)建
壩體材料(除混凝土及基巖外)均按非線性彈性材料考慮,計(jì)算模型采用鄧肯EB模型。面板與墊層間采用Goodman接觸單元模擬,周邊縫、面板間垂直縫等接縫采用接縫單元模擬。有限元模型見圖2和圖3,模型為8節(jié)點(diǎn)等參單元,單元數(shù)量=6 004,節(jié)點(diǎn)數(shù)量=7 503,黃色為Goodman接觸面單元,藍(lán)色為橫縫單元,綠色為周邊縫、趾板-連接板,連接板-防滲墻接縫單元。
計(jì)算中需要處理的接觸面和接縫共有9種,見表1。
面板-墊層(擠壓墻)接觸面采用非線性接觸面材料模型和無厚度Goodman單元,接觸面參數(shù)對(duì)面板應(yīng)力數(shù)值有較大影響,巴貢面板壩工程專門進(jìn)行了面板與擠壓邊墻間接縫材料力學(xué)性能試驗(yàn),研究了無接縫材料、不同厚度乳化瀝青(1 mm、2 mm、3 mm)、兩層乳化瀝青中間夾沙、瀝青油氈、土工膜等7種情況??紤]到擠壓邊墻技術(shù)的普遍采用,此次計(jì)算參照了巴貢面板壩的試驗(yàn)成果,按照面板+1 mm乳化瀝青+擠壓墻對(duì)應(yīng)的接觸面參數(shù)進(jìn)行取值(見表2)。橫縫和周邊縫按1層金屬止水+1 cm厚度橡膠填充物考慮。
1.4 材料計(jì)算參數(shù)
對(duì)大壩實(shí)際填筑料場(chǎng)的灰?guī)r料進(jìn)行三軸試驗(yàn),其靜力計(jì)算參數(shù)見表3。
2 地震反應(yīng)特性分析
2.1 三維動(dòng)力計(jì)算參數(shù)及加速度的輸入
(1)動(dòng)力計(jì)算參數(shù)。
常用的考慮圍壓的HardinDrnevich雙曲線模型假定主干線為一條雙曲線,見圖4。
通過試驗(yàn)測(cè)得動(dòng)剪切模量比Gd/Gdmax和動(dòng)阻尼比λd與動(dòng)剪應(yīng)變?chǔ)胐的關(guān)系曲線。動(dòng)力計(jì)算時(shí)輸入相應(yīng)關(guān)系曲線的控制數(shù)據(jù),根據(jù)應(yīng)力應(yīng)變值進(jìn)行內(nèi)插和外延取值,用于計(jì)算。本工程壩料的動(dòng)剪切模量比Gd/Gdmax和動(dòng)阻尼比λd與動(dòng)剪應(yīng)變?chǔ)胐的關(guān)系曲線試驗(yàn)結(jié)果見表4,壩料K′,n′值見表5。
由于該面板堆石壩工程缺乏壩料地震殘余變形試驗(yàn)參數(shù),本次計(jì)算中壩料的殘余變形計(jì)算參數(shù)參考公伯峽的資料并根據(jù)該面板堆石壩工程的特點(diǎn)進(jìn)行選取。主堆石和次堆石的地震殘余變形計(jì)算的相關(guān)參數(shù)見表6和7,其它材料的參數(shù)根據(jù)壩料相似的原則進(jìn)行選取。
高程方向豎直加速度輸入,依據(jù)水工建筑物抗震設(shè)計(jì)規(guī)范,將其峰值折減2/3(由規(guī)范反應(yīng)譜人工生成輸入的地震波,順河向加速度峰值為力豎向加速度峰值為水平向峰值的2/3);z方向?yàn)檠貕屋S方向橫向加速度輸入。圖5為100年超越概率2%的地震加速度曲線。計(jì)算中將整個(gè)地震歷程劃分為24個(gè)大時(shí)段,每個(gè)大時(shí)段又劃分為50個(gè)小時(shí)段,因此,積分計(jì)算的時(shí)間步長(zhǎng)為002 s。
2.2 三維非線性地震反應(yīng)特性
由表8可知最大加速度反應(yīng)位于0+170斷面,因此計(jì)算結(jié)果選取基本設(shè)計(jì)工況壩體最大斷面(0+170樁號(hào))的成果進(jìn)行分析,動(dòng)力有限元計(jì)算成果特征量匯總見表9。壩體位移反應(yīng)、面板應(yīng)力反應(yīng)及防滲墻地震反應(yīng)見圖6至圖8。
順河向絕對(duì)加速度最大為9 m/s2,放大系數(shù)為45,豎直向絕對(duì)加速度最大為10 m/s2,放大系數(shù)為50[21]。順河向最大位移反應(yīng)為11 cm,豎直向[CM(22]最大位移反應(yīng)為65 cm,均發(fā)生在下游壩頂附近。
壩體第一主應(yīng)力最大為053 MPa,第三主應(yīng)力最大值為051 MPa,最大動(dòng)剪應(yīng)力為035 MPa,壩體不會(huì)被剪壞。面板順坡向最大壓應(yīng)力為75 MPa。面板的最大動(dòng)撓度為95 cm,由地震引起的面板與趾板之間的最拉伸量和最大壓縮量均小于29 mm;垂直縫的最大剪切位移為36 mm。順河向最大永久變形為15 cm,豎直向最大永久變形為49 cm,均發(fā)生壩頂位置,地震沉陷量為壩高的04%。因此,此壩體在地震作下不會(huì)發(fā)生大范圍剪切破壞。防滲墻第一主應(yīng)力最大為22 MPa,發(fā)生在防滲墻底部;第三主應(yīng)力最大值為19 MPa,同樣發(fā)生在防滲墻底部,由此可見在地震作用下,防滲墻動(dòng)應(yīng)力較小,不會(huì)發(fā)生破壞。三維分析中,堆石體的水平絕對(duì)加速度反應(yīng)極值為9 m/s2,最大放大系數(shù)為42,堆石體、面板最大地震反應(yīng)位于壩頂局部位置,存在明顯的鞭稍效應(yīng)(即在地震作用下,大壩頂部突出部分振幅劇烈增大的現(xiàn)象),需要結(jié)合計(jì)算成果在壩頂進(jìn)行抗震加固。
2.3 三維動(dòng)力參數(shù)敏感性分析
經(jīng)進(jìn)一步計(jì)算,將壩體材料最大動(dòng)剪切模量的模數(shù)減小10%和20%后,壩體與面板的動(dòng)力反應(yīng)均有較大變化。最大動(dòng)剪切模量的模數(shù)減小20%后,壩體最大加速度反應(yīng)順河向由9 m/s2減小到8 m/s2,垂直向由10 m/s2減小到8 m/s2;最大位移反應(yīng)變化不大,只有豎直向稍有減?。欢咽w應(yīng)力無明顯變化;面板撓度在參數(shù)降低10%時(shí)稍有增大,但在參數(shù)降低到20%時(shí)又恢復(fù)到95 cm,這也說明了三維狀態(tài)下,面板變形的復(fù)雜性;受堆石體及面板變形增大的影響,接縫變形明顯增大,其中面板和周邊縫的張開值都增大2 mm左右;地震永久變形變化較明顯,其中豎向位移由49 cm減小到38 cm。
因此,動(dòng)力參數(shù)降低后,速度反應(yīng)和地震永久變形等均有所減小,而接縫位移反應(yīng)等均有所增大。但是,壩體地震反應(yīng)的分布規(guī)律是一致的,地震反應(yīng)數(shù)值的變化不大。
3 結(jié)論
基于等效線性法,采用有限元方法建立動(dòng)力運(yùn)動(dòng)方程對(duì)某高面板堆石壩進(jìn)行地震動(dòng)力反映分析,計(jì)算結(jié)果如下。
(1) 無論順河向還是豎直向最大永久變形均發(fā)生在壩頂位置,地震引起的沉降量為04%,大壩變形總體不大。
(2) 地震期間面板動(dòng)拉應(yīng)力反應(yīng)值較小,出現(xiàn)拉應(yīng)力的區(qū)域很小,面板整體呈現(xiàn)壓應(yīng)力為主,防滲墻動(dòng)應(yīng)力較小,不會(huì)發(fā)生破壞,整體表明設(shè)計(jì)地震作用下大壩是安全的。
(3) 對(duì)于最大地震反應(yīng)位于壩頂?shù)拇髩味?,需關(guān)注地震中的鞭梢效應(yīng),必要時(shí)應(yīng)進(jìn)行抗震加固處理。
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