盧芳琴， 孫 紅， 石玉成

(1.中國地震局蘭州地震研究所，甘肅 蘭州 730000； 2.上海交通大學 船舶海洋與建筑工程學院，上海 200240；3.中國地震局 甘肅省黃土地震工程重點實驗室，甘肅 蘭州 730000)

砂土液化引起大位移對地下管道影響的非線性分析①

盧芳琴1，3， 孫 紅2， 石玉成1

(1.中國地震局蘭州地震研究所，甘肅 蘭州 730000； 2.上海交通大學 船舶海洋與建筑工程學院，上海 200240；3.中國地震局 甘肅省黃土地震工程重點實驗室，甘肅 蘭州 730000)

地下管線是生命線工程的主要部分，已經(jīng)成為現(xiàn)代工農(nóng)業(yè)生產(chǎn)和城鎮(zhèn)生活的大動脈。已有震害調(diào)查表明，飽和砂土液化引起的地基大變形(側(cè)向變形和沉降)是導(dǎo)致強震區(qū)生命線工程震害的主要原因。采用三維非線性有限差分分析方法來研究砂土液化引起的大位移對地下管道的破壞特征，分析砂土液化的斜坡變形特征、孔隙水的演化過程。結(jié)果表明，砂土液化引起的大位移對地下管道有破壞作用, 導(dǎo)致管道變形規(guī)律與其斜坡的位移規(guī)律相同，地下管線的變形隨著振動頻率和幅值的增加其非線性增大。

液化； 地下管線； 大位移；三維； 非線性

0 引言

地下管線是生命線工程的主要部分，如通信、天然氣、城市供水、上下水道系統(tǒng)、農(nóng)業(yè)灌溉和石油運輸?shù)龋呀?jīng)成為現(xiàn)代工農(nóng)業(yè)生產(chǎn)和城鎮(zhèn)生活的大動脈。近年來的大地震中，管線破壞引起了人們越來越多的注意，如日本1993年的Nansei—Old地震[1]、1993年Kushim—Oki地震和1994年Hokkaido—Toho—Oki地震[2]。地震中由于供水管線的破壞引起城市缺水，進而導(dǎo)致火災(zāi)等次生災(zāi)害發(fā)生，使得整個城市的基本生活癱瘓。已有震害調(diào)查表明[3]，飽和砂土地層液化引起的地基大變形(側(cè)向變形和沉降)是導(dǎo)致強震區(qū)生命線工程震害的主要原因。

對地下管線抗震方面的研究，大多偏重于地震直接作用(如地震波和斷層錯動)方面，很少研究地震間接作用(如滑坡、砂土液化和不均勻沉降等)方面。管道的破損一般與管周土變形有關(guān)。以往的研究中很少考慮地震時地下管道周邊土的變形，特別是液化引起的地面?zhèn)认虼笞冃蔚挠绊?，忽視了土與管道之間的相互作用。目前對于液化地基生命線工程的破壞研究得比較少，特別是對液化引起的地面大變形對生命線工程的破壞。

Miyajima M.[4]和Kalliontzis C.等[5]用靜力分析方法來分析地下管道特征。徐鳳萍[6]、Takada S.等[7]和Prashar Y.等[8]采用有限元法分析土體液化造成地面大位移時地下管線的內(nèi)力和變形。吳懿等[9]運用可靠度理論分析地震液化引起地面大位移對地下管線的影響。

目前已經(jīng)開展砂土液化引起大變形的三維化研究[10]，但國內(nèi)外對液化引起的大變形對地下管道破壞的機理研究還不深入。本文應(yīng)用非線性有效應(yīng)力方法分析砂土液化對地下管線的影響，分析管線破壞的變形特征。

1 三維動態(tài)分析

砂土液化地基中地下管線的穩(wěn)定性問題屬于三維問題，使用Flac軟件，利用有限差分格式和有效應(yīng)力方法對埋于液化的斜坡地基中地下管線進行三維大變形非線性分析，考慮到網(wǎng)格尺寸和邊界條件對計算結(jié)果有影響，采用大的斜坡模型進行計算，網(wǎng)格劃分見圖1。地基模型由兩部分組成，下部為40 m厚的飽和砂，上部為20 m厚的干砂。靜水位在飽和砂的表面。斜坡水平尺寸和垂直尺寸比例為1∶2。

圖1 數(shù)值網(wǎng)格劃分和模型邊界(單位：m)Fig.1 Numerical mesh and boundary of the model (unit：m)

飽和砂用Mohr-Coulomb 與Finn 模型(孔隙水壓力增長模型)耦合分析，干砂使用Mohr-Coulomb模型分析，模型參數(shù)見表1 。

表1 數(shù)值模型的基本參數(shù)

管道在坡頂下埋深10 m，使用結(jié)構(gòu)的梁單元進行模擬，與周邊的土關(guān)系采用剪切和法向彈簧模擬。管的彈性模量為1.2×108kPa，泊松比為 0.25，密度為 7 000 kg/m3， 直徑為300 mm。 土與管之間的關(guān)系為雙線性彈性關(guān)系，見圖2。液化前彈性模量為3×104kPa ，液化后模量為30 kPa，采用0.5% Raleigh阻尼。

圖2 土與管的雙線性關(guān)系Fig.2 Bilinear relationship between soil and pipe

地基邊界分兩步設(shè)置，初始應(yīng)力分析時底部邊界的水平和垂直方向固定；側(cè)面邊界在水平方向上固定，垂直方向不固定；在動態(tài)分析時側(cè)邊界使用自由場邊界(Free-field boundaries)，使波的反射最小化，底部不是固定邊界，利于加水平荷載。

2 動態(tài)分析結(jié)果

首先進行初始靜態(tài)應(yīng)力條件分析，然后進行動態(tài)時程分析，水平荷載為多頻率和多幅值的正弦波。

2.1 位移和孔隙水壓力

本文采用的荷載為速度0.5 m/s、頻率5 Hz的正弦波。圖3為該荷載加載后的斜坡位移向量?？梢钥闯鲂逼律喜亢突A(chǔ)發(fā)生沉降，斜坡下部和坡腳與左側(cè)之間的區(qū)域向上發(fā)生運動。

圖3 速度為0.5 m/s，頻率為5 Hz的正弦波加載后振動10 s時的位移向量圖Fig.3 Displacement vectors diagram at 10 seconds after vibration under the load of a sine wave with velocity=0.5 m/s， frequency=5 Hz

圖4是坡腳和坡頂位置距離地表面10 m深的位移與時間關(guān)系圖。從圖中可見，位移隨時間的增加呈非線性增長，5 s前位移變化速率較快，5 s后位移變化放緩，并且坡腳下的位移明顯大于坡頂下的位移，說明邊坡坡腳在地震砂土液化過程中穩(wěn)定性急劇降低。這一現(xiàn)象進一步解釋了管道不能埋設(shè)在坡腳下的理由。

圖4 速度為0.5 m/s，頻率為5 Hz的正弦波加載后坡腳和坡頂位置距離地表面10 m深的位移與時間關(guān)系圖Fig.4 Displacement vs time of the toe and crest of the slope at a depth of 10 m below the surface under the load of a sine wave with amplitude=0.5 m/s，f=5 Hz

圖5是最大孔隙水壓力時程曲線圖。初期孔隙水壓力隨著時間的增加而增長，當達到最大值時砂土發(fā)生液化，然后孔隙水慢慢消散，孔壓慢慢降低，最后基本趨于穩(wěn)定。在同一深度，坡頂下的最大孔壓值大于坡腳下的值，這是因為砂土液化時重力和動應(yīng)力不再由土骨架承擔，而是由水來承擔，即孔壓升高，坡頂位置的地基上覆重力大于坡腳位置的上覆重力，所以孔壓會大于后者。

圖5 速度為0.5 m/s，頻率為5 Hz的正弦波時坡腳和坡頂下距離地表面10 m深度的最大孔壓時程圖 Fig.5 Maximum pore water pressure versus time of the toe and crest of the slope at a depth of 10 m below the surface under the load of a sine wave with amplitude=0.5 m/s，f=5 Hz

2.2 管的動態(tài)反應(yīng)

地面變形引起的管位移隨著振動時間的增加而增大。圖6是管道中間節(jié)點的水平和垂直位移。管道的位移隨著時間的增加而非線性地增長，在變形的初期階段，管的垂直方向略微地向上移動，但隨著時間增加位移快速增長，當5 s后位移變化緩慢，尤其是垂直位移基本穩(wěn)定，而水平位移變化速度明顯比前階段小。說明砂土的液化產(chǎn)生的大位移對管道的影響巨大，管道隨著土體的非線性位移而相應(yīng)發(fā)生非線性位移，變化規(guī)律基本一致。

2.3 動力荷載對管道位移的影響

為考察動力荷載的幅值和速度頻率對管道位移的影響，分別進行多頻率和多速度幅值的多工況計算。工況分為兩類：一類是正弦波頻率為5 Hz，幅值分別為0.5、1、2、3、4及5 m/s；二類是正弦波幅值為1 m/s，頻率為0.5、1、2、3、4及5 Hz的計算。

圖7是正弦波為5 Hz時波的幅值與管的位移的關(guān)系圖。圖8 是正弦波幅值為1 m/s時，管的位移和速度頻率的關(guān)系圖。管的位移隨著幅值和頻率的增加而非線性增加，在幅值和頻率小的階段位移增長較快，而在幅值和頻率大的階段位移增長緩慢。

圖6 速度為0.5 m/s，頻率為5 Hz的正弦波時管中部位移 Fig.6 Displacement in the middle of pipe versus time under the load of a sine wave with amplitude=0.5 m/s，f=5 Hz

圖7 頻率為0.5 Hz的正弦波振動10 s時管節(jié)點位移速度幅值關(guān)系圖 Fig.7 Displacement of pipe versus velocity amplitude at 10 s after vibration under the load of a sine wave with of f=0.5 Hz

圖8 速度幅值為1.0 m/s的正弦波振動10 s時管節(jié)點位移與速度頻率關(guān)系圖 Fig.8 Displacement of pipe versus velocity frequency at 10 s after vibration under the load of a sine wave with A=1.0 m/s

3 結(jié)論

本文對斜坡砂土液化地基的地下管線進行三維非線性有效應(yīng)力大變形分析，發(fā)現(xiàn)液化會引起砂土斜坡產(chǎn)生大的位移，并對地下管線有巨大影響，地下管線的位移隨著時間的增加而增長，發(fā)展規(guī)律與斜坡變形的非線性規(guī)律相一致，地下管線的變形隨著頻率和振幅的增大而非線性增大。使用非線性方法模擬土與管的共同作用是有效可行的。

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Nonlinear Analysis of Influence of Large Displacement Induced by Sand Liquefaction on Underground Pipeline

LU Fang-qin1，3， SUN Hong2， SHI Yu-cheng1

(1.LanzhouInstituteofSeismology，CEA，Lanzhou，Gansu73000，China；2.SchoolofNavalArchitecture，OceanandCivilEngineering，ShanghaiJiaotongUniversity，Shanghai200240，China；3.KeyLaboratoryofLoessEarthquakeEngineering，CEA，Lanzhou，Gansu730000，China)

Underground pipelines are the big arteries of present-day industry，agriculture，and city life.It is important to ensure the safety of pipelines in operation，especially under seismic loading.For underground pipelines，seismic damages can be classified as either wave-propagation damage or permanent ground-displacement damage.There have been some events where pipe damage has been due only to wave propagation.More typically，pipeline damage is due to a combination of hazards.However，the damage from large ground displacements typically occurs in isolated areas of ground failure and tends to be greater，whereas wave propagation tends to cause less damage.Large liquefaction-induced displacement (lateral displacement and settlement) is a potential source of major damage to underground pipelines during earthquakes.Therefore，soil liquefaction does major damage to underground pipelines during earthquakes.In order to analyze the damage to underground pipelines under a slope due to sand liquefaction，a three-dimensional nonlinear analysis was carried out to study the pipe characteristics damaged by liquefaction-induced large displacements using the FLAC finite-difference method and to analyze the displacement characteristics of the slope due to sand liquefaction and the pore water pressure buildup.A numerical model was established，which is similar to the real engineering project dimensions.The model consists of the saturated sand and dry sand layers，as well as the pipeline buried under the slope.The saturated sand on the foundation was modeled using a Mohr-Coulomb soil model coupled with a Finn model，which is the pore water pressure generation model.The dry sand of the slope was also modeled as a Mohr-Coulomb model without the pore water pressure generation model.The soil-pipe interaction was simulated by a bilinear elastic model，in which the elastic modulus before liquefaction is 103 times that after liquefaction.The base boundary was a rigid boundary.The calculation process is divided into two stages of static and dynamic analysis.In the initial static analysis，in order to compute the gravity stresses，the base boundary was fixed both horizontally and vertically，and the side boundaries were only fixed horizontally.In the dynamic analysis，free-field boundaries were used，and the sine waves were applied to the base boundary.After computing the static stress conditions，a time history dynamic analysis was carried out for sine wave velocities with different frequencies and amplitudes.It was shown that the occurrence of sand liquefaction and large displacement was caused by large sine waves.The displacement of the slope increased with time，which was different in the various parts of the slope.The displacement below the toe of the slope was bigger than that below the crest of the slope，and the sand above the slope had a trend of slipping into the foot of the foundation.The displacement of the pipe increased linearly in the first stage，and then increased nonlinearly with the increase in damage.The liquefaction-induced large displacement does damage to the buried pipe；the displacement of the pipe increases with an increase in the amplitude and frequency of applied sine waves.It is possible to use the nonlinear method to simulate the soil-structure interaction.It is necessary to find a simplified analysis method for predicting pipe damage.

liquefaction； underground pipeline； large displacement； three-dimension； nonlinear

2015-03-30

國家自然科學基金項目(51248005)；中國地震局地震預(yù)測研究所基本科研業(yè)務(wù)費項目(2012IESLZ02)

盧芳琴(1987-)，女，碩士研究生，研究方向：巖土工程及結(jié)構(gòu)抗震.E-mail：498214265@qq.com

TU435

A

1000-0844(2015)02-0362-05

10.3969/j.issn.1000-0844.2015.02.0362