基于沉降測(cè)量的管道力學(xué)性狀分析及誤差評(píng)估

李素貞　彭興華　李新亮

摘要：結(jié)合管道沿線沉降觀測(cè)和間接平差理論，提出了基于彈性地基梁撓曲微分方程通解函數(shù)式的擬合模型，用以獲得管道的連續(xù)撓曲線，進(jìn)而實(shí)現(xiàn)管道結(jié)構(gòu)的力學(xué)性狀分析和安全評(píng)估.針對(duì)擬合誤差的影響，采用誤差傳遞理論進(jìn)行撓曲方程及內(nèi)力解算值的精度評(píng)定.通過集中和均布荷載下管道變形擬合的算例分析對(duì)比了地基梁通解函數(shù)式擬合模型和傳統(tǒng)的多項(xiàng)式擬合模型.結(jié)合某道路下天然氣管道在鄰近超高層建筑施工過程中的沉降監(jiān)測(cè)探討了本文方法的有效性.結(jié)果表明：與多項(xiàng)式擬合模型相比，本文提出的模型在埋地管道撓曲線重構(gòu)及應(yīng)力解算方面精度更高，可用于高層結(jié)構(gòu)施工期間周邊埋地管道的力學(xué)性狀分析及安全評(píng)價(jià).

關(guān)鍵詞：埋地管道；沉降測(cè)量；平差理論；誤差評(píng)估；彈性地基梁

中圖分類號(hào)：TU990.3 文獻(xiàn)標(biāo)識(shí)碼：A

Abstract：Based on Winkler foundation model and indirect adjustment theory， this paper proposed a fitting model to reconstruct the deflection curve for the structural performance evaluation of the buried pipeline by using multipoint subsidence measurements. According to error propagation theory， the precision of the derived deflection and the stress of the pipeline structure were investigated. Two analytical examples of the pipelines under a concentrated load and a uniformly distributed load were given， which demonstrate that the proposed model has achieved greater accuracy in the estimation of pipeline deflection and stress by comparing with the conventional polynomial model. Combined with the application to a practical project regarding a buried gas pipeline in the vicinity of the construction site of a highrise building， the effectiveness of the fitting model in the stress analysis and safety evaluation of buried pipeline was verified as well.

Key words：buried pipeline； subsidence measurement； adjustment theory； error assessment； winkler foundation model

管網(wǎng)系統(tǒng)是保證社會(huì)經(jīng)濟(jì)發(fā)展和人民生活的重要生命線工程.埋地管道上受到直接或間接作用的荷載主要有管道結(jié)構(gòu)的自重、覆土壓力、管內(nèi)流體的重量等恒載以及車輛荷載、地面荷載＼[1＼]、溫度變化所引起的脹縮力、管道內(nèi)壓、上浮荷載、地震荷載、城市建設(shè)施工干擾等活荷載.城市埋地管道受高層建設(shè)或基坑開挖引起土體不均勻沉降而導(dǎo)致的破壞現(xiàn)象較明顯＼[2-3＼].這些荷載導(dǎo)致管道的沉降變形，沿管道的整體均勻沉降將不會(huì)引起管道的安全破壞，但局部沉降變形將嚴(yán)重威脅管道的安全運(yùn)行＼[4＼].

埋地管道沉降變形的監(jiān)測(cè)手段可有沉降測(cè)量、應(yīng)變片測(cè)量、傾角測(cè)量等，其中基于管道沉降位移的測(cè)量值來評(píng)估管道的安全狀況是較為直接簡(jiǎn)便的方法.地震、沉降等土體移動(dòng)引起的管道內(nèi)力的計(jì)算方法已經(jīng)有很多種＼[5-7＼].項(xiàng)式Limura根據(jù)在管道三點(diǎn)處的沉降位移測(cè)量值來線性插值求取這三點(diǎn)間管道的沉降位移，進(jìn)而結(jié)合Winkler地基梁理論求解管道內(nèi)力＼[8＼].高田至郎等根據(jù)彈性地基梁理論對(duì)受到地基沉降影響的4種情形下埋地管線進(jìn)行模型化處理，提出了計(jì)算管線最大彎曲變形、接頭轉(zhuǎn)角、最大接頭伸長(zhǎng)量的設(shè)計(jì)公式＼[9＼].基于有限元方法的埋地管道變形受力分析為埋地管道的設(shè)計(jì)提供了先驗(yàn)的判斷評(píng)估＼[10＼].李大勇等考慮了基坑圍護(hù)結(jié)構(gòu)、土體與地下管線的耦合作用，建立了地下管線、土體以及基坑圍護(hù)結(jié)構(gòu)為一體的三維有限元模型，分析了地下管線的管材、埋深、距離基坑遠(yuǎn)近、下臥層土質(zhì)、管道彈性模量與周圍土體彈性模量比等因素對(duì)地下管線的影響規(guī)律，并總結(jié)、歸納了地下管線的安全性判別方法及地下管線的工程監(jiān)測(cè)和保護(hù)措施＼[11-12＼].而考慮到埋地管道變形測(cè)量誤差對(duì)變形曲線擬合的影響的研究甚少，Orynyak等對(duì)埋地管道變形測(cè)量的誤差做了一些討論＼[13＼]，但對(duì)測(cè)量誤差到內(nèi)力計(jì)算的誤差傳遞未明確.

5結(jié)論

基于管道沿線各點(diǎn)的沉降觀測(cè)，本文提出了結(jié)合彈性地基梁模型的平差擬合算法，用以獲得連續(xù)的管道撓曲方程，進(jìn)而實(shí)現(xiàn)管道結(jié)構(gòu)的力學(xué)性狀分析和安全評(píng)估.本文主要結(jié)論如下：

1）根據(jù)埋地管道在集中和均布荷載作用下?lián)锨€的擬合和應(yīng)變解算的誤差評(píng)估，地基梁撓曲方程通解式擬合模型比多項(xiàng)式擬合模型精度高，并且適用于管道大沉降下的撓曲線擬合.

2）在管道受集中荷載或均布荷載作用下，地基梁撓曲方程通解擬合模型不具有擬合模型誤差，故在對(duì)管道沉降位移到其撓曲線的擬合過程中，可僅考慮沉降位移測(cè)量誤差的影響.

3）在本工程狀況下，地基梁撓曲方程通解中特解y1（x）取二次多項(xiàng)式（m=2）對(duì)擬合周邊管道的撓曲線并用于管道結(jié)構(gòu)力學(xué)性狀分析的最佳擬合次數(shù).

參考文獻(xiàn)

[1]闕小平，李平木.埋地剛性管道上的地面荷載計(jì)算＼[J＼].混凝土與水泥制品，2010，26（3）：31.

QUE Xiaoping， LI Pingmu. Ground load calculation of buried rigid pipes＼[J＼]. China Concerete and Cement Products， 2010，26（3）：31.（In Chinese）

＼[2＼]BRANKO Glisic， YAO Yao. Fiber optic method for health assessment of pipelines subjected to earthquakeinduced ground movement＼[J＼].Structural Health Monitoring， 2012，11（6）： 696-711.

＼[3＼]LI Suzhen， ZHAO ming. Structural health monitoring of continuously welded underground pipelines based on quasidistributed wireless inclinometers＼[C＼]//Research and Applications in Structural Engineering， Mechanics and Computation ，SEMC 2013， Capa Town， South Africa， 2013：2205-2209.

＼[4＼]HYOUNGSIK kim， WOOSIK kim.Analysis of stresses on buried natural gas pipelinne subjected to ground subsidence＼[C＼]//International Pipeline ConferenceProceedings of the International Pipeline Conference， IPC.Calgary， Can， 1998，V2：749-756.

＼[5＼]SAITO K， NISHIO N， KATAYAMA T. Recommended practice for earthquakeresistant design medium and lowpressure gas pipelines＼[C＼]//Earthquake Behavior and Safety of Oil and Gas Storage Facilities， Buried Pipelines and Equipment， Presented at 1983 International Symposium on Lifeline Earthquake Engineering at the 4th National Congress on Pressure Vessel and Piping Technnology. Portland， OR，USA， 1983：340-348.

＼[6＼]OISHI H. Considerations on behavior of underground pipelines caused by ground settlement＼[C＼]//Proc JSCE 1985.Japan，1985：379-386.

＼[7＼]TANABLE K，TAKADA S. Design formulae of buried pipes subjected to large ground settlement and their application＼[C＼]// Proc JSCE 1986.Japan，1986：593-602.

＼[8＼]LIMURA S. Simplified mechanical model for evaluating stress in pipeline subjected to settlement＼[J＼]. Construction and Building Materials，2004，18：469-479.

＼[9＼]高田至郎. 受地基沉降影響的地下管線的設(shè)計(jì)公式及應(yīng)用＼[C＼]//地下管線抗震.北京：學(xué)術(shù)書刊出版社，1990：374-390.

SHIRO Takada. Formulation and application of underground pipeline design influenced by foundation settlement ＼[C＼]// Seismic Design of Underground Pipeline. Beijing： Academic Press，1990：374-390.（In Chinese）

＼[10＼]李新慧. 天然氣埋地管道沉降的有限元分析＼[J＼]. 巖土工程學(xué)報(bào)，2013，S1：259-263.

LI Xinhui. Finite element analysis of settlement of buried natural gas pipelines＼[J＼]. Chinese Journal of Geotechnical Engineering， 2013，S1：259-263.（In Chinese）

＼[11＼]李大勇，龔曉南，張土喬. 軟土地基深基坑周圍地下管線保護(hù)措施的數(shù)值模擬＼[J＼].巖土工程學(xué)報(bào)，2001，23（6）：736-740.

LI Dayong，GONG Xiaonan， ZHANG Tuqiao. Numerical stimulation of the buried pipelines protection adjacent to deep excavation＼[J＼] . Chinese Journal of Geotechnical Engineering，2001， 23（6）： 736-740. （In Chinese）

＼[12＼]李大勇，龔曉南，張土喬. 軟土地基深基坑工程鄰近柔性接口地下管線的性狀分析＼[J＼]，土木工程學(xué)報(bào)，2003，36（2）：77-80.

LI Dayong，GONG Xiaonan， ZHANG Tuqiao. Response of jointed ductile pipeline to deep excavation in soft soil＼[J＼]. China Civil Engineering Journal，2003， 36 （2）： 77-80. （In Chinese）

＼[13＼]ORYNYAK L V， LOKHMAN L V.Determination of curve characteristics by its discrete points measured with an error and its application to stress analysis for buried pipeline＼[J＼].Strength of Materials， 2012，44（3）：268-284.

＼[14＼]王穂輝.誤差理論與測(cè)量平差＼[M＼].上海：同濟(jì)大學(xué)出版社，2010：115-122.

3）在本工程狀況下，地基梁撓曲方程通解中特解y1（x）取二次多項(xiàng)式（m=2）對(duì)擬合周邊管道的撓曲線并用于管道結(jié)構(gòu)力學(xué)性狀分析的最佳擬合次數(shù).

參考文獻(xiàn)

[1]闕小平，李平木.埋地剛性管道上的地面荷載計(jì)算＼[J＼].混凝土與水泥制品，2010，26（3）：31.

QUE Xiaoping， LI Pingmu. Ground load calculation of buried rigid pipes＼[J＼]. China Concerete and Cement Products， 2010，26（3）：31.（In Chinese）

＼[2＼]BRANKO Glisic， YAO Yao. Fiber optic method for health assessment of pipelines subjected to earthquakeinduced ground movement＼[J＼].Structural Health Monitoring， 2012，11（6）： 696-711.

＼[3＼]LI Suzhen， ZHAO ming. Structural health monitoring of continuously welded underground pipelines based on quasidistributed wireless inclinometers＼[C＼]//Research and Applications in Structural Engineering， Mechanics and Computation ，SEMC 2013， Capa Town， South Africa， 2013：2205-2209.

＼[4＼]HYOUNGSIK kim， WOOSIK kim.Analysis of stresses on buried natural gas pipelinne subjected to ground subsidence＼[C＼]//International Pipeline ConferenceProceedings of the International Pipeline Conference， IPC.Calgary， Can， 1998，V2：749-756.

＼[5＼]SAITO K， NISHIO N， KATAYAMA T. Recommended practice for earthquakeresistant design medium and lowpressure gas pipelines＼[C＼]//Earthquake Behavior and Safety of Oil and Gas Storage Facilities， Buried Pipelines and Equipment， Presented at 1983 International Symposium on Lifeline Earthquake Engineering at the 4th National Congress on Pressure Vessel and Piping Technnology. Portland， OR，USA， 1983：340-348.

＼[6＼]OISHI H. Considerations on behavior of underground pipelines caused by ground settlement＼[C＼]//Proc JSCE 1985.Japan，1985：379-386.

＼[7＼]TANABLE K，TAKADA S. Design formulae of buried pipes subjected to large ground settlement and their application＼[C＼]// Proc JSCE 1986.Japan，1986：593-602.

＼[8＼]LIMURA S. Simplified mechanical model for evaluating stress in pipeline subjected to settlement＼[J＼]. Construction and Building Materials，2004，18：469-479.

＼[9＼]高田至郎. 受地基沉降影響的地下管線的設(shè)計(jì)公式及應(yīng)用＼[C＼]//地下管線抗震.北京：學(xué)術(shù)書刊出版社，1990：374-390.

SHIRO Takada. Formulation and application of underground pipeline design influenced by foundation settlement ＼[C＼]// Seismic Design of Underground Pipeline. Beijing： Academic Press，1990：374-390.（In Chinese）

＼[10＼]李新慧. 天然氣埋地管道沉降的有限元分析＼[J＼]. 巖土工程學(xué)報(bào)，2013，S1：259-263.

LI Xinhui. Finite element analysis of settlement of buried natural gas pipelines＼[J＼]. Chinese Journal of Geotechnical Engineering， 2013，S1：259-263.（In Chinese）

＼[11＼]李大勇，龔曉南，張土喬. 軟土地基深基坑周圍地下管線保護(hù)措施的數(shù)值模擬＼[J＼].巖土工程學(xué)報(bào)，2001，23（6）：736-740.

LI Dayong，GONG Xiaonan， ZHANG Tuqiao. Numerical stimulation of the buried pipelines protection adjacent to deep excavation＼[J＼] . Chinese Journal of Geotechnical Engineering，2001， 23（6）： 736-740. （In Chinese）

＼[12＼]李大勇，龔曉南，張土喬. 軟土地基深基坑工程鄰近柔性接口地下管線的性狀分析＼[J＼]，土木工程學(xué)報(bào)，2003，36（2）：77-80.

LI Dayong，GONG Xiaonan， ZHANG Tuqiao. Response of jointed ductile pipeline to deep excavation in soft soil＼[J＼]. China Civil Engineering Journal，2003， 36 （2）： 77-80. （In Chinese）

＼[13＼]ORYNYAK L V， LOKHMAN L V.Determination of curve characteristics by its discrete points measured with an error and its application to stress analysis for buried pipeline＼[J＼].Strength of Materials， 2012，44（3）：268-284.

＼[14＼]王穂輝.誤差理論與測(cè)量平差＼[M＼].上海：同濟(jì)大學(xué)出版社，2010：115-122.

3）在本工程狀況下，地基梁撓曲方程通解中特解y1（x）取二次多項(xiàng)式（m=2）對(duì)擬合周邊管道的撓曲線并用于管道結(jié)構(gòu)力學(xué)性狀分析的最佳擬合次數(shù).

參考文獻(xiàn)

[1]闕小平，李平木.埋地剛性管道上的地面荷載計(jì)算＼[J＼].混凝土與水泥制品，2010，26（3）：31.

QUE Xiaoping， LI Pingmu. Ground load calculation of buried rigid pipes＼[J＼]. China Concerete and Cement Products， 2010，26（3）：31.（In Chinese）

＼[2＼]BRANKO Glisic， YAO Yao. Fiber optic method for health assessment of pipelines subjected to earthquakeinduced ground movement＼[J＼].Structural Health Monitoring， 2012，11（6）： 696-711.

＼[3＼]LI Suzhen， ZHAO ming. Structural health monitoring of continuously welded underground pipelines based on quasidistributed wireless inclinometers＼[C＼]//Research and Applications in Structural Engineering， Mechanics and Computation ，SEMC 2013， Capa Town， South Africa， 2013：2205-2209.

＼[4＼]HYOUNGSIK kim， WOOSIK kim.Analysis of stresses on buried natural gas pipelinne subjected to ground subsidence＼[C＼]//International Pipeline ConferenceProceedings of the International Pipeline Conference， IPC.Calgary， Can， 1998，V2：749-756.

＼[5＼]SAITO K， NISHIO N， KATAYAMA T. Recommended practice for earthquakeresistant design medium and lowpressure gas pipelines＼[C＼]//Earthquake Behavior and Safety of Oil and Gas Storage Facilities， Buried Pipelines and Equipment， Presented at 1983 International Symposium on Lifeline Earthquake Engineering at the 4th National Congress on Pressure Vessel and Piping Technnology. Portland， OR，USA， 1983：340-348.

＼[6＼]OISHI H. Considerations on behavior of underground pipelines caused by ground settlement＼[C＼]//Proc JSCE 1985.Japan，1985：379-386.

＼[7＼]TANABLE K，TAKADA S. Design formulae of buried pipes subjected to large ground settlement and their application＼[C＼]// Proc JSCE 1986.Japan，1986：593-602.

＼[8＼]LIMURA S. Simplified mechanical model for evaluating stress in pipeline subjected to settlement＼[J＼]. Construction and Building Materials，2004，18：469-479.

＼[9＼]高田至郎. 受地基沉降影響的地下管線的設(shè)計(jì)公式及應(yīng)用＼[C＼]//地下管線抗震.北京：學(xué)術(shù)書刊出版社，1990：374-390.

SHIRO Takada. Formulation and application of underground pipeline design influenced by foundation settlement ＼[C＼]// Seismic Design of Underground Pipeline. Beijing： Academic Press，1990：374-390.（In Chinese）

＼[10＼]李新慧. 天然氣埋地管道沉降的有限元分析＼[J＼]. 巖土工程學(xué)報(bào)，2013，S1：259-263.

LI Xinhui. Finite element analysis of settlement of buried natural gas pipelines＼[J＼]. Chinese Journal of Geotechnical Engineering， 2013，S1：259-263.（In Chinese）

＼[11＼]李大勇，龔曉南，張土喬. 軟土地基深基坑周圍地下管線保護(hù)措施的數(shù)值模擬＼[J＼].巖土工程學(xué)報(bào)，2001，23（6）：736-740.

LI Dayong，GONG Xiaonan， ZHANG Tuqiao. Numerical stimulation of the buried pipelines protection adjacent to deep excavation＼[J＼] . Chinese Journal of Geotechnical Engineering，2001， 23（6）： 736-740. （In Chinese）

＼[12＼]李大勇，龔曉南，張土喬. 軟土地基深基坑工程鄰近柔性接口地下管線的性狀分析＼[J＼]，土木工程學(xué)報(bào)，2003，36（2）：77-80.

LI Dayong，GONG Xiaonan， ZHANG Tuqiao. Response of jointed ductile pipeline to deep excavation in soft soil＼[J＼]. China Civil Engineering Journal，2003， 36 （2）： 77-80. （In Chinese）

＼[13＼]ORYNYAK L V， LOKHMAN L V.Determination of curve characteristics by its discrete points measured with an error and its application to stress analysis for buried pipeline＼[J＼].Strength of Materials， 2012，44（3）：268-284.

＼[14＼]王穂輝.誤差理論與測(cè)量平差＼[M＼].上海：同濟(jì)大學(xué)出版社，2010：115-122.