框架锚杆锚固寒区边坡的多场耦合分析
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摘要
为了明确寒区框架锚杆边坡支护结构的工作机理,建立了框架锚杆支护冻土边坡的水热力耦合计算模型,采用有限元法进行了求解,基于MATLAB软件平台编写了计算程序,并通过已有的试验考证了程序的正确性。算例分析给出了边坡温度场、水分场、应力场和支护结构冻融反应的分布规律。结果表明:坡面上部受气温影响较大,融化时活动层含水量接近饱和,坡脚附近出现过饱和的"水泡";冻结时剪应力最大值是融化时的2倍,且分布均匀,边坡处于稳定状态,融化时剪应力在活动层和稳定冻土层交界面发生突变,边坡处于不稳定状态,该交界面是潜在滑移面;在一个冻融周期内,锚杆轴力、立柱内力和水平位移均先增大后减小,且随坡高逐渐增大,3种工况下结构内力和水平位移的关系为冻结时大于融化时大于初始时;冻胀时各层锚杆锚头处轴力增量最明显,增幅沿杆轴方向逐渐减小,融化时锚杆轴力和立柱内力大幅减小,且留有残余变形。因此,框架锚杆支护冻土边坡时,建议支护结构应按冻胀工况进行设计和计算。
In order to clarify the working mechanism of frame supporting structure with anchors in the cold region,a coupled mathematical calculation model of heat-moisture-stress was established.The coupled model was analyzed by the finite element method,and a calculation program was written based on the MATLAB software.Besides,the program was verified by the existing experimental research.Through the examples,the distribution laws of the temperature field,moisture field and stress field of the slope and the freeze-thaw reaction of the supporting structure were obtained.The results show that the upper part of slope is greatly influenced by temperature,and the active layer is nearly saturated when it melts.And there exists the supersaturated"bubble"at the bottom of slope.In addition,the shear stress in the process of the freezing whose maximumvalue is twice as large as that in the process of thawing is evenly distributed.The slope is stable during this process.While there appears a shear stress mutation at the interface between active layer and stable frozen soil layer during the thawing.The slope is unstable,and the interface is the potential slip surface.In a freeze-thaw cycle,the axial force of anchor bolt,the internal force of column and the horizontal displacement increase first and then decrease,and all of them increase with the increase of the slope height.The laws of structural internal force and horizontal displacement under the three conditions from the largest to the smallest are freezing stage,thawing stage and the initial stage.The axial force at the anchor head in each soil layer dramatically increases during the frost heaving process,while the increase amplitude gradually decreases in the axial direction.In the process of thawing,the anchor force and the internal force of column decrease significantly,with a residual deformation produced.Therefore,when the permafrost slope is supported by frame anchor,the supporting structure is supposed to be designed and calculated under the frost heaving condition.
In order to clarify the working mechanism of frame supporting structure with anchors in the cold region,a coupled mathematical calculation model of heat-moisture-stress was established.The coupled model was analyzed by the finite element method,and a calculation program was written based on the MATLAB software.Besides,the program was verified by the existing experimental research.Through the examples,the distribution laws of the temperature field,moisture field and stress field of the slope and the freeze-thaw reaction of the supporting structure were obtained.The results show that the upper part of slope is greatly influenced by temperature,and the active layer is nearly saturated when it melts.And there exists the supersaturated"bubble"at the bottom of slope.In addition,the shear stress in the process of the freezing whose maximumvalue is twice as large as that in the process of thawing is evenly distributed.The slope is stable during this process.While there appears a shear stress mutation at the interface between active layer and stable frozen soil layer during the thawing.The slope is unstable,and the interface is the potential slip surface.In a freeze-thaw cycle,the axial force of anchor bolt,the internal force of column and the horizontal displacement increase first and then decrease,and all of them increase with the increase of the slope height.The laws of structural internal force and horizontal displacement under the three conditions from the largest to the smallest are freezing stage,thawing stage and the initial stage.The axial force at the anchor head in each soil layer dramatically increases during the frost heaving process,while the increase amplitude gradually decreases in the axial direction.In the process of thawing,the anchor force and the internal force of column decrease significantly,with a residual deformation produced.Therefore,when the permafrost slope is supported by frame anchor,the supporting structure is supposed to be designed and calculated under the frost heaving condition.
引文
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[5]张智浩,马凛,韩晓猛,等.季节性冻土区深基坑桩锚支护结构冻胀变形控制研究[J].岩土工程学报,2012,34(增):65-71.ZHANG Zhi-hao,MA Lin,HAN Xiao-meng,et al.Frost Heaving Deformation Control of Pile-anchor Retaining Structure of Deep Foundation Pits in Seasonal Frozen Soil Regions[J].Chinese Journal of Geotechnical Engineering,2012,34(S):65-71.
[6]梁波,王家东,严松宏,等.多年冻土地区L型挡土墙土压力(冻胀力)的分析与试验[J].冰川冻土,2002,24(5):628-633.LIANG Bo,WANG Jia-dong,YAN Song-hong,et al.Experiment and Analysis of the Earth Pressure(Frost Heaving Forces)on L-type Retaining Wall in Permafrost Regions[J].Journal of Glaciology and Geocryology,2002,24(5):628-633.
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[8]赖远明,刘松玉,吴紫汪.寒区挡土墙温度场、渗流场和应力场耦合问题的非线性分析[J].土木工程学报,2003,36(6):88-95.LAI Yuan-ming,LIU Song-yu,WU Zi-wang.Nonlinear Analyses for Retaining Walls in Frigid Zone—A Coupled Problem of Temperature,Seepage,and Stress Fields[J].China Civil Engineering Journal,2003,36(6):88-95.
[9]赖远明,吴紫汪,朱元林,等.寒区隧道温度场、渗流场和应力场耦合问题的非线性分析[J].岩土工程学报,1999,21(5):529-533.LAI Yuan-ming,WU Zi-wang,ZHU Yuan-lin,et al.Nonlinear Analyses for the Couple Problem of Temperature,Seepage and Stress Fields in Cold Region Tunnels[J].Chinese Journal of Geotechnical Engineering,1999,21(5):529-533.
[10]董建华,董旭光,朱彦鹏.随机地震作用下框架锚杆锚固边坡稳定性可靠度分析[J].中国公路学报,2017,30(2):41-47.DONG Jian-hua,DONG Xu-guang,ZHU Yan-peng.Reliability Analysis on Stability of Slope Reinforced by Frame with Pre-stress Anchors Under Random Earthquake Action[J].China Journal of Highway and Transport,2017,30(2):41-47.
[11]董建华,张媛,朱彦鹏,等.框架预应力锚杆边坡锚固结构的随机地震反应及动力可靠度分析[J].中国公路学报,2015,28(10):26-33.DONG Jian-hua,ZHANG Yuan,ZHU Yan-peng,et al.Random Seismic Response and Dynamic Reliability Analysis of Frame with Prestressed Anchors for Slope Stability[J].China Journal of Highway and Transport,2015,28(10):26-33.
[12]董建华,朱彦鹏,马巍,等.框架预应力锚杆边坡支护结构抗震简化设计方法[J].中国公路学报,2012,25(5):38-46.DONG Jian-hua,ZHU Yan-peng,MA Wei,et al.Simplified Seismic Design Method of Frame Supporting Structure with Prestressed Anchors for Slope Stability[J].China Journal of Highway and Transport,2012,25(5):38-46.
[13]孔祥谦.有限单元法在传热学中的应用[M].3版.北京:科学出版社,1998.KONG Xian-qian.Application of Finite Element Method on Heat Transfer[M].3rd ed.Beijing:Science Press,1998.
[14]赖远明,张明义,李双洋,等.寒区工程理论与应用[M].北京:科学出版社,2009.LAI Yuan-ming,ZHANG Ming-yi,LI Shuang-yang,et al.Theory and Application of Cold Regions Engineering[M].Beijing:Science Press,2009.
[15]毛雪松.多年冻土区路基水热力场耦合效应研究[D].西安:长安大学,2004.MAO Xue-song.Study on Coupling Model of the Moisture-heat-stress Fields in the Permafrost Subgrade[D].Xi'an:Chang'an University,2004.
[16]王家林,陈山林.钢筋混凝土平面问题的含梁组合单元模型[J].郑州大学学报:工学版,2005,26(2):72-75.WANG Jia-lin,CHEN Shan-lin.A Beam-embedded Plane Finite Element Model of Reinforced Concrete[J].Journal of Zhengzhou University:Engineering Science,2005,26(2):72-75.
[17]董旭光.多年冻土区新型框架热锚管边坡支护结构的工作机理及试验研究[D].兰州:兰州理工大学,2017.DONG Xu-guang.Research on the Working Mechanism and Experiment of the New Frame Heat Anchor Pipe Supporting Structure for Permafrost Slope[D].Lanzhou:Lanzhou University of Technology,2017.
[18]代涛.框架锚杆支护冻土边坡的多场耦合分析[D].兰州:兰州理工大学,2016.DAI Tao.Analysis on Coupling Model of Permafrost Slope Supported by Frame Structure with Anchors[D].Lanzhou:Lanzhou University of Technology,2016.
[19]SHEN M,LADANYI B.Modelling of Coupled Heat,Moisture and Stress Field in Freezing Soil[J].Cold Regions Science and Technology,1987,14:237-246.
[20]何敏,李宁,刘乃飞.饱和冻土水热力耦合模型解析及验证[J].岩土工程学报,2012,34(10):1858-1865.HE Min,LI Ning,LIU Nai-fei.Analysis and Validation of Coupled Heat-moisture-deformation Model for Saturated Frozen Soils[J].Chinese Journal of Geotechnical Engineering,2012,34(10):1858-1865.
[2]熊治文,廖小平,徐兵魁,等.青藏铁路多年冻土边坡与斜坡路基研究综述[J].铁道学报,2010,32(4):102-107.XIONG Zhi-wen,LIAO Xiao-ping,XU Bing-kui,et al.Summary on Research on Slope and Slope Embankment in Permafrost Region of Qinghai-Tibet Railway[J].Journal of the China Railway Society,2010,32(4):102-107.
[3]丁靖康,娄安金.水平冻胀力的现场测定方法[J].冰川冻土,1980,2(增1):33-36.DING Jing-kang,LOU An-jin.Site Measurement Method of Horizontal Frost Heaving Force[J].Journal of Glaciology and Geocryology,1980,2(S1):33-36.
[4]徐学燕,丁靖康,娄安金.冻融界面土体的长期抗剪强度指标确定[J].哈尔滨建筑工程学院学报,1992,25(3):37-42.XU Xue-yan,DING Jing-kang,LOU An-jin.Determining the Long Term Shear Strength at the Frozen-unfrozen Interface[J].Journal of Harbin Architecture&Civil Engineering Institute,1992,25(3):37-42.
[5]张智浩,马凛,韩晓猛,等.季节性冻土区深基坑桩锚支护结构冻胀变形控制研究[J].岩土工程学报,2012,34(增):65-71.ZHANG Zhi-hao,MA Lin,HAN Xiao-meng,et al.Frost Heaving Deformation Control of Pile-anchor Retaining Structure of Deep Foundation Pits in Seasonal Frozen Soil Regions[J].Chinese Journal of Geotechnical Engineering,2012,34(S):65-71.
[6]梁波,王家东,严松宏,等.多年冻土地区L型挡土墙土压力(冻胀力)的分析与试验[J].冰川冻土,2002,24(5):628-633.LIANG Bo,WANG Jia-dong,YAN Song-hong,et al.Experiment and Analysis of the Earth Pressure(Frost Heaving Forces)on L-type Retaining Wall in Permafrost Regions[J].Journal of Glaciology and Geocryology,2002,24(5):628-633.
[7]苗天德,郭力,牛永红,等.正冻土中水热迁移问题的混合物理论模型[J].中国科学:D辑,1999,29(增1):8-14.MIAO Tian-de,GUO Li,NIU Yong-hong,et al.Modeling on Coupled Heat and Moisture Transfer in Freezing Soil Using Mixture Theory[J].Science in China:Series D,1999,29(S1):8-14.
[8]赖远明,刘松玉,吴紫汪.寒区挡土墙温度场、渗流场和应力场耦合问题的非线性分析[J].土木工程学报,2003,36(6):88-95.LAI Yuan-ming,LIU Song-yu,WU Zi-wang.Nonlinear Analyses for Retaining Walls in Frigid Zone—A Coupled Problem of Temperature,Seepage,and Stress Fields[J].China Civil Engineering Journal,2003,36(6):88-95.
[9]赖远明,吴紫汪,朱元林,等.寒区隧道温度场、渗流场和应力场耦合问题的非线性分析[J].岩土工程学报,1999,21(5):529-533.LAI Yuan-ming,WU Zi-wang,ZHU Yuan-lin,et al.Nonlinear Analyses for the Couple Problem of Temperature,Seepage and Stress Fields in Cold Region Tunnels[J].Chinese Journal of Geotechnical Engineering,1999,21(5):529-533.
[10]董建华,董旭光,朱彦鹏.随机地震作用下框架锚杆锚固边坡稳定性可靠度分析[J].中国公路学报,2017,30(2):41-47.DONG Jian-hua,DONG Xu-guang,ZHU Yan-peng.Reliability Analysis on Stability of Slope Reinforced by Frame with Pre-stress Anchors Under Random Earthquake Action[J].China Journal of Highway and Transport,2017,30(2):41-47.
[11]董建华,张媛,朱彦鹏,等.框架预应力锚杆边坡锚固结构的随机地震反应及动力可靠度分析[J].中国公路学报,2015,28(10):26-33.DONG Jian-hua,ZHANG Yuan,ZHU Yan-peng,et al.Random Seismic Response and Dynamic Reliability Analysis of Frame with Prestressed Anchors for Slope Stability[J].China Journal of Highway and Transport,2015,28(10):26-33.
[12]董建华,朱彦鹏,马巍,等.框架预应力锚杆边坡支护结构抗震简化设计方法[J].中国公路学报,2012,25(5):38-46.DONG Jian-hua,ZHU Yan-peng,MA Wei,et al.Simplified Seismic Design Method of Frame Supporting Structure with Prestressed Anchors for Slope Stability[J].China Journal of Highway and Transport,2012,25(5):38-46.
[13]孔祥谦.有限单元法在传热学中的应用[M].3版.北京:科学出版社,1998.KONG Xian-qian.Application of Finite Element Method on Heat Transfer[M].3rd ed.Beijing:Science Press,1998.
[14]赖远明,张明义,李双洋,等.寒区工程理论与应用[M].北京:科学出版社,2009.LAI Yuan-ming,ZHANG Ming-yi,LI Shuang-yang,et al.Theory and Application of Cold Regions Engineering[M].Beijing:Science Press,2009.
[15]毛雪松.多年冻土区路基水热力场耦合效应研究[D].西安:长安大学,2004.MAO Xue-song.Study on Coupling Model of the Moisture-heat-stress Fields in the Permafrost Subgrade[D].Xi'an:Chang'an University,2004.
[16]王家林,陈山林.钢筋混凝土平面问题的含梁组合单元模型[J].郑州大学学报:工学版,2005,26(2):72-75.WANG Jia-lin,CHEN Shan-lin.A Beam-embedded Plane Finite Element Model of Reinforced Concrete[J].Journal of Zhengzhou University:Engineering Science,2005,26(2):72-75.
[17]董旭光.多年冻土区新型框架热锚管边坡支护结构的工作机理及试验研究[D].兰州:兰州理工大学,2017.DONG Xu-guang.Research on the Working Mechanism and Experiment of the New Frame Heat Anchor Pipe Supporting Structure for Permafrost Slope[D].Lanzhou:Lanzhou University of Technology,2017.
[18]代涛.框架锚杆支护冻土边坡的多场耦合分析[D].兰州:兰州理工大学,2016.DAI Tao.Analysis on Coupling Model of Permafrost Slope Supported by Frame Structure with Anchors[D].Lanzhou:Lanzhou University of Technology,2016.
[19]SHEN M,LADANYI B.Modelling of Coupled Heat,Moisture and Stress Field in Freezing Soil[J].Cold Regions Science and Technology,1987,14:237-246.
[20]何敏,李宁,刘乃飞.饱和冻土水热力耦合模型解析及验证[J].岩土工程学报,2012,34(10):1858-1865.HE Min,LI Ning,LIU Nai-fei.Analysis and Validation of Coupled Heat-moisture-deformation Model for Saturated Frozen Soils[J].Chinese Journal of Geotechnical Engineering,2012,34(10):1858-1865.