路基下伏矩形溶洞的稳定性解析法
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摘要
为评价荷载作用下的路基下伏矩形溶洞的稳定性,首先根据岩溶区路基承载特性建立简化的力学分析模型,并进一步得到等效计算模型。其次,基于复变函数理论,提出矩形溶洞任意截面映射函数的确定方法,并给出常用矩形截面映射函数的具体表达式。然后,求得矩形溶洞在自重与路基荷载联合作用下的地层应力;在此基础上,进一步求得任意截面的最大、最小主应力,同时引入Griffith强度准则,对溶洞的稳定性进行评价。最后,通过数值方法及工程实例对本文计算方法进行验算。研究结果表明:该方法所得水平应力和切应力与数值结果误差在5%以内,竖直应力误差在8%以内,工程实际情况与理论计算结果吻合良好,对岩溶区路基设计计算有一定的参考价值;值得注意的是,矩形溶洞4个顶点处的水平应力及竖向应力值都比较大,应力变化幅度较为明显,存在严重的应力集中现象,说明矩形溶洞的4个顶点比较容易破坏,在工程实践中应特别注意该处的验算。
In order to present a stability assessment method for subgrade with underlying cavity,a simplified mechanical analysis model was established based on the bearing capacity of subgrade in Karst areas,and equivalent calculation model was further obtained.By dint of the complex variable function,the mapping function identification of arbitrary cross sections of the rectangular cavity was proposed.Meanwhile,the specific expressions of mapping functions for common rectangular sections were also presented.The geostatic stress field influenced by a combination factors between the gravity and subgrade loads was obtained in semi-finite space.On this basis,the major and minor principal stresses were obtained,and the stability of the cavity was evaluated based on Griffith failure criterion.In addition,the theoretical result was validated by case records and the numerical method.The results show that the errors between the predictions and the numerical results are less than 5% for the horizontal stress as well as the shear stress,and 8%for the vertical stress.Besides,the proposed results are in good agreement with the observations in engineering practices,and the proposed method has a reference for the preliminary design.It is worth noting that the lager horizontal and vertical stresses appear at the four corners.The stressvariation ranges are significant due to stress concentrations.In particular,the four corners are easy to be failed in the actual engineering,and the checking computations should be paid special attention.
In order to present a stability assessment method for subgrade with underlying cavity,a simplified mechanical analysis model was established based on the bearing capacity of subgrade in Karst areas,and equivalent calculation model was further obtained.By dint of the complex variable function,the mapping function identification of arbitrary cross sections of the rectangular cavity was proposed.Meanwhile,the specific expressions of mapping functions for common rectangular sections were also presented.The geostatic stress field influenced by a combination factors between the gravity and subgrade loads was obtained in semi-finite space.On this basis,the major and minor principal stresses were obtained,and the stability of the cavity was evaluated based on Griffith failure criterion.In addition,the theoretical result was validated by case records and the numerical method.The results show that the errors between the predictions and the numerical results are less than 5% for the horizontal stress as well as the shear stress,and 8%for the vertical stress.Besides,the proposed results are in good agreement with the observations in engineering practices,and the proposed method has a reference for the preliminary design.It is worth noting that the lager horizontal and vertical stresses appear at the four corners.The stressvariation ranges are significant due to stress concentrations.In particular,the four corners are easy to be failed in the actual engineering,and the checking computations should be paid special attention.
引文
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[2]KIYOSUMI M,KUSAKABE O,OHUCHI M.Model Tests and Analyses of Bearing Capacity of Strip Footing on Stiff Ground with Voids[J].Journal of Geotechnical and Geoenvironmental Engineering,2011,137(4):363-375.
[3]程跃辉,周基,崔颖超,等.地下岩溶暗河诱因路堤塌陷失稳机理模拟分析[J].中外公路,2007,27(4):178-181.CHENG Yue-hui,ZHOU Ji,CUI Ying-chao,et al.Instability Analysis of Embankment Collapse Due to the Underground Karst River[J].Journal of China and Foreign Highway,2007,27(4):178-181.
[4]刘铁雄.岩溶顶板与桩基作用机理分析与模拟试验研究[D].长沙:中南大学,2003.LIU Tie-xiong.Analysis and Model Test Research of Mechanism Between Cavity Roof and Pile Foundation[D].Changsha:Central South University,2003.
[5]程晔,赵明华,曹文贵.基桩下溶洞顶板稳定性评价的强度折减有限元法[J].岩土工程学报,2005,27(1):38-41.CHENG Ye,ZHAO Ming-hua,CAO Wen-gui.Study on Stability Evaluation of Karst Cave Roof with Strength Reduction FEM[J].Chinese Journal of Geotechnical Engineering,2005,27(1):38-41.
[6]曹文贵,程晔,赵明华.公路路基岩溶顶板安全厚度确定的数值流形方法研究[J].岩土工程学报,2005,27(6):621-625.CAO Wen-gui,CHENG Ye,ZHAO Ming-hua.Studies on Numerical Manifold Method for Determination of Safe Thickness of Karst Roof in Roadbed[J].Chinese Journal of Geotechnical Engineering,2005,27(6):621-625.
[7]赵明华,邱志博,张锐.岩溶区地基极限承载力上限有限元数值模拟分析[J].水文地质工程地质,2014,41(6):57-62.ZHAO Ming-hua,QIU Zhi-bo,ZHANG Rui.Numerical Simulation Analysis of Foundation Ultimate Bearing Capacity in Karst Area Using Upper Bound Finite Element Method[J].Hydrogeology&Engineering Geology,2014,41(6):57-62.
[8]胡庆国,张可能,阳军生.溶洞上方条形基础地基极限承载力有限元分析[J].中南大学学报:自然科学版,2005,36(4):694-697.HU Qing-guo,ZHANG Ke-neng,YANG Jun-sheng.Finite Element Analysis of Ultimate Bearing Capacity of Strip Footing Above Karst Cave[J].Journal of Central South University:Science and Technology,2005,36(4):694-697.
[9]VAZIRI H H,JALALI J S,ISLAM R.An Analytical Model for Stability Analysis of Rock Layers Over a Circular Opening[J].International Journal of Solids and Structures,2001,38(21):3735-3757.
[10]刘之葵,梁金城,朱寿增,等.岩溶区土洞地基稳定性分析[J].水文地质工程地质,2003,30(3):24-28.LIU Zhi-kui,LIANG Jin-cheng,ZHU Shou-zeng,et al.Stability Analysis of Soil Cave Foundation in Karst Area[J].Hydrogeology&Engineering Geology,2003,30(3):24-28.
[11]蒋冲,赵明华,胡柏学,等.路基溶洞顶板稳定性影响因素分析[J].公路工程,2009,34(1):5-9.JIANG Chong,ZHAO Ming-hua,HU Bo-xue,et al.Stability Factors Analysis for Subgrade Karst Roof[J].Highway Engineering,2009,34(1):5-9.
[12]WANG M C,HSIEH C W.Collapse Load of Strip Footing Above Circular Void[J].Journal of Geotechnical Engineering,1987,113(5):511-515.
[13]李倩倩,张顶立,房倩.含空洞地层初始破坏的复变函数解析研究[J].岩土工程学报,2014,36(11):2110-2117.LI Qian-qian,ZHANG Ding-li,FANG Qian.Analytic Solution to Initial Damage of Cavern Strata by Complex Function Method[J].Chinese Journal of Geotechnical Engineering,2014,36(11):2110-2117.
[14]陈子荫.围岩力学分析中的解析方法[M].北京:煤炭工业出版社,1994.CHEN Zi-ying.Theoretical Methods About the Analysis of Adjoining Rock Mass[M].Beijing:China Coal Industry Publishing House,1994.
[15]萨文G N.孔附近的应力集中[M].卢鼎霍,译.北京:科学出版社,1958.SAVIN G N.Stress Concentration by Cavity[M].Translated by LU Ding-huo.Beijing:Science Press,1958.
[16]王桂芳.隧道计算[M].成都:成都科技大学出版社,1992.WANG Gui-fang.Tunnel Calculation[M].Chengdu:University of Science and Technology of Chengdu Press,1992.
[17]刘佑荣,唐辉明.岩体力学[M].武汉:中国地质大学出版社,1999.LIU You-rong,TANG Hui-Ming.Rock Mechanics[M].Wuhan:China University of Geosciences Press,1999.