岩石地基中柱下圆形独立基础的力学特性与破坏模式研究
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摘要
近年的工程建设中,大荷载作用下岩石地基中柱下圆形独立基础的应用常常遇到。现行规范中关于岩石地基中圆形独立基础的设计方法主要是在土质地基的理论之上形成的,而且对于圆形独立基础的设计提及甚少,另外对于基础体内应力场的研究基本没有涉及。由于岩石地基具有承载力高、刚度大、变形小等显著特点,岩石地基中柱下圆形独立基础体内应力场研究以及基础的破坏模式在理论上和实践中均有一定不足。
本文采用理论推导研究、现场试验、和ANSYS有限元数值计算等方法,对岩石地基中柱下圆形独立基础的基底反力分布、圆形独立基础体内应力场分布和圆形独立基础破坏模式进行了一定深度的研究。主要工作和成果如下:
①针对岩石地基中柱下圆形独立基础,看作是轴对称的空间问题,不计体力。从齐次拉梅方程出发,采用空间柱坐标,利用布西内克斯-伽辽金(Boussinesq-Galerkin)通解形式,通过试取勒夫应变函数,验算得到了满足简化圆形独立基础四个精确边界条件的勒夫应变势函数,最后得到了岩石地基中柱下圆形独立基础的体内应力场的理论解。
②通过现场试验,分析得出岩石地基中柱下圆形独立基础的基底反力分布的非线性特点较为显著,呈现中间小、两边大的趋势。在圆形独立基础中部,基底反力分布比较均匀,沿着半径逐渐向外,基底反力分布的非线性愈发显著,到圆形独立基础边缘时,由于应力集中和应力重分布导致基础基底反力又有减小的趋势。针对于一般的岩石地基而言,按规范中将基底反力看作是均匀线性分布的荷载可能与实际工程情况有差异。
③通过ANSYS有限元分析得出圆形独立基础体内应力场,并与理论计算得到的应力场进行对比分析,总结出岩石地基中柱下圆形独立基础体内应力场的分布趋势。另外通过ANSYS有限元分析与现场试验结果相对比,总结出了岩石地基中柱下圆形独立基础受荷破坏模式,二者在工程上为圆形独立基础的设计提供理论基础。
本文得到的岩石地基中柱下圆形独立基础的研究成果,无论是在学术研究还是在工程实践应用中都具有参考价值。
In recent construction, circular foundations in rock subgrade subjected to large loading have been adopted more frequently. The design methods for circular foundation in current specifications are all from theories based on soil, and the methods are very rough. The stress field of spread foundations was not considered.Because the rock subgrade has obvious characteristics of high capacity, high rigidity and little distortion, There are some shortage in theory and in practice of circular foundations in rock subgrade, especially it’s internal stress field and failure mode.
In this article, by methods of theoretical analysis, field test and ANSYS FEM numerical analysis, some researches have been done to the subgrade reaction’s distribution of circular foundation in rock, internal stress field in circular foundation, the failure mode of circular foundation in rock subgrade. The main work and efforts are as follows:
①For the circular foundations in rock subgrade, regardless of the physical load, look as axisymmetric space problems. From the homogeneous lame equation, adopting spatial cylindrical coordinates, use the general equation solution of Boussinesq-Galerkin, through the test taken Love strain function, checking the four accurate boundary conditions of circular independent foundation, finally we got the theoretical solution of internal stress field in circular foundation on rock subgrade.
②According to test results and test phenomenon, it summarizes the subgrade reaction’s distribution of circular foundation in rock subgrade, form relevant tables and curves, gets the rule of distribution curve of subgrade reaction. The subgrade reaction’s distribution is nonlinear significant, it is intermediate small and uniform, both sides big. Due to stress concentration and stress redistribution, the distribution to the edge of the foundation decreases. But the subgrade reaction’s distribution is uniform linear distribution in current specifications. For the general rock subgrade, there are some difference between specifications and actual engineering.
③Based on ANSYS FEM numerical analysis, we got the internal stress field in circular foundation. Contrast the theoretical calculation, Summarized the trend of internal stress field in circular foundation. Contrast the field test results, Summarized the failure mode of circular foundation.Both of them provides the theory basis for circular foundation’s design method in engineering.
The research results about circular foundations in rock subgrade in this article, have its own value both in theoretical research and in engineering applications.
本文采用理论推导研究、现场试验、和ANSYS有限元数值计算等方法,对岩石地基中柱下圆形独立基础的基底反力分布、圆形独立基础体内应力场分布和圆形独立基础破坏模式进行了一定深度的研究。主要工作和成果如下:
①针对岩石地基中柱下圆形独立基础,看作是轴对称的空间问题,不计体力。从齐次拉梅方程出发,采用空间柱坐标,利用布西内克斯-伽辽金(Boussinesq-Galerkin)通解形式,通过试取勒夫应变函数,验算得到了满足简化圆形独立基础四个精确边界条件的勒夫应变势函数,最后得到了岩石地基中柱下圆形独立基础的体内应力场的理论解。
②通过现场试验,分析得出岩石地基中柱下圆形独立基础的基底反力分布的非线性特点较为显著,呈现中间小、两边大的趋势。在圆形独立基础中部,基底反力分布比较均匀,沿着半径逐渐向外,基底反力分布的非线性愈发显著,到圆形独立基础边缘时,由于应力集中和应力重分布导致基础基底反力又有减小的趋势。针对于一般的岩石地基而言,按规范中将基底反力看作是均匀线性分布的荷载可能与实际工程情况有差异。
③通过ANSYS有限元分析得出圆形独立基础体内应力场,并与理论计算得到的应力场进行对比分析,总结出岩石地基中柱下圆形独立基础体内应力场的分布趋势。另外通过ANSYS有限元分析与现场试验结果相对比,总结出了岩石地基中柱下圆形独立基础受荷破坏模式,二者在工程上为圆形独立基础的设计提供理论基础。
本文得到的岩石地基中柱下圆形独立基础的研究成果,无论是在学术研究还是在工程实践应用中都具有参考价值。
In recent construction, circular foundations in rock subgrade subjected to large loading have been adopted more frequently. The design methods for circular foundation in current specifications are all from theories based on soil, and the methods are very rough. The stress field of spread foundations was not considered.Because the rock subgrade has obvious characteristics of high capacity, high rigidity and little distortion, There are some shortage in theory and in practice of circular foundations in rock subgrade, especially it’s internal stress field and failure mode.
In this article, by methods of theoretical analysis, field test and ANSYS FEM numerical analysis, some researches have been done to the subgrade reaction’s distribution of circular foundation in rock, internal stress field in circular foundation, the failure mode of circular foundation in rock subgrade. The main work and efforts are as follows:
①For the circular foundations in rock subgrade, regardless of the physical load, look as axisymmetric space problems. From the homogeneous lame equation, adopting spatial cylindrical coordinates, use the general equation solution of Boussinesq-Galerkin, through the test taken Love strain function, checking the four accurate boundary conditions of circular independent foundation, finally we got the theoretical solution of internal stress field in circular foundation on rock subgrade.
②According to test results and test phenomenon, it summarizes the subgrade reaction’s distribution of circular foundation in rock subgrade, form relevant tables and curves, gets the rule of distribution curve of subgrade reaction. The subgrade reaction’s distribution is nonlinear significant, it is intermediate small and uniform, both sides big. Due to stress concentration and stress redistribution, the distribution to the edge of the foundation decreases. But the subgrade reaction’s distribution is uniform linear distribution in current specifications. For the general rock subgrade, there are some difference between specifications and actual engineering.
③Based on ANSYS FEM numerical analysis, we got the internal stress field in circular foundation. Contrast the theoretical calculation, Summarized the trend of internal stress field in circular foundation. Contrast the field test results, Summarized the failure mode of circular foundation.Both of them provides the theory basis for circular foundation’s design method in engineering.
The research results about circular foundations in rock subgrade in this article, have its own value both in theoretical research and in engineering applications.
引文
[1]林图,地基基础设计.华中理工大学出版社,1996.
[2]阴可,程毅等.岩石地基上扩展基础的基底反力实测分析[J].重庆建筑大学学报,2006,28(6).
[3]陈明.半无限弹性体地基基础的地基反力计算[J].四川水利,2003,15(1).
[4]王国体,地基反力的数值模拟和基础结构的内力响应[J].土木工程学报, 2002.4, 35(2):103-107.
[5]杜佐龙,毕生等基于弹塑性有限单元法的地基极限承载力形状效应修正分析[J].勘察科学技术, 2010.3.
[6]艾智勇,吴超.分层地基上矩形刚性基础的基底反力、沉降和倾斜计算[J].力学季刊, 2008, 29(1).
[7]朱爱军等.岩石地基上扩展基础基底反力分布的分析[J].工业建筑,2002,32(8):32-35.
[8]邓安福.岩石地基上扩展基础基底反力分布的分析[J].工业建筑,2002,32(8).
[9]王振宇.砂卵石地区高层建筑箱基基底反力实测研究[J].建筑结构学报,2000.8, 21(4):72-75.
[10]蔚旭灿,郑传超.圆形均布荷载作用下半空间伯格斯模型粘弹性体的理论解[J].西安建筑科技大学学报(自然科学版),2008.12, V40(6).
[11]杨小礼,李亮.圆形基础极限分析下限解探讨[J].铁道学报,2001.12, Vol.23No.6.
[12]蒋益平,熊巨华.方形和圆形基础地基极限承载力分析[J].岩土力学,2005.12, Vol.26No.12.
[13]范静海,非线性接触力学模型在地基-基础相互作用弹性分析中的应用[J].岩土力学, 2004, 25(2): 154-159.
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[15]周晓兵,王飞龙.竖向荷载下圆形基础承载力分析[J].采矿技术,2002.3, Vol.2No.1.
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[18]吴能森,谢成新.基底压力分布对扩展基础冲切承载力影响的研究[J].西北建筑工程学院学报,2002,19(1).
[19]赖庆文,岩石地基基础受剪计算方法探讨[J].工业建筑, 2002, 32(8):32-35.
[20]肖常安,岩石地基上独立柱基抗剪问题的探讨[J].贵州工业大学学报, 2002, 6:52-55.
[21] Johnson, Gordon R.; Christiano, Paul; Epstein, Howard I.Stiffness coefficients for embedded footings,American Society of Civil Engineers, Journal of the Geotechnical Engineering Division, v 101, n 8, p 789-800, Aug 1975.
[22] Dunham, L.; Valsangkar, A.J.; Schriver, A.B.Centrifuge modeling of rigid square footings on weak jointed rock:Geotechnical Testing Journal, v 28, n 2, p 133-143, March 2005.
[23] Hallgren.M, Kinnunen.S, Nylander,B. Punching Shear Tests on Column Footings[J]. Nordic Concrete Research,1998,21(1): 1–22.
[24] Mikael Hallgren, Mats Bjerke. Non-linear finite element analyses of punching shear failure of column footings[J]. Cement And Concrete Composites, 2002,24: 491–496.
[25] Richart,F.E, Reinforced concrete wall and column footing[J]. Journal of the American Concrete Institute, 1948,11.
[26] Castellanza.R. Model footing load tests on soft rocks[J].Geotechnical Testing Journal, 2009, 32(3):262-272.
[27] Yang Xiao-Li. Seismic bearing capacity of a strip footing on rock slopes [J]. Canadian Geotechnical Journal, 2009, 46(8):943-954.
[28] Merifield,R.S. Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek-Brown criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(6):920-937.
[29] Chang,J.C. Bearing behavior and failure mechanism of a shallow foundation located on/behind the crest of a poorly cemented artificial sandstone [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(8):1508-1518.
[30] Vianna,Ana Paula Fontana. Influence of footing size and matric suction on the behavior of shallow foundations in collapsible soil [J]. Soils and Rocks , 2007, 30(3):127-137.
[31] Sokol,Nikolas. Design of rock shafts adjacent to heavily loaded columns [C]. 9th North American Tunneling Conference, NAT 2008.North American Tunneling 2008 Proceedings,2008:218-224.
[32] EI Ganainy,H. Efficient 3D nonlinear Winkler model for shallow foundations [J]. Soil Dynamics and Earthquake Engineering, 2009, 29(8):1236-1248.
[33] Raychowdhury,Prishati. Performance evaluation of a nonlinear Winkler-based shallow foundation model using centrifuge test results [J]. Earthquake Engineering and Structural Dynamics, 2009, 38(5):679-698.
[34]赫文化.ANSYS土木工程应用实例[M].北京:中国水利水电出版社,2005:75-120.
[35]华南理工大学东南大学浙江大学等,地基基础.中国建筑工业出版社,1998.
[36]王重穆.柱下单独基础抗弯强度的若干问题[J],建筑结构,1995,(2).
[37]白生翔,钢筋混凝土扩展基础设计方法的改进建议.工业建筑[J], 2005,35(2) :.88-92.
[38] Samual E.French, Introduction to Soil Mechanics and Shallow Foundations Design. 1989.
[39]刘廉纯,柱下独立基础抗弯强度塑性分析和设计探讨[J].建筑结构,1998(5):23-27.
[40]重庆市地基基础设计规范(DB50/5001—1997)[S].重庆:重庆市建设委员会,1997.
[41]孙仁博,王天明,材料力学[M].北京:中国建筑工业出版社,1995:175-179.
[42]张莉.不同岩基上独立基础基底反力分布的研究[J].有色金属设计,2006,33(3):34-38.
[43]天津大学同济大学等,混凝土结构(上册).中国建筑工业出版社,2001.
[44]吴家龙等,弹性力学.高等教育出版社,2001.
[45]程昌钧,王颖坚,马文华,李家仁等,弹性力学.高等教育出版社,1999.
[46]程毅,岩石地基上扩展基础的抗剪性能研究.《重庆大学硕士论文》2006.
[47]林灌南,岩石地基刚度对基底反力影响的研究.《重庆大学硕士论文》2009.
[48]康庆宁,岩石地基上扩展基础受力性能研究.《重庆大学硕士论文》2010.
[49]刘伟,岩石地基上混凝土扩展式基础的受力分析研究.《贵州大学硕士论文》2009.
[50]邹洋,岩石地基上扩展基础破坏模式及承载性能研究.《贵州大学硕士论文》2009.
[2]阴可,程毅等.岩石地基上扩展基础的基底反力实测分析[J].重庆建筑大学学报,2006,28(6).
[3]陈明.半无限弹性体地基基础的地基反力计算[J].四川水利,2003,15(1).
[4]王国体,地基反力的数值模拟和基础结构的内力响应[J].土木工程学报, 2002.4, 35(2):103-107.
[5]杜佐龙,毕生等基于弹塑性有限单元法的地基极限承载力形状效应修正分析[J].勘察科学技术, 2010.3.
[6]艾智勇,吴超.分层地基上矩形刚性基础的基底反力、沉降和倾斜计算[J].力学季刊, 2008, 29(1).
[7]朱爱军等.岩石地基上扩展基础基底反力分布的分析[J].工业建筑,2002,32(8):32-35.
[8]邓安福.岩石地基上扩展基础基底反力分布的分析[J].工业建筑,2002,32(8).
[9]王振宇.砂卵石地区高层建筑箱基基底反力实测研究[J].建筑结构学报,2000.8, 21(4):72-75.
[10]蔚旭灿,郑传超.圆形均布荷载作用下半空间伯格斯模型粘弹性体的理论解[J].西安建筑科技大学学报(自然科学版),2008.12, V40(6).
[11]杨小礼,李亮.圆形基础极限分析下限解探讨[J].铁道学报,2001.12, Vol.23No.6.
[12]蒋益平,熊巨华.方形和圆形基础地基极限承载力分析[J].岩土力学,2005.12, Vol.26No.12.
[13]范静海,非线性接触力学模型在地基-基础相互作用弹性分析中的应用[J].岩土力学, 2004, 25(2): 154-159.
[14]程传林.近圆形结构下地基变形的简易计算[J].钢陵学院学报,2008.6.
[15]周晓兵,王飞龙.竖向荷载下圆形基础承载力分析[J].采矿技术,2002.3, Vol.2No.1.
[16]阴可,殷杰.岩石地基上扩展基础的受力特性分析,重庆建筑大学学报, 2008年02期.
[17]冯文化.柱下单独基础破坏模式分析及配筋合理计算,工业建筑,1996,26(9).
[18]吴能森,谢成新.基底压力分布对扩展基础冲切承载力影响的研究[J].西北建筑工程学院学报,2002,19(1).
[19]赖庆文,岩石地基基础受剪计算方法探讨[J].工业建筑, 2002, 32(8):32-35.
[20]肖常安,岩石地基上独立柱基抗剪问题的探讨[J].贵州工业大学学报, 2002, 6:52-55.
[21] Johnson, Gordon R.; Christiano, Paul; Epstein, Howard I.Stiffness coefficients for embedded footings,American Society of Civil Engineers, Journal of the Geotechnical Engineering Division, v 101, n 8, p 789-800, Aug 1975.
[22] Dunham, L.; Valsangkar, A.J.; Schriver, A.B.Centrifuge modeling of rigid square footings on weak jointed rock:Geotechnical Testing Journal, v 28, n 2, p 133-143, March 2005.
[23] Hallgren.M, Kinnunen.S, Nylander,B. Punching Shear Tests on Column Footings[J]. Nordic Concrete Research,1998,21(1): 1–22.
[24] Mikael Hallgren, Mats Bjerke. Non-linear finite element analyses of punching shear failure of column footings[J]. Cement And Concrete Composites, 2002,24: 491–496.
[25] Richart,F.E, Reinforced concrete wall and column footing[J]. Journal of the American Concrete Institute, 1948,11.
[26] Castellanza.R. Model footing load tests on soft rocks[J].Geotechnical Testing Journal, 2009, 32(3):262-272.
[27] Yang Xiao-Li. Seismic bearing capacity of a strip footing on rock slopes [J]. Canadian Geotechnical Journal, 2009, 46(8):943-954.
[28] Merifield,R.S. Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek-Brown criterion [J]. International Journal of Rock Mechanics and Mining Sciences, 2006, 43(6):920-937.
[29] Chang,J.C. Bearing behavior and failure mechanism of a shallow foundation located on/behind the crest of a poorly cemented artificial sandstone [J]. International Journal of Rock Mechanics and Mining Sciences, 2008, 45(8):1508-1518.
[30] Vianna,Ana Paula Fontana. Influence of footing size and matric suction on the behavior of shallow foundations in collapsible soil [J]. Soils and Rocks , 2007, 30(3):127-137.
[31] Sokol,Nikolas. Design of rock shafts adjacent to heavily loaded columns [C]. 9th North American Tunneling Conference, NAT 2008.North American Tunneling 2008 Proceedings,2008:218-224.
[32] EI Ganainy,H. Efficient 3D nonlinear Winkler model for shallow foundations [J]. Soil Dynamics and Earthquake Engineering, 2009, 29(8):1236-1248.
[33] Raychowdhury,Prishati. Performance evaluation of a nonlinear Winkler-based shallow foundation model using centrifuge test results [J]. Earthquake Engineering and Structural Dynamics, 2009, 38(5):679-698.
[34]赫文化.ANSYS土木工程应用实例[M].北京:中国水利水电出版社,2005:75-120.
[35]华南理工大学东南大学浙江大学等,地基基础.中国建筑工业出版社,1998.
[36]王重穆.柱下单独基础抗弯强度的若干问题[J],建筑结构,1995,(2).
[37]白生翔,钢筋混凝土扩展基础设计方法的改进建议.工业建筑[J], 2005,35(2) :.88-92.
[38] Samual E.French, Introduction to Soil Mechanics and Shallow Foundations Design. 1989.
[39]刘廉纯,柱下独立基础抗弯强度塑性分析和设计探讨[J].建筑结构,1998(5):23-27.
[40]重庆市地基基础设计规范(DB50/5001—1997)[S].重庆:重庆市建设委员会,1997.
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