非均质与各向异性临坡地基承载力上限计算
|
摘要
为探究土体非均质与各向异性对临坡地基承载力的影响,运用极限分析上限方法,结合单侧临坡条形基础地基破坏模式,引入土体内摩擦角、黏聚力、基础与边坡坡顶距离等参数,分析临坡地基极限承载力的变化趋势。首先,根据极限分析上限理论,建立破坏模式的机动许可速度场,考虑非均质与各向异性原理,在计算中导入非均质系数与各项异性系数,得到机构各部分内能耗散计算公式,推导出地基承载力系数N_c的计算表达式。在此基础上,设定机构所需满足的约束条件并导入用Matlab软件编制的优化程序,程序考虑了非均质与各向异性对地基破坏面位置及形状的影响,最终得到地基承载力最小上限解所对应的非均质与各向异性下地基承载力系数N′_c。结果表明,计算数据与现有成果具有较好的一致性,揭示了非均质与各向异性对临坡地基承载力系数N′_c的作用规律。当非均质系数η增大时,N′_c随之增大;当各向异性系数k增大时,N′_c随之减小,且减小幅度趋缓,有效地弥补在临坡地基承载力中土体非均质与各向异性研究领域的不足。当破坏模式转化为水平地基形式时,所得结果与其他方法计算结果很好吻合,证明了此方法解决水平地基问题的可行性。
In order to study the influence of soil heterogeneity and anisotropy on bearing capacity of foundation adjacent to slope, by using the upper bound analysis and the failure mode of strip foundation adjacent to a side of slope, considering internal friction angle, cohesion, the distance between foundation and top of slope,etc., the change trend of the ultimate bearing capacity of foundation adjacent to slope is analyzed. First, according to the upper bound analysis theory, a mobile permissible velocity field of the failure mode is established. Using the principle of heterogeneity and anisotropy, the heterogeneity and anisotropy coefficients are introduced to obtain the calculation formula of internal energy dissipation of each part of the mechanism, and then the formula of foundation bearing capacity coefficient N_c is derived. On this basis, setting the constraints the mechanism needs and putting them into the optimization program compiled with Matlab software, which considering the influence of heterogeneity and anisotropy on the position and shape of the foundation failure surface. Finally, the bearing capacity coefficient N′_c of non-homogenous and anisotropic foundation when getting the minimum upper bound solution of foundation bearing capacity is obtained. The result shows that(1) The calculated data agree well with the results in the existing literatures, which revealed the action regularity of heterogeneity and anisotropy on N′_c. N′_c increases with the increase of heterogeneity coefficient η, while N′_c decreases with the increase of anisotropy coefficient k, and the decrease amplitude goes slowly, which can effectively make up for the lack of research on the soil heterogeneity and anisotropy in the bearing capacity of the foundation adjacent to slope.(2) When the failure mode converts to horizontal foundation, the calculation result totally agrees well with those of other methods, which proved the feasibility of this method for solving the horizontal foundation problem.
In order to study the influence of soil heterogeneity and anisotropy on bearing capacity of foundation adjacent to slope, by using the upper bound analysis and the failure mode of strip foundation adjacent to a side of slope, considering internal friction angle, cohesion, the distance between foundation and top of slope,etc., the change trend of the ultimate bearing capacity of foundation adjacent to slope is analyzed. First, according to the upper bound analysis theory, a mobile permissible velocity field of the failure mode is established. Using the principle of heterogeneity and anisotropy, the heterogeneity and anisotropy coefficients are introduced to obtain the calculation formula of internal energy dissipation of each part of the mechanism, and then the formula of foundation bearing capacity coefficient N_c is derived. On this basis, setting the constraints the mechanism needs and putting them into the optimization program compiled with Matlab software, which considering the influence of heterogeneity and anisotropy on the position and shape of the foundation failure surface. Finally, the bearing capacity coefficient N′_c of non-homogenous and anisotropic foundation when getting the minimum upper bound solution of foundation bearing capacity is obtained. The result shows that(1) The calculated data agree well with the results in the existing literatures, which revealed the action regularity of heterogeneity and anisotropy on N′_c. N′_c increases with the increase of heterogeneity coefficient η, while N′_c decreases with the increase of anisotropy coefficient k, and the decrease amplitude goes slowly, which can effectively make up for the lack of research on the soil heterogeneity and anisotropy in the bearing capacity of the foundation adjacent to slope.(2) When the failure mode converts to horizontal foundation, the calculation result totally agrees well with those of other methods, which proved the feasibility of this method for solving the horizontal foundation problem.
引文
[1] 黄茂松,秦会来,郭院成.非均质和各向异性黏土地基承载力的上限解[J].岩石力学与工程学报,2008,27(3):511-518.HUANG Mao-song,QIN Hui-lai,GUO Yuan-cheng. Upper Bound Solution for Bearing Capacity of Nonhomogeneous and Anisotropic Clay Foundation[J]. Chinese Journal of Rock Mechanics and Engineering,2008,27(3):511-518.
[2] CHEN W F. Limit Analysis and Soil Plasticity[M]. NewYork:Elsevier Scientific Publishing Company,1975.
[3] REDDY A S,RAO K N V. Bearing Capacity of Strip Footing on c-φ Soils Exhibiting Anisotropy and Non-homogeneity in Cohesion[J].Soils and Foundations, 1982,22(1):49-60.
[4] REDDY A S, RAO K N V. Bearing Capacity of Strip Footing on Anisotropic and Nonhomogeneous Clays[J]. Journal of the Japanese Society of Soil Mechanics & Foundation Engineering, 1981, 21(1):1-6.
[5] UGAI K A. New Admissible Velocity Field for Bearing Capacity Calculations of Strip Footings[J].Soils & Foundations, 2008, 26(2):133-142.
[6] Al-SHAMRANI M A. Upper-bound Solutions for Bearing Capacity of Strip Footings over Anisotropic Nonhomog-eneous Clays[J].Soils and Foundations,2005,45(1):109-124.
[7] TANI K,CRAIG W H. Bearing Capacity of Circular Foundations on Soft Clay of Strength Increasing with Depth[J]. Soils and Foundations,1995,35(4):21-35.
[8] LEE J K, JEONG S, LEE S. Undrained Bearing Capacity Factors for Ring Footings in Heterogeneous Soil[J].Computers and Geotechnics,2016,75:103-111.
[9] GOURVENEC S, RANDOLPH M. Effect of Strength Non-homogeneity on the Shape of Failure Envelopes for Combined Loading of Strip and Circular Foundations on Clay[J]. Géotechnique, 2003, 53(6):575-586.
[10] DAVIS E H,BOOKER J R. The Effect of Increasing Strength with Depth on the Bearing Capacity of Clays[J]. Geotechnique,1973,23(4):551-563.
[11] 黄俐,梁鹏.非均质性和各向异性黏土地基承载力上限分析[J].湖南科技大学学报,2016,31(2):71-77. HUANG Li,LIANG Peng. Upper Bound Analysis for the Bearing Capacity of the Inhomogeneous and Anisotropic Clay Foundation[J].Journal of Hunan University of Science & Technology: Natural Science Edition,2016,31(2):71-77.
[12] 徐干成,李成学,刘平.各向异性和非均质地基土上浅基础的极限承载力[J].岩土工程学报,2007,29(2):164-168.XU Gan-cheng,LI Cheng-xue,LIU Ping. Ultimate Bearing Capacity of Shallow Footing on Anisotropic and Nonhomogeneous Clays [J].Chinese Journal of Geotechnical Engineering,2007,29(2):164-168.
[13] 秦会来,黄茂松,王玉杰,等.非均质与各向异性地基承载力系数Nc计算[J].岩土工程学报,2010,32(8):1194-1199.QIN Hui-lai,HUANG Mao-song,WANG Yu-jie,et al. Calculations of Nc for Anisotropic and Nonhomogeneous Soils[J].Chinese Journal of Geotechnical Engineering,2010,32(8):1194-1199.
[14] 秦会来,王玉杰,唐志丹,等.非均质各向异性黏土光滑条基承载力上限解[J].岩土力学,2011,32(2):611-616. QIN Hui-lai,WANG Yu-jie,TANG Zhi-dan,et al. Upper Bound Solutions for Bearing Capacity of Smooth Rigid Strip Foundations on Anisotropic and Non-homogeneous Clay[J]. Rock and Soil Mechanics,2011,32(2):611-616.
[15] LUMB P, SCHMERTMANN J H. Stability of Slopes in Anisotropic Soils[J]. Journal of Soil Mechanics & Foundations Division,1965, 91(4):85-106.
[16] 胡卫东,曹文贵.基于非对称破坏模式的临坡地基承载力上限极限分析方法[J].中国公路学报,2014,27(6):1-9.HU Wei-dong,CAO Wen-gui. Upper Limit Analysis Method for Ultimate Bearing Capacity of Ground Foundation Adjacent to Slope Based on Asymmetry Failure Mode[J]. China Journal of Highway and Transport,2014,27(6):1-9.
[17] 陈希有,龚晓南,曾国熙.具有各向异性和非均质性的c-φ土上条形基础的极限承载力[J].土木工程学报,1987,20(4):74-82.CHEN Xi-you,GONG Xiao-nan, ZENG Guo-xi. Bearing Capacity of Strip Footing on c-φ Soils Exhibiting Anisotropy and Nonhomogeneity in Cohesion[J].China Civil Engineering Journal,1987,20(4):74-82.
[18] 杨峰,阳军生,张学民,等.斜坡地基单侧滑移破坏模式及承载力上限解[J].工程力学,2010,27(6):162-168.YANG Feng,YANG Jun-sheng,ZHANG Xue-min,et al. One-side Slip Failure Mechanism and Upper Bound Solution for Bearing Capacity of Foundation on Slope[J]. Engineering Mechanics,2010,27(6):162-168.
[2] CHEN W F. Limit Analysis and Soil Plasticity[M]. NewYork:Elsevier Scientific Publishing Company,1975.
[3] REDDY A S,RAO K N V. Bearing Capacity of Strip Footing on c-φ Soils Exhibiting Anisotropy and Non-homogeneity in Cohesion[J].Soils and Foundations, 1982,22(1):49-60.
[4] REDDY A S, RAO K N V. Bearing Capacity of Strip Footing on Anisotropic and Nonhomogeneous Clays[J]. Journal of the Japanese Society of Soil Mechanics & Foundation Engineering, 1981, 21(1):1-6.
[5] UGAI K A. New Admissible Velocity Field for Bearing Capacity Calculations of Strip Footings[J].Soils & Foundations, 2008, 26(2):133-142.
[6] Al-SHAMRANI M A. Upper-bound Solutions for Bearing Capacity of Strip Footings over Anisotropic Nonhomog-eneous Clays[J].Soils and Foundations,2005,45(1):109-124.
[7] TANI K,CRAIG W H. Bearing Capacity of Circular Foundations on Soft Clay of Strength Increasing with Depth[J]. Soils and Foundations,1995,35(4):21-35.
[8] LEE J K, JEONG S, LEE S. Undrained Bearing Capacity Factors for Ring Footings in Heterogeneous Soil[J].Computers and Geotechnics,2016,75:103-111.
[9] GOURVENEC S, RANDOLPH M. Effect of Strength Non-homogeneity on the Shape of Failure Envelopes for Combined Loading of Strip and Circular Foundations on Clay[J]. Géotechnique, 2003, 53(6):575-586.
[10] DAVIS E H,BOOKER J R. The Effect of Increasing Strength with Depth on the Bearing Capacity of Clays[J]. Geotechnique,1973,23(4):551-563.
[11] 黄俐,梁鹏.非均质性和各向异性黏土地基承载力上限分析[J].湖南科技大学学报,2016,31(2):71-77. HUANG Li,LIANG Peng. Upper Bound Analysis for the Bearing Capacity of the Inhomogeneous and Anisotropic Clay Foundation[J].Journal of Hunan University of Science & Technology: Natural Science Edition,2016,31(2):71-77.
[12] 徐干成,李成学,刘平.各向异性和非均质地基土上浅基础的极限承载力[J].岩土工程学报,2007,29(2):164-168.XU Gan-cheng,LI Cheng-xue,LIU Ping. Ultimate Bearing Capacity of Shallow Footing on Anisotropic and Nonhomogeneous Clays [J].Chinese Journal of Geotechnical Engineering,2007,29(2):164-168.
[13] 秦会来,黄茂松,王玉杰,等.非均质与各向异性地基承载力系数Nc计算[J].岩土工程学报,2010,32(8):1194-1199.QIN Hui-lai,HUANG Mao-song,WANG Yu-jie,et al. Calculations of Nc for Anisotropic and Nonhomogeneous Soils[J].Chinese Journal of Geotechnical Engineering,2010,32(8):1194-1199.
[14] 秦会来,王玉杰,唐志丹,等.非均质各向异性黏土光滑条基承载力上限解[J].岩土力学,2011,32(2):611-616. QIN Hui-lai,WANG Yu-jie,TANG Zhi-dan,et al. Upper Bound Solutions for Bearing Capacity of Smooth Rigid Strip Foundations on Anisotropic and Non-homogeneous Clay[J]. Rock and Soil Mechanics,2011,32(2):611-616.
[15] LUMB P, SCHMERTMANN J H. Stability of Slopes in Anisotropic Soils[J]. Journal of Soil Mechanics & Foundations Division,1965, 91(4):85-106.
[16] 胡卫东,曹文贵.基于非对称破坏模式的临坡地基承载力上限极限分析方法[J].中国公路学报,2014,27(6):1-9.HU Wei-dong,CAO Wen-gui. Upper Limit Analysis Method for Ultimate Bearing Capacity of Ground Foundation Adjacent to Slope Based on Asymmetry Failure Mode[J]. China Journal of Highway and Transport,2014,27(6):1-9.
[17] 陈希有,龚晓南,曾国熙.具有各向异性和非均质性的c-φ土上条形基础的极限承载力[J].土木工程学报,1987,20(4):74-82.CHEN Xi-you,GONG Xiao-nan, ZENG Guo-xi. Bearing Capacity of Strip Footing on c-φ Soils Exhibiting Anisotropy and Nonhomogeneity in Cohesion[J].China Civil Engineering Journal,1987,20(4):74-82.
[18] 杨峰,阳军生,张学民,等.斜坡地基单侧滑移破坏模式及承载力上限解[J].工程力学,2010,27(6):162-168.YANG Feng,YANG Jun-sheng,ZHANG Xue-min,et al. One-side Slip Failure Mechanism and Upper Bound Solution for Bearing Capacity of Foundation on Slope[J]. Engineering Mechanics,2010,27(6):162-168.