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| Layered coefficient method for solving the loading problem of
nonhomogeneous soil |
| WANG Yu1，WANG Jinhua2，LI Wei3，LIU Zhe4 |
| (1. China Academy of Safety Science and Technology，Beijing 100012，China；2. China Airport Planning and Design Institute Co.，Ltd.，Beijing 100029，China；3. School of Civil Engineering，Beijing Jiaotong University，Beijing 100044，China；4. Institute
of Technical Standards，China Railway Economic and Planning Research Institute Co.，Ltd.，Beijing 100038，China) |
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Abstract The existing methods for solving the load problem of layered foundation are not perfect. The transfer matrix method often has ill conditioned matrix and data overflow，while the analytical layer element method or stiffness matrix method has some defects，such as difficult inversion of high-order matrix. Firstly，the matrix solution of soil state variables with undetermined coefficients is derived based on the basic equation of three-dimensional elastic statics and Fourier positive transformation. Then，combined with the boundary conditions，the transformation relationship of undetermined coefficients of soil state variables and the inverse Fourier transform，the known coefficient solution of layered foundation state variables is obtained. Finally，the method verification and parameter analysis are carried out for homogeneous semi infinite foundation，three-layer unequal thickness foundation and generalized Gibson foundation. The results show that compared with transfer matrix method and analytical layer element method，this method is not only reasonable and accurate，but also has the advantages of stable numerical calculation，faster solution speed，self-check and unlimited number of applicable soil layers. The relative displacement of interlayer contact surface is directly proportional to the interface slip coefficient and inversely proportional to the distance between loading surface and interlayer contact surface. The change value of interface relative displacement is twice the change value of load distribution width. The number of layers of generalized Gibson foundation is 40，which can meet the requirements of calculation accuracy. Under different Poisson's ratio and load depth，the volume strain and displacement decrease with the increase of heterogeneous parameter m. The influence of parameter m on the vertical state variable of soil is more significant，and the value of m is more noteworthy when it is 0.0–0.5.
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| [1] 梁志孟，崔春义，许成顺，等. 双向非均质土中大直径管桩纵向振动动力阻抗解析模型与解答[J]. 岩石力学与工程学报，2021，40(9)：1 933–1 944.(LIANG Zhimeng，CUI Chunyi，XU Chengshun，et al. Analytical model and solution for the longitudinal impedance of large-diameter pipe piles in radial inhomogeneous layered soils[J]. Chinese Journal of Rock Mechanics and Engineering，2021，40(9)：1 933–1 944.(in Chinese))
[2] 付 鹏，胡安峰，李 龙，等. 成层地基中海洋高桩基础水平动力阻抗分析[J]. 岩石力学与工程学报，2019，38(增2)：3 790–3 798. (FU Peng，HU Anfeng，LI Long，et al. Lateral dynamic impedance of offshore elevated piles in layered soils[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(Supp.2)：3 790–3 798.(in Chinese))
[3] BUTTERFIELD R，BANERJEE P K. The elastic analysis of compressible piles and pile groups[J]. Geotcchnique，1971，21(1)：43–60.
[4] BAHAR L Y. Transfer matrix approach to layered systems[J]. Journal of Engineering Mechanics，1972，98(5)：1 159–1 172.
[5] 钟 阳. 多层弹性半空间问题解的精确刚度矩阵法[J]. 应用力学学报，2008，25(2)：316–319.(ZHONG Yang. Explicit solution of multilayered elastic half space by exact stifness matrix method[J]. Chinese Journal of Applied Mechanics，2008，25(2)：316–319.(in Chinese))
[6] 艾智勇，曾 凯，曾文泽. 层状地基三维问题的解析层元解[J]. 岩土工程学报，2012，34(6)：1 154–1 158.(AI Zhiyong，ZENG Kai，ZENG Wenze. Analytical layer-element solution for three-dimensional problem of multilayered foundation[J]. Chinese Journal of Geotechnical Engineering，2012，34(6)：1 154–1 158.(in Chinese))
[7] AI Z Y，JIANG X B，HU Y D. Analytical layer-element solution for 3D transversely isotropic multilayered foundation[J]. Soils and Foundations，2014，54(5)：967–973.
[8] ZHANG L，ZHAO M H，ZOU X J. Behavior of laterally loaded piles in multilayered soils[J]. International Journal of Geomechanics，2015，15(2)：06014017.
[9] YANG K，LIANG R. Numerical solution for laterally loaded piles in a two-layer soil profile[J]. Journal of Geotechnical and Geoenvironmental Engineering，2006，132(11)：1 436–1 443.
[10] 江 杰，柴文成，欧孝夺，等. 基于Timoshenko-Pasternak模型的多向受荷桩水平动力响应分析[J]. 岩石力学与工程学报，2022，41(1)：172–185.(JIANG Jie，CHAI Wencheng，OU Xiaoduo，et al. Horizontal dynamic response analysis of multi-directional loaded pile based on Timoshenko-Pasternak model[J]. Chinese Journal of Rock Mechanics and Engineering，2022，41(1)：172–185.(in Chinese))
[11] BOOKER J R，BALAAM N P，DAVIS E H. The behaviors of an elastic non-homogeneous half-space. Part I—Line and point loads[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1985，9(4)：353–367.
[12] BOOKER J R，BALAAM N P，DAVIS E H. The behaviour of an elastic non‐homogeneous half‐space. Part II—Circular and strip footings[J]. International Journal for Numerical and Analytical Methods in Geomechanics，1985，9(4)：369–381.
[13] 杜秦文，张绍骞. 广义Gibson地基内部作用线源荷载的基本解[J]. 科学技术与工程，2020，20(13)：5 283–5 289.(DU Qinwen，ZHANG Shaoqian. The basic solution of the line source load in the generalized Gibson subgrade[J]. Science Technology and Engineering，2020，20(13)：5 283–5 289.(in Chinese))
[14] 周凤玺，赖远明，米海珍. 非均匀地基与均匀地基解答之间的相似关系[J]. 岩土力学，2013，34(12)：3 372–3 376.(ZHOU Fengxi，LAI Yuanming，MI Haizhen. Analogous relationship between solutions of nonhomogeneous and homogeneous foundations[J]. Rock and Soil Mechanics，2013，34(12)：3 372–3 376.(in Chinese))
[15] 周凤玺，周志雄，柳鸿博. 非均匀地基与均匀地基解答之间的相似关系：弹性波速[J]. 岩土力学，2021，42(4)：892–898.(ZHOU Fengxi，ZHOU Zhixiong，LIU Hongbo. Analogous relationship between the solutions of non-homogeneous foundation and homogeneous foundation: elastic wave velocity[J]. Rock and Soil Mechanics，2021，42(4)：892–898.(in Chinese))
[16] 赵明华，胡 倩，杨超炜，等. 考虑地基土非线性固结的桩侧负摩阻力计算方法研究[J]. 岩土工程学报，2016，38(8)：1 417–1 424. (ZHAO Minghua，HU Qian，YANG Chaowei，et al. Negative skin friction of piles considering nonlinear consolidation of soil[J]. Chinese Journal of Geotechnical Engineering，2016，38(8)：1 417–1 424.(in Chinese))
[17] 徐芝纶. 弹性力学[M]. 5版. 北京：高等教育出版社，2016：212–226. (XU Zhilun. Elasticity[M]. 5th ed. Beijing：Higher Education Press，2016：212–226.(in Chinese))
[18] 钟 阳，殷建华. 弹性层状体的求解方法[M]. 北京：科学出版社，2007：212–226.(ZHONG Yang，YIN Jianhua. Solving method of elastic layered body[M]. Beijing：Science Press，2007：212–226.(in Chinese))
[19] 王 雨，陈文化，王凯旋. 地埋管线周围土体抗力系数的正交各向异性解析分析[J]. 岩石力学与工程学报，2019，38(3)：606–618. (WANG Yu，CHEN Wenhua，WANG Kaixuan. An analytical method for evaluating orthogonal anisotropy of soil resistance coefficients around buried pipelines[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(3)：606–618.(in Chinese))
[20] MATSUI K，MAINA J W，INOUE T. Axi-symmetric analysis of elastic multilayer system considering interface slips[C]// International Symposium on Maintenance and Rehabilitation of Pavements and Technological Control Segundo Simposio Sobre Manutencao E Rehabilitacao De Pavimentos E Controle Technologico. Auburn： [s. n.]，2001：122–129.
[21] 颜可珍，满建宏，石挺魏，等. 基坑考虑层间接触状态的横观各向同性结构动力响应解析解[J]. 湖南大学学报：自然科学版，2019，46(11)：97–105.(YAN Kezhen，MAN Jianhong，SHI Tingwei，et al. Analytical solution for dynamic response of transversely isotropic structures considering the state of interlayer contact state[J]. Journal of Hunan University：Natural Science，2019，46(11)：97–105.(in Chinese))
[22] BETTI E. Teoria della elasticita?[J]. Nuovo Cimento，1872，7–8(1)：69–97.
[23] 付宝连. 三维线弹性力学修正的功的互等定理及其应用[J]. 应用数学和力学，2015，36(5)：523–538.(FU Baolian. Corrected reciprocal theorem for 3D linear elasticity and its application[J]. Applied Mathematics and Mechanics，2015，36(5)：523–538.(in Chinese))
[24] MINDLIN R D. Force at a point in the interior of a semi-infinite solid[J]. Journal of Applied Physics，1936，7(5)：195–202.
[25] 王 雨，陈文化. 地埋梁与横观各向同性层状地基相互作用的广义Vesic解答[J]. 岩土工程学报，2018，40(12)：2 241–2 248.(WANG Yu，CHEN Wenhua. Generalized Vesic solutions for interaction of buried beams and transversely isotropic layered soils[J]. Chinese Journal of Geotechnical Engineering，2018，40(12)：2 241–2 248.(in Chinese))
[26] 朱桂春，史培新，王占生. 层状横观各向同性地基变形问题的一个近似解[J]. 岩土工程学报，2020，42(4)：790–796.(ZHU Guichun，SHI Peixin，WANG Zhansheng. Approximate solution for deformation problems of transversely isotropic multi-layered soils[J]. Chinese Journal of Geotechnical Engineering，2020，42(4)：790–796.(in Chinese))
[27] 周泽林，陈寿根，涂 鹏，等. 基坑开挖对邻近隧道影响的耦合分析方法[J]. 岩土力学，2018，39(4)：1 440–1 449.(ZHOU Zelin，CHEN Shougen，TU Peng，et al. Coupling method for analyzing the influence on existing tunnel due to adjacent foundations pit excavation[J]. Rock and Soil Mechanics，2018，39(4)：1 440–1 449.(in Chinese))
[28] 吴君涛，王奎华，刘 鑫，等. 缺陷桩周围成层土振动响应解析解及其在旁孔透射波法中的应用[J]. 岩石力学与工程学报，2019，38(1)：203–216.(WU Juntao，WANG Kuihua，LIU Xin，et al. An analytical solution of dynamic responses of multi-layered soil around defect piles and its application in parallel seismic method[J]. Chinese Journal of Rock Mechanics and Engineering，2019，38(1)：203–216.(in Chinese)) |
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2022, Vol. 41 
