虚土桩法可行性初步研究与分析
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摘要
虚土桩法是为了解决桩与桩侧土、桩端土相互作用而提出的一种新方法,该方法将桩端投影面以下直到基岩的土层看成为“土桩”,建立土体动力平衡方程、桩体和虚土桩体动力平衡方程,并结合具体边界条件来研究桩土耦合振动特性。虚土桩法可以考虑桩与桩侧土、桩端土的耦合作用,桩端以下土体的非均质性和成层性,基岩埋置深度的影响以及沉降随时间发展的过程等多方面因素,具有广阔的应用前景。
本文基于虚土桩思想,进行了以下三方面的研究:
1、结合土体平衡方程和虚土桩体平衡方程,对静力条件时刚性圆盘下弹性地基表面和内部的应力场和位移场进行研究,得到了虚土桩中心线和不同深度土层竖向应力和位移的分布以及虚土桩顶的刚度。同时分析影响土体竖向应力和位移分布的各种因素,并与其他学者的研究成果进行对比,分析虚土桩法在刚性圆盘下地基静力分析时的适用性。
2、结合土体动力平衡方程和虚土桩体动力平衡方程,对简谐荷载时刚性圆盘下均质滞回材料阻尼土体的振动特性进行研究,得到了土层阻抗因子、桩顶位移幅频、桩顶复刚度、速度导纳等振动特性,同时分析影响上述振动特性的各种因素,并与其他学者的研究成果进行对比。
3、结合单桩沉降计算的荷载传递法,根据桩及虚土桩体平衡方程、接触面处力和位移的相容条件,得到弹性状态下单桩沉降解析解。结合单桩沉降的弹性理论法,采用Mindlin位移解,考虑桩和虚土桩侧摩阻力的相互作用,得到单桩沉降的解析解。根据土体平衡方程、桩体平衡方程和虚土桩体平衡方程,结合边界条件和相容条件,得到桩顶沉降的解析解。对上述三种方法得到的桩顶荷载-沉降关系进行对比,并分析桩长、泊松比、桩土弹性模量、虚土桩长度等因素的影响。同时与现有的荷载传递法和弹性理论法进行对比,分析虚土桩法的可行性。
本文对虚土桩法在地基静动力特性和单桩沉降计算中应用的可行性和适用条件进行的初步分析,推动了虚土桩法在桩的动静特性方面的应用研究。
Method of virtual pile of soil is a new method to solve the interaction between pile and the soil under the pile. In this method, the soil between pile tip and bedrock is taken as a virtual pile to study the dynamic soil-pile interaction problem. Then the interaction between soil and pile, non-homogeneity or stratification of the soil, depth of the bedrock and settlement of pile over time can be taken into consideration in analysis of pile dynamic or static characteristics. Therefore, method of virtual pile of soil has broad prospects for application.
This thesis which is based on the method of virtual pile of soil has done the main original work as follows:
1. The static equilibrium equations of soil and virtual pile are solved according to the boundary condition and the stress and displacement fields of elastic soil under a rigid circular plate are investigated. The vertical stress and displacement along the center line of the virtual pile and at various depths is investigated and the stiffness at the top of virtual pile is studied. Some main influencing factors, such as the length of virtual pile, Poisson's ratio, modulus of soil are analyzed to illustrate the distribution of vertical stress and displacement. Meanwhile, the results are compared with other existing researches to illustrate the applicability of the virtual pile of soil method.
2. According to the dynamic equilibrium equations of soil and virtual pile, dynamic characteristics of hysteretic damping soil under a rigid circular plate at the harmonic load are investigated. The influence on the resistance factor and vibration modes of soil, curves of settlement-frequency, complex stiffness-frequency and mobility wave-frequency of virtual pile caused by length of virtual pile, Poisson's ratio and hysteretic damping ratio is discussed. And the relationship of complex stiffness and frequency is compared with other existing researches.
3. Firstly, according to the static equilibrium equations of pile and virtual pile and the consistency conditions at the interface, the analytic solution of single pile settlement based on the load transfer method is yielded. Secondly, using the elastic theory method based on Mindlin's displacement solution, the analytic solution of single pile settlement is obtained when the interaction of the shear stress along the pile and the virtual pile is considered. Thirdly, combining the static equilibrium of soil, pile and virtual pile with the boundary and consistency conditions, the analytic solution of the settlement at the pile top is obtained. Finally, influencing factors, such as length of pile and virtual pile, modulus of pile and soil are analyzed and the load-settlement curves of the three methods above are compared. Meanwhile, the results are compared with other existing researches to illustrate the feasibility of virtual pile of soil method.
The preliminary feasibility studies and analysis in this thesis will promote the development of researches in the static and dynamic characteristics of piles using virtual pile of soil method.
本文基于虚土桩思想,进行了以下三方面的研究:
1、结合土体平衡方程和虚土桩体平衡方程,对静力条件时刚性圆盘下弹性地基表面和内部的应力场和位移场进行研究,得到了虚土桩中心线和不同深度土层竖向应力和位移的分布以及虚土桩顶的刚度。同时分析影响土体竖向应力和位移分布的各种因素,并与其他学者的研究成果进行对比,分析虚土桩法在刚性圆盘下地基静力分析时的适用性。
2、结合土体动力平衡方程和虚土桩体动力平衡方程,对简谐荷载时刚性圆盘下均质滞回材料阻尼土体的振动特性进行研究,得到了土层阻抗因子、桩顶位移幅频、桩顶复刚度、速度导纳等振动特性,同时分析影响上述振动特性的各种因素,并与其他学者的研究成果进行对比。
3、结合单桩沉降计算的荷载传递法,根据桩及虚土桩体平衡方程、接触面处力和位移的相容条件,得到弹性状态下单桩沉降解析解。结合单桩沉降的弹性理论法,采用Mindlin位移解,考虑桩和虚土桩侧摩阻力的相互作用,得到单桩沉降的解析解。根据土体平衡方程、桩体平衡方程和虚土桩体平衡方程,结合边界条件和相容条件,得到桩顶沉降的解析解。对上述三种方法得到的桩顶荷载-沉降关系进行对比,并分析桩长、泊松比、桩土弹性模量、虚土桩长度等因素的影响。同时与现有的荷载传递法和弹性理论法进行对比,分析虚土桩法的可行性。
本文对虚土桩法在地基静动力特性和单桩沉降计算中应用的可行性和适用条件进行的初步分析,推动了虚土桩法在桩的动静特性方面的应用研究。
Method of virtual pile of soil is a new method to solve the interaction between pile and the soil under the pile. In this method, the soil between pile tip and bedrock is taken as a virtual pile to study the dynamic soil-pile interaction problem. Then the interaction between soil and pile, non-homogeneity or stratification of the soil, depth of the bedrock and settlement of pile over time can be taken into consideration in analysis of pile dynamic or static characteristics. Therefore, method of virtual pile of soil has broad prospects for application.
This thesis which is based on the method of virtual pile of soil has done the main original work as follows:
1. The static equilibrium equations of soil and virtual pile are solved according to the boundary condition and the stress and displacement fields of elastic soil under a rigid circular plate are investigated. The vertical stress and displacement along the center line of the virtual pile and at various depths is investigated and the stiffness at the top of virtual pile is studied. Some main influencing factors, such as the length of virtual pile, Poisson's ratio, modulus of soil are analyzed to illustrate the distribution of vertical stress and displacement. Meanwhile, the results are compared with other existing researches to illustrate the applicability of the virtual pile of soil method.
2. According to the dynamic equilibrium equations of soil and virtual pile, dynamic characteristics of hysteretic damping soil under a rigid circular plate at the harmonic load are investigated. The influence on the resistance factor and vibration modes of soil, curves of settlement-frequency, complex stiffness-frequency and mobility wave-frequency of virtual pile caused by length of virtual pile, Poisson's ratio and hysteretic damping ratio is discussed. And the relationship of complex stiffness and frequency is compared with other existing researches.
3. Firstly, according to the static equilibrium equations of pile and virtual pile and the consistency conditions at the interface, the analytic solution of single pile settlement based on the load transfer method is yielded. Secondly, using the elastic theory method based on Mindlin's displacement solution, the analytic solution of single pile settlement is obtained when the interaction of the shear stress along the pile and the virtual pile is considered. Thirdly, combining the static equilibrium of soil, pile and virtual pile with the boundary and consistency conditions, the analytic solution of the settlement at the pile top is obtained. Finally, influencing factors, such as length of pile and virtual pile, modulus of pile and soil are analyzed and the load-settlement curves of the three methods above are compared. Meanwhile, the results are compared with other existing researches to illustrate the feasibility of virtual pile of soil method.
The preliminary feasibility studies and analysis in this thesis will promote the development of researches in the static and dynamic characteristics of piles using virtual pile of soil method.
引文
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[3]Awojobi A.O.,Estimation of the dynamic surface modulus of a generalized Gibson soil from the rocking frequency of rectangular foundations,Geotechnique,1973a,23(1),p23-p31
[4]Awojobi A.O.,Plane strain and axially symmetric problems of a linearly nonhomogeneous elastic half-space,Mech.Appl.Math.,1973b,ⅩⅨⅥ(3),p285-p302
[5]Baranov V.A.,On the calculation of excited vibrations of an embedded foundation,Voprosy Dynamiki i Prochnocti,Polytechnic Institute of Riga,1967,p195-p209
[6]Biot M.A.,Theory of propagation of elastic waves in a fluid-saturated porous solid Ⅰ.low-frequencyrange,J.Acoust.Society America,1956,28(2),p168-p178
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[10]Butterfield R.,Banerjee P.K.,The elastic analysis of compressible piles and pile groups,Geotechnique,1971,21(1),p43-p60
[11]Cooke J.C.,A solution of Tranter's dual integral equations problem,Quart.J.Mech.and Applied Math.,1956,9,p103-p110
[12]Cooke R.W.,The settlement of friction piles foundations,Proceedings,Conference on tall buildings,KualaLumpur,Malaysia,1974
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[14]Eva Part-Enander等,Matlab 5手册,机械工业出版社,2000
[15]Gardner W S,Consideration in the design of drilled piers,Design,Construction and Performance of Deep Foundation,1975
[16]Gibson R.E.,et al,Some results concerning displacements in a non-homogeneous elastic layer,Journal of applied mathematics and physics(ZAMP),1971,22,p855-p864
[17]H.G.Poulos,E.H.Davis,Pile Foundation Analysis and Design,John Wiley & Sons,1980,p74-p83
[18] Kezdi A., The bearing capacity of piles and pile group, Proceedings of 4~(th) International Conference on Soil Mechanics and Foundation Engineering, London, 1957, p46-p51
[19] Kraft L M, Ray R P, Kagawa T, Theoretical development of t-z curves, Journal of Geotechnical Engineering, 1981, 107(11), p1543-p1561
[20] Krenk S., Schmidt H., Vibration of an elastic circular plate on an elastic half space-a direct approach, 1981, 48(1), p161-p168
[21] Lamb H., On the propation of tremors over the surface of an elastic solid, Philosophical transaction of the royal society of London, 1904, 203, p 1 -p42
[22] Luco J. E., Westmann R. A., Dynamic response of a rigid footing bounded to an elastic half-space, J. Appl. Mech., 1972, 39, p527-p534
[23] Luco J. E., Impedance functions for a rigid foundation on a layered medium, Nuclear Engineering and Design, 1974, 31, p204-p217
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