基于虚土桩法的桩土纵向耦合振动理论及应用研究
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摘要
桩与土体的动力相互作用是一个复杂的接触问题,也是桩基础防震、减震设计以及各种基桩动态测试方法的理论基础。纵观桩基振动理论研究的发展历程可以看出,关于桩-桩侧土动力相互作用模型的研究已经相当广泛而深入。相比之下,由于对桩-桩端土建立严格耦合模型的难度较大,现有成果关于该课题的研究显得非常薄弱。鉴于此,基于虚土桩法,本文采用解析的方法较系统地研究了均质地基、成层地基、径向非均质地基中弹性桩、粘弹性桩及大直径管桩的桩土纵向耦合振动问题。主要工作和创新成果如下：
1.考虑土体的竖向波动效应及其粘弹性性质,基于虚土桩法建立了均质地基中桩-桩侧土、桩-桩端土严格耦合的动力相互作用模型。采用分离变量法,得到了土体纵向振动位移解析解,进一步根据桩土接触面上的位移、应力连续条件,采用积分变换求解了桩身动力控制方程,得到了桩顶频域响应解析解。在此基础上,利用Fourier逆变换和卷积定理,求得了半正弦脉冲激励作用下桩顶速度时域响应的半解析解。基于所得解,详细讨论了不同桩身设计参数时桩端土厚度对桩顶动力响应的影响。结果表明,桩端土对桩身动力响应的影响存在一个临界影响厚度,在临界影响厚度范围内,桩端土厚度的变化将会对桩身动力响应产生很大影响。
2.研究了成层地基中受任意纵向激振荷载作用下的粘弹性桩与土的耦合振动问题,提出了土层层间相互作用简化模型。利用均质地基中给出的求解方法,通过阻抗函数的递推求解得到虚土桩顶部纵向振动复刚度,将其作为实际桩端的支承刚度代入到粘弹性桩的边界条件中,进而得到了桩顶动力响应的理论解,并通过与单层严格解的对比论证了土层层间相互作用简化模型的精确性和适用性。基于所得解,详细讨论了成层桩端土性质、桩端沉渣对桩顶动力响应的影响。
3.为考虑施工效应引起的桩侧土体和桩端土体的径向非均质特性,提出了考虑土体竖向波动效应及粘弹性性质时的土体复刚度传递模型。结合边界条件,对桩侧任意圈层的土体平衡方程由外而内逐圈层求解,求得土体与桩接触面上的剪切复刚度,采用成层地基中给出的求解方法,进而求解得到桩顶动力响应的理论解。基于所得解,详细讨论了桩侧土施工扰动效应、桩端土挤密效应对桩顶动力响应的影响,并系统分析了任意段变阻抗桩的纵向振动特性。
4.基于横观各向同性材料的本构方程以及单相弹性土介质的运动方程,给出了考虑土体竖向位移及其粘弹性性质的土体动力控制方程,采用成层地基中给出的求解方法,通过严格求解得到桩顶动力响应的理论解。基于所得解的参数分析表明,不管是桩端土还是桩侧土,竖直面上的剪切模量对桩顶动力响应的影响程度要比水平面上的剪切模量的影响大的多。因此,当考虑土体竖向波动效应时,竖直面上的剪切模量对桩土系统振动特性起着主导作用。
5.分别以内壁侧摩阻力及附加质量的方式考虑土塞对管桩的动力作用,建立了考虑土塞效应时大直径管桩纵向振动的定解问题,通过严格求解分别得到了管桩桩顶频域响应的解析解及半正弦脉冲激励作用下桩顶速度时域响应的半解析解。基于所得解的参数分析表明,不管是大直径混凝土管桩还是钢管桩,管桩壁厚越小,管桩的有效测试长度越短；在桩顶速度时域响应曲线上,土塞顶部界面位置处会出现类似扩颈桩段的反向反射信号；由于土塞的存在,填充土塞桩段的综合波速会小于管桩材料的一维弹性纵波波速,且土塞高度越高,填充土塞桩段的综合波速越小。基于理论分析的结果和模型试验的验证结果,本文定义了一个工程上很有用的概念,即管桩的视在波速。并指出,在工程测试时,应该选用管桩的视在波速作为测试波速。
本文提出的虚土桩法是对桩-桩端土相互作用模型的一个有益补充,基于本文工作所得出的一些新结论、新现象可以用于桩基础防震、抗震设计、动力基础减振设计及基桩动态测试分析中。
The pile-soil dynamic interaction is a complicated contact problem. The pile vibration theory can provide a valuable guide for both earthquake-resistance design and various dynamic testing methods of pile. Over the past decades, many dynamic interaction models have been presented to investigate the behavior of surrounding soil-pile dynamic interaction. It can be noted that extensive and in-depth research work has been done in the field of surrounding soil-pile dynamic interaction. By contrast, less attention is attracted by the topic on underlying soil-pile dynamic interaction. Therefore, by means of fictitious soil pile method, this paper systematically investigates the dynamic response of elastic and viscoelastic pile and large diameter pipe pile, which are embedded in homogeneous foundation, layered foundation and radial inhomogeneous foundation. The principal contents and original work are as follows:
1.Considering vertical wave effect and viscoelastic property of soil, the dynamic interaction model of pile-surrounding soil, pile-underlying soil is established by using fictitious soil pile method when the pile is embedded in homogeneous foundation. The dynamic equilibrium equations of soil undergoing arbitrary vertical exciting force are solved by virtue of the separation of variables technique. Then, according to the boundary conditions at the interface of soil and pile, the theoretical solutions for the dynamic response of pile in the frequency domain are derived by using integral transform technique to solve the dynamic governing equation of pile. By means of inverse Fourier transform technique and convolution theorem, the semi-analytical solution for the velocity response of a pile undergoing half-cycle sine pulse at the pile head is obtained in the time domain. Based on these solutions, a parametric study is conducted to study emphatically the effects of parameters of underlying soil on dynamic response at the pile head. It is shown that the finite underlying soil layer adjacent to the pile toe has a significant influence on the pile dynamic response and there is a critical influence depth for underlying soil.
2.To investigate the dynamic response of a viscoelastic pile embedded in layered foundation and subjected to arbitrary vertical exciting force, a simplified and practical mathematical model is developed for simulating dynamic interaction of the adjacent soil layers. By means of the same solving methods presented in homogeneous foundation and through the recursion of the impedance function, the complex stiffness at the fictitious soil pile head is derived and used as boundary condition at the pile toe to obtain the theoretical solutions of pile dynamic response. Furthermore, the accuracy and feasibility of the simplified model is verified by comparing with the homogeneous foundation rigorous solution. Based on these solutions, the influence of the properties of layered underlying soil and pile end sediment on pile dynamic response is thoroughly analyzed.
3. The complex stiffness transform model is developed to simulate the radially inhomogeneous property of surrounding soil and underlying soil of pile which caused by pile construction effect. Then, combining the boundary conditions between radially adjacent soil zones, the dynamic equilibrium equations of all soil zones are solved one by one from undisturbed region to disturbance region and the complex stiffness of the interface of pile and its surrounding soil is derived. By means of the same solving methods presented in layered foundation, the theoretical solutions of pile dynamic response are obtained both in frequency domain and time domain. Based on these solutions, the influence of construction effect of pile surrounding soil and compaction effect of pile end soil on pile dynamic response are analyzed in detail. The dynamic response of a pile with arbitrary variable impedance are systematically investigated.
4. Based on the stress-strain relationships of transversely isotropic medium and dynamic equations of single phase elastic soil, the dynamic governing equations of the layered transversely isotropic soils are obtained in cylindrical coordinates considering their vertical wave effect and viscoelastic property. By virtue of the same solving methods developed in layered foundation, the theoretical solutions of pile dynamic response are derived both in frequency domain and time domain. The parametric studies show that the influence of vertical shear modulus on the vertical dynamic response of pile is more significant than the influence of horizontal shear modulus. So, it can be noted that the vertical shear modulus plays a dominant role in the vibration characteristics of the pile-soil system when the vertical wave effect of layered soils is taken into consideration.
5. By using plane strain model and additional mass method to simulate the dynamic interaction of soil plug and pipe pile, the definite problem of large diameter pipe pile embedded in layered foundation is established by considering the soil plugging effect. The analytical solutions of dynamic response at the pipe pile head are derived in the frequency domain and its corresponding semi-analytical solution for the velocity response of a pile undergoing half-cycle sine pulse at the pipe pile head is obtained in the time domain. The parametric studies show that the effective test length of pipe pile decreases as the thickness of pipe pile decreases for both large diameter concrete pipe pile and large diameter steel pipe pile. It also can be noted that there is reverse reflection signal at the position of soil plug top in the velocity response curves of pipe pile in the time domain. Due to the presence of soil plug, the integrated velocity of the pile section filling soil plug is less than the elastic longitudinal wave velocity of pipe pile, and the higher the height of soil plug is, the smaller the integrated velocity of the pile section filling soil plug is. Moreover, the conception of Apparent Wave Velocity of Pipe Pile (AWVPP) is defined in this paper, which is of great importance in foundation pile integrity testing. And, it is stated that the AWVPP should be choosed as the testing velocity in the engineering test.
The fictitious soil pile method is an useful supplement to the research of dynamic interaction of pile and its underlying soil. The new results and new phenomenons presented in this paper can be used in earthquake-resistance design of pile foundation, anti-vibration design of dynamic foundation and dynamic testing of pile.
1.考虑土体的竖向波动效应及其粘弹性性质,基于虚土桩法建立了均质地基中桩-桩侧土、桩-桩端土严格耦合的动力相互作用模型。采用分离变量法,得到了土体纵向振动位移解析解,进一步根据桩土接触面上的位移、应力连续条件,采用积分变换求解了桩身动力控制方程,得到了桩顶频域响应解析解。在此基础上,利用Fourier逆变换和卷积定理,求得了半正弦脉冲激励作用下桩顶速度时域响应的半解析解。基于所得解,详细讨论了不同桩身设计参数时桩端土厚度对桩顶动力响应的影响。结果表明,桩端土对桩身动力响应的影响存在一个临界影响厚度,在临界影响厚度范围内,桩端土厚度的变化将会对桩身动力响应产生很大影响。
2.研究了成层地基中受任意纵向激振荷载作用下的粘弹性桩与土的耦合振动问题,提出了土层层间相互作用简化模型。利用均质地基中给出的求解方法,通过阻抗函数的递推求解得到虚土桩顶部纵向振动复刚度,将其作为实际桩端的支承刚度代入到粘弹性桩的边界条件中,进而得到了桩顶动力响应的理论解,并通过与单层严格解的对比论证了土层层间相互作用简化模型的精确性和适用性。基于所得解,详细讨论了成层桩端土性质、桩端沉渣对桩顶动力响应的影响。
3.为考虑施工效应引起的桩侧土体和桩端土体的径向非均质特性,提出了考虑土体竖向波动效应及粘弹性性质时的土体复刚度传递模型。结合边界条件,对桩侧任意圈层的土体平衡方程由外而内逐圈层求解,求得土体与桩接触面上的剪切复刚度,采用成层地基中给出的求解方法,进而求解得到桩顶动力响应的理论解。基于所得解,详细讨论了桩侧土施工扰动效应、桩端土挤密效应对桩顶动力响应的影响,并系统分析了任意段变阻抗桩的纵向振动特性。
4.基于横观各向同性材料的本构方程以及单相弹性土介质的运动方程,给出了考虑土体竖向位移及其粘弹性性质的土体动力控制方程,采用成层地基中给出的求解方法,通过严格求解得到桩顶动力响应的理论解。基于所得解的参数分析表明,不管是桩端土还是桩侧土,竖直面上的剪切模量对桩顶动力响应的影响程度要比水平面上的剪切模量的影响大的多。因此,当考虑土体竖向波动效应时,竖直面上的剪切模量对桩土系统振动特性起着主导作用。
5.分别以内壁侧摩阻力及附加质量的方式考虑土塞对管桩的动力作用,建立了考虑土塞效应时大直径管桩纵向振动的定解问题,通过严格求解分别得到了管桩桩顶频域响应的解析解及半正弦脉冲激励作用下桩顶速度时域响应的半解析解。基于所得解的参数分析表明,不管是大直径混凝土管桩还是钢管桩,管桩壁厚越小,管桩的有效测试长度越短；在桩顶速度时域响应曲线上,土塞顶部界面位置处会出现类似扩颈桩段的反向反射信号；由于土塞的存在,填充土塞桩段的综合波速会小于管桩材料的一维弹性纵波波速,且土塞高度越高,填充土塞桩段的综合波速越小。基于理论分析的结果和模型试验的验证结果,本文定义了一个工程上很有用的概念,即管桩的视在波速。并指出,在工程测试时,应该选用管桩的视在波速作为测试波速。
本文提出的虚土桩法是对桩-桩端土相互作用模型的一个有益补充,基于本文工作所得出的一些新结论、新现象可以用于桩基础防震、抗震设计、动力基础减振设计及基桩动态测试分析中。
The pile-soil dynamic interaction is a complicated contact problem. The pile vibration theory can provide a valuable guide for both earthquake-resistance design and various dynamic testing methods of pile. Over the past decades, many dynamic interaction models have been presented to investigate the behavior of surrounding soil-pile dynamic interaction. It can be noted that extensive and in-depth research work has been done in the field of surrounding soil-pile dynamic interaction. By contrast, less attention is attracted by the topic on underlying soil-pile dynamic interaction. Therefore, by means of fictitious soil pile method, this paper systematically investigates the dynamic response of elastic and viscoelastic pile and large diameter pipe pile, which are embedded in homogeneous foundation, layered foundation and radial inhomogeneous foundation. The principal contents and original work are as follows:
1.Considering vertical wave effect and viscoelastic property of soil, the dynamic interaction model of pile-surrounding soil, pile-underlying soil is established by using fictitious soil pile method when the pile is embedded in homogeneous foundation. The dynamic equilibrium equations of soil undergoing arbitrary vertical exciting force are solved by virtue of the separation of variables technique. Then, according to the boundary conditions at the interface of soil and pile, the theoretical solutions for the dynamic response of pile in the frequency domain are derived by using integral transform technique to solve the dynamic governing equation of pile. By means of inverse Fourier transform technique and convolution theorem, the semi-analytical solution for the velocity response of a pile undergoing half-cycle sine pulse at the pile head is obtained in the time domain. Based on these solutions, a parametric study is conducted to study emphatically the effects of parameters of underlying soil on dynamic response at the pile head. It is shown that the finite underlying soil layer adjacent to the pile toe has a significant influence on the pile dynamic response and there is a critical influence depth for underlying soil.
2.To investigate the dynamic response of a viscoelastic pile embedded in layered foundation and subjected to arbitrary vertical exciting force, a simplified and practical mathematical model is developed for simulating dynamic interaction of the adjacent soil layers. By means of the same solving methods presented in homogeneous foundation and through the recursion of the impedance function, the complex stiffness at the fictitious soil pile head is derived and used as boundary condition at the pile toe to obtain the theoretical solutions of pile dynamic response. Furthermore, the accuracy and feasibility of the simplified model is verified by comparing with the homogeneous foundation rigorous solution. Based on these solutions, the influence of the properties of layered underlying soil and pile end sediment on pile dynamic response is thoroughly analyzed.
3. The complex stiffness transform model is developed to simulate the radially inhomogeneous property of surrounding soil and underlying soil of pile which caused by pile construction effect. Then, combining the boundary conditions between radially adjacent soil zones, the dynamic equilibrium equations of all soil zones are solved one by one from undisturbed region to disturbance region and the complex stiffness of the interface of pile and its surrounding soil is derived. By means of the same solving methods presented in layered foundation, the theoretical solutions of pile dynamic response are obtained both in frequency domain and time domain. Based on these solutions, the influence of construction effect of pile surrounding soil and compaction effect of pile end soil on pile dynamic response are analyzed in detail. The dynamic response of a pile with arbitrary variable impedance are systematically investigated.
4. Based on the stress-strain relationships of transversely isotropic medium and dynamic equations of single phase elastic soil, the dynamic governing equations of the layered transversely isotropic soils are obtained in cylindrical coordinates considering their vertical wave effect and viscoelastic property. By virtue of the same solving methods developed in layered foundation, the theoretical solutions of pile dynamic response are derived both in frequency domain and time domain. The parametric studies show that the influence of vertical shear modulus on the vertical dynamic response of pile is more significant than the influence of horizontal shear modulus. So, it can be noted that the vertical shear modulus plays a dominant role in the vibration characteristics of the pile-soil system when the vertical wave effect of layered soils is taken into consideration.
5. By using plane strain model and additional mass method to simulate the dynamic interaction of soil plug and pipe pile, the definite problem of large diameter pipe pile embedded in layered foundation is established by considering the soil plugging effect. The analytical solutions of dynamic response at the pipe pile head are derived in the frequency domain and its corresponding semi-analytical solution for the velocity response of a pile undergoing half-cycle sine pulse at the pipe pile head is obtained in the time domain. The parametric studies show that the effective test length of pipe pile decreases as the thickness of pipe pile decreases for both large diameter concrete pipe pile and large diameter steel pipe pile. It also can be noted that there is reverse reflection signal at the position of soil plug top in the velocity response curves of pipe pile in the time domain. Due to the presence of soil plug, the integrated velocity of the pile section filling soil plug is less than the elastic longitudinal wave velocity of pipe pile, and the higher the height of soil plug is, the smaller the integrated velocity of the pile section filling soil plug is. Moreover, the conception of Apparent Wave Velocity of Pipe Pile (AWVPP) is defined in this paper, which is of great importance in foundation pile integrity testing. And, it is stated that the AWVPP should be choosed as the testing velocity in the engineering test.
The fictitious soil pile method is an useful supplement to the research of dynamic interaction of pile and its underlying soil. The new results and new phenomenons presented in this paper can be used in earthquake-resistance design of pile foundation, anti-vibration design of dynamic foundation and dynamic testing of pile.
引文
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