改进的虚土桩法及其在非等截面桩纵向振动中的应用研究
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摘要
目前,国内外研究桩与桩底土相互作用关系的模型,大多数是非连续模型,且缺乏对桩底土作用的研究。为了建立桩与桩底土的严格耦合关系,本文提出了一种改进的虚土桩法。并基于该方法,分析了桩底土对单桩纵向振动特性的影响,研究了焊缝在多级混凝土管桩完整性检测中的作用及不同条件下静钻根植竹节桩这一新桩型的动力特性。主要的工作与创新成果如下：
(1)基于地基中圆形竖向荷载下的Mindlin附加应力,提出了考虑应力扩散效应的虚土桩法。进一步结合平面应变模型,通过Laplace变换和卷积定理等数学方法,求得任意激振力作用下的桩体振动频域响应解析解和时域响应半解析解。通过分析桩底土体参数对桩动力响应的影响,发现土体剪切模量是决定桩底支撑刚度的重要因素,土体模量提高,将引起桩底支撑刚度和阻尼显著增大。桩底土对桩身动力响应的影响存在临界厚度,约5-7倍的桩体半径,在此范围内,桩体刚度与桩底土层厚度成反比关系,阻尼与之成正比关系。
(2)将虚土桩法从平面应变模型发展到轴对称连续土体模型中,考虑土体的径向和竖向两相位移,建立三维波动效应下的桩土体系纵向振动模型。通过引入位移势函数和Laplace变换的手段,采用分离变量法将竖向和径向位移进行解耦,进而通过阻抗传递法求得桩体的频域响应,通过Laplace逆变换得到桩体的时域响应。根据所求得的解,对比了轴对称连续模型与平面应变模型下虚土桩法的差异,发现轴对称模型能更好地反映桩土体系的自振频率。
(3)提出了混凝土管桩焊接缝的简化模型,将影响焊缝质量的物理因素转化到等效的刚度体系中,从而实现了可对焊缝进行理论拟合的目的。借助本文所提出的虚土桩法,求得多级混凝土焊接管桩桩顶的动力响应。经过分析有效焊接断面、焊接高度等参数的大小对桩顶速度响应的影响,表明焊接深度不应小于5mm,焊缝高度宜控制在2mm范围内。实测数据的拟合结果表明,该简化模型能有效地反映焊缝质量对管桩反射波信号的影响,可为桩基完整性检测提供指导。
(4)根据静钻根植竹节桩的成桩机理,确立了径向非均质理论与虚土桩法相结合的桩土动力模型。结合系数矩阵传递法,求得径向非均质土体下竹节形根植桩的桩顶动力响应。分析了竹节及桩周水泥土等对桩顶动力响应的影响,结果表明桩体刚度与竹节密度和竹节半径成正比,桩侧水泥土的硬化程度越高,桩顶刚度越大,阻尼越小,且泥浆的水泥配合比为40%时,性价比较高。通过对工程数据的反演拟合验证了桩侧水泥土的硬化规律。
完善地模拟桩与桩底土的作用关系是本文的核心,即文中提出的虚土桩法。以此来解决工程中出现的实际问题是本文的目的。基于此,本文提出的新方法、得到的新结论可为桩基工程设计及检测工作提供参考。
Currently, the existing models for the pile-soil interaction problem are mostly non-continuous and lack of extensive investigation on the effect of soil beneath the pile. In order to establish a precise coupling relationship between the pile and soil, a fictitious soil pile method was proposed in this research project to include the effect of stress dispersion at the tip of piles. Based on this method, the influence of soil on the longitudinal vibration behavior of single plies, the impact of welding on the integrity detection of multistage concrete tubular piles, as well as the dynamic characteristics of bored PHC nodular piles under different conditions were thoroughly studied. The main finished work and innovative achievements of this article are listed as following:
(1) A fictitious soil pile method was proposed to consider the effect of stress dispersion based on the Mindlin additional stress distribution under the circular vertical loading on the foundation. Further, in combination with the plane strain model, the analytical solutions of longitudinal vibration response of piles in frequency domain and the corresponding semi-analytical solutions in time domain were obtained using Laplace transform and convolution theorem. It is shown that shear stiffness of soil is crucial to determine the complex stiffness of piles according to a parametric study of the influence of different parameters of soil on the dynamic response of piles. The increase of shear stiffness of soil will enhance the stiffness and damping of pile significantly. It was also found that there is a critical value of the thickness of soil between pile tip and bedrock that causing influence on the dynamic response of piles, and this value is about5-7times of the pile radius. Within this range, the stiffness of piles is proportional while the damping of piles is inversely proportional to the thickness of soil.
(2) The fictitious pile soil model was further developed from the plane strain model to the axial symmetric continuous soil model, with which the longitudinal vibration model of pile-soil system taking into account of the three-dimensional wave effect of soil around the pile was built considering the radial and longitudinal displacement of soil. Then the displacement potential function and Laplace transform were imported, and the vertical and radial displacement was decoupled by the method of variable separation. Consequently the response of piles in frequency domain was obtained by the impedance transmission and the response of piles in time domain was obtained using Laplace inverse transform. The results obtained by fictitious pile soil method based on the axial symmetric continuous model was compared with that based on the plane strain model, and the drawed conclusion is that the axial symmetric continuous model is better to reflect the natural frequency of pile-soil system.
(3) A simplified model of the welding seam of concrete tubular piles was proposed, in which the physical factors that affecting the welding quality are included in the effective stiffness, hence the welding can be theoretically simulated. The fictitious pile soil method was applied to solve the dynamic response at the top of multistage concrete welded tubular piles. The influec of parameters including the effective cross-section and height of welding on the velocity response at the top of piles were analyzed, and it was found that the depth of welding should be less than5mm and the height of welding should be limited to2mm. The fitted results using measured data show that this simplified model can effectively diagnose the influence of welding quality on the reflected wave of tubular piles, thus can provides guidance for the integrity detection of piles.
(4) According to the forming mechanism of bored PHC nodular piles, a pile-soil dynamic model was developed regarding to the characteristics of radial nonhomogeneity of soil and the fictitious pile soil method. The dynamic response at the top of bored PHC nodular piles with surrounding nonhomogeneous soil was determined using the transmission method of coefficient matrix. The influence of some factors like the properties of nodular and surrounding cemented soil on the dynamic response of bored PHC nodular piles were also investigated, and the results show that the stiffness of piles is proportional to the density and radius of nodular. It was also found that when the hardening level of surrounding cemented soil is higher, the stiffness of pipe bolck is larger and the damping is smaller, and the cement with mix proportion of40%is most cost efficient. Finally, the hardening rule of surrounding cemented soil of piles was proven through inversion fitting of engineering data.
The core achievement of this research is improvement of simulating the pile-soil interaction by proposing the fictitious pile soil method. With the aim of solving problems occurred in engineering practice, the newly proposed method and drawed conclusions in this article will provide reference for the engineering design of pile foundations.
(1)基于地基中圆形竖向荷载下的Mindlin附加应力,提出了考虑应力扩散效应的虚土桩法。进一步结合平面应变模型,通过Laplace变换和卷积定理等数学方法,求得任意激振力作用下的桩体振动频域响应解析解和时域响应半解析解。通过分析桩底土体参数对桩动力响应的影响,发现土体剪切模量是决定桩底支撑刚度的重要因素,土体模量提高,将引起桩底支撑刚度和阻尼显著增大。桩底土对桩身动力响应的影响存在临界厚度,约5-7倍的桩体半径,在此范围内,桩体刚度与桩底土层厚度成反比关系,阻尼与之成正比关系。
(2)将虚土桩法从平面应变模型发展到轴对称连续土体模型中,考虑土体的径向和竖向两相位移,建立三维波动效应下的桩土体系纵向振动模型。通过引入位移势函数和Laplace变换的手段,采用分离变量法将竖向和径向位移进行解耦,进而通过阻抗传递法求得桩体的频域响应,通过Laplace逆变换得到桩体的时域响应。根据所求得的解,对比了轴对称连续模型与平面应变模型下虚土桩法的差异,发现轴对称模型能更好地反映桩土体系的自振频率。
(3)提出了混凝土管桩焊接缝的简化模型,将影响焊缝质量的物理因素转化到等效的刚度体系中,从而实现了可对焊缝进行理论拟合的目的。借助本文所提出的虚土桩法,求得多级混凝土焊接管桩桩顶的动力响应。经过分析有效焊接断面、焊接高度等参数的大小对桩顶速度响应的影响,表明焊接深度不应小于5mm,焊缝高度宜控制在2mm范围内。实测数据的拟合结果表明,该简化模型能有效地反映焊缝质量对管桩反射波信号的影响,可为桩基完整性检测提供指导。
(4)根据静钻根植竹节桩的成桩机理,确立了径向非均质理论与虚土桩法相结合的桩土动力模型。结合系数矩阵传递法,求得径向非均质土体下竹节形根植桩的桩顶动力响应。分析了竹节及桩周水泥土等对桩顶动力响应的影响,结果表明桩体刚度与竹节密度和竹节半径成正比,桩侧水泥土的硬化程度越高,桩顶刚度越大,阻尼越小,且泥浆的水泥配合比为40%时,性价比较高。通过对工程数据的反演拟合验证了桩侧水泥土的硬化规律。
完善地模拟桩与桩底土的作用关系是本文的核心,即文中提出的虚土桩法。以此来解决工程中出现的实际问题是本文的目的。基于此,本文提出的新方法、得到的新结论可为桩基工程设计及检测工作提供参考。
Currently, the existing models for the pile-soil interaction problem are mostly non-continuous and lack of extensive investigation on the effect of soil beneath the pile. In order to establish a precise coupling relationship between the pile and soil, a fictitious soil pile method was proposed in this research project to include the effect of stress dispersion at the tip of piles. Based on this method, the influence of soil on the longitudinal vibration behavior of single plies, the impact of welding on the integrity detection of multistage concrete tubular piles, as well as the dynamic characteristics of bored PHC nodular piles under different conditions were thoroughly studied. The main finished work and innovative achievements of this article are listed as following:
(1) A fictitious soil pile method was proposed to consider the effect of stress dispersion based on the Mindlin additional stress distribution under the circular vertical loading on the foundation. Further, in combination with the plane strain model, the analytical solutions of longitudinal vibration response of piles in frequency domain and the corresponding semi-analytical solutions in time domain were obtained using Laplace transform and convolution theorem. It is shown that shear stiffness of soil is crucial to determine the complex stiffness of piles according to a parametric study of the influence of different parameters of soil on the dynamic response of piles. The increase of shear stiffness of soil will enhance the stiffness and damping of pile significantly. It was also found that there is a critical value of the thickness of soil between pile tip and bedrock that causing influence on the dynamic response of piles, and this value is about5-7times of the pile radius. Within this range, the stiffness of piles is proportional while the damping of piles is inversely proportional to the thickness of soil.
(2) The fictitious pile soil model was further developed from the plane strain model to the axial symmetric continuous soil model, with which the longitudinal vibration model of pile-soil system taking into account of the three-dimensional wave effect of soil around the pile was built considering the radial and longitudinal displacement of soil. Then the displacement potential function and Laplace transform were imported, and the vertical and radial displacement was decoupled by the method of variable separation. Consequently the response of piles in frequency domain was obtained by the impedance transmission and the response of piles in time domain was obtained using Laplace inverse transform. The results obtained by fictitious pile soil method based on the axial symmetric continuous model was compared with that based on the plane strain model, and the drawed conclusion is that the axial symmetric continuous model is better to reflect the natural frequency of pile-soil system.
(3) A simplified model of the welding seam of concrete tubular piles was proposed, in which the physical factors that affecting the welding quality are included in the effective stiffness, hence the welding can be theoretically simulated. The fictitious pile soil method was applied to solve the dynamic response at the top of multistage concrete welded tubular piles. The influec of parameters including the effective cross-section and height of welding on the velocity response at the top of piles were analyzed, and it was found that the depth of welding should be less than5mm and the height of welding should be limited to2mm. The fitted results using measured data show that this simplified model can effectively diagnose the influence of welding quality on the reflected wave of tubular piles, thus can provides guidance for the integrity detection of piles.
(4) According to the forming mechanism of bored PHC nodular piles, a pile-soil dynamic model was developed regarding to the characteristics of radial nonhomogeneity of soil and the fictitious pile soil method. The dynamic response at the top of bored PHC nodular piles with surrounding nonhomogeneous soil was determined using the transmission method of coefficient matrix. The influence of some factors like the properties of nodular and surrounding cemented soil on the dynamic response of bored PHC nodular piles were also investigated, and the results show that the stiffness of piles is proportional to the density and radius of nodular. It was also found that when the hardening level of surrounding cemented soil is higher, the stiffness of pipe bolck is larger and the damping is smaller, and the cement with mix proportion of40%is most cost efficient. Finally, the hardening rule of surrounding cemented soil of piles was proven through inversion fitting of engineering data.
The core achievement of this research is improvement of simulating the pile-soil interaction by proposing the fictitious pile soil method. With the aim of solving problems occurred in engineering practice, the newly proposed method and drawed conclusions in this article will provide reference for the engineering design of pile foundations.
引文
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