摘要
本文分析了虚土桩扩散角对桩土动静特性的影响。虚土桩法是为了解决桩和桩端土相互作用而提出的一种新方法,该方法将桩身正下方到基岩之间的土体假设为“土桩”—即虚土桩,虚土桩的求解按照桩的一维杆件理论进行,参数选取实际土体的参数。与传统理论相比,虚土桩模型具有一定的优势。主要体现在：可以充分考虑桩端土的成层性、基岩的埋置深度,其参数的选取也与土层的实际参数联系紧密。
本文基于虚土桩法,做了如下4项工作：
1.在忽略土体的径向位移条件下,考虑虚土桩扩散角并假定扩散角沿深度变化为一常数,对简谐荷载作用时刚性圆盘下均质滞回材料土体的振动特性进行研究,得到了刚性圆盘底部土体的实际支承复刚度以及土层在简谐荷载作用下的动力特性。分析泊松比、阻尼等参数对桩土动力特性的影响,同时还与其它学者的研究成果进行对比,分析虚土桩法在求解桩土动力耦合问题中的适用性和精度等问题。
2.桩端土单层条件下,采用平面应变模型,研究桩土耦合作用时虚土桩扩散角对桩土动力特性的影响。对桩的动力方程进行Laplace变换,通过复刚度传递法,递推求解得到桩顶受纵向激振力作用下的复刚度、速度导纳、位移幅频在频域表达式,再利用卷积定理和Fourier逆变换得到桩顶时域响应半解析解。研究不同土质、不同桩长条件下等条件下虚土桩扩散角对桩的动力特性的影响,同时分析端承桩桩底沉渣特性对桩顶动力响应的影响,并结合工地实测资料进行拟合对比。
3.桩端土单层条件下,采用连续介质模型,研究桩土耦合作用时虚土桩扩散角对桩土动力特性的影响,同时对平面应变模型和连续介质模型在相同条件下得到的解进行分析对比。对桩土动力耦合方程进行Laplace变换,根据边界条件求解得到桩顶动力特性在频域内的解析解以及时域内的半解析解。分析粘性阻尼对桩的动力特性的影响并研究不同桩端土性质下虚土桩扩散角对桩的振动特性的影响。
4.从三维轴对称模型出发,建立桩土体系静力平衡方程,通过积分变换,得到桩顶沉降在频域内的解析解和在时域内的半解析解,进而分析单桩随时间变化的规律,同时利用虚土桩模型计算得到的结果与实测数据进行拟合对比。
In this dissertation, the effect of cone angle on dynamic and static response of pile was studied. Virtual pile model is a new method proposed to solve the interaction between soil and pile. The soil among the pile and bedrock is assumed to "virtual pile". The vibration of virtual pile can be solved by one-dimensional bar theory, while the parameter of virtual pile was completely the same as soil. Compared with the traditional theory, the virtual pile model has certain advantages, mainly reflected in: You can give full consideration to the influence of multilayered soil; you can also consider the burying depth of bedrock; the parameter of virtual pile selection is also closely linked to the actual soil property.
Based on virtual pile model, the following four tasks have been finished:
1. Ignoring the radial displacement of soil and assuming that cone angle of virtual pile is a constant, the vibration of pile-and-soil system is investigated when harmonic force loaded on rigid circular plate. Then the bearing complex stiffness and dynamic characteristics are obtained. By analyzing Poisson's ratio, damping and some other factors, and comparing with other research results, the applicability and accuracy of virtual soil pile method in solving the problem of dynamic response of pile is studied.
2. Assume that the soil under pile is single, by plane strain model a research on dynamic response of pile and soil is presented. By using complex stiffness method, the dynamic characteristics and complex stiffness in frequency domain is reached. Using the convolution theorem and Fourier inverse transform, the semi-analytical solution in time domain is reached too. Based on the above solution, the response of piles is studied under different conditions, and the solution is compared to fit with the engineering data.
3. Assume that the soil under pile is single, by continuum model another research on dynamic response of pile and soil is presented. The effect of viscous damping is analyzed, while the solution under plane strain model and continuum model are compared with the same conditions.
4. According to three-dimensional axial symmetry model, static equilibrium equation of pile and soil is built. By integral transformation, the settlement of pile top in frequency domain and time domain is obtained. The results are measured with project data.
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