饱和土中任意排列的非连续屏障对弹性波的多重散射机理研究

In order to compensate the limitation of traditional single scattering theory and single-phase homogeneous soil hypothesis, an improved theoretical method based on both wave motions equation of saturated soil and multiple scattering theory of acoustic and electromagnetic wave is established. The two-dimensional vibration isolation problems by arbitrary arrangement of discontinuous barriers with various cross-sections such as cavities, in-filled cavities, solid piles, tubular piles and square piles are solved by employing both wave function expansion and integral equation method. Thus the general solution of multiple scattering is achieved. On the basis of two-dimensional solution, the three-dimensional semi-analytical solution is obtained by assuming scatterers as Euler-Bernoulli beams. The influences of certain parameters on isolation effectiveness are investigated under different kinds of vibration sources, materials of barrier and soil. Afterwards, some large scale model tests are carried out to examine the response in front or behind ground with various kinds of barriers by vibrations under various loading patterns. Three-dimensional isolation effects are simulated on the base of field tests datum by ABAQUS for the sake of proving the hypothesis and revising the theoretical method as well. Finally this methodology is refined so that it can be served in isolation vibration engineering and to provide reasonable advices as theoretical basis for abating environmental vibration pollutions induced by artificial vibration sources.

理论上为了弥补以往散射理论中单重散射假设的不足和土介质均一的局限性，同时基于饱和土的波动方程和声波、电磁波的多重散射理论，采用波函数展开和积分方程法求解任意排列、任意截面尺寸的非连续屏障（空穴，填充孔，实心桩，空心管桩，方桩）等对体波的二维屏蔽问题，得到非连续屏障的多重散射一般解，在此基础上将隔离体假设为欧拉-伯努利梁，求解饱和土体中任意排列、任意截面尺寸非连续屏障对面波的多重散射三维半解析解，对不同振源，屏障与土体介质的隔离效果进行参数分析；其次于饱和土场地内进行大比尺模型试验，测试不同振源、不同加载方式情况下不同形式屏障前后场地振动的响应情况；再次基于试验数据在通用有限元软件ABAQUS中模拟非连续屏障的三维隔振效果并对理论计算假设和求解方法进行验证和修正，完善该理论体系，最终将其服务于工程隔振领域，从而可作为理论基础对人工振源引起的环境振动污染治理提供合理的建议。

随着城市化进程的加速，大规模建设带来的人工振动日益频繁，软土地区采用非连续屏障作为振动污染的治理手段已成为土动力学领域的重要研究课题之一。本项目结合理论研究、室内试验和现场实测，求解了饱和土中非连续屏障对弹性波的多重散射问题，分析了影响隔振效果的几何、材料和物理参数，并提出了屏障设计的建议指标。具体包括：基于Biot饱和波动方程和声波、电磁波的多重散射理论，采用波函数展开法，求解了全空间内非连续屏障对弹性波多重散射的理论解，根据多种形式的非连续屏障（排孔、弹性桩、管桩等），得到了不同边界条件下的散射系数，从而获得了散射波和总波场的解。数值计算结果表明，多重散射假设因其考虑将散射波作为次生波源，弥补了以往单重散射假设中忽略后续散射波相干散射的缺陷，故工程隔振设计中不可忽略后续散射对计算结果造成的误差。基于不考虑固液耦合的饱和土波动方程，将弹性桩视为欧拉-伯努利梁，利用多重散射法，通过位移边界条件和动力平衡条件，采用最小二乘法求得了饱和半空间内非连续屏障对面波多重散射的半解析解。通过现场大比尺模型试验和实测结果对理论模型进行了验证，讨论了影响隔振效果的几何参数、物理参数和材料参数等，总结和归纳了饱和介质中多个圆柱形非连续屏障对弹性波多重散射的机理。此外，还采用了多重散射法对多个空穴和衬砌受弹性波入射时的动力响应问题进行了求解与分析。本项目的研究成果可为隔离环境振动的非连续屏障设计提供理论依据，尤其对大面积饱和软土分布的南方地区具有较大意义。