Preliminary study on the similitude of physical modelling of ground improvement by vibro stone columns
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摘要: 正确认识振冲器的振源特性和碎石桩成桩过程,对揭示振冲碎石桩加固机理有重要意义。由于实际工程中难以观测地基内部的振冲施工过程,开展物理模拟重现该过程并观测振动响应是一种可行的研究手段。从原型振冲器与模型振冲器对地基土体作用荷载相似的角度出发,首先将振冲器圆锥摆运动简化为平面内摆动,通过力矩平衡分析推导了振冲器对周围土体的振动压力表达式;然后基于Buckingham π定理,通过量纲分析获得了振动压力相似常数,发现振冲器偏心块质量、偏心距、偏心块转动角速度和重力加速度是关键影响参数;最后通过方程分析法推导了振冲器产生的最大输出机械功率、激振力和激振加速度等振源特性参数的相似常数。据此提出了一种可用于常重力和超重力环境的模型振冲器相似律设计方法,为实现振冲碎石桩施工过程物理模拟提供了科学依据。Abstract: The source mechanism of vibrator and the installation process of vibro stone columns play important role in revealing the improvement mechanism of stone column-improved ground. As it is difficult to observe the motion of vibrator and the installation process of vibro stone columns in engineering sites, it is more practical to reproduce such a complex problem and observe the vibration response by physical modelling. In this study, firstly the conical oscillation motion of the vibrator is simplified as in-plane oscillation, and the expression for the vibration-induced pressure on the surrounding soil is derived through the torque balance analysis. Then based on the Buckingham's π theorem, the scaling factor of vibration-induced pressure is obtained through the dimensional analysis, and it is found that the mass of the eccentric block, eccentricity, rotational angular velocity of the eccentric block and gravitational acceleration are the key factors. Finally the scaling factors of the vibration source parameters such as the maximum output mechanical power, excitation force and excitation acceleration generated by the vibrator are derived through the equation analysis, and then the scaling law for the model vibrator under 1g or hypergravity (Ng) environments is preliminarily proposed. This study provides the preliminary scaling law for the physical modelling of ground improvement by the vibro stone columns.
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Keywords:
- vibro stone column /
- vibration source mechanism /
- model vibrator /
- physical modelling /
- similitude
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表 1 振冲器对土体振动压力涉及量相似设计量纲与相似常数
Table 1 Similitude design of vibration-induced pressure on soil of model vibrator
序号 物理量 相似常数 量纲 序号 物理量 相似常数 量纲 1 振动压力px ML-1T-2 11 偏心块偏心距 L 2 地基平均黏聚力 ML-1T-2 12 振冲器总长 L 3 偏心块质量 M 13 激振体上沿距零振幅点距离 L 4 振冲器总质量 M 14 偏心块重心距零振幅点距离 L 5 振冲器壳体质量 M 15 壳体重心距零振幅点距离 L 6 土体平均密度 ML-3 16 振冲器重心距零振幅点距离 L 7 土体平均内摩擦角 17 振冲器惯性半径 L 8 偏心块超前角 18 计算点距零振幅距离 L 9 偏心块旋转角速度 T-1 19 激振体上沿距土体表面距离 L 10 重力加速度 LT-2 表 2 其他振冲器动力特性参数相似设计表
Table 2 Summary of scaling law of other parameters of vibrator
动力特性参数 计算公式 相似准数 相似常数 最大输出机械功率 激振力 激振
加速度 -
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