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 同济大学学报(自然科学版)  2019, Vol. 47 Issue (6): 815-823, 841.  DOI: 10.11908/j.issn.0253-374x.2019.06.011 0

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ZHOU Ying, CHEN Jin. Uniform Dynamic Similitude Method and Experimental Study for the Track-Subgrade System[J]. Journal of Tongji University (Natural Science), 2019, 47(6): 815-823, 841. DOI: 10.11908/j.issn.0253-374x.2019.06.011

文章历史

1. 同济大学 土木工程防灾国家重点实验室，上海 200092;
2. 长安大学 建筑工程学院，陕西 西安 710061

Uniform Dynamic Similitude Method and Experimental Study for the Track-Subgrade System
ZHOU Ying 1, CHEN Jin 1,2
1. State Key Laboratory of Disaster Reduction in Civil Engineering, Tongji University, Shanghai 200092, China;
2. School of Civil Engineering, Chang'an University, Xi'an 710061, China
Abstract: In order to consider the dynamic responses of track and subgrade of the scaled track-subgrade model and the interaction between them, a uniform dynamic similitude method for the track-subgrade system was first proposed. The dynamic similitude design of the track was conducted and the acceleration-scaling factor of the track-subgrade model was assigned as 1.0. Then, the track and subgrade follow the same length scaling factor and the shear wave of the subgrade model was controlled to perform the dynamic design of the subgrade structure. By using the proposed approach, the similitude design of a 1/4-scaled track-subgrade model system was conducted and a series of dynamic tests of the model system under the excitations with different frequencies were carried out. The acceleration responses of different positions of the model were measured and analyzed. The first-order frequency of the test system was obtained. The results show that there exists time delay in the process of downward transfer of acceleration. Under the excitations with a certain frequency, the characteristic frequencies, which were obtained by using the spectrum analysis of acceleration, of different structural layers are consistent.
Key words: high-speed railway subgrade    track-subgrade system    similitude design    dynamic test    soil structure interaction

1 基于轨道-路基体系的组合控制动力相似设计方法 1.1 方法的提出

(1) 轨道结构设计采用结构动力相似设计方法；

(2) 不允许重力失真，即不附加配重，轨道-路基体系加速度相似比Sa为1；

(3) 路基和轨道结构遵循相同的长度相似比Sl

(4) 通过模型路基与原型路基各层材料(基床表层、基床底层、路堤、地基)的剪切波速相似关系来定义模型材料的长度相似比Sl

(5) 必须考虑施工条件和试验能力.

 $\frac{S_{\sigma}}{S_{\rho} S_{a} S_{l}}=1$ (1)

 $S_{v}=\sqrt{S_{a} S_{l}}$ (2)
 $V_{\mathrm{sm}}=S_{v} \cdot V_{\mathrm{sp}}=\sqrt{S_{a} S_{l}} \cdot V_{\mathrm{sp}}$ (3)

1.2 模型相似设计

 $M^{\mathrm{p}}=f_{y}^{\mathrm{p}} A_{s}^{\mathrm{p}} h_{0}^{\mathrm{p}}$ (4)
 $M^{\mathrm{m}}=f_{y}^{\mathrm{m}} A_{s}^{\mathrm{m}} h_{0}^{\mathrm{m}}$ (5)
 $S_{M}=\frac{M^{\mathrm{m}}}{M^{\mathrm{p}}}=\frac{f_{y}^{\mathrm{m}} A_{s}^{\mathrm{m}} h_{0}^{\mathrm{m}}}{f_{y}^{\mathrm{p}} A_{s}^{\mathrm{p}} h_{s}^{\mathrm{m}}}=\frac{A_{s}^{\mathrm{m}}}{A_{s}^{\mathrm{p}}} S_{l} S_{f_{y}}$ (6)
 $A_s^{\rm{m}} = A_s^{\rm{p}}\frac{{{S_M}}}{{{S_l}{S_{{f_y}}}}} = A_s^{\rm{p}}\frac{{{S_\sigma }S_l^2}}{{{S_{{f_y}}}}} = A_s^{\rm{p}}\frac{{{S_\sigma }S_l^2}}{{{S_{{f_y}}}}}$ (7)

 图 1 弯曲元试验 Fig.1 Bender element test
2 轨道-路基模型体系动力试验 2.1 模型制作

2.1.1 钢轨和扣件系统

2.1.2 轨道结构

 图 3 轨道板支模(平面) Fig.3 Form erecting of track slab (plan view)

 图 4 轨道结构施工(侧面) Fig.4 Construction of track structure (side view)

 图 5 钢轨、扣件安装 Fig.5 Installation of rails and fasteners
2.1.3 路基结构

 图 6 模型基床表层填料拌合 Fig.6 Mixing filler of surface layer for the subgrade
 图 7 夯土机夯实路基 Fig.7 Compaction of subgrade by rammer compactor
2.1.4 地基

2.2 试验加载方法及输入荷载

 $F=1933 \sin 2 \pi f t+2707$ (8)

2.3 传感器布置

 图 8 传感器布置图 Fig.8 Arrangement diagram of sensors
3 轨道-路基模型体系动力试验结果分析 3.1 路基各点加速度随时间的变化关系

 图 9 25 Hz时钢轨下方路基1~5位置加速度时程曲线 Fig.9 Acceleration history curve of the subgrade at the position 1~5 under the rail at 25 Hz
 图 10 25 Hz时钢轨下方路基6~7位置加速度时程曲线 Fig.10 Acceleration history curve of subgrade at the position 6~7 under the rail at 25 Hz

 图 11 路基1~5位置加速度频谱曲线 Fig.11 Acceleration spectrum curve of subgrade at the position 1~5
 图 12 路基6~7位置加速度频谱曲线 Fig.12 Acceleration spectrum curve of subgrade at the position 6~7

3.2 不同频率下路基的动力反应规律

 图 13 路基内部各点加速度随频率变化关系 Fig.13 Relationship between accelerations and frequency at various points within the subgrade

3.3 不同频率下路基加速度的衰减规律

 图 14 各点加速度沿着路基横断面的分布特征 Fig.14 Distribution characteristics of accelerations along the cross section of roadbed at various points

4 足尺数值模型路基加速度结果与模型试验结果对比

 图 15 路基加速度模拟结果与试验结果对比 Fig.15 Comparison of numerical simulation and experimental results of subgrade acceleration
5 结论

(1) 提出了轨道-路基体系一致动力相似设计方法，并进行了轨道-路基结构的相似设计、模型制作和动力试验，方法的可靠性得到了验证.

(2) 发现了加速度在向下传递过程中存在时间尺度上的滞后效应，越接近路基表面位置的加速度传感器，到达峰值点相差的时间越短，说明能量传递是一个先快后慢的过程.

(3) 同一激振频率下，路基不同结构层处加速度频谱分析的特征频率一致，说明虽然路基由散粒材料构成，但其仍是以共同工作的整体参与了动力传递和衰减.

(4) 确定了轨道-路基试验模型体系一阶固有频率值为21 Hz.