Influences of water level rise on dynamic responses and long-term settlement of high-speed railway subgrade
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摘要: 基于Biot理论，建立了轨道-路基-多层饱和土地基耦合系统的2.5维有限元分析模型，提出了考虑实际列车循环荷载作用的路基累积沉降计算方法，分析了水位抬升、列车速度和列车轴重对路基动力响应与长期沉降的影响。研究结果表明：水位抬升对土体振动强度的放大作用并不是局限在水位变化的深度范围内，而是会导致整个路基和地基断面的振动增大，并且这种全断面式的振动放大效应随着列车速度的提高而增强；水位抬升至路基内部时，路基内部会出现显著的超静孔压，最大值达到27.52 kPa，导致有效应力大幅下降，路基内土单元的应力路径向破坏线靠近；当水位仅在地基内抬升时，路基在列车循环荷载作用下的累积变形较小，线路沉降主要来自于地基，当水位抬升至路基内部时，路基累积变形随加载次数的增加发展迅速，100万次加载后变形为19.54 mm，远超容许值，说明路基防水对于线路的长期累积沉降控制具有关键作用；路基和地基的累积变形受列车速度和列车轴重的影响，随着列车轴重的增加而显著增大，并且轴重的增加对路基累积变形的影响相较于地基更强烈，在设计时需要格外关注。Abstract: Based on the Biot theory, a 2.5-dimensional finite element analysis model of the track-subgrade-multilayered saturated soil foundation coupling system was established, and a calculation method for the cumulative settlement of the subgrade considering the actual train cyclic load was proposed. The influences of water level rise, train speed, and axle load on subgrade dynamic response and long-term settlement were discussed. Research results show that the amplification effect of water level rise on the soil vibration intensity is not limited to the depth of water level change, but will lead to the increase in the vibration of the entire subgrade and foundation section. This full-section vibration amplification effect increases with train speed. When the water level rises to the inside of the subgrade, significant excess pore pressure will generate inside the subgrade, and the maximum value can reach 27.52 kPa, resulting in a large drop in the effective stress. Then, the stress path of the soil element in the subgrade will approach the failure line. When the water level only rises within the foundation, the cumulative deformation of the subgrade under the train cyclic load is small, and the railway settlement mainly comes from the foundation. When the water level rises to the inside of the subgrade, the cumulative deformation of the subgrade develops rapidly with the loading cycles, which is 19.54 mm after one million times of loading and exceeds the allowable value largely, indicating that the subgrade waterproofing plays a key role in the long-term cumulative settlement control of the railway line. The train speed and axle load affect the cumulative deformation of the subgrade and foundation, and the increase significantly with the axle load of the train. The increase in the axle load has a stronger influence on the cumulative deformation of the subgrade than the foundation. Thus, the effect of axle load on the cumulative deformation should be well considered in the design.
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图 2 2.5维有限元解与半解析解对比
Figure 2. Comparison of 2.5-dimensional finite element solutions and semi-analytical solutions
图 5 2.5维有限元结果与试验结果对比
Figure 5. Comparison of 2.5-dimensional finite element results and test results
图 8 不同工况下位移响应最大值沿深度的分布
Figure 8. Maximum displacement response distributions along depth under different cases
图 9 不同深度处的位移最大值随列车速度的变化曲线
Figure 9. Changing curves of maximum displacement on train speed at different depths
图 10 超静孔压最大值随深度发展趋势
Figure 10. Developing trends of maximum excess pore pressure with depth
图 11 不同速度下B点处的超静孔压时程曲线
Figure 11. Time history curves of excess pore pressure at point B under different speeds
图 12 不同列车速度和不同工况下yOz平面内超静孔压响应分布
Figure 12. Excess pore pressure response distributions in yOz plane under different train speeds and cases
图 13 有效应力最大值随深度发展趋势
Figure 13. Developing trends of maximum effective stress with depth
图 15 不同列车速度和不同工况下yOz平面内有效应力响应分布
Figure 15. Effective stress response distributions in yOz plane under different train speeds and cases
图 17 累积变形随加载次数的发展曲线
Figure 17. Developing curves of cumulative deformation with loading cycles
图 18 不同列车轴重下累积变形随加载次数的发展曲线
Figure 18. Developing curves of cumulative deformation with loading cycles under different axle weights
图 19 不同工况中列车速度对累积变形的影响
Figure 19. Influences of train speed on cumulative deformation in different cases
表 1 饱和地基参数
Table 1. Parameters of saturated foundation
参数 取值 α 0.95 M/GPa 5 G/GPa 30 υ 0.125 ρs/(kg·m-3) 2 500 ρf/(kg·m-3) 1 000 n 0.3 kD/(m·s-1) 10-6 η/(kg·m-3) 6 670 
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表 2 土层初始参数
Table 2. Initial parameters of soil layers
土层 α M/MPa E/MPa υ ρs/(kg·m-3) ρf/(kg·m-3) D0 n kD/(m·s-1) 路基表层 0.001 0.001 240 0.25 2 500 0.001 0.05 0.001 10-20 路基底层 0.001 0.001 140 0.30 2 200 0.001 0.05 0.001 10-20 土层1 0.001 0.001 113 0.35 2 700 0.001 0.05 0.001 10-20 土层2 0.001 0.001 113 0.35 2 700 0.001 0.05 0.001 10-20 土层3 0.001 0.001 135 0.35 2 700 0.001 0.05 0.001 10-20
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表 3 饱和土层参数
Table 3. Parameters of saturated soil layers
土层 α M/MPa E/MPa υ ρs/(kg·m-3) ρf/(kg·m-3) D0 n kD/(m·s-1) 路基表层 0.001 0.001 240 0.25 2 500 1 000 0.05 0.001 100 路基底层 1.000 6 400 80 0.30 2 700 1 000 0.05 0.300 10-6 土层1 1.000 3 520 45 0.35 2 700 1 000 0.05 0.600 10-6 土层2 1.000 3 520 45 0.35 2 700 1 000 0.05 0.600 10-8 土层3 1.000 3 520 60 0.35 2 700 1 000 0.05 0.600 10-6
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表 4 CRH2列车参数
Table 4. Parameters of CRH2 train
参数 数值 车厢质量/kg 45 000 转向架质量/kg 3 600 轮对质量/kg 1 700 车厢长度/m 24.8 相邻转向架中心距/m 14.9 转向架长度/m 2.5
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表 5 板式轨道参数
Table 5. Parameters of slab track
轨道参数 数值 钢轨质量/(kg·m-1) 60.64 钢轨抗弯刚度/(MN·m2) 6.625 轨道板弯曲刚度/(MN·m2) 40 轨道板质量/(kg·m-1) 950 混凝土底座弯曲刚度/(MN·m2) 190 混凝土底座质量/(kg·m-1) 1 800 扣件刚度/(kN·mm-1) 28.5 扣件阻尼/(N·s·m-1) 5.0×104
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表 6 正常路基/地基拟合参数(工况1)
Table 6. Fitting parameters of normal subgrade/foundation (case 1)
参数 基床表层 基床表层(未饱和) 地基(未饱和) ε0 3.710 0.993 0.873 B 0.058 0.078 0.108 k 4.20 3.85 2.78 s′ 2.07 64.00 53.00 m′ 2.1 9.5 163.2 υ* 0.4 0.3 0.3
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表 7 饱和路基/地基拟合参数(工况4、5)
Table 7. Fitting parameters of saturated subgrade/ foundation (cases 4 and 5)
参数 基床表层 基床表层(饱和) 地基(饱和) ε0 3.710 -0.002 -0.023 B 0.058 -0.697 -0.403 k 4.20 0.59 0.74 s′ 2.07 64.00 2.12 m′ 2.1 9.5 33.0 υ* 0.4 0.3 0.3
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