Checking and Analysis of Reinforcement Arrangement Scheme for Slab Track Based on Comprehensive Index Method
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摘要: 为优化无砟轨道配筋后结构受力的均衡性，基于综合指数法提出了轨道配筋检算评估方法，选取形状改变能密度与高斯曲率作为评价分量构造了量化的配筋检算指标；建立了无砟轨道配筋检算有限元模型，以CRTSⅢ型普通板式无砟轨道板配筋为例，研究了不同钢筋排布方式对无砟轨道板整体受力性能的影响. 研究结果表明：相较传统应力变形指标，构建的综合指数指标能够凸显轨道板的不均匀受力区域；配筋时在轨下位置额外密布钢筋能够提升轨道板抵抗垂向车辆荷载的能力；局部配筋过于集中的方案会降低轨道板适应温度荷载的能力；在升温荷载作用下其轨道板端部的综合指数较最优工况时至少增大了1倍；综合来看，钢筋直径较大、排列稀疏的方案受力均衡性较差，无砟轨道板应选择钢筋直径较小、排列密布且轨下位置适当加密的配筋方案.Abstract: To optimize the mechanical performance of the slab track after reinforcement, an evaluation method for track reinforcement was proposed based on comprehensive index method. The shape change energy density and Gaussian curvature were selected as the evaluation components to construct the quantitative checking index of the reinforcement. Taking CTRS Ⅲ ordinary type slab track as an example, a finite element model for slab reinforcement checking was established, and the influence of different reinforcement schemes on the overall mechanical performance of slab was analyzed. The results indicate that the proposed comprehensive index could highlight the uneven stress area of the track slab. The centralized reinforcement under the rail position can improve the resistance of the track slab to the vertical vehicle load. However, the excessively concentrated reinforcement will lead to a worse adaptability to the temperature load. Compared to the optimum scheme, the comprehensive index of the end of the track plate of the excessively concentrated reinforcement scheme under the heating load is more than doubled. The scheme with larger steel bar diameter and sparse arrangement has poor force balance. The track slab should choose a reinforcement scheme with smaller steel bar diameter, densely arranged, and appropriate centralized under the rail.
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Key words:
- slab track /
- reinforcement /
- temperature effect /
- structural optimization /
- comprehensive index method
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图 3 CRTSⅢ型普通板式无砟轨道配筋检算模型
Figure 3. Reinforcement checking calculation model of CRTS Ⅲ ordinary steel type slab track
图 4 车辆荷载作用下轨道板典型力学指标分布（方案1）
Figure 4. Distribution of typical mechanical indexes of track slab under vehicle load (scheme 1)
图 5 整体升温下轨道板板顶、底综合指数分布
Figure 5. Comprehensive index distribution of top and bottom of track slab under overall temperature rising load
图 6 整体升温时各方案钢筋von-Mises应力分布
Figure 6. von-Mises stress distribution of reinforcement of different schemes under overall temperature rising load
表 1 数值仿真模型材料参数
Table 1. Material parameters of numerical model
结构部件 弹性模量/MPa 泊松比 密度/(kg•m−3) 线胀系数/℃ 垫层刚度/(kN•mm−1) 垂向刚度/(MPa•m−1) 轨道板 36500 0.200 2500 1× 10−5 自密实混凝土 34000 0.167 2500 1× 10−5 底座 28000 0.167 2500 凹槽弹性垫层 30 路基 76 
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表 2 保证相同配筋率条件下不同普通钢筋配置方案
Table 2. Different reinforcement arrangement scheme under same reinforcement ratio
方案名称 上层纵向钢筋 下层纵向钢筋 上层横向钢筋 下层横向钢筋 方案 1 9ϕ16 9ϕ16 11ϕ16 11ϕ16 方案 2、3 17ϕ12 17ϕ12 21ϕ12 21ϕ12
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表 3 横纵向钢筋在轨道板内部的具体位置
Table 3. Specific position of transverse and longitudinal reinforcement inside the rail plate
方案名称 横向钢筋在轨道板内部的具体位置 纵向钢筋在轨道板内部的具体位置 方案 1 
方案 2 
方案 3 
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表 4 车辆荷载作用下不同普通钢筋配置方案下板底指标对比
Table 4. Comparison of statistical indexes of bottom of track slab for each scheme under vehicle load
方案名称 纵向应力 垂向位移 综合指数 峰值/Pa 均方差/Pa2 变异系数 峰值/mm 均方差/×10−5mm2 变异系数 峰值/×10−8 均方差/×10−8 变异系数 方案 1 240443 62520.44 1.00302 0.336899 8.4307 0.16550 5.76 0.37 4.89 方案 2 220511 56545.35 0.94748 0.316384 7.8893 0.16631 4.87 0.31 4.82 方案 3 220434 56409.00 0.94488 0.316378 7.8896 0.16551 4.82 0.30 4.81
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表 5 车辆荷载作用下不同普通钢筋配置方案下板顶各综合指数指标对比
Table 5. Comparison of statistical indexes oftrack slab top for each scheme under vehicle load
方案 峰值/×10−7 均方差/×10−8 变异系数 方案 1 5.29 2.17 9.90 方案 2 4.39 1.80 9.75 方案 3 4.30 1.76 9.71
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表 6 整体升温作用下不同普通钢筋配置方案板顶、底各综合指数指标对比
Table 6. Comparison of comprehensive statistical indexes of different schemes under overall temperature rising load
方案名称 顶面 底面 峰值/×10−5 均方差/×10−6 变异系数 峰值/×10−6 均方差/×10−7 变异系数 方案 1 1.654 95 1.533 0.60 7.601 9 6.800 0.36 方案 2 1.430 19 1.273 0.46 4.966 3 4.005 0.20 方案 3 3.354 46 2.767 0.91 10.108 9 9750 0.91
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表 7 正、负温度梯度作用下不同普通钢筋配置方案综合指数指标
Table 7. Comprehensive index of different reinforcement schemes under positive and negative temperature gradients
温度阶梯 方案名称 顶面 底面 峰值/×10−8 均方差/×10−8 变异系数 峰值/×10−7 均方差/×10−8 变异系数 正 方案 1 5.97 1.39 0.40 2.080 1.31 1.46 方案 2 5.97 1.35 0.38 1.831 1.20 1.25 方案 3 5.98 1.35 0.38 1.827 1.20 1.25 负 方案 1 37.87 0.10 0.65 2.633 0.06 0.73 方案 2 37.69 0.10 0.65 2.644 0.06 0.73 方案 3 37.69 0.10 0.65 2.644 0.06 0.73
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表 8 不同荷载作用下各方案综合比较（以方案2为参照）
Table 8. Comparison of different schemes under different loads (referring to scheme 2)
方案名称 车辆荷载作用 整体升降温作用 正温度梯度作用 负温度梯度作用 方案 1 ↓ ↓ ↓ — 方案 2 — — — — 方案 3 ↑ ↓↓ — — 注：“↑”为表示此方案更优；“↓”表示此方案表现更劣；“—”表明方案间相差不大.
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