Optimized design of construction parameters for submerged water jet breaking construction based on response surface analysis
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摘要: 针对水射流破土过程中射流孔深度及径宽难以确定的问题，以圆柱形喷嘴为研究对象，基于拉格朗日-欧拉流固耦合算法建立了淹没水射流破土的有限元模型，并通过室内实验验证了该有限元模型计算结果的准确性。基于响应面法建立了射流孔深度与径宽的预测模型，分析了喷嘴直径、射流靶距和射流压力3个因素及其交互作用对射流孔深度及径宽的影响规律，结合满意度函数对破土施工参数进行优化。结果表明：当选取特定破土深度(10 cm、15 cm和20 cm)时，较大的射流压力(7.2 MPa)、较小的射流靶距(1 cm)及合适的喷嘴直径(0.928 mm、1.164 mm和1.345 mm)可最大程度地保证射流孔的稳定性。针对特定目标破土深度，优化后的射流孔深度及径宽的预测值与实验值的误差均小于15 %，表明预测结果合理可靠。Abstract: This study proposes a finite element model for submerged water jet excavation using a cylindrical nozzle with an aim to determine the depth and diameter of jet orifices during water jet excavation. The model's accuracy was verified through indoor experiments, employing the Lagrangian-Eulerian fluid-solid coupling algorithm. The response surface method was utilized to establish a predictive model for the depth and diameter of jet orifices, which includes the impact of nozzle diameter, jet standoff distance, jet pressure, and their interactions. The construction parameters for jet excavation were optimized using a satisfaction function. Results indicated that for excavation depths of 10 cm, 15 cm, and 20 cm, keeping the stability of the jet orifices to the maximum required higher jet pressure(7.2 MPa), smaller jet standoff distance(1 cm), and an appropriate nozzle diameter(0.928 mm, 1.164 mm, and 1.345 mm). After optimization, the predicted values of jet orifice depth and diameter for the specific target excavation depths showed an error of less than 15 % compared to the experimental values, demonstrating the credibility and reliability of the predictions.
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图 3 实验与模拟射流孔形态对比
Figure 3. Comparison of experimental and simulated jet hole morphology
图 5 射流孔径宽响应曲面及等高线
Figure 5. Response surface and contour diagram of jet aperture width
表 1 土体材料参数
Table 1. Material parameter of soil
参数 测试方法 数值 密度ρ/(g·cm-3) 比重瓶法 2.69 含水率ω/% 烘干法 23.4 剪切模量G/Pa 微型十字板 2.50×106 体积模量K/Pa 旁压仪 1.20×107 黏聚力C/Pa 直剪实验 2.00×104 内摩擦角φ/(°) 4.10×10-1 
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表 2 模拟与实验数据
Table 2. Simulation and experimental data
工况 深度/cm 径宽/cm 模拟结果 实验结果 模拟结果 实验结果 1 12.40 10.89 4.83 6.69 2 8.60 6.73 3.60 5.13 3 6.30 5.68 3.07 4.91 4 12.90 11.19 3.00 4.13 5 9.20 9.17 4.40 6.15 6 6.46 5.55 2.45 3.21 7 10.60 9.30 3.60 5.12 8 17.36 15.10 4.87 7.19
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表 3 实验因素及水平
Table 3. Test factors and levels
因素 编码 水平 -1 0 1 喷嘴直径/mm X1 0.9 1.2 1.5 射流靶距/cm X2 1.0 3.0 5.0 射流压力/MPa X3 3.2 5.0 7.2
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表 4 响应面实验设计及结果
Table 4. Response surface test design and results
序号 X1/mm X2/cm X3/MPa Y1/cm Y2/cm 1 -1 -1 0 5.0 3.1 2 1 -1 0 11.3 4.3 3 -1 1 0 4.2 4.0 4 1 1 0 8.1 6.3 5 -1 0 -1 2.5 3.4 6 1 0 -1 7.6 5.1 7 -1 0 1 8.4 4.6 8 1 0 1 19.9 6.6 9 0 -1 -1 7.7 3.0 10 0 1 -1 4.2 4.0 11 0 -1 1 15.8 4.0 12 0 1 1 8.4 5.7 13 0 0 0 9.3 5.1 14 0 0 0 9.3 5.1 15 0 0 0 9.3 5.1 16 0 0 0 9.3 5.1 17 0 0 0 9.3 5.1
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表 5 射流孔深度模型方差的分析结果
Table 5. Analytical results of variance of jet hole depth model
方差来源 平方和 自由度 平均方差 F值 P值 显著性 回归模型 265.15 9 29.46 13.16 0.001 3 显著 X1 89.78 1 89.78 40.10 0.000 4 — X2 27.64 1 27.64 12.34 0.009 8 — X3 117.07 1 117.07 52.29 0.000 2 — X1 X2 1.46 1 1.46 0.65 0.445 2 — X1 X3 10.23 1 10.23 4.57 0.069 9 — X2 X3 3.95 1 3.95 1.77 0.225 6 — X12 2.55 1 2.55 1.14 0.321 4 — X22 8.06 1 8.06 3.60 0.099 7 — X32 4.92 1 4.92 2.20 0.181 9 — 残差 15.67 7 2.24 — — — 失拟度 15.67 3 5.22 — — — 纯误差 0.00 4 0.00 — — — 总和 280.83 16 — — — —
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表 6 射流孔径宽模型方差的分析结果
Table 6. Analytical results of variance of jet hole diameter width model
方差来源 平方和 自由度 平均方差 F值 P值 显著性 回归模型 17.16 9 1.91 853.50 < 0.000 1 显著 X1 6.52 1 6.52 2 916.67 < 0.000 1 — X2 3.96 1 3.96 1 774.50 < 0.000 1 — X3 3.57 1 3.57 1 597.17 < 0.000 1 — X1 X2 0.33 1 0.33 149.33 < 0.000 1 — X1 X3 0.02 1 0.02 9.33 0.018 5 — X2 X3 0.13 1 0.13 58.33 0.000 1 — X12 0.001 4 1 0.001 4 0.61 0.459 0 — X22 2.31 1 2.31 1 032.19 < 0.000 1 — X32 0.23 1 0.23 103.77 < 0.000 1 — 残差 0.02 7 0.002 2 — — — 失拟度 0.02 3 0.005 2 — — — 纯误差 0.00 4 0.00 — — — 总和 17.18 16 — — — —
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表 7 破土施工参数优化设计目标
Table 7. Objectives for optimizing design of construction parameters of ground breaking
待优化参数 取值范围 目标值 最小值 最大值 X1/mm 0.9 1.5 0.9~1.5 X2/cm 1 5 1~5 X3/MPa 3.2 7.2 3.2~7.2 Y1/cm 2.4 20 10，15，20 Y2/cm 2.9 6.5 最小值
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表 8 响应面优化设计结果
Table 8. Results of response surface optimized design
方案 设计变量 目标函数值 满意度 喷嘴直径/mm 射流靶距/cm 射流压力/MPa 射流孔深度/cm 射流孔径宽/cm 1 0.928 1 7.2 10 3.33 0.948 2 1.164 1 7.2 15 3.858 0.868 3 1.345 1 7.2 20 4.277 0.757
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表 9 优化结果验证
Table 9. Optimization result verification
方案 射流孔深度/cm 误差/% 射流孔径宽/cm 误差/% 预测值 实验值 预测值 实验值 1 10 8.943 11.81 3.33 3.789 12.12 2 15 13.905 7.87 3.858 3.94 2.28 3 20 17.545 13.99 4.277 4.366 2.06
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