A quantitative evaluation method regarding the natural void ratio of undisturbed loess
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摘要:
天然孔隙比是初始结构的基本表征参数, 故从岩土角度对黄土天然孔隙比分布规律进行分析和预测, 对于掌握原位黄土灾变力学行为并进行灾害预警工作具有重要意义。通过选取典型场地不同层位原状黄土开展了颗粒分析试验、X射线衍射(XRD)试验、天然孔隙比试验和一维固结试验, 分析得到了天然孔隙比与颗粒组分、应力历史的相关规律。结果表明, 天然孔隙比受应力历史和颗粒级配影响, 上覆压力越大, 级配越均匀, 天然孔隙比越小, 同时含水状态也可能是天然孔隙比变化的原因之一。在此基础上, 以层位埋深、颗粒级配不均匀系数和曲率系数、天然含水量作为影响因素, 基于BP神经网络对天然孔隙比进行了定量评价。引入麻雀算法(SSA)与粒子群优化算法(PSO), 建立了BP、SSA-BP与PSO-BP神经网络的天然孔隙比预测模型。随机选取51组实测数据进行了模型训练, 将训练后的模型对16组验证与测试数据进行了预测, 并将预测结果与实测天然孔隙比进行了对比。结果表明基于PSO-BP的神经网络模型预测效果显著优于SSA-BP、BP神经网络模型, 可以有效预测天然孔隙比。
Abstract:Objective The natural void ratio is the most frequently used and important characterisation parameter of the initial structure at the macroscopic level. Therefore, the analysis and prediction of the distribution pattern of the natural void ratio of loess is important for understanding undisturbed loess disaster mechanics behaviour and for disaster early warning from the geotechnical point of view.
Methods In this study, particle analysis tests, XRD tests, natural void ratio tests and 1D consolidation tests were carried out on in situ soil samples from different layers of a typical loess site to analyse the correlation between the natural void ratio and particle fraction and stress history. The results show that the natural void ratio can be affected by the stress history and particle size distribution. The higher the overburden pressure is, the more uniform the grading is and the smaller the natural pore ratio is. The water content may be one of the reasons for the variation in the natural void ratio.
Results On this basis, the burial depth of the layer, the inhomogeneous coefficient and curvature coefficient of particle gradation, and the natural water content are selected as the influencing factors, and the natural void ratio is evaluated quantitatively based on the machine learning algorithm. The SSA and PSO algorithm were introduced to optimise the weights and thresholds of the BP neural network, and natural void ratio predicted models based on the BP, SSA-BP and PSO-BP neural networks were established. The trained BP, SSA-BP and PSO-BP neural network models were then used to predict 16 sets of validation and test data, and the predicted results were compared with the measured natural void ratios.
Conclusion The results show that the PSO-BP-based neural network model predicts significantly better than the SSA-BP and BP neural network models, and can effectively predict the natural void ratio.
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Key words:
- undisturbed loess /
- natural void ratio /
- particle gradation /
- stress history /
- BP neural network
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图 3 粒径级配曲线
a.T0探井粒径微分质量分数曲线; b.T0探井累计质量分数曲线; c.T5探井粒径微分质量分数曲线; d. T5探井累计质量分数曲线; e.T8探井粒径微分质量分数曲线; f.T8探井累计质量分数曲线
Figure 3. Particle size distribution curves
图 4 Q3黄土(a)、古土壤(b)以及Q2黄土(c)的XRD曲线
Figure 4. XRD curves of Q3 loess(a), paleosols (b) and Q2 loess (c)
图 5 天然孔隙比与Q3黄土、古土壤和Q2黄土的固结曲线
Figure 5. Natural void ratio and consolidation curves of Q3 loess, paleosols and Q2 loess
图 6 天然孔隙比随天然含水量变化散点图
Figure 6. Scatter plot of the natural void ratio versus water content
图 9 不同训练集组数下验证集部分评价指标图
Figure 9. Partial evaluation index chart of the validation set with different numbers of trainings
图 10 天然孔隙比预测值与真实值对比图
Figure 10. Compared values of predicted and measured natural void ratio
表 1 一维固结试验方案
Table 1. One-dimensional consolidation test scheme
土层类型 固结压力/kPa Q3黄土 14.35, 64.40, 120.45, 222 古土壤 259, 333 Q2黄土 370, 480 
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表 2 天然孔隙比部分实测数据
Table 2. Selected measured data for soil with natural void ratio
类型 孔隙比 深度/m 曲率系数 不均匀系数 天然含水量/% 验证集 0.975 16 0.880 4 7.511 5 15.28 0.773 18 0.890 4 9.123 3 15.46 1.030 8 0.950 8 12.406 2 11.46 1.029 10 0.728 1 13.472 8 13.48 1.149 4 1.355 0 8.730 0 12.19 1.133 2 1.396 0 8.796 0 11.66 0.903 26 1.026 9 7.860 8 15.35 0.741 20 1.372 7 9.001 8 16.93 0.937 12 0.835 9 8.548 1 14.02 0.835 24 1.446 6 9.107 3 17.27 1.003 6 1.278 6 8.668 2 7.33 0.913 24 1.571 4 7.516 5 19.51 1.094 8 1.356 8 8.966 8 15.03 测试集 1.194 3.3 2.240 0 6.170 0 10.10 0.802 19.3 1.570 0 11.480 0 15.70 0.762 17.3 1.420 0 7.800 0 8.60
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表 3 隐含层激活函数对BP神经网络验证集预测结果影响
Table 3. Influence of the hidden layer activation function on the BP neural network validation set predicted results
隐含层函数 相关系数R2 均方误差MSE/% 平均绝对误差MAE/% 平均绝对百分比误差MAPE/% 纯均方误差MSPE/% Logsig 0.682 0.47 6.01 6.62 14.86 Tansig 0.729 0.40 5.64 6.16 13.57
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表 4 不同训练集组数下BP神经网络预测结果
Table 4. Predicted results of the BP neural network under different numbers of trainings
训练集组数 相关系数R2 均方误差MSE/% 平均绝对误差MAE/% 平均绝对百分比误差MAPE/% 纯均方误差MSPE/% 51 0.729 0.40 5.64 6.16 1.357 52 0.733 0.46 5.92 6.61 1.483 53 0.681 0.42 5.78 6.36 1.418 54 0.739 0.33 5.70 6.26 1.275 55 0.737 0.32 6.14 6.77 1.267 56 0.665 0.38 6.43 7.33 1.361
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表 5 BP神经网络、SSA-BP神经网络、PSO-BP神经网络预测结果
Table 5. Predicted results of the BP neural network, SSA-BP neural network, PSO-BP neural network
类型 预测方法 相关系数R2 均方误差MSE/% 平均绝对误差MAE/% 平均绝对百分比误差MAPE/% 纯均方误差MSPE/% 验证集 BP神经网络 0.729 0.40 5.64 6.16 13.57 SSA-BP神经网络 0.769 0.35 5.45 6.05 12.97 PSO-BP神经网络 0.772 0.33 5.12 5.41 11.39 测试集 BP神经网络 0.756 0.21 9.39 10.77 10.19 SSA-BP神经网络 0.860 0.22 7.08 8.86 11.53 PSO-BP神经网络 0.946 0.09 6.33 6.71 6.00
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