Prediction of the compression index and swell index of soft soils via an optimized multiple-output neural network
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摘要:
软弱土的压缩指数$ {C_{\mathrm{c}}} $和回弹指数$ {C_{\mathrm{s}}} $是计算土体沉降和回弹的重要参数，采用机器学习算法可高效预测$ {C_{\mathrm{c}}} $和$ {C_{\mathrm{s}}} $，减少室内试验周期和费用。引入孔压静力触探（CPTU）原位测试数据，利用土类指数${I_{\mathrm{c}}}$量化土层信息，融合室内试验和原位测试数据，改进遗传算法优化的BP神经网络（GA-BPNN），实现多输出功能，同时预测$ {C_{\mathrm{c}}} $和$ {C_{\mathrm{s}}} $。通过相关性分析，确定多输出GA-BPNN模型输入参数，利用TC 304标准场地数据库，将预测结果与多输出BPNN模型、单输出GA-BPNN模型比较，进而验证多输出GA-BPNN模型能效，并获得预训练模型参数。在南京有限场地数据条件下，进一步讨论多输出GA-BPNN模型的优越性，分析预训练、原位测试数据对模型效果的影响，最后进行敏感性分析。结果表明，利用标准场地数据获得预训练多输出GA-BPNN模型，在有限数据条件下，可有效预测$ {C_{\mathrm{c}}} $和$ {C_{\mathrm{s}}} $；加入原位测试数据的的GA-BPNN模型预测$ {C_{\mathrm{c}}} $(${R^2} = 0.96$)和$ {C_{\mathrm{s}}} $(${R^2} = 0.97$)精确度较高，预测结果更加接近实测值，预测结果相关性与已有研究保持一致。通过预训练的多输出GA-BPNN模型，可在有限场地数据条件下，快速准确预测软弱土的$ {C_{\mathrm{c}}} $和$ {C_{\mathrm{s}}} $，对工程实践中的多元参数预测具有良好的应用前景。
Abstract:Objective The compression index
C c and swell indexC s of soil are critical parameters for calculating soil settlement and swelling. Utilizing machine learning algorithms to predict these indices quickly and efficiently can significantly reduce testing duration and costs.Methods In this study, we introduce Piezocone Penetration Test (CPTU) in-situ data and quantify soil layer information using the Soil Behaviour Type (SBT) index
I c. We then combine laboratory data with CPTU data to develop a multi-output genetic algorithm-optimized backpropagation neural network (GA-BPNN) model. The input parameters for the multi-output GA-BPNN model were determined through correlation analysis. Using the TC304 standard site database, the prediction results from the multi-output GA-BPNN model were compared with those from the multi-output BPNN model and the single-output GA-BPNN model, verifying the effectiveness of the multi-output GA-BPNN model and obtaining pre-trained model parameters. For sites with limited data in Nanjing, the superiority of the multi-output BPNN model was further evaluated by analyzing the impact of pre-training and in-situ test data on model performance. A sensitivity analysis was also conducted to assess the robustness of the model.Results The results demonstrate that the pre-trained multi-output GA-BPNN model, derived from standard site data, can effectively predict the compression and swell indices under limited data conditions. When combined with in-situ test data, the multi-output GA-BPNN model exhibits high prediction accuracy for these indices, with predicted values closely matching measured data. The consistency of the predicted results aligns well with existing studies.
Conclusion The pre-trained multi-output GA-BPNN model can efficiently predict the compression and swell indices of soft soil under limited data conditions. The proposed method shows significant potential for multi-parameter prediction in engineering practice, enhancing the efficiency and reliability of geotechnical engineering assessments.
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Key words:
- compression index /
- swell index /
- multiple-output /
- optimized neural network /
- GA-BPNN model /
- soft soil
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图 6 TC304场地模型训练过程均方误差变化曲线
Figure 6. Error variation curve during model training at the TC304 site
图 7 TC304场地BPNN和GA-BPNN训练集性能对比
Figure 7. Comparison of the performance of the BPNN model and GA-BPNN model training sets at the TC304 site
图 8 TC304场地BPNN和GA-BPNN测试集性能对比
Figure 8. Comparison of testing set performance of BPNN model and GA-BPNN model at the TC304 site
图 10 TC304场地回弹指数$ {C_{\mathrm{s}}} $和压缩指数$ {C_{\mathrm{c}}} $相关性
Figure 10. Compression and swell index correlation at the TC304 site
图 12 南京场地压缩指数$ {C_{\mathrm{c}}} $和回弹指数$ {C_{\mathrm{s}}} $相关性
Figure 12. Compression and swell index correlation at the Nanjing site
图 13 南京场地GA-BPNN模型与经验公式预测结果对比
Figure 13. Comparison of the GA-BPNN model and empirical formula prediction results at the Nanjing site
图 15 南京场地GA-BPNN训练集性能对比
Figure 15. Comparison of the training set performance of the GA-BPNN at the Nanjing site
图 16 南京场地GA-BPNN模型测试集性能对比
Figure 16. Comparison of the testing set performance of the GA-BPNN model at the Nanjing site
图 17 南京场地模型预测值和实测值对比
Figure 17. Comparison of the predicted and measured values at the Nanjing site
表 1 经验预测公式总结
Table 1. Summary of the empirical prediction formulas
压缩性指数 参数 相关性 适用土类 参考文献 ${C_{\mathrm{c}}}$ $ {{{w}}_{\text{n}}} $ $ {C_{\mathrm{c}}} = 0.01{{{w}}_{\text{n}}} - 0.05 $ 所有土 AZZOUZ等[9] $ {C_{\mathrm{c}}} = 0.01{{{w}}_{\text{n}}} $ 黏土 KOPPULA等[10] $ {C_{\mathrm{c}}} = 0.01{{{w}}_{\text{n}}}-{0}{\text{.075}} $ 黏土 HERRERO[11] $ {C_{\mathrm{c}}} = 0.013{{{w}}_{\text{n}}} - 0.115 $ 黏土 PARK等[12] $ {C_{\mathrm{c}}} = 0.008{{{w}}_{\text{n}}} + 0.063 $ 淤泥 赵有明等[13] $ {C_{\mathrm{c}}} = 0.008{{{w}}_{\text{n}}} - 0.024 $ 淤泥 顾小芸[14] $ {C}_{{\mathrm{c}}}=1.843（0.01{{w}}_{\text{n}}-0.222） $ 淤泥质土 魏道垛等[15] e ${C_{\mathrm{c}}} = 0.54{{e - 0}}{\text{.19}}$ 黏土 NISHIDA[16] ${C_{\mathrm{c}}} = 0.43{{e - 0}}{\text{.11}}$ 黏土 COZZOLINO[17] ${C_{\mathrm{c}}} = 0.49{{e - 0}}{\text{.11}}$ 黏土 PARK等[12] ${C_{\mathrm{c}}} = 0.521{{e - 0}}{\text{.2874}}$ 黏土 朱小林[18] ${{{w}}_{\text{L}}}$ ${C_{\mathrm{c}}} = 0.006{{{w}}_{\mathrm{L}}}{{ - 0}}{\text{.054}}$ 黏土 AZZOUZ等[9] ${C_{\mathrm{c}}} = \dfrac{{({{{w}}_{\mathrm{L}}}{{ - 13)}}}}{{109}}$ 黏土 MAYNE[19] ${C_{\mathrm{c}}} = 0.014{{{w}}_{\mathrm{L}}}{{ - 0}}{\text{.168}}$ 黏土 PARK等[12] ${C_{\mathrm{c}}} = 0.022{{{w}}_{\mathrm{L}}}{- {0}}{\text{.528}}$ 淤泥质土 孙更生等[20] $ {{w}}_{\text{n}}，{{w}}_{\text{L}} $ ${C_{\mathrm{c}}} = 0.009{{{w}}_{\text{n}}} + 0.005{{{w}}_{\text{L}}}$ 黏土 KOPPULA等[10] ${C_{\mathrm{c}}} = 0.009{{{w}}_{\text{n}}} + 0.002{{{w}}_{\text{L}}} - 0.001$ 黏土 AZZOUZ等[9] $ {{w}}_{\text{n}}，{e} $ ${C_{\mathrm{c}}} = 0.4{{e + 0}}{\text{.000\ 4}}{{{w}}_{\text{n}}}{{ - 0}}{\text{.01}}$ 黏土 AZZOUZ等[9] ${C_{\text{s}}}$ ${{{w}}_{\text{n}}}$ ${C_{\mathrm{s}}} = 0.000\ 87{{{w}}_{\text{n}}}$ 海相黏土 ALPTEKIN等[21] $ {C_{\mathrm{s}}} = 0.013\ 3{{\text{e}}^{0.036{{{w}}_{\text{n}}}}} $（式中e为自然底数） 淤泥质土 IŞIK[22] ${{{w}}_{\text{L}}}$ $ {C_{\mathrm{s}}} = 0.021\ 4 + 0.001\ 3{{{w}}_{\text{L}}} $ 海相黏土 ALPTEKIN等[21] $ {{w}}_{\text{L}}，{{G}}_{\text{s}} $ ${C_{\mathrm{s}}} = 0.000\ 463{{{w}}_{\text{L}}} \cdot {{{G}}_{\text{s}}}$ 所有土 NAGARAJ等[23] ${{{w}}_{\text{P}}}$ ${C_{\mathrm{s}}} = 0.001\ 94({{{w}}_{\text{P}}}{{ - 4}}{\text{.6)}}$ 黏土 NAKASE等[24] ${I_{\text{p}}}$ ${C_{\mathrm{s}}} = 0.003{I_{\text{p}}} - 0.005$ 粉质黏土 楼晓明等[2] ${{e}}$ ${C_{\mathrm{s}}} = 0.0121{{{{\mathrm{e}}}}^{1.313\ 1{{e}}}}$（底数中e为自然底数） 淤泥质土 IŞIK[22] $ {e}，\rho ，{{w}}_{\text{L}} $ ${C_{\mathrm{s}}} = - 0.05 + 0.075e + 0.015\rho + 0.000\ 3{{{w}}_{\text{L}}}$ 海相黏土 ALPTEKIN等[21] 注：wn. 含水率；e. 孔隙比；wL. 液限指数；wP. 塑限指数；IP. 塑性指数；Gs. 相对密度；ρ. 密度；下同 
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表 2 室内试验数据统计分析
Table 2. Statistical analysis of laboratory data
参数 H/m wn/% γ/(KN·m−3) e wL/% wp/% Ip IL $\sigma {'_{\mathrm{v}}}$/kPa ${C_{\mathrm{c}}}$ ${C_{\mathrm{s}}}$ 平均值 7.153 43.352 17.59 1.198 44.922 23.504 21.419 1.249 65.476 0.315 0.05 最小值 0.3 23 14.98 0.520 19 12 1 0.150 4 0.052 0.012 最大值 20.1 74.9 20.6 2.360 94 39 60.6 6.183 213.82 0.700 0.15 标准误差 0.463 0.958 0.083 0.025 1.452 0.332 1.216 0.085 4.594 0.011 0.003 注：参数含义见正文
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表 3 土类指数${I_{\mathrm{c}}}$分类表[47]
Table 3. Soil behaviour type index ${I_{\mathrm{c}}}$ chart
土类 ${I_{\mathrm{c}}}$ 砾砂−砂 ${I_{\mathrm{c}}} < 1.31$ 砂土：纯净砂−粉质砂土 $1.31 < {I_{\mathrm{c}}} < 2.05$ 砂土混合物：粉质砂土−砂质粉土 $2.05 < {I_{\mathrm{c}}} < 2.60$ 粉土混合物：黏质粉土−粉质黏土 $2.60 < {I_{\mathrm{c}}} < 2.95$ 黏土：黏土−粉质黏土 $2.95 < {I_{\mathrm{c}}} < 3.60$ 有机质土−泥炭 ${I_{\mathrm{c}}} > 3.60$
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表 4 多模型输入数据相关性分析
Table 4. Model input data correlation analysis
参数 e wn/% wL/% wp/% $\gamma $/(kN·m−3) $ \sigma {'_v} $/kPa H/m Ip IL Ic e 1 0.93 0.49 0.42 0.76 0.37 0.22 0.47 0.07 0.26 wn/% 1 0.44 0.34 0.70 0.48 0.32 0.44 0.16 0.31 wL/% 1 0.77 0.47 0.51 0.48 0.99 0.51 0.09 wp/% 1 0.40 0.27 0.25 0.64 0.39 0.44 $\gamma $/(kN·m−3) 1 0.21 0.14 0.46 0.18 0.23 $ \sigma {'_v} $/kPa 1 0.94 0.54 0.07 0.05 H/m 1 0.50 0.17 0.04 Ip 1 0.50 0.15 IL 1 0.27 Ic 1 注：参数含义见正文
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表 5 南京场地不同GA-BPNN模型检验结果
Table 5. Different GA-BPNN model test results at the Nanjing site
模型 数据集 输出参数 ${R^2}$ 均方根误差
RMSE平均绝对偏差
MAE模型1 训练集 $ {C_{\mathrm{c}}} $ 0.79 2.2×10−2 1.9×10−2 $ {C_{\text{s}}} $ 0.81 5.0×10−3 4.0×10−3 测试集 $ {C_{\mathrm{c}}} $ 0.82 2.9×10−2 2.5×10−2 $ {C_{\text{s}}} $ 0.84 6.0×10−3 5.0×10−3 模型2 训练集 $ {C_{\mathrm{c}}} $ 0.93 1.4×10−2 1.0×10−2 $ {C_{\text{s}}} $ 0.99 1.0×10−3 1.0×10−3 测试集 $ {C_{\mathrm{c}}} $ 0.96 1.3×10−2 1.1×10−2 $ {C_{\text{s}}} $ 0.97 2.0×10−3 1.0×10−3
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