<p>This research aimed to determine whether unconfined compressive strength (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(UCS\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">UCS</mi> </mrow> </math></EquationSource> </InlineEquation>) of low-quality granular materials saturated with natural pozzolanic geopolymer can be predicted using machine learning. The models to predict <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(UCS\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">UCS</mi> </mrow> </math></EquationSource> </InlineEquation> were effectively established via the use of the Extremely Randomized Tree (<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(ETR\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">ETR</mi> </mrow> </math></EquationSource> </InlineEquation>) and Decision Tree (<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(DT\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">DT</mi> </mrow> </math></EquationSource> </InlineEquation>) methodologies. Hippopotamus Optimizer (<InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="39" /> </InlineMediaObject> <EquationSource Format="TEX">\(HiO\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">HiO</mi> </mrow> </math></EquationSource> </InlineEquation>) utilized for hyperparameter tuning to improve the expected precision and durability of the <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq4.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\(DT\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">DT</mi> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq3.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="43" /> </InlineMediaObject> <EquationSource Format="TEX">\(ETR\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">ETR</mi> </mrow> </math></EquationSource> </InlineEquation> models. The results showed how well machine training-driven methods can assess granular materials stability and provide a useful analysis for enhancing geotechnical engineering methods through the utilization of data-driven modeling application tools. Based on the information provided, it was probable that <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="TEX">\(Hi{O}_{ETR}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mi>i</mi> <msub> <mi>O</mi> <mrow> <mi mathvariant="italic">ETR</mi> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(Hi{O}_{DT}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mi>i</mi> <msub> <mi>O</mi> <mrow> <mi mathvariant="italic">DT</mi> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation> would both calculate <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="42" /> </InlineMediaObject> <EquationSource Format="TEX">\(UCS\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">UCS</mi> </mrow> </math></EquationSource> </InlineEquation> accurately. The <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq8.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="64" /> </InlineMediaObject> <EquationSource Format="TEX">\(Hi{O}_{ETR}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mi>i</mi> <msub> <mi>O</mi> <mrow> <mi mathvariant="italic">ETR</mi> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation> yielded low <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq12.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="60" /> </InlineMediaObject> <EquationSource Format="TEX">\(RMSE\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="italic">RMSE</mi> </mrow> </math></EquationSource> </InlineEquation> index values, namely 0.3302 for the training stage and 0.3542 for the testing stage. The <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40515_2025_701_Article_IEq9.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="55" /> </InlineMediaObject> <EquationSource Format="TEX">\(Hi{O}_{DT}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <mi>i</mi> <msub> <mi>O</mi> <mrow> <mi mathvariant="italic">DT</mi> </mrow> </msub> </mrow> </math></EquationSource> </InlineEquation> findings during the training and testing phases demonstrated greater reliability than previous results, with improvement percentages of -16.523% in training and −14.177% in testing.</p>

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Prediction of Unconfined Compressive Strength in Pozzolanic Geopolymer-Stabilized Granular Materials Using Tree-Based Models

  • Mahzad Esmaeili-Falak,
  • Afshin Letafat

摘要

This research aimed to determine whether unconfined compressive strength ( \(UCS\) UCS ) of low-quality granular materials saturated with natural pozzolanic geopolymer can be predicted using machine learning. The models to predict \(UCS\) UCS were effectively established via the use of the Extremely Randomized Tree ( \(ETR\) ETR ) and Decision Tree ( \(DT\) DT ) methodologies. Hippopotamus Optimizer ( \(HiO\) HiO ) utilized for hyperparameter tuning to improve the expected precision and durability of the \(DT\) DT and \(ETR\) ETR models. The results showed how well machine training-driven methods can assess granular materials stability and provide a useful analysis for enhancing geotechnical engineering methods through the utilization of data-driven modeling application tools. Based on the information provided, it was probable that \(Hi{O}_{ETR}\) H i O ETR and \(Hi{O}_{DT}\) H i O DT would both calculate \(UCS\) UCS accurately. The \(Hi{O}_{ETR}\) H i O ETR yielded low \(RMSE\) RMSE index values, namely 0.3302 for the training stage and 0.3542 for the testing stage. The \(Hi{O}_{DT}\) H i O DT findings during the training and testing phases demonstrated greater reliability than previous results, with improvement percentages of -16.523% in training and −14.177% in testing.