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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mater.</journal-id>
<journal-title>Frontiers in Materials</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mater.</abbrev-journal-title>
<issn pub-type="epub">2296-8016</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1270082</article-id>
<article-id pub-id-type="doi">10.3389/fmats.2023.1270082</article-id>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Materials</subject>
<subj-group>
<subject>Original Research</subject>
</subj-group>
</subj-group>
</article-categories>
<title-group>
<article-title>Study on the mechanical properties of embankment soil under long-term immersion conditions</article-title>
<alt-title alt-title-type="left-running-head">Zhang et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/fmats.2023.1270082">10.3389/fmats.2023.1270082</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Zhang</surname>
<given-names>Kun</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/2386959/overview"/>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/data-curation/"/>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/methodology/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Feng</surname>
<given-names>Di</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<role content-type="https://credit.niso.org/contributor-roles/conceptualization/"/>
<role content-type="https://credit.niso.org/contributor-roles/funding-acquisition/"/>
<role content-type="https://credit.niso.org/contributor-roles/investigation/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Zhikui</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<role content-type="https://credit.niso.org/contributor-roles/formal-analysis/"/>
<role content-type="https://credit.niso.org/contributor-roles/writing-original-draft/"/>
<role content-type="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/"/>
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<aff id="aff1">
<sup>1</sup>
<institution>Department of Civil and Transportation Engineering</institution>, <institution>Hohai University</institution>, <addr-line>Nanjing</addr-line>, <country>China</country>
</aff>
<aff id="aff2">
<sup>2</sup>
<institution>China Railway Construction Underwater Shield Tunnel Engineering Laboratory</institution>, <institution>China Railway 14th Bureau Group Co., Ltd.</institution>, <addr-line>Jinan</addr-line>, <country>China</country>
</aff>
<author-notes>
<fn fn-type="edited-by">
<p>
<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/857096/overview">Yunchao Tang</ext-link>, Guangxi University, China</p>
</fn>
<fn fn-type="edited-by">
<p>
<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2397484/overview">Shu Fang</ext-link>, Guangzhou University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1465856/overview">Jue Li</ext-link>, Chongqing Jiaotong University, China</p>
<p>
<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/1564938/overview">Abdoullah Namdar</ext-link>, Huaiyin Institute of Technology, China</p>
</fn>
<corresp id="c001">&#x2a;Correspondence: Di Feng, <email>fengdi@126.com</email>
</corresp>
</author-notes>
<pub-date pub-type="epub">
<day>26</day>
<month>10</month>
<year>2023</year>
</pub-date>
<pub-date pub-type="collection">
<year>2023</year>
</pub-date>
<volume>10</volume>
<elocation-id>1270082</elocation-id>
<history>
<date date-type="received">
<day>31</day>
<month>07</month>
<year>2023</year>
</date>
<date date-type="accepted">
<day>16</day>
<month>10</month>
<year>2023</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2023 Zhang, Feng and Wang.</copyright-statement>
<copyright-year>2023</copyright-year>
<copyright-holder>Zhang, Feng and Wang</copyright-holder>
<license xlink:href="http://creativecommons.org/licenses/by/4.0/">
<p>This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</p>
</license>
</permissions>
<abstract>
<p>During flood season, embankments are often submerged in high water levels for extended periods, leading to deterioration in their soil mechanics performance and increasing the risk of slope instability and other hazards. In order to investigate the changes in mechanical properties of embankment slopes during long-term water immersion, direct shear tests were conducted. Scanning electron microscopy, chemical composition analysis, and laser particle size analysis were conducted on samples taken at different immersion periods. Clay samples were taken from the embankments at Jiangxinzhou in Nanjing, Jiangsu Province, China. Results showed the shear strength of the soil gradually decreases with the increase of immersion time, while the cohesive force and internal friction angle gradually decrease as well. This suggests that immersion has a softening effect on the shear strength of the soil. As the immersion time increases, the colloidal particles (soluble salt) rapidly dissolves, the microstructure of the soil is destroyed, and sticky particles increases, resulting in a change in the shear strength of the soil. The research results provide a basis for flood control and prevention of embankments immersed in high water levels for long periods during the flood season.</p>
</abstract>
<kwd-group>
<kwd>embankment soil</kwd>
<kwd>shear strength</kwd>
<kwd>long-term immersion</kwd>
<kwd>mechanical properties</kwd>
<kwd>slope instability</kwd>
</kwd-group>
<custom-meta-wrap>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Structural Materials</meta-value>
</custom-meta>
</custom-meta-wrap>
</article-meta>
</front>
<body>
<sec id="s1">
<title>1 Introduction</title>
<p>In recent years, due to the frequent occurrence of extreme weather events during the flood season (<xref ref-type="bibr" rid="B28">Xie et al., 2023</xref>), the water levels of rivers, lakes, and seas have continued to rise under continuous heavy rainfall and have remained at high levels for a long time. The action of water leads to various forms of deterioration of the embankment soil, which can easily lead to dangerous situations such as landslides, collapses, and pipeline surges (<xref ref-type="bibr" rid="B3">Fujii et al., 2020</xref>; <xref ref-type="bibr" rid="B6">Lemmens et al., 2016</xref>; <xref ref-type="bibr" rid="B33">Zhou et al., 2023</xref>). On the early morning of 8 November 2017, around 5 o&#x2019;clock, a river collapsed near Zhinan Village, Sanmao Street, Yangzhong City, Jiangsu Province, China. On the morning of 17 August 2020, at 7 o&#x2019;clock, during an inspection, the government of Luoshui Town, Shifang City, Deyang City, Sichuan Province, China, discovered a dangerous situation in the Zhonghekou section of Shitingjiang, Luoshui Town. Due to the erosion of floodwaters, more than 250&#xa0;m of the embankment collapsed, resulting in an economic loss of more than 4&#xa0;million.</p>
<p>Existing literature has shown that soil strength is a critical parameter in assessing slope stability (<xref ref-type="bibr" rid="B5">Kimura et al., 2014</xref>; <xref ref-type="bibr" rid="B8">Lian et al., 2020</xref>; <xref ref-type="bibr" rid="B16">Namdar et al., 2020</xref>; <xref ref-type="bibr" rid="B21">Sassa et al., 2004</xref>; <xref ref-type="bibr" rid="B26">Wen and He, 2012</xref>) and that clay exhibits strong sensitivity to water (<xref ref-type="bibr" rid="B20">Philip, 1961</xref>). Changes in the water environment can cause changes in soil performance (<xref ref-type="bibr" rid="B9">Liang et al., 2018</xref>; <xref ref-type="bibr" rid="B12">Ma et al., 2023</xref>; <xref ref-type="bibr" rid="B29">Xu et al., 2012</xref>). For instance, <xref ref-type="bibr" rid="B13">Maihemuti et al. (2016)</xref> studied the influence of periodic changes in reservoir water level on landslide stability, while <xref ref-type="bibr" rid="B30">Ying et al. (2021)</xref> investigated the impact of long-term inundation on the chemical and mechanical properties of silty soil in the Three Gorges Reservoir area. After different immersion periods, <xref ref-type="bibr" rid="B27">Wen and Ji (2018)</xref> explored the residual strength changes of different slip zones in five large landslides. During flood season, embankments are often immersed in high water levels for extended periods, leading to the deterioration of soil characteristics due to the interaction between soil and water. It is generally recognized that water level fluctuations play a crucial role in the stability of embankment slopes. However, more attention must be paid to the strength variation and causes of disturbed clay in embankments immersed in high water levels for extended periods during flood season.</p>
<p>In addition, the particle size distribution of soil, soil bonding materials, and mechanical properties are closely related to the strength of the soil (<xref ref-type="bibr" rid="B17">Namdar et al., 2014</xref>; <xref ref-type="bibr" rid="B19">Nie et al., 2021</xref>; <xref ref-type="bibr" rid="B22">Song and Hong, 2020</xref>). The composition and properties of bonding materials determine the strength of the soil. Coarse mineral particles play a skeletal role in the soil structure, while finer particles often fill the gaps between the coarse particles. Bonding materials such as clay minerals and water-soluble salts also fill the gaps between coarse and fine particles, playing a bonding role. <xref ref-type="bibr" rid="B2">Fan et al. (2017)</xref> found that the volume and strength of loess samples decrease as the particle size decreases. <xref ref-type="bibr" rid="B14">Manmatharajan et al. (2023)</xref> studied how particle size distribution, acceptable powder content, and compressibility affect the strength after liquefaction in simple shear tests. Based on the above literature, laser particle size analyzers can obtain the particle size distribution under different immersion conditions and explore particle composition&#x2019;s influence on the soil&#x2019;s shear strength.</p>
<p>Using scanning electron microscopy, <xref ref-type="bibr" rid="B10">Lin and Cerato (2014)</xref> studied the applications of investigating the microstructure of shale weathering expansive soil during the expansion-contraction cycle, while <xref ref-type="bibr" rid="B34">Zhu et al. (2022)</xref> observed changes in the loess&#x2019;s particle and pore size distribution. These studies demonstrate the potential of scanning electron microscopy for analyzing changes in soil structure and pore characteristics (<xref ref-type="bibr" rid="B7">Li et al., 2019</xref>; <xref ref-type="bibr" rid="B23">Sun et al., 2023</xref>; <xref ref-type="bibr" rid="B24">Tang et al., 2020</xref>). The impact of immersion time on disturbance-induced changes in clay structure in embankments remains unclear.</p>
<p>The embankment project refers to the water-retaining buildings built along rivers, lakes, canals, coasts, or flood zones. Flood zones, the edge of the part, are essential to China&#x2019;s flood control engineering system. In recent years, the water level of rivers, lakes, and the sea has continued to increase due to the frequent occurrence of extreme weather during the flood season. The embankment has been in a submerged environment for a long time, resulting in an embankment deterioration phenomenon that can easily lead to landslides, subsidence, tube surge, and other dangerous situations. The research on the performance change of embankment body soil under long-term submergence conditions is still relatively small. This paper studies the deterioration mechanism of embankment flooding under long-term high-water level conditions during flood season.</p>
<p>Based on the above considerations, this research used direct shear tests, X-ray fluorescence spectrometry, laser particle size analyzers, and scanning electron microscopy techniques to explore the reasons for the change in the strength of disturbed clay in embankments with immersion time. The gray correlation entropy analysis algorithm was used to analyze the correlation between particle composition and soil strength indicators. The research results provide a basis for flood control and prevention of embankments immersed in high water levels for long periods during the flood season.</p>
</sec>
<sec sec-type="materials|methods" id="s2">
<title>2 Materials and methods</title>
<sec id="s2-1">
<title>2.1 Materials</title>
<p>
<xref ref-type="fig" rid="F1">Figure 1</xref> presents a schematic diagram of the sampling positions. Per the soil mechanics testing standard (GB/T50123-2019) (2019), the specific gravity, liquid limit, maximum dry density, and optimum moisture content of the soil were determined through experimentation and shown in <xref ref-type="table" rid="T1">Table 1</xref>.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Sampling site in Nanjing, China.</p>
</caption>
<graphic xlink:href="fmats-10-1270082-g001.tif"/>
</fig>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Basic physical characteristics.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">G<sub>s</sub>
</th>
<th align="center">Maximum dry unit weight</th>
<th align="center">Optimum water content (%)</th>
<th align="center">
<italic>w</italic>
<sub>
<italic>L</italic>
</sub> (%)</th>
<th align="center">
<italic>w</italic>
<sub>
<italic>p</italic>
</sub> (%)</th>
<th align="center">
<italic>I</italic>
<sub>
<italic>p</italic>
</sub>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">2.72</td>
<td align="center">1.68&#xa0;g/cm3</td>
<td align="center">19.86</td>
<td align="center">39.17</td>
<td align="center">19.48</td>
<td align="center">19.69</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The soil was placed in a drying box at 105&#xb0;C to dry and then crushed. The dried soil sample was passed through a 2&#xa0;mm sieve. It was then sprayed with distilled water until the water content reached 10%, stirred well, and sealed in a plastic bag for 48&#xa0;h to allow the sample to be water-balanced.</p>
</sec>
<sec id="s2-2">
<title>2.2 Methods</title>
<p>Weigh according to the target dry density (1.5&#xa0;g/cm<sup>3</sup>). Please place them in a mold with a diameter of 61.8&#xa0;mm and a height of 20&#xa0;mm, and samples are then made using the press sample method. After compaction, remove the molded samples. Eight groups of four samples each were prepared as remodeled soil samples with 10% water content and 1.5&#xa0;g/cm<sup>3</sup> density. After saturation by vacuum pumping method, one group was directly taken out and immersed in water for 1, 3, 5, 7, 10, 15, and 20&#xa0;days.</p>
<p>Samples with different immersion times were placed in a shear box. The upper box was fixed, while the lower box could slide horizontally. Vertical pressures of 100, 200, 300, and 400&#xa0;kPa were applied, respectively. Then, the horizontal shear force was gradually applied to the lower box of the shear box until the sample was sheared. The shear rate was set at v &#x3d; 2&#xa0;mm/min, the shear displacement was 6&#xa0;mm, and the readings were recorded for every 0.2&#xa0;mm shear displacement.</p>
<p>After drying and cooling the samples with different immersion times, they were ground into fine particles using a grinding rod. The prepared samples were stored in preservation bags. The samples were immersed in water for 0 and 20&#xa0;days, respectively. The soil was tested using an X-ray fluorescence spectrometer.</p>
<p>The gradient of sample immersion time was 0, 1, 3, 5, 7, 10, 15, and 20&#xa0;days. Appropriate quantities of samples were taken at each immersion time point for the tests. Perform particle size analysis on soil samples using a laser particle size analyzer. The impact of particle composition on soil shear strength was explored using the gray correlation entropy analysis algorithm.</p>
<p>The gradient of water immersion time was 0, 5, 10, and 20&#xa0;days in order, and the samples were dried. A cubic rod of approximately 1&#xa0;cm &#xd7; 1&#xa0;cm &#xd7; 2&#xa0;cm was cut from the middle of the ring knife sample after different immersion times and used as a scanning electron microscope sample. The specific operation steps of SEM testing were mentioned by <xref ref-type="bibr" rid="B18">Ni et al. (2020)</xref>.</p>
</sec>
</sec>
<sec id="s3">
<title>3 Results and analysis</title>
<sec id="s3-1">
<title>3.1 Analysis of direct shear test results</title>
<p>The shear stress-shear displacement curves of samples at different immersion times were obtained through direct shear tests, as shown in <xref ref-type="fig" rid="F2">Figure 2</xref>. It can be observed that both vertical stress and immersion time have significant influences on the shear stress-shear displacement curves of the soil.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Straight shear test curve of samples under different immersion days. <bold>(A)</bold> 0&#xa0;d; <bold>(B)</bold> 1&#xa0;d; <bold>(C)</bold> 3&#xa0;d; <bold>(D)</bold> 5&#xa0;d; <bold>(E)</bold> 7&#xa0;d; <bold>(F)</bold> 10&#xa0;d; <bold>(G)</bold> 15&#xa0;d; <bold>(H)</bold> 20&#xa0;d.</p>
</caption>
<graphic xlink:href="fmats-10-1270082-g002.tif"/>
</fig>
<p>Based on the experimental results, the failure strength curve of the sample under different immersion days and the shear strength curve of the test under different vertical pressures were drawn. As shown in <xref ref-type="fig" rid="F3">Figure 3</xref>, the shear strength of the sample decreases with the increase of immersion days, indicating that immersion has a softening effect on the shear strength of the soil. At 400&#xa0;kPa, with the increase of immersion days, the cumulative attenuation value of the failure and shear strengths is 18.4&#xa0;kPa. When the vertical stress is low, the attenuation of shear strength is also low. When the axial pressure is 100&#xa0;Pa, the cumulative attenuation value is 10.7&#xa0;kPa.</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Failure strength curve and shear strength line of samples under different immersion days. <bold>(A)</bold> Relationship between sample shear stress and immersion time; <bold>(B)</bold> Relationship between sample shear strength and vertical stress.</p>
</caption>
<graphic xlink:href="fmats-10-1270082-g003.tif"/>
</fig>
<p>The relationship curve between cohesive force, internal friction angle, and immersion time is shown in <xref ref-type="fig" rid="F4">Figure 4</xref>. The cohesive force gradually decreases with the increase of immersion time, while the internal friction angle also gradually decreases. After immersion for 20&#xa0;days, the cohesive force of the clay decreased by 57.6%, while the internal friction angle decreased by 8.43%, with a smaller decrease range.</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Relationship between sample strength index and immersion days.</p>
</caption>
<graphic xlink:href="fmats-10-1270082-g004.tif"/>
</fig>
</sec>
<sec id="s3-2">
<title>3.2 Analysis of change in chemical composition</title>
<p>SiO<sub>2</sub>, AL<sub>2</sub>O<sub>3</sub>, and Fe<sub>2</sub>O<sub>3</sub> are the soil&#x2019;s primary chemical binding materials (<xref ref-type="bibr" rid="B11">Liu zhikui et al., 2017</xref>; <xref ref-type="bibr" rid="B15">Mou Chunmei and Wei Yux, 2019</xref>), with a total content of 88.01% of the soil&#x2019;s chemical composition.</p>
<p>As shown in <xref ref-type="fig" rid="F5">Figure 5</xref>, after immersion for 20&#xa0;days, the SiO<sub>2</sub> content increased by 1.69%, related to the hydrolysis equilibrium of SiO<sub>2</sub> in the aqueous solution. AL<sub>2</sub>O<sub>3</sub> and Fe<sub>2</sub>O<sub>3</sub> content was lower than those of the unsoaked samples. The AL<sub>2</sub>O<sub>3</sub> and Fe<sub>2</sub>O<sub>3</sub> in the soil react with the aqueous solution, destroying the original binding structure of the soil and further crushing the original soil structure. The Na<sub>2</sub>O content decreased mainly due to the alternation adsorption of cations, which caused Na<sup>&#x2b;</sup> to leave the soil with the infiltrating liquid. CaO mainly exists in carbonate and sulfate minerals, and MgO and K<sub>2</sub>O mainly exist in calcite and orthoclase, respectively. The decrease in their content reflects the dissolution of corresponding mineral components. All these chemical reactions are beneficial to weaken the structural strength of the soil.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Changes in the main chemical composition of the sampless after different immersion days. <bold>(A)</bold> 0d; <bold>(B)</bold> 20&#xa0;d.</p>
</caption>
<graphic xlink:href="fmats-10-1270082-g005.tif"/>
</fig>
</sec>
<sec id="s3-3">
<title>3.3 Analysis of LPS test</title>
<p>Using a laser particle size analyzer, the experimental particle size distribution was tested, and the sand content (d &#x3e; 0.075&#xa0;mm), powder content (0.005&#xa0;mm &#x3c; d &#x3c; 0.075&#xa0;mm), and clay content (d &#x3c; 0.005&#xa0;mm) of the soil samples after different immersion times were statistically analyzed and plotted. As shown in <xref ref-type="table" rid="T2">Table 2</xref>, the particle size of the soil continuously became finer with the increase in immersion time. For example, after immersion for 20 days, the mass fraction of sand content (d &#x3e; 0.075&#xa0;mm) decreased by 9.47% due to its smaller base but significant decomposition, while the mass fraction of clay (d &#x3c; 0.005&#xa0;mm) increased by 5.83%, and the mass fraction of powder (0.005&#xa0;mm &#x3c; d &#x3c; 0.075&#xa0;mm) increased by 3.64%. Throughout the immersion process, the changes in soil particles mainly involved the transformation of medium and fine sand into powder, while powder gradually transformed into clay, and the mass fraction of sand gradually decreased. In contrast, the mass fraction of clay and powder gradually increased. Therefore, it can be concluded that once the soil is immersed in water, its structure is destroyed, the coarse particles disperse and decompose, and the content of medium and fine particles increases. With the increase of immersion days, the coarse particles further disperse and decompose, and the content of clay and powder gradually increases.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Proportion of clay, silt and sand content (%).</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th align="center">0&#xa0;d</th>
<th align="center">1&#xa0;d</th>
<th align="center">3&#xa0;d</th>
<th align="center">5&#xa0;d</th>
<th align="center">7&#xa0;d</th>
<th align="center">10&#xa0;d</th>
<th align="center">15&#xa0;d</th>
<th align="center">20&#xa0;d</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">0-5um</td>
<td align="center">28.83</td>
<td align="center">29.3</td>
<td align="center">30.61</td>
<td align="center">30.98</td>
<td align="center">31.79</td>
<td align="center">32.87</td>
<td align="center">34.66</td>
<td align="center">34.66</td>
</tr>
<tr>
<td align="center">5-75um</td>
<td align="center">57.92</td>
<td align="center">57.62</td>
<td align="center">59.19</td>
<td align="center">59.93</td>
<td align="center">60.37</td>
<td align="center">60.90</td>
<td align="center">61.11</td>
<td align="center">61.56</td>
</tr>
<tr>
<td align="center">&#x3e;75um</td>
<td align="center">13.25</td>
<td align="center">13.08</td>
<td align="center">10.2</td>
<td align="center">9.09</td>
<td align="center">7.84</td>
<td align="center">6.23</td>
<td align="center">4.23</td>
<td align="center">3.78</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>After different immersion periods, statistical analysis was conducted on the usual particle size (including the characteristic particle size with cumulative particle distribution of 10%, 30%, 60%, and 99%). The specific data and changes are shown in <xref ref-type="table" rid="T3">Table 3</xref>. It can be observed from <xref ref-type="table" rid="T3">Table 3</xref> that with the increase in immersion time, the characteristic particle size with cumulative particle distribution of 10%, 30%, 60%, and 99% of the soil particles continuously decreased. The change of the characteristic particle size with a cumulative particle distribution of 10% and 30% slowly decreased with the increase of immersion days. The decrease of the characteristic particle size with a cumulative particle distribution of 60% was divided into the pre-immersion period (0&#x2013;10&#xa0;days) and the pre-and post-immersion period (10&#x2013;20&#xa0;days). The usual particle size with a cumulative particle distribution of 99% decreased from 0 to 1&#xa0;day.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Characteristic particle size.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center"/>
<th align="center">0&#xa0;d</th>
<th align="center">1&#xa0;d</th>
<th align="center">3&#xa0;d</th>
<th align="center">5&#xa0;d</th>
<th align="center">7&#xa0;d</th>
<th align="center">10&#xa0;d</th>
<th align="center">15&#xa0;d</th>
<th align="center">20&#xa0;d</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">
<italic>d<sub>10</sub>
</italic>(mm)</td>
<td align="center">1.479</td>
<td align="center">1.408</td>
<td align="center">1.379</td>
<td align="center">1.392</td>
<td align="center">1.344</td>
<td align="center">1.303</td>
<td align="center">1.149</td>
<td align="center">1.189</td>
</tr>
<tr>
<td align="center">
<italic>d<sub>30</sub>
</italic>(mm)</td>
<td align="center">5.462</td>
<td align="center">5.252</td>
<td align="center">4.732</td>
<td align="center">4.652</td>
<td align="center">4.302</td>
<td align="center">4.263</td>
<td align="center">3.862</td>
<td align="center">3.608</td>
</tr>
<tr>
<td align="center">
<italic>d<sub>60</sub>
</italic>(mm)</td>
<td align="center">11.12</td>
<td align="center">10.83</td>
<td align="center">10.57</td>
<td align="center">10.44</td>
<td align="center">10.11</td>
<td align="center">9.713</td>
<td align="center">9.632</td>
<td align="center">9.578</td>
</tr>
<tr>
<td align="center">
<italic>d<sub>99</sub>
</italic>(mm)</td>
<td align="center">130.7</td>
<td align="center">115.8</td>
<td align="center">113.3</td>
<td align="center">111.5</td>
<td align="center">106.8</td>
<td align="center">98.13</td>
<td align="center">96.14</td>
<td align="center">87.37</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The correlation between the content of clay particles, fine particles, sand particles, and soil strength indicators was calculated using gray correlation entropy analysis. The grey correlation analysis method was used to determine various factors&#x2019; varying degrees of influence on the dependent variable in complex systems (<xref ref-type="bibr" rid="B1">Deng et al., 2023</xref>; <xref ref-type="bibr" rid="B31">Zhang et al., 2019</xref>). <xref ref-type="bibr" rid="B32">Zhang Qishan et al. (1996)</xref> analyzed the two significant shortcomings of the existing gray correlation methods in 1996 and, based on Deng Julong&#x2019;s gray correlation theory, introduced the concept of gray entropy and proposed the gray correlation analysis method, called the gray correlation entropy analysis method. The specific introduction of the gray correlation entropy analysis method is as follows (<xref ref-type="bibr" rid="B25">Wang et al., 2014</xref>).</p>
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<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd>
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">X</mml:mi>
<mml:mi mathvariant="normal">k</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">k</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">k</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">k</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">k</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>Using the comparative sequence as a reference, the gray correlation coefficient of each comparative sequence is calculated using the following formula:<disp-formula id="equ3">
<mml:math id="m9">
<mml:mrow>
<mml:mi mathvariant="normal">&#x3b3;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:munder>
<mml:mi>min</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
</mml:munder>
<mml:munder>
<mml:mi>min</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:munder>
<mml:mrow>
<mml:mfenced open="|" close="|" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mn>0</mml:mn>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mi mathvariant="normal">&#x3be;</mml:mi>
<mml:munder>
<mml:mi>max</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
</mml:munder>
<mml:munder>
<mml:mi>max</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:munder>
<mml:mrow>
<mml:mfenced open="|" close="|" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mn>0</mml:mn>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mfenced open="|" close="|" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mn>0</mml:mn>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2b;</mml:mo>
<mml:mi mathvariant="normal">&#x3be;</mml:mi>
<mml:munder>
<mml:mi>max</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
</mml:munder>
<mml:munder>
<mml:mi>max</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:munder>
<mml:mrow>
<mml:mfenced open="|" close="|" separators="|">
<mml:mrow>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mn>0</mml:mn>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msubsup>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
<mml:mo>&#x2032;</mml:mo>
</mml:msubsup>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>According to the mapping relationship between the distribution of gray correlation coefficients between the reference sequence and the comparison sequence, the mapping value <inline-formula id="inf7">
<mml:math id="m10">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">h</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1,2</mml:mn>
<mml:mo>,</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>,</mml:mo>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is obtained, where the coefficient <inline-formula id="inf8">
<mml:math id="m11">
<mml:mrow>
<mml:mi mathvariant="normal">&#x3be;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> &#x2208;[0,1] is the resolution coefficient and is usually set to 0.5.<disp-formula id="equ4">
<mml:math id="m12">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="normal">&#x3b3;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mo>&#x2211;</mml:mo>
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mi mathvariant="normal">m</mml:mi>
</mml:munderover>
</mml:mstyle>
<mml:mrow>
<mml:mi mathvariant="normal">&#x3b3;</mml:mi>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">x</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:mi mathvariant="normal">i</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</disp-formula>
<inline-formula id="inf9">
<mml:math id="m13">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> also known as the density value of a distribution. For gray connotation sequence <inline-formula id="inf10">
<mml:math id="m14">
<mml:mrow>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mn>1</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mn>2</mml:mn>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:mo>&#x22ef;</mml:mo>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> (each element is not less than 0, and the sum is equal to 1), its gray entropy is:<disp-formula id="equ5">
<mml:math id="m15">
<mml:mrow>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mo>&#x2211;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>ln</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">a</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>By substituting <inline-formula id="inf11">
<mml:math id="m16">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> into Formula, we obtain the grey correlation entropy of each comparison sequence.<disp-formula id="equ6">
<mml:math id="m17">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mo>&#x2211;</mml:mo>
<mml:msub>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
</mml:msub>
<mml:mo>&#x2061;</mml:mo>
<mml:mi>ln</mml:mi>
<mml:msub>
<mml:mi mathvariant="normal">P</mml:mi>
<mml:mi mathvariant="normal">h</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>Finally, the grey entropy correlation degree of each comparative sequence was obtained through the following formulaic calculation:<disp-formula id="equ7">
<mml:math id="m18">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mi mathvariant="normal">r</mml:mi>
</mml:msub>
<mml:mrow>
<mml:mfenced open="(" close=")" separators="|">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">X</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">H</mml:mi>
<mml:mi mathvariant="normal">j</mml:mi>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mtext>lnm</mml:mtext>
</mml:mrow>
</mml:mfrac>
</mml:mrow>
</mml:math>
</disp-formula>
</p>
<p>Sequence <inline-formula id="inf12">
<mml:math id="m19">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">X</mml:mi>
<mml:mi mathvariant="normal">a</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is more closely aligned with the reference sequence than sequence <inline-formula id="inf13">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">X</mml:mi>
<mml:mi mathvariant="normal">b</mml:mi>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and as a result, it makes a greater contribution to the alignment of sequence <inline-formula id="inf14">
<mml:math id="m21">
<mml:mrow>
<mml:msub>
<mml:mi mathvariant="normal">X</mml:mi>
<mml:mn>0</mml:mn>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>As shown in <xref ref-type="fig" rid="F6">Figure 6</xref>, the results indicate the highest gray correlation degree between cohesion and sand content, followed by silt and clay particles. The gray correlation degree of the three is more significant than 0.95, all of which have vital statistical significance. The gray correlation degree between the internal friction angle and the silt content is the highest, followed by clay particles, and the sand content is the lowest. The gray correlation degree of the three is more significant than 0.95, all of which have vital statistical significance.</p>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Grey entropy relevance between clay particles, powder particles, sand particles and a indicators of strength. <bold>(A)</bold> Grey entropy relevance between clay particles, powder particles, sand particles and cohesion; <bold>(B)</bold> Grey entropy relevance between clay particles, powder particles, sand particles and internal friction angle.</p>
</caption>
<graphic xlink:href="fmats-10-1270082-g006.tif"/>
</fig>
</sec>
<sec id="s3-4">
<title>3.4 Analysis of SEM test</title>
<p>As depicted in <xref ref-type="fig" rid="F7">Figure 7</xref>, SEM microstructure images of samples immersed for 0, 5, 10, and 20&#xa0;days are presented, the magnification factor being &#xd7;2000. With the increase in immersion time, the soil particles were still composed of cohesive or aggregated flakes, forming a stacked structure. However, the original compactness of the soil weakened, and the orientation and arrangement could be more explicit. The particles within the field of view were severely fragmented, the area decreased, and the boundary between particles and pores blurred. The stacking of particles and pores increased, and there were more small voids at the edges of particle-to-particle or particle-to-edge contact, with some local inter-particle pores connected. Overall, the soil structure within the field of view became loose as the immersion time increased.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>SEM images of samples under different immersion days. <bold>(A)</bold> 0&#xa0;d; <bold>(B)</bold> 5&#xa0;d; <bold>(C)</bold> 10&#xa0;d; <bold>(D)</bold> 20&#xa0;d.</p>
</caption>
<graphic xlink:href="fmats-10-1270082-g007.tif"/>
</fig>
<p>There was a general decreasing trend in pore area and an increasing trend in pore number. This indicates that as the number of days of immersion increased, the colloidal particles (soluble salts) in the soil dissolved rapidly, large pores decreased, and tiny pores increased. The overall soil structure within the field of view becomes loose as the immersion days increased.</p>
</sec>
</sec>
<sec sec-type="discussion" id="s4">
<title>4 Discussions</title>
<p>Based on the study&#x2019;s results, the process of soil property change under long-term immersion was sorted out, as shown in <xref ref-type="fig" rid="F8">Figure 8</xref>. The dissolution of a small amount of colloidal particles in the soil after long-term immersion caused a decrease in the force between soil particles. The dispersion of soil particle aggregates led to particle size refinement, and the cohesive force was also reduced. The content of fines and cohesive particles in the soil increased after particle size refinement and the increase in the fines content led to a decrease in the angle of internal friction.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Schematic diagram of soil property changes under long-term immersion.</p>
</caption>
<graphic xlink:href="fmats-10-1270082-g008.tif"/>
</fig>
<p>Under long-term immersion, a series of complex microphysical and chemical reactions occur, which cause changes in the particle size of the soil. With the increase of immersion time, and the number of fine particles increases rapidly. When the content of clay in the soil increases, although increasing the content of fine particles can help to produce more particles with a &#x201c;bonding&#x201d; effect, the soil skeleton is destroyed due to the sharp decrease of coarse particle content. The interaction between coarse and fine particles weakens, resulting in a decreasing trend of soil cohesion.</p>
<p>During the soil samples&#x2019; shear, the friction between irregular and coarse particles on the surface primarily provides the frictional resistance between soil particles. Fine particles exist between coarse particles in the soil sample, so the more fine particles present in the soil sample, the more these particles will soften under the surrounding moisture during shear failure and act as a &#x201c;lubricant&#x201d; on the surface of the coarse particles, reducing the frictional resistance between them. As a result, the internal friction angle of the soil sample decreases.</p>
</sec>
<sec sec-type="conclusion" id="s5">
<title>5 Conclusion</title>
<p>In the embankment remodeling soil study, the samplings were subjected to straight shear tests, chemical composition tests, laser particle size tests, and SEM tests at different immersion times. The following conclusions can be drawn based on the experimental results and the previous discussion:<list list-type="simple">
<list-item>
<p>1. Conducting direct shear tests on soil samples with different immersion times, it was discovered that the influence of immersion time on the shear strength of remolded clay is exceptionally significant. This was mainly manifested by a continuous weakening of the shear strength as the immersion time increased. The cohesion and the angle of internal friction decreased gradually with the increase of immersion time, but the change in the internal friction angle was insignificant.</p>
</list-item>
<list-item>
<p>2. The long-term physicochemical effects of water on soil are significant: laser particle size analyzer tests show that long-term immersion leads to the refinement of soil particle size, with a consequent increase in the number of fine particles. X-ray fluorescence spectrometry tests show changes in the chemical composition of the specimens after 20 days of immersion, and these chemical reactions favor the weakening of the structural strength of the soil and the promotion of pore development. The refinement of soil particles was also associated with changes in chemical composition. After processing the SEM images of the samples that had been soaked for different periods, it was observed that continuous immersion increased the number of pores in the samples, the number of large pores decreased, the number of tiny pores increased, and the structure of the soil in the field of view became looser.</p>
</list-item>
<list-item>
<p>3. Under long-term immersion, the soil undergoes a series of complex microphysical and chemical reactions, resulting in the macroscopic manifestation of strength weakening and water immersion aging. The mechanism analysis is as follows: in the early stage of immersion, the colloidal particles (easily soluble salt) dissolved rapidly, the soil microstructure was destroyed, and the cohesive force significantly decreased; with the increase of immersion time, the content of clay particles increased, and the fine particles and clay particles content of the soil increased after particle size refinement, which led to a decrease in the internal friction angle.</p>
</list-item>
</list>
</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s6">
<title>Data availability statement</title>
<p>The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.</p>
</sec>
<sec id="s7">
<title>Author contributions</title>
<p>KZ: Conceptualization, Data curation, Investigation, Methodology, Writing&#x2013;original draft, Writing&#x2013;review and editing. DF: Conceptualization, Funding acquisition, Investigation, Writing&#x2013;review and editing. ZW: Formal Analysis, Writing&#x2013;original draft, Writing&#x2013;review and editing.</p>
</sec>
<sec id="s8">
<title>Funding</title>
<p>The author(s) declare financial support was received for the research, authorship, and/or publication of this article. The present authors are appreciated to the financial support from the National Natural Science Foundation of China Joint Fund Key Project (Grant No. U2240210).</p>
</sec>
<ack>
<p>The authors thank the National Natural Science Foundation of China Joint Fund Key Project (Grant No. U2240210).</p>
</ack>
<sec sec-type="COI-statement" id="s9">
<title>Conflict of interest</title>
<p>Author ZW was employed by the company China Railway 14th Bureau Group Co., Ltd.</p>
<p>The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="disclaimer" id="s10">
<title>Publisher&#x2019;s note</title>
<p>All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.</p>
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