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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Mater.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Materials</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Mater.</abbrev-journal-title>
</journal-title-group>
<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">1774063</article-id>
<article-id pub-id-type="doi">10.3389/fmats.2026.1774063</article-id>
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<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>Performance evaluation of ternary solid waste-based geopolymer subgrade materials</article-title>
<alt-title alt-title-type="left-running-head">Li 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.2026.1774063">10.3389/fmats.2026.1774063</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Li</surname>
<given-names>Dongguo</given-names>
</name>
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</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Cui</surname>
<given-names>Yuhang</given-names>
</name>
<xref ref-type="aff" rid="aff1"/>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
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</contrib>
<contrib contrib-type="author">
<name>
<surname>Guo</surname>
<given-names>Fanghui</given-names>
</name>
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</contrib>
<contrib contrib-type="author">
<name>
<surname>Chen</surname>
<given-names>Ziqi</given-names>
</name>
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<contrib contrib-type="author">
<name>
<surname>Zhou</surname>
<given-names>Qinyu</given-names>
</name>
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</contrib>
</contrib-group>
<aff id="aff1">
<institution>School of Civil Engineering, Changchun Institute of Technology</institution>, <city>Changchun</city>, <country country="CN">China</country>
</aff>
<author-notes>
<corresp id="c001">
<label>&#x2a;</label>Correspondence: Yuhang Cui, <email xlink:href="mailto:cuiyh0424@163.com">cuiyh0424@163.com</email>
</corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-02-18">
<day>18</day>
<month>02</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2026</year>
</pub-date>
<volume>13</volume>
<elocation-id>1774063</elocation-id>
<history>
<date date-type="received">
<day>23</day>
<month>12</month>
<year>2025</year>
</date>
<date date-type="rev-recd">
<day>02</day>
<month>02</month>
<year>2026</year>
</date>
<date date-type="accepted">
<day>02</day>
<month>02</month>
<year>2026</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2026 Li, Cui, Guo, Chen and Zhou.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Li, Cui, Guo, Chen and Zhou</copyright-holder>
<license>
<ali:license_ref start_date="2026-02-18">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. 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.</license-p>
</license>
</permissions>
<abstract>
<p>This study employed three industrial by-products-cement kiln dust (CKD), fly ash (FA), and phosphogypsum (PG)&#x2014;as precursors to develop one-part geopolymer stabilized subgrade materials. The principal objective was to quantify how binder proportioning influences the mechanical and durability performance of the resulting mixtures. The findings support the large-scale recycling of solid wastes and the development of alternative low-carbon cementitious materials for pavement engineering. Unconfined compressive strength (UCS), water stability, freeze-thaw (F-T) cycle, and ultrasonic pulse velocity (UPV) tests were conducted on ten mixtures. The total CKD-PG dosage ranged from 42% to 90%. The results indicate that increasing the total CKD-PG dosage resulted in a denser internal structure, which in turn improved both mechanical performance and durability. When the total CKD-PG dosage exceeded 70%, the geopolymer exhibited substantially higher UCS, enhanced water stability, and a compressive strength loss of only 2.6% after 15 F-T cycles. These results were markedly better than those for mixtures with a total CKD-PG dosage below 70%. UPV measurements corroborated that this proportion yielded the greatest internal compactness. The optimal formulation was 46% CKD, 44% PG, and 10% FA (C46P44). This mix delivered the best combination of strength, frost resistance, and density and satisfied requirements for highway subgrade applications. The study provides experimental evidence for large-scale reuse of CKD, FA, and PG and identifies a key mix proportion for geopolymer use in highway subgrade construction.</p>
</abstract>
<kwd-group>
<kwd>freeze-thaw cycle</kwd>
<kwd>geopolymer</kwd>
<kwd>solid waste</kwd>
<kwd>ultrasonic pulse velocity</kwd>
<kwd>unconfined compressive strength</kwd>
<kwd>water stability</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declared that financial support was received for this work and/or its publication. This research was financially supported by Science and Technology Department Plan Project of Jilin Province, China (Grant No. 20240304146SF). The funder provided the necessary financial resources for the conduct of the research but had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript.</funding-statement>
</funding-group>
<counts>
<fig-count count="4"/>
<table-count count="7"/>
<equation-count count="0"/>
<ref-count count="63"/>
<page-count count="00"/>
</counts>
<custom-meta-group>
<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Structural Materials</meta-value>
</custom-meta>
</custom-meta-group>
</article-meta>
</front>
<body>
<sec sec-type="intro" id="s1">
<label>1</label>
<title>Introduction</title>
<p>Long-term structural performance and service life of highway pavements are governed primarily by the stability of the pavement system. The subgrade serves as the primary load-bearing layer. It transmits traffic-induced stresses to the subgrade and distributes those stresses uniformly (<xref ref-type="bibr" rid="B8">Dan et al., 2023</xref>; <xref ref-type="bibr" rid="B14">Hamed et al., 2025</xref>). Consequently, the engineering properties of the subgrade material critically affect overall pavement performance. Cement-stabilized aggregate (CSA) is commonly adopted for road bases because it provides adequate strength and stiffness (<xref ref-type="bibr" rid="B23">Liu et al., 2025</xref>; <xref ref-type="bibr" rid="B55">Yang G. et al., 2025</xref>). However, Portland cement is an energy-intensive, high CO<sub>2</sub>-emitting binder. Its production consumes about 4 GJ&#xb7;t<sup>-1</sup> of energy and releases approximately 0.8 t CO<sub>2</sub> eq&#xb7;t<sup>-1</sup> of clinker (<xref ref-type="bibr" rid="B48">Sun et al., 2025</xref>; <xref ref-type="bibr" rid="B56">Yang X. et al., 2025</xref>). CSA also depends heavily on natural sand and gravel, and their overexploitation has caused severe ecological degradation (<xref ref-type="bibr" rid="B56">Yang X. et al., 2025</xref>). Simultaneously, large quantities of industrial by-products&#x2014;namely cement-kiln dust (CKD), fly ash (FA), and phosphogypsum (PG)&#x2014;are produced annually. China alone produces roughly 20 Mt CKD, 600 Mt FA, and 30 Mt PG annually, yet their utilization ratios remain low (<xref ref-type="bibr" rid="B40">Shi et al., 2025</xref>). Stockpiled wastes cause dust storms, soil alkalization, and eutrophication of surface waters. These impacts pose serious environmental risks (<xref ref-type="bibr" rid="B50">Wang et al., 2025a</xref>). Converting these residues into construction materials that partially replace cement has become a central objective at the intersection of pavement and environmental engineering (<xref ref-type="bibr" rid="B47">Sun et al., 2024</xref>; <xref ref-type="bibr" rid="B61">Zhao et al., 2025</xref>). Alkali-activated geopolymers offer a promising route. These inorganic aluminosilicate binders are synthesized mainly from industrial wastes. They provide high compressive strength, exhibit low drying shrinkage, and show superior sulfate resistance (<xref ref-type="bibr" rid="B34">Mostafa et al., 2026</xref>; <xref ref-type="bibr" rid="B33">Mohammad et al., 2025</xref>). Energy-demand and carbon-footprint assessments indicate that geopolymer production consumes about 30% of the energy and emits roughly 20% of the CO<sub>2</sub> associated with Portland cement. Additionally, it enables waste substitution levels above 70% (<xref ref-type="bibr" rid="B53">Xie et al., 2026</xref>; <xref ref-type="bibr" rid="B38">Ramadan et al., 2022</xref>). Over the past decade, geopolymers have been demonstrated successfully in structural concrete (<xref ref-type="bibr" rid="B19">Kaoutar et al., 2025</xref>), contaminated-soil solidification (<xref ref-type="bibr" rid="B3">An et al., 2024</xref>), and pavement applications (<xref ref-type="bibr" rid="B24">Lv et al., 2025</xref>). Their promising freeze-thaw and moisture-damage resistance make them suitable as subgrade materials in cold and wet service environments (<xref ref-type="bibr" rid="B59">Zhang et al., 2025</xref>; <xref ref-type="bibr" rid="B51">Wang XX. et al., 2025</xref>). However, several challenges must be addressed to realize these benefits in practical subgrade applications. Key issues include raw material system design, activator selection, and coordination of key performance attributes.</p>
<p>Currently, raw materials for geopolymers have evolved from single-source solid wastes to formulations that emphasize diversified, synergistic utilization. Fly ash-based geopolymers predominate because of the wide availability of feedstock (<xref ref-type="bibr" rid="B62">Zhou Y. et al., 2025</xref>). The synergistic benefits of binary systems (e.g., fly ash-slag) are well established (<xref ref-type="bibr" rid="B46">Sun et al., 2023</xref>; <xref ref-type="bibr" rid="B41">Singh et al., 2024</xref>). However, the compositional space of these systems remains relatively constrained, and further gains in performance face bottlenecks. Consequently, exploring novel ternary systems that introduce cement kiln dust (CKD), phosphogypsum (PG), or other industrial solid wastes as a third component is important. Such systems can expand geopolymer feedstock options and create new avenues for performance tuning. To date, studies on these ternary systems remain limited, and the fundamental synergistic mechanisms are not yet understood. Existing research has mainly used PG as an auxiliary binder or as a sulfate activator in alkali-activated systems (<xref ref-type="bibr" rid="B10">Feng and Lu, 2024</xref>; <xref ref-type="bibr" rid="B27">Majdoubi et al., 2023</xref>). Investigations of its synergistic binding mechanisms with high-calcium components under acidic conditions are insufficient. CKD has been employed primarily as an alkali activator or auxiliary additive (<xref ref-type="bibr" rid="B25">Mahdi et al., 2022</xref>; <xref ref-type="bibr" rid="B7">Dahash and Humad, 2025</xref>; <xref ref-type="bibr" rid="B39">Shaqour, 2024</xref>). Its potential role as a primary calcium-bearing raw material remains underexplored. Systematic investigations of the combined use of CKD, PG, and fly ash (FA) are scarce. In particular, studies that probe the interaction between CKD&#x2019;s high-calcium character and PG&#x2019;s sulfate anion under acidic activation are lacking. Mix-design-performance relationships for this ternary system as subgrade material are also inadequately established. Alkali activation is the prevailing activation method because it offers high reaction efficiency and controllable cost (<xref ref-type="bibr" rid="B1">Abdellah and Mohamed, 2024</xref>; <xref ref-type="bibr" rid="B4">Bandopadhyay and Giri, 2025</xref>). However, in high-calcium CKD-PG systems, alkali activation can exacerbate drying shrinkage and increase the risk of alkali-aggregate reactions. The strongly alkaline environment may also hinder stable immobilization of sulfate in PG. In contrast, acid activation (e.g., with phosphoric acid) can produce dense Si-O-Al-O-P networks. These networks are promising for enhancing water resistance and freeze-thaw (F-T) durability. Experimental evidence shows that phosphoric acid concentration strongly influences both the mechanical properties and microstructural densification of geopolymers (<xref ref-type="bibr" rid="B63">Zhou E. et al., 2025</xref>; <xref ref-type="bibr" rid="B58">Zhang et al., 2020</xref>; <xref ref-type="bibr" rid="B16">He et al., 2023</xref>). Most studies focused on single- or binary solid-waste systems such as FA-slag (<xref ref-type="bibr" rid="B21">Li et al., 2024</xref>; <xref ref-type="bibr" rid="B37">Pu et al., 2021</xref>) or binary acid-activated combinations such as FA-metakaolin (<xref ref-type="bibr" rid="B15">He, 2025</xref>). When acid activation is applied to the more complex CKD-PG-FA ternary system, in which calcium, sulfur, and Si-Al phases coexist, systematic investigations are lacking. The individual responses to acidity, the competing reaction mechanisms, and the combined effects on compactness remain insufficiently understood.</p>
<p>Existing studies have typically characterized the basic mechanical properties and durability of geopolymers. However, most examinations treat individual performance metrics in isolation (<xref ref-type="bibr" rid="B17">Hu et al., 2025</xref>; <xref ref-type="bibr" rid="B57">Zhang and Jia, 2025</xref>). For subgrade materials, service performance depends on several interrelated properties, including unconfined compressive strength (UCS), water stability, and frost resistance. The interactions among these properties within specific mix-design systems remain insufficiently explored. In particular, mutual constraints and synergistic effects that arise from changes in the material&#x2019;s internal structure have not been systematically quantified. The intrinsic coupling mechanisms that develop with structural evolution also remain poorly understood. Subgrade layers are exposed to combined stresses from moisture, F-T cycles, and traffic loads. A deficiency in any single property can therefore undermine overall service life. Although some studies have examined the frost resistance of geopolymers (<xref ref-type="bibr" rid="B5">Carvalho et al., 2023</xref>), coordinated investigations that integrate frost resistance, strength development, and water-induced deterioration mechanisms within a unified mix-design framework are still lacking. This is particularly true for ternary acid-activated systems such as CKD-PG-FA. Current research also lacks a physical metric that quantifies the internal structural state and links it quantitatively to the relevant macroscopic properties. Studies of unbonded granular materials correlated macroscopic behavior with quantified morphological indicators (<xref ref-type="bibr" rid="B60">Zhao et al., 2020</xref>). Building on these findings, this study introduced UPV as a sensitive, comprehensive physical indicator of internal density and homogeneity. The objective was to establish quantitative correlation models between ultrasonic pulse velocity (UPV) and key pavement-relevant properties, including UCS, water stability, and frost resistance. This approach enabled rapid, non-destructive assessment of macroscopic performance. It also adopted a unified perspective on structural evolution and provided a new research paradigm and analytical toolkit to elucidate the mechanisms governing performance development and degradation in the ternary acid-activated geopolymer system.</p>
<p>Considerable progress has been made in geopolymer research. However, most studies have concentrated on binary alkali-activated systems based on FA and slag. The synergistic cementation mechanisms and optimal proportioning principles for a ternary blend of CKD-PG-FA under acid activation remain unexplored. CKD serves as a source of calcium and reactivity. PG regulates setting and induces micro-expansion. FA supplies silica and alumina. In such ternary mixtures, alkali activation can impair volumetric stability and F-T resistance. In contrast, the potential of acid activation (e.g., phosphoric acid) to increase density and durability in these blends has not been demonstrated. No systematic studies have optimized performance and clarified mechanisms of acid-activated ternary geopolymers from a multi-criteria perspective. Important criteria include UCS, wet-dry stability, and F-T resistance for use as subgrade materials. Therefore, this study used CKD, FA, and PG&#x2014;three industrial solid wastes&#x2014;as raw materials and activated them with phosphoric acid. The objectives were to: (1) elucidate how mix proportions affect UCS, water stability, and F-T resistance; (2) clarify the relationship between internal compactness and macroscopic performance using UPV; and (3) identify an optimal mix proportion that satisfies subgrade material requirements for cold-region highways. The findings provide new theoretical foundations and empirical data to support synergistic use of multiple industrial wastes and the development of high-performance, durable geopolymer subgrade materials.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Materials and specimen preparation</title>
<sec id="s2-1">
<label>2.1</label>
<title>Materials</title>
<sec id="s2-1-1">
<label>2.1.1</label>
<title>CKD</title>
<p>CKD used in this experiment was collected from a cement plant in Jilin City. It was a gray-brown powder that exhibited relatively high reactivity and both air-hardening and hydraulic-hardening behavior. Major chemical components and their concentrations are listed in <xref ref-type="table" rid="T1">Tables 1</xref>, <xref ref-type="table" rid="T2">2</xref>.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Chemical components of raw materials.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Materials</th>
<th align="center">CaO</th>
<th align="center">SiO<sub>2</sub>
</th>
<th align="center">Fe<sub>2</sub>O<sub>3</sub>
</th>
<th align="center">Al<sub>2</sub>O<sub>3</sub>
</th>
<th align="center">MgO</th>
<th align="center">K<sub>2</sub>O</th>
<th align="center">SO<sub>3</sub>
</th>
<th align="center">Na<sub>2</sub>O</th>
<th align="center">FCaO</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">CKD</td>
<td align="center">45.6</td>
<td align="center">22.86</td>
<td align="center">3.85</td>
<td align="center">5.8</td>
<td align="center">0.88</td>
<td align="center">1.22</td>
<td align="center">1.38</td>
<td align="center">0.62</td>
<td align="center">14.66</td>
</tr>
<tr>
<td align="center">PG</td>
<td align="center">42.4</td>
<td align="center">2. 1</td>
<td align="center">0.7</td>
<td align="center">0.6</td>
<td align="center">0.5</td>
<td align="center">0.7</td>
<td align="center">52. 1</td>
<td align="center">0.28</td>
<td align="center">0.09</td>
</tr>
<tr>
<td align="center">FA</td>
<td align="center">2.3</td>
<td align="center">42.7</td>
<td align="center">5.5</td>
<td align="center">30.2</td>
<td align="center">2.5</td>
<td align="center">2.05</td>
<td align="center">0.727</td>
<td align="center">0.888</td>
<td align="center">2.7</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>Physical properties of raw materials.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Materials</th>
<th align="center">Density (kg &#xd7; m<sup>-3</sup>)</th>
<th align="center">28days activity index (%)</th>
<th align="center">Specific surface area (m<sup>2</sup>&#xd7;kg)</th>
<th align="center">Water content (%)</th>
<th align="center">Fineness (%)</th>
<th align="center">Ignition loss (%)</th>
<th align="center">Water demand ratio</th>
<th align="center">Sulphur content (%)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td rowspan="2" align="center">CKD</td>
<td rowspan="2" align="center">2,770</td>
<td rowspan="2" align="center">&#x3e;100</td>
<td rowspan="2" align="center">650</td>
<td rowspan="2" align="center">&#x2014;</td>
<td align="center">&#x3c;0.08 mm</td>
<td rowspan="2" align="center">8.2</td>
<td rowspan="2" align="center">&#x2014;</td>
<td rowspan="2" align="center">1.5</td>
</tr>
<tr>
<td align="center">89.1</td>
</tr>
<tr>
<td rowspan="2" align="center">PG</td>
<td rowspan="2" align="center">2,130</td>
<td rowspan="2" align="center">&#x2014;</td>
<td rowspan="2" align="center">220</td>
<td rowspan="2" align="center">&#x2014;</td>
<td align="center">&#x3c;45 &#x3bc;m</td>
<td rowspan="2" align="center">19</td>
<td rowspan="2" align="center">&#x2014;</td>
<td rowspan="2" align="center">21</td>
</tr>
<tr>
<td align="center">30</td>
</tr>
<tr>
<td rowspan="2" align="center">FA</td>
<td rowspan="2" align="center">970</td>
<td rowspan="2" align="center">67</td>
<td rowspan="2" align="center">311</td>
<td rowspan="2" align="center">8.2</td>
<td align="center">&#x3c;0.3 mm</td>
<td rowspan="2" align="center">10.6</td>
<td rowspan="2" align="center">108</td>
<td rowspan="2" align="center">1.2</td>
</tr>
<tr>
<td align="center">95</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s2-1-2">
<label>2.1.2</label>
<title>FA</title>
<p>FA for this study was collected from a power plant in Changchun. Key physical and chemical parameters&#x2014;including density, moisture content, fineness, loss on ignition, and chemical composition&#x2014;were determined following the <italic>&#x201c;Test Methods of Materials Stabilized with Inorganic Binders for Highway Engineering&#x201d; (JTG 3441-2024)</italic> (<xref ref-type="bibr" rid="B32">Ministry of Transport of the People&#x2019;s Republic of China, 2024</xref>) and <italic>&#x201c;Methods for Chemical Analysis of Cement&#x201d; (GB/T 176-2017)</italic> (Standardization administration of the people&#x2019;s Republic of China, 2017). Test results are presented in <xref ref-type="table" rid="T1">Tables 1</xref>, <xref ref-type="table" rid="T2">2</xref>. All performance indicators met the requirements for subgrade materials specified in <italic>&#x201c;Technical Specifications for Construction of Highway Pavement Base&#x201d; (JTJ 034-2018)</italic> (<xref ref-type="bibr" rid="B30">Ministry ofTransport of the People&#x2019;s Republic of China, 2018</xref>). According to the national standard <italic>&#x201c;Fly Ash Used for Cement and Concrete&#x201d; (GB/T 1596-2017)</italic> (<xref ref-type="bibr" rid="B42">Standardization Administration of the People&#x2019;s Republic ofChina, 2017</xref>), the fly ash was classified as Class F, Grade III.</p>
</sec>
<sec id="s2-1-3">
<label>2.1.3</label>
<title>PG</title>
<p>PG used in this study was obtained as industrial waste from a conglomerate in Jilin City. The material was gray-white and rich in calcium and sulfur. Chemical characterization was performed according to <italic>&#x201c;Methods for Chemical Analysis of Gypsum&#x201d; (GB/T 5484-2024)</italic> (<xref ref-type="bibr" rid="B45">Standardization Administration of thePeople&#x2019;s Republic of China, 2024</xref>)<italic>, &#x201c;Phosphogypsum&#x201d; (GB/T 23456-2019)</italic> (<xref ref-type="bibr" rid="B43">Standardization administration of the people Republic ofChina, 2019</xref>), and <italic>&#x201c;Methods for Chemical Analysis of Cement&#x201d; (GB/T 176-2017)</italic> (<xref ref-type="bibr" rid="B44">Standardization administration of the people Republic ofChina, 2017</xref>). Analytical results are presented in <xref ref-type="table" rid="T1">Table 1</xref>. Physical properties are listed in <xref ref-type="table" rid="T2">Table 2</xref>.</p>
</sec>
<sec id="s2-1-4">
<label>2.1.4</label>
<title>Acid activator</title>
<p>The acid activator was phosphoric acid supplied by a supplier in Jilin City. To achieve complete and uniform incorporation of the activator during specimen preparation, the measured activator was first dissolved in water at the optimum moisture content and stirred until a homogeneous solution was obtained. The resulting solution was then added to the pre-mixed composite formulated according to the prescribed mix proportions.</p>
</sec>
</sec>
<sec id="s2-2">
<label>2.2</label>
<title>Specimen preparation</title>
<sec id="s2-2-1">
<label>2.2.1</label>
<title>Design of mix proportion</title>
<p>A uniform design was used to determine the mix proportions of geopolymer specimens. The experimental factors were CKD dosage (X1), PG dosage (X2), and FA dosage (X3). X1 and X2 were treated as control variables at 10 discrete levels. The level increments for X1 and X2 were 2% and 4%, respectively (see <xref ref-type="table" rid="T3">Table 3</xref>). Guided by previous studies (<xref ref-type="bibr" rid="B36">Peng, 2015</xref>; <xref ref-type="bibr" rid="B18">Ji et al., 2006</xref>), the component bounds were set as 0.14 &#x2264; X1 &#x2264; 0.5, 0.16 &#x2264; X2 &#x2264; 0.52, and 0.1 &#x2264; X3 &#x2264; 0.58, with X1 &#x2b; X2 &#x2b; X3 &#x3d; 1. The formulation comprised only three constituents. As a result, fixing the dosages of CKD and PG determined the required FA dosage. Specimen mixes were arranged using the U&#xd7;10 (10<sup>8</sup>) uniform design table (see <xref ref-type="table" rid="T4">Table 4</xref>). The resulting formulations are listed in <xref ref-type="table" rid="T5">Table 5</xref>. For two-factor experiments, columns 1 and 6 of the U&#xd7;10 (10<sup>8</sup>) table were employed. Consequently, the FA dosage was computed as X3 &#x3d; 1 &#x2212; X1 &#x2212; X2. Specimen labels use <italic>&#x201c;C&#x201d;</italic> to denote CKD and <italic>&#x201c;P&#x201d;</italic> to denote PG; the following number gives the percentage of that constituent. For example, C14P40 indicates 14% CKD and 40% PG, while the FA dosage is 46%.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Factor level table.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Factor level</th>
<th align="center">1</th>
<th align="center">2</th>
<th align="center">3</th>
<th align="center">4</th>
<th align="center">5</th>
<th align="center">6</th>
<th align="center">7</th>
<th align="center">8</th>
<th align="center">9</th>
<th align="center">10</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">CKD (%)</td>
<td align="center">14</td>
<td align="center">18</td>
<td align="center">22</td>
<td align="center">26</td>
<td align="center">30</td>
<td align="center">34</td>
<td align="center">38</td>
<td align="center">42</td>
<td align="center">46</td>
<td align="center">50</td>
</tr>
<tr>
<td align="center">PG (%)</td>
<td align="center">16</td>
<td align="center">20</td>
<td align="center">24</td>
<td align="center">28</td>
<td align="center">32</td>
<td align="center">36</td>
<td align="center">40</td>
<td align="center">44</td>
<td align="center">48</td>
<td align="center">52</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>U &#xd7; 10 (10<sup>8</sup>) uniform design table.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Test number</th>
<th align="center">1</th>
<th align="center">2</th>
<th align="center">3</th>
<th align="center">4</th>
<th align="center">5</th>
<th align="center">6</th>
<th align="center">7</th>
<th align="center">8</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">1</td>
<td align="center">1</td>
<td align="center">2</td>
<td align="center">3</td>
<td align="center">4</td>
<td align="center">5</td>
<td align="center">6</td>
<td align="center">9</td>
<td align="center">10</td>
</tr>
<tr>
<td align="center">2</td>
<td align="center">2</td>
<td align="center">4</td>
<td align="center">6</td>
<td align="center">8</td>
<td align="center">10</td>
<td align="center">3</td>
<td align="center">7</td>
<td align="center">9</td>
</tr>
<tr>
<td align="center">3</td>
<td align="center">3</td>
<td align="center">6</td>
<td align="center">9</td>
<td align="center">1</td>
<td align="center">4</td>
<td align="center">10</td>
<td align="center">5</td>
<td align="center">8</td>
</tr>
<tr>
<td align="center">4</td>
<td align="center">4</td>
<td align="center">8</td>
<td align="center">1</td>
<td align="center">5</td>
<td align="center">9</td>
<td align="center">6</td>
<td align="center">3</td>
<td align="center">7</td>
</tr>
<tr>
<td align="center">5</td>
<td align="center">5</td>
<td align="center">10</td>
<td align="center">4</td>
<td align="center">9</td>
<td align="center">3</td>
<td align="center">2</td>
<td align="center">1</td>
<td align="center">6</td>
</tr>
<tr>
<td align="center">6</td>
<td align="center">6</td>
<td align="center">1</td>
<td align="center">7</td>
<td align="center">2</td>
<td align="center">8</td>
<td align="center">9</td>
<td align="center">10</td>
<td align="center">5</td>
</tr>
<tr>
<td align="center">7</td>
<td align="center">7</td>
<td align="center">3</td>
<td align="center">10</td>
<td align="center">6</td>
<td align="center">2</td>
<td align="center">5</td>
<td align="center">8</td>
<td align="center">4</td>
</tr>
<tr>
<td align="center">8</td>
<td align="center">8</td>
<td align="center">5</td>
<td align="center">2</td>
<td align="center">10</td>
<td align="center">7</td>
<td align="center">1</td>
<td align="center">6</td>
<td align="center">3</td>
</tr>
<tr>
<td align="center">9</td>
<td align="center">9</td>
<td align="center">7</td>
<td align="center">5</td>
<td align="center">3</td>
<td align="center">1</td>
<td align="center">8</td>
<td align="center">4</td>
<td align="center">2</td>
</tr>
<tr>
<td align="center">10</td>
<td align="center">10</td>
<td align="center">9</td>
<td align="center">8</td>
<td align="center">7</td>
<td align="center">6</td>
<td align="center">4</td>
<td align="center">2</td>
<td align="center">1</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Mix proportion of specimens.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Mix proportions</th>
<th align="center">X1 (%)</th>
<th align="center">X2 (%)</th>
<th align="center">X3 (%)</th>
<th align="center">X1&#x2b;X2 (%)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">C14P40</td>
<td align="center">14</td>
<td align="center">40</td>
<td align="center">46</td>
<td align="center">54</td>
</tr>
<tr>
<td align="center">C18P24</td>
<td align="center">18</td>
<td align="center">24</td>
<td align="center">58</td>
<td align="center">42</td>
</tr>
<tr>
<td align="center">C22P52</td>
<td align="center">22</td>
<td align="center">52</td>
<td align="center">26</td>
<td align="center">74</td>
</tr>
<tr>
<td align="center">C26P36</td>
<td align="center">26</td>
<td align="center">36</td>
<td align="center">38</td>
<td align="center">62</td>
</tr>
<tr>
<td align="center">C30P20</td>
<td align="center">30</td>
<td align="center">20</td>
<td align="center">50</td>
<td align="center">50</td>
</tr>
<tr>
<td align="center">C34P48</td>
<td align="center">34</td>
<td align="center">48</td>
<td align="center">18</td>
<td align="center">82</td>
</tr>
<tr>
<td align="center">C38P32</td>
<td align="center">38</td>
<td align="center">32</td>
<td align="center">30</td>
<td align="center">70</td>
</tr>
<tr>
<td align="center">C42P16</td>
<td align="center">42</td>
<td align="center">16</td>
<td align="center">42</td>
<td align="center">58</td>
</tr>
<tr>
<td align="center">C46P44</td>
<td align="center">46</td>
<td align="center">44</td>
<td align="center">10</td>
<td align="center">90</td>
</tr>
<tr>
<td align="center">C50P28</td>
<td align="center">50</td>
<td align="center">28</td>
<td align="center">22</td>
<td align="center">78</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s2-2-2">
<label>2.2.2</label>
<title>Preparation process</title>
<p>Tests followed the <italic>&#x201c;Standard for Test Method of Basic Properties of Construction Mortar&#x201d; (JGJ/T 70-2009)</italic> (<xref ref-type="bibr" rid="B28">Ministry of Housing and Urban Rural Development of the People&#x2019;s Republic of China, 2009</xref>). CKD, PG, and FA were dried in an electric blast drying oven manufactured by Tianjin Diyuan Experimental Instrument Co., Ltd. The dried materials were batched according to predetermined mix proportions and amended with a phosphoric acid activator at 1.5% by mass of total solids. The activator was dissolved in water pre-weighed to achieve the optimum moisture content, and the mixture was homogenized. This activator dosage was adopted from an industrial partner&#x2019;s process formulation. The established proportion served as the basis for systematic investigation of the reaction mechanisms and macroscopic properties of the CKD-PG-FA composite. The findings provide a theoretical foundation for optimizing this solid-waste utilization scheme.</p>
<p>The mass of each component was calculated to prepare specimens at the optimum dry density and optimum moisture content determined by the Proctor test, following the <italic>&#x201c;Test Methods of Soils for Highway Engineering&#x201d; (JTG 3430-2020)</italic> (<xref ref-type="bibr" rid="B31">Ministry of Transport of the People&#x2019;s Republic of China, 2020</xref>). Accordingly, the quantities required to cast a standard 50 mm &#xd7; 50 mm cylindrical specimen were determined. All material quantities were increased by a safety factor of 1.2 to allow for potential loss. The phosphoric activator was dissolved in the mixing water and added directly to the dry mixture. No pre-wetting or resting of the mixture was performed, since these steps would alter the test results. Individual materials were weighed on an electronic balance with 0.1 g precision. The measured mixture was placed into the mold in five layers. Each layer was compacted using a tamping rod. Filter paper was laid flat on the mold base before filling. After the final layer was placed, filter paper was positioned above the mixture and the upper plunger was installed. Filled molds were statically compacted and demolded using an LD189 demolding machine. The demolded specimens were tightly wrapped in preservative film and cured in a standard constant-temperature, constant-humidity chamber at (20 &#xb1; 2) &#xb0;C and relative humidity &#x2265;95% for subsequent testing.</p>
</sec>
</sec>
</sec>
<sec id="s3">
<label>3</label>
<title>Experimental methods</title>
<sec id="s3-1">
<label>3.1</label>
<title>UCS test</title>
<p>UCS tests followed the <italic>&#x201c;Technical Guidelines for Construction of Highway Roadbases&#x201d; (JTG/T F20-2015)</italic> (<xref ref-type="bibr" rid="B29">Ministry of Transport of thePeople&#x2019;s Republic of China, 2015</xref>). Cylindrical specimens (50 mm &#xd7; 50 mm) were cured in a constant-temperature, constant-humidity chamber at (20 &#xb1; 2) &#xb0;C and relative humidity &#x2265;95% for 7 days. Tests were performed on a universal testing machine at a constant loading rate of 1 mm &#xd7; min<sup>-1</sup>. Six specimens were tested per group. Specimens subjected to F-T cycling were removed after the prescribed number of cycles and immediately tested under the same loading conditions.</p>
</sec>
<sec id="s3-2">
<label>3.2</label>
<title>Water stability test</title>
<p>Specimens were cured for 7 days in accordance with the <italic>&#x201c;Test methods of materials stabilized with inorganic binders for highway engineering&#x201d; (JTG 3441-2024)</italic> (<xref ref-type="bibr" rid="B32">Ministry of Transport of the People&#x2019;s Republic of China, 2024</xref>). Water immersion tests were performed for ten mix proportions. Each mix proportion included six specimens. The specimens were fully submerged in water for 1 day. Subsequently, UCS was measured for specimens showing no obvious corner damage.</p>
</sec>
<sec id="s3-3">
<label>3.3</label>
<title>F-T cycle tests</title>
<p>This test evaluated the F-T resistance of ternary geopolymer mixtures. Cylindrical specimens measuring 50 mm in diameter and 50 mm in height were tested using an air-air F-T protocol (dry-freezing method). This protocol reproduces the unsaturated conditions of subgrade in cold regions that undergo seasonal F-T cycling. Specimens remained in the chamber atmosphere during freezing and thawing and did not contact liquid water. Specimens were placed directly on the chamber racks. Temperature was decreased from ambient temperature to &#x2212;20 &#xb0;C over 30 min and maintained at &#x2212;20 &#xb0;C for 4 h. It was then increased to 20 &#xb0;C over 30 min and maintained at 20 &#xb0;C for 4 h. One complete sequence constituted a single F-T cycle. Fifteen cycles were chosen as the evaluation endpoint following conventional rapid screening methods for novel cementitious materials. This cycle count has been widely adopted in similar solid-waste-based geopolymer studies (<xref ref-type="bibr" rid="B22">Liu et al., 2021</xref>; <xref ref-type="bibr" rid="B49">Wang et al., 2020</xref>) and was sufficient to discriminate performance differences among mix proportions and to provide preliminary durability guidance for engineering applications. Specimens were removed after 3, 6, 10, and 15 cycles to determine UCS. Compressive strength loss rate was calculated in accordance with the <italic>&#x201c;Test methods of materials stabilized with inorganic binders for highway engineering&#x201d; (JTG 3441-2024)</italic> (<xref ref-type="bibr" rid="B32">Ministry of Transport of the People&#x2019;s Republic of China, 2024</xref>).</p>
</sec>
<sec id="s3-4">
<label>3.4</label>
<title>UPV test</title>
<p>Different mix proportions yield varying amounts of cementitious products, which in turn alter the specimens&#x2019; pore structures and overall compactness. UPV testing was employed to assess internal heterogeneities and detect defects. UPV serves as an indicator of internal defects: higher UPV indicates greater compactness. This technique is widely applied to nonmetallic materials because UPV decreases when waves pass through pores or cracks. Therefore, comparison of UPVs among specimens with varying mix proportions enabled identification of the suitable mix ratio range for CKD-PG-FA-based geopolymer.</p>
<p>A TICO-type nonmetallic ultrasonic tester equipped with a 150 kHz transducer center frequency was used. The test path distance L was set to 50 mm to match the specimen dimensions (50 mm diameter, 50 mm height). A through-transmission method was employed. Coupling agent was applied uniformly to the transducer faces and to both ends of each cylindrical specimen. The probes were then positioned at the centers of the specimen end faces, and good probe-specimen contact was confirmed before measurement. The instrument was activated to record UPV. Each specimen was measured at least three times to minimize error. When consecutive measurements were consistent or showed only minor variation, the repeated value was taken as the specimen&#x2019;s UPV.</p>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Results and analysis</title>
<p>Although this study focused on results at a 7-day curing age, the findings were relevant to long-term performance. Geopolymer research has corroborated this pattern. For example, Dong et al. showed that, for optimized geopolymer mortars, the 7-day compressive strength reaches more than 73% of the 28-day strength (<xref ref-type="bibr" rid="B9">Dong, 2021</xref>); Nie et al. reported that, for vanadium&#x2013;titanium ore tailing&#x2013;based geopolymers, the ratio can be as high as approximately 90% (<xref ref-type="bibr" rid="B35">Nie, 2024</xref>). Collectively, these reports indicate that early-age strength reliably predicts subsequent strength development. In the present study, long-term durability metrics such as freeze&#x2013;thaw resistance and water stability are largely governed by the structural compactness established at early ages (<xref ref-type="bibr" rid="B6">&#xc7;elikten et al., 2025</xref>). Previous work has likewise emphasized that achieving a dense early-age microstructure through mix-proportion optimization is essential to confer superior freeze&#x2013;thaw and corrosion resistance (<xref ref-type="bibr" rid="B9">Dong, 2021</xref>; <xref ref-type="bibr" rid="B35">Nie, 2024</xref>). Our results extend this relationship to the novel ternary system of kiln ash&#x2013;phosphogypsum&#x2013;fly ash. The strong correlations we observed among 7-day strength, ultrasonic velocity, and indicators of freeze&#x2013;thaw resistance and water stability (see <xref ref-type="table" rid="T1">Tables 1</xref>&#x2013;<xref ref-type="table" rid="T7">7</xref>; <xref ref-type="fig" rid="F1">Figures 1</xref>&#x2013;<xref ref-type="fig" rid="F4">4</xref>) provide concrete evidence that early-age properties effectively indicate long-term durability in this system. The primary objective was to establish a quantitative relationship between mixture proportion and early-age performance for this novel ternary geopolymer system (<xref ref-type="bibr" rid="B20">Li et al., 2026</xref>), thereby enabling mixture optimization. Consequently, the 7-day performance database enables precise identification of promising proportion ranges and provides a solid foundation for subsequent, more comprehensive studies of long-term durability (e.g., 28-day and 90-day assessments).</p>
<table-wrap id="T6" position="float">
<label>TABLE 6</label>
<caption>
<p>UCS loss extent of CKD-PG-FA-based geopolymer.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th rowspan="2" align="center">Specimens</th>
<th colspan="5" align="center">UCS loss extent (%)</th>
</tr>
<tr>
<th align="center">0 cycle</th>
<th align="center">3 cycles</th>
<th align="center">6 cycles</th>
<th align="center">10 cycles</th>
<th align="center">15 cycles</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">C14P40</td>
<td align="center">0</td>
<td align="center">2.14</td>
<td align="center">4.89</td>
<td align="center">11.93</td>
<td align="center">24.77</td>
</tr>
<tr>
<td align="center">C18P24</td>
<td align="center">0</td>
<td align="center">2.71</td>
<td align="center">8.53</td>
<td align="center">13.57</td>
<td align="center">20.54</td>
</tr>
<tr>
<td align="center">C22P52</td>
<td align="center">0</td>
<td align="center">0.70</td>
<td align="center">2.80</td>
<td align="center">6.07</td>
<td align="center">8.88</td>
</tr>
<tr>
<td align="center">C26P36</td>
<td align="center">0</td>
<td align="center">1.71</td>
<td align="center">5.43</td>
<td align="center">11.71</td>
<td align="center">19.14</td>
</tr>
<tr>
<td align="center">C30P20</td>
<td align="center">0</td>
<td align="center">3.50</td>
<td align="center">9.79</td>
<td align="center">17.48</td>
<td align="center">25.52</td>
</tr>
<tr>
<td align="center">C34P48</td>
<td align="center">0</td>
<td align="center">0.95</td>
<td align="center">2.86</td>
<td align="center">6.11</td>
<td align="center">7.44</td>
</tr>
<tr>
<td align="center">C38P32</td>
<td align="center">0</td>
<td align="center">0.82</td>
<td align="center">2.47</td>
<td align="center">4.74</td>
<td align="center">7.63</td>
</tr>
<tr>
<td align="center">C42P16</td>
<td align="center">0</td>
<td align="center">3.47</td>
<td align="center">6.07</td>
<td align="center">9.83</td>
<td align="center">12.72</td>
</tr>
<tr>
<td align="center">C46P44</td>
<td align="center">0</td>
<td align="center">0.31</td>
<td align="center">1.08</td>
<td align="center">1.69</td>
<td align="center">2.62</td>
</tr>
<tr>
<td align="center">C50P28</td>
<td align="center">0</td>
<td align="center">0.87</td>
<td align="center">2.17</td>
<td align="center">3.91</td>
<td align="center">5.00</td>
</tr>
</tbody>
</table>
</table-wrap>
<table-wrap id="T7" position="float">
<label>TABLE 7</label>
<caption>
<p>Multi-criteria decision matrix for ternary geopolymer mixtures.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="center">Specimens</th>
<th align="center">7-day UCS (MPa)</th>
<th align="center">Billing</th>
<th align="center">7-day immersion strength (MPa)</th>
<th align="center">Billing</th>
<th align="center">UCS loss rate after 15 F-T cycles (%)</th>
<th align="center">Billing</th>
<th align="center">UPV (m &#xd7; s<sup>-1</sup>)</th>
<th align="center">Billing</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="center">C46P44</td>
<td align="center">6.49</td>
<td align="center">1</td>
<td align="center">6.33</td>
<td align="center">1</td>
<td align="center">2.62</td>
<td align="center">1</td>
<td align="center">1870</td>
<td align="center">1</td>
</tr>
<tr>
<td align="center">C50P28</td>
<td align="center">4.6</td>
<td align="center">3</td>
<td align="center">4.21</td>
<td align="center">4</td>
<td align="center">5.00</td>
<td align="center">2</td>
<td align="center">1,640</td>
<td align="center">4</td>
</tr>
<tr>
<td align="center">C34P48</td>
<td align="center">5.24</td>
<td align="center">2</td>
<td align="center">4.84</td>
<td align="center">2</td>
<td align="center">7.44</td>
<td align="center">3</td>
<td align="center">1790</td>
<td align="center">2</td>
</tr>
<tr>
<td align="center">C38P32</td>
<td align="center">4.85</td>
<td align="center">4</td>
<td align="center">4.49</td>
<td align="center">3</td>
<td align="center">7.63</td>
<td align="center">4</td>
<td align="center">1,380</td>
<td align="center">7</td>
</tr>
<tr>
<td align="center">C22P52</td>
<td align="center">4.28</td>
<td align="center">5</td>
<td align="center">3.85</td>
<td align="center">5</td>
<td align="center">8.88</td>
<td align="center">5</td>
<td align="center">1780</td>
<td align="center">3</td>
</tr>
<tr>
<td align="center">C42P16</td>
<td align="center">3.46</td>
<td align="center">7</td>
<td align="center">3.05</td>
<td align="center">7</td>
<td align="center">12.72</td>
<td align="center">6</td>
<td align="center">1,450</td>
<td align="center">5</td>
</tr>
<tr>
<td align="center">C26P36</td>
<td align="center">3.5</td>
<td align="center">6</td>
<td align="center">3.24</td>
<td align="center">6</td>
<td align="center">19.14</td>
<td align="center">7</td>
<td align="center">1,430</td>
<td align="center">6</td>
</tr>
<tr>
<td align="center">C18P24</td>
<td align="center">2.58</td>
<td align="center">10</td>
<td align="center">2.07</td>
<td align="center">10</td>
<td align="center">20.54</td>
<td align="center">8</td>
<td align="center">1,070</td>
<td align="center">10</td>
</tr>
<tr>
<td align="center">C14P40</td>
<td align="center">3.27</td>
<td align="center">8</td>
<td align="center">2.65</td>
<td align="center">8</td>
<td align="center">24.77</td>
<td align="center">9</td>
<td align="center">1,240</td>
<td align="center">9</td>
</tr>
<tr>
<td align="center">C30P20</td>
<td align="center">2.86</td>
<td align="center">9</td>
<td align="center">2.18</td>
<td align="center">9</td>
<td align="center">25.52</td>
<td align="center">10</td>
<td align="center">1,250</td>
<td align="center">8</td>
</tr>
</tbody>
</table>
</table-wrap>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>UPV as a function of total CKD-PG dosage (mean &#xb1; standard deviation).</p>
</caption>
<graphic xlink:href="fmats-13-1774063-g001.tif">
<alt-text content-type="machine-generated">Line graph showing ultrasonic velocity, measured in meters per second, increasing with C&#x2b;P percentage. Data points, represented by black squares with error bars, indicate a general upward trend with minor fluctuations.</alt-text>
</graphic>
</fig>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Variation of 7-day UCS with the total CKD-PG content (mean &#xb1; standard deviation).</p>
</caption>
<graphic xlink:href="fmats-13-1774063-g002.tif">
<alt-text content-type="machine-generated">Line graph showing 7-day unconfined compressive strength (UCS) in megapascals on the vertical axis and C plus P percentage on the horizontal axis, with UCS increasing as C plus P percentage rises. Error bars indicate variability.</alt-text>
</graphic>
</fig>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Relationship between total CKD-PG content and water stability (mean &#xb1; standard deviation).</p>
</caption>
<graphic xlink:href="fmats-13-1774063-g003.tif">
<alt-text content-type="machine-generated">Line graph with black square markers and error bars shows seven-day immersed unconfined compressive strength (UCS) in megapascals on the y-axis versus C plus P percentage on the x-axis, demonstrating a general upward trend as C plus P increases.</alt-text>
</graphic>
</fig>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Relationship between the number of F-T cycles and the UCS loss extent of geopolymer.</p>
</caption>
<graphic xlink:href="fmats-13-1774063-g004.tif">
<alt-text content-type="machine-generated">Line graph showing compressive strength loss extent in percent on the y-axis versus freeze-thaw cycles on the x-axis for ten material compositions. Loss extent increases with cycles, with C30P20 and C14P40 showing the highest loss after fifteen cycles.</alt-text>
</graphic>
</fig>
<sec id="s4-1">
<label>4.1</label>
<title>UPV</title>
<p>
<xref ref-type="fig" rid="F1">Figure 1</xref> showed that the 7-day UPV of the ternary geopolymer increased as the total CKD-PG dosage rose. It increased from 1,070 m &#xd7; s<sup>-1</sup> (C18P24) to 1,870 m &#xd7; s<sup>-1</sup> (C46P44). This trend indicated that the total CKD-PG dosage governed internal compactness. The pronounced UPV increase reflected a macroscopic reduction in internal porosity and improved continuity of the solid skeleton. These results corroborated Mahmood et al. (<xref ref-type="bibr" rid="B26">Mahmood et al., 2022</xref>), who identified UPV as a reliable indicator of geopolymer reaction progress and structural densification. Notably, the UPV growth curve showed a pronounced inflection at approximately 70% total CKD-PG dosage. Below this threshold, UPV increased slowly. At or above this threshold, the increase became markedly steeper. This pattern indicated that once reactive calcium and sulfate sources exceeded a critical level of &#x223c;70%, gelation reactions and structure-forming mechanisms interacted synergistically and induced a qualitative change in pore architecture. As UPV is a key macroscopic indicator of internal compactness, it provides essential structural evidence to explain subsequent variations in mechanical performance and durability. A comparable trend was reported for FA-based engineered geopolymer composites (FA-EGC), where UPV increases were attributed to matrix densification caused by pore filling with gel products (<xref ref-type="bibr" rid="B12">Guo and Li, 2023</xref>). The maximum UPV measured in this study reached 1,870 m &#xd7; s<sup>-1</sup>, a relatively high value. Therefore, these results indicated that the current ternary system strongly promotes the development of a highly dense microstructure.</p>
</sec>
<sec id="s4-2">
<label>4.2</label>
<title>7-day UCS</title>
<p>
<xref ref-type="fig" rid="F2">Figure 2</xref> present the 7-day UCS results for geopolymers prepared with varying mix proportions. The 7-day UCS increased with total CKD-PG dosage. It rose from 2.58 MPa for C18P24 to 6.49 MPa for C46P44 (<xref ref-type="fig" rid="F2">Figure 2</xref>). This trend closely paralleled changes in UPV. Both UCS and UPV exhibited accelerated gains when the total CKD-PG dosage exceeded 70%. The concurrent increases indicated that strength development was closely linked to densification of the internal microstructure. Higher CKD-PG dosage increased the availability of reactive species (e.g., Ca<sup>2&#x2b;</sup>). Interaction with sulfate anions promoted geopolymerization efficiency and improved binding of reaction products. These effects produced a more robust solid framework. The C46P44 mix exhibited the highest 7-day UCS (6.49 MPa) and the greatest structural compactness (UPV &#x3d; 1,870 m &#xd7; s<sup>-1</sup>).</p>
<p>Moreover, the 7-day UCS values of the geopolymers satisfy the requirements for highway subgrade. 7-day UCS exceeded 6 MPa. This value is well above the &#x3e;0.8 MPa threshold for conventional lime-FA stabilized-materials specified in the <italic>&#x201c;Technical guidelines for construction of highway roadbases (JTG/T F20-2015)&#x201d;</italic> (<xref ref-type="bibr" rid="B29">Ministry of Transport of the People&#x2019;s Republic of China, 2015</xref>). The 7-day UCS of the C46P44 mixture exceeded the typical range reported for cement-stabilized materials (4-6 MPa).</p>
</sec>
<sec id="s4-3">
<label>4.3</label>
<title>Water stability</title>
<p>
<xref ref-type="fig" rid="F3">Figure 3</xref> showed that post-immersion strength increased as total CKD-PG dosage rose. This trend matched changes in UPV. Water stability was governed by a geopolymer&#x2019;s resistance to moisture ingress and softening. That resistance depended directly on internal structure. Higher UPV therefore signified a denser microstructure. Such densification more effectively blocked capillary moisture transport and internal penetration. Consequently, the observed improvement in water stability was primarily attributable to the physical barrier provided by structural densification rather than to the pre-immersion strength alone. This interpretation clarified the apparent anomaly in <xref ref-type="fig" rid="F3">Figure 3</xref>, where C38P32 (total CKD-PG dosage &#x3d; 70%) showed better water stability than C22P52 (total CKD-PG dosage &#x3d; 74%). Small changes in mix proportions near performance thresholds can substantially alter the degree of geopolymer network densification and thus produce fluctuations in water resistance. This finding aligns with studies of binary FA-slag geopolymer systems that identify specific component ratios as key regulators of final performance (<xref ref-type="bibr" rid="B13">Guo et al., 2026</xref>). The present study further demonstrated that, once total CKD-PG dosage exceeded the performance threshold, the CKD:PG ratio decisively controlled the extent of structural densification and the composite&#x2019;s overall performance.</p>
</sec>
<sec id="s4-4">
<label>4.4</label>
<title>Loss extent of UCS</title>
<p>Damage to the ternary geopolymer specimens increased with the number of F-T cycles, and UCS progressively decreased. <xref ref-type="table" rid="T6">Table 6</xref> and <xref ref-type="fig" rid="F4">Figure 4</xref> summarize the UCS loss extents for each mix proportion. The UCS loss extent rose steadily as the number of F-T cycles increased. After 15 cycles, the largest strength loss extent of 25.52% occurred in specimen C30P20. This value exceeded the code-specified limit of 25%. This outcome is primarily attributable to the low PG content (20%) combined with a high FA proportion. FA contained few constituents that promote early strength development. As a result, it formed a loose microstructure and exhibited a low baseline 7-day UCS, which in turn exacerbated subsequent strength loss. After 15 F-T cycles, specimen C46P44 exhibited the smallest strength loss extent of 2.62%. Therefore, it demonstrated superior frost resistance. This performance is attributed to the lower FA content and higher total CKD-PG dosage, which increased the concentration of chemical species that promote early strength development and produced a denser geopolymer matrix.</p>
<p>
<xref ref-type="fig" rid="F4">Figure 4</xref> revealed a distinct threshold in the geopolymer&#x2019;s F-T resistance. A total CKD-PG dosage of 70% (i.e., 30% FA) served as the breakpoint for specimen behavior. When total CKD-PG dosage was less than 70%, specimens experienced relatively large UCS losses after 15 F-T cycles. For example, C26P36, C18P24, and C14P40 lost 19.14%, 20.54%, and 24.77% of UCS, respectively. These values approached the code-specified limit of 25%. In contrast, when total CKD-PG dosage was greater than or equal to 70%, strength losses after 15 F-T cycles were much smaller. C50P28, C38P32, and C34P48 exhibited loss extents of 5%, 7.63%, and 7.44%, respectively. This performance bifurcation at the 70% total CKD-PG dosage stems fundamentally from differences in the materials&#x2019; initial structural compactness. The principle that structural integrity governs F-T durability has been demonstrated in other cementitious systems, such as slag-FA-based fiber-reinforced controllable low-strength materials (SGF-CLSM) (<xref ref-type="bibr" rid="B54">Xu et al., 2025</xref>). Low CKD-PG formulations contain higher proportions of FA and developed a loosely bound microstructure because early-stage binding was insufficient. As a result, these formulations retained a larger fraction of freezable pore water. During F-T cycles, expansion stresses produced by freezing pore water readily damaged the fragile solid framework and caused substantial strength loss. In contrast, high CKD-PG formulations with lower FA content developed a denser microstructure. This reduced the volume of freezable water and yielded a stronger skeleton that resisted and redistributed internal pressures generated by ice crystal growth. This mechanism&#x2014;where differences in structural compactness control F-T resistance&#x2014;agreed with the densification trends observed in UPV measurements.</p>
</sec>
<sec id="s4-5">
<label>4.5</label>
<title>Determination of the optimal proportion based on multi-criteria decision making</title>
<p>
<xref ref-type="table" rid="T7">Table 7</xref> showed that the C46P44 mixture ranked first on all four metrics. C46P44 therefore outperformed the other mixtures across individual properties and achieved a balanced superiority in strength, durability, and internal structural density. Other mixtures displayed deficiencies in at least one critical metric. For example, C50P28 demonstrated suboptimal strength and UPV, while C38P32 was deficient in moisture stability and frost resistance.</p>
<p>Multi-criteria decision-making methods provide an effective framework for resolving trade-offs among composite performance metrics in material design and optimization (<xref ref-type="bibr" rid="B11">Gao and Y, 2014</xref>). Following this framework, the present study constructed a multi-criteria decision matrix (<xref ref-type="table" rid="T7">Table 7</xref>) and conducted a systematic comparison. The results showed that the mixture composed of 46% CKD, 44% PG, and 10% FA (C46P44) outperformed the other mixtures across all key pavement-use performance indicators. Accordingly, C46P44 was identified as the optimal formulation. This selection reflects coordinated multi-criteria optimization rather than the maximization of any single property.</p>
</sec>
</sec>
<sec sec-type="discussion" id="s5">
<label>5</label>
<title>Discussion</title>
<sec id="s5-1">
<label>5.1</label>
<title>Comparison with binary alkali-activated systems</title>
<p>The optimal mix C46P44 (46% CKD, 44% PG, 10% FA) achieved a 7-day UCS of 6.49 MPa. UCS loss after 15 F-T cycles was only 2.62%. UPV reached 1,870 m &#xd7; s<sup>-1</sup>. These results indicated excellent overall performance. The present ternary, acid-activated system offers a greater capacity for waste incorporation and improved F-T resistance. Its reaction mechanisms differ from those of prevailing alkali-activated binary systems composed of FA and slag. Recent studies indicate that typical alkali-activated systems retain high strength only when waste content is generally below 80% (<xref ref-type="bibr" rid="B62">Zhou Y. et al., 2025</xref>). The current system attains waste incorporation levels up to 90%. The optimal mix reported here exhibited a UCS loss rate of only 2.62% after 15 F-T cycles. This value is substantially lower than losses recently reported for alkali-activated systems, which often exceed 10% (). This discrepancy arises from fundamentally distinct reaction mechanisms. Activation with phosphoric acid formed a dense network dominated by Si-O-Al-O-P linkages, which conferred superior frost resistance. In contrast, alkali-activated systems formed in high-calcium environments are prone to drying shrinkage and alkali-aggregate reactions. These phenomena compromise long-term volumetric stability and degrade F-T durability (<xref ref-type="bibr" rid="B2">Aiken et al., 2023</xref>). Therefore, the ternary acid-activated system offers higher waste utilization capacity and superior F-T performance for subgrade materials in cold regions.</p>
</sec>
<sec id="s5-2">
<label>5.2</label>
<title>Mechanistic investigation of F-T resistance loss caused by high FA content</title>
<p>The experimental results showed that when FA content exceeded 30% (i.e., the total CKD-PG dosage was less than 70%), geopolymer F-T resistance declined markedly. For example, the specimen C30P20 experienced a UCS loss rate of 25.52% after 15 F-T cycles. This deterioration in F-T durability is primarily attributable to two factors. First, a high FA proportion impeded early structural densification. This was evidenced by the specimen&#x2019;s low 7-day UPV (1,250 m &#xd7; s<sup>-1</sup>). FA exhibits low early reactivity in alkali-activated systems, which reduces the formation of reaction products and thereby impairs initial matrix formation and densification (<xref ref-type="bibr" rid="B62">Zhou Y. et al., 2025</xref>). Second, increasing FA content lowers the material&#x2019;s overall capacity to resist F-T damage. Wang et al. (<xref ref-type="bibr" rid="B52">Wang et al., 2025c</xref>) demonstrated that at 70% FA content, post-F-T performance deteriorated substantially. The relative dynamic elastic modulus dropped to 83.8% and mass loss reached 1.74%. Together, these observations confirmed that excessive FA weakened the system&#x2019;s resistance to moisture-induced frost heave and accelerated macroscopic strength loss.</p>
</sec>
<sec id="s5-3">
<label>5.3</label>
<title>Synergistic mechanisms underlying the enhanced performance of the optimal mix C46P44</title>
<p>Mixture C46P44 exhibited the highest UCS, water stability, frost resistance, and UPV. These outcomes reflected synergistic interactions among material composition, activation method, and macroscopic structure. The combined addition of FA and PG reached 90%. This configuration provided abundant reactive components that promoted binding-phase formation. This chemical enrichment underlay the observed high UCS (6.49 MPa). Phosphate activation produced an acidic environment that favored formation of stable Ca<sup>2&#x2b;</sup> and PO<sub>4</sub>
<sup>3-</sup> associations. These phases increased overall structural density and improved water resistance. Macroscopically, the mixture achieved the highest UPV (1,870 m &#xd7; s<sup>-1</sup>). This value indicated the most compact internal structure and optimal continuity. These physical features account for the enhanced UCS and F-T performance. The superior performance of C46P44 emerged only after a defined composition threshold (total CKD-PG dosage &#x2265;70%) was exceeded. Optimizing the proportions of reactive constituents and limiting FA content yielded systematic improvements in reaction efficiency and structural integrity.</p>
</sec>
</sec>
<sec sec-type="conclusion" id="s6">
<label>6</label>
<title>Conclusion</title>
<p>Three industrial solid wastes&#x2014;CKD, PG, and FA&#x2014;were used as raw materials to synthesize a ternary geopolymer activated by phosphoric acid. Systematic tests evaluated early-age performance and identified optimal mix proportions for potential use as subgrade materials. This work constituted the first phase of performance characterization for this novel ternary geopolymer system. It established the relationship between mix proportion and early-age behavior and provided a basis for rapid screening. The main conclusions are as follows.<list list-type="order">
<list-item>
<p>The macroscopic behavior of the geopolymer was governed by the total CKD-PG dosage. A distinct performance optimization threshold was identified. When the total CKD-PG dosage reached or exceeded 70% (i.e., FA content &#x2264;30%), UPV, UCS, and water stability exhibited synergistic improvements. The formulation C46P44 (total CKD-PG dosage &#x3d; 90%) delivered the best overall performance. It yielded a 7-day UCS of 6.49 MPa and an UPV of 1,870 m &#xd7; s<sup>-1</sup>.</p>
</list-item>
<list-item>
<p>The F-T resistance of geopolymers exhibited a threshold at a total CKD-PG dosage of 70%. Mixtures with a total CKD-PG dosage greater than or equal to 70% developed a dense microstructure that substantially reduced the amount of freezable water. Strength loss after 15 F-T cycles was only 2.62%, which demonstrated excellent frost durability. In contrast, mixtures with a total CKD-PG dosage less than 70% experienced compressive strength losses that approached or exceeded the standard limit of 25%.</p>
</list-item>
<list-item>
<p>Comparison of overall performance showed that the optimal mix comprised 46% CKD, 44% PG, and 10% FA (C46P44). The 7-day UCS exceeded the 4-6 MPa range specified for cement-stabilized materials in the <italic>&#x201c;Technical Guidelines for Construction of Highway Roadbases&#x201d; (JTG/T F20-2015).</italic> These results demonstrated the mechanical feasibility of C46P44 as a substitute subgrade material.</p>
</list-item>
<list-item>
<p>Macroscopic performance tests established an empirical mix proportion-structure-performance relationship for the ternary alkali-activated binder system. This relationship provides practical guidance for resource-efficient mix design. The study is the first to systematically investigate the synergistic evolution of macroscopic properties in a CKD-PG-FA ternary system activated by phosphoric acid. A total CKD-PG dosage of 70% was identified as a performance threshold. A multi-indicator cooperative evaluation that included UPV revealed the intrinsic link between structural compactness and macroscopic performance. These results address the existing lack of systematic studies on this system under acid-activation conditions.</p>
</list-item>
</list>
</p>
<p>Future research should focus on optimizing mix proportions and evaluating long-term strength development, drying shrinkage, and resistance to carbonation. Such investigations will support the translation of the material into practical engineering applications. Microstructural techniques such as XRD and SEM should be employed to elucidate the synergistic cementation mechanisms induced by phosphoric acid activation. Finally, a service-performance prediction model should be developed to provide a theoretical foundation for standardized application.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s7">
<title>Data availability statement</title>
<p>The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.</p>
</sec>
<sec sec-type="author-contributions" id="s8">
<title>Author contributions</title>
<p>DL: Project administration, Resources, Supervision, Writing &#x2013; review and editing. YC: Conceptualization, Formal Analysis, Methodology, Software, Visualization, Writing &#x2013; original draft, Writing &#x2013; review and editing. FG: Investigation, Validation, Writing &#x2013; review and editing. ZC: Investigation, Writing &#x2013; review and editing. QZ: Investigation, Writing &#x2013; review and editing.</p>
</sec>
<sec sec-type="COI-statement" id="s10">
<title>Conflict of interest</title>
<p>The author(s) declared that this work 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="ai-statement" id="s11">
<title>Generative AI statement</title>
<p>The author(s) declared that generative AI was not used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p>
</sec>
<sec sec-type="disclaimer" id="s12">
<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>
</sec>
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<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/2127862/overview">Zenian Wang</ext-link>, Jiangsu University, China</p>
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