## 2 Materials and Methods
### Specim Design  
The proportioning design of ISWs in stabilized aeolian sand specimens was programmed according to the following steps: (a) determination of a basic dosage based on TCM of OPC; (b) establishment of the ISW dosage range using the basal dosage as a reference point; and (c) configuration of experimental points by defining the dosage range's supper and lower limits within the simplex lattice design framework.  
The reference OPC, compliant with Chinese Portland cement standards [57] and supplied by China United Cement Corporation, was used to determine the basic proportion of ISWs through TCM methodology. Based on the oxide composition of the clinker (SiO\({}_{2}\), Al\({}_{2}\)O\({}_{3}\), Fe\({}_{2}\)O\({}_{3}\), and CaO as listed in Table 1), its TCM were calculated using Equations (1)-(3), yielding values of \(SM=2.29\), \(IM=1.47\), and \(KH=0.91\). By integrating the oxide compositions of ISWs, a quaternary linear equation system (Equation (4)) was formulated. In Equation (4), rows of the coefficient matrix represent oxide contents within ISWs, while columns correspond to distinct oxide components. The right-hand vector denotes the required oxide quantities to achieve TCM equivalence with the reference OPC. As a result, the basic proportion of ISWs was determined as SS:GGBFS:PS:CS = 10.0:18.1:26.8:57.1.  
\[SM=\frac{\text{SiO}_{2}}{\text{Al}_{2}\text{O}_{3}+\text{Fe}_{2}\text{O}_{3}}, \tag{1}\]  
\[IM=\frac{\text{Al}_{2}\text{O}_{3}}{\text{Fe}_{2}\text{O}_{3}}, \tag{2}\]  
\[KH=\frac{\text{CaO}-1.65\text{Al}_{2}\text{O}_{3}-0.35\text{Fe}_{2}\text{O}_{3 }}{2.8\text{SiO}_{2}}, \tag{3}\]  
\[\left\{\begin{array}{l}17.18m_{\text{SS}}+31.07m_{\text{GGBFS}}+44.89m_{ \text{IPS}}+2.31m_{\text{CS}}=20.24\\ 30.01m_{\text{SS}}+38.22m_{\text{GGBFS}}+43.97m_{\text{IPS}}+70.35m_{\text{ ICS}}=60.93\\ 29.1m_{\text{SS}}+0.88m_{\text{GGBFS}}+0.01m_{\text{IPS}}+1.03m_{\text{CS}}=3.58 \\ 8.43m_{\text{SS}}+16.5m_{\text{GGBFS}}+3.88m_{\text{IPS}}+0.89m_{\text{CS}}=5.2 6\end{array}\right. \tag{4}\]  
where \(m_{i}\) stand for dosages of ISWs \(i\).  
The experimental determination of cementitious material for aeolian sand stabilization constitutes a typical mixture design with specific constraints requiring the summation of all component dosages to equal 100%. The simplex lattice method (SLM) serves as a conventional framework for such experimental configurations. Given that the binder developed in this study comprises four types of ISWs, the experimental points were distributed within a regular tetrahedron, as illustrated in Figure 3, where each axis represents a distinct ISW component and each vertex corresponds to a specific proportion. The lattice degree of SLM was specified as three, establishing three compositional levels for each ISW, and the design was augmented with axial points and centroid point. A total of 26 test specimens were designed, comprising 25 SLM-designed proportions and one basic proportion. Additionally, the binder content was set at 11% of the aeolian sand mass, while water content was set at 9%, which has the maximum stabilization aeolian sand strength according to previous study [30]. The proportion of experiment points is listed in Table 2. Additionally, to compare the effectiveness of ISW-CMs and cement in stabilizing aeolian sand, a control group utilizing cement with an equivalent dosage was established.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multicolumn{4}{c}{**Proportion of ISWs (\%)**} \\ \cline{2-5}  & **SS** & **GGBFS** & **PS** & **CS** \\ \hline  
CE & - & - & - & - \\ \hline \hline \end{tabular}
\end{table}
Table 2: Proportion of ISWs in design experiment points.