Strength Prediction and Mixture Optimization of Cement–Industrial-Solid-Waste-Stabilized Waste Soil Using Projection Pursuit Regression

Abstract

Waste soil generated by building and underground construction is commonly characterized by high water content and low strength, while conventional cement stabilization entails high cement consumption. This study develops two low-cement binders incorporating ordinary Portland cement (P), carbide slag (CS), ground granulated blast-furnace slag (GGBS), and fly ash (FA) and establishes projection pursuit regression (PPR) models for predicting the unconfined compressive strength (UCS) of stabilized soil. Orthogonal and supplementary tests were conducted by varying total binder content, curing age, solid-waste replacement ratio, and compaction pressure. Separate PPR models were calibrated for the P–CS–GGBS (PC) and P–CS–GGBS–FA (PF) systems using 12 training and 10 within-domain validation mixtures. The mean relative errors for the training and validation sets were 3.46% and 5.68% for PC and 3.09% and 4.87% for PF, respectively. For both systems, the solid-waste replacement ratio was the dominant variable, followed by curing age, binder content, and compaction pressure. Model-based optimization identified binder compositions containing 75% solid waste for PC and 60% for PF, with recommended internal proportions of 25% P–18.75% CS–56.25% GGBS and 40% P–15% CS–22.5% GGBS–22.5% FA, respectively. The proposed framework provides a practical tool for strength prediction and mixture design of low-cement-stabilized waste soil.

1. Introduction

Rapid urbanization and the expansion of building and underground-space construction generate substantial quantities of excavated soil from foundation pits, basements, utility corridors, and related earthworks [1,2,3,4]. Such materials commonly exhibit high water content, low strength, and high compressibility, which restrict their direct reuse as engineered fill [5,6,7]. Conventional stockpiling or off-site disposal also increases land occupation, transportation demand, and the risk of secondary environmental impacts. Developing technically reliable routes for converting excavated soil into usable construction material is therefore important for both resource efficiency and sustainable construction.

Ordinary Portland cement is widely used to improve the mechanical properties of weak soils because its hydration products bind soil particles and fill internal pores [8,9,10,11,12]. Nevertheless, cement-intensive stabilization increases material cost and embodied carbon, which conflicts with the demand for lower-carbon construction practices [13,14]. Partial replacement of ordinary Portland cement with industrial solid wastes provides a potentially effective alternative [15,16,17]. In particular, carbide slag is rich in calcium-bearing alkaline phases, ground granulated blast-furnace slag contains reactive calcium–silicate–aluminate components, and fly ash can contribute additional siliceous and aluminous phases [18,19,20,21,22]. When appropriately proportioned, these materials may promote the formation of cementitious reaction products, densify the soil skeleton, and reduce the amount of virgin cement required [23,24,25].

Previous studies have demonstrated that combinations of slag, fly ash, carbide slag, gypsum, steel slag, red mud, and other industrial by-products can improve the strength, bearing capacity, water stability, and durability of different soils [26]. However, the reported performance varies markedly with soil type, binder chemistry, curing condition, and compaction procedure. In particular, FA [27,28,29] generally reacts more slowly than highly calcium-rich constituents, whereas CS [30,31] can alter the alkalinity of the reaction environment, and GGBS [32,33,34] can contribute to both early- and later-age strength development. Consequently, the mechanical response of cement–solid-waste-stabilized soil cannot be inferred from the effect of an individual component alone. The coupled influences of total binder content, curing age, solid-waste replacement ratio, and compaction pressure must be evaluated simultaneously.

Most mixture-design studies on stabilized soils rely on orthogonal tests, response-surface analysis, or conventional regression to identify influential variables and optimum proportions [35,36,37]. These approaches are useful, but they may provide limited representations when the response is nonlinear and several factors interact. More complex machine learning models can improve prediction accuracy, although their internal relationships are often difficult to interpret, and their reliability may be uncertain for small experimental datasets. Projection pursuit regression (PPR) offers an alternative by expressing a multivariable response as a sum of smooth ridge functions constructed from linear projections of the original predictors [38]. This formulation can capture nonlinear relationships while reducing the effective dimensionality of the problem. Nevertheless, its use for jointly predicting strength and supporting mixture optimization in cement–industrial-solid-waste-stabilized excavated soil remains comparatively limited.

The present study investigates two composite binder systems: a P–CS–GGBS blend, denoted as PC, and a P–CS–GGBS–FA blend, denoted as PF. The solid-waste replacement ratio is defined as the mass fraction of CS, GGBS, and, where applicable, FA in the total binder. Orthogonal and supplementary experiments were conducted by varying total binder content, curing age, solid-waste replacement ratio, and compaction pressure, with unconfined compressive strength (UCS) used as the principal performance indicator. Separate PPR models were then developed and validated for the PC and PF systems. The research findings can provide a scientific reference for the mixture design of stabilized construction excavated soil under different strength requirements.

2. Materials and Methods

2.1. Materials

The waste soil used in this study was collected from an excavation site of a foundation pit project in Hangzhou, Zhejiang Province, China. The basic physical properties of the waste soil were determined according to the Test Methods of Soils for Highway Engineering (JTG 3430-2020) [39], and the results are summarized in Table 1. The particle size distribution of the soil used in the experiment is shown in Figure 1.

Table 1. Basic physical properties of the waste soil.

Liquid Limit (wL, %)	Plastic Limit (wP, %)	Plasticity Index (IP)	Maximum Dry Density (ρd, g·cm−3)	Optimum Water Content (wopt, %)
28.8	11.3	17.5	1.67	18.00

Figure 1. Particle size distribution curve of experimental soil.

The cementitious materials used in this study included ordinary Portland cement (P), ground granulated blast-furnace slag (GGBS, S₇₅ grade), Class C fly ash (FA), and carbide slag (CS). The P was supplied by Tianshan Cement Co., Ltd., Urumqi, China. The GGBS was obtained from Baoxin Shengyuan Co., Ltd., Urumqi, China. The fly ash was collected from a thermal power plant located in Changji, Xinjiang, China. The carbide slag was obtained from the acetylene production process of Huatai Chemical Co., Ltd., Xinjiang, China. The physical appearances of the cementitious materials are shown in Figure 2. The chemical compositions of P, CS, FA, and GGBS were determined using XRF analysis, and the results are presented in Table 2.

Figure 2. Photographs of cementitious materials: (a) P; (b) GGBS; (c) FA; (d) CS.

Table 2. Chemical compositions of cementitious materials (wt.%).

	SiO2	Al2O3	Fe2O3	CaO	MgO	SO3	K2O	Na2O
P	21.3	4.3	3.4	61.3	2.4	2.5	1.4	0.2
CS	4.71	1.36	0.85	69.6	0	0.1	0.03	0.06
FA	48.68	17.53	8.28	12.72	2.49	1.06	1.13	1.04
GGBS	37.94	18.43	0.92	39	2.14	0.22	0.11	0.11

The mineralogical characteristics of the cementitious materials were further analyzed using XRD. As shown in Figure 3, the main characteristic diffraction peaks corresponded to quartz, calcite, and portlandite, which represent the primary calcium source and aluminosilicate components required for alkali-activation reactions.

Figure 3. XRD patterns of cementitious materials: (a) CS; (b) GGBS; (c) FA.

2.2. Sample Preparation and UCS Testing Method

The stabilized waste soil specimens were prepared according to the Test Methods of Materials Stabilized with Inorganic Binders for Highway Engineering (JTG 3441-2024) [40]. Cylindrical specimens with dimensions of 50 mm in diameter and 50 mm in height were prepared using steel molds. According to the design mix proportion, the required amounts of dry waste soil and bonding material were accurately weighed and mixed evenly, where the sum of the content of dry waste soil and bonding material is 100%. Then, 12% water by mass of the dry mixture was added, and the mixture was stirred for 2 min. The mixtures were then gradually placed into the molds in several layers. The filled molds were placed on a universal testing machine and compacted under predetermined pressures. After compaction, the specimens were maintained under pressure for 2 min to ensure sufficient densification and structural stability. Subsequently, the specimens were demolded, and their dimensions and masses were measured using a vernier caliper and electronic balance. The prepared specimens were wrapped with plastic film, labeled, and cured in a controlled curing chamber. The curing conditions were maintained at a temperature of 20 ± 2 °C and a relative humidity above 95%. Specimens were collected at different curing ages for subsequent UCS testing.

UCS testing method:

The UCS is tested using the CMT5204 Electronic Universal Testing Machine (Shandong Wanchen Testing Machine Co., Ltd., Jinan, China). The loading rate of the device is fixed at 1 mm/min, and each set of experiments is repeated three times. The strength values used in this study are the arithmetic mean values calculated from the three replicate measurements. These mean values were explicitly used as the target values in the PPR modeling.

2.3. Experimental Design of Cement–Solid-Waste-Stabilized Waste Soil

Preliminary tests were conducted to develop two optimal geopolymer binder formulations, namely the 25% CS + 75% GGBS system (C) and the 25% CS + 37.5% GGBS + 37.5% FA system (F) [41], and the optimal proportions of each component were determined. The two geopolymer mixtures were adopted to partially replace P. A four-factor and four-level orthogonal test with an L16(4⁴) design was implemented to investigate the mechanical performance of stabilized waste soil. The orthogonal experimental scheme is listed in Table 3.

Table 3. Orthogonal experimental design for stabilized waste soil.

Level	Factors
	Binder Content A/%	Curing Age B/d	Binder Type C	Compaction Pressure D/MPa
1	12	7	C	15
2	15	14	F	20
3	18	28	PC	25
4	21	56	PF	30

The four influencing factors and corresponding levels included: binder content (A) of 12%, 15%, 18%, and 21%; curing age (B) of 7 d, 14 d, 28 d, and 56 d; binder type (C) including C, F, PC, and PF (for the PC group, CS + GGBS blends account for 50% of the total binder, while cement accounts for the other 50%; for the PF group, the CS + GGBS + FA mixture replaces 50% of the cement within the total binder); and compaction pressure (D) of 15 MPa, 20 MPa, 25 MPa, and 30 MPa. A total of 16 groups of experimental combinations were designed.

Based on the measured post-compaction dimensions and masses of all specimens, the 15, 20, 25, and 30 MPa molding pressures corresponded to average compaction degrees of approximately 93.7%, 96.5%, 98.2%, and 99.6%. Thus, the optimum molding pressure of 25 MPa identified in this study corresponds to a compaction degree of approximately 98.22% under the laboratory conditions investigated.

2.4. Projection Pursuit Regression-Based UCS Prediction Model

Projection pursuit regression (PPR) is a nonlinear statistical modeling approach that transforms high-dimensional datasets into low-dimensional projection spaces [42]. By identifying optimal projection directions and analyzing the structural characteristics of projected data, PPR can establish nonlinear relationships between multiple input variables and output responses without assuming a predefined mathematical function.

Assuming that X represents a p-dimensional independent variable vector and Y represents the dependent variable, the general expression of the PPR model can be written as:

$$\stackrel{\wedge }{\mathrm{y}}=E\left(\left.y\right|x\right)=\overline{y}+{\displaystyle \sum _{i=1}^M{\beta }_i{f}_i\left({\displaystyle \sum _{j=1}^P{\alpha }_{ij}{x}_j}\right)}$$

(1)

where f_i represents the ith ridge function; M is the maximum predefined number of candidate ridge functions; M_u is the number of significant ridge functions actually retained in the final model; β_i represents the contribution coefficient of each ridge function; and α_ij represents the projection direction coefficient.

The projection direction satisfies: $E{f}_i=0,E{f}_i^2=1,{\displaystyle \sum ^P{\alpha }_{ij}^2=1}$.

The PPR model determines the optimal projection direction through iterative optimization. The objective function can be expressed as:

$$L_2={\displaystyle \sum _{i=1}^Q{W}_{i}E\left[Y_i-E{Y}_i-{\displaystyle \sum _{i=1}^{M_u}{\beta }_i{f}_i{\left({\displaystyle \sum _{j=1}^P{\alpha }_{ij}{X}_j}\right)}^2}\right]}=min$$

(2)

where W_i is the weighting coefficient.

In this study, UCS data obtained from the orthogonal experiments were used to construct PPR prediction models. The model accuracy was evaluated by comparing predicted and measured UCS values. A relative error of ≤10% was considered an acceptable prediction result.

The modeling procedure followed a chronological sequence to ensure predictive consistency:

(1)

Experimental data were divided into training samples and within-domain validation samples.

(2)

The initial PPR model was established using solely the training samples under a trial Span value.

(3)

The within-domain validation dataset was then introduced to evaluate the prediction error.

(4)

If the prediction accuracy did not meet the adopted engineering tolerance, the Span parameter was adjusted, and the model was rebuilt using the training set.

This tuning process was repeated until the predictive consistency on the validation set was satisfactory, after which the final performance evaluation was conducted.

Parameter settings for assumption-free modeling and calculation of the PPR model are specified as follows: P denotes the number of influencing factors in the model; Q stands for the number of dependent variables; and Span is the smoothing coefficient that determines the sensitivity of the calculation model, with a value ranging from 0 to 1. Establish the PPR model by adjusting the value of Span.

The projection direction of the model is determined based on experimental data, followed by the calculation of ridge functions and their corresponding contribution weight coefficients β. Combined with Formulas (1) and (2), the calculation model for unconfined compressive strength is established using the obtained ridge functions. Meanwhile, the weight coefficients of each influencing factor are quantified. Ultimately, the stability and prediction accuracy of the constructed model are verified with within-domain validation samples. If the predicted values of the constructed model deviate significantly from the values of the within-domain validation samples, it is necessary to change the value of Span, rebuild the model, and then loop until the constructed model has stability and prediction accuracy.

3. Results

3.1. UCS Test Results of Cement–Solid-Waste-Stabilized Waste Soil

The UCS results obtained from the orthogonal experiments are summarized in Table 4. The numbers before the parentheses represent the factor levels, while the values in parentheses indicate the corresponding experimental parameters, including binder content, curing age, binder type, and compaction pressure.

Table 4. Orthogonal experimental results of stabilized waste soil.

No.	Factors				UCS (Mean ± SD)/MPa
	Binder Content A/%	Curing Age B/d	Binder Type C	Compaction Pressure D/MPa
1	1 (12)	1 (7)	1 (C)	1 (15)	0.68 ± 0.022
2	1	2 (14)	2 (F)	2 (20)	0.6 ± 0.027
3	1	3 (28)	3 (PC)	3 (25)	4.69 ± 0.121
4	1	4 (56)	4 (PF)	4 (30)	5.98 ± 0.156
5	2 (15)	1	2	3	0.78 ± 0.022
6	2	2	1	4	2.13 ± 0.051
7	2	3	4	1	5.59 ± 0.170
8	2	4	3	2	6.87 ± 0.156
9	3 (18)	1	3	4	4.97 ± 0.120
10	3	2	4	3	5.68 ± 0.212
11	3	3	1	2	5.46 ± 0.100
12	3	4	2	1	3.22 ± 0.092
13	4 (21)	1	4	2	5.05 ± 0.106
14	4	2	3	1	5.52 ± 0.110
15	4	3	2	4	3.74 ± 0.104
16	4	4	1	3	6.03 ± 0.108
K1	11.95	11.48	14.30	15.01	-
K2	15.37	13.93	8.34	17.98	-
K3	19.33	19.48	22.05	17.18	-
K4	20.34	22.10	22.30	16.82	-
k1	2.99	2.87	3.58	3.75	-
k2	3.84	3.48	2.09	4.50	-
k3	4.83	4.87	5.51	4.30	-
k4	5.09	5.53	5.58	4.21	-
R	2.10	2.66	3.49	0.74	-

According to the orthogonal experimental results, specimen No.8 (A₂B₄C₃D₂) exhibited the highest stabilization performance, with a UCS value of 6.87 MPa. The corresponding experimental conditions were a binder content of 15%, curing age of 56 days, PC binder type, and compaction pressure of 20 MPa.

The range analysis results showed that the range values (R) of binder content, curing age, binder type, and compaction pressure were 2.10, 2.66, 3.49, and 0.74, respectively. Therefore, the sensitivity of UCS to the investigated factors followed the order: binder type > curing age > binder content > compaction pressure.

The binder type exhibited the greatest influence on UCS development, indicating that the chemical composition and reaction activity of the cement–solid-waste binder system played a dominant role in controlling the strength evolution of stabilized waste soil. Therefore, PPR models were further developed for PC and PF stabilization systems to reveal the nonlinear relationships between influencing factors and UCS.

3.2. Performance Analysis of PC-Stabilized Waste Soil

3.2.1. PPR-Based UCS Prediction Model

The PPR model was established based on the UCS results of PC-stabilized waste soil. Twelve experimental datasets were selected as training samples, while ten additional experimental datasets were used for model validation. The training samples were first employed to establish the nonlinear prediction model, and the within-domain validation samples were subsequently introduced to evaluate the predictive capability and stability of the model. The PPR parameters were set as follows: P = 4, Q = 1, Span = 0.5, M = 5, Mu = 3.

After PPR optimization, the projection direction vector of the PC stabilization model was obtained as:

$${\left(\begin{array}{c}{\overrightarrow{\alpha }}_1\\ {\overrightarrow{\alpha }}_2\\ {\overrightarrow{\alpha }}_3\end{array}\right)}_{PC}=\left(\begin{array}{cccc}0.9705& 0.1794& -0.1479& -0.0636\\ -0.1437& 0.2438& 0.0714& 0.9565\\ 0.9531& -0.0101& 0.0326& -0.3006\end{array}\right)$$

(3)

The contribution coefficients of the ridge functions were calculated as:

$${\beta }_{PC}=\left(\begin{array}{ccc}0.9433& 0.2636& 0.1633\end{array}\right)$$

(4)

By substituting the projection directions, ridge functions, and contribution coefficients into Equation (1), the UCS prediction model for PC-stabilized waste soil was obtained.

The nonlinear relationships between individual influencing factors and UCS are illustrated by the ridge functions in Figure 4.

Figure 4. Ridge functions of the PPR model for UCS prediction of PC-stabilized waste soil: (a) f₁; (b) f₂; (c) f₃.

After establishing the PPR model, the contribution coefficients of different influencing factors were calculated. The results are presented in Table 5.

Table 5. Relative importance coefficients of influencing factors in the PC-PPR model.

Factors	Binder Content	Curing Age	Solid-Waste Replacement Ratio	Compaction Pressure
Relative importance coefficients	0.66	0.792	1	0.391

As shown in Table 5, the influence ranking of the investigated factors on the UCS of PC-stabilized waste soil was: solid-waste replacement ratio > curing age > binder content > compaction pressure.

The solid-waste replacement ratio exhibited the highest importance coefficient, indicating that the proportion of solid-waste-based binder replacing P was the critical parameter affecting strength development.

To verify the prediction accuracy of the PPR model, the predicted and measured UCS values of both training and within-domain validation samples were compared, and the results are shown in Figure 5. A relative error within ±10% was considered acceptable. The standard regression performance indicators of the PC-PPR model are shown in Table 6.

Figure 5. Comparison between measured and predicted UCS values of PC-stabilized waste soil: (a) training samples; (b) within-domain validation samples.

Table 6. Standard regression-performance metrics for the PC-PPR model.

Dataset	R2	RMSE (MPa)	MAE (MPa)
Training samples (N = 12)	0.9923	0.2151	0.1808
Test samples (N = 10)	0.9683	0.4372	0.3480

All predictions for both the training and within-domain validation datasets fell within the adopted ±10% engineering tolerance. The average relative errors were 3.46% and 5.68%, respectively. The narrow difference between the training and validation errors indicates good within-domain predictive consistency for the investigated dataset. These results indicate that the developed PPR model provides practically acceptable predictions within the specified experimental domain for PC-stabilized waste soil.

3.2.2. Effect of Solid-Waste Replacement Ratio on UCS of PC-Stabilized Waste Soil

Figure 6 illustrates the variation in UCS of PC-stabilized waste soil under different solid-waste replacement ratios and curing ages at a binder content of 12%.

Figure 6. Effect of solid-waste replacement ratio and curing age on UCS of PC-stabilized waste soil.

As shown in Figure 6, the UCS of fully solid-waste-based alkali-activated stabilized soil (solid-waste replacement ratio = 100%) remained relatively stable at different curing ages, indicating that the alkali-activated binder exhibited relatively rapid reaction characteristics during early curing. However, the UCS of the fully solid-waste-based system was only approximately 2 MPa, corresponding to about 30% of the strength achieved by P-stabilized waste soil. This result indicates that, although solid-waste-based binders possess certain cementitious activity, complete replacement of P may significantly reduce early-age strength.

The strength development of PC-stabilized waste soil was mainly controlled by the P content in the composite binder. Increasing the solid-waste replacement ratio reduced the amount of reactive cement clinker available for hydration, thereby decreasing the formation of hydration products and weakening particle bonding.

At the same curing age, the UCS of PC-stabilized waste soil decreased continuously with increasing solid-waste replacement ratio. In contrast, increasing curing age promoted continuous strength development due to the gradual generation of hydration products and densification of the internal structure.

These results demonstrate that partial replacement of P with solid-waste-based alkali-activated materials is feasible. By appropriately controlling the ratio between P and solid-waste-based binders, a balance between mechanical performance and environmental benefits can be achieved. Under suitable curing conditions, solid-waste-based materials can effectively reduce cement consumption while maintaining acceptable stabilization performance.

3.3. Performance Analysis of PF-Stabilized Waste Soil

3.3.1. PPR-Based UCS Prediction Model

The UCS prediction model for PF-stabilized waste soil was developed using the same PPR methodology described above. Twelve experimental datasets were selected as training samples, and ten additional experimental datasets were employed as within-domain validation samples. The training samples were used to establish the nonlinear regression relationship between input parameters and UCS, while the within-domain validation samples were applied to assess model reliability. The PPR parameters were set as follows: P = 4, Q = 1, Span = 0.5, M = 5, Mu = 3.

After optimization, the projection direction matrix of the PF stabilization model was obtained:

$${\left(\begin{array}{c}{\overrightarrow{\alpha }}_1\\ {\overrightarrow{\alpha }}_2\\ {\overrightarrow{\alpha }}_3\end{array}\right)}_{PF}=\left(\begin{array}{cccc}0.9792& 0.1288& -0.1518& 0.0386\\ -0.8266& -0.1015& -0.0070& 0.5535\\ -0.9707& 0.0124& -0.0327& 0.2377\end{array}\right)$$

(5)

The contribution coefficients of the ridge functions were calculated as:

$${\beta }_{PF}=\left(\begin{array}{ccc}0.9696& 0.1711& 0.2965\end{array}\right)$$

(6)

By substituting the projection directions, ridge functions, and contribution coefficients into Equation (1), the UCS prediction model for PF-stabilized waste soil was established.

The ridge functions describing the nonlinear relationships between different factors and UCS are shown in Figure 7.

Figure 7. Ridge functions of the PPR model for UCS prediction of PF-stabilized waste soil: (a) f₁; (b) f₂; (c) f₃.

The relative importance coefficients of the influencing factors obtained from the PPR model are summarized in Table 7.

Table 7. Relative importance coefficients of influencing factors in the PF-PPR model.

Factors	Binder Content	Curing Age	Solid-Waste Replacement Ratio	Compaction Pressure
Relative importance coefficients	0.366	0.407	1	0.196

The influence ranking of the investigated factors on the UCS of PF-stabilized waste soil was: solid-waste replacement ratio > curing age > binder content > compaction pressure.

The solid-waste replacement ratio remained the dominant factor controlling UCS development. Compared with the PC system, the curing age exhibited a greater influence on PF-stabilized waste soil, indicating that the incorporation of fly ash enhanced the long-term strength development capability of the composite binder.

This phenomenon can be attributed to the relatively slow pozzolanic reaction of fly ash. During early curing stages, fly ash particles exhibit limited activity; however, with increasing curing time, continuous dissolution of aluminosilicate components promotes the formation of additional cementitious products, resulting in progressive densification of the stabilized soil structure.

To evaluate the prediction accuracy of the PF-PPR model, the predicted UCS values were compared with the measured values, and a relative error within ±10% was considered acceptable. The results are shown in Figure 8. The standard regression performance indicators of the PF-PPR model are shown in Table 8.

Figure 8. Comparison between measured and predicted UCS values of PF-stabilized waste soil: (a) training samples; (b) within-domain validation samples.

Table 8. Standard regression-performance metrics for the PF-PPR model.

Dataset	R2	RMSE (MPa)	MAE (MPa)
Training samples (N = 12)	0.9959	0.1801	0.1200
Test samples (N = 10)	0.9925	0.2780	0.2380

All predictions for both the training and within-domain validation samples fell within the adopted ±10% engineering tolerance. The average relative errors were 3.09% and 4.87%, respectively. The narrow difference between the training and validation errors indicates good within-domain predictive consistency for the investigated dataset. These results confirm that the PPR model provides satisfactory interpolation accuracy within the specified experimental domain for PF-stabilized waste soil.

3.3.2. Effect of Solid-Waste Replacement Ratio on UCS of PF-Stabilized Waste Soil

Figure 9 presents the variation in UCS of PF-stabilized waste soil under different solid-waste replacement ratios and curing ages at a binder content of 18%.

Figure 9. Effect of solid-waste replacement ratio and curing age on UCS of PF-stabilized waste soil.

For comparison, the UCS values at curing ages of 7, 14, and 28 days were analyzed. As shown in Figure 9, the fully solid-waste-based PF binder system (solid-waste replacement ratio = 100%) exhibited significant strength development with increasing curing age. The UCS values at 7, 14, and 28 days were 1.73, 2.19, and 3.04 MPa, respectively, corresponding to an increase of 1.31 MPa from 7 to 28 days.

Furthermore, the strength growth rate increased with increasing solid-waste replacement ratio and curing age. This indicates that PF-stabilized waste soil possesses superior long-term strength development characteristics compared with early-age performance.

The relatively slower early-age strength development of PF-stabilized waste soil is mainly associated with the incorporation of fly ash. Compared with P, fly ash has lower early reactivity due to its glassy aluminosilicate structure. However, under alkaline conditions provided by carbide slag and cement hydration products, the aluminosilicate components in fly ash gradually dissolve and participate in secondary pozzolanic reactions, continuously generating additional calcium aluminosilicate hydrate (C–A–S–H) gels [26,27].

Therefore, although PF-stabilized waste soil exhibits relatively lower initial strength, it maintains continuous strength growth during long-term curing. This characteristic makes PF binders suitable for engineering applications where long-term mechanical performance is required.

3.4. Effect of Compaction Pressure on UCS of Stabilized Waste Soil

Figure 10 illustrates the relationship between compaction pressure and UCS of PC- and PF-stabilized waste soil. To eliminate the effects of binder content and curing age, all specimens were prepared with a binder content of 18% and cured for 28 days. P_XC_YF_Y represents the proportion of P, C, and F in the binder. For example, P₅₀F₅₀ denotes a binder containing 50% P and 50% F blend; P₀C₁₀₀ denotes a binder containing 100% C blend without P.

Figure 10. Effect of compaction pressure on UCS of stabilized waste soil: (a) PC-stabilized waste soil; (b) PF-stabilized waste soil.

The notation in Figure 10 represents the binder composition. For example, P₁₀₀C₀ indicates that the binder consists of 100% P and 0% solid-waste-based binder, whereas P₅₀F₅₀ represents a binder containing 50% P and 50% PF-based binder.

As shown in Figure 10a, compaction pressure significantly affected the UCS of PC-stabilized waste soil. Moreover, the optimal compaction pressure corresponding to maximum UCS increased with decreasing solid-waste replacement ratio.

For the fully solid-waste-based binder system, the maximum UCS was achieved at a compaction pressure of 20 MPa. Further increasing the pressure resulted in a slight reduction in UCS. With decreasing solid-waste replacement ratio, the pressure required to reach the maximum UCS increased to 25 MPa, after which the UCS gradually decreased. This behavior can be explained by the effect of compaction on particle arrangement and pore structure. Moderate compaction improves particle contact, reduces void ratio, and enhances the effectiveness of hydration products in bonding soil particles. However, excessive compaction may disrupt the internal structure and restrict pore connectivity required for hydration reactions, resulting in reduced strength development.

In contrast, the influence of compaction pressure on PF-stabilized waste soil was relatively limited (Figure 10b). Increasing compaction pressure from 15 MPa to 30 MPa increased UCS by only approximately 0.7 MPa on average. Moreover, when the pressure increased from 25 MPa to 30 MPa, the improvement became insignificant.

Therefore, under the studied conditions, the recommended compaction pressures for the PC and PF stabilization systems are 25 MPa and 20 MPa, respectively. Further increasing compaction pressure does not provide additional strength improvement and may even negatively affect UCS development.

4. Discussion

4.1. Optimization of Solid-Waste-Based Binder System for PC-Stabilized Waste Soil

To further optimize the PC stabilization system, the optimal compaction pressure was determined as 25 MPa, and curing ages of 14 and 28 days were selected. The established PC-PPR model was then used to predict UCS under different binder contents and solid-waste replacement ratios. Based on the PPR prediction results, UCS contour maps were generated to investigate the combined effects of binder content and solid-waste replacement ratio, as shown in Figure 11.

Figure 11. UCS contour maps of PC-stabilized waste soil at different curing ages: (a) 14 days; (b) 28 days.

The contour distribution demonstrates clear variation patterns between binder content, solid-waste replacement ratio, and UCS. Under identical curing conditions and compaction pressure, increasing binder content resulted in continuously increasing UCS, whereas increasing solid-waste replacement ratio reduced strength development.

Comparison between 14-day and 28-day curing conditions showed that UCS increased continuously with curing age, while the influence trend of solid-waste replacement ratio remained unchanged. This confirms that curing age promotes strength development but does not alter the dominant controlling factors.

Based on the PPR optimization results and practical engineering requirements, the optimization objective was to maximize the solid-waste replacement ratio while maintaining UCS ≥ 5 MPa under the specified binder-content, curing-age, and compaction-pressure constraints. Where the binder content generally ranges from 15% to 18% and the strength requirement is greater than 5 MPa, the recommended solid-waste replacement ratio for the PC system was determined to be 75%. It should be noted that this selected ratio represents recommended values specifically within the investigated experimental domain rather than universally optimal mixtures.

4.2. Optimization of Solid-Waste-Based Binder System for PF-Stabilized Waste Soil

To further optimize the PF stabilization system, the optimal compaction pressure was determined as 20 MPa based on the previous experimental results. The UCS prediction model developed by PPR was employed to evaluate the effects of binder content and solid-waste replacement ratio on the strength performance of PF-stabilized waste soil under curing ages of 14 and 28 days. The predicted UCS values were used to construct contour maps, as shown in Figure 12.

Figure 12. UCS contour maps of PF-stabilized waste soil at different curing ages: (a) 14 days; (b) 28 days.

As illustrated in Figure 12, the variation trends of PF-stabilized waste soil were generally consistent with those observed in the PC system. Under identical curing age and compaction pressure conditions, increasing binder content resulted in a continuous increase in UCS. However, the PF system exhibited improved long-term strength development compared with the PC system. The incorporation of fly ash contributed to sustained strength enhancement during extended curing periods.

The comparison between 14-day and 28-day curing conditions demonstrated that prolonged curing significantly enhanced UCS while maintaining the same influence trends of binder content and solid-waste replacement ratio. This indicates that curing age mainly affects the degree of reaction but does not change the dominant mechanisms controlling strength development.

Based on the experimental results and PPR model predictions, the recommended solid-waste replacement ratio for the PF stabilization system was determined to be 60% with practical binder contents of 15–18%, achieving a strength requirement greater than 5 MPa. It should be noted that this selected ratio represents recommended values specifically within the investigated experimental domain rather than universally optimal mixtures.

4.3. Sustainability and Cost–Benefit Analysis

The incorporation of industrial solid wastes, including CS, GGBS, and FA, into stabilization binders can effectively reduce P consumption and improve the sustainability of waste soil treatment. Since P production is one of the major sources of the industrial raw-material-stage carbon footprint, replacing cement with industrial by-products provides significant environmental benefits [43].

To quantitatively evaluate the sustainability performance of the proposed stabilization systems, the energy consumption, raw-material-stage carbon footprint, and material costs of P and solid-waste-based materials were compared. As suggested by the functional unit clarification, this analysis represents a preliminary raw-material-stage comparison rather than a complete life-cycle assessment (LCA). Table 9 summarizes the environmental impact and cost per ton of individual raw materials.

Table 9. Energy consumption, raw-material-stage carbon footprint, and costs of raw materials.

Raw Material	Cenergy/MJ·t−1	CCO2/kg·t−1	Unit Price/CNY·t−1
CS	0	0	300~350
GGBS	2379	152	320~360
FA	100	4	310~350
P	5500	1000	450~500

Note: Zero values for CS follow the by-product allocation approach. Downstream processes (transportation, mixing, compaction, curing) are not included. This is a preliminary embodied carbon comparison, not a full LCA. The capital letter C in the table represents consumption.

Based on the single-component data in Table 9, the subsequent quantitative comparison was strictly conducted based on one ton of blended binder. The production cost of ordinary Portland cement is estimated at 450–500 CNY/t, with a carbon footprint of 1000 kg CO₂/t and an energy consumption of 5500 MJ/t. In contrast, the emissions and costs associated with industrial solid wastes are significantly lower due to their by-product characteristics.

By calculating the weighted average of the components, the metrics per ton of blended binder were determined. Compared with conventional 100% P stabilization, the optimized PC binder system (25% P, 18.75% CS, 56.25% GGBS) reduces the binder material cost to 348.8–393.1 CNY/t. Meanwhile, the raw-material-stage carbon footprint and energy consumption are reduced to 335.5 kg CO₂/t and 2713.2 MJ/t, respectively.

Similarly, for the optimized PF binder system (40% P, 15% CS, 22.5% GGBS, 22.5% FA), the cost is reduced to 366.8–412.3 CNY/t, while the carbon footprint and energy consumption are lowered to 435.1 kg CO₂/t and 2757.8 MJ/t, respectively.

These results demonstrate that partial replacement of P with industrial solid wastes can simultaneously achieve economic and environmental benefits. The proposed cement–solid-waste composite stabilization systems not only reduce dependence on energy-intensive cement production but also provide an effective pathway for large-scale utilization of industrial solid wastes. From the perspective of sustainable geotechnical engineering, the developed stabilization strategy demonstrates preliminary potential for contributing to circular economy principles by transforming industrial by-products into value-added construction materials at the laboratory scale. Life-cycle and field-scale assessments are required to confirm these benefits in actual infrastructure development.

4.4. Applicability and Limitations of the Optimized Mixtures

The recommended solid-waste replacement ratios of 75% for the PC system and 60% for the PF system were obtained using a specific waste soil collected from Hangzhou and specific binder materials sourced from Xinjiang. These values should therefore be interpreted as recommended proportions within the material characteristics and experimental ranges investigated in this study, rather than as universally applicable optimum values. Variations in soil mineralogy, grading, organic content, water demand, and binder oxide composition, fineness, and reactivity may alter the soil–binder interaction and consequently shift the appropriate replacement ratio. Before applying the proposed mixtures to waste soils or industrial by-products from other regions or production batches, material characterization and laboratory-scale recalibration should be performed.

The mechanical characterization in this study was limited to UCS at curing ages of 7, 14, 28, and 56 days. Tensile strength (splitting or flexural), elastic modulus, and 90-day or longer-term strength were not evaluated. While UCS is the primary design parameter for preliminary mixture proportioning of stabilized soils and the observed monotonic strength increase up to 56 days indicates strength development during the investigated curing period, long-term durability requires further validation. Additional mechanical tests—particularly if the optimized mixtures are intended for load-bearing subgrade layers in actual projects—should be conducted before field application. The empirical correlations between UCS and other mechanical properties commonly adopted in preliminary design should be used with caution for these specific material systems.

5. Conclusions

This study developed cement–solid-waste composite stabilization systems using CS, GGBS, FA, and P for engineering waste soil treatment. Orthogonal experiments and PPR models were employed to investigate strength development mechanisms, quantify influencing factors, and optimize binder compositions. The main conclusions are summarized as follows:

(1)

The replacement of P with solid-waste-based binders is feasible for waste soil stabilization. The developed cement–solid-waste composite systems (PC and PF) exhibited effective strength-regulation capabilities. The PPR models established for both systems demonstrated good within-domain predictive performance, with all predictions for both training and within-domain validation datasets falling within the adopted ±10% engineering tolerance. The influence ranking of factors affecting UCS was determined as follows: solid-waste replacement ratio > curing age > binder content > compaction pressure.

(2)

The incorporation of fly ash improved the long-term strength development of PF-stabilized waste soil. Increasing the solid-waste replacement ratio generally reduced UCS, whereas increasing binder content and curing age enhanced strength development. Compaction pressure exhibited a significant influence on the PC system but a relatively limited effect on the PF system. Considering mechanical performance and engineering applicability, a compaction pressure of 25 MPa is recommended for the PC system and 20 MPa for the PF system. Under practical binder contents of 15–18%, within the investigated material sources and experimental domain, the recommended solid-waste replacement ratios were 75% for the PC system and 60% for the PF system.

(3)

The utilization of industrial solid wastes as partial replacements for P shows preliminary potential for reducing cement consumption, lowering embodied carbon, and decreasing material costs at the raw material stage. The optimized cement–solid-waste stabilization systems provide a laboratory-scale basis for developing more sustainable approaches to waste soil treatment.