Machine Learning-Based Optimization of Fine Aggregate Packing and Shape Characteristics for Cement Reduction in Concrete Mixtures

Abstract

Reducing cement consumption in mortar systems is essential for lowering the environmental impact of cement-based materials. Conventional mix design approaches rely mainly on particle size distribution and fineness modulus, which do not fully capture the effects of aggregate packing, morphology, and petrographic composition on paste demand and mechanical performance. Fourteen fine aggregates of distinct geological origins were experimentally characterized in terms of physical and petrographic properties. A dataset of 211 mortar mixtures, yielding 633 transverse-strength observations, was used to train a Random Forest Regressor (RFR) model for strength prediction. The model achieved $R^2=0.762$ (RMSE = 0.223 kN; MAE = 0.165 kN), demonstrating its reliability as a surrogate screening tool. This study presents a hybrid framework that integrates particle packing theory with machine learning to optimize fine aggregate blends. By introducing a Paste Demand Index (PDI)—combining normalized uncompacted void content, surface texture, and shape—the framework enables the identification of mixtures that minimize paste demand while maintaining mechanical performance under strength constraints. Results confirm that the proposed PDI and strength-based filtering are robust, offering a physically grounded decision-support methodology for narrowing the design space. Ultimately, this approach provides an efficient strategy for resource optimization, effectively bridging the gap between computational screening and laboratory validation in cement-reduction initiatives driven by the cement-based tile manufacturing industry.

1. Introduction

1.1. Background

Due to its availability, mechanical performance, and relatively low cost [1], concrete is the most widely used construction material after water. However, cement production contributes approximately 8% of global CO₂ emissions and is projected to account for 20–30% of CO₂ emissions by 2050. This situation may be further exacerbated if alternative cementitious materials, such as fly ash (FA), ground granulated blast furnace slag (BFS), silica fume, limestone dust, cement kiln dust, and natural or manufactured pozzolans, fail to provide environmentally and economically viable solutions [2].

Consequently, reducing cement content in mix designs has become a key objective in the construction industry and an active area of research in recent decades [3,4,5,6,7]. Aggregates play a critical role in influencing mixture properties and performance, as they constitute approximately 70–80% of the total volume of concrete and mortar mixtures [7]. Therefore, optimizing aggregate characteristics represents a promising pathway for enhancing mixture performance while reducing cement demand.

Traditional concrete mix design approaches typically rely on parameters such as fineness modulus (FM) and particle size distribution (PSD). However, these parameters do not explicitly account for particle shape, surface texture, packing efficiency, or petrographic characteristics, all of which strongly influence fresh and hardened behavior.

As a result, concrete and mortar mixtures are often under- or over-designed to compensate for suboptimal aggregate characteristics. Variations in aggregate composition, such as the relative proportions of quartz and calcite, can significantly affect microstructural properties, particularly within the interfacial transition zone (ITZ), influencing hydration, carbonation, and mechanical performance. Additionally, the presence of aggregates such as basalt and granite has been shown to affect fracture mechanisms and stress response in cement-based composites [8].

Recent studies have demonstrated that optimizing aggregate packing density together with physicochemical properties can significantly improve strength and durability compared to conventional approaches [6,9,10].

Despite these advances, aggregate characterization in concrete and mortar systems still relies heavily on costly and time-consuming laboratory testing. In recent years, machine learning (ML) techniques have emerged as powerful tools capable of learning complex relationships from experimental data, enabling prediction and automation in mix design processes. These approaches offer significant potential for improving efficiency and supporting decision-making in industrial applications.

In this context, the development of reliable and well-structured datasets is essential for implementing robust ML models in concrete technology [3,4,11]. This aligns with emerging Industry 5.0 paradigms, which aim not only to enhance efficiency but also to prioritize sustainability and human-centered innovation [12,13].

1.2. Research Gap

Despite the growing application of machine learning techniques in concrete and mortar mix design, most existing approaches remain predominantly data-driven and do not explicitly incorporate physically meaningful descriptors of aggregate characteristics. In particular, the combined influence of particle packing, morphology, and petrographic composition on paste demand and mechanical performance remains insufficiently explored within ML-based frameworks.

Furthermore, current optimization strategies typically focus on maximizing mechanical strength as the primary objective, without explicitly considering paste demand as a governing parameter for sustainability. As a result, the potential for reducing cement consumption through improved aggregate packing and interaction remains underexplored.

To address these limitations, this study proposes a hybrid grey-box framework that integrates physically interpretable descriptors with data-driven machine learning models. Unlike conventional approaches that treat aggregates as inert fillers defined primarily by fineness modulus, the proposed framework considers aggregates as active contributors to mixture behavior through their morphology, packing characteristics, and petrographic composition.

Specifically, this work:

(i)

Introduces a strength-constrained optimization strategy in which mechanical performance is treated as a constraint rather than the primary objective.

(ii)

Proposes a Paste Demand Index (PDI) as a physically interpretable metric for evaluating expected paste demand.

(iii)

Combines experimental characterization with surrogate modeling to evaluate a wide range of aggregate combinations without additional laboratory testing.

(iv)

Performs a sensitivity analysis to assess the robustness of the proposed framework with respect to key modeling assumptions, including the weighting scheme of the Paste Demand Index and the strength constraint threshold.

This approach provides a physically grounded and transferable framework for supporting sustainable mortar mix design and optimizing aggregate utilization in industrial applications.

2. State of the Art

Due to concrete components variability, accurately interpreting the relationship among concrete mix constituents, properties and proportions is one of the more complex tasks to be achieved by concrete researchers, and one of the potentially significant concrete mix optimization research contributions that requires costly and time-consuming empirical testing consisting of lab-based experimentation and daunting mathematical calculations [14].

In recent years, ML techniques have gained significant attention for identifying patterns that are difficult to recognize and reproduce by human empirical tests. However, the literature confirms that collecting, selecting, preparing, and processing large, diverse datasets to train ML algorithms represents a significant challenge for AI in industry processes, and hurdles remain in terms of choosing the most suitable approach to optimize ML predictive models [15]. In this context, concrete researchers and scholars are focused on integrating experimental research and ML techniques to ultimately converge on an accurate and efficient pathway to model and predict complex non-linear interactions among concrete mix design parameters, properties, and performance derived from extensive data sets trained in ML models; Artificial Neural Networks (ANNs), Support Vector Machine (SVM), Decision Trees (DTs), Random Forest Regressor (RFR), XGBoost Regressor (XGBR), and Genetic Algorithms (GA) successfully validated for: (1) The inclusion of a wider range of input variables for addressing environmental, performance, and cost demands of contemporary concrete designs. (2) Large dataset training without the need for costly and time-consuming experimental tests. (3) Accurately correlating the influence of variables on concrete mix design to provide significant support to concrete industry processes with reliable databases and application of suitable algorithms, model optimization, and a friendly user platform [14]. These three objectives aligned with 4.0 industry efficiency goals are considered in industry 5.0 as part of a global resilient sustainable manufacturing plan supported by automated ML prediction models that will make possible “for humans and machines, not only to operate, but also to learn together, transforming today’s smart factory into a self-learning factory” [12]. Self-learning factories transforming data into reliable and valuable information with the aid of experience, context, interpretation, reflection, and the support of technological tools are laying the ground for more decentralized Manufacturing Execution Systems (MESs) that will allow industries to reduce costs, increase efficiency, and achieve more sustainable industry processes [3,4].

In this challenging technological context, the more carefully the variables used in a model are selected, the more reliable the model becomes for supporting decision-making processes in industrial applications [16]. Regarding the concrete industry, achieving more sustainable production processes by reducing cement consumption [7] and limiting the exploitation of natural aggregates has become a major research objective. Several aggregate-alternative concrete mix optimization approaches have been proposed, including the use of waste materials such as concrete demolition waste (CDW), end-of-life manufactured material waste, and recycled forest or agricultural residues. However, these approaches are often limited by the difficulty of accurately estimating the optimal recycled content while complying with construction standards [17]. In the same research line, several studies have investigated the influence of crushed fine aggregates on mortar rheological properties such as workability, yield stress, and plastic viscosity. These studies have shown that the irregular particle shape of heterogeneous crushed aggregates may limit the ability to achieve suitable aggregate grading. As a consequence, mixtures may require higher water demand, which can reduce workability and increase yield stress and plastic viscosity, ultimately leading to higher cement consumption. Other aggregate replacement approaches, such as the use of fly-ash-based geopolymer mortar, have shown that as long as proper aggregate grading is achieved, geopolymer binders can reach higher tensile, compressive, and transverse strengths. Marine sediment-based aggregate replacement, in contrast, often resulted in reduced mechanical performance and lower workability due to the additional water demand required. As a result, this latter approach has been mainly limited to non-structural concrete elements [5]. In this context, the literature confirms that optimizing aggregate packing density and selecting suitable aggregate physico-chemical, petrographic, and morphological properties can significantly improve concrete and mortar mix performance while reducing cement consumption.

Regarding the impact of aggregate particle packing density optimization on mix designs, Kosmatka states that fewer voids to be filled with a lower w/c ratio will produce a homogeneous particle size distribution of aggregates, resulting in higher mix density and suitable workability [18]. In general, aggregates that show a smooth grading curve for suitable aggregate particle packing and higher density will produce the most satisfactory mix designs. “To achieve the best mechanical properties, concrete must have a granular skeleton packed as densely as possible, and the amount of cement paste necessary to fill the voids it leaves.” [19]. Further, the shape and particle size distribution of fine aggregates have also been demonstrated to have a great impact on mortar mix properties, water demand, and the overall mortar mix design optimization [6,20,21]. Some other investigations support this theory, confirming that mortar strength and absorptivity are mainly ruled by the packing density of the mixture, independently of the grading and the shape of sand used to demonstrate that packing density represents a determinant mortar property [10]. As for fine aggregates, they represent three-quarters of mortar mix designs, with the quality control of their properties essential to improve the mix interface transition zone (ITZ) in which the durability and strength of the composite is set.

Objective

This study aims to develop a hybrid grey-box framework that integrates petrographic and morphological descriptors into a decision-support model. The framework integrates petrographic composition, morphological descriptors, and particle packing theory to optimize aggregate selection, reduce cement paste demand, and improve mixture efficiency. The proposed approach seeks to assess the interplay between petrographic composition, particle morphology, and packing density in mortar systems.

Specific objectives:

• Normalization of qualitative aggregate descriptors (petrographic and morphological) into numerical indices to enable quantitative analysis and their integration into machine learning models [22].
• To experimentally characterize the packing density of mortar mixtures and the physicochemical, morphological, and petrographic properties of fine aggregates, including uncompacted void content [23], particle shape, surface texture, and petrographic composition.
• To develop an RFR model capable of predicting the transverse strength of mortar mixtures using physically meaningful mixture-level descriptors.
• To implement a strength-constrained optimization framework based on the Paste Demand Index (PDI), integrating aggregate packing density and physicochemical, morphological, and petrographic descriptors to identify aggregate blends with cement-reduction potential.

Despite the growing body of research on mortar and concrete mix optimization, most existing studies rely on empirical mix design approaches or data-driven models that do not explicitly incorporate physically meaningful descriptors of aggregate characteristics. In particular, the combined influence of petrographic composition, particle morphology, and packing density on mortar performance remains insufficiently explored within machine learning frameworks.

The main contribution of this study aims toward the development of a physics-informed machine learning framework that integrates aggregate petrographic, morphological, and packing-related descriptors into a predictive model for mortar mixture optimization. Unlike previous approaches, the proposed framework links physically interpretable aggregate properties with data-driven prediction to identify aggregate combinations that maintain mechanical performance while reducing cement paste demand.

3. Methodology

This section presents the overall methodology adopted in this study. The proposed framework integrates experimental characterization of fine aggregates, mortar mixture preparation and testing, and a machine learning-based modeling approach to predict transverse strength while optimizing aggregate combinations.

The methodology is structured into four main stages: (1) experimental design and mortar mixture preparation, (2) characterization of aggregate physical, morphological, and petrographic properties, (3) development and validation of an RFR model, and (4) optimization of aggregate combinations based on a strength-constrained Paste Demand Index (PDI).

3.1. Experimental Design

A total of 211 mortar mixtures were prepared, encompassing both factory-optimized control designs and experimental blends specifically engineered to optimize the aggregate skeleton. These laboratory trials successfully demonstrated the potential of reducing cement content by 5–10% through enhanced particle packing efficiency, with results further validated in an industrial production environment to confirm scalability. For each of these 211 mixtures, nine cylindrical specimens (20 mm height × 100 mm diameter) were produced, totaling 1899 specimens. The reference mortar composition is summarized in

Table 1. Mortar mix proportions.

Compound	Kg
Cement	1.79
Fine aggregate	7.31
w/c	0.38–0.50

.

The w/c ratio range was not an independent experimental variable, but a process-dependent adjustment required for industrial roofing tile production. In these zero-slump semi-dry systems, workability is highly sensitive to the specific surface area and void content of the aggregate skeleton. Consequently, the water content was adjusted within the specified range to ensure each mixture achieved a target state of compaction, allowing the mechanical performance to reflect aggregate skeleton efficiency rather than rheological variations. Given this earth-moist consistency, conventional workability metrics (such as slump or flow table tests) were inapplicable. Instead, workability was assessed using the industry-standard ‘snowball test’—an empirical evaluation protocol where the fresh mortar’s ability to remain cohesive and maintain its shape under controlled manual pressure serves as a proxy for high-pressure extrusion performance. This confirms visual homogeneity and ensures the material possesses sufficient internal cohesion to preserve its geometric profile immediately following demolding, validating that each mixture meets the rheological requirements for industrial forming processes.

To ensure statistical robustness and account for laboratory variability, transverse strength was evaluated for each mixture at 1, 7, and 28 days. The nine replicate specimens tested at each curing age were averaged to obtain a representative mean value, resulting in a high-fidelity dataset of 633 observations (211 mixtures × 3 ages). This aggregation effectively filters out stochastic experimental noise, providing a stable target variable for the RFR. All tests were conducted using a universal multi-speed load frame under a three-point bending configuration until failure. Figure 1 illustrates the resulting transverse strength evolution.

3.2. Fine Aggregates

Fourteen fine aggregates (1_A to 14_N) of distinct geological origins were selected to represent a wide range of mineralogical, morphological, and packing characteristics. The aggregates included natural sands, crushed sands, and recycled materials. This diversity was intentionally introduced to maximize variability in packing behavior and morphological effects, thereby strengthening the robustness of the subsequent machine learning framework. All aggregates were oven-dried prior to testing to eliminate moisture-related variability, as summarized in

Table 2. Chemical composition of fine aggregates.

Compound	1_A	2_B	3_C	4_D	5_E	6_F	7_G	8_H	9_I	10_J	11_K	12_L	13_M	14_N
SiO2	82.98	52.18	92.15	93.64	94.04	92.64	68.96	93.42	93.74	71.20	53.48	93.44	68.97	79.42
Al2O3	6.40	12.16	2.18	2.11	2.00	2.11	14.56	2.64	2.18	14.70	15.16	2.24	14.82	2.67
Fe2O3	2.95	9.13	3.45	2.90	2.70	2.90	2.95	1.86	1.51	1.63	8.13	1.17	2.96	1.97

.

The elemental composition was determined by X-Ray Fluorescence (XRF) to ensure the chemical consistency and mineralogical origin of the raw materials throughout the experimental campaign. The selected oxides (SiO₂, Al₂O₃, and Fe₂O₃) effectively capture the mineralogical variability of the aggregates—representing quartz, feldspathic, and iron-bearing phases—which indirectly influence particle behavior. These chemical data were integrated with petrographic classification to derive the normalized (0–1) indices utilized in our model. XRD analysis was considered outside the scope of this work, as the research focus remains on physical packing mechanics and aggregate morphology rather than cement hydration kinetics, which would be the primary objective of a phase-based mineralogical analysis.

The PSD curves were evaluated against the upper and lower grading limits (UL/LL) defined for mortar aggregates. Compliance with these limits was assessed using the so-called tarantula method, which quantifies the number of sieve points whose retained percentages fall within the acceptable grading envelope.

Figure 2 illustrates the particle size distribution of the analyzed sands. The vertical axis represents the percentage retained on each sieve (%Retained), indicating the proportion of particles remaining on a sieve of a given opening size during the sieving process. Higher retained percentages correspond to a greater proportion of particles with sizes close to that sieve opening, whereas lower values indicate fewer particles within that size range.

Thus, the curves describe the particle size distribution within each sand. Variations in these distributions reflect differences in aggregate grading, which directly influence packing behavior and the structure of the granular skeleton in mortar mixtures.

3.3. Fine Aggregates Petrographic, Shape, and Texture Classification

Petrographic class, aggregate type, particle shape, and surface texture were classified according to standard petrographic and morphological criteria. Qualitative descriptors were transformed using the [22] procedure into normalized indices ranging from 0 to 1, while preserving the physical ordering associated with material hardness, particle angularity, and surface roughness, enabling quantitative analysis and subsequent machine learning modeling.

Table 3. Petrographic classification and normalized indices (0–1).

Sand	Aggregate Type	Type Index
1_A	Crushed sandstone	0.60
2_B	Tuff	0.75
3_C	Quartz	0.00
4_D	Quartzose	0.15
5_E	Quartz	0.00
6_F	Quartz	0.00
7_G	Recycled material	1.00
8_H	Quartz	0.00
9_I	Quartz	0.00
10_J	Granite	0.40
11_K	Tuff	0.75
12_L	Gravel	0.50
13_M	Granite	0.40
14_N	Recycled material	1.00

illustrates the resulting classification and normalized indices. This approach allowed categorical petrographic information to be incorporated into regression-based and predictive models without introducing artificial bias.

Four categories were defined for particle shape: rounded, subrounded, subangular, and angular, based on the degree of angularity and the presence of sharp edges. In parallel, surface texture was classified into three categories—smooth, moderately rough, and rough—reflecting the microscale roughness of the particle surface. Although ASTM D3398 [22] is qualitative in nature and does not provide direct numerical measurements, it allows for a consistent classification of particle morphology. These morphological characteristics are known to influence mortar and concrete properties, particularly workability, water demand, and paste–aggregate interaction.

In addition to their qualitative classification, particle shape and surface texture are associated with the physical mechanisms governing particle packing and interactions. Angular particles and rough surfaces increase interparticle friction and promote geometric interlocking, thereby limiting particle rearrangement and reducing packing efficiency. These effects are commonly described in granular materials as wedging effects, where finer particles become constrained between coarser grains, and wall effects, where irregular particle geometries disrupt local packing arrangements. Although these mechanisms are not explicitly modeled in this study, their influence is indirectly captured through the normalized shape and texture indices incorporated into the machine learning framework.

These ordinal classifications were converted into continuous numerical indices through linear normalization within the [0, 1] interval, assigning equidistant values to each category. This procedure preserves the inherent physical order of particle angularity and surface roughness while enabling the quantitative incorporation of morphological parameters into statistical analyses and machine learning models.

The fine aggregate optimization strategy consisted of combining sands with varying proportions of quartz, crushed sandstone, tuff, granite, and recycled materials. These petrographic fractions were subsequently normalized to a continuous scale ranging from 0 to 1 to enable quantitative analysis. Mineralogical composition influences aggregate stiffness, surface roughness, and water demand, thereby affecting both fresh and hardened mortar behavior.

Table 4. Morphological classification and normalized indices (0–1).

Sand	Particle Shape	Shape Index	Surface Texture	Texture Index
1_A	Angular to sub-angular	0.835	Rough to moderately rough	0.835
2_B	Angular to sub-angular	0.835	Rough to moderately rough	0.835
3_C	Angular to rounded	0.500	Rough to smooth	0.500
4_D	Angular to rounded	0.500	Moderately rough to smooth	0.335
5_E	Angular to rounded	0.500	Moderately smooth to moderately rough	0.500
6_F	Angular to rounded	0.500	Moderately smooth	0.330
7_G	Angular to sub-angular	0.835	Rough and porous	1.000
8_H	Rounded to sub-rounded	0.165	Moderately smooth to moderately rough	0.500
9_I	Sub-rounded to rounded	0.165	Slightly rough to smooth	0.125
10_J	Angular	1.000	Rough to moderately rough	0.835
11_K	Angular to sub-angular	0.835	Rough to moderately rough	0.835
12_L	Rounded to sub-rounded	0.165	Moderately smooth to moderately rough	0.500
13_M	Angular	1.000	Rough to moderately rough	0.835
14_N	Angular to sub-angular	0.835	Rough and porous	1.000

and

Table 5. Interpretation of morphological characteristics and expected fresh-state behavior of fine aggregates.

Sand	Morphology	Expected Packing and Fresh-State Effect
1_A	A–SA = rough	High friction, higher voids, increased paste demand.
2_B	A–SA = rough	Poor packing efficiency; reduced workability.
3_C	A–WR = rough–smooth	Intermediate packing; moderate paste demand.
4_D	A–WR = mod. rough–smooth	Balanced packing; moderate workability.
5_E	A–R = mod. smooth–rough	Mixed accommodation; moderate paste demand.
6_F	A–R = mod. smooth	Improved packing; better workability.
7_G	A–SA = rough, porous	High absorption; high paste demand.
8_H	R–SR = mod. smooth–rough	Good packing; reduced paste requirement.
9_I	SR–R = slightly rough–smooth	Efficient packing; low paste demand.
10_J	A = rough	High interlocking; increased paste demand.
11_K	A–SA = rough	Reduced flow; higher paste requirement.
12_L	R–SR = mod. smooth–rough	Dense packing; improved workability.
13_M	A = rough	High interlocking; increased paste demand.
14_N	A–SA = rough, porous	High absorption; high paste demand.

illustrate the morphological classification and normalized indices (0–1) of the investigated aggregates, together with the interpretation of their morphological characteristics and the expected fresh-state behavior.

3.4. Fine Aggregate Uncompacted Void Content and Packing Density

The uncompacted void content of fine aggregates was determined in accordance with [23]. This test method evaluates the packing ability of fine aggregates in a loose condition, without the application of external compaction energy, allowing the material to flow freely into a container of known volume. The uncompacted void content, expressed as a percentage of the total volume, was calculated based on [23] using the mass of the loose aggregate, the container volume, the bulk specific gravity of the aggregate, and the density of water.

The resulting parameter provided an indirect measure of the combined influence of particle shape, surface texture, and gradation, since more angular or rough particles tended to generate higher void contents in the loose state. Consequently, the uncompacted void content strongly correlates with fresh concrete workability, paste demand, and granular packing efficiency, making it a useful indicator for comparing different fine aggregate sources, including natural, crushed, and recycled sands.

In addition to the experimental determination following ASTM C1252, uncompacted void content was also estimated from physical loose, bulk properties:

$$U(\%)=\left(1-{\displaystyle \frac{{\rho }_{\mathrm{loose},\mathrm{bulk}}}{{\rho }_{\mathrm{particle}}}}\right)\times 100$$

(1)

where ${\rho }_{\mathrm{loose},\mathrm{bulk}}$ is the loose bulk density and ${\rho }_{\mathrm{particle}}$ is the particle density of the aggregate. This formulation [23] provides an approximation of packing porosity under loose conditions; however, it should be noted that it is not strictly equivalent to the ASTM C1252 [23] procedure, which standardizes the aggregate deposition method to ensure reproducibility. The estimated values were therefore used solely as supporting indicators for trend comparison, while the experimentally determined values were used as primary inputs in the machine learning framework.

Packing density ($\eta$) was calculated from the uncompacted void content as:

$$\eta =1-{\displaystyle \frac{U}{100}}$$

(2)

A lower packing density corresponds to a higher void volume and, consequently, to a greater paste demand.

Packing density plays a key role in governing fresh-state behavior since the volume of paste required to fill inter-particle voids depends directly on the packing density of the granular skeleton. Although higher packing density reduces the paste volume required to fill voids, the optimization strategy seeks to proportionally reduce the total paste content, which may slightly decrease the excess paste available for particle lubrication and therefore reduce workability. As a result, higher packing density generally improves mechanical efficiency while slightly reducing workability under constant paste-reduction conditions. Conversely, lower packing density increases void volume and paste demand, reducing granular efficiency and requiring additional paste to maintain adequate compactability. This establishes a direct physical relationship between packing density, paste demand, and workability.

Table 6. Packing behavior and interpretative assessment of fine aggregates.

Sand	U (%)	Workability	Packing Level	Paste Demand	Key Interpretation
1_A	≈46.3	0.3203	Medium	Moderate	Crushed sandstone promotes interlocking; limited workability.
2_B	≈46.3	0.3203	Medium	Moderate–High	Tuff origin may increase absorption and water sensitivity.
3_C	≈39.2	0.7849	High	Low	Quartz-rich composition enables dense packing and improved workability.
4_D	≈48.3	0.4714	Low	High	Reduced packing efficiency; higher paste volume required.
5_E	≈39.6	0.7697	High	Low–Moderate	Quartz mineralogy supports efficient packing.
6_F	≈38.6	0.8695	Very High	Low	Best natural sand; improved fresh-state performance.
7_G	≈49.6	0.1298	Low	High	Recycled material increases porosity and paste demand.
8_H	≈44.2	0.6434	Medium–High	Moderate	Quartz origin provides balanced packing behavior.
9_I	≈45.4	0.7202	Medium	Moderate	Acceptable packing with stable workability.
10_J	≈43.7	0.3983	Medium–High	Moderate	Granite may increase friction but maintains packing.
11_K	≈52.0	0.0862	Very Low	Very High	Highest void content; reduced workability unless compensated.
12_L	≈40.3	0.8016	High	Low	Gravel-based fines show good particle accommodation.
13_M	≈50.4	0.1231	Low	High	Granite-derived sand increases inter-particle friction.
14_N	≈50.2	0.1023	Low	High	Recycled material increases porosity and paste demand.

illustrates the interpretative assessment of fine aggregates.

3.5. Physical and Morphological Properties of Fine Aggregates and Implications for Packing Behavior

Table 7. Physical and morphological properties of fine aggregates (1_A to 14_N).

Parameter	1_A	2_B	3_C	4_D	5_E	6_F	7_G	8_H	9_I	10_J	11_K	12_L	13_M	14_N
Particle Density (G ssd) (Kg/m3)	2700	2700	2650	2590	2650	2590	2260	2740	2730	2610	2750	2580	2640	2210
Fineness Modulus (FM)	1.63	2.60	2.70	2.63	2.95	2.73	3.06	2.75	2.27	2.62	2.36	2.78	3.15	3.08
Loose Bulk D. (gamma b) (Kg/m3)	1450	1450	1610	1340	1600	1590	1140	1530	1490	1470	1320	1540	1310	1100
Water Absorption (%)	0.5	0.5	0.2	0.2	0.9	0.7	9.4	0.1	0.1	0.2	0.2	0.3	0.2	10.8
Uncompacted Voids, u (%)	46.3	46.3	39.25	48.26	39.62	38.61	49.56	44.16	45.42	43.68	52.00	40.31	50.38	50.23
Packing Density ($\eta =1-u/100$)	0.54	0.54	0.61	0.52	0.60	0.61	0.50	0.56	0.55	0.56	0.48	0.60	0.50	0.50
Petrographic Class	css	t	q	qzo	q	q	rm	q	q	g	t	grav	g	rm
Petrographic Class Index (0–1)	0.60	0.75	0.00	0.15	0.00	0.00	1.00	0.00	0.00	0.40	0.75	0.50	0.40	1.00
Particle Shape (qualitative)	a/sa	a/sa	a/r	a/r	a/r	a/r	a/sa	r/sr	sr/r	a	a/sa	r/sr	a	a/sa
Particle Shape Index (0–1)	0.83	0.83	0.50	0.50	0.50	0.50	0.83	0.16	0.16	1.00	0.83	0.16	1.00	0.83
Surface Texture (qualitative)	r/mr	r/mr	r/sm	mr/sm	ms/mr	ms	r/p	ms/mr	sr/sm	r/mr	r/mr	ms/mr	r/mr	r/p
Surface Texture Index (0–1)	0.83	0.83	0.50	0.33	0.50	0.33	1.00	0.50	0.12	0.83	0.83	0.50	0.83	1.00

Petrographic classification: crushed sandstone (css), Tuff (t), quartz (q), quartzose (qzo) gravel (grav), granite (g), recycled material (rm). Particle shape: angular to sub-angular (a/sa), angular to rounded (a/r), rounded to sub-rounded (r/sr), sub-rounded to rounded (sr/r), angular (a). Surface texture: rough to moderately rough (r/mr), rough to smooth (r/sm), moderately rough to smooth (mr/sm), moderately smooth to moderately rough (ms/mr), moderately smooth (ms), rough and porous (rp), slightly rough to smooth (sr/sm).

highlights the significant variability in the physical and morphological properties of the fourteen fine aggregates investigated. Substantial differences were observed in particle density, fineness modulus, loose bulk density, water absorption, and uncompacted void content, reflecting the contrasting geological origins and particle morphologies of the materials.

Particle density ranged from 2210 to 2750 kg/m³, reflecting mineralogical variability between quartz-rich sands and recycled or porous materials. Quartz-dominated aggregates exhibited higher density and lower water absorption, whereas recycled materials showed significantly higher absorption values, exceeding 9%, which directly affects paste demand and water adjustment.

Uncompacted void content varied between 38.6% and 52.0%, corresponding to packing densities ($\eta =1-U/100$) from 0.48 to 0.61. Aggregates such as 3_C and 6_F exhibited high packing efficiency ($\eta \approx 0.61$), while others such as 11_K and 13_M showed poor packing behavior ($\eta =0.48$–0.50), indicating higher paste demand.

Morphological characteristics further explain these differences. Angular and rough-textured particles (e.g., 10_J and 14_N) presented higher shape and texture indices (≈0.83), leading to increased inter-particle friction and void content. In contrast, rounded particles with smoother textures (e.g., 8_H and 9_I) showed lower indices (0.16–0.50), facilitating improved packing.

These results demonstrate that packing efficiency is governed not only by grading but also by particle morphology. Consequently, packing density provides a more physically meaningful descriptor of granular efficiency than fineness modulus alone.

This observed variability in void structure and particle interaction establishes the physical basis for the Paste Demand Index (PDI), which integrates void content, shape, and texture into a unified indicator of expected paste demand.

4. Optimization and Paste Demand Index (PDI)

4.1. Conceptual Framework

The mortar mix optimization strategy was formulated to identify aggregate blends that minimize expected paste demand while preserving mechanical performance.

Unlike traditional approaches focused primarily on maximizing strength, the present framework adopts a constrained optimization strategy in which mechanical performance is treated as a constraint, whereas paste demand reduction is defined as the main objective.

According to the excess paste theory, the total paste volume is partitioned into a fraction required to fill the inter-particle voids of the granular skeleton and an excess fraction responsible for lubrication. In this context, the uncompacted void content (U), determined according to ASTM C1252, serves as a direct proxy for minimum paste demand. As packing density ($\eta$) increases (i.e., as U decreases), the paste volume required for void filling is reduced, enabling either improved workability at constant paste volume or a reduction in cement content while maintaining adequate fresh-state performance.

4.2. Candidate Mixture Generation

A combinatorial search procedure was implemented to explore virtual aggregate blends. Candidate mixtures were generated by combining between $r_{min}=2$ and $r_{max}=4$ sands using discrete percentage increments of 10%.

For each candidate mixture:

1.

The particle size distribution (PSD) was used to characterize the granulometric profile of each sand and to identify complementary size distributions. By combining sands with different PSDs, packing efficiency is improved, reducing void content and optimizing the granular skeleton.

2.

Grading compliance was verified using the tarantula curve.

3.

Mixture-level descriptors were calculated as proportion-weighted averages of the corresponding aggregate properties.

Specifically, the mixture-level property $X_{mix}$ was computed as:

$$X_{mix}=\sum _i{p}_i{X}_i$$

where $p_i$ is the mass fraction of each constituent sand and $X_i$ is the corresponding property.

4.

Transverse strength was predicted using the trained RFR model.

4.3. Workability and Paste Demand Index

To support the interpretation of fresh-state behavior in semi-dry systems, a workability score (WS) was defined as:

$$WS=w_U(1-U_{norm})+w_T(1-T_{norm})+w_S(1-S_{norm})$$

(3)

where $U_{norm}$, $T_{norm}$, and $S_{norm}$ are normalized variables representing uncompacted void content, surface texture, and particle shape, respectively. The adopted weights ($w_U=0.55$, $w_T=0.30$, $w_S=0.15$) reflect the dominant influence of packing efficiency, followed by frictional and interlocking effects.

The workability score should be interpreted as a relative indicator of compactability derived from aggregate properties and packing characteristics. In zero-slump systems, where conventional rheological tests are not applicable, such indicators provide a consistent basis for comparing mixtures under identical conditions rather than an absolute measure of workability. Therefore, the WS is explicitly defined as a compactability proxy for extrusion-based manufacturing, distinct from standard rheological flow measurements.

To evaluate paste demand, a Paste Demand Index (PDI) was defined as:

$$PDI=w_U·U_{norm}+w_T·T_{norm}+w_S·S_{norm}$$

(4)

where lower PDI values indicate mixtures with improved packing efficiency and reduced expected paste demand.

The weighting factors ($w_U=0.60$, $w_T=0.30$, $w_S=0.10$) were defined based on their relative physical contribution to paste demand. Uncompacted void content (U) was assigned the highest weight due to its direct volumetric relationship with the paste required to fill inter-particle voids, representing the primary governing mechanism in excess paste theory. Surface texture (T) was assigned an intermediate weight, as it influences inter-particle friction and affects particle rearrangement during compaction. Particle shape (S) was assigned the lowest weight, reflecting its secondary role in geometric interlocking.

This hierarchical scheme ($w_U>w_T>w_S$) is consistent with particle packing theory and established frameworks such as excess paste theory and compressible packing models [24]. The PDI is intended as a physically interpretable ranking metric rather than a predictive model, and its linear formulation was adopted to preserve transparency.

To evaluate the robustness of the proposed formulation, a sensitivity analysis was conducted by varying the weighting factors and normalized indices within a range of $\pm 10\%$, while preserving their relative ordering. The results indicate that these variations do not significantly affect model predictions or the relative ranking of candidate mixtures.

Furthermore, the framework combines these physically based descriptors with a non-linear RFR model, which captures interaction effects (e.g., loosening and wall effects) not accounted for by linear approximations. Therefore, although the weights are not obtained through numerical optimization, they are physically grounded and yield consistent and objective decision-making outcomes without the need for parameter fitting.

4.4. Strength Constraint

To prevent performance loss, a strength-based filtering criterion was imposed:

$$\widehat{f}\ge \alpha {\widehat{f}}_{max}$$

(5)

A reference value of $\alpha =0.95$ was adopted to retain mixtures with near-optimal performance. This threshold is consistent with common engineering practice, where acceptable performance ranges between 90 and 100% are used to account for variability and design tolerances.

It should be noted that the predictive performance of the Random Forest model ($R^2\approx 0.76$) is moderate. However, the model is not intended for precise strength prediction, but rather for the relative comparison and ranking of candidate mixtures within the optimization framework. In this context, the achieved accuracy is sufficient to preserve the relative ordering of mixtures, which constitutes the primary objective of the surrogate model.

To evaluate the sensitivity of the optimization results to the selected strength threshold, additional analyses were performed considering values of $\alpha$ in the range of 0.90 to 1.00.

4.5. Results

The maximum predicted transverse strength was:

$${\widehat{f}}_{max}=1.518\mathrm{kN}$$

After application of the strength constraint, a subset of high-performance mixtures was retained.

Table 8. Sensitivity of optimization results to the strength threshold ($\alpha$).

$\mathit{\alpha }$	Candidates	Strength (kN)	Packing Density	Workability Score	U (%)
0.90	8	1.367	0.602	0.798	39.72
0.92	7	1.397	0.603	0.797	39.67
0.95	5	1.443	0.604	0.793	39.56
0.97	3	1.473	0.605	0.790	39.46
1.00	1	1.518	0.606	0.787	39.36

Note: Values represent the arithmetic mean properties of the candidate mixtures meeting the specified strength threshold ($\alpha$). Packing Density and Workability Score are dimensionless indices.

illustrates the influence of the strength threshold ($\alpha$) on the size and characteristics of the feasible solution space. As $\alpha$ increases, the number of candidate mixtures decreases, reflecting an increasingly restrictive selection criterion. Notably, the optimization framework shows a consistent trend: higher thresholds drive the selection toward mixtures with higher packing density and, consequently, lower void content (U). This demonstrates that the model effectively identifies configurations where the structural skeleton is optimized to maximize mechanical performance.

These results suggest that the strength threshold primarily controls the size of the feasible solution space while maintaining a stable selection of high-performing mixtures. Therefore, $\alpha =0.95$ is proposed as a balanced trade-off between solution diversity and mechanical performance. Furthermore, a clear trade-off is observed: while increasing packing density enhances strength and reduces void content, it slightly reduces the workability score, consistent with the lower paste volume available for lubrication in denser aggregate skeletons.

Finally, the applicability of this framework is confined to the experimental domain of semi-dry mortar systems. The methodology serves as a targeted decision-support tool rather than a universally generalizable model, and extrapolation to distinct material compositions requires further validation.

5. Machine Learning-Based Optimization Framework

The objective of this machine learning (ML) framework is to develop a surrogate model capable of predicting the transverse strength of mortar mixtures based on physically interpretable descriptors and aggregate characteristics. In this framework, transverse strength is defined as the dependent variable, while mix design parameters, aggregate physical/morphological descriptors, and packing-related indices serve as independent variables. The input features include curing age, water-to-cement ratio, fresh density, packing density, uncompacted void content, fineness modulus, shape index, particle density, texture index, and petrographic index.

The overall workflow consists of dataset construction, preprocessing, model training, validation, and optimization. To capture non-linear relationships between these descriptors and transverse strength, the model was implemented using a Random Forest Regressor. RFR was selected as the core predictive engine due to its optimal balance between non-linear predictive power and physical interpretability. Given the dataset size ($n=633$) and the intricate dependencies between aggregate morphology and paste demand, RFR proves superior to both simple linear approximations and over-parameterized ‘black-box’ deep learning architectures. Furthermore, the model’s capacity for feature importance analysis enables a direct interpretation of how each physical descriptor influences mortar performance, aligning with our objective of maintaining a grounded engineering approach. To validate the model’s robustness and mitigate overfitting, a 5-fold cross-validation procedure was systematically implemented. The consistent performance observed across the five folds provides a quantitative measure of reliability, which serves as the statistical foundation for the uncertainty management within our proposed decision-support framework.

5.1. Dataset Construction

The dataset originates from the experimental campaign detailed in Section 3, comprising 633 validated observations of transverse strength. These data points represent 211 distinct mortar mixtures assessed at curing ages of 1, 7, and 28 days. The experimental matrix encompasses a broad range of water-to-cement ratios, aggregate volume fractions, and grading distributions, specifically engineered to reflect the semi-dry mortar compositions prevalent in industrial manufacturing. Consequently, the dataset captures the complex, non-linear variability inherent in aggregate packing and inter-particle interactions. Rather than relying on theoretical approximations, these mixtures are grounded in a comprehensive industrial program. This study incorporates factory-optimized mix designs as benchmarks, alongside experimental formulations where the cementitious content was reduced by 5–10% through the application of advanced particle packing theory. Since these formulations were validated within a concrete roofing tile production environment, the model is trained on high-fidelity, industrially relevant data rather than isolated, small-scale laboratory samples.

Each data instance was represented by a set of mixture-level predictors computed from aggregate properties and mix design parameters. Curing age was explicitly included as an input variable, allowing each observation to represent a distinct physico-mechanical state of the material. The dataset therefore captures both compositional variability (across mixtures) and temporal evolution (across curing ages), providing a comprehensive basis for training and evaluating the predictive model.

While a large number of candidate mixtures were evaluated,

Table 9. Categories of input variables used in the machine learning framework.

Category	Variables	Physical Interpretation
Directly measured mix-design parameters	Curing time; water-to-cement ratio (w/c); fresh density	Represent hydration development, paste rheology, and mixture compactness.
Proportion-weighted aggregate
physical properties	Texture index; shape index; petrographic index; particle density	Capture mineralogical composition, particle morphology, and inter-particle friction effects.
Packing- and grading-related
indices (standardized tests)	Uncompacted void content (ASTM C1252); packing density ($\eta$)	Quantify granular skeleton efficiency and conformity with target PSD limits.

presents the framework’s input structure. The 12_L/3_C blend family is discussed here as a representative subset, as it clearly illustrates the trade-off between packing efficiency, strength, and workability. The consistent trends observed across all evaluated blend families confirm that the proposed optimization framework is not case-specific but exhibits robust general applicability within the defined experimental domain.

5.2. Data Preprocessing

To ensure robust model training, all records were first filtered for completeness and physical consistency, including validation of mixture proportions summing to 100% and correct assignment of curing ages (1, 7, and 28 days). A fixed random seed was used throughout preprocessing and model training to ensure reproducibility. Although the dataset includes 633 observations, these correspond to 211 unique mixture compositions evaluated at three curing ages. For each mixture and curing age, transverse strength was calculated as the average of replicate specimens, yielding a single representative value for each mixture–age condition. This approach reduces experimental noise and avoids pseudo-replication in the machine learning dataset.

To prevent information leakage and overestimation of model performance, the dataset was split at the mixture level rather than at the individual record level. Each mixture corresponds to a unique composition tested at three curing ages, generating three associated records. All records belonging to the same mixture were grouped and assigned entirely to either the training or testing subset. An 80/20 partition was applied to the set of unique mixtures, resulting in independent training and testing subsets composed of distinct compositions. This grouped splitting strategy ensures that all observations associated with a given mixture are assigned to a single subset, thereby preventing information leakage and enabling model evaluation on unseen mixtures.

To assess the representativeness of the training and testing subsets, descriptive statistics of key input variables—including uncompacted void content (U), particle shape index, surface texture, petrographic, and packing density indices—were compared between both subsets (

Table 10. Descriptive statistics of key input variables for training and testing datasets.

Variable	Training Set			Testing Set
	Mean	Std. Dev.	Range	Mean	Std. Dev.	Range
U (Void Content, %)	43.78	3.34	38.93–52.00	43.57	3.12	38.93–50.30
Shape Index	0.497	0.129	0.165–1.000	0.487	0.132	0.165–0.984
Texture Index	0.464	0.129	0.125–0.934	0.465	0.132	0.125–0.852
Petrographic Index	0.166	0.150	0.000–0.900	0.170	0.148	0.000–0.625
Packing Density	0.562	0.033	0.480–0.611	0.564	0.031	0.480–0.611

). The comparison indicates that the distributions are consistent, with similar mean values, dispersion, and ranges across both subsets. This confirms that the testing set adequately represents the variability of the entire dataset, thereby supporting an unbiased evaluation of the model’s performance.

Regarding variable representation, the selected input variables consist of physically meaningful descriptors expressed on comparable scales. Consequently, no additional feature scaling was required for the Random Forest Regressor (RFR) model, as this algorithm is inherently insensitive to variable scaling. Descriptive statistics were further analyzed to define the model’s domain of validity and to prevent extrapolation beyond the experimental range, which is critical for evaluating virtual mixtures during the optimization stage.

Categorical descriptors related to particle morphology and petrographic composition were transformed into continuous indices within the [0, 1] range using an ordered scaling scheme. This transformation enables their integration into the machine learning model while preserving the ordinal nature of the original classifications. The assigned scaling follows a physically informed hierarchy, in which increasing values represent higher angularity, surface roughness, or mineralogical complexity—characteristics known to influence inter-particle friction, particle interlocking, and ultimately packing efficiency.

Although an equidistant scaling was adopted for simplicity and interpretability, this represents a linear approximation of potentially non-linear physical effects. However, given that the model is intended for the relative comparison and ranking of mixtures rather than precise absolute prediction, minor variations in the assigned indices are not expected to significantly impact the comparative evaluation of mixtures within the defined experimental domain. This assumption is further supported by the observed stability of model predictions and mixture rankings. Finally, a sensitivity analysis conducted by varying the assigned index values within a reasonable range confirmed that these variations do not significantly affect model predictions or the relative ranking of mixtures, indicating that the adopted scaling does not introduce bias into the modeling framework.

5.3. Random Forest Regressor

Due to its ability to capture nonlinear relationships, the RFR was selected to model the interactions among packing density, aggregate morphology, and mix design parameters. The dataset was randomly divided into a training subset (80%) and an independent testing subset (20%). As illustrated in Figure 3, the model demonstrates a strong correlation between experimental and predicted transverse strength values, confirming its capability for reliable mixture ranking.

The RFR achieved $R^2=0.762$, RMSE = 0.223 kN, and MAE = 0.165 kN on the independent test set (20% of unique mixture compositions). The 5-fold cross-validation on the training set yielded consistent performance across all folds, confirming the absence of overfitting. The transverse strength values in the dataset ranged from 0.413 to 2.424 kN (mean = 1.17 kN). Normalized metrics indicate that the prediction error is small relative to the inherent variability of the system (NRMSE = 0.111; NMAE = 0.082), supporting the suitability of the model for comparative analysis. Given the reported RMSE, the variation introduced by model uncertainty is low relative to the strength differences between mixtures, ensuring that the identification of the optimal solution remains robust.

While explicit uncertainty quantification was not implemented, the ensemble nature of the RFR provides an inherent reduction in prediction variance. Reliability is highest within the central data distribution, where data density is greater. Overall, the RFR provides a reliable framework for screening candidate mixtures within the experimental domain.

5.4. Feature Importance Analysis

To enhance the physical interpretation of the proposed framework, a feature importance analysis was conducted using permutation importance derived from the trained RFR model. This approach provides a model-agnostic assessment of the relative contribution of each input variable to the prediction of transverse strength.

As shown in Figure 4, curing age and mixture density exhibit the highest contribution to the model predictions, reflecting their dominant role in hydration processes and overall compactness of the mixture.

Among the aggregate-related descriptors, uncompacted void content (U) presents the most significant contribution, highlighting the importance of packing efficiency in the mechanical response. Morphological descriptors, including particle shape and surface texture indices, as well as the petrographic index, exhibit a comparatively lower influence. These variables act primarily as secondary modifiers of particle interaction, influencing inter-particle friction and geometric interlocking rather than directly controlling strength.

The feature importance rankings were found to be stable across training runs due to the ensemble nature of the RFR model, reinforcing the robustness and physical consistency of the identified dominant predictors.

Overall, the feature importance results are consistent with particle packing theory and support the physically interpretable nature of the proposed machine learning framework.

5.5. Evaluation of Virtual Mixtures

Once validated, the trained model was used as a surrogate model to evaluate virtual candidate mixtures generated under grading constraints. For virtual mixtures, fresh density was estimated using the same proportion-weighted approach applied to experimental mixtures, ensuring consistency between the training dataset and the prediction domain.

Predicted transverse strength was used as a screening criterion, while paste-demand minimization was addressed through the PDI-based ranking.

6. Discussion

The predictive performance of the model must be interpreted within the context of industrial data. Although the $R^2$ of 0.762 is moderate by controlled laboratory standards, it reflects a high degree of industrial fidelity, capturing the inherent variability in quarry-derived mineralogy and moisture fluctuations. Thus, the model demonstrates robust generalizability within the operational boundaries of semi-dry mortar production.

This study specifically targets semi-dry roofing tile production, where compactability and green strength prevail over traditional rheological parameters. In these zero-slump systems, workability is defined by the mixture’s ability to consolidate under high-pressure extrusion. This domain-specific focus enables a high-resolution optimization framework; however, it limits direct applicability to other rheological regimes, and extrapolation to high-slump or self-compacting systems warrants further validation.

The results confirm that transverse strength is governed by aggregate packing characteristics. Specifically, uncompacted void content emerges as the primary factor influencing paste demand and mechanical performance, while particle shape and surface texture act as secondary modifiers of inter-particle friction. The machine learning model captures these nonlinear relationships by integrating physically interpretable descriptors—such as packing indices, morphology, and petrographic properties—thereby ensuring the physical consistency of the proposed framework.

This framework is primarily designed as a robust computational screening tool for identifying promising regions within the design space rather than a high-precision deterministic predictor. By interpreting model outputs as expected performance ranges, we effectively mitigate the impact of inherent model variance while maintaining a physically grounded basis for decision support. Consequently, any industrial implementation should be accompanied by confirmatory experimental validation. Future work is already underway to bridge this gap, focusing on laboratory-scale testing of the optimal mixtures identified by the model. This multi-phase strategy—transitioning from high-resolution digital screening to targeted experimental verification—ensures the necessary balance between industrial performance and efficient resource consumption.

Regarding workability, the proposed score serves as a physically informed proxy for compactability, addressing a critical gap where conventional rheological tests are inapplicable. Optimization results demonstrate the feasibility of reducing paste demand while maintaining mechanical performance within acceptable limits. Although an estimated cement reduction of 5–10% may appear modest, its significance at the industrial scale is substantial. Given that cement production accounts for approximately 8% of global anthropogenic CO₂ emissions [25], a 5% clinker reduction—achieved solely through aggregate skeleton optimization—represents an efficient, readily implementable sustainability strategy.

Furthermore, optimal mixtures are not necessarily those that maximize strength, but rather those that balance packing efficiency and mechanical performance, highlighting the importance of aggregate characteristics as key design variables. While the recent literature increasingly applies machine learning to cementitious materials [26], direct comparisons remain limited by variations in datasets and evaluation metrics. Unlike existing approaches focused on high-workability concrete and bulk parameters [27], this study addresses zero-slump systems where particle interactions dominate. By incorporating the Paste Demand Index (PDI), this framework bridges the gap between purely data-driven models and particle packing theory, offering a mechanistically grounded approach.

Ultimately, the contribution of this work lies in the development of a physically informed, interpretable, and industrially applicable framework for mixture optimization under constrained conditions.

6.1. Sensitivity Analysis of PDI Weighting

To evaluate the robustness of the proposed Paste Demand Index (PDI), a sensitivity analysis was conducted by varying the weighting factors assigned to uncompacted void content, surface texture, and particle shape.

Table 11. Sensitivity of PDI ranking under representative weighting combinations.

Mixture (12_L/3_C)	PDI	Rank	${\mathit{w}}_{\mathit{U}}$	${\mathit{w}}_{\mathit{T}}$	${\mathit{w}}_{\mathit{S}}$
(10/90)	0.100	1	0.6	0.3	0.1
(20/80)	0.171	2	0.6	0.3	0.1
(30/70)	0.243	3	0.6	0.3	0.1
(10/90)	0.200	1	0.5	0.3	0.2
(20/80)	0.243	2	0.5	0.3	0.2
(30/70)	0.286	3	0.5	0.3	0.2
(10/90)	0.100	1	0.7	0.2	0.1
(20/80)	0.186	2	0.7	0.2	0.1
(30/70)	0.271	3	0.7	0.2	0.1

presents the ranking of candidate mixtures under different PDI weighting combinations.

Although variations in the weighting factors ($w_U$, $w_T$, $w_S$) lead to changes in the absolute PDI values, the relative ranking of candidate mixtures remains unchanged across all evaluated combinations.

In particular, the mixture 12_L/3_C (10/90) consistently achieves the lowest PDI, while 12_L/3_C (80/20) remains the least favorable configuration.

This indicates that the PDI formulation is robust with respect to reasonable variations in the weighting factors, and that mixture ranking is primarily governed by the underlying physical parameters, particularly uncompacted void content.

Therefore, the proposed PDI serves as a stable and physically meaningful ranking metric rather than a weight-sensitive optimization function.

6.2. Multi-Criteria Interpretation of Strength, Paste Demand, and Workability

While the PDI-based ranking provides valuable insight into paste demand, practical mix design requires balancing multiple performance criteria simultaneously. In semi-dry mortar systems, mechanical performance and workability must be considered alongside packing efficiency to ensure both manufacturability and structural adequacy.

In this context, workability was incorporated as an additional parameter to interpret the behavior of the optimized mixtures. Unlike strength and PDI, workability was not used as a direct optimization constraint, but rather as a complementary indicator of mixture compactability under semi-dry conditions.

Table 12. Variation in predicted strength, PDI, packing density, and workability for 12_L/3_C mixtures.

S12_L(%)	S3_C (%)	Strength (kN)	PDI	Packing Density	Workability
10	90	1.518	0.100	0.60644	0.78663
20	80	1.496	0.178	0.60538	0.78829
30	70	1.493	0.257	0.60432	0.78995
40	60	1.468	0.336	0.60326	0.79162
50	50	1.452	0.414	0.60220	0.79328
60	40	1.431	0.493	0.60114	0.79494
70	30	1.419	0.571	0.60008	0.79661
80	20	1.381	0.650	0.59902	0.79827

presents the variation in predicted transverse strength, PDI, packing density, and workability for the 12_L/3_C aggregate combinations. A clear and consistent trend is observed: as the proportion of 12_L increases, the PDI increases from 0.10 to 0.65, while the predicted transverse strength decreases from 1.518 kN to 1.381 kN. At the same time, the workability score increases from 0.786 to 0.798, reflecting the greater paste availability for particle lubrication as paste demand increases, at the expense of packing efficiency and mechanical performance.

As shown in Figure 5, a clear trade-off exists between strength, paste demand, and workability. Mixtures with lower PDI values exhibit higher predicted strength due to improved packing efficiency and reduced void content, but lower workability, consistent with the reduced paste volume available for particle lubrication in denser aggregate skeletons. Conversely, higher PDI values enhance workability at the expense of mechanical performance.

Although the variation in workability is moderate (≈1.5%), the trend is consistent and reflects the role of paste in particle lubrication and compactability.

These results indicate that workability acts as a balancing parameter, defining a feasible design space in which mixtures can be selected based on specific performance requirements. Its inclusion therefore enhances the practical relevance of the proposed methodology.

6.3. Limitations

Despite the promising results, several limitations of the present study should be acknowledged.

First, the dataset is derived from a single, high-fidelity experimental campaign focused on semi-dry (zero-slump) mortar systems for concrete roofing tile production. While this domain-specificity limits direct extrapolation to other concrete systems, it is a strategic design choice rather than a limitation. By focusing on this specific industrial context, we maintain strict control over key variables—notably aggregate morphology and packing—that would otherwise be obscured by stochastic noise in broader, less-controlled datasets. Consequently, the model is precisely calibrated to the industrial operational reality of the targeted sector, ensuring high predictive fidelity. While its generalization to other mortar systems requires further validation using independent datasets, the current framework demonstrates robust performance within its defined experimental domain.

Second, the workability score (WS) serves as a physically grounded, quantitative proxy for the empirical ‘snowball test’ traditionally used in factory floor quality control. By formalizing this qualitative assessment into a standardized index, the framework enables predictive optimization of mixture compactability, providing a digital counterpart to manual field assessments.

Third, while the computation of mixture-level properties as proportion-weighted averages assumes linear additivity, this represents an initial approximation of the input space. It is important to note that the Random Forest Regressor (RFR) model is employed precisely to compensate for this simplification, as its non-linear architecture is capable of capturing complex interdependencies—such as wall effects or particle wedging—that are not explicitly defined in the input indices. Consequently, while the input indices are linear proxies, the framework’s predictive output successfully accounts for the non-linear physical behavior of the mortar system.

Fourth, the Paste Demand Index (PDI) is intended as a relative ranking metric rather than an exact quantitative predictor, as its weighting scheme is based on physically informed parameters used in this study.

7. Conclusions

This study proposes a hybrid methodology that integrates physical packing mechanics, particle morphology, and petrographic descriptors into a data-driven framework to optimize fine aggregate blends in semi-dry mortar systems.

Main findings:

1.

Uncompacted void content (U) and packing density ($\eta$) emerged as relevant descriptors of aggregate efficiency by effectively capturing the synergy between particle morphology and granular arrangement.

2.

The RFR model demonstrated the capacity to map the complex, nonlinear relationships between mix-design parameters and transverse strength, providing sufficient predictive accuracy ($R^2=0.762$) for the screening of candidate mixtures within the industrial operational domain.

3.

The proposed Paste Demand Index (PDI) was shown to be a reliable, physically interpretable metric for ranking mixtures and providing a meaningful proxy for compactability in zero-slump systems.

4.

The results demonstrate that cement reduction in semi-dry mortar systems can be effectively achieved through optimized fine aggregate selection, specifically by balancing packing density and workability requirements under transverse strength constraints.

5.

This framework demonstrates its potential as an efficient, sustainability-oriented tool for the pre-experimental screening of mortar compositions, serving as an effective clinker-reduction strategy within the concrete roofing tile industry.

The optimization framework developed in this research demonstrates significant potential for the roof tile manufacturing industry, serving as a preliminary decision-screening tool to enable the reduction in cement content in mortar mixtures while maintaining optimal transverse strength and workability.