A Mesoscale Comparative Analysis of the Elastic Modulus in Rock-Filled Concrete for Structural Applications

Abstract

Rock-filled concrete (RFC) is an advanced construction material that integrates high-performance self-compacting concrete (HSCC) with large rocks exceeding 300 mm, providing advantages such as reduced hydration heat and increased construction processes. The elastic modulus of RFC is a critical parameter that directly influences its structural performance, making it vital for modern construction applications that require strength and stiffness. However, there is a scientific gap in understanding the effects of rock size, shape, arrangement, and volumetric ratio on this parameter. This study investigates these factors using mesoscale finite element models (FEMs) with spherical and polyhedral rocks. The results reveal that polyhedral rocks increase the elastic modulus compared to spherical rocks, enhancing RFC’s load-bearing capacity. Additionally, a 5% increase in the elastic modulus was observed when the rockfill ratio was increased from 50% to 60%, demonstrating a direct correlation between rock volume and mechanical performance. Furthermore, the elastic modulus rises significantly in the early stages of placement, followed by a gradual increase over time. Optimal rock sizes and a balanced mix of rock shapes allow for improved concrete flow and mechanical properties, making RFC a highly efficient material for construction. These findings offer valuable insights for designers and engineers looking to optimize RFC for structural applications.

1. Introduction

Rock-filled concrete (RFC) represents a novel advancement in mass concrete construction, providing significant benefits such as decreased cement consumption, increased compressive strength, and reduced shrinkage deformation. The concrete utilized in RFC is referred to as high-performance self-compacting concrete (HSCC). During the construction process, HSCC is meticulously poured into the interstitial spaces between large rocks (>300 mm), as illustrated in Figure 1. This method optimizes material usage and enhances the resulting composite structure’s mechanical properties and durability [1,2]. Owing to its exceptional workability and resistance to segregation, HSCC can flow effectively and fill in voids driven by gravity [3]. This construction technology allows for rapid construction of the RFC structure when HSCC is continuously poured, which has rapidly promoted the use of RFC technology in over two hundred projects [4].

RFC comprises two distinct materials with significant mechanical strength differences: large rocks and HSCC. HSCC gradually transitions from a flowable state to hardened solid concrete, with an increasing elastic modulus and strength [5]. The elastic modulus, representing the material’s ability to deform elastically under stress, emerges as a key parameter shaping the mechanical response of rock-filled concrete structures. In infrastructure design, the significance of the elastic modulus of rock-filled concrete cannot be overstated [6].

Understanding this property is essential for predicting deformations, assessing load-bearing capacities, and ensuring the longevity of structures. The unique nature of rock-filled concrete introduces challenges in accurately determining the elastic modulus [7,8]. The heterogeneity arising from the combination of SCC and large rocks, coupled with variations in particle sizes and distribution, complicates the characterization of this fundamental property. Rock-filled concrete’s dynamic and evolving nature requires a comprehensive understanding of its elastic modulus under various conditions, ranging from static to dynamic loading scenarios [9,10,11]. Through a combination of experimental investigations and analytical modeling, this study seeks to elucidate the influences of rockfill characteristics, such as size, shape, and distribution, on the elastic modulus [2,12].

The influence of different aggregate shapes on the elastic modulus of concrete represents a critical aspect of understanding the mechanical behavior of concrete [13,14]. The varied geometries of rock fragments embedded within the concrete matrix can significantly impact the composite material’s overall stiffness and deformation characteristics [15,16]. While existing research has explored the general effects of rock content and size on concrete properties, the specific investigation into how distinct rock shapes influence the elastic modulus remains relatively uncharted territory [17,18].

The geometric configuration of rocks, encompassing aspects such as angularity, sphericity, and irregularity, plays a crucial role in determining the interlocking and stress transfer mechanisms within the RFC [19]. The irregularity in rock shapes creates a complex matrix, affecting the material’s distribution and transmission of loads. For instance, angular or irregular rock shapes may enhance interlocking, but could also introduce localized stress concentrations, potentially influencing the elastic modulus [14,20,21]. Conversely, more rounded or spherical rocks might facilitate better load distribution, but may alter the overall packing density, consequently impacting stiffness. Finite element simulations will complement experimental findings, providing a deeper understanding of the micro-mechanical interactions between the concrete matrix and various rock shapes [22,23,24].

Unlike traditional concrete, self-compacting concrete (SCC) does not require external vibration or compaction to achieve self-consistency and self-compatibility. This is due to its unique rheological properties, which allow it to flow and fill even the most congested areas without segregation [25,26]. However, in the case of rock-filled SCC, the curing process can significantly impact its compressive and split tensile strengths and other mechanical properties [27,28,29].

The age-adjusted effective modulus methodology is a fundamental way to estimate creep effects in aging concrete. Concrete’s modulus of elasticity has a wide range of values, making it unique. Multiple factors must be considered to ensure a sufficient modulus of elasticity in complex concrete structures. Curing, and more specifically, maintaining the concrete temperature to prevent water loss or shrinkage, is crucial [30,31,32]. During the initial compression phases, the stress–strain relationship in concrete exhibits linearity. This behavior is why the modulus of elasticity is frequently utilized. Nevertheless, as the load is further increased, inelastic creep induces nonlinearity in the stress–strain curve, even at lower stress levels [33].

The morphology of aggregates significantly impacts the elastic modulus of concrete, which is a crucial measure of its structural soundness. Angular aggregates improve the arrangement of particles, leading to a better transfer of load inside the material and resulting in higher modulus values [34,35,36]. Their coarse surface texture promotes enhanced bonding with the cement paste, resulting in improved adhesion at the interface and increased overall stiffness. In addition, angular particles provide enhanced internal friction, which hinders deformation and ensures more effective load distribution. On the other hand, when it comes to rounded aggregates, they show a lower level of interlocking and have a decreased surface area for bonding [23,37,38].

Consequently, this leads to lower values of elastic modulus and can potentially negatively impact the performance of concrete when subjected to loading. The overall morphology and surface characteristics of aggregates substantially impact the mechanical properties of concrete. Angular particles improve the material’s ability to bear weight and withstand damage, increasing its resistance to cracking and deformation [39]. Conversely, using rounded aggregates can diminish the structure’s overall strength and can result in early collapse. This emphasizes the significance of carefully choosing the appropriate type of aggregate to achieve the best performance in concrete construction [40,41].

This study aims to investigates the influence of large rocks on the mechanical properties of rock-filled concrete (RFC). It emphasizes the substantial impact of rock shape on the elastic modulus of RFC. Two separate groups of simulation models were created, one with spherical rocks and the other with polyhedral rocks, and the rockfill ratios range from 50% to 60% for each. Through analysis at different curing ages, it was found that the simulation models with polyhedral rocks showed significantly higher elastic moduli than those with spherical rocks. Moreover, a direct relationship between the rockfill ratio and the elastic modulus was established, indicating a continuous increase in modulus with a higher rockfill ratio. These discoveries highlight the crucial role of rock shape and rockfill ratio in determining the mechanical performance of RFC, providing valuable insights for optimizing the design and construction of concrete structures that incorporate large rock aggregates.

2. Generation of RFC Model with a Finite Element Technique

2.1. Strength Evolution of Rock-Filled Concrete

In the conventional approach, SCC is considered a composite material consisting of three phases: aggregates, mortar, and an interfacial transition zone (ITZ) at the mesoscale (Figure 2). However, models for predicting the evolution of the elastic modulus in rock-filled concrete (RFC) as a structural element over time have not accurately depicted the temporal effects on concrete strength throughout different stages. Random distribution models have been inadequate in capturing the complete range of temporal effects on the structural integrity of concrete [19,42,43].

Rock-filled concrete (RFC) is an innovative composite material that combines the advantages of self-compacting concrete (SCC) and large rocks. The composition of RFC is governed by the requirement that the size of the rocks used must exceed 300 mm [1]. The integration of SCC with large rocks in RFC produces a composite material that effectively combines the advantageous properties of both components. The exceptional flowability and self-compacting nature of SCC allow it to envelop and intricately embed the large rocks within the mix, creating a homogeneous matrix. This synergy between the fluid SCC and the substantial rock elements ensures a cohesive structure that minimizes voids, thereby significantly enhancing the material’s overall load-bearing capacity. This approach leverages the strengths of both SCC and rocks, resulting in a more robust and durable composite material [25,44].

The benefits of RFC are multifaceted. Firstly, the use of SCC facilitates easy placement and distribution of the mixture, ensuring efficient filling even in complex and densely reinforced structures. Secondly, the incorporation of large rocks significantly enhances the material’s resistance to compressive and shear forces, making RFC particularly well suited for applications requiring high load-bearing capacity. Additionally, the presence of these rocks contributes to improved durability and abrasion resistance, positively influencing the material’s long-term performance. This combination of SCC and large rocks in RFC thus creates a highly resilient and efficient construction material ideal for demanding structural applications [45]. Once the elastic modulus of the concrete is known, determining the overall model’s elastic modulus becomes a straightforward process. During the computation of the concrete’s elastic modulus, the resulting values will be observed at different time intervals, representing the progressive transformation of the concrete from its initial placement to its eventual attainment of full strength [46,47,48].

This computational exercise allows us to gain insights into how the evolving properties of concrete influence the behavior of the models over time. The analysis encompasses various critical stages, including hydration, curing, and the progressive development of the material’s full strength. By examining these stages, we can better understand the time-dependent changes in the concrete’s mechanical properties and how they affect the overall performance and structural integrity of the models [49,50,51]. The analysis allows us to appreciate how these transformations contribute to the models’ overall behavior and mechanical properties, including the elastic modulus [30,52]. The RFC models’ elastic modulus demonstrates the consequence seen by the SCC curve. The elastic modulus curve of RFC increases rapidly at the early stage, and later it increases slowly because the specific elastic modulus of SCC determines it. However, RFC’s elastic modulus exceeds the concrete elastic modulus values.

Empirical methods allow the modulus of elasticity to be estimated based on compressive strength [53,54]. However, these models must be utilized cautiously since compressive strength and modulus of elasticity are independent mechanical characteristics controlled differently by concrete factors [55].

2.2. Model Generation of Heterogeneous RFC

To address this, six 3D mathematical models were developed, incorporating various sizes, proportions, and configurations of randomly selected rocks to represent the behavior of RFC more accurately (Figure 3). Among these models, three feature spherical rocks, while the others include polyhedron rocks. The overall size of the specimen is 2.2 m cube, consisting of rocks ranging from 300 mm to 800 mm. The models were prepared in two sets, each with three different rockfill ratios: r = 50%, r = 55%, and r = 60%. The rockfill ratio in the models is controlled by adjusting the diameters and arrangements of the rocks. Various rockfill ratios are generated by controlling the spectrum of rock diameters (as can be seen in Figure 4 and Figure 5).

This study established two categories of model groups, each including three models. The first set consists of spherical rock models designated M-1S, M-2S, and M-3S (Figure 4). The second set comprises models of polyhedron-shaped rocks, designated M-1P, M-2P, and M-3P (Figure 5).

This study’s models include two distinct rock shapes, spherical and polyhedral, with rock volumes varying from 50% to 60%. All variants are cubic with dimensions of 2.2 m. The displacement of these models is oriented downward along the -z axis.

There is a significant deficiency of study on the effective elastic modulus of rock-filled concrete at the mesoscale using random large-rock models. While the material properties of the three models under review are consistent, the number of rocks varies in each model. This research seeks to investigate the influence of rock volume on the elastic modulus of rock-filled concrete. The finite element method (FEM) models of rock-filled concrete (RFC) incorporate various rock shapes to assess their impact on structural performance. By simulating the interactions between different geometries, such as polyhedral and spherical rocks, the models aim to elucidate how these variations influence the elastic modulus and load-bearing capabilities of the concrete mix. This comparative analysis not only enhances the understanding of material behavior under different loading conditions, but also provides valuable insights for optimizing rockfill compositions in practical applications, ultimately contributing to more efficient and resilient concrete structures.

This approach helps enhance comprehension of the behavior and mechanical characteristics of rock-filled concrete at the mesoscale level. The following are models of rock-filled concrete (RFC) with various percentages of rock volume:

These figures show that the volume of rocks in Model-1, Model-2, and Model-3 are 50%, 55%, and 60%, respectively. The models consisting of spherical rocks are denoted with ‘S’ and those with polyhedrons denoted with ‘P’. The purpose of developing six different models is to figure out if the change in volume and shape of rocks in RFC will affect its elastic modulus.

2.3. Elastic Modulus Evolution of HSCC

The elastic modulus of self-compacting concrete is calculated here. We need an equation that can provide us with calculation responses according to time to calculate the elastic modulus of the SCC. The 28-day compression strength of the concrete is used to calculate the elastic modulus of the concrete over time. The equation which is used to calculate the elastic modulus of concrete according to time is below:

$$E\left(t^{\prime }\right)=E\left(28\right){\left[{\displaystyle \frac{t^{\prime }}{4+0.85t^{\prime }}}\right]}^{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$$

(1)

In Equation (1) [33], $t^{\prime }$ is the time in days, E ($t^{\prime }$) is the required elastic modulus of the concrete according to time in days, and E (28) is the known elastic modulus of the concrete. The elastic modulus increases as the stress level rises. We start by calculating the bottom force, which will lead to the stress in the model being discovered. The elastic modulus of SCC at 28 days is 22.09 GPa. These computations will follow our specified time frame, as shown in Figure 6. This will help in attaining better outcomes and comprehension.

The average compressive strength exhibited by the standardized SCC specimens is 17.2 MPa [2]. This numerical representation, derived from empirical evidence, highlights the material’s inherent capacity to withstand and endure compressive forces. It is important to note that the compressive strength value mentioned here is specific to the standardized cubic SCC samples and may vary based on factors such as mix design, curing conditions, and testing methods.

2.4. Material Properties of Rock and HSCC

Material properties such as Young’s Modulus, Poisson’s ratio, and shear strength were defined based on the characteristics of the simulated rocks. These properties influence how the rocks deform and react under applied stress. The parameters used to prepare the models are given in

Table 1. The input parameters of the material.

	E (GPa)	v	P (kg/m³)
Rock	53.8	0.25	2725
SCC	22.09	0.167	2300
ITZ	22.09	0.167	2300

. Three different volumes of rocks are used with SCC, which are given below in

Table 2. SCC and volume of rocks for models.

Characteristics	SCC	Rocks	RFC
Model-1	50%	50%	100%
(M-1S and M-1P)
Model-2	45%	55%	100%
(M-2S and M-2P)
Model-3	40%	60%	100%
(M-3S and M-3P)

.

2.5. Calculation Procedure of RFC Elastic Modulus

To determine the elastic modulus of the models, we modified the value of Ec over time. After each adjustment, we submitted the file for analysis to assess the results. This iterative process allows for a thorough examination of the changes in elastic modulus and helps in understanding the behavior of the models (Figure 7). It ensures that any modifications made to the Ec value are carefully analyzed, providing valuable insights for further optimization and improvement [55]. Three distinct sets of rockfill ratios commonly employed in engineering projects were meticulously chosen to assess the impact of varying rockfill ratios comprehensively. These models incorporate diverse rock diameters, shapes, and spatial configurations, comprehensively exploring these factors’ influence on the models’ structural behavior. The careful adjustment of rock sizes during the model’s creation allows us to derive distinct values, contributing to a nuanced understanding of the dynamic interplay between rock characteristics and structural outcomes.

3. Results

3.1. Validation of Elastic Modulus between Simulations

This study conducted a thorough analysis of simulation models for rock-filled concrete, focusing on two unique groups: one consisting of spherical rocks and the other consisting of polyhedral rocks. The rockfill ratios examined varied between 50% and 60%, while the remaining fill consisted of high-performance self-compacted concrete.

The numerical simulation results of this study compare with the previous study by Y. Li et al., 2020 [8], which is an experimental study (Figure 8). The average elastic modulus of the 15 prismatic cut specimens from a large-scale 2.2 m cube, with a 55% rockfill ratio, is 34.06 GPa, with a standard deviation of 2.96 GPa. The observed test results, which vary between 28.65 GPa and 38.52 GPa, exhibit a range of values. This variability might be attributed to the unequal distribution of rockfill ratio and the rock skeleton structure within each block after cutting it from the full-scale test blocks. Notably, that study utilized random rock shapes without considering their geometric characteristics, which may have influenced the elastic modulus results. This highlights the complexity of material behavior in rock-filled concrete and underscores the importance of accounting for rock shape in both numerical and experimental assessments.

The investigation revealed significant disparities between the two groups. The elastic modulus values of models containing spherical rocks were consistent with the findings of a previous study that used comparable rock forms. However, models incorporating polyhedral rocks exhibited much higher values, especially when the rockfill ratios were increased. The difference in performance can be explained by the improved capacity of polyhedral rocks for interlocking, highlighting their potential to improve structural performance. The research suggests that the geometric attributes of rocks are crucial in determining the mechanical properties of rock-filled concrete buildings. The increased elastic modulus values reported in models containing polyhedral rocks highlight the potential benefits of incorporating such rock shapes in actual applications to enhance structural strength and durability.

3.2. Simulation Results for the Analysis of RFC Elastic Modulus

The comparison between two groups of models, each comprising three variations with rockfill ratios of 50%, 55%, and 60%, respectively, introduces an intriguing exploration into the influence of rock shapes on structural behavior. The two groups are distinguished by the morphology of their constituent rocks, with one group featuring spherical rocks and the other polyhedral ones. The primary focus is assessing the simulation results encompassing displacement, stress, strain, and reaction force, all pivotal parameters in understanding the structures’ response to applied loads.

Beginning with displacement, this metric is a key indicator of the structures’ deformations under external forces. A meticulous examination of the results within each group can reveal trends and patterns, offering insights into the structures’ stability. If polyhedral rock models consistently exhibit lower displacements than their spherical counterparts, it suggests superior structural stability associated with the former.

Moving to stress distribution, a critical factor in assessing structural integrity, examining stress concentrations can provide valuable information (Figure 9). Lower stress values in the polyhedral rock models imply a more even distribution of loads, indicative of a structure better equipped to handle external forces without concentrated weak points.

Strain, representing the material’s deformation, offers additional nuance to the analysis. Lower strain in polyhedral rock models suggests a reduced tendency for deformation under load, reinforcing the notion of enhanced elasticity and structural robustness.

The evaluation of reaction forces further complements the analysis, shedding light on how each structure responds to applied loads. Higher reaction forces in the polyhedral rock models point towards their potential to withstand more substantial loads before reaching failure points, showcasing resilience in the face of external forces.

Ultimately, the key parameter of interest, the elastic modulus, provides a quantitative measure of stiffness. The polyhedral rock models consistently demonstrate a higher elastic modulus across varying rockfill ratios; it serves as a conclusive indication that structures composed of polyhedral rocks outperform their spherical counterparts in terms of stiffness and resistance to deformation. This holistic assessment, considering displacement, stress, strain, reaction forces, and elastic modulus, collectively elucidates the superior performance of models with polyhedral rocks, substantiating their efficacy in achieving enhanced structural integrity and resilience.

In this study, we conducted simulations using six models with varying volumes of rocks to investigate the impact of rock volume and shape on the elastic modulus of the RFC. The models consisted of two sets, one with spherical rocks and the other with polyhedron rocks, each with volumes of 50%, 55%, and 60%. To analyze the results, we compared the elastic modulus values obtained for each model from the initial hardening stage up to 28 days. Figure 10 illustrates the elastic modulus curves, providing insights into how shape and rock volume changes affect the RFC’s modulus.

This comparison shows us any disparities in the elastic modulus values among the different models. By analyzing the curves, we can gain a deeper understanding of how variations in rock volume influence the mechanical properties of the RFC. This information can be beneficial in optimizing the design and construction of rockfill structures, allowing engineers to enhance the efficiency and performance of such structures. Furthermore, the simulation results and figures obtained for all the models under different effects are available for examination in the previous discussion. These additional insights contribute to a comprehensive understanding of the relationship between rock volume, shape, and the elastic modulus of the RFC.

The simulation results demonstrate that RFC containing polyhedral rocks exhibits a higher elastic modulus than models with spherical rocks. This difference is attributed to the angular and interlocking nature of polyhedral shapes, which provide better load distribution and resistance to deformation. As a result, the polyhedral rocks contribute to a more rigid structure, enhancing the overall mechanical properties of the RFC. These findings underscore the significance of rock shape in optimizing the performance of rock-filled concrete, particularly in applications requiring higher stiffness and strength.

The elastic modulus values of these models with rock volumes of 50–60% are between 32.63 GPa and 36.48 GPa (

Table 3. The results of SCC and models with spherical and polyhedron rocks.

Rockfill Ratio	SCC (GPa)	Models Consist of Spherical Rocks (GPa)	Models Consist of Polyhedron Rocks (GPa)
r = 50%	22.09	33.15	33.93
r = 55%	22.09	34.43	34.94
r = 60%	22.09	35.18	36.48

). The rocks are placed further apart in Model-1S and Model-1P, with more SCC filling between rocks. As previously stated, Model-1 contains 50% of the volume of the rocks; thus, the other 50% will be filled with SCC. Model-2S and Model-2P have a higher starting point than that of the Model-1 curve. Model-2 is slightly stronger than Model-1, since it has a 55% volume of rocks and a 45% volume of SCC. Model-3’s elastic modulus curve has a high value from start to end. The volume of rocks in this model is 60%, with the remaining 40% filled with SCC.

The simulation-driven examination of elastic modulus in rock-filled concrete (RFC), utilizing both spherical and polyhedral rocks, elucidates the pronounced influence of rock geometry on the material’s mechanical characteristics. The simulation outcomes indicate that RFC configurations incorporating polyhedral rocks demonstrate a marginally elevated elastic modulus compared to those utilizing spherical rocks. This phenomenon can be attributed to the intricate interlocking mechanisms and augmented surface contact area inherent to polyhedral geometries, which collectively enhance the stiffness and structural robustness of the concrete matrix. These findings accentuate the critical role of rock morphology in modulating the elastic behavior of RFC, suggesting that the strategic employment of polyhedral rocks could be advantageous in optimizing concrete formulations for applications necessitating superior stiffness and load-bearing capacity. Consequently, this research contributes to a more nuanced understanding of the interplay between rock shape and the mechanical performance of RFC, laying the groundwork for future inquiries and potential advancements in high-performance construction materials.

3.3. Stress Transfer at RFC Interfaces

In a concrete model with embedded rocks, stress transfer occurs at the points where these materials come into contact. This stress transfer from one material to another happens due to the interaction between their surfaces. The properties of both the rocks and concrete influence stress transfer (Figure 11). Key factors include their stiffness (elastic modulus), how they deform under stress (Poisson’s ratio), and their ability to withstand shear forces (shear strength). Materials with higher stiffness tend to transfer stresses more effectively. The conditions at the interface where rocks and concrete meet affect stress transfer. Friction between the surfaces can help resist sliding and enhance stress transmission. Adhesion, or the sticking together of surfaces, can also play a role in stress transfer. The loads applied to the system, such as external forces or self-weight, determine how stress is distributed. Areas with higher load concentration will likely experience more pronounced stress transfer at the interface.

4. Conclusions

This study utilized finite element modeling to rigorously evaluate the elastic modulus of rock-filled concrete (RFC) incorporating spherical and polyhedral rocks. The findings yield significant scientific and practical insights:

• The simulation results reveal that RFC incorporating polyhedral rocks exhibits a superior elastic modulus compared to RFC with spherical rocks. This enhancement in stiffness, combined with greater load-bearing capacity, positions polyhedral-rock-filled RFC as particularly advantageous for applications demanding increased structural resilience and rigidity.
• A clear and direct correlation was identified between rock volume and elastic modulus. Specifically, increasing the rockfill ratio from 50% to 60% resulted in an approximate 5% increase in elastic modulus. This underscores the critical role of rock volume in fine-tuning the mechanical properties of RFC, suggesting a pathway for optimizing its structural performance.
• The elastic modulus of RFC is governed by several factors, including rock pattern, size, volume, and shape. Notably, a significant rise in elastic modulus was observed during the early curing stages, followed by a more gradual increase over time. This temporal progression highlights the importance of early-age mechanical properties in predicting the long-term performance of RFC.
• Achieving optimal rock size distribution within RFC is crucial. It requires balancing a sufficient flow of self-compacting concrete (SCC) around the rocks while avoiding the pitfalls of overfilling. A strategically varied mix of rock sizes is recommended to enhance the homogeneity and mechanical efficacy of the RFC composite.

This study offers substantial contributions to both the scientific understanding and practical application of RFC. By elucidating the influence of rock geometry and volume on the elastic properties of RFC, this research provides a deeper understanding of how these parameters can be manipulated to improve the material’s structural performance. This is particularly relevant for large-scale infrastructure and water conservation projects where material resilience and durability are paramount.

To further advance the field, future research should focus on the mesoscale mechanical behavior of RFC, particularly the interactions between different rock geometries and types, and the influence of environmental factors on crack initiation and propagation. These areas of inquiry hold the potential to develop more advanced and optimized RFC composites, tailored for specific engineering applications. The numerical techniques and insights presented in this study establish a robust foundation for such future explorations, with the potential to significantly enhance both the theoretical framework and practical deployment of RFC in complex engineering contexts.