Proportioning optimization of transparent rock-like specimens with different fracture structures

Clarifying the principles of proportioning optimization for brittle transparent rock-like specimens with differential fracture structures is crucial for the visualization study of the internal fracture and seepage evolution mechanisms in rock masses. This study, utilizing orthogonal experimental methods, uncovers the influence mechanisms, extents, and patterns by which the ratios of resin, hardener, and accelerator, along with the freezing duration, impact the mechanical characteristics of transparent rock-like specimens. Notably, it was observed that as the accelerator ratio and freezing time are increased, there’s a general decline in the uniaxial compressive strength, tensile strength, and elastic modulus of the specimens. In contrast, an increase in the hardener ratio initially leads to an enhancement in these mechanical properties, followed by a subsequent decrease. Under uniaxial compressive loading, the specimens exhibit four typical modes of failure: bursting failure, splitting failure, single inclined plane failure, and bulging failure. As the hardener and accelerator ratios increase, the mode of failure gradually shifts from bulging to bursting, with freezing time having a minor overall impact on the evolution of failure modes. The study proposes a method for inducing random three-dimensional closed fractures within the specimens and further clarifies the principles for optimizing the proportions of specimens with different fracture structures, such as intact, embedded regular, and random three-dimensional fractures. This research facilitates the in-depth application of transparent rock-like materials in various scenarios and provides theoretical guidance and technical support for visualizing the evolution of fracture and seepage characteristics within the fractured rock mass.

the category of regularly filled fractures.There is a lack of appropriate specimen preparation technology for closed random fractures, which are widely developed in hard rocks, thereby restricting the progress of related studies.
This article involves the preparation of transparent rock-like materials using unsaturated resin, hardener, and accelerator, with an enhancement of their mechanical properties through low-temperature freezing.A 3-factor, 5-level orthogonal experiment was conducted, focusing on the hardener ratio, accelerator ratio, and freezing time as influencing factors.Based on the results of uniaxial compression and Brazilian split tests of transparent rock-like specimens, the study reveals the mechanisms, extents, and patterns of how these factors affect the mechanical properties of the specimens.It summarizes the typical failure modes of transparent rocklike specimens under various proportioning conditions and, along with the compressive-tensile strength ratio, systematically evaluates the similarity of these materials in simulating rock mechanical behavior.Finally, based on the experimental results with intact and fractured specimens, the study clarifies the proportioning optimization principles for different fracture structure specimens, including intact, embedded regular three-dimensional filled fractures, and random three-dimensional closed fractures.This research advances the in-depth application of transparent rock-like materials in multiple scenarios and provides theoretical guidance and technical support for the visualization study of the internal fracture and seepage evolution processes in the fractured rock mass.

Specimen preparation and experimental design Selection of raw materials
The raw material selected in this article is transparent unsaturated epoxy resin, which has the advantages of fast curing time and high transparency.Cobalt octoate is chosen as the accelerator and phenolsulfonic acid as the hardener, to adjust and improve the resin's brittleness characteristics.The detailed parameters of the raw materials are shown in Table 1.

Specimen preparation method
Based on the results of trial specimen preparation, the specimen preparation method was continuously refined and optimized to reduce the impact of the preparation method on the transparency and homogeneity of the specimens.The specific specimen preparation steps are as follows: 1. Preparation of raw materials: Prepare the resin, hardener, and accelerator required for the experiment according to the material types listed in Table 1. 2. Mold preparation: Rectangular and cylindrical molds are used to prepare rectangular specimens for the uniaxial compression test and cylindrical specimens for the Brazilian split test, respectively.The rectangular mold is composed of 5 pieces of 5 mm thick transparent acrylic boards, including two rectangular boards each of 50 mm × 60 mm and 50 mm × 100 mm, and one 60 mm × 110 mm rectangular board.These are taped together to form a rectangular mold box with an open top and internal dimensions of 50 mm × 50 mm × 100 mm, as shown in Fig. 1a.The mold for preparing cylindrical specimens is custom-made from polytetrafluoroethylene (PTFE) material, containing several cylindrical grooves of Φ50 mm × 25 mm.This material does not bond with the resin material, making it easy to demold later, as shown in Fig. 1b.For the preparation of rectangular specimens, a transparent mold is used to facilitate the real-time observation of the fracture position and specimen preparation effect during the preparation process of the specimens with three-dimensional fractures.3. Specimen Preparation: According to the designed raw material proportions, specific weights of resin, hardener, and accelerator are separately measured using a beaker and a small measuring cup.First, the preweighed accelerator is poured into a beaker containing resin.It is stirred in a fixed direction for about two  minutes.Once the resin becomes transparent and clear, it is left to stand for about a minute, allowing any bubbles generated during stirring to dissipate on their own.Then, the pre-weighed hardener is slowly poured into the beaker, stirring gently along the fixed direction to minimize the generation of excess bubbles.After the curing agent and resin have completely blended, they are poured into the mold using a glass rod for further processing.4. Specimen Demolding: After the specimen has solidified and returned to room temperature, carefully remove the mold to prevent damage to the edges and corners of the specimen.The demolded square and cylindrical specimens are shown in Fig. 1c,d, respectively.Number the specimens after demolding.There are a total of 25 groups of specimens, with 3 specimens made for each group, numbered as follows: x-1, x-2, x-3 (where x ranges from 1 to 25). 5. Specimen Curing: Use sandpaper to smooth out any uneven areas on the specimens.Then, place the specimens in a −25 ℃ low-temperature refrigerator for curing, and retrieve them before conducting the test.

Experimental design
The orthogonal experimental method is adopted to study the influence of raw material ratios and freezing time on the mechanical characteristics of specimens.The orthogonal experimental design uses the mass percentage of hardener to resin (hardener ratio A), the mass percentage of accelerator to resin (accelerator ratio B), and the freezing time C as the three factors of the orthogonal experiment, with each factor set at 5 levels.Preliminary exploratory experimental results show: when the A is less than 0.5, the specimens cannot cure; when the A is more than 2.0, the transparency of the specimens significantly decreases.When the B is less than 0.2, the effect of the accelerator is weak; when the B is more than 1.0, the curing process of the specimens is intense, releasing a large amount of heat, and random defect-type damages occur, making the specimen forming process unstable and difficult to form a intact specimen.When the freezing time is less than 6 h, the specimens exhibit obvious toughness; after more than 48 h, there is no significant difference in the mechanical properties of the specimens.Therefore, the ranges of the A, B, and C are set to 0.5 ~ 2.0, 0.2 ~ 1.0, and 6 ~ 48 h, respectively, with the levels of each factor set as shown in Table 2.This experiment adopts a 3-factor 5-level orthogonal design scheme L25 (5 3 ), designing 25 sets of ratio combination experiments.Each set of experiments contains 3 specimens, and the ratio combinations are shown in Table 3.  show that the basic mechanical parameters of transparent rock-like materials under different ratios exhibit significant differences.Specifically, the range of uniaxial compressive strength is 55.82 to 119.15 MPa, the range of tensile strength is 4.72 to 10.93 MPa, and the modulus of elasticity ranges from 1.48 to 2.45 GPa.Therefore, it is evident that varying raw material ratios and freezing times can lead to significant differences in the mechanical characteristics of transparent rock-like materials, especially in terms of uniaxial compressive strength and tensile strength.Thus, further clarifying the degree and pattern of influence of each ratio factor on the mechanical properties of the materials is of great significance for the preparation of transparent rock-like specimens with different brittleness characteristics.

Sensitivity analysis of factors affecting mechanical parameters
To reveal the degree and pattern of the influence of various factors on the mechanical properties of transparent rock-like specimens, a sensitivity analysis of the basic mechanical parameters of the specimens was conducted.
According to the theory of orthogonal experiments, the mechanical parameters at the same level of each factor are averaged, and the range is the difference between the maximum and minimum values of the mechanical parameters at each level.A larger range indicates that the different levels of that factor produce more significant Figure 2. Experimental apparatus and transparent rock-like specimens.
differences, making it an important factor with a significant impact on the experimental results.Let y i (i = 1, 2, …, 5) represent the average mechanical parameter value at level i of a factor.For example, in the analysis of the range of σ c under the influence of the hardener ratio, y i represents the average σ c when the hardener ratio is at level i, under different accelerator ratios and freezing times.The results of the range analysis of the basic mechanical parameters of transparent rock-like specimens are shown in Table 4. Table 4 shows that the factors affecting the σ c and E of transparent rock-like specimens in descending order of impact are accelerator ratio, freezing time, and hardener ratio; for σ t , the order is accelerator ratio, hardener ratio, and freezing time.It can be observed that the accelerator ratio is the most significant factor affecting the mechanical characteristics of transparent rock-like specimens.To more intuitively display the influence of each factor on the mechanical properties of transparent rock-like specimens, a chart depicting the variation of mechanical parameters at different levels of each factor was created, as shown in Fig. 4. From the chart, it is evident that with the increase in accelerator ratio and freezing time, the σ c , σ t , and E of the transparent rock-like specimens generally show a decreasing trend.With the increase in hardener ratio, σ c and E generally show an increasing and then decreasing trend, while the impact of hardener ratio on σ t shows fluctuations with a range of 2 MPa, but overall still presents an increasing and then decreasing trend.
To gain a deeper understanding of the influence of various factors on the σ c , σ t and E of transparent rock-like specimens, the impact mechanisms of these factors on the mechanical properties of the specimens are further revealed from the perspective of raw material reaction molding and specimen structural characteristics.The higher the content of the hardener, the faster the curing speed, but excessively high levels of the hardener ratio can lead to a rushed and insufficient curing process of the resin.With the increase in the hardener ratio, σ c and   www.nature.com/scientificreports/E gradually increase initially.This is because the increase in the hardener ratio enhances the viscosity and epoxy value of the material, thereby strengthening the curing effect and consequently enhancing the σ c and E of the transparent rock-like specimens, with the impact being quite direct.As the hardener ratio further increases, σ c and E decrease, which is attributed to the excessive amount of hardener causing incomplete curing reactions in the resin, leading to an increase in internal bubbles in the specimens.The impact of the hardener ratio on σ t is characterized by fluctuations; σ t reaches its maximum value when the hardener ratio is 1.3, and overall, the impact on σ t also shows an increasing and then decreasing trend.Therefore, it is evident that the impact of the hardener ratio on the mechanical properties of the specimens exhibits a clear peak and turning effect, that is, when the curing ratio is 1.3, the specimens exhibit stronger mechanical behavior.In the reaction process of resin, the accelerator can cause changes in active groups, thereby accelerating the cross-linking process and enhancing the curing rate of the resin.With the increase in the accelerator ratio, σ c , σ t , and E generally show a downward trend.This is because the increase in the amount of accelerator accelerates the curing degree of the specimen.The specimen preparation process shows that as the accelerator ratio increases, a large amount of heat is generated during the curing process, which induces the formation of defect-related damage within the specimen, such as small cracks, leading to the deterioration of the mechanical properties of the specimen.The specimens were subjected to freezing treatment at −25 ℃ to physically reduce their viscosity and increase their brittleness.
Compared to the hardener ratio and accelerator ratio, the influence of freezing time on the mechanical properties of the specimens is relatively small.As the freezing time increases, the mechanical parameters of the specimens generally show a decreasing trend.This is mainly because as the freezing time increases, the effect of internal defects in the specimens is magnified.That is, under the action of force, internal micro-cracks and bubbles in the specimens are more likely to induce structural fracturing, leading to an overall decrease in mechanical properties.However, based on the fluctuations in data points, it can be seen that when the freezing time reaches 18 h, the σ c and E of the specimens are at their maximum values, and when the freezing time reaches 12 h, σ t is at its maximum.This indicates that under a combined effect, when the freezing time is between 12 and 18 h, the mechanical properties of the specimens show a certain degree of enhancement.However, as the freezing time continues to increase, the weakening effect of pores and cracks intensifies, and the combined impact leads to a fluctuating deterioration trend in the mechanical properties of the specimens.

Brittle characteristics and failure modes
Brittleness is an important factor affecting the failure mechanism and characteristics of rocks.When using rocklike materials to study the failure mechanisms and characteristics of rocks, the similarity in brittleness is a key indicator for evaluating the resemblance between rock-like specimens and the original rock.The application fields of resin materials generally favor the toughness, wear resistance, and other properties of resin materials.However, when applied to rock-like materials, their transparency is often utilized to study the expansion characteristics of three-dimensional fractures.Therefore, many scholars are dedicated to researching how to enhance the brittleness index, i.e., the compressive-tensile strength ratio, to ensure its similarity to real rock materials.To compare with previous research results, the compressive-tensile strength ratio is used to quantitatively evaluate the brittleness characteristics of transparent rock-like specimens.The statistical distribution characteristics of the compressivetensile strength ratio of transparent rock-like specimens are shown in Fig. 5a, with the distribution range of the ratio being 6.22 to 19.34.Compared to the length of the range interval of the compressive-tensile strength ratio, which is 13.12, the range analysis results (Table 5) show that the hardener ratio, accelerator ratio, and freezing time have a comparable impact on the compressive-tensile strength ratio, exhibiting a fluctuating influence pattern, as shown in Fig. 5b.Based solely on the numerical values of the compressive-tensile strength ratio, the prepared transparent rock-like specimens can well meet the range requirements of the compressive-tensile strength ratio for brittle rocks.However, the experimental results show that transparent rock-like specimens www.nature.com/scientificreports/with higher compressive-tensile strength ratios tend to exhibit non-brittle failure modes.Therefore, to reasonably evaluate the similarity of transparent rock-like materials in simulating the mechanical behavior of brittle rocks, a comprehensive analysis combining the compressive-tensile strength ratio and the failure mode of the specimens should be conducted.Under uniaxial compression load, transparent rock-like specimens exhibit four typical failure modes, namely bursting failure, splitting failure, single inclined plane failure, and bulging failure.The uniaxial compression stress-strain curves, macroscopic failure modes, and microscopic structural characteristics of the fracture surfaces of the specimens are shown in Table 6.
Table 6 shows that under uniaxial compression conditions, the stress-strain curve of transparent rock-like specimens exhibits evolutionary characteristics of an upward concave section, a linear section, a downward concave section, and a steep drop section.These correspond respectively to the initial compaction stage, linear deformation stage, crack development stage, and failure stage of the specimens, which is similar to the failure process of real rocks, and its failure modes can better simulate some failure characteristics of common rocks, as shown in Table 7.  Specimens exhibiting bursting failure, after undergoing a brief initial compaction phase, enter the linear deformation stage.They exhibit instantaneous brittle bursting failure without a noticeable crack development stage.At the moment of failure, fragments of the specimen are violently ejected.The fracture surface features a distinct roughness, with noticeable dimples and tear patterns observed near the crack lines, along with the formation of numerous fine root-like branches.This indicates a significant stress dispersion phenomenon, and the formation of the fracture surface is intense.Specimens exhibiting splitting failure, after a relatively short initial compaction phase, also enter the linear deformation stage.They then progress to the crack development stage, where cracks initiate and gradually propagate throughout the entire specimen due to local micro-cracks or pores, leading to brittle splitting failure.The surfaces of the split fractures tend to be smooth locally, with distinct crack lines developing in a straight line.The phenomenon of stress dispersion disappears, presenting typical brittle fracture striations.The formation of the fracture surface is crisp and straightforward.Specimens exhibiting single inclined plane failure have a noticeably elongated initial compaction phase.After undergoing the linear deformation stage, they gradually form a steeply inclined failure surface.The formation of this failure surface is characterized by a longer crack development stage.Once the fracture surface becomes continuous, the specimen fails, and the entire failure process of the specimen shows a certain degree of plastic deformation.On the fracture surface, the crack lines become dense, the number of stress bands increases, and there are no obvious tears.The stress dispersion effect is apparent, and the formation of the fracture surface is gentle.Specimens exhibiting bulging failure show typical plastic deformation.After a relatively long initial compaction phase, the specimens enter the linear deformation stage and then progress to the plastic deformation stage.As the specimens bulge, tearing occurs in the middle of the specimens, leading to failure.The fracture surfaces of the specimens have dense crack lines in a discontinuous and curved form, with a significant stress dispersion effect.The formation of the fracture surface is gentle.
The compressive-tensile strength ratio of transparent rock-like specimens under different ratios and their corresponding failure modes are shown in Fig. 6. Figure 6 shows: 1. Bulging failure occurs under conditions of low accelerator ratio and medium or lower hardener ratio.Single inclined plane failure occurs under conditions of low accelerator ratio and higher or high hardener ratio,  www.nature.com/scientificreports/or lower accelerator ratio and medium or below hardener ratio.Splitting failure occurs under conditions of lower accelerator ratio and higher or high hardener ratio, or medium accelerator ratio and any hardener ratio, or higher or high accelerator ratio and low hardener ratio.Bursting failure occurs under conditions of higher or high accelerator ratio and lower or above hardener ratio.2. There are more specimens exhibiting splitting failure, followed by bursting failure, and then single inclined plane failure and bulging failure.As the levels of hardener ratio and accelerator ratio increase, the failure mode gradually transforms from bulging failure to bursting failure.Overall, the accelerator ratio is the main factor controlling the failure mode of the specimens, with the increase of the accelerator ratio, the failure mode is gradually transformed from plastic to brittle failure; under the same level of accelerator ratio, the hardener ratio accelerates the process of transformation of the failure mode to brittle failure.The influence of freezing time on the overall evolution trend of the failure mode is relatively small.3. The range of compressive-tensile strength ratios of the transparent rock-like specimens is 6.22 to 19.34, which falls within the range of compressive-tensile strength ratios for real rocks, i.e. 2.7 to 39 31 .Among them, specimens with bulging failure show a significant yield hardening effect and higher compressive strength, with the compressive-tensile strength ratio consistently above 14.0, with an average value of 16.82; The compressive-tensile strength ratios of both single inclined plane failure and splitting failure specimens fluctuated above and below 12.0; The mean value of the compressive-tensile strength ratio of the bursting failured specimens is 13.04, with a relatively large fluctuation range of 9.27 to 19.21.

Proportioning optimization of different fractured specimen
The greatest advantage of transparent rock-like materials lies in their transparency.Currently, transparent rocklike materials are mainly used in research on the crack propagation mechanisms and modes of rock with threedimensional fractures under loading or hydraulic pressure, as well as the coupled mechanisms of fracture surface shear and seepage flow.For different research objectives, based on the above findings of this article, the ratio of transparent rock-like materials should be further optimized and clarified.This ensures the rational selection of the ratio for the targeted transparent rock-like specimens, thereby guaranteeing the success rate of specimen preparation.
The selection of the ratio for intact transparent rock-like specimens can be based on the conclusions of the previous studies.By considering the comprehensive characteristics of basic mechanical parameters, failure modes, and the compressive-tensile strength ratio, a transparent rock-like material ratio similar to the mechanical properties of the target rock can be chosen to prepare rock-like specimens, and to carry out the related studies, such as the study of shear seepage and blasting characteristics of the rock mass 26,27,29,30 .By optimising the comprehensive similarity between intact transparent rock-like materials and real rocks, a more accurate representation of shear fracture, seepage and blasting characteristics of the rock mass can be achieved.Therefore, selecting transparent rock-like materials with mechanical properties similar to the target rock is crucial for the accuracy of the experimental results, rather than merely pursuing their visualization capabilities or similarity in a single mechanical indicator.

Regular fractured specimens
Three-dimensional fracture networks are extensively developed within rock masses and cannot be directly observed during their expansion and penetration under load conditions.Additionally, fracture networks typically develop in harder rocks, and the control effect of fractures is significantly manifested in hard and brittle rocks.Hence, enhancing the brittleness of transparent rock-like materials is key to accurately approximating the failure mechanisms of the fractured rock mass.
Currently, the common method for preparing transparent rock-like specimens with three-dimensional fractures involves fixing mica sheets with the cotton thread inside a transparent mold box as shown in Fig. 7a, followed by pouring liquid resin to cure into a regular fractured specimen as shown in Fig. 7b.To determine the reasonable ratio for preparing regular fractured specimens, attempts were made to prepare transparent rock-like www.nature.com/scientificreports/specimens with regular three-dimensional fractures at different angles using specimen ratios similar to the mechanical properties of hard rocks, specifically those exhibiting splitting and bursting failure modes.During the specimen preparation process, it was found that not any combination of ratios could successfully achieve the preparation of the regular fractured specimens.Under certain accelerator and hardener ratios, specifically those used for specimens with splitting and bursting failures, the resin curing process tends to be relatively intense.Due to the insertion of mica sheets, which act as foreign objects within the specimen, secondary cracks can form along the edges of the mica sheets during the heat-releasing curing process, as shown in Fig. 7c.Sometimes, these cracks may even extend through the entire specimen, preventing the successful preparation of the desired fracture structure.The preparation effects of transparent rock-like specimens with three-dimensional regular fractures under various ratio conditions are shown in Table 8.It is evident that under conditions of low and lower hardener ratios, medium and above accelerator ratios, or medium hardener ratios, medium and higher accelerator ratios, the specimens have good effects and a high success rate in preparation.Based on this ratio pattern, a successful preparation of transparent rock-like specimens with embedded mica sheets was achieved using a medium level of accelerator and hardener ratios.Figure 8a shows the progressive failure characteristics of the specimen with a single three-dimensional regular fracture at 30°dip angle under uniaxial compression conditions.Initially, feather-like cracks develop at the tips of the pre-existing fracture.With an increase in load, these feather-like cracks gradually extend into envelope-shaped wing cracks, then further expand to form petal-shaped cracks.Eventually, the specimen undergoes complete splitting failure, as illustrated in Fig. 8b.This represents the typical behavior of progressive expansion of cracks at three-dimensional fracture tip under uniaxial compression conditions.The stress-strain curve of the fractured specimen rapidly drops after peak stress, leading to a brittle failure, as shown in Fig. 8c.Therefore, using this composition to prepare transparent rock-like specimens with three-dimensional regular fractures is highly suitable for studying the fracturing evolution mechanism of the rock mass with three-dimensional regular fractures.

Random fractured specimens
In strict terms, the properties of three-dimensional fractures prepared using the cotton thread-fixed mica sheet method are considered as filled fractures, with mica sheets serving as the filling material.In contrast, the commonly developed three-dimensional fractures tend to be in a closed state.Additionally, the regular boundaries of the specimen box and the open boundaries determine that it is not possible to prepare arbitrary configuration fractures within the specimen.Lastly, when there are a significant number of pre-existing fractures inside the specimen, an excessive number of intersecting fixed cotton threads can affect the mechanical properties of the specimen.Based on the phenomenon of secondary cracks induced by mica sheets and the composition Table 8.Effects of specimen preparation for specimens with three-dimensional regular fractures under various mix proportion conditions.

Low and lower Medium and above
The transparency of the specimen is high, no secondary cracks occur at the edges of the mica sheets, the success rate of prefabricated threedimensional regular fractures is high, and the specimen preparation effect is good Medium Medium and higher Higher Lower and above There is a high probability of secondary cracks forming at the edges of the mica sheets, resulting in a low success rate of specimen preparation Medium High High Higher and high Secondary cracks occur at the edges of the mica sheets and expand intensely, sometimes even penetrating the entire specimen, making it very difficult to successfully prepare the specimen Figure 8. Fracture evolution process and stress-strain curve of the transparent rock-like specimen with a single three-dimensional regular fracture at 30° dip angle.
conditions, a method for preparing transparent rock-like specimens with self-induced random fractures inside is proposed.This method can achieve the preparation of three-dimensional random closed fractured specimens.Experimental results have shown that using irregular metallic shavings as foreign bodies for inducing fractures can ensure a higher fracture induction rate, as shown in Fig. 9.Under different mixing ratios and the addition of accelerator and hardener, the results of preparing random fractured specimens vary significantly, as shown in Table 9.Under conditions where the reaction process is relatively slow (low and lower hardener ratio, medium and above accelerator ratio, or medium hardener ratio, medium and higher accelerator ratio), due to slow heat release, the waiting time for the test until metallic shavings are placed is long, and the success rate of inducing random fractures is very low.Under conditions where the reaction process is very intense (high hardener ratio, higher and high accelerator ratio), the specimen solidifies rapidly, and after the metallic shavings are added, they stop sinking at the top of the specimen, making it impossible to control the location of fractures.In severe cases, the intense curing reaction can cause the specimen to develop through fractures and split open, so the above-mentioned mixing conditions are not suitable.Preliminary experiments have shown that using the conditions with higher hardener ratio and lower to high accelerator ratio or medium hardener ratio and high accelerator ratio, which result in splitting or bursting failure, yields a higher success rate in inducing fractures through metallic shavings.Furthermore, the fracture does not significantly expand during the specimen curing process.
In different proportioning conditions, the curing time varies.To ensure a high success rate of inducing random fractures, the state of the resin during the insertion of metal shavings needs to be controlled based on experimental phenomena.When adding metal shavings, the surface of the resin mixture should be viscous but not yet jelly-like.The shaving will move slowly and stop at a certain position in the specimen box as the curing reaction proceeds.By observing the movement speed of the shaving and adjusting the time of metal shavings insertion, the final resting position of the metal shaving can be controlled.This, in turn, induces random fractures during the heat release process of specimen curing, ultimately creating a transparent rock-like specimen with random fractures.Taking the random fractured specimen shown in Fig. 10 as an example, the specimen successfully induced two three-dimensional closed random fractures with two metal shavings.During the fracture generation process, due to the obstruction of the initially generated inclined random fracture, the longitudinal random fracture stopped expanding upon contact with it.This process of fracture generation can effectively simulate the formation pattern of fractures in actual rock masses.The progressive failure process and the stress-strain curve of this random fractured specimen under uniaxial compression are shown in Fig. 11a,b, respectively.Under uniaxial compression, the expansion pattern of the random fractures is similar to that of the three-dimensional regular fractures.The upper tip of the inclined random fracture expands to form feather-like cracks, which gradually evolve into wing-shaped and petal-shaped cracks as the load increases.Due to the influence of the longitudinal random fracture, the tip crack of the inclined random fracture does not extend downward.The longitudinal  The curing process is fast, making it difficult to successfully position the metal shavings.The heat release during curing is intense, and the specimen may even burst random fracture is nearly parallel to the loading direction and is also affected by the inclined random fracture, preventing the tip crack from extending upwards.When the load reaches its peak value, the tip crack of the inclined random fracture rapidly expands and connects with the longitudinal random fracture, causing the specimen to undergo splitting failure, displaying characteristics of brittle fracture.This process shows certain similarities to the progressive expansion characteristics of specimens with three-dimensional regular fractures.At the same time, it clearly reveals the interaction effect of the random fracture network and its control effect on the progressive failure of the specimen.

Discussion
1. Due to the limitations of experimental conditions, this study only conducted low-temperature treatment at −25 ℃ for the specimens.However, previous studies have shown that low-temperature treatment below -30 ℃ can significantly increase the brittleness of transparent rock-like materials.Therefore, to further enhance the brittleness of transparent rock-like materials, explorations can be conducted on the basis of this study by further reducing the freezing temperature.2. The current method of inducing the formation random closed fractures using metal shavings can only control the location of fracture initiation, but the spatial orientation and size of the fractures are still not well controlled.Future research could focus on the size and shape of the inducing materials, in combination with fine adjustments to the accelerator ratio and hardener ratio content.This approach aims to explore further the main controlling factors of the orientation and size of random fractures.By doing so, it may be possible to achieve a more orderly generation of complex random fracture networks.
https://doi.org/10.1038/s41598-024-59886-8www.nature.com/scientificreports/Sensitivity analysis of material proportion factors Basic mechanical parameters of the specimens For the 25 ratio combinations of the orthogonal design, uniaxial compression tests and Brazilian split tests were conducted sequentially on transparent rock-like specimens.The test apparatus and specimens are shown in Fig. 2. The statistical distribution characteristics of the uniaxial compressive strength σ c , tensile strength σ t , and the tangent modulus of elasticity E at 50% of the peak compressive strength are shown in Fig. 3.The test results

Figure 3 .
Figure 3. Statistical distribution of mechanical parameters of transparent rock-like specimens.

Figure 4 .
Figure 4. Influence of various factors on the mechanical properties of transparent rock-like specimens.

Figure 6 .
Figure 6.Distribution characteristics of compressive-tensile strength ratio of transparent rock-like specimens with different failure modes.

Figure 7 .
Figure 7. Preparation effect of transparent rock-like specimens with three-dimensional regular fractures.
The heat release process during curing is slow, requiring a wait of more than 10 min, and the success rate of inducing fractures is very low Medium Medium and higher Higher Lower and above The curing time is 2 ~ 4 min, providing sufficient time to insert the metal shavings, and the success rate of inducing fractures is high Medium High High Higher and high

Figure 10 .
Figure 10.Transparent rock-like specimen with three-dimensional random fractures.

Figure 11 .
Figure 11.Fracture evolution process and stress-strain curve of the transparent rock-like specimen with threedimensional random fractures.

Table 1 .
Basic parameters of raw materials.

Table 2 .
Orthogonal test factor level settings for transparent rock-like materials.The freezing temperature is set at -25 ℃.The freezing temperature during the experiment is a fixed quantity, and no changes were made to the temperature.

Table 3 .
Orthogonal design combination scheme for transparent rock-like materials.

Table 4 .
Range analysis of the mechanical parameters of transparent rock-like specimens.

Table 5 .
Range analysis of the compressive-tensile strength ratio of transparent rock-like specimens.

Table 6 .
Typical failure modes of transparent rock-like specimens under uniaxial compression condition.

Table 7 .
Examples of real rock failure modes under uniaxial compression.