Assessing the limits of applicability of photopolymer 3D printing
for physical modeling in geosciences

Introduction

To overcome the shortage of core material and enable its repeated use in research, investigators have proposed using approximate copies of rock specimens, that is, replicas produced by 3D additive manufacturing technologies [1, 2]. This approach is increasingly employed in the mining [3] and oil and gas industries [4] to investigate the mechanical properties and permeability of rocks in relation to their internal structure and loading conditions. A key advantage of such replicas is that they allow the required number of specimens to be produced for a wide range of studies, including destructive tests [5, 6].

A variety of technologies are currently available for fabricating 3D rock models. The choice of printing method and material depends on the purpose of the study [7]. Specimens may be produced by material extrusion using thermoplastic filament (FDM/FFF), by stereolithography (SLA) based on the layer-by-layer curing of liquid photopolymer resin, by binder jetting of gypsum [8] or cement–silica–water mixtures [9], or by binder jetting of quartz sand using specific binder systems, including cyanoacrylate adhesive [11] and furfuryl alcohol- and phenolic resin-based binders [12]. Thus, these 3D-printing methods differ primarily in the type of material used [12].

In experimental studies involving the physical modeling of rocks, materials with physical and mechanical properties similar to those of natural rocks, such as gypsum and sand–cement mixtures, are generally preferred. However, existing mineral-based printing methods offer low resolution and do not allow the internal structure of specimens to be reproduced [13]. Specimens produced by material extrusion using thermoplastic filament (FDM/FFF) are rarely suitable as rock replicas because of their low printing resolution and because their structure and material properties differ markedly from those of natural rocks [14].

Stereolithographic 3D printing (SLA), based on the layer-by-layer curing of photopolymer resins, provides the highest print quality and is widely used in both industrial applications and research [15]. Depending on the method used to expose the photopolymer resin, SLA techniques are classified as laser-based [16], digital light processing (DLP) [17], and liquid-crystal-display-based stereolithography (LCD) [18]. SLA offers the highest printing resolution, making it possible to reproduce with high accuracy the microscale heterogeneities inherent in the original objects; for this reason, it is widely used to fabricate porous and fractured rock replicas [19]. LCD-based printing is the most accessible and fastest stereolithographic method and is therefore particularly promising for the production of rock replicas for geomechanical investigations, as it allows a high degree of replication to be achieved at minimal cost and within a short time frame [20].

Thus, an analysis of previous studies has shown that 3D-LCD printing is the most promising method for producing accurate rock replicas. The aim of this study was to experimentally evaluate the applicability of this method to the fabrication of rock replicas for investigating their geomechanical characteristics and to determine the limits of its applicability in physical modeling. To achieve this aim, the following objectives were pursued:

• to examine the microstructure of 3D-LCD replicas and assess its influence on their elastic and mechanical properties;
• to carry out comparative uniaxial compression tests on the replicas and natural rocks;
• to investigate the effect of layer orientation during printing on the Young’s modulus of the specimens.

1. Theoretical background

A considerable number of studies have examined the mechanical properties of materials produced by 3D-LCD printing and have shown that these properties are influenced most strongly by printing conditions [21–23] and curing conditions [24, 25]. However, all other factors being equal, the defining feature of 3D-LCD printing is the inherent heterogeneity associated with the layered structure of the fabricated parts [26, 27]. This layered structure gives rise to anisotropy in mechanical properties depending on layer orientation, owing to the heterogeneity inherent in each layer and the presence of interlayer interfaces.

A review of the literature has shown that the results of experimental studies on the effect of layer orientation are often contradictory. Independent research groups investigating the effect of print orientation on the tensile and compressive strength of printed parts have concluded that specimens with layers parallel to the tensile loading direction exhibit the highest Young’s modulus and strength [28–30]. Under compression, however, some studies have reported that specimens with inclined layers exhibit the best mechanical properties [31, 32]. Li and Tang [28] attributed this behavior to weaker bonding between adjacent layers, suggesting that layer inclination affects interlayer bond strength. They also noted that strength is influenced by printing-related defects, such as irregular edges, air bubbles, and foreign inclusions.

Other studies [21, 25, 33] have experimentally shown that the strength of specimens with layers oriented parallel to the tensile load is lower than that of specimens in which the layers are oriented perpendicular to the load. The authors of [22] attribute this to the effect of the laser path during curing. Study [34] showed that specimens loaded in tension along the layering direction exhibit the highest Young’s modulus, whereas specimens with inclined layers demonstrate greater strength and deformation. It has also been established that reducing the layer thickness improves both strength and elastic properties [33]. In specimens with layers perpendicular to the load, Young’s modulus is slightly higher, whereas strength is noticeably lower at any layer thickness. A reduction in layer thickness increases the brittleness of the material, resulting in greater stiffness and lower strength.

Thus, despite the available studies on the effect of layer orientation on the strength of parts produced by 3D-LCD printing, a substantial gap remains in understanding how mechanical properties vary with loading direction. Most studies have focused primarily on tensile strength, whereas comparatively few have examined compressive strength, and the reported findings are often contradictory. These inconsistencies hinder understanding of the failure mechanisms involved and of the factors governing changes in strength as a function of layer orientation. This limited understanding of material behavior also constrains the use of 3D-LCD printing for the fabrication of rock replicas in geomechanical investigations.

The present study addresses these issues. Its novelty lies in establishing the relationship of the mechanical properties of 3D-LCD rock replicas to print orientation and material microstructure, as well as in defining the limits of applicability of such replicas for physical modeling. Based on the results of the experimental program and comparative analysis, the study concludes that 3D-LCD printing is suitable for the physical modeling of geotechnical processes.

2. Methodology

2.1. Specimen fabrication

Digital specimen models were designed with an initial length of 70 mm and diameter of 35 mm, corresponding to a length-to-diameter ratio of 2 : 1, consistent with the specimen geometry specified in ASTM D7012-23. The models were exported in STL format for subsequent print preparation. Using dedicated software, the specimens were arranged on the build platform corresponding to the movable platform of the 3D printer. The models were then sliced layer by layer at different layer inclinations (Fig. 1, a), with three specimens prepared for each print orientation. Angles of 90°, 60°, 30°, and 0° correspond to the angle between the layer plane and the specimen axis. All specimens were printed with supports and oriented along the printer’s Y-axis.

Fig. 1. Specimen fabrication:
a – schematic illustration of specimen printing at different layer orientations;
b – printing of the specimens; c – printed specimens;
d – specimen machining; e – finished specimen fitted with axial and lateral strain gauges and acoustic emission (AE) sensors

The specimens were printed on an Anycubic Photon Mono X printer using LCD-based stereolithography (see Fig. 1, a). A layer exposure time of 2 s was identified in preliminary tests as optimal for achieving high print quality while maintaining an adequate printing rate. The layer thickness was 50 μm, the standard setting for this printer model. Anycubic Basic Resin Black was used as the printing resin; the black color was selected to minimize the effect of stray light on print quality.

After printing, the specimens were cleaned in an ultrasonic bath containing isopropyl alcohol. This yielded cylindrical specimens with a nominal diameter of 35 mm and a length of 70 mm (Fig. 1, b, c). These dimensions were selected for the following reasons.

First, the limited build area of the Anycubic Photon Mono X printer does not allow a large number of large specimens to be fabricated simultaneously. However, the simultaneous fabrication of a batch of specimens printed at the same orientation is critical for ensuring within-batch uniformity.

Second, owing to the specific features of the technology, namely the layer-by-layer curing of the resin and the separation of each printed layer from the LCD screen, increasing specimen size increases the contact area with the screen and, consequently, substantially increases the separation force. This may lead to premature delamination of the replicas, detachment of the supports, as well as layer sagging and deviations of the actual layer thickness and inclination from the specified values.

Specimens printed with parallel and inclined layers (see Fig. 1, c) exhibited deviations from the cylindrical shape because of layer sagging during printing. Because of these visible defects, they were machined on a lathe to obtain the correct cylindrical geometry (Fig. 1, d). Machining yielded specimens with parallel end faces, a diameter of 29 mm, and a length of 58 mm, preserving the 2 : 1 length-to-diameter ratio required for testing.

The finished specimens were post-cured in a UV chamber. Before and after machining, they were stored in a dark place to minimize exposure to ambient light. The temperature and humidity during storage corresponded to normal room conditions, and all specimens were kept in the same environment, thereby excluding any influence of storage conditions on the test results [25, 33, 35].

2.2. Natural rocks

Because the rock replicas were regarded as homogeneous materials, natural rocks with a homogeneous fine-crystalline structure were selected for comparison, namely silicites (microcrystalline quartz), silicified dolomites, and opoka, a carbonate-siliceous sedimentary rock. To evaluate mechanical properties over a wide strength range and to investigate anisotropy, specimens representing different lithotypes were selected. Silicites were assigned to Groups 1 and 2, silicified dolomites to Group 3, and opoka to Group 4.

Fig. 2. Cylindrical specimens of silicites (1, 2), silicified dolomites (3), and opoka (4) for uniaxial compression tests

The specimens were cut perpendicular to bedding (Groups 1 and 3) and parallel to bedding (Groups 2 and 4). Cylindrical specimens measuring 30 mm in diameter and 60 mm in length were prepared for the mechanical tests (Fig. 2).

2.3. Uniaxial compression testing procedure

Uniaxial compression tests were carried out using a Rock Mechanics Test System 816. To measure axial and lateral strains, strain gauges were bonded to the lateral surface of the specimens, and the data were recorded using the system’s data acquisition unit. Two pairs of strain gauges were positioned with reference to the printer axes. An acoustic emission (AE) sensor was also attached to the central portion of the lateral specimen surface to record signals during loading. The sensor arrangement is shown in Fig. 1, e.

During loading, data from the load cell, strain gauges, and the AE recording system were continuously recorded on a computer. An A-Line 32D measuring system was used to record AE signals. The specimens were loaded to failure at a constant rate of 0.1 MPa/s, in accordance with ASTM D7012-23.

2.4. Nondestructive methods for strength assessment

The nondestructive methods employed in this study included measurements of the propagation velocities of longitudinal and transverse elastic waves. Changes in these velocities over time reflect changes in the mechanical properties of the material and make it possible to assess anisotropy in both the replicas and the natural rocks. Such methods are particularly important for strength assessment in photopolymer resins because these materials undergo property changes during post-processing, including ultraviolet irradiation and storage, and also possess a layered structure [25, 33]. Elastic-wave velocity measurements were performed using an Ultrazvuk instrument (EcogeosProm LLC, Russia).

3. Results

3.1. Changes in mechanical properties during processing

Stabilization of elastic-wave velocity was used as the criterion for determining the sufficient duration of post-curing UV exposure. The relationships between elastic-wave velocity and UV post-curing time are shown in Fig. 3. After 1 min of exposure, elastic-wave velocity increased sharply relative to the untreated specimen and then changed only slightly, indicating that 1 min was sufficient for surface hardening. Four minutes of UV exposure was sufficient to achieve complete polymerization of the material, as longer exposure produced no further changes in mechanical properties. This is confirmed by the constancy of elastic-wave velocity after 8 min of treatment: UV radiation no longer penetrated into the interior of the specimen, and prolonged irradiation was therefore unnecessary.

Fig. 3. Effect of post-curing UV exposure time on elastic-wave velocity (a) and on the calculated values of Young’s modulus and shear modulus (b)

Storage time was also found to have no effect on internal polymerization of the material under room conditions in a dark place. The velocities of longitudinal and shear waves remained unchanged after 14 days of storage (see Fig. 3).

3.2. Anisotropy

Specimen anisotropy was evaluated in the axial and radial directions, that is, parallel and perpendicular to the printed layers, respectively (Fig. 4). These directions are sufficient for analysis because layered materials exhibit the greatest differences in mechanical properties along them [25]. Ultrasonic measurements showed that wave velocities measured across and along the layers were identical within experimental error. The identical Young’s and shear moduli (see Fig. 3) indicate a high degree of isotropy in the elastic properties of the 3D-LCD specimens, as determined by nondestructive testing.

Fig. 4. Measurement of elastic-wave velocity in the axial (a) and radial (b) directions

Nondestructive testing is effective for assessing the stability of replica properties during storage and in long-term test programs, as well as for evaluating the effect of ambient curing on the material. Ultrasonic methods are useful as an auxiliary tool for the indirect assessment of elastic properties; however, they do not provide information about the actual behavior of the material under loading up to failure. Another limitation of these methods is that elastic-wave velocity depends on density and on the presence of heterogeneities and voids, including artificially created cracks and pores. In addition, such methods are applicable only to undamaged specimens of regular shape.

Importantly, specimens produced by 3D-LCD printing do not exhibit initial anisotropy. This ensures clarity in the interpretation of results, high reproducibility of the experimental data, and the possibility of fine adjustment of test parameters.

3.3. Uniaxial compression test results

The uniaxial compression tests showed that the highest strength was exhibited by specimens with layers oriented at 60° to the loading vector, with an average compressive strength of 158 MPa (maximum 162 MPa, minimum 156 MPa). The lowest strength was observed in specimens with a layer inclination of 30°, for which the average value was 138 MPa, with a maximum of 140 MPa and a minimum of 120 MPa (Fig. 5). Specimens with layers oriented parallel (0°) and perpendicular (90°) to the loading direction showed similar strength values, averaging 146 and 147 MPa, respectively.

Fig. 5. Stress–strain curves and cumulative AE signal plots for specimens with layer inclinations of 0° (a), 30° (b), 60° (c), and 90° (d). The light blue line represents stress, and the dark blue line represents the cumulative number of AE signals. The quasi-elastic deformation zone is highlighted in blue

The tests yielded stress–strain curves and cumulative AE signal plots (see Fig. 5). The stress–strain curves indicate elasto-viscoplastic behavior of the specimens. Under loading up to 20 MPa, all specimens exhibited a quasi-elastic deformation zone, highlighted in blue in Fig. 5, in which stress varied linearly with strain. In this zone, no AE signals exceeding the 40 dB filter threshold were recorded, indicating either a very low level of internal damage or its complete absence.

This quasi-elastic deformation zone is of the greatest engineering interest because structural elements retain their mechanical properties within the elastic range. Young’s modulus values for specimens with different layer orientations were determined from the slope of the stress–strain curve in this region. The stress–strain relationships in the quasi-elastic zone are described by the following equations:

σ₀ = 4272.2ε_α + 0.5489;                                          (1)

σ₃₀ = 4060.8ε_α + 0.4588;                                        (2)

 σ₆₀ = 3892.7ε_α + 0.5892;                                        (3)

σ₉₀ = 4006.8ε_α + 0.4912,                                         (4)

where σ is stress, MPa (the subscript corresponds to the angle between the layers and the loading vector), and ε_α is axial strain.

The coefficients on the right-hand side of the equations correspond to Young’s modulus values and range from 3893 MPa for specimens with a layer inclination of 60° to 4272 MPa for specimens with layers parallel to the loading direction. These values indicate a fairly high degree of uniformity in elastic properties at stresses up to 20 MPa.

The highest Young’s modulus was recorded for specimens with layers parallel to the loading vector, whereas the lowest was found for specimens with a layer inclination of 60°. Overall, Young’s modulus tended to decrease as the layer orientation increased relative to the specimen axis (Eqs. (1)–(4)). At the same time, the modulus of specimens with layers perpendicular to the load (90°) was comparable to that of specimens with a layer inclination of 30°.

Specimens with layer orientations of 0° and 30° combined relatively low strength with a high Young’s modulus in the quasi-elastic deformation zone, indicating greater stiffness but relatively brittle failure. By contrast, specimens with a layer inclination of 60°, although exhibiting the highest strength, showed the lowest Young’s modulus values and therefore lower stiffness. This mismatch between strength and elastic modulus suggests that different failure mechanisms operate depending on layer orientation.

A comparative analysis of the AE data and uniaxial compression results (see Fig. 5) showed that, despite the similar overall shape of the stress–strain curves, the failure mechanisms differed among specimens with different layer inclinations relative to the loading vector. Combined analysis of the AE signals and compression curves makes it possible to determine with high accuracy the deformation stage reached by a specimen at a given load level. The comparison further showed that the duration of each deformation stage depended on the layer inclination relative to the loading vector. For example, the longest elasto-viscoplastic stage was observed in specimens with layers perpendicular to the load (Fig. 5, d), whereas the shortest occurred in specimens with a layer inclination of 30° to the loading axis (Fig. 5, b). Thus, the combined analysis of AE and uniaxial compression data showed that geomechanical studies must take into account the fact that the failure mechanisms of rock-specimen replicas printed by the 3D-LCD method vary with layer orientation.

3.4. Uniaxial compression of rocks

The results of the uniaxial compression tests on the natural rocks are presented in Fig. 6 as stress–strain curves.

Fig. 6. Stress–strain curves and cumulative AE count plots for natural rock specimens: silicites cut perpendicular to bedding (a); silicites cut parallel to bedding (b); silicified dolomites (c); opoka (d). The light blue line represents stress, and the dark blue line represents cumulative AE counts. The red line indicates the linear elastic or quasi-elastic segment used to calculate Young’s modulus

All natural rock specimens exhibited a compaction zone at the initial stage of loading, in which stress increased nonlinearly with strain (see Fig. 6). This zone is associated with the presence of relaxation microcracks oriented perpendicular to the principal stress and, as a rule, parallel to bedding. Closure of such cracks under loading occurs without failure, as confirmed by the absence of acoustic emission activity. As the microcracks close, the material becomes denser and stiffer, which is reflected in an increasing slope of the stress–strain curve.

Because of the nonuniform stress distribution, some microcracks remain unclosed, and new ones may also form. Once the strain reaches 0.001, stress redistribution causes a sharp increase in AE activity. Further loading promotes closure of both relaxation microcracks and newly formed microcracks, so that the specimen becomes nearly fully compacted and then enters a linear deformation stage.

In all specimens, the linear segment of the stress–strain curve is characterized by a linear increase in stress with strain and by the absence, or low intensity, of AE activity. The lowest AE intensity was observed in silicite specimens drilled perpendicular to bedding (Fig. 6, a). In silicite specimens with the bedding plane parallel to the loading vector, as well as in opoka, AE activity remained relatively high despite the linearity of the stress–strain curve in this region (Fig. 6, b, d).

The tangents to the stress–strain curves in the linear elastic or quasi-elastic segment are described by the following equations:

σ₁ = 6775.7ε_α – 5.64;                                              (5)

σ₂ = 6144.5ε_α – 0.85;                                              (6)

σ₃ = 14609.0ε_α – 34.70;                                          (7)

σ₄ = 2480.3ε_α – 0.95.                                              (8)

The subscript corresponds to the specimen group. The coefficients on the right-hand side of the equations represent the Young’s moduli of the specimens.

Beyond the elastic or quasi-elastic segment, the intensity of microcracking increased, as reflected in a marked rise in cumulative AE counts. In specimens shown in Fig. 6, a, c, and d, this stage was accompanied by hardening, as indicated by the increasing slope of the stress–strain curve. In contrast, in silicite specimens drilled parallel to bedding, microcracking led to degradation of the mechanical properties, as indicated by the descending branch of the curve (Fig. 6, b). After the strength limit was exceeded, all specimens failed.

The highest uniaxial compressive strength was observed in specimens drilled perpendicular to bedding, namely 117 MPa for silicites and 186 MPa for silicified dolomites. The lowest strength was recorded in specimens drilled parallel to bedding, namely 86 MPa for silicites and 51 MPa for opoka. Specimens with bedding perpendicular to the load also exhibited the greatest total strains (see Fig. 6a, c), which is attributable to the orientation of relaxation cracks perpendicular to the loading vector.

4. Discussion

Effect of 3D-LCD printing features and layer orientation on anisotropy. Because the LCD-based 3D-printing method is inherently layer-by-layer, it results in a layered internal structure in the finished parts. Such a structure may give rise to anisotropy in the properties of the printed specimens depending on layer angle and orientation. However, the present study showed that these features do not affect the uniformity of the elastic properties measured by nondestructive methods or under uniaxial compression in the stress range up to 20 MPa. Anisotropy associated with layer angle and orientation becomes apparent only above this threshold.

Comparison of rocks and replicas. Despite differences in layer angle and orientation, the rock replicas exhibit relative uniformity, as evidenced by the similar shape of their stress–strain curves. In natural rocks, by contrast, anisotropy is controlled by bedding and has a pronounced effect on mechanical behavior under loading.

To assess whether the replicas could be used as analogs of natural rocks, materials spanning a broad strength range were selected, namely homogeneous high-strength rocks (silicites and silicified dolomites) and weak opoka. The test results showed that even rocks with a high degree of structural uniformity exhibit pronounced anisotropy in their mechanical properties.

Comparative analysis of the stress–strain curves showed that the Young’s moduli of the replicas are lower than those of silicified dolomites and silicites, but higher than that of opoka. At the same time, the elastic deformation range of the replicas coincides with the elastic deformation range of the natural rocks (Fig. 7). Thus, the replicas may be regarded as analogs of natural rocks, but only within the stress range that does not exceed the elastic limit.

Fig. 7. Stress–strain curves for rocks (blue line) and replicas (red line). The shaded area indicates the elastic deformation zone of the rocks. The black line is tangent to the stress–strain curves of the replicas

At stresses above 40 MPa, microdamage begins to develop in the replicas, and, because of their structural features, the stress–strain curves start to diverge. The greater strains observed in the replicas compared with the natural rocks are attributable to the predominance of cohesive bonding and the very low level of internal friction. Because internal friction is essentially absent, the layers slide relative to one another without substantial resistance. This behavior is related to the polymeric nature of the resin, which contains no solid particles.

Nevertheless, the replicas exhibit uniaxial compressive strength values comparable to those of natural rocks and, in some cases, even higher. Depending on layer inclination, the compressive strength of the replicas ranges from 138 to 162 MPa, whereas that of the natural rocks ranges from 51 to 186 MPa. At the same time, the replicas accumulate substantial strain before failure, reaching values of up to 0.37, and the specimens assume a barrel-shaped form (Fig. 8, b). In natural rocks, strain remains barely noticeable even after failure (Fig. 8, d, e) and does not exceed 0.015.

Fig. 8. Photographs of specimens under load: replica and natural rock specimen before loading (a, d); replica before failure (b); failed replica and rock specimen (c, e)

Fig. 9. Micrographs of specimen fracture surfaces: a – replica; b – silicite

Fig. 10. Natural rock specimens after uniaxial compression testing. Specimens drilled perpendicular (a, c) and parallel (b, d) to bedding

Micrographs of the fracture surfaces (Fig. 9) show that the replica has a smooth fracture surface, indicating that nothing impedes interlayer sliding or the propagation of microcracks. The fine-grained structure of the natural rocks, by contrast, provides high cohesion and substantial internal friction because of their granular texture. This impedes smooth crack propagation, so the fracture surfaces of the rocks are irregular and rough (Fig. 9, b).

The failure pattern of the natural rock specimens does not show a pronounced dependence on bedding angle, unlike that of the replicas. Silicites drilled perpendicular and parallel to bedding exhibit a similar type of failure characterized by extensive fragmentation and longitudinal macrocracks propagating toward the specimen ends (Fig. 10, a, b). Despite differences in strength and bedding angle, silicified dolomites and opoka (Fig. 10, c, d) both exhibit high brittleness, as reflected in pronounced fragmentation. The abundance of cracks at the specimen ends indicates that brittle failure predominates over ductile deformation.

In replicas with a layer orientation of 0°, numerous cracks are also observed at the specimen ends; however, unlike those in natural rocks, these cracks result from delamination and are characteristic only of this specimen group. In replicas with layer inclinations of 60° and 90°, in which prolonged hardening stages were previously observed, no longitudinal brittle cracks were found at the specimen ends, confirming that failure in these specimens is predominantly ductile.

5. Practical applications

The results of this study have high practical potential and can be directly used in laboratory geomechanical testing in the mining, oil and gas, and construction industries. The findings confirm that 3D-LCD printing technology enables the cost-effective batch production of rock replicas with reproducible physical and mechanical properties. This makes it possible to replace scarce core material and substantially reduce the costs associated with field drilling, transportation, and storage of expensive specimens.

The use of 3D rock replicas improves the efficiency of experimental studies by eliminating the costly and time-consuming procedures involved in sampling and preparing natural specimens. The economic benefit is achieved through reduced testing costs and shorter testing times, as well as through the possibility of repeatedly reproducing identical specimens for parallel experiments.

Practical implementation of the proposed approach makes it possible to create physical models of rock masses for assessing excavation stability, calculating drilling parameters, predicting fracture development, and evaluating the filtration properties of reservoir rocks. In addition, the results may be used in the development of digital testbeds and in the verification of numerical geomechanical models. Thus, the use of 3D-LCD rock replicas helps reduce experimental costs, improve the accuracy of engineering predictions, and accelerate the design stage in the mining and oil and gas industries.

3D-LCD printing technology can be effectively used not only for fabricating rock specimen replicas but also for laboratory-scale physical modeling of various mining objects, including the assessment of the stability of mine workings and underground structures, the calculation of the load-bearing capacity of supports and pillars, and the optimization of their shape and arrangement. This opens up new opportunities for the rapid and cost-effective evaluation of design solutions in mining and construction.

Conclusion

The results of the experimental study confirmed the applicability of 3D-LCD printing for producing rock replicas suitable for physical modeling of geomechanical behavior under elastic loading. The aim of the study was achieved, and all the stated objectives were fully accomplished.

The study showed that the optimal post-curing time for the photopolymer material is 4 min, which ensures complete polymerization without further changes in mechanical properties. The resulting specimens were shown to exhibit isotropy of elastic properties: differences in the propagation velocities of longitudinal and transverse waves in the axial and radial directions did not exceed the measurement error. For the printed replicas, Young’s modulus determined from nondestructive testing and uniaxial compression tests falls within the range of 3.89–4.27 GPa, which is comparable to the corresponding values for natural silicites and silicified dolomites.

The effect of printed-layer orientation on specimen strength was established experimentally: the highest strength was recorded at an angle of 60° (average 158 MPa), whereas the lowest was observed at 30° (138 MPa). The mechanical tests were accompanied by acoustic emission monitoring, which made it possible to identify differences in failure mechanisms as a function of layer orientation.

Comparison with the results obtained for natural rocks revealed similar patterns of deformation behavior under elastic loading, confirming the suitability of 3D-LCD replicas for modeling geomechanical processes. The scientific novelty of the study lies in the quantitative determination of the relationships between elastic modulus, compressive strength, and layer orientation angle, as well as in the experimental confirmation of the isotropy and stability of the elastic properties of photopolymer replicas. These findings expand the scope of 3D-LCD printing in geotechnical research and demonstrate its high reproducibility and cost-effectiveness.