Shape characteristics and deformation properties of granite crushed stone during compression

Abstract

The shape of particles plays a significant role in determining the mechanical properties of granular materials. This study systematically investigated the effects of particle shape on the crushing behaviors of granite crushed stone using a 3D particle measurement system, image processing techniques, and lateral restraint compression tests. The results indicate that the particle shape parameters, such as sphericity and flat index, vary with particle size, and the stress-strain curves during compression follow an exponential function. Tetrahedral particles exhibited the highest deformation under identical stress conditions, while hexahedral particles demonstrated the lowest deformation. Field tests conducted in the − 1465 m belt roadway chamber of the Sha-ling Gold Mine validated the theoretical model. The field tests were crucial in verifying the reliability of the theoretical analysis.

Introduction

Rock fragments are common encountered in geotechnical engineering, particularly in contexts such as slopes from large-scale excavations, underground mine goaf areas, and fault breccia zones. The control of deformation in fractured surrounding rock in tunnels, surface subsidence in goaf areas, and backfilling efforts in these regions are all closely linked to the deformation characteristics of the fractured rock mass. Following underground excavation, the stress in the surrounding rock continuously readjusts, leading to the progressive compression of the fractured rock mass under overburden pressure. Particle crushing has a direct impact on gradation, which subsequently affects the overall strength, deformation, and permeability characteristics of the materials^1,2. Since fractured rock mass usually exists in a loose form, conducting in-situ field tests poses significant challenges. Consequently, researchers often resort to laboratory tests and numerical simulations to study how factors like crushed stone strength, particle size, grading, and loading methods affect deformation characteristics during compression.

Experimental results indicate that the stress-strain relationship during the compression of fractured rock mass follows an exponential function^3,4,5,6,7. Under identical loading conditions, higher crushed stone strength corresponds to smaller strain. During the initial loading stage, smaller-sized crushed stones exhibit a higher strain growth rate, while larger-sized crushed stones demonstrate a lower rate. However, as the load increases, the strain growth rate for larger-sized crushed stones eventually surpasses that of smaller-sized ones^3,4. Under cyclic loading and unloading, the stress-strain relationship of the fractured rock mass remains exponential, but the final strain value is greater than that observed under continuous loading⁵. For fractured rock mass of the same lithology but different particle sizes, the final strain value increases with the grading index^7,8. Lei et al.⁹ numerically simulated the compression characteristics of fractured rock mass based on laboratory tests, providing a robust description of the compression behavior evident in experiments. In addition, Zhu et al.¹⁰ proposed a method to construct a three-dimensional model of fractured rock masses using discrete element software. Moreover, Zhang et al.^11,12 analyzed the effects of particle size on the compression characteristics of fractured rock mass through discrete element methods, highlighting changes in porosity and stress during compression. Furthermore, Wang et al.¹³ conducted triaxial shear numerical tests on monodisperse and binary particle systems using the FDEM method. In terms study, Liang et al.¹⁴ established a numerical model of halite particles using the discrete element method to investigate the influences of particle microstructure on macroscopic mechanical properties and failure processes. Hu et al.¹⁵ simulated the settling process of granular sand using a coupled CFD-DEM framework. The deformation properties of granite crushed stone during compression are affected by several factors, such as particle size distribution, moisture content, and compression energy. Researchers demonstrate that achieving optimal compression enhances load-bearing capacity and minimizes settlement.

While progress has been made in studying the deformation characteristics during the compression of fractured rock mass, most studies are focused on the effects of crushed stone strength, particle size, grading, and loading methods. However, fractured rock mass consists of particles of various shapes, and the shape of crushed stones also impacts their mechanical properties¹⁶. The peak strength increases with the sphericity of the crushed stones, while the ultimate stress ratio decreases as sphericity increases¹⁷. The more complex the shape of the crushed stones, the greater the interlocking effect, resulting in increased shear strength^18,19. Chang et al.²⁰ noted that as the aspect ratio of particles rises, both peak and residual strengths increase significantly, along with a gradual increase in the axial strain corresponding to peak strength. Kodicherla et al.²¹ investigated the strength and fabric anisotropy of granular materials on the deviatoric stress and volumetric strains, and the anisotropy of granular materials under true triaxial configurations. They proposed a quantitative relationship between shape parameters and mechanical responses. An investigation by Cai et al.²² quantitatively characterized the shapes of recycled brick (RB), recycled concrete (RC), and recycled mortar (RM) particles, along with an analysis of crushing modes, fractal attributes, strength, and energy, supplemented by a comparative study using the discrete element method (DEM). In their study, Fan et al.²³ applied the Discrete Element Method (DEM) to simulate the shearing process of polyhedral particles, elucidating how factors such as the elongation indices (EI), flatness indices (FI), angularity indices (AI), and roughness (G) independently affect the mechanical responses at both macro and micro levels. Furthermore, Das et al.²⁴ introduced a rate-dependent model for predicting the strain rate-dependent particle crushing and dilation features that affect the critical state of granular materials. Li et al.²⁵ explored the compression and mechanical properties of recycled concrete aggregate and recycled brick aggregate, focusing particularly on the impact of particle fragmentation and shape characteristics on these properties. They conducted triaxial shear tests to examine the effects of particle shape, degree of compression, and confining pressure on shear characteristics.

Despite these advancements, it is still essential to have a thorough understanding of how shape characteristics and the deformation properties of granite crushed stone interact during the compression process. Therefore, this study aims to characterize the shape of granite crushed stones using a particle shape parameter measurement system and conduct compression tests to explore how the shape of crushed stones influences deformation characteristics during compression. Ultimately, this research seeks to elucidate the deformation mechanisms of broken surrounding rock and offer insights into deformation control in tunnels and surface subsidence management in goaf areas.

Characterization of granite crushed stones shape

Experimental materials

The granite crushed stones used in this study were sourced from the − 1465 m belt roadway chamber of the Sha-ling Gold Mine after blasting. The mineral composition of the granite mainly consists of feldspar, quartz, and mica. Prior to the experiment, the granite crushed stones were manually crushed, thoroughly cleaned, and air-dried. The crushed stones were then sieved using square-hole sieves and categorize into four different particle size groups: 5–10 mm, 10–15 mm, 15–20 mm, and 20–25 mm. Figure 1 illustrates the sieved granite crushed stones for each particle size group.

Fig. 1

Size groups of granite crushed stone.

The shapes of crushed stone fragments vary widely. Li et al.²⁶ categorized the fragments produced from blasting into five types: tetrahedron, pentahedron, hexahedron, flaky and elongated particles, and irregular polyhedron. According to the aggregate testing procedures for highway engineering²⁷, irregular polyhedrons are defined as crushed stones with more than six polygonal faces, while flaky and elongated particles are those with a length-to-width ratio greater than 3. To explore the impact of particle shape on the strength and deformation of rockfill materials, Yang et al.¹⁶ created three types of cement blocks: regular triangular prisms, cubes, and cylinders. Currently, there is no standardized method for classifying the shapes of crushed stones. Using the classification methods for blasting-generated crushed stone shapes, a manual count was performed to categorize granite crushed stones of the same particle size group, which were fractured manually, into four types: tetrahedron, pentahedron, hexahedron, and irregular polyhedron. For each size group (5–10, 10–15, 15–20 and 20–25 mm), the shape is classified as tetrahedron, pentahedron, hexahedron or irregular polyhedron. Fig. 2 displays physical images of different-shaped granite crushed stones in the 15–20 mm size range after sieving.

Fig. 2

Photographs of 15–20 mm granite crushed stones.

The classification results of crushed stones were analyzed to assess the quantities of tetrahedrons, pentahedrons, hexahedrons, and irregular polyhedrons. This analysis facilitated the measurement of shape and the evaluation of compression characteristics for granite crushed stones of various forms. The statistical findings are presented in (Table 1), which offers a clear overview of the relationship between particle shape and size. Table 1 outlines the quantities of tetrahedron, pentahedron, hexahedron, and irregular polyhedron crushed stones in various particle size groups used for the test. In the 5–10 mm and 10–15 mm size groups, the quantities of tetrahedron, pentahedron, hexahedron, and irregular polyhedron crushed stones are all 30 each. For the 15–20 mm size group, there are 32 pieces of tetrahedron, pentahedron, hexahedron, and irregular polyhedron crushed stones. However, in the 20–25 mm particle size group, only 12 tetrahedron crushed stones are counted, while the number of pentahedron crushed stones is estimated at 36. The limited number of tetrahedral crushed stones in the 20–25 mm size group is due to their reduced quantity after crushing; most of the crushed stones in this size group consists of pentahedron shapes. As a result of the limited raw materials available, only 12 pieces of tetrahedron crushed stones were counted.

Table 1 Number of granites crushed stones in each size group.

Measurement of shape parameters of granite crushed stones

The shape of crushed stones is primarily quantified using two-dimensional (2D) and three-dimensional (3D) parameters. Sun et al.²⁸ introduced a multi-level characterization method for the two-dimensional cross-sections of irregular voids, employing the Fourier transform to effectively describe their shapes. Zhang et al.²⁹ utilized an image-measuring instrument along with a custom-designed fixture to assess the shape of crushed stones. Through image processing software and programming, shape parameters of particles were extracted^30,31. Zhang et al.³² characterized the shape features of concrete aggregates and advocated for the use of angularity and surface texture indices to describe the shapes of these aggregates. Xi et al.³³ focused on the characterization and classification of the roundness and sphericity of crushed stones through the analysis of 2.5D point clouds. Another widely employed method for obtaining particle shape parameters is three-dimensional laser scanning technology^34,35. Zou et al. highlighted that relying on 2D parameters for describing the shape of crushed stones leads to an underestimation of particle sphericity when compared to 3D parameters³⁴. As a result, this study adopts 3D parameters to quantify the shape of crushed stones, emphasizing three key parameters: flat index, sphericity, and form factor.

$${\text{Flat index: }}\; F=L/S$$

(1)

$${\text{Sphericity: }}\; \alpha =\sqrt[3]{{IS/{L^2}}}$$

(2)

$${\text{Form factor: }}\; K=S/\sqrt {L \times I}$$

(3)

In the equations, L, I, and S represent the dimensions corresponding to the long axis, intermediate axis, and short axis of the crushed stones, respectively.

Flat index (F) serves as a thorough descriptor of the elongation and flattening of crushed stone particle shapes. Sphericity (α) measures how closely a particle resembles a spherical form; as the lengths of the three axes become more similar, the sphericity increases, indicating a more spherical particle. The form factor (K) assesses the regularity of the crushed stone particle’s shape; a larger form factor signifies a more uniform particle shape.

To determine the three-dimensional dimensions of crushed stones exhibiting four distinct shapes and particle sizes, a particle shape parameter measurement system³⁶ was utilized to assess the shape parameters of granite crushed stones. The steps for measuring the shape of crushed stone are illustrated in Fig. 3. The standardized procedure for assessing gravel morphology comprises four essential phases. Initially, specimens are thoroughly cleaned and desiccated to remove any surface contaminants. Next, each gravel particle is securely mounted onto a specialized photogrammetric apparatus. A high-resolution digital camera then captures systematic orthogonal projections through multi-angle image acquisition. These images are subsequently analyzed using Image-Pro Plus imaging software to extract quantitative morphological parameters. The custom-built measurement system consists of five key components, namely a dual-panel imaging platform, a 90° right-angle fixture, a fixed camera mount, a high-definition camera, and a scale reference object. The 90° right-angle fixture ensures that panels A and B remain orthogonal throughout the measurement process. The procedure for measurement is outlined as follows:

• (1) Secure panels A and B together using the 90° right-angle fixture.

• (2) Affix the classified crushed stones to panel B using double-sided tape, and capture an overhead photograph of the crushed stones with the camera.

• (3) Rotate panel B 90° to align it with panel A while maintaining the camera’s position, and take a second photograph of the crushed stones.

• (4) Import both photographs into Image Pro Plus 6.0 to calculate the shape parameters of the crushed stones with varying shapes.

Fig. 3

Crushed stones particle shape parameter measurement system.

Distribution patterns of granite crushed stones shape characteristics

Distribution patterns of tetrahedron crushed stones

The distribution patterns of F, α, and K for tetrahedron crushed stones across various particle size groups are illustrated in Fig. 4. As shown in (Fig. 4a), the tetrahedron crushed stones have the lowest median and mean flatness values for the 5–10 mm size group. More specifically, the median and mean F values for the 10–15 mm size group are the highest, indicating that the stones in this range exhibit more elongated and flattened shapes.

From Fig. 4b, it is evident that the median and mean α values of tetrahedron crushed stones remain relatively consistent across different particle sizes, ranging from 0.65 to 0.75. Notably, the 15–20 mm particle size group displays the largest interquartile range for α, suggesting that the differences between the long, intermediate, and short axes of the crushed stones in this size range are minimal, making them closer to a spherical shape.

As depicted in Fig. 4c, the median and mean K values for tetrahedron crushed stones are fairly uniform across the various particle sizes, falling within the range of 0.38 to 0.72. The 5–10 mm particle size group registers the highest median and mean K values, whereas the 10–15 mm group reflects the lowest values. This trend indicates that the regularity of shape is greatest for tetrahedron crushed stones in the 5–10 mm size range and least for those in the 10–15 mm range.

Fig. 4

Distribution of tetrahedron crushed stones particle shapes.

Distribution patterns of pentahedron crushed stones

The distribution patterns of F, α, and K for pentahedron crushed stones across various particle size groups are illustrated in Fig. 5. As depicted in Fig. 5a, the F of pentahedron crushed stones exhibits a trend of initial increase followed by a subsequent decrease with respect to increasing particle size groups. Notably, the median, mean, and interquartile range of F for the 10–15 mm particle size group are significantly higher than those of the other groups, suggesting that pentahedron crushed stones within this size range are characterized by more elongated and flattened geometries.

In Fig. 5b, a discernible trend in the α of pentahedron crushed stones is observable, showing a general decrease followed by an increase as particle size groups increase. The median and mean α values for the 5–10 mm particle size group surpass those of the remaining groups, indicating that the dimensional discrepancies among the long, intermediate, and short axes of crushed stones in this size range are minimal, rendering these particles closest to a spherical form. Conversely, the α values for the 10–15 mm particle size group are markedly lower than those of the other categories, indicating substantial disparities among the three axes and, consequently, a pronounced deviation from α.

Furthermore, as illustrated in Fig. 5c, the K value of pentahedron crushed stones reveals a trend of decrease followed by an increase across the particle size groups. The median and mean K values for the 20–25 mm particle size group exhibit the highest levels among the analyzed groups, signifying the greatest shape regularity for pentahedron crushed stones within this size range. In contrast, the K values for the 10–15 mm particle size group are the lowest, indicating a diminished level of shape regularity within this specific particle size range.

Fig. 5

Distribution of pentahedron crushed stones particle shapes.

Distribution patterns of hexahedron crushed stones

The distribution patterns of F, α, and K factors for hexahedron crushed stones across various particle size groups are illustrated in Fig. 6. As indicated in Fig. 5a, the median and mean F values of hexahedron crushed stones remain relatively consistent among different particle sizes, hovering around 1.75. Notably, the 10–15 mm particle size group exhibits the highest median and mean F, suggesting that crushed stones within this size range tend to exhibit more elongated and flattened shapes.

From Fig. 5b, it is evident that the median and mean α values of hexahedron crushed stones are also closely aligned across the particle size groups, with values around 0.78. The 10–15 mm particle size group stands out with the highest median, mean, and interquartile range in terms of α, indicating that the disparities between the long, intermediate, and short axes of the crushed stones in this size range are minimal, rendering these particles closest to a spherical shape.

As demonstrated in Fig. 5c, the K value of hexahedron crushed stones generally shows a decreasing trend followed by an increase as particle size groups increase. The median and mean K values for the 20–25 mm particle size group are higher than those of the other three groups, suggesting the highest degree of shape regularity for hexahedron crushed stones within this range. In contrast, the median and mean K values for the 10–15 mm particle size group are lower than those of the other groups, indicating the lowest level of shape regularity in this size range.

Fig. 6

Distribution of hexahedron crushed stones particle shapes.

Distribution patterns of irregular polyhedron crushed stones

The distribution patterns of F, α, and K for irregular polyhedron crushed stones across various particle size groups are illustrated in Fig. 7. As shown in Fig. 7a, the F value of these crushed stones tends to increase initially and then decrease with larger particle size groups. Notably, the median, mean, and interquartile range of F for the 15–20 mm particle size group are significantly greater than those of the other groups, suggesting that stones within this size range exhibit more elongated and flattened shapes.

In Fig. 7b, it is evident that the α of the irregular polyhedron crushed stones generally rises with increasing particle size groups. The median and mean α values for the 15–20 mm size group surpass those of the other three groups, indicating that the differences between the long, intermediate, and short axes of the crushed stones in this range are the smallest. Therefore, these particles are closest to having a spherical shape among the irregular polyhedron crushed stones.

As depicted in Fig. 7c, the K value of irregular polyhedron crushed stones typically decreases and then increases with larger particle sizes. The median and mean K values for the 20–25 mm particle size group are higher than those of the other groups, implying that these stones exhibit the highest degree of shape regularity. Conversely, the median and mean K values for the 15–20 mm particle size group are lower than those of the other groups, indicating that they have the lowest shape regularity in this size range.

Fig. 7

Distribution of irregular polyhedron crushed stones particle shapes.

Compression tests of granite crushed stones

Experimental apparatus

Given that crushed stones naturally exist in a loose state, they were placed inside a cylindrical container to facilitate the compression process. During compression, the crushed stones are compressed axially and the crushed stones receive lateral confinement from the cylinder walls. To ensure the accuracy of the compression tests, it is essential that the cylinder does not deform laterally; thus, it must possess adequate stiffness and sufficient wall thickness.

The compression apparatus was constructed from 45# steel that underwent a quenching treatment, which imparts high strength and exceptional resistance to deformation. This apparatus has a Poisson’s ratio of 0.3 and a Young’s modulus of 190 GPa. The cylinder features an inner diameter of 80 mm, a wall thickness of 13 mm, and a height of 140 mm. A depiction of the compression apparatus is provided in Fig. 8.

Fig. 8

Photograph of the compression device.

Compression test procedure

The loading device utilized for the compression test of granite crushed stones was a hydraulic universal testing machine with a maximum capacity of 300 KN, which adequately meets the requirements for this test. The compression test system is illustrated in Fig. 9. During the test, the loading was regulated by applying a force at a rate of 80 N/s. Loading was ceased once the force reached 80 KN, which corresponds to a stress level of 28 MPa based on the cross-sectional area of the cylinder, to simulate the stress-strain characteristics of granite crushed stones under an in-situ stress of 28 MPa. The axial compression displacement of the crushed stones was measured using a displacement sensor.

Fig. 9

Compression test system.

Stress-strain relationship during compression

The axial stress during the compression test of crushed stone can be expressed as:

$$\sigma =P/A$$

(4)

where P is the axial pressure acting on the crushed stones, and A is the inner circular area of the cylinder.

The axial strain during the compression test of crushed stone can be expressed as:

$$\varepsilon =\Delta h/h$$

(5)

where Δh is the compression of the sample, and h is the initial height of the sample.

To account for size effects during the tests, it is generally required that the diameter of the compression apparatus be greater than five times the maximum particle size of the crushed stones. In this study, the compression apparatus had an inner diameter of 80 mm, which led to the selection of the 5–10 mm, 10–15 mm, and 15–20 mm particle size groups for testing the compression of different shapes of crushed stones.

Figure 10 illustrates the stress-strain curves for tetrahedron, pentahedron, hexahedron, and irregular polyhedron granite crushed stones during compression for the various particle sizes. As demonstrated in Fig. 10, the strain behavior of different shapes of granite crushed stones during compression varies under continuous loading conditions. For instance, at a stress level of 28 MPa, the strain values for the 5–10 mm particle size group were 0.44 for tetrahedron crushed stones, 0.38 for pentahedron crushed stones, 0.40 for hexahedron crushed stones, and 0.44 for irregular polyhedron crushed stones.

The strain of granite crushed stones during compression is affected by both particle size and shape; however, the strain patterns tend to be generally consistent. The stress-strain curve for granite crushed stones can be categorized into three distinct stages: an approximate linear growth in strain, followed by a rapid growth, and finally, a slow growth strain phase. This deformation behavior aligns with the characteristics observed during the compression of fractured rock found in coal seam roofs^4,6.

Initially, during the loading process, the contact points between crushed stones are predominantly characterized as “point-to-point” or “point-to-line,” with numerous “primary” voids existing between the particles. In this early loading phase, the compression of these voids plays a dominant role, leading to a rapid increase in deformation. As the load intensifies, finer particles created from the crushing of larger ones begin to fill the voids, thereby reducing their size. Concurrently, as compression increases, the contact between particles transitions from “point-to-point” or “point-to-line” to “face-to-face” or “interlocking contact,” enhances the crushed stones’ resistance to deformation. As a result, the increase in strain during the later stages of loading is diminished.

Fig. 10

Stress-strain curves of compacted crushed stones with different shapes and size groups.

Influence of crushed stones shape on the Stress-Strain relationship during compression

To examine the impact of crushed stone shape on the stress-strain relationship during compression, we analyzed the compression stress-strain curves of various crushed stone shapes within the 5–10 mm and 10–15 mm particle size groups. Figure 11 displays the compression stress-strain curves for these crushed stones.

In Fig. 11a, for the 5–10 mm particle size group, tetrahedron crushed stones demonstrated the greatest strain under identical pressure, followed by irregular polyhedron crushed stones. Both pentahedron and hexahedron crushed stones exhibited the least strain, with their stress-strain curves being nearly identical. The analysis indicates that during the initial phase of the compression test, crushed stones make contact in a point to surface manner. Since the pentahedron and hexahedron gravel particles differ by only one planar face, the difference in stress-strain curves between the two during the compression process is minimal.

For the 10–15 mm particle size group, as illustrated in (Fig. 11b), tetrahedron crushed stones continued to show the highest strain. During the initial loading stage, the stress-strain curves for pentahedron, hexahedron, and irregular polyhedron crushed stones were similar. However, once the loading pressure exceeded 12 MPa, the strain of hexahedron crushed stones increased notably, followed closely by pentahedron crushed stones, while irregular polyhedron crushed stones exhibited the least strain.

For the 15–20 mm particle size group, as illustrated in (Fig. 11c), the stress-strain curves of tetrahedron and pentahedron crushed stones exhibit similar growth trends, while the growth trends of hexahedron and irregular polyhedron crushed stones are identical. During loading, the rate of strain growth in hexahedron and irregular polyhedron crushed stones surpasses that of tetrahedron and pentahedron.

Fig. 11

Influence of crushed stones shape on compression stress-strain curves.

Influence of crushed stones shape on the parameters of the Stress-Strain curve

As illustrated in Fig. 10, the relationship between stress and strain during the compression of granite crushed stones with various shapes and particle sizes, including tetrahedron, pentahedron, hexahedron, and irregular polyhedron, can be characterized by an exponential function. The stress- strain relationship for each particle size group corresponding to these shapes can be represented as:

$$\sigma =\theta {e^{\gamma u}}$$

(6)

Where $\theta$ and $\gamma$ are parameters related to the shape, particle size, and gradation of the crushed stones. These parameters can be obtained through curve fitting of the compression test results.

To assess the influence of crushed stone morphology on the parameters of the stress- strain curve, we performed trendline regression analyses on the stress-strain curves of granite crushed stones characterized by varying shapes and particle sizes. The results of this investigation are synthesized in (Table 2).

Table 2 Stress-strain relationships during compression of crushed stones with different shapes.

As indicated in Table 2, the parameters θ and γ in the regression equations for various shapes and particle sizes of crushed stones demonstrate distinct differences. To examine the impact of crushed stone shape on the stress-strain relationship during compression, parameters derived from the regression equations in Table 2 were plotted in Fig. 12.

Figure 12a illustrates the effect of crushed stone shape on the parameter θ in the stress-strain curve. The θ values for tetrahedral crushed stones range from 0.16 to 0.18, with an average of 0.17. For pentahedral crushed stones, θ values range from 0.33 to 0.39, averaging at 0.36. In contrast, the θ values for hexahedral and irregular polyhedron crushed stones exhibit greater variability, with the average θ value for hexahedral crushed stones at 0.48 and that for irregular polyhedron crushed stones at 0.33. Among the examined shapes, hexahedral crushed stones display the highest θ value, followed by pentahedral stones, while tetrahedral stones have the lowest.

Figure 12b presents the influence of crushed stone shape on the parameter γ. The average γ values for various crushed stone shapes are as follows: 11.22 for tetrahedral crushed stones, 11.43 for pentahedral crushed stones, 10.85 for hexahedral crushed stones, and 11.62 for irregular polyhedron crushed stones. These average γ values for tetrahedral, pentahedral, hexahedral, and irregular polyhedron crushed stones are relatively close, ranging from 10.85 to 11.62, suggesting that the differences in γ values among the differing shapes are minimal.

Fig. 12

Influence of crushed stones shape on parameters of stress-strain curves.

Field tests on the deformation patterns of broken surrounding rock

Background of the test

The location of the broken rock at the − 1465 m belt roadway chamber is indicated in Fig. 13. The distance from the broken rock to the bottom plate of the chamber is approximately 1 m. The total design length of the belt roadway chamber is 15 m, with construction progressing in increments of 3 m at a time. Once the construction of the belt roadway chamber is completed, excavation will continue along the shaft, with a progress rate of 4 m for each session. At the Sha-ling Gold Mine, the broken surrounding rock in the arch waist of the − 1465 m belt roadway chamber extends approximately 6.8 m in length, with thickness varying between 0.8 and 1.1 m. This surrounding rock dips toward the west-east direction at angles ranging from 5° to 28°. The lithology of the broken zone consists of granite, exhibiting colors that range from grayish-white to light flesh-red. The broken surrounding rock is classified as Grade IV, characterized by well-developed joints and fractures, a shattered structure, and a blocky fabric, which contributes to its low rock strength.

Fig. 13

Location of the broken rock at −1465 m belt roadway chamber.

Test plan

To enable real-time monitoring of stress and strain within the broken surrounding rock of a large-section excavation, a monitoring system was developed specifically for assessing the stress and strain of the broken rock mass. This system comprises monitoring steel bars, vibrating wire strain gauges, pressure cells, a multi-channel data acquisition device, along with data processing and analysis equipment.

Three monitoring points were strategically placed along the dip direction of the broken surrounding rock, with an approximate interval of 2 m between each point. Considering the thickness of the broken rock mass, which ranges from 0.8 to 1.1 m, two surface strain gauges were welded onto each steel bar, and the average reading from these two gauges was used to represent the strain value at that monitoring point. The ends of the steel bars, which houses the welded strain gauges, were anchored into the intact surrounding rock using anchoring agents and expansion bolts. Additionally, surface strain gauges were installed adjacent to the pressure cells. The layout of the pressure cells and surface strain gauges for the broken rock mass, located at -1465 m in Sha-ling Gold Mine, is illustrated in Fig. 14.

Fig. 14

Layout of pressure cells and surface strain gauges in the broken surrounding rock.

Analysis of test results

Stress variation patterns in broken surrounding rock

The variations in stress within the broken surrounding rock are illustrated in Fig. 15. As depicted in Fig. 15, tensile stress was recorded at monitoring points 1 and 3, while compressive stress was noted at monitoring point 2. Although both points 1 and 3 showed tensile stress, the magnitudes of stress at these two locations differed significantly. The broken surrounding rock in the study area is characterized by considerable heterogeneity and discontinuity, largely due to the presence of joints. The joints distribution is shown in Fig. 16.

The stress levels experienced by the surrounding rock at all three monitoring points were relatively low, ranging from approximately 0.004 to 0.014 MPa. However, as excavation of the chamber progressed, the stress in the broken surrounding rock steadily increased. By the 70th day of monitoring, the tensile stress at point 1 had escalated to 0.19 MPa, the compressive stress at point 2 had risen to 0.45 MPa, and the tensile stress at point 3 had reached 0.28 MPa.

Following the excavation of the surrounding rock, the stress continuously adjusted and was gradually released. After the excavation of the chamber, the broken rock is subjected to a biaxial stress state. As excavation continues, the section being dug transitions from a triaxial stress state to a biaxial stress state, leading to a release of stress. During this adjustment and release of stress, the pressure within the broken zone continued to rise.

Fig. 15

Stress variations broken surrounding rock.

Fig. 16

The joints distribution of broken rock.

Strain variation patterns in broken surrounding rock

The variations in strain observed in the broken surrounding rock are illustrated in Fig. 17. As depicted, the strain at monitoring points 1, 2, and 3 initially increased at a slow rate before accelerating. Notably, the strain at point 1 began to rise sharply on the 11th day of monitoring, while points 2 and 3 experienced a rapid increase starting on the 21st day. Throughout the entire monitoring period, the strain at all three points continued to escalate.

At point 2, the surrounding rock exhibited compressive strain, with the maximum compressive strain reaching 1380 µε during the monitoring period. In contrast, points 1 and 3 experienced tensile strain, albeit with differing trends. The tensile strain at point 1 consistently increased but remained relatively low, peaking at 800 µε. Conversely, point 3 displayed a more dynamic fluctuation in tensile strain, achieving a maximum value of 1400 µε.

These findings indicate that the strain behavior in the broken surrounding rock is influenced by local stress conditions and the heterogeneity of the rock mass, resulting in varied strain responses at each monitoring point.

Fig. 17

Strain variations in the broken surrounding rock.

Conclusions from the stress and strain monitoring results of broken surrounding rock at Sha-ling Gold Mine (-1465 m). The monitoring results of stress and strain in the broken surrounding rock at -1465 m in Sha-ling Gold Mine are summarized as follows:

Monitoring points 1 and 3: The broken surrounding rock at these points is under tensile stress, and the corresponding strain is tensile. This suggests that the broken rock mass at points 1 and 3 is primarily undergoing horizontal movement.

Monitoring point 2: The surrounding rock at this point exhibits compressive strain, indicating that it is subjected to vertical compression from the overlying rock mass. The presence of crushed rock and clay beneath point 2 further confirms the vertical compressive movement due to the overlying rock mass.

These observations underscore that the broken surrounding rock in deep excavations displays considerable heterogeneity and discontinuity. Following the excavation, the processes of stress adjustment and release result in both shear and compressive movements within the broken rock mass. The stress-strain variation patterns observed at monitoring point 1 are illustrated in Fig. 18.

Fig. 18

Stress-strain curve of surrounding rock at monitoring point 1.

As illustrated in Fig. 16, the initial strain of the broken surrounding rock is minimal, accompanied by a low strain growth rate. As the stress adjusts, the strain of the surrounding rock progressively increases, leading to a corresponding rise in the strain growth rate. The stress-strain relationship of the broken surrounding rock at monitoring point 1 can be described by an exponential function. The stress-strain relationships at monitoring points 2 and 3 align with those at point 1 and will not be reiterated here. Therefore, the stress-strain relationship for the broken surrounding rock at monitoring point 1 can be expressed as:

$$\sigma =0.001{e^{0.0065\varepsilon }}$$

(7)

where σ is the stress of the broken surrounding rock, and$\varepsilon$is the strain of the broken surrounding rock.

In Sect. 2.3, the regression equations for the stress-strain curves of crushed stones of varying shapes and particle sizes were derived. By averaging the coefficients from these regression equations, the relationship between pressure and strain during the compression of crushed stone can be articulated as follows:

$$\sigma =0.34{e^{11.28u}}$$

(8)

From Eqs. (7) and (8), it can be seen that the pressure-strain curve of the broken surrounding rock after shaft excavation and the pressure-strain curve of compacted crushed stone are both exponential functions.

Discussion

The shape parameters and the mechanical behavior of crushed stone significantly impact tunnel reinforcement in deep mining environments. The exponential relationship between the stress-strain curve of grains crushed stone and their morphology indicates that selecting granular materials for shotcrete or pouring should prioritize uniformity in inclination and shape to enhance bearing capacity. For instance, hexahedron particles demonstrate minimal deformation under compression, making them ideal for strategic incorporation into support systems in high-stress areas, such as the 1465 m strip road chamber analyzed in this study. This approach can help reduce long-term settlement and improve structural integrity.

On the other hand, the higher deformation sensitivity of tetrahedron particles emphasizes the necessity for local reinforcement strategies in areas with irregularly shaped aggregates. Such strategies may include the use of denser mesh liners or hybrid support systems that combine rigid and flexible elements to address shape-induced instability.

Additionally, the size-dependent changes in sphericity and flat indices of crushed stone particles underscore the importance of optimizing both particle size and shape in backfill mixtures. This supports the use of engineered fillers with controlled particle geometry to enhance long-term ground stability in deep mines. These insights can refine empirical design specifications by incorporating quantitative shape indicators into mechanical performance standards.

Conclusions

The key findings presented in this paper can be outlined as follows:

• (1) The shape of crushed granite stones is characterized by measurement systems and image processing technology, and the distribution laws of α, F, and K of gravel in different particle size groups of tetrahedrons, pentahedrons, hexahedrons, and irregular polyhedrons are obtained. The α, F, and K of granite crushed stones exhibit variations based on particle size and shape.

• (2) The stress-strain curves of crushed granite stones with various shapes during compression can be described by an exponential function and are divided into three distinct stages, namely rapid strain, slow strain, and stable strain. Among these, tetrahedron-shaped crushed stones demonstrate the highest level of strain under the same stress conditions.

• (3) The impact of crushed stone shape on the parameters of the compression stress-strain function is summarized as follows: The θ value is highest for hexahedron-shaped crushed stones, followed by pentahedron-shaped stones, and the lowest θ value is observed in tetrahedron-shaped stones.

• (4) On-site monitoring of broken rock has revealed that the stress-strain curves of broken rock are exponential functions. Understanding the characteristics of broken rock and conducting compression tests are crucial for guiding engineering practices.