Experimental study of uniaxial compressive mechanical properties of rough jointed rock masses based on 3D printing

2.1 Serrated joint surface

To ensure the consistency of structural planes and reduce the complexity, regular serrated joint was selected to conduct basic study on mechanical characteristics of grouted jointed rock masses with gypsum simulating serrated joint and cement mortar simulating rock. In line with the fractal theory of Xie [4], joint roughness coefficient (JRC) can be determined by the following equations:

where D is the fractal dimension of serrated joint surface. H and L are the average height and base length of the serrated joint surface, respectively.

To investigate the influence of inclination and roughness on static compressive properties and failure mode of jointed rock, JRC varies from 0 to 20 with an increment of 5 at inclination angle of 0°, 30°, 45°, 60°, and 90°. Figure 1 illustrates the schematic diagram of serrated joint surface.

Figure 1

Schematic diagram of serrated joint surface.

Figure 2

Serrated joint surface. (a) 3D model and (b) 3D serrated joint surface mold.

3D molds with serrated joint surface were carried out as follows:

1. Create a 3D model of serrated joint surface in STL format in line with the parameters calculated from the above equations by Geomagic Design X software, as shown in Figure 2(a).

2. Import the 3D model in STL format into CHITUBOX software for slicing processing, and get the constructed 3D model in STB format file which can be directly 3D printed.

3. Input the constructed 3D model into 3D printing apparatus, then print the 3D serrated joint surface mold, as shown in Figure 2(b).

2.2 Jointed specimen preparation

Experimental study on natural rock has some limitations. Physical and mechanical parameters of natural rock may be varied due to the various internal defects which results in inconsistency of parallel test results. Moreover, rough joints are difficult to process in natural rock. Hence, cement mortar is adopted to simulate the natural rock, and cement mortar specimens can be casted into designed joint shapes.

Based on relevant literature [27,28,29] and orthogonal test, five mix proportions were considered, which were cement:water:fine sand = 1:0.4:0.6; 1:0.4:0.7; 1:0.4:1.1; 1:0.3:0.7; and 1:0.5:0.7. 42.5 grade ordinary Portland cement was selected, and the particle size of fine sand was no bigger than 0.6 mm. Uniaxial compression tests were performed for cylindrical specimens with 50 mm in diameter and 100 mm in height by a DNS-300 microcomputer-controlled electronic universal tester. To alleviate the discreteness of uniaxial compressive test, three parallel specimens were considered for each mix proportion. The stress–strain curves for five mix proportions were obtained and shown in Figure 3. All stress–strain curves underwent initial compaction, linear elastic, plastic deformation, and failure stages. The compressive strength and deformation modulus were measured. After comprehensive consideration, the compressive strength, directly related to the bearing capacity in practice, was finally selected as the key performance index. Therefore, the mix proportion of 1:0.4:0.7 with the highest compressive strength was selected as the final mix proportion. As shown in Figure 4, the cement mortar material under this mix proportion exhibited a failure mode similar to brittle sandstone.

Figure 3

Stress–strain curves for various mix proportions.

Figure 4

Failure mode for 1:0.4:0.7 mix proportion.

Table 1 gives the physical and mechanical properties of cement mortar for 1:0.4:0.7 mix proportion [9]. f is the uniaxial compressive strength (UCS), ρ is the density, E is the elastic modulus, and μ is the Poisson’s ratio.

The manufacture process of serrated joint cement mortar specimens is described as follows:

1. Load the 3D serrated joint surface mold in a cylindrical mold tightly and apply the oil on serrated joint surface and its inner wall.

2. Put the weighed fine sand and cement into a mixer to mix, then load the water and keep mixing for 4 min.

3. Load fresh mixture into cylinder mold and vibrate for 1.5 min.

4. Take off the cylinder mold after 24 h curing, and the half jointed specimens with different JRCs are displayed in Figure 5(a).

5. Combine two half jointed specimens with gypsum after 28 days curing, and the serrated joint specimens are illustrated in Figure 5(b).

Figure 5

Serrated joint specimens. (a) Half serrated joint specimen and (b) serrated joint specimen after bonding.

The diameter and height of cylindrical jointed cement mortar specimens were 50 and 100 mm, respectively, and the thickness of filled serrated joints was 1 mm. To ensure the consistency of joint thickness, the size of cylindrical jointed specimen should be controlled when making the half jointed specimens. During the bonding process, first put the lower half jointed specimen into the cylindrical mold, then apply the prepared gypsum evenly on the serrated joint surface, finally load the upper half jointed specimen into the cylindrical mold and make the top surface flat with the mold. Polish the ends of jointed specimens before test to make the non-parallelism less than 0.02 mm.

2.3 Test equipment and experimental procedure

Uniaxial compression test was conducted by a DNS-300 microcomputer-controlled electronic universal tester, as shown in Figure 6(a). The maximum loading capacity is 300 kN and the precision of both force sensor and displacement sensor is ±0.5%. As illustrated in Figure 6(b), cylindrical jointed specimen was put vertically on the test bench. During the uniaxial compression test, first apply a preloading force of 0.1 kN to cylindrical jointed specimen, then set the loading control method to displacement control at a loading rate of 0.10 mm/min. To alleviate the discreteness of test results, three parallel specimens were considered for each condition, and mean value of three parallel specimens were used for subsequent analyses. The data were analyzed by Origin software.

Figure 6

DNS-300 universal tester. (a) Testing machine and (b) layout of specimen.

3.1 Stress–strain curve

Under the condition of conventional uniaxial compression, stress–strain curves for various JRCs under different inclination angles are shown in Figure 7a–e. Rough jointed specimens undergoes four stages from compression to failure: microcrack compaction, elastic deformation, yield, and failure. The stress–strain curves of rough joint specimens display a significant difference for various JRC values. With the increase in JRC, the microcrack compaction stage is obviously postponed and becomes more apparent. Table 2 summarizes the peak stress and peak strain of serrated joint specimens for various JRCs under different inclination angles. The peak stress is the UCS.

Figure 7

Stress–strain curves for various JRCs under different inclination angles: (a) JRC = 0; (b) JRC = 5; (c) JRC = 10; (d) JRC = 15; and (e) JRC = 20.

As seen from Figure 7 and Table 2, when the inclination angle equals 0° or 90°, the peak stress and strain of jointed specimen are not sensitive to the change in JRC. When the inclination angle varies from 30° to 60°, the peak stress and peak strain of jointed specimen increase with the increase in the JRC, and the effect of joint roughness is obvious. This is mainly because the failure mode of jointed specimen at 0° and 90° is mainly splitting failure, while the failure mode at 30°–60° is mainly shear slip failure, which is more likely to cause shear deformation of joint surface at this angle. The roughness of serrated joints at this angle can enhance the resistance ability to shear deformation, and this ability increases with the increase in the roughness of serrated joints. In addition, the specimens at this angle will have different degrees of stress reduction before the peak stress, and this phenomenon is most obvious when JRC is 10. This is mainly because when the JRC is low, the serrated anastomosis of joint surface is low, resulting in the shear stress of joint surface first reaching the peak shear strength under axial pressure, and shear slip failure occurs. With the increase in the JRC, the coincidence degree of joint surface serration increases. When the specimen does not reach the peak compressive strength and the joint surface serration has reached the peak shear strength, the joint surface serration shears off, and the load continues to be borne by undamaged serration parts. With the further increase in JRC value, the shear resistance of joint serration is further enhanced, and greater axial pressure is required to destroy, which is reflected in the increase in peak stress and strain at stress drop point or in the joint serration. Before reaching the peak shear strength, the specimen has been destroyed, so that there is no longer a peak stress drop point.

3.2 Deformation characteristics

The stress–strain curve is approximately a straight line in the elastic deformation stage, and the slope of this straight line is taken as the deformation modulus E _β of rough jointed specimen. The variation in deformation modulus at various JRCs with inclination angle is given in Figure 8. As seen from Figure 8, the curve of E _β and β is approximately U-shape, showing obvious deformation anisotropy. When β is 60°, E _β reaches the minimum value, which indicates that the deformation modulus decreases with the inclination angle varying from 0° to 60°. When β is 60° to 90°, E _β increases rapidly with the inclination angle. Under the same inclination angle, the larger the JRC value, the larger the deformation modulus of rough jointed specimen. There is also a special phenomenon that the deformation modulus decreases slightly with the increase in the JRC, for example, when β is 30°. This may be related to the homogeneity of rock-like material and the error of specimen preparation process. The maximum deformation modulus is obtained at β = 90°, but it is still less than that of a complete specimen. Therefore, under the same stress conditions, rough joints have a weakening effect on the resistance to deformation, and the degree of weakening is related to the inclination and roughness of serrated joints.

Figure 8

Variation in deformation modulus with the inclination angle.

The trend of peak strain relative to the inclination angle is depicted in Figure 9. At a constant JRC, peak strain first gradually decreases when β ranges from 0° to 60°, then gradually increases when β is between 60° and 90°. Generally, the maximum peak strain exists at β of 0°, while the minimum exists at β of 60°. During loading, jointed specimen with an inclination angle of 60° fails first and exhibits the smallest peak strain.

Figure 9

Variation in peak strain with the inclination angle.

When the inclination angle β equals 0° or 90°, the JRC has little effect on the peak strain. When β ranges from 30° to 60°, the peak strain increases with JRC value. Hence, the peak strain of rough jointed specimen demonstrates varying sensitivity to the joint inclination angle. The sensitivity first decreases then increases with the increase in the inclination angle. Deformation modulus shows a similar variation.

3.3 Effect of joint parameters on wave velocity

The production, number, and filling of joint surfaces affect the longitudinal wave velocity of jointed rock masses [30,31]. When JRC is 0, average wave velocities and its loss rates for five inclination angles are illustrated in Figure 10. Wave velocity loss rate is the ratio of the difference between average wave velocity of jointed specimen and complete specimen to that of complete specimen. The average wave velocity of complete specimen is 4,033 m/s.

Figure 10

Variation in average wave velocity with the inclination angle when JRC is 0.

As seen from Figure 10, with the increase in the angle between joint surface and longitudinal wave propagation direction, average wave velocity increases gradually, and wave velocity loss rate decreases gradually. When JRC is 0, the average wave velocity for inclination angle of 0°, 30°, 45°, 60°, and 90° is 3,415, 3,478, 3,543, 3,666, and 3,839 m/s, respectively. The wave velocity loss rate is 15.3, 13.8, 12.1, 9.1, and 4.8%, respectively. According to the theoretical analysis, the particle vibration velocity of joint surface is related to the stiffness of joint surface [32,33]. The larger the stiffness, the larger the particle velocity. As the inclination angle increases, the wave path becomes more inclined with respect to the joint surface. The inclination increases the stiffness in the wave propagation direction. Hence, the joint inclination angle significantly affects the longitudinal wave velocity.

In addition to the inclination angle, the JRC also affects the longitudinal wave velocity. When the inclination angle β equals 0°, average wave velocities and its loss rates for five JRCs are illustrated in Figure 11.

Figure 11

Variation in average wave velocity with JRC when inclination angle is 0°.

As illustrated in Figure 11, with the increase in JRC, average wave velocity decreases gradually, and wave velocity loss rate increases gradually. The average wave velocity for JRC of 0, 5, 10, 15, and 20 is 3,415, 3,393, 3,380, 3,348, and 3,313 m/s, respectively. The wave velocity loss rate is 15.3, 15.9, 16.2, 17.0, and 17.9%, respectively. Average wave velocity of jointed rock is the largest at JRC of 0. The rougher the serrated joint surface, the more the scattering of elastic wave, the less the elastic wave transmitting through joints [34,35]. Rough joints display a great influence on the transmission coefficient of elastic waves.

3.4 Effect of joint roughness on compressive strength

To research the effect of roughness on mechanical characteristics of jointed rock masses, a dimensionless normalized compressive strength σ _cr is adopted to directly show the influence degree of roughness and is defined as the ratio of UCS of serrated joint specimen to that of complete specimen.

where σ _cr is the normalized compressive strength, and σ _β and σ _i are the UCS of serrated joint specimen with inclination angle β and complete specimen, respectively.

When the inclination angle β equals 30°, the normalized compressive strength for five JRCs are given in Figure 12.

Figure 12

Variation in normalized compressive strength with JRC at an inclination of 30°.

As seen from Figure 12, the normalized compressive strength for JRC of 0, 5, 10, 15, and 20, is 0.34, 0.44, 0.58, 0.75, and 0.83, respectively. The normalized compressive strength for JRC of 5, 10, 15, and 20 is about 129.41, 170.59, 220.59, and 244.12% of that for JRC of 0, respectively. Generally, the smaller the normalized compressive strength σ _cr, the greater the weakening effect of rough joints on the UCS. When JRC ranges from 0 to 15, the joint roughness strengthens the UCS of jointed rock masses. But when JRC is greater than 15, the strengthening ability of joint roughness for UCS of jointed rock masses begins to weaken. Hence, under the same joint inclination angle, rough joints have a strengthening effect on the resistance ability to the vertical load, and the degree of strengthening is related to the joint roughness.

3.5 Strength anisotropy

To further reveal the strength anisotropic characteristics of rough jointed specimens, a three-dimensional surface relationship between UCS, joint inclination, and JRC is drawn in Figure 13.

Figure 13

Relationship between UCS, inclination, and JRC.

As shown in Figure 13, the variation in UCS with joint inclination is approximately a U-shaped curve and shows obvious strength anisotropy characteristics. JRC affects the UCS of jointed rock under the same joint inclination angle. The UCS of jointed specimens increases significantly with the JRC. Average UCS of jointed specimens with a 60° inclination angle is 1.08, 2.68, 4.7, 6.55, and 13.93 MPa at JRCs of 0, 5, 10, 15, and 20, respectively, which is 96.2, 90.6, 83.5, 77.1, and 51.2% lower than that of complete specimen, respectively. When the JRC is the same, the UCS decreases nonlinearly with the inclination angle increasing from 0° to 60°. When the inclination angle β ranges from 60° to 90°, the UCS shows an overall growth trend. Hence, UCS of jointed specimens is the lowest at the inclination angle β of 60°. When the inclination angle β equals 0° or 90°, the joint inclination is perpendicular or parallel to the loading direction, the UCS of jointed specimens is close to that of complete specimen, which indicates that the shear capacity is not greatly weakened and the joint roughness has little effect on UCS.

The level of anisotropy for UCS of rocks can be evaluated quantitatively by a dimensionless anisotropy ratio to reveal the influence of inclination on the anisotropy of rough jointed rock masses [36,37,38]. The dimensionless anisotropy ratio A _σ is defined as the ratio of maximum UCS to minimum UCS of serrated joint specimens for various inclination angles at the same JRC.

where σ β max and σ β min represent the maximum UCS and minimum UCS of serrated joint specimens for various inclination angles at the same JRC, respectively.

The calculated anisotropy ratios of rough jointed specimen for various JRCs are shown in Table 3. Table 4 gives the classification of anisotropy ratio [39].

As seen from Tables 3 and 4, the anisotropy ratio A _σ of rough jointed specimens is 24.62 at JRC of 0, which belongs to very high anisotropy. With the increase in JRC, the anisotropy ratio of rough jointed specimens decreases. The larger the JRC, the smaller the influence of inclination angle on the UCS of jointed specimens. Therefore, JRC weakened the strength anisotropy of rough jointed specimens induced by joint inclination angle.

In line with the literature [36], the UCS of jointed rock can be predicted by the following equation:

where σ r ( β ) is the UCS of jointed specimen with an inclination angle β, and β m is the joint inclination angle when the UCS is the smallest, namely β _m is 60°, in this study. A and D are the constants.

In the analysis process, the UCS can be replaced by the dimensionless normalized compressive strength, then equation (5) can be expressed as follows:

where σ cr ( β ) is the normalized compressive strength of jointed specimen with inclination angle β, and A ′ and D ′ are constants.

Both A' and D' can be determined using the UCS at an inclination angle of 0°, 60°, and 90°. When the JRC is 10, the equations for predicting the normalized compressive strength are obtained as follows:

Figure 14 shows a comparison of prediction curve and test values of normalized compressive strength of rough jointed specimens. For inclination angle β ranging from 0° to 60°, the deviation between the prediction curve and the actual test values is relatively large, and the prediction curve underestimates the UCS of rough jointed specimens. Furthermore, for inclination angle β ranging from 60° to 90°, the predictions agree with the actual test values. In essence, rough joints are essentially different from the original schistosity or cleavage formed inside the rock mass. Hence, using equation (6) to predict the normalized compressive strength of rough jointed rock masses will produce specific errors, especially when the inclination angle β is small. The prediction of UCS of rough jointed rock mass needs further systematic research.

Figure 14

Comparison of prediction curve and test values of normalized compressive strength of rough jointed rock mass.

3.6 Failure mode

The failure modes of serrated joint specimens for various JRCs at joint inclination of 45° are shown in Figure 15. Figure 16 gives the failure modes of serrated joint specimens for various inclination angles at JRC of 10.

Figure 15

Failure mode of serrated joint specimens for various JRCs when β is 45°: (a) JRC = 0; (b) JRC = 5; (c) JRC = 10; (d) JRC = 15; and (e) JRC = 20.

Figure 16

Failure mode of serrated joint specimens for various inclination angles when JRC is 10: (a) β = 0°; (b) β = 30°; (c) β = 45°; (d) β = 60°; and (e) β = 90°.

As seen from Figures 15 and 16, the fragmentation of the column and the splitting or slipping of joint surface cause the final failure of serrated joint specimen. Failure modes vary with the inclination angle and JRC. There are three typical failure modes of serrated joint specimens.

1. Splitting tensile failure. As shown in Figure 15(e), the JRC is large, the shear resistance of rough joint surface is strong, and splitting failure parallel to axial force direction causes the failure of jointed specimen. As shown in Figure 16(a) and (e), no matter how the JRC value changes, the failure of rough joint specimen is dominated by the splitting failure parallel to axial force direction, accompanied by obvious lateral expansion.

2. Shear slip failure. As shown in Figure 15(a), the shear strength of smooth joint surface is low, and the slip along the smooth joint surface leads to the failure of jointed specimen, and both sides of slip surface are relatively complete. As shown in Figure 15(b) and (c), the slight increase in JRC, namely, 5, cannot prevent the relative dislocation along the joint surface. As illustrated in Figure 16(d), the shear performance at this angle is the lowest, resulting in relative dislocation of rough joint surface.

3. Compound splitting tensile and shear failure. As shown in Figure 15(c) and (d), the failure mode of the jointed specimen changes from shear failure to compound splitting tensile and shear failure due to the increase in the roughness of joint surface. As shown in Figure 16(b) and (c), the failure surface is partly through the complete model material and partly along the joint surface as a result of combined action of tensile failure and shear failure.

4.1 Effect of joint roughness on failure mode

To study the influence of rough joints in rock masses on failure mode, serrated joint specimens at inclination angle of 45° are taken as an example (as shown in Figure 15) to analyze the crack propagation process after loading. Failure modes of jointed specimens at JRC values of 5 and 10 are roughly the same. Serrated joint specimens mainly undergo shear failure along the joint surface. With the increase in compressive stress, obvious shear slip surface gradually forms in the specimens, and a few tensile cracks appear at the edge of the specimens. When JRC is 10, the specimen begins to break along the area with larger roughness and gradually expands along the axial stress loading direction, and some fragments fall off at the top. When JRC is 15 and 20, the fracture degree increases, and the longitudinal cracks increase.

As shown in Figure 16, when the JRC is 10, the failure degree of jointed specimen decreases first and then increases with the increase in the inclination angle. When the joint inclination angle is 0°, the splitting failure occurs in the axial direction of cylindrical specimen to produce multiple cracks. The distribution of tensile cracks in the specimen is not uniform, and the crack density on both sides is more significant than that in the middle. When the joint inclination angle is between 30° and 60°, the joint surface has some roughness, the shear strength is moderate, and the final fracture form changes from compound splitting tensile and shear failure to shear slip failure. When the joint inclination angle is 90°, the direction of the external force is almost parallel to the rough surface of the joint of the sample. The jointed specimen undergoes a tensile splitting failure, and the main crack runs through the bottom and top.

According to Figures 15 and 16, the failure mode of serrated joint specimen is dominated by the inclination and JRC, and the degree of failure increases with the JRC. As the roughness can effectively restrain the shear slip of rock mass around the joint surface, the overall bearing capacity of jointed rock is improved.

4.2 Application of joint characteristics in engineering

Rock masses are closely associated with many engineering projects, and mechanical properties of rock masses significantly impact the successful execution of these projects. Roughness and inclination of rock joints influence the stability, construction expenses, and risk evaluation of engineering projects. Unreasonable handling of rock joints in underground mining and tunnel construction could result in rock collapses and failures of support structures.

This study may unveil the intimate link between joint roughness, inclination angle, and excavation stability. To mitigate engineering risks, engineers can employ these findings to formulate precise excavation plans for varying joint characteristics. Jointed rock exhibits distinct characteristics, which necessitates specific support materials and construction approaches. With this discovery in mind, engineers can select suitable materials according to the specific conditions of jointed rock. Moreover, the construction efficiency can be improved by optimizing the construction process. Coupled with research findings, engineers can identify potential rock stability issues more precisely by considering joint roughness and inclination angle, thereby implementing commensurate risk management strategies to diminish the occurrence of project-related accidents and ensure both personnel safety and project advancement.

While this study has yielded valuable insights, certain aspects remain ripe for deeper investigation, for instance, investigating the impact of distinct joint characteristics on the mechanical response to dynamic loads, or employing artificial intelligence to predict rock joint features. These forthcoming studies will deepen the comprehensive understanding of rock engineering behavior.