Influence of Structural Plane Microscopic Parameters on Direct Shear Strength

Structural plane is a key factor in controlling the stability of rock mass engineering. To study the influence of structural plane microscopic parameters on direct shear strength, this paper established the direct shear mechanical model of the structural plane by using the discrete element code PFC2D. From the mesoscopic perspective, the research on the direct shear test for structural plane has been conducted. (e bonding strength and friction coefficient of the structural plane are investigated, and the effect of mesoscopic parameters on the shear mechanical behavior of the structural plane has been analyzed. (e results show that the internal friction angle φ of the structural plane decreases with the increase of particle contact stiffness ratio. However, the change range of cohesion is small. (e internal friction angle decreases first and then increases with the increase of parallel bond stiffness ratio. (e influence of particle contact modulus EC on cohesion c is relatively small. (e internal friction angle obtained by the direct shear test is larger than that obtained by the triaxial compression test. Parallel bond elastic modulus has a stronger impact on friction angle φ than that on cohesion c. Under the same normal stress conditions, the shear strength of the specimens increases with particle size. (e shear strength of the specimen gradually decreases with the increase of the particle size ratio.


Introduction
e large-scale existence of structural plane has severely damaged the continuity and integrity of rock mass, thereby exerting a profound influence on the strength of the rock mass.Structural plane is a key factor in controlling the stability of rock mass engineering [1][2][3][4][5].e destruction and damage of jointed rock mass is mainly along the structural plane.us, studies on the shear strength, failure mode, and shear damage of a structural plane are significant.Many scholars have conducted relevant research [6][7][8][9][10][11][12].Yang et al. [13] study the relationship between the 3D morphological characteristics and the peak shear strength through several tilt tests.Fardin et al. [14] carried out investigations to understand the effect of scale on the surface roughness of rock joints.Park and Song [15] have numerically simulated rock joints and performed an extensive series of the direct shear tests using the code PFC3D.PFC3D represents that the interaction of circular particles by the distinct element method (DEM) can simulate joint movement.Achieving the specified JRC value for real rock samples and considering the homogeneity of rocks are difficult because the shear test for the same roughness cannot be investigated under different conditions of laboratory tests [16][17][18].In recent years, the application of discrete element numerical methods in geotechnical engineering has become extensive, and scholars have used this method to investigate the mechanical properties of joints [19][20][21][22][23][24][25].Farahmand et al. [26] used a synthetic rock mass (SRM), model coupling discrete fracture networks (DFNs), and a discrete element grainbased model (DEM) to characterize the mechanical properties of moderately jointed rock masses under confined and unconfined conditions.Shang et al. [27] present a numerical investigation of the effects of boundary conditions on the failure mechanism of incipient rock discontinuities in direct shear.In this paper, the direct shear mechanical model of the structural plane is established by using the discrete element code PFC2D.From the mesoscopic perspective, the research on the direct shear test for structural plane has been conducted.e bonding strength and friction coefficient of the structural plane are investigated, and the e ect of mesoscopic parameters on the shear mechanical behavior of the structural plane has been analyzed.

Modeling
Numerical simulation of the shear strength test is divided into two categories, namely, nonlimit and restrictive shear strength tests.e nonlimit shear strength test only has shear stress on the shear surface without the existence of normal stress.e restricted shear strength test has normal stress in addition to the shear stress on the shear plane [28][29][30][31].In this paper, the restrictive shear strength test is adopted to apply a speci c normal stress on the sample, and the normal stress is set as 2.5, 5.0, 7.5, 10.0, 12.5, and 15 MPa.e size of the direct shear test is 100 mm × 100 mm, and the speed boundary condition is applied to the upper part of the model.Results show that the internal friction angle φ 20.30 °and cohesion c 9.29 MPa.

Particle Contact Sti ness Ratio.
e impact of particle contact sti ness ratio k n /k s on shear strength is shown in Table 1.e internal friction angle φ of the structural plane decreases with the increase of particle contact sti ness ratio k n /k s .However, the change range of cohesion is small, indicating that particle contact sti ness ratio k n /k s has less e ect on the cohesion.e e ect of particle contact sti ness ratio on the internal friction angle is shown in Figure 1.
e normal sti ness of particles increased gradually with the particle contact sti ness ratio of k n /k s .In the conventional triaxial compression simulation test, shear failure is the specimen failure mode, and the internal friction angle in the shear strength parameter is approximately the same as that obtained in the direct shear simulation test.However, in the direct shear simulation experiment, the particle contact sti ness ratio of k n /k s 1.45 and k n /k s 0.5, and the size di erences between internal friction angle is extremely small, indicating if the normal sti ness is close to the tangential sti ness, then the friction angle will decrease.In the direct shear test, when the particle contact sti ness ratio increases gradually, the internal friction angle of the structure increases gradually.When the particle contact sti ness ratio of k n /k s 2.0, the internal friction angle reaches the peak of the specimens, which is φ 24.56 °.For particle contact sti ness ratio k n /k s 1.0, the internal friction angle is also relatively large at φ 24.28 °.  e internal friction angle of the specimen can be increased when the contact between particles is equal to the tangential sti ness.If the normal sti ness of the particle is greater than the tangential sti ness, then the di erence between the normal and tangential sti ness is less, and the internal friction angle is less than the internal friction angle when the particle method is equal to the tangential sti ness.When the normal sti ness is twice the tangential sti ness, the internal friction angle is maximized.Particle contact sti ness ratio k n /k s increases to a certain value.
e particles during normal sti ness are larger than those during tangential sti ness.A small internal friction angle can enhance shear strength.However, the general trend means that the internal friction angle of the specimens decreases with the increase of the particle contact sti ness ratio.e in uence of particle contact sti ness ratio on cohesion is analyzed, as shown in Figure 2. e cohesion c of the specimen is less than that of the conventional triaxial compression simulation test under the same k n /k s .Under the two test conditions, the cohesion of the specimen has the same change trend as that of k n /k s , and the in uence of k n /k s on adhesion c is relatively small.

Parallel Bond Sti ness Ratio.
Parallel bond sti ness ratio is a speci c parameter in the simulation of parallel bonding model, which represents the ratio of the normal sti ness to the tangential sti ness between two particles.e shear strength parameter values of di erent parallel bond sti ness ratios are recorded, as shown in Table 2. e internal friction angle uctuates with the increase of parallel bond sti ness ratio k n /k s .When the particle parallel bond sti ness ratio is   Advances in Civil Engineering k n /k s 2, the result of the internal friction angle is less than k n /k s 0.5 because the model is a parallel bond model, which is in accordance with the shear failure model.Moreover, the particle cementing material between normal sti ness is large.e internal friction angle decreases rst and then increases with the increase of parallel bond sti ness ratio k n /k s .e reason is that the di erence between normal sti ness and tangential sti ness is increasing, that is, the increase of di erence decreases the stability and strength of the specimen.erefore, the internal friction angle is reduced appropriately, but not the cohesion.e internal friction angle increases with the parallel bond sti ness ratio.
e reason is that the increase of the sti ness ratio of the parallel bond causes the rigid contact between particles.Furthermore, the overall "rigidity" of the experimental model increases, and its macrodamage gradually becomes tensile failure.c max 9.29 MPa is reached when the cohesion c of the direct shear test model is at the parallel bond sti ness ratio of k n /k s 1.45.When k n /k s < 1.45, the cohesion of the specimen increases and then decreases with k n /k s .e in uence of parallel bond sti ness on internal friction angle is analyzed, as shown in Figure 3.In the conventional triaxial compression test, the internal friction angle increases with the ratio of parallel bond sti ness.In the direct shear test, the internal friction angle decreases with the increase of parallel bond sti ness ratio between particles, and its variation range is approximately 21%.k n /k s 6, the internal friction angle of the conventional triaxial compression simulating test is φ 29.22 °, and internal friction angle in the direct shear test is φ 18.83 °.When k n /k s > 3, the internal friction angle of the specimen decreases gradually in the direct shear test.e in uence of parallel bond sti ness on cohesion is analyzed, as shown in Figure 4.In the same parallel bond sti ness ratio, the cohesion obtained by the direct shear test is less than that of the conventional triaxial test but with a slight di erence.
e change trend of cohesion in the specimen is similar in both test conditions, that is, cohesion increases with k n /k s  Advances in Civil Engineering and reaches maximum and then decreases gradually at k n /k s 2.

Particle Contact Modulus (EC)
. EC is the Young's modulus between particles, and the shear strength parameter values under di erent particle contact moduli are recorded, as shown in Table 3.In the direct shear test, internal friction angle and cohesion change due to the change of EC and the large variation amplitude.e internal friction angle is increasing gradually.When EC 2.8 GPa, the internal friction angle of the specimens suddenly decreased to φ 20.30 °, and cohesion reached the maximum value of c 9.29 MPa.Although the internal friction angle decreases, the increased cohesion can enhance the shear strength of the structural plane.When the particle contact modulus is small, which is 1 ≤ E C ≤ 2.8 GPa, the change internal friction angle is signi cant, with a di erence of 6.3 °. e particle contact modulus, which strongly in uences the internal friction angle, is relatively small.In actual simulation, EC should be adjusted constantly to match the actual internal friction angle.If EC is large, then the internal friction angle changes with it.e in uence of EC on cohesion c is relatively small, with a di erence of 1.79 MPa between the maximum cohesion and the minimum bond force, and the di erence is approximately 19%.e friction angle of the maximum and minimum values is 10.74 °, with a di erence of approximately 35%.
e in uence of EC on friction angle is shown in Figure 5. e internal friction angle obtained by the direct shear test is larger than that obtained by the triaxial compression test.With the increase of EC, the internal friction angle of the two experiments shows an increasing trend.e variation of internal friction angle in the direct shear test is large, whereas that in the triaxial compression test is stable.e in uence of EC on cohesion is analyzed, as shown in Figure 6.Under the condition of two types of tests, the change trend of cohesion c is similar, but the cohesion obtained from the triaxial compression test is greater than that obtained from the direct shear test.e law is opposite from the internal friction angle changing law.

Parallel Bond Elastic Modulus.
e elastic modulus E c of the parallel bond is the Young's modulus of the bond between two particles.In the direct shear test, shear strength parameters φ and cohesion decrease with the increase of the parallel bond elastic modulus, as shown in Table 4. Parallel bond elastic modulus has a stronger impact on friction angle φ than that on cohesion c. e scope of the change of the internal friction angle is 5.44 °or approximately 22%. e variation range of cohesion is 1.11 MPa or approximately 11%.Considering that friction angle and cohesion have a similar change trend with the parallel elastic modulus, the rule of Coulomb criterion [32][33][34][35] shows that larger parallel bond modulus means smaller internal friction angle and cohesion and shear strength.is phenomenon is due to the increase in the parallel bond elastic modulus, in which the mechanical properties of the specimens are changed, "rigidity" is enhanced, and shear strength is weakened.
e in uence of the parallel bond elastic modulus on the internal friction angle is analyzed, as shown in Figure 7.In the triaxial compression and direct shear tests, the e ect of  the elastic modulus (E c ) of the parallel bond on the internal friction angle is much the same.e internal friction angle decreases and the internal friction angle of the triaxial compression test is larger than that of the straight shear test with the increase of the elastic modulus E c of the parallel bond.When the parallel bond elastic modulus is equal to 6 GPa, the internal friction angle obtained in the two experiments is approximately equal.e di erence in the internal friction angle is small under the condition of two kinds of test along with the increase of E c when E c 7 GPa.A large parallel-bonded elastic modulus can be achieved by using the internal friction angle from the conventional triaxial compression test as the actual internal friction angle.Figure 8 shows the e ect of the parallel bond elastic modulus on cohesion.e variations of cohesion and internal friction angle and the in uence trend of the adhesive modulus are roughly the same.In addition, the cohesion obtained under the two test conditions is approximately the same.Only when E c < 2, the di erence between the two conditions is large and the cohesion obtained by the triaxial compression test is larger than that obtained by the direct shear test.

Particle Size.
According to the numerical simulation test and studies by other scholars, the size of a particle signicantly in uences the shear strength of the specimen [1].erefore, the in uence of particle size on shear strength parameters is discussed.e minimum particle size is set to 0.20, 0.25, 0.28, 0.4, 0.5, 0.8, 1.0, 1.2, and 1.5 mm. e particle diameter ratio of the specimen was set to 1.5, and the shear strength of the specimens with di erent particle sizes was obtained under normal stress by controlling the particle size ratio, as shown in Table 5.Under the same normal stress conditions, the shear strength of the specimens increases with particle size.When the particle size was more than 0.8 mm, the particle size has less in uence on shear strength.e e ect of particle size on shear strength decreases with the increase of normal stress.When the minimum particle size is 0.8 mm and 1.5 mm, the shear strength is closer to the increase of the normal stress.
Table 6 shows that in the direct shear test, the in uence of the particle size of a specimen on the friction angle φ is greater than cohesion c.Cohesion increases with the particle size, and the range is 2.86 MPa or approximately 26%. e e ect of the particle size of a specimen on internal friction angle is large, the range is 8.85 °or approximately 36%, and  Advances in Civil Engineering the internal friction angle decreases without obvious regularity.For a minimum particle size of 0.25 mm and 1.2 mm, the internal friction angle reaches its maximum and minimum values of φ max � 24.28 °and φ min � 15.43 °, respectively.

Particle Size Ratio.
e particle size ratio is the ratio of the maximum particle size to the minimum particle size.Controlling the minimum particle size (0.28 mm), changing the particle size ratio of 1.5, 2.0, 2.5, and 3.0, and obtaining the shear strength of the specimens with different particle size ratios under normal stress are shown in Table 7. e direct shear test is conducted when the normal stress is 2.5 MPa, and the shear strength of the specimen gradually decreases with the increase of the particle size ratio.When the normal stress exceeds 2.5 MPa, the shear strength of the specimen reaches the maximum when the particle size ratio is 2.0.
ereafter, the shear strength decreases with the increase of particle size ratio.e direct shear test is conducted on a certain particle size ratio, and the shear strength of the specimen increases continuously with the increase of normal stress.In summary, although the increase of the particle size ratio increases the instability of the specimen, the shear strength of the particle size is highest when the particle size ratio is 2.0.e shear strength parameter values of different particle size ratios (Table 8) show that in the direct shear test, the impact of particle size ratio on the cohesion of the specimen is relatively small.Cohesion decreases with the increase of the particle size ratio, and the decrease range is 1.11 MPa or approximately 12%, indicating that the increase of particle size ratio decreases the overall mechanical property of the specimen.Shear strength is the largest when the particle size ratio is 2.0 because of the increase in shear strength due to the increase of the friction angle when the cohesion decreases.e overall shear performance of the specimen decreases with the increase of the particle size ratio mainly due to the decrease of cohesion.

Conclusions
(1) e internal friction angle φ of the structural plane decreases with the increase of particle contact stiffness ratio.e internal friction angle decreases first and then increases with the increase of parallel bond stiffness ratio.(2) In the same parallel bond stiffness ratio k n /k s , the cohesion obtained by the direct shear test is less than that of the conventional triaxial test but with a slight difference.Cohesion increases with k n /k s and reaches maximum and then decreases gradually at k n /k s � 2. (3) e influence of particle contact modulus EC on cohesion c is relatively small.e internal friction angle obtained by the direct shear test is larger than that obtained by the triaxial compression test.With the increase of EC, the internal friction angle shows an increasing trend.(4) e shear strength of the specimens increases with particle size.Cohesion increases with the particle size.e shear strength of the specimen gradually decreases with the increase of the particle size ratio.e impact of particle size ratio on the cohesion of the specimen is relatively small.

Figure 1 :
Figure 1: In uence of particle contact sti ness on friction angle.

Figure 3 :Figure 4 :Figure 2 :
Figure 3: In uence of parallel bond sti ness on friction angle.

Figure 5 :Figure 6 :
Figure 5: In uence of particle contact modulus on friction angle.

Figure 7 :Figure 8 :
Figure 7: e e ect of parallel bond elastic modulus on friction angle.

Table 1 :
Shear strength parameter values of di erent particle contact sti ness ratio.

Table 2 :
Shear strength parameter values of di erent parallel bond sti ness ratios.

Table 3 :
Shear strength parameter values under di erent particle contact moduli.

Table 5 :
Shear strength of di erent particle size specimens under normal stress.

Table 4 :
Shear strength parameters of di erent parallel bond elastic moduli.

Table 6 :
Shear strength parameter values of different particle sizes.

Table 8 :
Shear strength parameter values of different particle size ratios.