Damage characteristics of rock induced by unloading in hole under true triaxial boundary stresses: Experimental study

In order to study the effect of unloading of underground rock excavation on the stability of surrounding rock, the true triaxial compression (TTC) and coupled true triaxial compression and in-hole loading-unloading tests (TTC-HU) were conducted on hollow cubic rock (100mm × 100mm × 100mm). The experimental results indicate that the compressive strengths of the specimens increase as confining pressure increases in the equal biaxial stressand increase with increasing intermediate principal stresses in the unequal biaxial stress. At low confining pressure (σ < 30 MPa), the internal stress at unloading damage in the hole of hollow cubic specimen increases with the increase of the three-directional boundary stresses. At high confining pressure (σ ⩾ 30 MPa), the specimen will not be damaged during the entire unloading process in the hole. The damage mode of the specimen is dominated by tensile damage. The shape of the holes in the specimens did not significant change, and hole wall of specimen have layered destruction along the circumference in low confining pressure. In high confining pressure, the hole area of the specimen undergoes significant deformation damage, forming a V-groove along the direction of the minimum principal stress, and the wall of the hole is completely peeled off. This study can reasonably predict the actual engineering damage patterns and guide the optimization of surrounding rock support.


Introduction
In recent years, resource mining gradually develops to the deep underground.Compared with the shallow depth, the deep rock mass is more prone to the occurrence of disaster accidents.In order to secure underground mining, it is critical to control the stability of the surrounding rock during the excavation.Rock excavation is essentially the process of unloading, then inducing the redistribution of stress state of the surrounding rock.Different means of support can be implemented according to the development of the surrounding rock structure to provide security for deep engineering.
So far, many scholars at home and abroad have studied and evaluated the mechanical behavior of rock mass after excavation and unloading and obtained a series of results.Wu Qiuhong et al. [1] conducted conventional triaxial tests on the hollow cylinder sandstone specimens containing different fillers to study the strength, deformation and damage characteristics of circular roadways under high confining pressure, and it was found that the fillers had an obvious effect on the mechanical properties of the specimens, which restored the inner wall of the specimen to a three-dimensional stress state.Jiang Yue et al. [2] took true triaxial experiment on the gray sandstone and found that the intermediate principal stress has a significant effect on the rock strength, and the minimum principal stress can strengthen the rock, which verifies that the exponential strength criterion can better reflect the real value of the rock strength.Gong Fengqiang et al. [3] used the perforated cubic red sandstone to simulate the entire process of slabbing and rockburst in deeply buried tunnels, and it is found that the rockburst can occur in the phase with constant stress and has time effect, and the optimization of cross-section dimensions of tunnel can enhance the structural stability.Zhang Houquan et al. [4] conducted the unloading test on the thick-walled cylinder rock specimen to study the zonal disintegration phenomenon of and the splitting tension damage of rock.Wang et al [5] studied the triaxial compressive strength of hollow cylindrical specimens in a non-uniform stress field and proposed that the nonlinear damage criterion better reflects the triaxial compressive strength characteristics.
However, most of the above results are the loading and unloading experiments on thick-walled cylinders, and there lacks the experimental studies on the in-hole loading and unloading of cubic specimens.In this paper, the true triaxial boundary stress loading coupled by in-hole loading and unloading are performed on the hollow cubic rock specimens.A non-uniform stress field is constructed within the rock specimen, and then the hydraulic pressure in the hole is rapidly unloaded to study the effect of unloading in the hole on the damage characteristics of rock under the true triaxial boundary stress condition, so as to physically simulate the effect of unloading process of the rock on the stability of the surrounding rock.

Specimen preparation
In this study, a hole with diameter of 30 mm was pre-drilled in the center of cubic red sandstone specimen with a side length of 100 mm to prepare a hollow cubic specimen shown in Fig. 1.All the specimens were divided into two groups, labeled as SC and SU, to be tested by the true triaxial compression test (TTC) and the coupled true triaxial compression and in-hole loading-unloading test (TTC-HU), respectively.The mechanical parameters of the rock material have been measured by the conventional triaxial compression tests and shown in Table 1.

Test equipment
In order to study the damage characteristics of in-hole unloading under the true triaxial boundary stress, the true triaxial boundary stresses and intra-hole stresses were applied to the end faces and hole walls of the hollow cubic block specimens through the TRW-3000 true triaxial electro-hydraulic servo-control test system and the in-hole loading and unloading system.As shown in Fig. 2, the systems used in the experiments mainly include the true triaxial electrohydraulic servo-control test system, the in-hole loading and unloading system and the true triaxial loading box.Among them, the in-hole loading and unloading system consists of an in-hole loading and unloading device, a high-pressure oil pipe, a pressure gauge and an electric high-pressure oil pump.The true triaxial loading box consists of six loading rods in the upper and lower, left and right, front and rear pairs, a fixed bar on the loading rods for fixing the extensometer sensors and lead wires, and a support guide box for supporting and guiding the loading rods.The hole loading and unloading device mainly consists of a hydraulic capsule for uniformly transferring hydraulic pressure to the cylindrical hole wall in the center of the sample and an end cover for uniformly transferring the axial pressure of Z-direction loading to the upper surface of the sample and guiding out the hydraulic line while being able to seal the hydraulic capsule.

Test methods
TTC tests were first performed on nine specimens labeled SC.The specific test steps were as follows: the confining pressure was applied synchronously in the x and y directions to a specific value, and then the confining pressure was kept constant, and then the axial pressure was applied in the z direction until the specimen was destroyed.The stress changes in the three orthogonal axial directions of each specimen were recorded.The loading form is shown in Figure 3(a).
Then the nine specimens marked SU were subjected to the true triaxial and in-hole coupling loading and unloading tests, in which the applied stress values in x and y axes were consistent with the SC specimens, the applied stress in z axis was 1.1 times of the stress at the time of destruction of the corresponding SC specimens, and the in-hole stresses were consistent with the x-axis stresses.The test methods were as follows: the x, y, and z-axis stresses and in-hole stresses were applied synchronously

True triaxial compression
The stress-strain curves of nine groups of specimens under TTC are plotted in Fig. 4, and the related parameters are shown in Table 2.According to the stress-strain curves, it can be clearly found that the specimens experienced four stages of compaction, elasticity, plastic deformation and damage during true triaxial compression.The strain shows nonlinear variation in the compression-dense stage, which indicates that there are some initial microfractures in the specimen.Subsequently, the specimen enters the linear deformation stage, and the yield occurs when the specimen reaches the peak strength, and the carrying capacity and plastic deformation of the specimen increase with the increase of confining pressure.When the minimum principal stress is low, the specimen reaches the peak strength with no obvious yielding platform.When the minimum principal stress r increases, the yielding platform is gradually obvious.Meanwhile, the larger the confining pressure is, the slower the stress fall after the specimen is damaged, indicating that the confining pressure can induce the damage mode of the specimen to change from brittle to ductile.From Table 2, it can be seen that the appropriate stress difference can increase the load carrying capacity of the specimen, but when the stress difference is too large, the load carrying capacity of the specimen will drop sharply, such as SC-7, the specimen strength is the lowest.

Coupled true triaxial compression and in-hole loading-unloading tests
The stress-strain curves of specimens under TTC-HU are plotted in Fig. 5. Compared with the true triaxial experiments, the presence of in-hole pressure increases the load carrying capacity of the specimen when the confining pressure of the specimen is the same.When the confining pressure is lower, the in-hole stress at unloading damage increases with the increase of the three-dimensional stresses, and it can be seen from the comparisons of SU-1 with SU-2, and SU-3 with SU-4, that the larger the stress difference is, the easier the specimen is damaged during unloading.When the confining pressure is higher, the specimen will not be damaged during the unloading process of in-hole stress.This can be understood as the in-hole pressure restricts the development of initial cracks as well as the generation of new cracks in the specimen during the in-hole stress loading process, and the lateral deformation of the specimen in the direction of the inner wall is restricted compared to the true triaxial loading without inhole pressure.Thus, the bearing capacity of the rock becomes larger.Especially at high confining pressures, the high in-hole stress can induce the closure of the initial microcracks in the specimen, which makes the rock specimen close to the flawless state, further improving the rock strength, and thus the specimen is not easy to be damaged during the decompression process.4. Failure analysis of specimens under TTC and TTC-HU Figure 6 shows the photographs of specimen failures under TTC.It can be found that the damage mode of the specimen is greatly affected by the confining pressure.At low confining pressure, shown in Fig. 6(a) and (b), it can be seen that the hole shape is maintained unchanged during the failure of the specimen, and there is a delamination peeling damage of the hole wall.With increase in the confining pressure, the rock material near the hole wall expands and protrudes to the hole, and there is a laminar destruction of hole wall [1].This can be explained as the existence of hole makes the stress distribution of the specimen is not uniform, the inner wall of the hole has no radial stress effect, so that the rock material near the hole wall firstly undergoes damage, and finally the whole specimen yields, which makes the laminar damage near the hole wall.From Fig. 6(c) and (d), it can be seen that the existence of the confining pressure difference leads to the extrusion deformation of the specimen along the side of the lower stress, the tensile stress is generated in the specimen, and a V-shaped groove is formed along the axial direction.
With the increase of the stress difference, the specimen ruptures directly along the V-shaped groove under the action of the tensile stress [6].At high confining pressure, such as Fig. 6(e) and (f), the obvious deformation damage occurs in the hole region, a V-shaped groove is formed along the direction of the minimum principal stress, and the hole wall is completely peeled off.
The unloading in the hole had a large impact on the strength and damage mode of the specimen.For the confining stress condition with (σx, σy)=(20 MPa, 60 MPa), as shownAin Fig. 7(a), the hole shape of specimen remained intact during the unloading damage in the hole, the inner wall of the hole did not have delamination and spalling phenomenon, and only V-shaped grooves appeared during the unloading of in-hole pressure.For the confining stress condition with (σx, σy)=(30 MPa, 120 MPa), two penetrating cracks were produced along the upper and lower ends of the hole in the specimen show in Fig. 7(b), which is due to the unloading of the in-hole pressure that makes the rock produce tensile cleavage damage [7].For the higher confining stresses and the corresponding in-hole pressure, no significant failure has occurred in rock, except for only a small area of peeling near the hole wall.

Conclusions
In this paper, the hollow cube specimen with a side length of 100 mm and an inner hole diameter of 30 mm is subjected to TTC and TTC-HU, and the following conclusions can be drawn: (1) The strength of the hollow cube specimen is affected by the confining pressure.When the biaxial confining stresses are equal, the specimen strength increases with increasing confining pressure.When the biaxial confining stresses are not equal, the appropriate stress difference can improve the strength of specimen, but when the stress difference is too large, it will lead to a sharp decrease in the strength of specimen.
(2) The presence of in-hole pressure can hinder the development of initial cracks in rock specimens, inhibit the lateral deformation of specimens toward the hole wall, and largely improve the strength of specimen.At low confining pressure, the in-hole pressure at unloading damage in the specimen hole increases with the increase of three-dimensional axial stresses.At high confining pressure, the specimen damage is not induced during unloading in the specimen hole.

Figure 1 .
Figure 1.(a) Schematic diagram of the specimen (b) Physical drawings of specimens

Figure 2 .
Figure 2. Experimental system: (a) the true triaxial electro-hydraulic servocontrol test system and the in-hole loading/unloading system, (b) the loading box, (c) the working drawing of the in-hole loading/unloading device, (d) the assembly drawing of the rock sample with in-hole loading/unloading device, (e) the in-hole loading/unloading device, and (f) the disassembly drawing of the in-hole loading/unloading device.
bar (×6) 32-Fixed rod for extensometer (×3) 33-Fixed rod for extension line (×3) 34-Cavity for placing rock 35up to the preset values, and the in-hole stress was then unloaded to the specimen destruction at a rate of 0.5 MPa/s.The loading form is shown in Figure 3(b).

Fig. 3
Fig. 3 Loading forms designed in tests, which include (a) true triaxial compression test and (b) unloading test along a cylindrical hole in cubic rock under true triaxial compression 3. Result

Fig. 4
Fig. 4 Stress-strain curves of cubic hollow rock specimens under TTC tests

Fig. 5
Fig.5 Stress-strain curves of cubic hollow rock specimens under TTC-HU tests

Table 1 .
Mechanical parameters of sandstone rock material

Table 2
Strength of hollow cubic rock under TTC tests

Table 3
Unloading characteristics of hollow cubic rock under TTC-HU tests