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The deep high prestatically loaded rock is often subjected to low-frequency dynamic disturbance and exhibits unusual strength characteristics, and thus, it is important to investigate the strength characteristics under the coupling effect of prestatic load and low-frequency dynamic disturbance loading conditions. In this study, a series of point load tests were conducted on the high prestatically loaded marble subjected to low-frequency disturbance by the MTS system, focusing on exploring the role of prestatic load level and low-frequency disturbance frequency in the process of rock strength change. Based on the average static failure load (_{max}) of samples under the static point loading, the high prestatic load levels (_{p}) were selected as 70%, 80%, and 90% of _{max}, the corresponding low-frequency dynamic disturbance was loaded by sinusoidal waves with amplitudes of 60%, 40%, and 20% of _{max}, and the low-frequency dynamic disturbance frequencies (_{p} or _{p} increases. Moreover, the point load strength weakening rate was proposed to characterize the degree of strength weakening. The comprehensive analysis demonstrates that _{p} has a greater effect on the point load strength weakening effect than _{p}, and the weakening degree is affected by

With the decrease of shallow mineral resources and the increasing demand for underground space, more and more underground projects extend to great depth. The deep surrounding rock has been subjected to high static stress before excavation [

To date, researchers have conducted a lot of experimental and theoretical studies to understand the fracture behavior and mechanism of high prestatically loaded rock. Gao et al. [

However, the above research on rock fracture failure subjected to coupled high prestatic load and dynamic load is mainly based on strong impact dynamic disturbance load, rarely involving low-frequency dynamic disturbance. Su et al. [

To further study the rock fracture characteristics of high preloaded rock subjected to low-frequency dynamic disturbance, a series of point load tests under these coupled load conditions were designed. In our study, the sum of all prestatic load levels and the corresponding one-half of the dynamic disturbance amplitude is equal to the average failure load (_{max}) under the static point load tests (i.e., the _{p} + 0.5_{d} = _{max}). Therefore, the prestatic load levels (_{p}) were set to 70%, 80%, and 90% of _{max}, while the corresponding low-frequency dynamic disturbance amplitudes (_{d}) were set as 60%, 40%, and 20% of _{max}. Moreover, a sinusoidal disturbance wave at low-frequency dynamic disturbance frequencies (_{p} and

The rock samples selected in the all point load tests were obtained from the marble blocks in Hezhou City (Guangxi Province, China) as it has good homogeneity. Petrographic thin section analysis indicates that the marble is fine-grained and well sorted, which is mainly composed of quartz (99%), and the matrix material composed of clay is about 1% of the sample [

Photomicrographs of marble samples. (a) Single polarization (Cal = calcite) [

For the marble preparation for the point load tests, the whole marble rock block was made into cylindrical samples of 50 × 50 mm^{2} (i.e., the ratio of the diameter (^{3},

Marble sample processing process.

The axial point load tests of the prestatically loaded marble subjected to low-frequency dynamic disturbance were conducted on the MTS Landmark servocontrolled testing system, as illustrated in Figure

Test equipment.

To obtain the relevant parameters of the point load test under the prestatically loaded marble subjected to low-frequency dynamic disturbance, the point load test under the static load was first carried out. The specific test process is as follows: (1) the cylindrical end of the loading cone was put into the clamping groove of MTS Landmark and the clamping force was adjusted to fix it; (2) the test piece was placed between the two pressure cones, and the loading cone was aligned at the center of the sample section; (3) after the sample was placed, a load of 0.5 kN was preapplied to fix it. In the static loading process, the sample was loaded at 5 kN/min until the sample was damaged. The calculation formula of the point load strength is given by [_{s} is the point load strength (MPa), _{e} is the “equivalent core diameter” (mm) [

Table _{max} = 6.51 kN, _{max} represents the maximum failure load), and the standard deviation is 2%, indicating that the sample has good homogeneity. Based on equation (

Point load test results under static load.

Sample | _{s} (MPa) | |
---|---|---|

S-1 | 6.44 | 2.01 |

S-2 | 6.48 | 2.03 |

S-3 | 6.61 | 2.07 |

Average | 6.51 | 2.03 |

Point load test under static load. (a) Load-displacement curve. (b) Failure mode.

In the prestatically loaded marble subjected to dynamic disturbance test, the marble samples were first loaded to the prestatic load level (_{P}) at the loading speed of 5 kN/min under the static loading, and then the sine-wave load with a specific low-frequency disturbance frequency (_{d}) was applied, as represented in Figure _{max} (i.e., 4.65, 5.21, and 5.86 kN), the corresponding low-frequency dynamic disturbance amplitudes are 60%, 40%, and 20% of _{max} (_{d} = _{max} − _{min}, where _{max} and _{min} are the maximum and minimum disturbance loads), and the low-frequency dynamic disturbance frequency is 1, 2, 5, and 10 Hz.

Point load test loading path of prestatically loaded marble subjected to low-frequency dynamic disturbance.

After processing the load and displacement data of all prestatically loaded marbles subjected to low-frequency dynamic disturbance, some typical load-displacement curves are obtained as illustrated in Figure _{P} is 80% of _{max}, the maximum failure load that the sample can withstand at _{P} and

Typical load-displacement curves under the point load test. (a) 70%-1 Hz; (b) 70%-10 Hz; (c) 80%-1 Hz; (d) 80%-10 Hz; (e) 90%-2 Hz; (f) 90%-10 Hz.

The results under different prestatic loads and dynamic disturbances.

Sample | _{p} (kN) (_{p}/_{max}) | _{min} (kN) | _{max} (kN) | ||
---|---|---|---|---|---|

70%-1 Hz | 4.56 (70%) | 2.60 | 6.51 | 1 | 6.38 |

70%-2 Hz | 2 | 6.30 | |||

70%-5 Hz | 5 | 6.23 | |||

70%-10 Hz | 10 | 6.14 | |||

80%-1 Hz | 5.21 (80%) | 3.91 | 6.51 | 1 | 6.29 |

80%-2 Hz | 2 | 6.27 | |||

80%-5 Hz | 5 | 6.21 | |||

80%-10 Hz | 10 | 6.11 | |||

90%-1 Hz | 5.86 (90%) | 5.21 | 6.51 | 1 | 6.26 |

90%-2 Hz | 2 | 6.23 | |||

90%-5 Hz | 5 | 6.18 | |||

90%-10 Hz | 10 | 6.03 |

Failure load under the point load test.

The failure loads in the point load test of the prestatically loaded marble subjected to low-frequency dynamic disturbance are significantly lower than that under the static point load test (Figure _{P} is 70% of _{max}, the point load strength of the sample at _{P} is 90% of _{max}, the point load strength of the sample is 1.87 MPa at

The point load strength of prestatically loaded marble subjected to dynamic disturbance.

Sample | PSWR (%) | ||
---|---|---|---|

70%-1 Hz | 6.38 | 1.99 | 2.39 |

70%-2 Hz | 6.30 | 1.96 | 3.65 |

70%-5 Hz | 6.23 | 1.95 | 4.30 |

70%-10 Hz | 6.14 | 1.91 | 6.20 |

80%-1 Hz | 6.29 | 1.96 | 3.57 |

80%-2 Hz | 6.27 | 1.95 | 4.07 |

80%-5 Hz | 6.21 | 1.93 | 4.98 |

80%-10 Hz | 6.11 | 1.90 | 6.51 |

90%-1 Hz | 6.26 | 1.95 | 4.32 |

90%-2 Hz | 6.23 | 1.94 | 4.71 |

90%-5 Hz | 6.18 | 1.92 | 5.71 |

90%-10 Hz | 6.03 | 1.87 | 8.00 |

Therefore, to quantitatively analyze the point load strength weakening effect, the point load strength weakening rate (PSWR) is proposed as follows:

Figure _{P} and _{P}, which indicates that the point load strength has obvious strength weakening effect. As shown, if _{P} is 70% of _{max}, the point load strength gradually decreases from 2.03 MPa under static loading to 1.99 MPa at _{max} and 1.95∼1.87 MPa at 90% of _{max}. These results imply that increasing _{P}, the point load strength weakening effect is more significant at the high frequencies. For instance, when _{P} is 80% of _{max}, the PSWR is between 3.57% and 6.51%, while if _{P} is 90% of _{max}, the PSWR is between 4.32% and 8.00%, which is much larger than that of other prestatic load levels. These results strongly demonstrate that _{P} is dominant in the point load strength weakening process, that is, the _{P} determines its strength weakening level.

The point load strength and the corresponding weakening rate change trend with the disturbance frequency. (a) Point load strength. (b) PSWR.

Figure _{P} under the same _{max} to 1.96 MPa at the 80% of _{max} as the _{P} increases, until the maximum decreases to 1.95 MPa at 90% of _{max}, and similar trends can also be observed at other disturbance frequencies. Moreover, _{P} promotes the point load strength weakening more significantly at high disturbance frequencies. As shown, when _{max}, and the PSWR can reach up to 4.71%. However, if _{P}, and the PSWR is as high as 8.00%, which is much higher than the decrease at other disturbance frequencies. Furthermore, the interval between the disturbance frequency between 5 Hz and 10 Hz is much larger than the interval between other disturbance frequencies, which implies that increasing _{P} can obviously promote the point load strength weakening if

The point load strength and the corresponding weakening rate change trend with the prestatic load level. (a) Point load strength. (b) PSWR.

These experiments indicated that, in the point load tests of the kind of high preloaded rock subjected to low-frequency dynamic disturbance load, the point load strength has a significant strength weakening effect, which is attributed to the corresponding _{P} and _{P} and _{P}, the more significant the point load strength weakening effect (as illustrated in Figure _{P} is dominant and determines its weakening level. At the same time, the test results also demonstrate that _{P}, and _{P} and _{P} reaches a certain degree, _{P} can promote the weakening process (Figure _{P} dominates and determines the weakening level, while the dynamic disturbance further induces the weakening process and

In this paper, the influence of the unloading process on rock strength is not considered. Our previous research shows that unloading can also weaken the rock strength [

After the deep rock engineering excavation, the surrounding rock has obvious strength weakening effects [_{P} is 90% under the coupled static-dynamic loading, the tensile strength decreases with _{P} is 80%. In the process of tensile strength weakening, _{P} still dominates the weakening level, while the dynamic disturbance induces strength weakening and

Failure mode of prestatically loaded marble subjected to dynamic disturbance.

Test results of BD samples. (a) Sample size. (b) Typical load-displacement curve [

In light of the comparison indicated above, the prestatic load rock subjected to low-frequency dynamic disturbance under the point load test or Brazilian disc test shows that the rock strength (point load strength and tensile strength) shows obvious strength weakening effect during the rock failure process. Moreover, in the process of rock strength weakening, _{P} dominates the strength weakening level and _{P} and

A series of point load tests were conducted on the prestatically loaded marble sample subjected to low-frequency dynamic disturbance, and several important conclusions were obtained as follows:

The point strength of the point load test under the prestatically loaded marble sample subjected to low-frequency dynamic disturbance loading tests is significantly lower than that under pure static loading, showing a significant strength weakening effect.

As long as _{P} and _{P}

During the whole point load strength weakening process, _{P} dominates and determines the weakening level, while

Both the point load test and the Brazilian disc test of the deep high prestatically loaded rock subjected to low-frequency dynamic disturbance show obvious strength weakening effects, and it is strongly proved that the strength weakening process is only related to _{P} and

All data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this article.

This work was supported by the National Natural Science Foundation of China (grant no. 42077244) and the Fundamental Research Funds for the Central Universities of Southeast University (grant no. 2242021R10080).