*3.4. Experimental Procedure*

The height of the crushed mudstone samples was set to 380 mm before the initiation of the compression tests. The experimental procedures are described as follows:


#### **4. Experimental Results**

#### *4.1. Axial Deformation*

4.1.1. Accumulated Axial Deformation

The stress-strain curves of the crushed mudstone samples for the entire loading process under the incremental loading were recorded in Figure 7. The figure clearly shows that the accumulated axial strain of the crushed mudstone samples increased with increasing axial stress. It can be seen that the accumulated axial strain of S-1, S-2, and S-3 were 14.5%, 10.64%, and 8% respectively when the axial stress *P* = 0.6 MPa (the fourth loading stage); When the axial stress *P* = 0.9 MPa (the sixth loading stage), the accumulated axial strain of S-1, S-2, and S-3 were 17.4%,13.93% and 10.1%. These results indicate that the accumulated axial strain of the samples decreased with increasing particle size under the same axial stress. Additionally, it was noted that the ultimate loading stage for S-1, S-2, S-3 was the 7th, 8th and 9th stage, respectively, which demonstrated that the lateral stress generated on the support structure by the crushed mudstones decreased as the particle size increased under the same axial stress as well. This conclusion will be explained precisely in Section 4.2.

**Figure 7.** The stress-strain curves of the tested crushed mudstone samples for the entire loading process under the incremental loading.

4.1.2. Periodic Axial Deformation

Figure 8 shows the change rule of axial strain increment corresponding to each loading stage (periodic axial stain) for S-1, S-2 and S-3. And the periodic axial stain values of each loading stage are listed in Table 1. For sample S-1 (Figure 8a), the periodic axial stain decreased with the loading stage increasing; In the case of samples S-2 and S-3, the periodic axial strain showed a decreasing trend in the early loading stages, but rebounded in the later loading stages, as seen in Figure 8b,c. This results indicated that there was a skeletal load-bearing effect in large-sized rushed mudstone samples (S-2, S-3).

**Figure 8.** The change rule of axial strain increment corresponding to each loading stage for S-1, S-2 and S-3.

**Table 1.** The periodic axial strain of crushed mudstone sample at each loading stage.


For crushed mudstone sample S-2 and S-3, the entire deformation process can be divided into structural adjustment, skeleton load-bearing and crushing cum filling phases, as presented in Figure 9. In the skeleton load-bearing phase, the periodic axial strain was relatively smaller, which indicated that the crushed rocks with large-sized particles have higher deformation resistance and stability in the skeleton load-bearing phase than other phases.

**Figure 9.** The entire deformation process of the crushed rock sample with skeleton load-bearing effect.

The periodic axial stress-strain curves of the crushed mudstone samples at each loading stage were presented in Figures 10–12. From these figures, we known that the periodic axial strain of the crushed mudstones was composed of instantaneous deformation and creep deformation. Observations of the instantaneous axial strain and axial creep strain of crushed mudstones at each loading stage were listed in Tables 2 and 3 respectively. Table 2 showed that the instantaneous axial strain of all samples decreased with increasing loading stage. From observations in Table 3, we know that the axial creep strain of sample S-1 at each loading stage was approximately similar, and most of them were between 0.7–0.8. But for sample S-2 and S-3, the axial creep strain was a minimum at the skeletal load-bearing stage. As it entered the crushing cum filling stage, the periodic creep deformation increased sharply.

**Table 2.** The periodic axial instantaneous strain of crushed mudstone samples at each loading stage.



**Table 3.** The periodic creep strain of crushed mudstone samples at each loading stage.

(**g**) The seventh loading stage

**Figure 10.** The periodic stress-strain curves of sample S-1 at each loading stage.

(**g**) The seventh loading stage (**h**) The eighth loading stage **Figure 11.** The periodic stress-strain curves of sample S-2 at each loading stage.

**Figure 12.** The periodic stress-strain curves of sample S-3 at each loading stage.

In addition, two types of periodic stress-strain curves were observed from the test results, which were "down-concave" type and "upper-convex" type, respectively. The "down-concave" type stress-strain curve appeared at the previous loading stages, which presented a large growth rate of axial strain at the earlier phases of the loading stage, and a smaller growth rate at the later phases of the loading stage. Conversely, for the "upper-concave type" stress-strain curve, the growth rate of axial strain at earlier phases of the loading stage was small (shown within a red colored frame in Figures 10–12). But after the axial stress reached a certain value, the axial strain increased continuously.

#### *4.2. Lateral Stress*

Figure 13 shows the lateral stress of the D column monitoring points on the simulated support structure in the tests. From the results, it can be seen that the lateral stress increased as the axial stress increased. With the increase of particle size, the lateral stress generated on the support structure decreases under the same axial stress. In addition, the test results showed that the lateral stress generated by the sample S-1 and S-2 consistently showed a better regularity than sample S-3.

**Figure 13.** The lateral stress of the D column monitoring points.

Using a curve fitting analysis, a linear relationship between the lateral stress generated by crushed mudstone rocks and the axial stress can be represented by the following equation:

$$
\sigma\_\mathbf{x} = a \sigma\_\mathbf{y} + b \tag{1}
$$

where *σ*<sup>x</sup> is the lateral stress from the crushed mudstones that was generated on the support structure; *σ*<sup>y</sup> is the axial stress applied on crushed mudstones; *a* and *b* are regression coefficients. The regression coefficients established for all the tests are itemized in Table 4. The most of correlation coefficients are greater than 0.95.


**Table 4.** Regression coefficients of the linear relationship between axial stress and lateral stress generated by crushed mudstones.

#### **5. Discussion**

The reasons for deformation of the crushed rocks include void space compression, particle crushing and particle splitting. The different types of periodic stress-strain curves represented different deformation mechanisms for crushed mudstones. As shown in Figure 14a, for "down-concave type" stress-strain curve, the rapid increase of axial strain in the early loading stage was caused by the compression of a large amount of void space. As the void space was primarily compressed and the rate of axial strain increase slowed down, thus making the stress-strain curve of crushed rocks to present a down-concave shape. Figure 14b shows the deformation mechanism for "upper-convex type" stress-strain curve. The crushed rocks with this type stress-strain curve usually indicate that the sample has a certain initial bearing strength. When the axial stress is greater than the bearing strength of the crushed rock sample, a large number of particles crush and fill the void spaces. This

provide a good explanation for the rapidly growth of axial strain of crushed rocks in the later loading stage.

**Figure 14.** The deformation mechanism of two types of stress-strain curves: (**a**) down-concave type; (**b**) upper-convex type.

From above experimental results, a poor regularity of lateral stress generated by sample S-3 was observed. The phenomenon was illustrated in Figure 15.

**Figure 15.** The schematic diagram for a poor regularity of lateral stress generated by larger-sized crushed rocks.

It can be seen that the contact between fine-sized crushed rocks and support structure is more sufficient than the larger-sized crushed rocks. Stress concentration (the first case of Figure 15) and zero-contact (the second case of Figure 15) are more likely to occur in larger-sized crushed rocks.

#### **6. Conclusions**

The conclusions drawn from this research are as follows:

(1) An innovative experimental device was developed to simulate the boundary conditions of the GERRF method. Using the device, the compressing tests were conducted to study the deformation behaviors of crushed rocks with different particle sizes in gob side of GERRF method.

(2) In tests, the accumulated axial deformation of the crushed rocks increased with increasing axial stress. As the particle size increased, the accumulated axial deformation decreased under the same axial stress. In addition, the skeletal loading-bearing effect was found in the samples with larger sized particles. And the entire deformation process of those samples can be divided into structural adjustment, skeleton load-bearing and crushing cum filling phases.

(3) The periodic deformation of the crushed mudstones includes instantaneous compressive deformation and creep deformation. Regardless of the particle size of the crushed rocks, the instantaneous compressive deformation decreased with the increase of loading stage. However, the different change laws of creep deformation were observed in the samples with different particle size. For the sample S-1, the creep deformations at each loading stage were roughly the same. But for samples S-2 and S-3, the creep deformation was minimum at the the skeletal load-bearing phase, but increased when it entered the crushing cum filling phase.

(4) There were two types of periodic stress-strain curves for crushed rocks. The "downconcave" stress-strain curve indicated that the deformation of crushed rocks was mainly caused by the compression of void spaces. While the "upper-convex" curve is the result of particles crushing and particles filling again.

(5) With the increase of particle size, the lateral stress generated on the support structure decreases under the same axial stress. Additionally, a poor regularity of lateral stress generated by crushed rocks with larger- sized particles was observed in tests. Under the condition that lateral pressure shows good regularity, a linear relationship between the axial stress and lateral stress generated by crushed rocks was established to be of the form: *σ*<sup>x</sup> = *aσ*<sup>y</sup> + *b*.

**Author Contributions:** All the authors contributed to this paper. Q.W. prepared and edited the manuscript. Z.G. provided theoretical and methodological guidance in the research process. S.Y., C.Z. and D.Y. partially participated in literature search and data processing. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported by the Science and Technology Project of Langfang City, China (grant number 2020013039), the Special Fund of Basic Research and Operating of North China Institute of Science & Technology (grant number 3142020001), and the State Scholarship Fund of China, the National Natural Science Foundation of China (grant number 51479195).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Acknowledgments:** We are grateful to China University of Mining and Technology for providing us with the experimental platform and all the reviewers for their specific comments and suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

