## 2 Roof Structure and Roof Self-Stability Concept in Backfilling Mining
### Roof Self-Stability Concept and Characteristic  
There are three types of structural forms of overlying rock beams in backfilling mining. The first type has a low backfill ratio in the goat and a small elastic foundation coefficient of backfilling body, which causes the failure of immediate and basic roofs, and obvious ground behaviors. It has an insignificant difference from collapse mining. The second type has a high backfill ratio in the goat and a large elastic foundation coefficient of backfilling body, which causes the failure of the immediate roof, the bending of the basic roof, and relieved ground behaviors. The third type has a particularly high backfill ratio in the goat, a high elastic foundation coefficient, and a large resistance on the roof. The immediate and basic roofs bend and sink, with no obvious ground behaviors [21].  
The concept of roof self-stability in backfilling mining is proposed on this basis. The roof beams are supported by the backfilling body to form a \"continuous curved beam\" structure, which maintains integrity and stability by its strength. The structure is manifested as the morphological characteristics of unbroken and continuous deformation and is described as a roof self-stability state (corresponding to the third type). If the support degree of the backfilling body is weak, the roof beams cannot form a \"continuous curved beam\" structure. It cannot maintain integrity and stability by its strength. The structure is manifested as the morphological characteristics of instability and fracture and described as a roof instability state (corresponding to the first and second types). The roof beams reconstruct the stable overlying strata structure to form curved beams in the form of curved arches rather than three-hinged arches. The relevant theory of beams can be used to solve the bending moments, stress, and deflections of continuous bending beams. Slope stress is redistributed to form a stress-relaxed area, a stress-concentrated area, and an initial rock stress area on the roof after collapse mining. The stress-concentrated area has a large stress concentration coefficient, which is not conducive to coal-body stability and safe mining.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Precise Backfilling** & **Long-Wall Caving** \\ \hline Strata control diagram & & \\ Cord  
Roof self-stability inhibits its movement during dense filling. A small stress concentration coefficient and unobvious strata behaviors contribute to ensuring the safety of underground workers. The immediate roof is bent out of shape under the support of the backfilling body according to the equivalent mining-height theory after the self-stabilization of the dense-packed roof. The surface sinks slightly to liberate the coal resources under buildings, water bodies, and railways. Besides, the backfilling body further absorbs the released elastic energy of overlying strata during the self-stabilization process, which reduces the risk of rock bursts.  
Roof self-stability is relevant to strike factors (the backfill compactness, support working resistance, unsupported-roof distance, and drilling depth), and the dip factors (the layout of the backfill mining system, coal-pillar width, and working face length). A theoretical model needs to be constructed for specific quantitative analysis. The mechanical models of roof self-stability are established along strike and dip to analyze the roof self-stabilizing strike effects of elastic foundation coefficients, support peak loads, unsupported-roof distances, advancing distances, and the roof self-stabilizing dip effects of working-face lengths and coal-pillar widths.