Hz=H−H0+ηH0 (2)

where η is the residual compression rate of solid filling body。

After that, solid backfilling mining subsidence can be calculated by the equivalent mining height and strata movement parameters in the coal mines。

horizontal deformation value in designed building area。

According to the former analysis, it can be concluded that in a certain working face, the ground subsidence and horizontal deformation are  decided by the equivalent height solely, thus the former principles of subsidence control can be illustrated briefly as:

Hz≤Hc

where Hz is the designed equivalent mining height of working face; Hc is the critical equivalent mining height calculated by fortification criteria of buildings and their attachment structures。

4。2 Subsidence control design methods of mining under buildings

The key part in the  application  of subsidence control principles by solid backfilling mining is to decide the designed and critical equivalent mining heights。 The designed equivalent mining height can be calculated according to Eq。 (2)。 Besides, the critical equivalent mining height can be got by the ground movement and

deformation fortification criteria of buildings and their attachment structures。 The flowchart is shown in Fig。 3。

Fig。 3 Flowchart for calculation of critical equivalent mining height

In the process of critical mining height computation, it is difficult to enable the prediction value of deformation to be the same with the fortification criteria。 So, if the difference between the prediction value of deformation and the fortification criteria is less than 5%, it is acceptable。 The prediction of buildings’ deformation is done with the probability integral method based on the equivalent mining height while the thin coal seam parameters are used in the process。

When the working face is critical mining and the maximum deformation value locates in the buildings’ area, the schedule for calculation of critical equivalent mining height can be simplified。 According to principles of probability integral method, the critical equivalent mining height can be expressed in the following formula, while the maximum subsidence in buildings’ area should be less than the subsidence criteria。

In practical, the smaller one of the two values, which are calculated by Eqs。 (3) and (4) respectively, can be selected to ensure the safety use of buildings。

5 Engineering example

5。1 Geological and mining conditions of working face

In this case, the working face is 450 m in length, 142 m in inclined width, 335 m in average depth, 8° in inclined angle and 3。3 m in thickness of coal seam。 For the roof management, solid backfilling is adopted。 The direct roof of working face mainly consists of siltstone- mudstone intercalation and post stone with the average thickness of 7。44 m。 Sandy shale is the main part of the floor whose average thickness is 4。81 m。 Villages, highways and other buildings locate above the working face and the land is flat。

5。2 Subsidence control design

Above the working face, there are several buildings such as villages, the industry square of coal mine, some roads and the shaft。 After researching the buildings’ qualities, and referencing to the 27th item of Regulations on Coal Pillar Design and Mining Regulations Under Buildings, Water, Railways [10], it is fixed that the fortification of subsidence in this district is 500 mm and the horizontal deformation criterion is 1。5 mm/m。 The subsidence prediction parameters are inversed by the thin coal seam measurement, that are subsidence coefficient 0。73, horizontal movement coefficient 0。34, tangent of main influence angle 1。8, deviation of inflection point 0。1H。 While the geological and mining conditions, and filling technology of this case are considered, the roof-to- floor convergence before backfilling is 100 mm and the gap between the backfilling body and roof is zero。