Table 8 Classification of surface movement deformation and its relationship with building protection levels40,41.

From: Short-wall roadway backfill method for sustainable mining

Movement and deformation

Variables

Formula

Relationship with building protection levels (earth-built houses)

Inclined deformation

i

\(i_{3 - 4} = \frac{{w_{4} - w_{3} }}{{l_{3 - 4} }} = \frac{\Delta w}{l}\;\left( {\text{mm/m}} \right)\)   (14)

Grade I: < 1.0

Curvature deformation

K

\(K = \frac{\Delta i}{l}\;( {{\text{mm/m}}^{2} } )\)   (15)

Grade I: < 0.05

Horizontal deformation

εx

\(\varepsilon_{3 - 4} = \frac{{u_{4} - u_{3} }}{{l_{3 - 4} }} = \frac{\Delta u}{l}\;\;\left( {\text{mm/m}} \right)\)   (16)

Grade I: < 1.0

  1. In the equation, u3, u4, w3, w4 as illustrated in Fig. 14, represent the distances in the horizontal and vertical directions before and after the movement of points 3 and 4, respectively; l34 represents the original distance between points 3 and 4.