关键词: 地表变形, 最小二乘法, 移动界限, 水平变形, 倾斜, 曲率

Abstract: The horizontal deformation，incline and curvature of the ground are the important indexes for evaluating ground deformation and determining the limit of the ground movement.The deformation indexes of ground surface varies with direction，however the traditional section method which calculates deformation indexes along strike of section，is not only possible to underestimate the surface deformation，but also difficult to get the contour map of the ground deformation.The ground is discrete to structural grid firstly；then，the horizontal deformation matrix，incline vector as well as curvature vector of each node in grid can be calculated according to the displacement information of neighbor nodes based on least square method；finally，the deformation fields of the whole ground can be obtained by shape function interpolation to the nodes.Examples show that this method can obtain the maximum deformation value and its direction of each ground point，and form the deformation contour map conveniently.It follows that the method overcomes the shortcoming of the section method，and provides a reasonable and effective means for evaluation of the surface movement caused by underground mining.

Key words: Ground deformation, Least square method, Limit of movement, Horizontal deformation, Incline, Curvature