Calculation of mining subsidence and ground principal strains using generalised influence function method G. Ren*, J. Li and J. Buckeridge A generalised influence function method is introduced using tabulated weighting factors in subsidence calculation. Tabulated weighting factors have the advantage of being more flexible than having to find a mathematical influence function. The values of weighting factors can be readily adopted either using a local observational database if available, or a published data source. The flexibility and adoptability of the method is demonstrated through a case study with subsidence contours, movement vectors and principal strains. It is also demonstrated that the method is a valuable tool in assessing subsidence effects on surface structures and utilities. Keywords: Mining subsidence, Influence function, Subsidence prediction, Subsidence effect, Subsidence factor, Angle of draw, Excavation Introduction The accurate prediction of ground movements asso- ciated with underground mining is essential for assessing surface damage and effective damage pre- vention. Various methods can be used for predicting mining subsidence and horizontal movements, includ- ing physical and numerical modelling methods, proﬁle function and inﬂuence function methods. 1 Of these numerous prediction methods, the inﬂuence function method is increasingly favoured due to its ﬂexibility and adoptability with computer programming. 2 Various mining conﬁgurations including irregular shaped panels, multiple extraction seams, inclined coal deposits and sloping ground can be taken into account using the inﬂuence function method. 3,4 The inﬂuence function method can be calibrated to suit local mining conditions to achieve better analytical results as demonstrated by Sheorey et al. 5 Ren et al. 6 suggested that the angle of draw, inter alia, is inﬂuenced by the strength of the overburden strata. The angle of draw deﬁnes the extent of the underground extraction at the ground surface. In the application of the conventional inﬂuence function method, it is usually necessary to use a predeﬁned inﬂuence function, which is a mathematical expression, to deﬁne the weighting factors. This paper presents a generalised inﬂuence function approach which makes use of weighting factors in a tabular form for subsidence calculations. Mining subsidence prediction using influence function method The inﬂuence function method used in subsidence prediction is based on the assumption that the effect of an underground extraction on the surface follows a prescribed mathematical expression, i.e. the inﬂuence function depends on the spatial relationship between the locations of the underground extraction and the surface point in question. This is illustrated in Fig. 1, where an underground extraction element creates a subsidence trough at the surface. The proﬁle for the subsidence trough can be prescribed by an inﬂuence function (Fig. 2), which can be expressed mathematically. A general form of an inﬂuence function may be expressed as k z 5f(x), where x can be either the zone angle h or as the radial distance r from the centre of the subsidence trough (see Fig. 2). A number of inﬂuence functions have been proposed by researchers, such as Bals, Sann, Ehrhardt and Sauer which were summarised by Kratzsch: 7 Bals’ inﬂuence function k z ~ cos 2 h (1) where h is the zone angle (see Fig. 2) Sann’s inﬂuence function k z ~2 : 256 1 r e {4r 2 (2) Ehrhardt and Sauer’s inﬂuence function k z ~0 : 1392e {0 : 5r 2 (3) where r is radial distance from centre of subsidence trough (see Fig. 2). School of Civil, Environmental and Chemical Engineering, RMIT University, GPO box 2476V, Melbourne 3001, Australia *Corresponding author, email gang.ren@rmit.edu.au 34 ß 2010 Institute of Materials, Minerals and Mining and The AusIMM Published by Maney on behalf of the Institute and The AusIMM Received 15 July 2009; accepted 9 March 2010 DOI 10.1179/037178410X12698490396994 Mining Technology 2010 VOL 119 NO 1