1、英文原文The new three-dimensional subsidence influencefunction denoted by nkgC. Gonza lez Niciezaa, M.I. A lvarez Ferna ndezaA. Mene ndez D azb, A.E. A lvarez VigilcAbstract：This study presents a three-dimensional development of the n k g influence function with the aim of predicting subsidence phenomen
2、a and characterizing the shape and dimensions of the corresponding trough. The parameters “n” and “k”characterize the ground and “g” is related to the gravity. This function depends on two physical concepts: the first is gravity, which characterizes the forces acting on the ground, and the second, t
3、he convergence of the roof and floor of the mine workings due to the stress state of the ground. Caving in of the roof generates direct subsidence, and the swelling of the floor, indirect subsidence, which allow us to establish the shape of the trough.The physical concepts introduced are fundamental
4、 in the mathematical implementation of the n k g influence function, allowing a more intuitive interpretation of the subsidence trough and notably facilitating the work of calibration, validation and sensitivity analysis. These concepts likewise allow the scope of application of influence functions
5、to be extended to non-horizontal seams, also taking into account the quality of the rock mass and the presence of preferential sliding directions, in both the roof and the floor of the seam.In the development of this paper, we shall first see the physical concepts considered, to then present the thr
6、ee-dimensional implementation of our n k g influence function. We shall see the results obtained when calibrating the proposed numerical model with real data obtained from subsidence measurements in a coalmine in the Coal Basin of Asturias, situated in the North of Spain.Keywords：Subsidence; Influen
7、ce functions; Underground mining1. IntroductionGround subsidence is the movement of the ground due to the loss in sustaining capacity of the sub-soil. In the majority of cases, this is directly related to human activities that either alter the water table or when carrying out deeppit mining of ore.
8、The ground that is above the excavated area is altered, collapses, is partially compacted and progressively subsides as the work of extraction advances.We may speak of two types of mining subsidence depending on its extension. On the one hand, there is localized subsidence, which is concentrated in
9、areas in the proximity of the excavated area and takes the form of a highly localized abrupt depression that is limited in extension. Extensive subsidence, on the other hand, results in the formation of a topographic depression on the surface (subsidence trough) that is more or less regular in shape
10、 and which is directly related to the depth of the excavated areas being exploited in the mine. In these cases, the subsidence is large in the central area and decreases progressively towards the sides, said subsidence being accompanied by horizontal displacement.The movements of the ground produced
11、 by these two types of subsidence may produce damage to buildings,roads, railway lines, oil pipelines or any other infrastructure in the surrounding areas. To estimate,quantify and prevent this damage, models must beestablished that allow us to determine a priori issues such as what the greatest ver
12、tical displacement of the surface of the ground will be and where it will be produced, or what the lateral extension of said subsidence will be.To answer these questions, different numerical methods have been developed in recent years 1 that include methods based on influence functions 2, cross sect
13、ion functions 3, empirical formulas 4, or numerical models based on finite elements or finite differences 5,6.The application of any of these numerical methods to real cases has to be accompanied by the development of three processes: calibration of real data, validation andsensitivity analysis.Cali
14、bration is the process of configuring a numerical model on the basis of the input data on the subsidence registered in the field. It implies executing several models, changing the parameters that characterize the subsidence until the model simulates the real behavior of the ground with the appropria
15、te degree of reliability.Validation is the process of confirming the goodness of the calibration, considering an independent data set to that used as input, which has been obtained subsequent to this calibration.Finally, sensitivity analysis consists in varying the parameters of the proposed mathema
16、tical models, with the aim of estimating how this affects the results. This allows us to determine the most significant parameters and to predict the subsidence that will be produced in the future.Having established these steps, we shall now go on to develop the approach that we have adopted in our work, initially describing the theoretical basis of our method and subsequently applying it to a series of real cases.2. Approach
