INTRODUCTION
In the construction of underground openings in complex geological formations the field observations of deformation behaviours during and after excavation are of great importance to verify the stability of the openings and to ensure the safety of the workers. Many different types of in-situ measurements have been and are being proposed and developed. Among the various kinds of instrumentation the displacement measurements done by convergence meter and borehole extensometer are simple and reliable compared with the stress measurements.
The failure criterion of a material is usually given in terms of stress. Therefore, in order to give a quantitative interpretation to the results of displacement measurements, the stress distributionaround the opening must be back-analyzed from the measured displacements, and compared with the failure criterion to assess the stability of the opening. This back-analysis of stress, however, is questionable inaccuracy as well as reliability because it requires knowledge of the stress-strain relationship of in-situ rock and soil which cannot be easily determined.
Considering such a shortcoming involved inthe interpretation of displacement measurements, the author proposes herein a direct interpretation method. According to the proposed method, an evaluation of the stability of the opening can be carried out directly from the measured displacements without analyzing the stress distribution. The method is based on the concept of strain rather than stress at failure, so that it does not require any stress analysis.
Let us consider that the displacements are measured at several points in the surrounding media, a continuous displacement function can be assumed so as to interpolate the measurements among measurementpoints. The strain distribution can then be derived by taking derivatives of the displacement function considering the relevant kinematic relationships in continuum mechanics. Comparison of the derived strain withthe allowable value of strain at failure makes it possible to assess the stability of the opening. If the derived strain tends to be greater than the allowable strain, an artificial support such as steel ribs aswell as rock bolts and sprayed concrete must be added to achieve the stability of the opening.
STRAIN DERIVED FROM DISPLACEMENT MEASUREMENTS
Let us consider the displacements aroundthe openings measured at certain points. In Fig.1 the points numbered 1 to 20 denote the measurement positions. The displacements in the region surrounded by the measurement points (shaded regions as shown in Fig.1)can be interpolated in terms of the measured displacements. In this paper the region surrounded by the measurement points is called the "element".
Fig.1 Measurement points around a opening (Available in full paper)
The shape of an element can be expressed in terms of interpolation functions and the coordinates of the measurement points, i.e., (Mathematic Equation)(Available in full paper) where Pi ( ¿,¿ ) i=l to N is the interpolation function in terms of the curvilinear coordinates ¿ and ¿. X,i and yi are, respectively, the x and y coordinates of measurement points i, and N is the total number of measurement points for the element.
If we assume an isoparametric element proposed by Zienkiewicz 1), the displacements in an element are expressed in terms of the same interpolation functions as for the shape function of an element
