Engineering Rock Mechanics

384 Design and analysis of underground excavations

The design objective is to study the form of the ground response curve for
any particular situation, and develop the support methods accordingly. We
now discuss how to produce a ground response curve.

Development of a ground response curve. Consider the mechanical behav-

iour of the rock round a circular excavation in a hydrostatic stress field. We

model the material first as an idealized elastic-brittle-plastic material, as

shown by the complete stressstrain curve illustrated in Fig. 20.26. The

associated relation between the major and minor principal strains and the

related volumetric strain are also shown in the figure.

From the data in the figure, a ground response curve can be constructed

by the following steps:

(a) substitute successive values of pi into equation (2) to obtain a series of

(b) substitute re into equation (4) with r = a to obtain values of rj;

(c) plot values of pi against corresponding values of Si = -ui to obtain the

ground response curve;

(d) the critical support pressure below which a fracture zone develops is

given by equation (1);

(e) this procedure applies to the sidewalls. More support pressure is

required to limit the measured displacments to these calculated values

in the roof, and less in the floor. The roof and floor ground response

curves are found from

values for re;

Displacement at elastic-plastic interface (r = re):

Ure = - -@ -P I)'e

2G

General displacements:

(3)

Figure 20.26 Material behaviour assumed in development of the ground response

curve, and the related equations.