At high levels of normal stress, an ‘equality point’ is reached when the shear strength of a rock joint approaches that of the rock material. This point can provide a valuable reference in the development of empirical relations for rock joint strength. Several writers have given methods of estimating this ‘equality point’. The different results produced from the application of these methods are compared from the viewpoint of practical consequences.

Au niveau eleve de contrainte normal un ‘point d'egalite’ est atteint quand la resistance au cisaillement d'une diaclase rocheuse se rapproche de celle d'une matrice rocheuse. Ce point peut fournir une reference precieuse dans le development des relations empiriques de la puissance de la disclase rocheuse. Plusieurs ecrivains ont dejà donne le procede de calculer ce ‘point d'egalite’. Les differents resultats provenant de l'application de cette methode sont d'un point de vue compares aux consequences pratiques.

Wenn die Normalspannung hohe Werte andeutet wird eine ‘Gleichheitspunkt’ erreicht wobei die Scherfestigkeit einer Felakluft diejenige des urspruenglichen Festgestein annahert. Dieser Punkt kann eine wertvolle Rolle spielen bei der Entwicklung von empirischen Verhaltnissen fuer die Festigkeit der Felskluft. Methoden fuer die Bewertung dieser ‘Gleichheitspunkt’ werden schon von mehreren Experten beschrieben. Die praktischen Konsequenzen, die aus einea Vergleich der verschiedenen Ergebnissen bei der Anwendung der obergennanten Methoden folgen, werden gezeigt.

In developing empirical relations for the shear strength of rock joints, Gerrard (1986) has emphasised the need to incorporate the physical constraints that apply at very low and very high levels of normal stress. When the normal stress approaches zero, the peak angle of dilation will be maximal and the total peak friction angle will consist of the sum of this dilation angle (Ψ) and the basic friction angle (b). At the other extreme, when the normal stress reaches a sufficiently high value, Ladanyi and Archambault (1970, 1980) suggest that the shear strength of the joint will approach that of the rock material at the ‘equality point’. This high level of normal stress is referred to as the ‘equality stress’. The ‘equality stress’ falls well outside the stress range of interest in practical rock mechanics applications, in most cases being well in excess of the uniaxial compressive stress(c). However, it does enable the position, and to a large extent the slope, of the *τ-σ* strength envelope for the rock joint to be fixed for the extreme case of highly elevated stress. In addition, when taken together with the constraints that apply to the location and slope of this envelope at very low levels of normal stress, it provides the opportunity to make an ‘educated’ interpolation into the practical stress range. This is shown in Figure 1 where the ‘equality point’ and the corresponding ‘equality stress’, f, for the shear strength envelope of a typical rock material (τ m) are marked. In addition, the constraints for *σ →* o are shown together with the interpolated shear strength envelope for the rock joint (τj). The estimation of the position of the ‘equality Point’ can be approached in two stages:

definition of the line that represents the shear strength envelope for the rock material, and

determination of the location alone this line that represents the ‘equality point’.

These two stages are discussed in subsequent sections of this paper. By drawing attention to the location of the ‘equality point’ this paper provides a necessary prerequisite to the further development of empirical relations for the shear strength of rock joints.

A comprehensive analysis of the data for the shear strength of rock material has been conducted by Hoek and Brown (1982). They found that, to a reasonable degree of approximation, the range of rock types could be grouped into five categories, referred to here as Groups I to V. For each group the shape of the failure envelope is independent of the uniaxial compressive strength, c. The physical significance of the quantity q is that it is equal to the value of the relative shear strength (τ*) corresponding to a relative normal stress *(σ*)* of I-t*. The exponent p has the effect of altering the curvature of the shear strength envelope, with increases in p producing an increased tendency toward linearity. The above points ate illustrated in Figure 2 where the values of q and t* are fixed and the effect of varying the exponent p is shown. Group I rocks consist of carbonate rocks with well developed crystal cleavage (e.g. dolomite, limestone and marble) and have the values of q(0.816), p(0.658), and t*(0.140). At the other extreme, Group V rocks are represented by coarse-grained polyminerallic igneous and metamorphic crystalline rocks (e.g. amphibolite, gabbro, gneiss, granite, norite, and quartzdiorite). The corresponding values of the parameters are q(1.220), p(0.705), and t* (0.040).