Analytical failure criterion for kink zone instability

ABSTRACT: Considering that dilatancy results directly from the development of kink zone instabilities, an analytical failure criterion is developed by adapting Rowe?s stress-dilatancy model to rotational deformation. Shear resistance through kink zone come principally from the work done against dilatancy. Peak strength calculated with this criterion show similar results to those obtained by experimental direct shear tests and by numerical simulations using UDEC. The main influencing factors on shear strength in this particular failure case are the normal pressure, the rotating slabs initial inclinations and slenderness. The criterion is valid for small normal pressures when there?s no sliding of the rotation axis and no rupture through intact rock.

1. INTRODUCTION

The stability of rock slopes, underground openings and other works in intensely foliated or in jointed rock masses, may be at risk with an unusual failure mode by kink zone instability. This type of instability is developed by buckling instability in brittle, ductile foliated or layered rock. Jointed and fractured rock masses also show the development of kink zone instability as a mode of failure or deformation. Goodman and Kieffer [1] classified this mode of failure as "buckling and kink band slumping". Geomechanical designs of works in jointed and foliated rock masses rarely takes into account such a mode of failure. Physical and numerical studies with models of jointed rock masses [2-7] lead to a better understanding of the critical conditions triggering kink band instabilities in fractured rock masses. This happens under particular condition of loading path, joint pattern geometry, joint relative orientation to the stress tensor, joint spacing relative to their length and the stress level. Very few theoretical studies were dedicated to progressive failure by shear zone and by kink instability. Several models are based on the elastic instability of a foliated medium [8, 9]. Unfortunately these models assume that deformation occurs at constant volume. Such an hypothesis contradict experimental observations showing important dilatancy within kink zones development [6, 10]. Another model uses the mechanics of generalized Cosserat continua to analyze rotationalshearing deformation or "bookshelf mechanism" [11]. Once implemented in a numerical simulation [12], this model predicts the shear strength of rock masses deformed by kink zone instabilitiy. However it is a continuum theory applied to a discontinuous medium and implies an important simplification of the reality. Considering that dilatancy is necessary to the development of kink zone instabilities [10] within jointed and fractured rock masses, this paper proposed an analytical failure criterion developed by adapting Rowe?s stress-dilatancy model [13, 14] to rotational deformation under direct shear conditions.

2. PROPOSED FAILURE CRITERION

2.1. Rowe's stress-dilatancy model Shearing through uniform, non-cohesive rod stacks can be modeled similarly to shearing along an indented surface (Fig. 1). The total shear force, S, may be considered as a sum of three components: (mathematical equation available in full paper)

Where, S1 = component due to external work done in dilating against the external normal force.

(mathematical equation available in full paper)

Figure 1: Shearing along an indented surface. (available in full paper)