Thermally-Induced Wedging–Ratcheting Failure Mechanism in Rock Slopes

Abstract

A thermally induced wedging–ratcheting mechanism for slope stability is investigated using a large-scale physical model and using a three-dimensional version of the numerical Distinct Element Method (3DEC). The studied mechanism consists of a discrete block that is separated from the rock mass by a tension crack filled with a wedge block or rock fragments. Irreversible block sliding is assumed to develop down a gently dipping sliding plane in response to climatic thermal fluctuations and consequent contraction and expansion of the sliding and wedge block materials. A concrete block assembly representing the rock mass is placed in a specially designed climate controlled room. An integrated measurement system tracks the block displacement and temperature evolution over time. Results of the numerical 3DEC model and an existing analytical solution are compared with the experimental results and the sensitivity of the numerical and analytical solutions to the input thermo-mechanical parameters is explored. To test the applicability of our physical and numerical models to the field scale, we compare our numerical simulations with monitored displacements of a slender block that was mapped in the East slope of Mount Masada, as up until recently the governing mechanism for this block displacement has been assumed to be seismically driven. By application of our numerical approach to the physical dimensions of the block in the field we find that, in fact, thermal loading alone can explain the mapped accumulated displacement that has surpassed by now 200 mm. We believe this new, thermally-induced, failure mechanism may play a significant role in slope stability problems due to the cumulative and repetitive nature of the displacement, particularly in rock slopes in fractured rock masses that are exposed to high temperature oscillations.

Appendix 1

We derive here the maximum sliding force required to reach limit equilibrium along the sliding surface (F_max). Consider the free body diagrams for the sliding and wedge blocks as shown in Fig. 18 in Appendix 1.

Fig. 18

a Free body diagrams of the sliding and the wedge blocks, b force polygon on the wedge block

The driving forces acting on the sliding and the wedge blocks are:

$$W_{1} \sin \eta _{1} + W_{2} \sin \eta _{1} + F_{{\max }}$$

(6)

The resisting friction forces parallel to the sliding plane are f₁ and f₂. In order to find f₂, consider the force polygon in Fig. 18 in Appendix 1 showing the weight of the wedge W₂ and the reactions along the wedge faces R and T:

$$\frac{{W_{2} }}{{\sin (90 - \eta _{2} )}} = \frac{T}{{\sin (90 - \eta _{1} )}} \Rightarrow T = W_{2} \frac{{\cos \eta _{1} }}{{\cos \eta _{2} }}$$

(7)

The friction force due to the reaction T, is:

$$f_{{\text{T}}} = T\tan \phi = W_{2} \frac{{\cos \eta _{1} }}{{\cos \eta _{2} }}\tan \phi$$

(8)

The component of f_T parallel to the sliding plain, is:

$$f_{2} = f_{{\text{T}}} \cos \eta _{2} = W_{2} \cos \eta _{1} \tan \phi$$

(9)

Therefore, the total resisting frictional forces parallel to the sliding plane are:

$$f_{1} + f_{2} = W_{1} \cos \eta _{1} \tan \phi + W_{2} \cos \eta _{1} \tan \phi$$

(10)

From limit equilibrium parallel to the sliding plane, we obtain the magnitude of F_max:

$$F_{{\max }} = W_{1} \cos \eta _{1} \tan \phi + W_{2} \cos \eta _{1} \tan \phi - W_{1} \sin \eta _{1} - W_{2} \sin \eta _{1}$$

(11)

Inserting the blocks weights:

$$W_{1} = L_{{\text{b}}} H_{{\text{b}}} \gamma ;\,\,W_{2} = \frac{{L_{{{\text{w}}1}} + L_{{{\text{w}}2}} }}{2}H_{{\text{W}}} \gamma$$

We get:

$$F_{{\max }} = (L_{{\text{b}}} H_{{\text{b}}} \gamma )\left( {\cos \eta _{1} \tan \phi - \sin \eta _{1} } \right) + \frac{{L_{{{\text{w}}1}} + L_{{{\text{w}}2}} }}{2}H_{{\text{W}}} \gamma \left[ {\cos \eta _{1} \tan \phi - \sin \eta _{1} } \right]$$

(12)

$$F_{\max } = \gamma \left( {\cos \eta_{1} \tan \phi - \sin \eta_{1} } \right)\left[ {L_{{\text{b}}} H_{{\text{b}}} + \frac{{L_{{{\text{w}}1}} + L_{{{\text{w}}2}} }}{2}H_{{\text{w}}} } \right]$$