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Rock Stability
Solution procedure
For each rock block resting on the polygonal slip surface the program applies the basic equation of the stability of rock slope sliding along the plane slip surface as:
| where: | R | - | resultant of all active forces |
| k1 ,k2 | - | coefficients depending on slope gradient, inclination of anchor force, angle of internal friction and factor of safety | |
| c | - | cohesion on slip surface | |
| G | - | weight of a rock body in danger of sliding |
such that the resultant of all active forces is assumed as an unknown interaction force Ki between rock blocks (see figure). If, apart from interaction force, the i-th rock block is further loaded by other external forces, it is possible to write the interaction force of the i-th block in the form:
| where: | ci | - | cohesion on slip surface of i-th block |
| Gi | - | weight of i-th rock block | |
| PiG | - | overall external force acting on i-th block in vertical direction | |
| PiK | - | overall external force acting on i-th block in the direction of interaction force | |
| KiG | - | magnitude of interaction force on i-th block in vertical direction | |
| KiK | - | magnitude of interaction force on i-th in the direction of K | |
| k1i | - | coefficient depending on gradient of slip surface α, gradient of external loading βi, stability of rock slope and angle of internal friction φi | |
| k2i | - | coefficient depending on gradient of slip surface α, gradient of external loading βi, stability of rock slope and angle of internal friction φi |
By combining the above forces it is possible to implicitly express the gradient of interaction force Ki of the i-th block as:
| where: | δi | - | gradient of interaction force Ki of i-th block |
| ci | - | cohesion on slip surface of i-th block | |
| Ai | - | slip surface of i-th rock block | |
| Ri | - | interaction force on i-th block | |
| F | - | ratio of maximal shear resistance and acting shear force | |
| φi | - | angle of internal friction on slip surface of i-th block |
Forces acting on slip surfaces between blocks (internal slip surfaces)
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