Catastrophe Theory Applied Research In The Anti-dumping Rock Slope Stability Evaluation

The stability of slope is always of great concern in the field of geotechnical engineering. With the high speed of growth of modem economy, the height of excavated slope is higher and higher, the geologic conditions are more and more complicated, and what is more, landslide and collapse frequently occurred in recent years, so the assessment of slope stability is getting more and more important. In the past people always emphasized on those slopes which have obvious structured weak discontinuities such as down-inclined slope when they are studying on slopes' stability, and they traditionally think that those up-inclined slopes which don't have controlling structured discontinuities are stable, so the latter is often ignored. Many engineering cases and geological process of landslides indicate that up-inclined slopes' failure has a large proportion in all failure examples, whose failure takes on characteristics of unobvious boding, good concealment, bursting and calamity. The deformation of slope is a gradual changing process, and failure will occur when it grows to some degree, which is a process of catastrophe. Catastrophe theory which belongs to nonlinear science mainly describes the catastrophe behavior of nonlinear system at critical point using quantitative method. This paper tries to assess rock slope's stability with catastrophe theory. A cusp catastrophe model is presented for buckling-tearing failure which is the most popular failure kind of up-inclined rock slope. Corresponding geological and mechanical models are also developed. Sufficient and necessary condition of failure is derived basing on potential function of system and the factor of safety is defined combining with present slope stability standard. At the same time, a visual programme is coded using computer language of Visual Basic.Studying on engineering examples has revealed that assessing the stability of up-inclined rock slope with catastrophe theory is applicable. We can derive sufficient and necessary condition of failure quantitatively. With the programme which has been coded, we can assess the stability of slope only when we get some necessary parameters of the slope. This can give reference to design and hazard evaluation in practice.