对边坡失稳潜滑带为两种介质的尖点突变模型研究的讨论

对将潜滑带假定为仅具弹性和兼具弹性、硬化和软化特性2种介质构成的边坡失稳问题归结为尖点突变模型研究的逻辑和结果进行分析后指出:坡体为刚体、潜滑带由上述2种介质构成的边坡失稳模型中无大量弹性能瞬间释放和突滑机制,不能与尖点突变平衡曲面上状态变量从一叶跃到另一叶的伴随大量能量释放的行为相对应;该边坡失稳模型势函数中只有①区段的弹性参数,而没有①区段残余强度参数,不能用于讨论边坡失稳、下滑问题;尖点突变平衡曲面上,状态变量可以上跃和下跃,且上跃到下跃处的参数滞后以及上、下叶的系统状态可以循环往复实现是尖点突变的基本特性。边坡失稳不可逆,既不能反向跳跃(即失稳下滑后边坡又突然恢复原状),又没有滞后特性,不能将尖点突变作为边坡失稳原型的数学模型。

DISCUSSION OF RESEARCH ON CUSP CATASTROPHE MODEL OF SLOPE FAILURE WITH POTENTIAL SLIDING ZONE COMPOSED OF TWO MEDIA

The logic and result that slope failure problem has been summed up as cusp catastrophe model research have been analyzed；and the potential sliding zone is supposed to be composed of two media only with characteristic of elasticity and with characteristics of elasticity，hardening and softening. Furthermore，it is pointed out that when slope is rigid body and potential sliding zone is composed of foregoing two media，there are not plenty of elastic energy instantaneous release and abrupt sliding mechanism in the slope failure model，which can not correspond to the action that on cusp catastrophe equilibrium curved surface there are plenty of energy release concomitant with state variable jumping from one sheet to another. The potential function of this slope failure model can not be applied to discussion of the problems about slope failure and slide，because there is only elastic parameter without residual strength parameter of section ① in it. On cusp catastrophe equilibrium curved surface，there are many basic characteristics of cusp catastrophe，such as state variable can jump upward and downward，the parameter of jumping upward lags behind that of jumping downward and system state of upper-lower sheets realize cyclically. The slope failure is irreversible，not only it can not jump backward，i.e. slope recovers original state abruptly again after its failure，but also it has no lag characteristic. Hence，cusp catastrophe can not be used as the mathematical model of slope failure prototype.