摘要
应用后屈曲能量准则建立的平衡稳定模态幅值方程,研究了不同类型层状边坡在分叉点附近的邻域及其溃屈极限长度,探讨了结构分叉后平衡路径的演化途径。研究发现,临空和临气边坡在确定分叉点附近的邻域时,具有相同的表达式,分叉点附近的邻域与岩体材料、结构几何特征及坡角有关;由坡角确定的剖分因子可剖分出各类边坡模态幅值的计算公式;边坡从初始屈曲到后屈曲的变形过程中,模态幅值与载荷间存在着单值的对应关系。研究结果表明,利用突变理论可从另一角度建立坡脚开裂的判据,也可确定边坡的变形模态;具有与尖点突变模型相同数学特点的状态变量,只有当剖分因子改变正负号时,才会从一个状态突跳至另一个状态。
In accordance with deformed specifities of all kinds of bedding rock slope,this paper studied the regions nearby equilibrium bifurcation point, limit lengths of slope buckling failure and evolutions along equilibrium path by using modality amplitude equation of equilibrium stability built on post-buckling energy criterion. It is pointed that for regions nearby bifurcation point, two kinds of bedding rock slope have the same expression, these regions are related to the mass of rock mass, the geometrical properties of side slope and angle of bedding slope; the ripping factor depended on bedding slope angle can give calculation formulas of all kinds of modality amplitude; in the process of side slope deformation from initial buckling to post-buckling, there exists single-valued relation between modality amplitude and load. The results indicate that both catastrophic criterion of crack initiation at bedding rock slope end is derived from another way, and modality of deformation for bedding slope are determined by using catastrophe theory, and the state variate in cusp catastrophe model jumps from one state to the other state only if ripping factor changes its plus-minus.
出处
《长安大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2005年第2期73-76,共4页
Journal of Chang’an University(Natural Science Edition)
关键词
岩土工程
后屈曲
分叉点
模态幅值
尖点突变
剖分因子
geotechnical engineering
post-buckling
bifurcation point
modality amplitude
cusp catastrophe
ripping factor
