边坡全长黏结锚杆自由振动特性分析

Characteristic analysis of full-length grouted anchor in slope under free vibration

假定锚杆及周边岩土体均视为连续均质的线性弹性体,锚杆与周边岩土体之间相互作用采用一线性弹簧和线性阻尼壶平行耦合方式模拟,以此建立了边坡全长黏结锚杆锚固系统自由振动力学模型,获得了锚固系统特征参数及对应振型计算公式,通过算例,结合他人锚杆锚固系统连续模型,对比验证了本文理论计算公式的可行性;指出边坡全长黏结锚杆锚固系统振动控制方程等式只可能小于零,振型函数共有三种类型,均对应三角函数型,按指数规律衰减的非周期蠕动,其中Ⅰ阶最小特征参数λ值对应第2类振动形式,之后振动类型1和2交替出现,类型1比类型2衰减特性明显,第3类特殊振动只有在锚固系统内部物理力学参数满足一定条件才能发生;各阶锚固系统特征参数λ中,对应第2类振型的λ对锚固系统的动力力学响应影响较大,尤以Ⅰ阶最为突出。开展此项研究,可为边坡锚杆锚固系统动力分析及锚固工程防灾减灾提供理论支撑,均具有重要的理论和实践意义。

Anchor and its surrounding rock / soil mass are assumed as continuous homogeneous linear elastic materials.The interaction between anchoring section and its surrounding rock / soil mass is simulated using the Kelvin-Voigt model by coupling a purely viscous damper and a purely elastic spring in parallel. According to the assumptions,the dynamic mechanical model was established for the full-length grouted anchor in slope under free vibration. The calculation formulas of characteristic parameter λ and the corresponding vibration mode for anchorage system were deduced.Compared to another method for the continuous model of anchorage system,the feasibility of the present theoretical calculation formulas was verified based on a specific example. It was found that the vibration control equation for the fulllength grouted anchor in slope can only be less than zero,the vibration functions can be categorized into three types,which all correspond to the trigonometric functions and follow the aperiodic peristalsis in accordance with exponential attenuation. The smallest characteristic parameter λ of order Ⅰ corresponds to the type 2 mode of vibration,and after that,the vibration types 1 and 2 may appear alternately,but the attenuation characteristics of type 1 is more obvious than that of type 2. Nevertheless,the type 3 mode happens only when the physical and mechanical parameters of anchorage system meet certain conditions. Among those characteristic parameters λ,the ones corresponding to type 2 mode of vibration have greater influences on the dynamic mechanical response of anchorage system,especially for orderⅠ. Therefore,it is of great theoretical and practical significance to carry out the characteristic analysis of full-length grouted anchor in slope under free vibration. The research can provide theoretical support for the dynamic analysis of slope anchorage system and for the disaster mitigation in anchorage engineering.