两端固支各向同性叠合岩梁受均布荷载的弹性力学解

Elastic solution of clamped laminated rock beam under uniformly distributed load

层间岩体存在着一组优势贯穿结构面,将层状岩体视为叠合岩梁求解力学问题,若只考虑无层间滑动的叠合岩梁并不满足工程实例的实际情况。为此,以软硬岩双层叠合固支岩梁为例,运用弹性力学中应力函数法,推导出叠合岩梁受均布荷载作用时的应力及位移表达式。在此基础上,探讨了软硬岩厚度、组合方式以及层间摩擦对其应力分布的影响,并将计算结果与FLAC3D数值解进行了对比。研究结果表明:水平位移在岩体分层处出现数值"跳跃"现象,垂直位移沿岩体走向呈抛物线变化;软硬岩组合方式对水平应力和剪应力影响较小,两者最大误差与最小误差的差值分别为1.4%和2%,对垂直应力影响较大,其最大误差与最小误差的差值可达8.2%;层厚对三种应力分布影响较小,但应力随着层间摩擦的增大而增大。实例中数值解与弹性理论解最大误差为9.8%,基本吻合,表明理论解析解可信度较高。

There exists a group of advantageous penetrating structure surface in the stratified rock mass.Layered rock mass is regarded as a composite rock beam to solve mechanical problems,if only the composite rock beam without interlayer sliding is considered,it can’t meet the actual engineering situation.Therefore,the soft and hard rock double layered clamped rock beam is taken as an example,using the stress function method in elastic mechanics,the stress and displacement expressions of laminated rock beam under distributed load are derived.On this basis,the influence of the thickness of soft and hard rock,the way of combination and the friction between layers on the stress distribution are discussed,and the calculation results are compared with the FLAC3D numerical solutions.The results show that there is a numerical'jumping'phenomenon in the horizontal displacement at the rock mass stratification,and the vertical displacement is parabolic along the rock mass;the combination of soft and hard rock has little influence on horizontal stress and shear stress,the differences between the maximum error and the minimum error are 1.4%and 2%,respectively,and have great influence on vertical stress,the error can reach 8.2%.The thickness has little influence on the three stress distributions,but the stress increases with the increase of interlayer friction.The maximum error between the numerical solution and the elastic solution is 9.8%,which is in good agreement with the theoretical solution.