深埋引水隧洞对应力波的散射与动应力集中  

Scattering of stress wave and dynamic stress concentration for deep diversion tunnel

作　　者：陶明[1] 向恭梁 赵瑞 TAO Ming;XIANG Gongliang;ZHAO Rui(School of Resources and Safety Engineering,Central South University,410083 Changsha,China)

机构地区：[1]中南大学资源与安全工程学院,长沙410083

出　　处：《应用力学学报》2022年第5期859-868,共10页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金资助项目(No.12072376)。

摘　　要：应力波在地下结构中的散射而引起的动应力集中是导致深部岩体损伤失稳的重要因素,运用波函数展开法,推导了无限空间弹性介质中充满流体的圆形衬砌硐室在平面P波作用下的解析解,分别分析了弹性和刚性衬砌对硐室周围动应力集中的影响;在稳态响应的基础上,将半正弦波作为入射函数,引入δ(x)函数和Heaviside阶跃函数结合傅里叶积分变换,得到了瞬态P波作用下充满流体圆形衬砌硐室周围动应力的解析解,分析了波长和时间对动态响应的影响。进一步通过有限元程序LS-DYNA模拟了瞬态波作用下衬砌与围岩的应力分布。结果表明:数值模拟结果与理论计算一致,波形参数、衬砌的厚度、材料的弹性模量对动态响应有不同程度的影响,增加衬砌厚度和适当调整衬砌材料的刚度能够起到更好的支护效果;在瞬态扰动下,围岩和衬砌中既会造成较大的压应力集中,又会出现拉应力持续时间较长的现象。The dynamic stress concentration ascribed to the scattering of stress wave encountering underground structures is an important factor affecting the damage of deep rock mass.The analytical solution of a circular lined tunnel filled with fluid in an infinite elastic medium subjected to a plane P wave was derived based on the wave function expansion methods.The influence of an elastic and rigid lining on the dynamic stress concentration around the tunnel was investigated,respectively.Moreover,the analytical solution of the transient P wave with Fourier integral transformation was obtained based on the state-steady response.Theδ(x)function and Heaviside step function are introduced to simplify the integral computation.Taking the unit of a half sin wave as an incident function,the influence of wavelength and time on dynamic response was analyzed.Further,the distribution of dynamic stress of lining and surrounding rock was simulated by the finite element program LS-DYNA.The results indicate that the numerical simulation results are consistent with theoretical calculations.Waveform parameters,lining thickness and elastic modu lus of lining materials have different effects on dynamic response,increasing the lining thickness and properly adjusting the stiffness of lining materials can play a better supporting effect.The peak value of dynamic stress concentration appears in the vertical incident direction and the value of the dynamic stress concentration factor along the incident direction is 0 or negative.Under the action of transient disturbance,which will not only cause large compressive stress concentration in surrounding rock and lining,but also occur the phenomenon of the duration of tensile stress is long.

关 键 词：平面P波 圆形衬砌隧洞 流体 动应力集中 瞬态响应 数值模拟 

分 类 号：TV223.1[水利工程—水工结构工程]