摘要
基于Biot波动理论,运用Laplace变换和波函数展开法,得到瞬态弹性波入射条件下饱和土体及圆柱形衬砌的位移应力表达式。利用饱和土体与衬砌结构的连续条件和衬砌结构内边界上的应力自由条件确定表达式中的未知系数。利用Laplace逆变换的数值方法给出了问题的数值解。研究了衬砌结构的动应力集中系数的波型特性及材料剪切模量和衬砌厚度对动应力集中系数的影响。结论表明随着阶数n的增大波型明显衰减;土体较衬砌结构软时动应力集中系数越大;衬砌结构厚度越大动应力系数越小。
Based on the Biot＇s dynamic theory,the expressions of displacements,stresses and pore pressures in saturated soil,and those of displacements and stresses on cylindrical lining in transient elastic wave condition are obtained by using the method of Laplace transform and wave function expansion.Employing the inner boundary stress free condition of the lining and the continuity conditions between the soil and the lining,the unknown coefficients in the expressions are determined.With the inverse Laplace transform,the numerical solution of the problem is presented.The wave pattern properties of dynamic stress concentration factor on the lining and influence of different shear modulus of material and thickness of lining on the dynamic stress concention factor are studied.The results show that the wave type demonstrates damping with the increase of the order n.The value of dynamic stress concentration factor is lower with the increase of the lining thickness and larger when the shear modulus of the lining is larger than that of the soil.
出处
《西北地震学报》
CSCD
北大核心
2012年第4期324-330,共7页
Northwestern Seismological Journal
基金
国家自然科学基金项目(50878155
51178342)
高等学校博士学科点专项基金项目(201037181200005)
