考虑治理荷载作用时井壁严格轴对称变形分析

为了研究约束内壁法治理井筒的力学效果,对特殊地层中井壁内侧处于约束状态的立井建立了严格轴对称弹性分析方法。通过线性叠加原理将相应应力边界分解为对称及反对称部分,利用两个子问题的对称性质,选择适当的级数形式的Love应力函数,应用双重级数展开法,侧面采用Fourier级数展开,端部采用Fourier-Bessel级数展开,通过对比正交系数的方法建立待定系数的方程组,联立求解方程组后获得了井壁满足所有侧面及端部边界条件的弹性解答。针对某井筒约束内壁治理给出算例,并应用第四强度理论研究了井壁的安全性,结果表明:约束段井壁内缘附近在约束后相当应力减小,安全性得到了有效的提高。

Strict axisymmetric deformation analysis of shaft linings considering shaft-curing load

For the mechanical effect of restricting inside linings to cure shafts,the strict axisymmetric deformation analysis method was established for the shafts under restricted state in special strata.The problem was divided into symmetrical and antisymmetric parts.Proper progressional form of Love stress function was selected by using the symmetic characters of each subproblem.The double series expansion method was applied.The lateral boundary was expanded in Fourier series while the end boundary was expanded in Fourier-Bessel series,and equations were established by comparing coefficients of the above series.Elastic solution of shaft linings under arbitrary axisymmetric lateral and end stress boundary was obtained by solving these equations.An example was presented for using restricting method to cure shaft linings,and the fourth strength theory was applied to study the security of the shafts.It was shown that the equivalent stress of the inner shaft part within the restricted area was decreased after restriction,and the shaft security was improved effectively.