A closed form solution is developed to quantify the stresses that develop in polymer liners installed within pressure pipes, where the liner spans across a joint or ring fracture in the ‘host’ pipeline that is subjected to axial extension as a result of ground movements. The solution considers the zones of slip between liner and host pipe on either side of the joint that is opening. The expression derived indicates that maximum axial liner stress is proportional to the square root of the product of the gap that opens across the joint, liner modulus, internal fluid pressure, coefficient of friction between liner and host pipe, and inverse of liner thickness. Calculations are presented for a typical liner installed within a cast iron water pipe, though research is needed to quantify liner-host pipe friction. Comparisons to finite element calculations demonstrated that the new solution characterises the liner as having higher stiffness than numerical analysis using thick shell elements. Initially the two solutions match, but the new closed form solution becomes more conservative with increasing gap size. FEA was then used to show that temporary reductions in water pressure decrease axial liner stresses significantly.

开发了一种封闭形式的解决方案来量化安装在压力管道内的聚合物衬里中产生的应力，其中衬里跨越“主体”管道中的接头或环断裂，由于地面运动而受到轴向延伸。该解决方案考虑了打开的接头两侧的衬管和主管之间的滑动区域。推导出的表达式表明，最大轴向衬管应力与跨接头开口的间隙、衬管模量、内部流体压力、衬管和主管之间的摩擦系数以及衬管厚度的倒数的乘积的平方根成正比。对安装在铸铁水管内的典型衬管进行了计算，但需要研究来量化衬管与主管道的摩擦。与有限元计算的比较表明，与使用厚壳单元的数值分析相比，新解决方案将衬管表征为具有更高的刚度。最初这两个解决方案匹配，但新的封闭形式解决方案随着间隙大小的增加而变得更加保守。然后使用 FEA 表明，水压的暂时降低会显着降低轴向衬管应力。