Abstract: Based on the elasticity viscoelasticity correspondence theory and the acquired elastic solution, assuming the formation obey the Kelvin viscoelastic constitutive relation, the theoretical solution of casing loads in rheological formation in tectonic field and the analytic expression of relaxation time are obtained. The results indicate that the casing load in tectonic field changes with time and it exists a critical time in which the casing load has the most value. The viscoelastic solution is coincidence with corresponding elastic solution when the time is long enough. The casing tectonic stress load defined by elastic solution is slightly less than the maximum pressure subjected by casing pipe in rheological formation. Therefore, the elastic computation load or safety coefficient should be increased properly in design to ensure the safety of the casing pipe.

Key words: rheological formation, elasticity viscoelasticity correspondence theory, tectonic stress, casing loads, analytical solution

摘要： 利用求解线性粘弹性问题的弹性粘弹性对应性原理，利用已有的弹性解，求得了考虑地层符合Kelvin流变规律的情况下，地应力场中套管载荷的理论解，并给出了松弛时间的解析表达式。研究表明，流变地层地应力场中套管载荷随时间变化，存在一临界时间，使得套管载荷有最值，当时间足够长时，粘弹性解与相应的弹性解一致。用套管弹性解定义的套管地应力载荷，稍低于流变地层中套管所受最大压力。因此在设计时，或者将弹性计算载荷适当增大，或者将安全系数适当增大，以保证套管安全。

关键词: 流变地层, 弹性粘弹性对应性原理, 地应力, 套管载荷, 理论解