岩体黏弹性蠕变计算的高阶数值流形法研究

Study of high-order numerical manifold method in viscoelastic creep of rock mass

数值流形法(numerical manifold method)是一种新型的数值计算方法,已成功应用于岩土工程的诸多领域,但该方法尚未应用于岩土工程蠕变分析。近年来对高阶流形法的研究表明,对复杂的岩土工程问题,使用高阶覆盖函数可明显提高流形法的计算精度。为此,开展了用高阶流形法模拟蠕变的研究,在高阶流形法中引入"时步-初应变"法计算蠕变,以广义开尔文体为基础,推导了相关的计算公式,并编制了相应的计算程序,同时还通过算例,验证了方法的可行性和合理性。结果表明,高阶流形可以方便地与"时步-初应变"法结合用于蠕变计算,可较好地模拟蠕变变形。算例分析表明,在不改变网格密度情况下,仅通过采用高阶覆盖函数,高阶流形法可大幅提高传统流形法的计算精度。

The numerical manifold method is a new developed numerical method and has been used in many fields of geotechnical engineering.But there is no research on numerical manifold method in creep.In recent years,the study of high-order manifold method shows that using high-order cover function could improve accuracy of manifold method in complex geotechnical engineering.The research on high-order numerical manifold method in creep is presented.The ＂time step-initial strain＂ method is combined with high-order numerical manifold method to simulate the creep of rock.Based on generalized Kelvin model,some relation equations are given;and a new code is developed.Some examples are used to check the feasibility and rationality of the method.The result shows that the high-order numerical manifold method could simulate the creep of viscoelastic rock very well combining with ＂time step-initial strain＂.It can improve accuracy of the solution only by using high-order cover function but without changing the mesh density.