Damage Creep Model of Viscoelastic Rock Based on the Distributed Order Calculus

Abstract

In this paper, the distributed order calculus was used to establish a creep damage theoretical model to accurately describe the creep properties of viscoelastic materials. Firstly, the definition and basic properties in math of the distributed order calculus were given. On this basis, the mechanical elements of the distributed order damper were built to describe the viscoelastic properties. Then, the distributed order damper was introduced into the three-parameter solid model to establish the distributed order three-parameter solid model. The inverse Laplace transform derived the operator’s contour integrals and the path integrals along Hankel’s path. The integral properties were analysed. Next, the creep properties and relaxation characteristics of the distributed order three-parameter solid model were studied in detail. Finally, taking the rock materials as an example, the distributed order damage damper model was established. Its operator integrals were calculated, and the properties were discussed. Meanwhile, taking the integer-order Nishihara model as the standard, the distributed order damage creep combined model of the rock mass was constructed. The calculation examples were given to study the damage creep properties of the rock mass.