Creep behavior of carbonaceous mudstone under triaxial hydraulic coupling condition and constitutive modelling

Understanding the hydraulic coupling creep mechanical behavior of carbonaceous mudstones and their macro and micro fracture mechanisms is important for rock engineering design and predicting the long-term evolution of the Earth's crust. In this study, triaxial hydraulic coupling creep tests were conducted on carbonaceous mudstone, and the damaged rock samples were scanned by electron microscopy to analyze the mechanical behavior of hydraulic coupling creep and the macro and micro fracture mechanisms of carbonaceous mudstone. Then, the permeability of carbonaceous mudstone was calculated and the permeability evolution with time was obtained. Finally, to describe the hydraulic coupling creep characteristics, the damage variable was introduced into the viscoelastic and viscoplastic processes with the use of variable-order fractional calculus, and a hydraulic coupling creep model based on variable-order fractional derivative was developed. The experimental results show the following. (1) With increasing osmotic pressure, the instantaneous strain steadily increases; however, the growth rate gradually slows down and finally tends to be stable. The creep strain increases with increasing osmotic pressure; however, under high osmotic pressure, the pressure solution effect is stronger, which makes the creep strain exhibit obvious fluctuations. (2) Tensile and shear fractures are two main types of macroscopic and mesoscopic fractures in carbonaceous mudstone. (3) The permeability change with time during creep of carbonaceous mudstone can be roughly divided into three stages: I-slowly decreasing, II-slowly increasing, and III-rapidly increasing. The regions before and after the expansion point correspond to phase I and phases II and III, respectively. (4) This model accurately describes and predicts the whole creep process under the combined action of seepage stress, and has six model combination units with a simple combination form.