Hysteresis Behavior Modeling of Hard Rock Based on the Mechanism and Relevant Characteristics

Abstract

The modeling of cyclic behavior in rock remains a challenge due to complex deformation characteristics. This paper studied the mechanical behaviors of granite samples under uniaxial cyclic loading and unloading through cyclic compression tests and acoustic emission (AE) monitoring. Then, a comprehensive body that consisted of an elastic element, plastic element, and friction element was proposed to describe the stress–strain relationship with respect to cyclic behavior, in which the friction element was connected in parallel with the serial combination of the elastic element and plastic element. Finally, the parameters of the proposed model were calibrated based on the mechanism analysis and backpropagation (BP) neural network. Results show that the behavior during unloading is primarily elastic and is accompanied by the obstruction of friction. During reloading, the behavior changes from elastic to elastic–plastic before and after the Kaiser point. The tangential modulus of the elastic element is dynamic in a linear positive correlation with elastic strain and a linear negative correlation with plastic strain; specifically, the elastic strain controls the variation process of the elastic modulus while the plastic strain determines the lower limit. The constitutive law of the plastic element is expressed by a logistic function, which means that the plastic strain increases in a trend of acceleration–deceleration. The friction element plays a major role in processing the massing effect, and the plastic element is prompted before the historical maximum stress, which reflects the ratcheting effect and Felicity effect. The reliability of the proposed constitutive model is confirmed by the comparison of the simulated stress–strain curves with the experimental curves.

Deformation Behaviour and Damage Evolution of Carbonaceous Phyllite under Cyclic Triaxial Loading

“…The assignment of total input energy during the whole cyclic loading process can be derived by Equation (4); likewise, the assignment of dissipation energy can also be derived by Equation (5). Taking the D10 specimen as an example, the corresponding results with regard to the assignments of U i and U hi are displayed in Figures 19 and 20, respectively.…”

“…However, as the stress level approaches the compressive strength, the damage accumulation exhibits a pattern of deceleration, stabilization, and then acceleration. (5) The damage of a specimen under monotonic loading is dominated by shear behaviour, which implies that the corresponding failure mode is shear failure. By contrast, the specimen under cyclic loading presents macroscopic shear surfaces and crushed grains, which implies that the corresponding failure mode is the combination of shear failure and fatigue failure.…”

“…The area enclosed by the unloading curve of the ith cycle and the loading curve of the i + 1th cycle (the area of hysteretic loop BCB in Figure 18) can be regarded as U hzi , and the remaining area obtained by subtracting U hzi from U hi is U hsi . The expressions of U hsi and U hzi are presented in Equation (5).…”

“…Due to the global economy’s continuous growth and the need to speed up the urbanization process, many engineering facilities related to the geotechnical field are being planned and constructed worldwide [ 1 , 2 ], such as reservoirs, railway tunnels and gas storage caverns, which are often faced with cyclic loading. Cyclic loading often causes the accumulation of internal damage and a reduction in strength with regard to rock [ 3 , 4 , 5 ]. Therefore, studying how cyclic loading affects the deformation and damage of rock is significant to maintain the safety and stability of rock engineering projects.…”