A strain-based fatigue damage model for naturally fractured marble subjected to freeze-thaw and uniaxial cyclic loads

The naturally fractured rock in the open pit slope is susceptible to irreversible damage caused by fatigue loads related to freeze-thaw weathering, blasting vibration, earthquakes and tramcar traffic. To ensure the safety of rock mass and reveal how natural fracture affects the damage modelling characteristics is of great concern. Hence, this work aims at investigating the fatigue damage evolution of rock from volumetric deformation caused by F-T and cyclic loads. The rock structural deterioration and damage accumulation were investigated as well as the stimulated natural fracture pattern. Results show the frost heaving force acted on natural fracture results in the rock volumetric changes. The damage variable expressed by volumetric strain presents a linear relationship with freeze-thaw cycles. In addition, the axial, lateral and volumetric strain of marble exposed to cyclic loads present a two-stage pattern, they first increase quickly and then get to steady and last for a long time. A new fatigue damage model was established by considering the freeze-thaw damage and mechanical damage simultaneously. The proposed coupling damage model can well describe rock damage accumulation. Moreover, the CT images further reveal the influence of the natural fracture on rock volumetric deformation and the final damage accumulation. It is suggested that the opening-mode natural fractures contribute a lot to rock freeze-thaw deformation and fatigue deformation.

A Mathematical Model of the Expansion Evolution of Magnesium Oxide in Mass Concrete Based on Hydration Characteristics

The low swelling property of magnesium oxide concrete is a significant feature that can be used to control the cracking of mass concrete. Based on the characteristics of the chemical reaction, this work proposes a coupled hydro-thermo-mechanical model that can be implemented with the finite element method for predicting the autogenous volumetric deformation of magnesium concrete. By introducing the degree of the hydration reaction of magnesia and the degree of the hydration reaction of cementitious materials as intermediate variables of the chemical reaction system, a prediction model of the concrete temperature and chemical fields is established, and using this model, the effect of the temperature on the reaction rate can be considered in real time. In addition, by combining the relationship between the degree of the hydration reaction of magnesium oxide and the comprehensive expansion of concrete, a mathematical model for calculating the expansion stress of magnesia concrete was established. The algorithms were derived by mathematical equations, and the simulation results were compared to the experimental temperature and autogenous volumetric strain curves, which showed that the hydration model provides a relatively high accuracy. The model was also applied to an arch dam, and the coupled thermo-chemical-mechanical responses of mass concrete during construction were investigated. Simulation results show that the increase in temperature (hydration of cementitious material) and expansion volumetric deformation (hydration of MgO) of the concrete on the upstream and downstream surfaces lags obviously behind that of the inner regions. Quantitative analysis for differences of internal and external expansion is worthy of further attention and study on a basis of further experimental data as well as monitored data.

A probabilistic and statistical model of rock deformation

A new approach to the study of strength characteristics of the rocks on the basis of probabilistic and statistical models of the deformation processes (models of dilatancy initiation processes) under conditions of uncertainty is presented. The main purpose of the study is to create geological and mathematical tools, which could be used to study the development of volumetric deformation (dilatancy, disintegration) of reservoirs at a constant tension, acting on the array. The information and analytical basis of the performed study consists of methods of mathematical statistics and probability theory and the sedimentary rocks research methods. The probabilistic-statistical approach is formed in the study of deformation processes of the productive stratum structure, taking into account the degree of heterogeneity of the reservoirs. The obtained analytical expressions allow us to determine the moment of the beginning of the volumetric deformation process (dilatancy, disintegration) in the rock, similar to the identification of the bifurcation point in the development of geological and dynamic systems