Statistical Constitutive Model of Thermal Damage for Deep Rock considering Initial Compaction Stage and Residual Strength

Abstract

From the theory of damage mechanics, based on the Hoek-Brown strength criterion and Weibull distribution law of rock microelement strength, a statistical constitutive model of rock thermal damage is established by using equivalent strain hypothesis, and the theoretical model is modified by considering the compression coefficient and residual strength correction coefficient. The rationality of the modified model is verified by experimental data. The results show that the stress-strain curves of rock can be divided into four stages: initial compaction, stable damage propagation, damage strengthening expansion, and damage failure according to the characteristics of rock damage evolution. The peak stress of rock increases exponentially with the increase of confining pressure, and the maximum damage evolution rate decreases exponentially with the increase of confining pressure, which indicates that confining pressure delays the development of cumulative damage. The peak stress and maximum damage evolution rate of rock decrease exponentially with the increase of temperature, which accelerates the damage of rock. The initial damage of rock is thermal damage caused by temperature, and the damage value increases with the increase of temperature. The revised theoretical curve reflects the characteristics of rock compaction stage and residual strength and improves the coincidence with the experimental curve. The research results provide a reference for the establishment of thermal damage constitutive model of rock in deep engineering.

Modeling for strain-softening rocks with lateral damage based on statistical physics

“…Suppose that the macroscopic rock is made up of N meso-elements which are continuous with each other. As the stress level increases, these meso-elements are destroyed, and their number N d increases, the damage variable D can be expressed as [ 18 – 20 ]: with substituting Eq ( 9 ) into Eq ( 10 ), the damage variable with maximum entropy can be expressed as …”

“…The mechanical properties of rock are directly affected by the stress level of the internal structure, and this approach is just in line with this point. However, the residual strength, that is, the strength of the softened area after the peak value of the rock, is difficult to be fully modeled, Xu [ 17 ] and Zhu [ 18 ] improved the statistical damage mode by introducing a damage correction factor, which only belonged to a mathematical concept and did not involve the mesoscopic model itself. In other similar studies, the development of rock damage is viewed as a slow process of damage accumulation, and the undamaged area would gradually change into the damaged area which still bear the load rather than become a hollow area [ 19 – 23 ].…”

Damage Evolution Modelling for Rock Materials Based on the Principle of Least Energy Dissipation Rate within Irreversible Thermodynamics

“…On the other hand, Krajcinovic and Silva [ 14 ] were the first to combine the continuous-strength damage theory with statistics to study the mechanical behavior of rocks. Subsequently, some improved statistical damage models were constantly proposed with the statistical microscopic damage mechanics [ 15 , 16 , 17 , 18 , 19 , 20 , 21 ]. The key to characterizing the damage evolution in statistical damage theory is establishing a probability density function of the micro-elements’ strength.…”

Static and dynamic failure mechanisms of circular granite under the condition of water-heat cycles

“…By studying the static and dynamic damage characteristics of deep rocks in high temperature environment, it was seen that the thermal damage delayed the rock crack process and weaken the brittleness 14 – 16 , and it was also found that static and dynamic compressive strength, tensile strength and shear strength decreased with the increasing temperature 17 – 20 . Part of scholars established the constitutive model of thermal damage in deep rocks based on damage mechanics and the influence of high temperature on the rock, which improve the accuracy of predicting the rock failure in the high-temperature condition 21 – 23 . The scholars in field of rock mechanics carried out exploratory studies on the damage failure mechanism of deep rocks affected by cool and hot water.…”