A Nonlinear Statistical Damage Constitutive Model for Porous Rocks

Abstract

In the current paper, the deformation behaviours of rocks during compression are studied by testing 10 groups of sandstone samples with different porosity characteristics. According to the energy theory, the rock material was divided into two parts: solid skeleton and voids. A statistical damage-based approach was adopted to establish a nonlinear statistical damage constitutive model. The validity of the statistical damage constitutive model is verified by the test data. The statistical damage constitutive model performs well in each stage of rock compression before failure. For different types of rocks, different confining pressures, and different water contents, the statistical damage constitutive model fits well. This model can be applied to most types of rocks and in most engineering environments.

Development of a Model for Initial Compaction Stage in Rock Based on Energy Dissipation

“…According to a previous study, the value of c varies roughly in a linear negative manner with the axial strain, and the initial value of c is close to 1 [3]. c cc and ε cc can be defined as the values of the proportional coefficient and the axial strain at the critical point of the initial crack compaction, respectively.…”

“…erefore, the constitutive model during the initial compression stage with voids can be established [3,35].…”

“…e compression under the loading of rock often proceeds through four stages, and the rst stage is always the compression of the initial microcracks, irrespective of the type of rock [1,2]. e length of the initial microcracks in the compression stage can be long or short due to the variations in the types of rock, pore size [3], and moisture content [4] that signi cantly a ect the establishment of the whole constitutive model of rock for the numerical simulation.…”

“…For instance, based on the parabolic strength criterion and the Weibull distribution, the void compaction stage was taken into consideration to formulate the damage evolution model [25]. Later, because of the upper concave stress-strain curve, which can be expressed as a parabola-like equation through the origin, the stress-strain curve during the initial compression stage was proposed [3]. Furthermore, the exp(− (F/F 0 ) m ) in the damage statistical constitutive model in the elastic stage and the yield stage was transformed as 1 − exp (− (F/F 0 ) m ), which could be suitable in the compacted section [26].…”

Method for Identifying and Forecasting Mining-Induced Earthquakes Based on Spatiotemporal Characteristics of Microseismic Activities in Fankou Lead/Zinc Mine

“…The AB section is the elastic deformation stage of the rock. At this stage, the stressstrain curve continues to vary linearly and obeys Hooke's law [48]. The curve keeps a single linear variation until point B.…”