Analysis of a microcrack model and constitutive equations for time-dependent dilatancy of rocks

Abstract

SUMMARY Based on experimental observations and theoretical analyses, the author introduces an ideal microcrack model in which an array of cracks with the same shape and initial size is distributed evenly in rocks. The mechanism of creep dilatancy for rocks is analysed theoretically. Initiation, propagation and linkage of pre‐existing microcracks during creep are well described. Also, the relationship between the velocity of microcrack growth and the duration of the creep process is derived numerically. The relationship agrees well with the character of typical experimental creep curves, and includes three stages of creep. Then the damage constitutive equations and damage evolution equations, which describe the dilatant behaviour of rocks, are presented. Because the dilatant estimated value is taken as the damage variable, the relationship between the microscopic model and the macroscopic constitutive equations is established. In this way the mechanical behaviour of rocks can be predicted.

Estudio de la fluencia de una calcarenita: la Piedra de San Julián (Alicante)

“…Los ensayos de compresión y fluencia que hemos realizado, mantienen las tensiones en el rango elástico del material en todo momento). Figure 4), [6] has been used. The parameters fitted to the rheological model are shown in Table 3.…”

“…The parameters fitted to the rheological model are shown in Table 3. Figure 5 shows the creep time-series of the rheological model (below, [6]) and the reference concrete according CEB-FIP (arrives, [5]) for the tested period of four days. In Figure 6 the same parameters for a period of 10000 days are also plotted.…”

“…Similarly, but simply relating the deferred deformation with the generation of micro-cracks, (6) analysed the volumetric deformation by means of a constitutive model. There are several works focused on the study of the influence of the type of test (stress-path) (7).…”

Magma‐driven subcritical crack growth and implications for dike initiation from a magma chamber

“…[5] Chen [2003] and Chen and Bai [2006] have previously analyzed creep growth process of microcracks in rocks and obtained the theoretical relationship between the microcrack growth velocity and various factors such as principal stresses, initial length of the microcrack, and material properties. Their approach will be used in this work to study the subcritical growth of a magma-filled crack from a magma chamber and is described as follows.…”

“…[4] This work studies dike initiation from a magma chamber based on the viscoelastic subcritical crack propagation model presented by Chen [2003] and Chen and Bai [2006]. We consider a dike subcritically growing from a magma chamber into a viscoelastic solid.…”