ABSTRACT
In order to describe the compaction stage of rock under compression, a compaction variable D0 is introduced to represent the extent of compaction. It similar to rock damage, the probabilistic method is used to define the compaction variable D0. In the compaction stage, the Young’s modulus increases with the increase of external load and it also reflects the extent of compaction. At the beginning of compaction stage, no compaction happens, so the compaction variable is equal to zero and then the Young’s modulus increases with the extent of rock compaction. At the end of compaction stage, the compaction variable increases to one and the Young’s modulus reaches to the peak value. The entropy theory is introduced to obtain the probabilistic distribution function, which can represent the compaction variable D0. The formula is expressed as
D f x dxc0 0∫ ( )ε (1) f x xc i
i) = exp ⎛ ⎝
⎞ ⎠⎟
∑λ + λcc0 1
4 (2)
u f x dx ci c ci( )x )∫ = (3) c p
E
1 εε =
cci
σ − σ
ε − ε
σ − σ
ε − ε
ε
1 (4)
where E is the adjoining modulus and σ, ε are the stress and strain can be obtained from experiment. Nc is the total quantity of experimental data of compaction stage. λci (i = 0, 1, 2, 3, 4) are achieved from Equation 3,4 through numerical calculation. The relation between stress and strain in compaction stage is
σ Ε εc D0 0 (5)
where σc is the stress corresponding to the compaction stage, ε is the strain, D0 is the compaction variable, E0 is the secant modulus at the end of compaction stage.
