Three-dimensional Time-dependent Analysis of Rock by Finite Element Method
Seisuke OKUBO, Katsunori FUKUI, Jiandong ZHANG
J. of MMIJ,Vol.114, No.2 ,pp.79-85 (1998)
A constitutive equation formerly proposed by Okubo et al for one- and two-dimensional analysis was extended to the three-dimensional. The constitutive equation was developed on the basis of the non-linear visco-elastic theory, and it was successfully applied to one- and two-dimensional problems such as long-term stability of circular tunnel.
In the three-dimensional analysis, a constant volume-modulus was assumed, and analogy with equations by Levy-Mises and Prantl-Reuss was discussed theoretically.
Comprehensive FEM analysis simulating constant-strain compression tests was carried out with tetrahedron, prism or brick elements changing number of elements, confinement of specimen ends, coefficient of variation of strength for each element and loading rate. The simulation was performed beyond the peak strength and the complete stress-strain curves were obtained for all cases. The three-dimensional results were analogous to the two-dimensional and conformed to the experimental results. For example, the peak and residual strengths were found to increase with loading rate.