DETERMINATION OF ELASTIC CONSTANTS OF TRANSVERSELY ISOTROPIC
BORYEONG SHALE
Seung-Beum Choi, Seokwon Jeon*
Seoul National University
sjeon@snu.ac.kr
ABSTRACT
In order to determine the five elastic constants of Boryeong Shale in Korea, which clearly presents
transverse isotropy, a series of laboratory tests were carried out. Among various methods for determining
elastic constants, Brazilian tests with iterative procedure which was proposed by Chou were selected. The
procedure, as same as the original proposal, requires constitutive equation, experimental results and
numerical simulation. The constitutive equation of transversely isotropic rock was transformed in
accordance with two geometric angles defined by the direction of isotropic plane. By taking two geometric
angles into account, applicability of the procedure was expanded to three dimensional cases at some degree.
When it comes to experimental results, Brazilian test was selected because of its simplicity while strain
components at the center of disk as well as applied load were measured during the test. Corresponding
stress components taking anisotropic deformation into account were calculated by numerical simulation.
The procedure was iterated until the measured strains matched with simulated stresses, which means
convergence of elastic constants. Results showed that the convergence was highly dependent on the two
geometric angles. The elastic constants were finally determined by solving simultaneous equations which
were derived from the constitutive equation and the coefficient matrix. Therefore, the applicability of the
procedure varied with the direction of isotropic plane. The applicability was quantitatively estimated by
calculating the condition number of the coefficient matrix. In addition, uniaxial compression tests were
carried out to obtain the elastic moduli in the conventional way. The results were compared with those
obtained in the newly proposed method in this study while they showed good agreement. Ratio of elastic
constants, E1/E2, 1/2 and G1/G2 were determined as 1.60, 1.11 and 1.33 respectively for Boryeong
shale used in this study which showed moderate anisotropy.
Figure 1 – Convergence of elastic constants with respect to iteration step
KEYWORDS
Transverse isotropy, Boryeong shale, Iterative procedure