13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- 2. Theoretical Results-Indentation The theoretical concepts that are used in the interpretation of plate loading tests conducted on brittle elastic geologic media are invariably based on the validity of the theory of elasticity. The analysis is frequently restricted to assumptions of isotropy of the rock mass, While this is considered to be a limitation for in situ testing, the characterization of elastic materials that are generally anisotropic (with 21 independent elastic constants), orthotropic (with 9 independent elastic constants), or transversely isotropic (with 5 independent elastic constants) [14, 15] is regarded as a difficult exercise even under highly controlled laboratory conditions [16]. The best that can be accomplished in an in situ plate loading test is to arrive at an effective deformability modulus of the region in which the plate load test is conducted. The simplest idealization that permits the use of an effective property is the assumption of isotropy of the tested region. It is relatively clear that if the geologic medium possesses dominant stratification then the deformability should be interpreted appropriately. The theoretical concepts can also be extended to include both transverse isotropy of the rock mass and elastic inhomogeneity of the geologic medium [17-20]; however, the inverse analysis for the elasticity parameter identification in these situations cannot be conducted using only the results of plate load tests. Even with the restrictions of isotropic and homogeneous behaviour of the rock mass, the results of a plate load test can only provide an overall estimate for the deformability of the rock mass that can include both the elastic constants encountered in the isotropic elastic model. The theoretical analysis of the plate load test involving no reactive anchor forces can be conducted by formulating the mixed boundary value problem of the indentation of an isotropic elastic halfspace by a rigid test plate. In order to formulate the mathematical problem, it is also necessary to identify the contact conditions that can be present at the interface between the test plate and the geomaterial. This largely depends on the condition of the test plate and the procedures used to either make the interface completely smooth or completely frictional, which will inhibit relative slip between the plate and the geomaterial. Finally, the extent of the geomaterial region that is tested is assumed to be large in comparison to the dimensions of the plate, enabling the region to be approximated by an elastic halfspace region. Reviews of contact problems of special interest to in situ plate loading tests are given in [21-25]. The axisymmetric mixed boundary value problem associated with the smooth indentation of a halfspace by a rigid circular test plate (Figure 1) is described by the boundary conditions ( ,0) , (0, ); ( ,0) 0, [ , ); ( ,0) 0, (0, ) z zz rz u r r a r r a r r σ σ =Δ ∀ ∈ = ∀ ∈ ∞ = ∀ ∈ ∞ (1) Figure 1. The classical indentation problem for a geomaterial halfspace.
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