A hybrid method for solving elasto-plastic problems in rock engineering is presented by coupling two existing methods, the boundary element method and the characteristics method. The formulation of this method is presented, as well as an efficient procedure for boundary determination, and it is discussed that this method is a powerful an~ accurate method in evaluating the extent of the plastic region around rock caverns, which is of prime importance for the construction of rock caverns. Then some typical examples, including underground power house cavern, are solved by this method in order to demonstrate its applicability in rock engineering.


It is well known that the characteristics method (Hill 1950, Mogami 1969) is an accurate method to solve the plastic equilibrium problem conditioned by the hyper- bolic-type partial differential equations. n the other hand, the boundary element method (Banerjee et al. 1981, Kobayashi b985) is a powerful method for solving boundary value problems of infinite homogeneous elastic fields. Therefore, it is desired to combine the both methods in order to make full use of their merits. (he method, so-called BEM-CM hybrid method fSugawara et al. 1987a and 1987b), is one of the effectual numerical methods applicable to practical important problems in rock engineering such as stability of rock caverns, rock slope stability, rock found ation problem and so on.

In the present paper, the BEM-CM hybrid method is applied to elasto-plastic problems of underground openings under bi- axial initial stress condition. The formula ion of the method is firstly presented,as well as an efficient scheme for deter mining the boundary between the plastic legion and the elastic region. Subsequently the application of the method to an underground power house cavern is prestented with another typical examples, and roe~ the applicability of the method in c engineering is discussed.


Let us consider a certain underground opening, as illustrated in Fig. 1, and suppose that the ground surrounding the opening consists of the elastic region:n1 and the plastic region: Ώ2. Additionally suppose that the whole of the ground is under compression, namely no tensile stress. Fig. 1(a) shows the full surface yielding of the opening, and (b) shows the partial yielding of the opening, of which the surface consists of the elastic range I'1 and the plastic range • In both cases, the boundary between Ώ 1 and Ώ 2 is assumed to be defined by.

If we designate the yield function of the ground by f(Oij)=0, the stress in n1 by Oije and the stress in nz by OijP, the stress state within the elastic region is conditioned by f(Oije):00 and that in the plastic region is conditioned by f(OijP)=O. Considerations of equilibrium demand that the stress component normal to.f3 and the shear stress parallel to I'3 should be the same on both sides, as well as the displacement components. The main problem is how to determine the geometrical shape of the plastic region.

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