A general approach to constitutive modelling of the elastoplastic behaviour of weak and strong rocks has been developed. It is based on the incremental theory of plastic flow for a work-hardening material. The dependences of the plastic potential and the yield function on stresses are assumed to be functions of only two stress invariants, the mean stress, and the generalised shear stress, with the hardening parameter equal to a total plastic work. Model calibration is based on triaxial test data. It involves the calibration along each loading path in the plane which brings material from elastic behaviour to failure through a phase of elastoplastic deformation. Then the interpolation of constitutive parameters into an entire range of stress variation is carried out.
Modelling of elastoplastic rock behaviour near a wellbore is a key issue in current approaches to wellbore stability and sanding problems. The main difficulty consists of keeping the balance between the complexity of the model and the accuracy and reliability of data which can be used for model calibration. The field data, if available at all, are normally poor and noisy due to mechanical damage of rock around the wellbore and natural variability of rock properties. This problem increases, in particular, in weak rocks where coring is often difficult. This is why, simple constitutive models, although they can be easily calibrated, do not provide reliable predictions of a failure initiation whereas comprehensive elastoplastic models often cannot be calibrated for different materials without serious modifications. For these reasons, we restricted our efforts to development of a relatively simple and robust elasto-plastic model which could be calibrated using standard triaxial test data and applied to a general 3D geometry.
If loading continues above an elastic limit, the material experiences simultaneously reversible or elastic deformation and irreversible or plastic deformation.
A standard triaxial test is carried out on a cylindrical specimen placed between two parallel stiff plates and subjected to compression or extension in the axial direction. The normal radial stress on the lateral surface of the specimen is maintained constant. The test usually starts from an isotropic initial stress state. During loading (compression test) or unloading (extension test) five parameters are measured: the axial stress, szz, the radial stress, sTT, the axial strain, ezz, and two radial strains in orthogonal directions giving the average radial strain, err.
The global model is constructed by combining the local approximations of the constitutive functions Q and ? which were obtained for each subdomain O between two neighbouring loading paths. Switching from one region could be easily done when the actual loading path crosses any loading path of triaxial test used in the model calibration. In accordance with the definitions of the local constitutive functions, the global functions ? and F are continuous everywhere as well as the derivatives of the plastic potential, Q'p and Q'T.
