Improved nonlinear elastic constitutive model for normal deformation of rock fractures

Some nonlinear elastic constitutive models for normal deformation of rock fracture were reviewed and the significant deviation of these models from experimental results at median stress level was pointed out.A new concept named half-closure stress σ1/2 was introduced to lay emphasis on the analysis of the mathematical defects of both the BB model and the classical exponential model.The generalized exponential model proposed by Malama and Kulatilake(2003) was treated as an example for further explanation of the necessity for model improvement,meanwhile the deficiency of physical meaning of the initial normal stiffness of fracture Kni because of the modification by accession of power function n on σn/σ1/2 was analyzed.Based on the above researches,a governing differential stress-displacement equation of fractures under monotonically raising normal compressive loading was established,and the concept of maximum allowable closure of pseudo fracture Dmax=ξdmax was defined.Then a new 3-parameter constitutive model which could improve the nonlinear elastic normal deformation behavior of fractures was proposed.It was strictly proved that the BB model and the classical exponential model were two special cases of the new model.The new parameter was easy to be determined,and the mathematical defects of the BB model and the classical exponential model were overcome.Counteracting the deviation of the simulated results of these traditional nonlinear models with the test results at median stress level,the physical meaning of Kni would not be lost with the accession of the new parameter.The predicated results fitted with the test results well in adopting the new model for the predication of other test data,which verified the feasibility of the new model.