Non-uniqueness of back-analyzed parameters of Ducan-Chang model

The fact that the back analysis procedure simultaneously selecting failure ratio R_f cohesion C, and frictional angle φ as objective parameters in Duncan-Chang hyperbolic constitutive model tends to fail is caused by numerical singularity because of non-uniqueness of the solution. The non-uniqueness arises from the co-relation of R_f C , and φ, which means there are innumerable groups of R_f, C, and φ which can form the same Rf S (product of failure ratio R_f and stress level S ) and produce the same tangent modulus E_t and tangent Poisson ratio ν_t under specific stress condition and finally provide the same objective value in back analysis. Effective methods are given to ensure the identification of Duncan-Chang hyperbolic constitutive model during back analysis by means of parameter reconstruction and parameter constraint.