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Unified strength theory considering the influence of the intermediate principal stress is widely used in geotechnical engineering, but the singularities bring inconvenience to the numerical calculation. A series of equivalent area circle yield criteria based on unified strength theory are derived. The parameters of the new yield criteria and Drucker-Prager criteria are discussed, and the flow vector coefficients of the new yield criteria are given. The new series of yield criteria are very convenient for numerical calculation and can be served as reference for the evaluation of the effects of strength theory.