Abstract
Despite the lack of test data of the coefficient of pressure sensitivity α and the shearing cohesion k, the Drucker–Prager criterion is commonly applied for numerical analyses of geotechnical engineering. To bridge the gap between the wide application and insufficient knowledge of strength parameters of the Drucker–Prager criterion, this study presents experimentally calibrated strength parameters of this criterion for the first time. This paper proposes a new method to measure α and k in the Drucker–Prager criterion. The square root of the second invariant of the deviatoric stress tensor J 2 is linearly fitted with the first invariant of the stress tensor I 1 in the stress space. The parameters φ and c in the Mohr–Coulomb criterion and α and k in the Drucker–Prager criterion are calibrated to the same set of triaxial compression tests of sandstones. With these testing results, five pairs of conversion formulae (which are most commonly used in the literature) are examined and the most appropriate pair of conversion formulae is identified. With parameters indicating cohesive strength (c and k) and parameters indicating frictional strength ( φ and α ), the evolutions of different strength components are compared with those in the cohesion-weakening friction-strengthening model. With an increase in plastic deformation, the cohesive strength parameters c and k firstly increase to a peak value and then decrease. The frictional strength parameters φ and α gradually increase at a decreasing rate after the initial yield point.
Highlights
Introduction e MohrCoulomb criterion and the Drucker–Prager criterion are often used in geotechnical engineering. e Mohr–Coulomb criterion assumes that the shearing stress on the failure plane is a function of the normal stress on the failure plane, which is expressed as [1,2,3]τ tan φ · σ + c, (1)where τ represents the shearing stress on the cross section, σ represents the normal stress on the cross section, φ represents the angle of internal frictional, and c represents the cohesion
To bridge the gap between the wide application and insufficient knowledge of strength parameters of the Drucker–Prager criterion, this study presents experimentally calibrated strength parameters of this criterion for the first time. is paper proposes a new method to measure α and k in the Drucker–Prager criterion. e square root of the second invariant of the deviatoric stress tensor J2 is linearly fitted with the first invariant of the stress tensor I1 in the stress space. e parameters φ and c in the Mohr–Coulomb criterion and α and k in the Drucker–Prager criterion are calibrated to the same set of triaxial compression tests of sandstones
Advances in Civil Engineering represents the first invariant of stress tensor, and k represents the shearing cohesion
Summary
It is common to obtain the cohesion c and angle of internal friction φ by conducting triaxial compression tests under different confining pressures and drawing a group of Mohr circles with the peak stresses σ1 and the confining pressures σ3. To inspect the evolution of the strength of rocks, the stress-strain curves need to be converted into curves of yield stress σs versus the plastic internal variable κ. When the Mohr–Coulomb criterion is used as a yield criterion, the cohesion c and the angle of internal friction φ are not constants anymore but vary with plastic strain.
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