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To study the mechanical characteristics of the disintegrated carbonaceous mudstone (DCM), consolidated drained triaxial tests were conducted on the DCM with three degrees of compaction (i.e., 90%, 93%, and 96%). Then, the nonlinear constitutive model suitable for the DCM was established based on test results using a logarithmic function. The stress-strain characteristics of the DCM were analyzed. The results revealed that the axial strain of the DCM was positively correlated with the deviatoric stress and lateral strain. The slopes of deviatoric stress-axial strain curves decreased with the increase of axial strain and so did the slopes of the axial strain-volumetric strain curves. The strength of the DCM increased with the increase of the confining pressure and the degree of compaction. In addition, the axial strain induced by dilatancy was also positively correlated with the degree of compaction and the confining pressure. Furthermore, under triaxial loading conditions, the relationship between the stress and strain of the DCM can be expressed by a logarithmic function; based on this, a nonlinear constitutive model with ten material parameters was derived. In addition, the results of numerical tests using the model showed similar stress-strain characteristics of the DCM comparing with the triaxial tests. Hence, it indicated that the nonlinear constitutive model based on the logarithmic function can reflect the nonlinear stress-strain characteristics of the DCM.