A three-dimensional Hoek-Brown elastic-perfectly plastic constitutive model based on an analytical explicit solution

This is the authors' abstract. We don't add key points for this paper.

The intermediate effective principal stress significantly influences rock strength as shown by true-triaxial tests. Therefore, a three-dimensional (3D) failure criterion incorporating all three principal stresses provides a more accurate rock failure prediction than criteria considering only the major ( σ 1 ′ ) and minor ( σ 3 ′ ) effective principal stresses. However, most existing 3D failure criteria usually require numerical solutions, limiting their practical application. This study presents analytical explicit solutions for 3D failure criteria based on the Mohr-Coulomb criterion, expressed in terms of σ 1 ′ . This approach facilitates the use of the instantaneous internal angle of friction ( φ ) and cohesion ( c ), allowing for extensions to Hoek-Brown versions which enhances accuracy when compared to the true-triaxial experimental data. One of these 3D Hoek-Brown based failure criteria has a simple form. Due to its simplicity, this criterion is employed as the yield function within an elastic–perfectly plastic framework. The proposed 3D Hoek-Brown based constitutive model performs well when compared to tunnel excavation experimental measurements in laboratory and field tests. This study illustrates the importance of considering the intermediate effective principal stress for rock strength.