Particle contact constitutive model [21].

Jointed rocks under local load are ubiquitous in civil engineering. The instability and failure of jointed rocks are fatal to engineering safety. This paper numerically investigated the effects of loading area and joint angle on the strength dividing points, energy evolution, and crack distribution characteristics of non-persistent jointed rocks. The results demonstrated that the closer the absolute value of joint angle to 45° and the smaller the loading area, the lower the strength dividing points of rocks. The curves of rock joint angle versus total energy at peak and of elastic energy versus amplitude of post-peak abrupt energy change render a W-shape distribution. Meanwhile, compared with joint angle, loading area has more influence on rock energy input. The larger the loading area, the higher the crack fractal dimension, the crack entropy, and the penetration rate. Tensile cracks outnumber shear cracks when jointed rocks are damaged, and shear cracks increases significantly at the post-peak stage.</div

Energy and crack evolution law of -75° non-persistent jointed rock under different loading areas.

Energy and crack evolution law of -75° non-persistent jointed rock under different loading areas.</p

Numerical simulation results and validation.

(a) Determination and division basis of strength dividing points of jointed rock with a 30° joint under the full-area load of S, (b) The cracks evolution of jointed rock under uniaxial compression in reference [4], and (c) Strain evolution of 30° jointed rocks under uniaxial compression in reference [30].</p

Relation curves between joint angle and <i>U</i>, <i>U</i>_e and <i>U</i>_d at peak strength of rocks under local load.

Relation curves between joint angle and U, Ue and Ud at peak strength of rocks under local load.</p

The deformable Trigon block model.

Jointed rocks under local load are ubiquitous in civil engineering. The instability and failure of jointed rocks are fatal to engineering safety. This paper numerically investigated the effects of loading area and joint angle on the strength dividing points, energy evolution, and crack distribution characteristics of non-persistent jointed rocks. The results demonstrated that the closer the absolute value of joint angle to 45° and the smaller the loading area, the lower the strength dividing points of rocks. The curves of rock joint angle versus total energy at peak and of elastic energy versus amplitude of post-peak abrupt energy change render a W-shape distribution. Meanwhile, compared with joint angle, loading area has more influence on rock energy input. The larger the loading area, the higher the crack fractal dimension, the crack entropy, and the penetration rate. Tensile cracks outnumber shear cracks when jointed rocks are damaged, and shear cracks increases significantly at the post-peak stage.</div

Mechanical parameters of jointed rock.

Jointed rocks under local load are ubiquitous in civil engineering. The instability and failure of jointed rocks are fatal to engineering safety. This paper numerically investigated the effects of loading area and joint angle on the strength dividing points, energy evolution, and crack distribution characteristics of non-persistent jointed rocks. The results demonstrated that the closer the absolute value of joint angle to 45° and the smaller the loading area, the lower the strength dividing points of rocks. The curves of rock joint angle versus total energy at peak and of elastic energy versus amplitude of post-peak abrupt energy change render a W-shape distribution. Meanwhile, compared with joint angle, loading area has more influence on rock energy input. The larger the loading area, the higher the crack fractal dimension, the crack entropy, and the penetration rate. Tensile cracks outnumber shear cracks when jointed rocks are damaged, and shear cracks increases significantly at the post-peak stage.</div

Distribution law of <i>D</i>, <i>K</i>_<i>f</i>, and <i>R</i>_<i>f</i> of post-peak cracks in jointed rocks under local load.

Distribution law of D, Kf, and Rf of post-peak cracks in jointed rocks under local load.</p

Effect of joint dip angles on strength dividing points of rocks.

Effect of joint dip angles on strength dividing points of rocks.</p

Relationship curves between rock joint angle and amplitude of post-peak abrupt energy change under local load.

(a) Abrupt change of Ue and (b) Abrupt change of Ud.</p

Stress-strain curves of jointed rocks under different loading areas.

Stress-strain curves of jointed rocks under different loading areas.</p