The incident directions of seismic waves can change the ground motions of slope topography. To elaborate on the influences of the directions of seismic waves, a dynamic analysis of the slope topography was performed. Seismic waves were input using an equivalent nodal force method combined with a viscous-spring artificial boundary. The amplification of ground motions in double-faced slope topographies was discussed by varying the angles of incidence. Meanwhile, the components of seismic waves (P waves and SV waves), slope materials and slope geometries were all investigated with various incident earthquake waves. The results indicated that the pattern of the amplification of SV waves was stronger than that of P waves in the slope topography, especially in the greater incident angels of the incident waves. Soft materials intensely aggravate the acceleration amplification, and more scattered waves are produced under oblique incident earthquake waves. The variations in the acceleration amplification ratios on the slope crest were much more complicated at oblique incident waves, and the ground motions were underestimated by considering only the vertical incident waves. Therefore, in the evaluation of ground motion amplification of the slope topography, it is extremely important to consider the direction of incident waves.

Based on the viscoelastic artificial boundary theory and the equivalent seismic load input method, this study develops a three-dimensional time-domain input method for obliquely incident SV waves; the validation of this input method was verified, and seismic response analysis was conducted on a biased rock tunnel. The results indicate that the structural seismic response under oblique wave incidence differs significantly from that under vertical incidence. With an increase in the incidence angle, the tunnel’s stress, acceleration, and damage zones all tend to concentrate toward the left arch foot and waist. At different times during the earthquake, stresses and plastic zones develop at the tunnel shoulder, along with the obliquely incident seismic wave propagation, and the stresses and plastic zones gradually concentrate in the direction facing the waves, causing damage at the tunnel foot near the earthquake source. Therefore, in tunnel structures located near the epicenter of an earthquake, the damage evolution at the foot of the tunnel facing the seismic waves should garner more attention.

Because of inaccurate descriptions of stress‒strain relationships for the tension–shear region of the Mohr–Coulomb strength criterion, a new hybrid strength criterion called the tension–shear strength criterion was proposed and established in this study. Based on uniaxial tensile tests (using a newly developed apparatus) and triaxial shear tests, the feature points of the failure envelopes were obtained. The tension–shear strength criterion was then derived according to these points. Subsequently, to solve the discontinuous derivatives of the singularities in the yield surface, the tension–shear strength criterion was converted into its numerical form based on a new rounded method, and a constitutive integral algorithm of the tension–shear strength criterion was given. Finally, several numerical examples with theoretical and empirical solutions were adopted to validate the effectiveness and accuracy of the numerical form of the tension–shear strength criterion.