An elastically asymmetric bonded-particle model for stress wave propagation in bimodular rock masses

Stress wave propagation in rock masses is strongly controlled by elastic properties. Conventional numerical models typically assume a symmetric elastic constitutive relationship with identical compressive ( E c ) and tensile ( E t ) moduli. However, real rock commonly exhibits tension–compression asymmetry, characterized by bimodular behavior with a tensile-to-compressive modulus ratio less than unity ( Ψ = E t / E c < 1.0). Numerical investigations of stress wave propagation that explicitly consider this elastic asymmetry remain limited. To address this issue, an elastically asymmetric bonded-particle model based on a bimodular parallel bond formulation is developed. Benchmark validation against pendulum impact experiments on an intact granite bar demonstrates that the proposed bimodular PBPM reproduces the delayed arrival, prolonged duration, and decreased amplitude characteristics of reflected waves more accurately than a conventional single-modulus model, confirming the physical relevance of explicitly accounting for bimodular elasticity. Numerical results show that in a bimodular rock mass, an incident compressive wave reflects from a free surface as a tensile wave, with frequency and amplitude attenuation intensifying as Ψ decreases. At fractures, the reflected signal exhibits a hybrid waveform consisting of an initial tensile component followed by a compressive one. Owing to the higher propagation velocity of compressive waves in bimodular media ( Ψ < 1.0), a catch-up effect occurs, whereby the compressive wave overtakes the preceding tensile wave. This superposition induces a tensile–compressive mutation, shifts the latter part of the signal toward higher frequencies, and enhances attenuation, thereby significantly influencing wave transmission in fractured rock masses.