Transmission of Seismic Waves With Tensile Components Across Cemented Rock Discontinuities Exhibiting Tension‐Softening Behavior

Abstract

Fault slip involves not only shear but also tensile motions, causing repeated opening and closure of fault‐zone discontinuities. This cyclic deformation progressively changes the mechanical stiffness, fundamentally impacting seismic wave transmission. However, most existing analytical models neglect tensile components. This study develops a unified analytical framework combining the established Barton‐Bandis (BB) model for compressive deformation with a proposed inverse hyperbolic‐linear (iHL) model to describe tensile loading and unloading behaviors of cemented rock fractures. Integrating this model into a displacement discontinuity model and method of characteristics, we present the analytical solution that simultaneously accounts for compression‐hardening and tension‐softening effects on stress wave propagation. The BB‐iHL model uses an effective stiffness evolving dynamically with the instantaneous stress state, enabling quantitative prediction of stress wave transmission during earthquake cycles. Validation against split Hopkinson pressure and tension bar experiments confirms the model's ability to reproduce more realistic wave propagation. Results demonstrate that tensile stiffness degradation strongly influences wave transmission coefficients, particularly at low frequencies and amplitudes, and that ignoring tensile effects underestimates transmitted energy and waveform complexity. A case study based on seismic data from the 2008 Wenchuan earthquake illustrates the potential of the proposed framework for analyzing field‐scale seismic wave transmission. These findings underscore the critical role of tensile deformation in fault‐zone dynamics and highlight the proposed model as a tool for more accurate seismic wave modeling and earthquake hazard assessment.