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Elastic wave interaction with a stressed half-space containing voids.

S M Abo-Dahab¹, Emad K Jaradat², Sharif Abu Alrub²

¹Mathematics Department, Faculty of Science, South Valley University, Qena, Egypt.

Scientific Reports

|July 10, 2026

Summary

This summary is machine-generated.

This study investigates how initial stress and voids affect shear vertical (SV) waves reflecting off elastic materials. The findings reveal distinct reflected compressional (P) and SV waves, with P-waves influenced by both stress and voids.

Keywords:

Elastic wave reflection Half-space Initial stress P-wave Plane strain Porous media Reflection coefficient SV-wave Void effect Wave propagation

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Area of Science:

Solid Mechanics
Wave Propagation
Materials Science

Background:

Elastic wave reflection is crucial for understanding material properties.
Initial stress and internal voids significantly alter wave dynamics.
Biot's theory and porous media theories provide frameworks for analyzing complex elastic behavior.

Purpose of the Study:

To analyze the reflection characteristics of plane shear vertical (SV) waves.
To investigate the influence of initial stress and voids on wave reflection.
To derive and evaluate analytical expressions for reflection coefficients.

Main Methods:

Formulation and analytical solution of governing equations under plane strain conditions.
Application of Biot's theory of incremental deformations.
Utilizing the generalized theory of porous elastic media.

Main Results:

Incident SV-waves generate reflected compressional (P) and SV waves.
Reflected SV-wave depends only on initial stress.
Reflected P-wave is affected by both initial stress and void parameters.
Reflection coefficients vary with incident angle, void parameters, and frequency.

Conclusions:

Initial stress and voids critically modify elastic wave reflection.
The distinct behaviors of reflected P and SV waves provide insights into material properties.
Results are applicable to porous geological media and stress-loaded materials.