# Relationship between surface deformation displacement and energy evolution of red sandstone under uniaxial compression

## TL;DR

This study explores how surface deformation and energy changes in red sandstone relate during compression, offering insights for engineering stability.

## Contribution

A novel correlation model linking surface deformation to energy input in red sandstone under uniaxial compression is established.

## Key findings

- Four distinct stages of surface deformation in red sandstone were identified during compression.
- Surface deformation stages correspond to axial deformation but occur at different times.
- A model correlating local surface deformation to energy input was developed.

## Abstract

The bedding structure, variations in cementation state, and pore network characteristics of red sandstone contribute to significant non-uniform deformation, critically influencing engineering stability. Existing research on external energy input to red sandstone primarily focuses on the relationship between overall rock deformation, axial deformation, and energy evolution, while studies exploring the correlation between red sandstone surface deformation caused by loads change and energy remain limited. To address these gaps, this study employs a 3D visualization test system to collect surface displacement data of red sandstone standard samples synchronously using multiple cameras, combined with micron-scale digital image correlation technology and energy analysis. The study systematically examines the relationship between surface deformation and energy evolution in red sandstone and reveals the surface deformation process of red sandstone. According to the surface deformation’s variation trend of the sample and the degree of change, four distinct stages of surface deformation, corresponding to axial deformation stages but with temporal discrepancies, are identified. By quantifying external energy input, the study establishes a correlation model linking obtained local surface deformation to energy input under unconfined conditions. The findings provide critical theoretical and technical support for stability evaluation and optimization design of red sandstone engineering, especially in deformation control and safety warning for slopes and other free-surface engineering projects.