# Piecewise Linear Strength Models for Analyzing Multiple Failure Mechanisms in Rocks Materials

## TL;DR

This paper introduces a new model to analyze rock material failures caused by multiple mechanisms, improving predictions and safety in rock engineering.

## Contribution

A piecewise linear strength model is proposed to capture multiple failure mechanisms in rocks using stress parameters.

## Key findings

- The model revealed distinct piecewise linear strength characteristics in sandstone and granite.
- The proposed model validated the rationality of analyzing multiple failure mechanisms in rocks.
- The model enhances predictive capabilities for rock structural failures.

## Abstract

Rock materials failures are accompanied by the co-existence of various failure mechanisms, including rock fracturing, shearing, and compaction yield. These mechanisms manifest macroscopically as multiple failure modes and nonlinear strength characteristics related to stress levels. Considering the limitations of current rock mechanics strength theories, which are primarily derived from single failure mechanisms, this study evaluates the applicability of alternative strength theories. Based on the extensional-strain criterion and the PMC (Paul-Mohr-Coulomb) model, a piecewise linear strength model was proposed that is suitable for analyzing multiple failure mechanisms in rocks, revealing the intrinsic mechanisms of multi-mechanism rock material failure. A multiple failure mechanism strength model in the form of inequalities was proposed, using the generalized shear stress, mean stress, and stress Lode angle as parameters. Strength tests conducted on sandstone and granite rock material samples under different stress conditions revealed distinct piecewise linear strength characteristics for both rock types, validating the rationality and applicability of the multiple failure mechanism model. The findings construct a multi-mechanism failure model for rocks, providing enhanced predictive capabilities and aiding in the prevention of rock structural failures.