# Investigating the closure stress and crack initiation stress in fractured rocks using the student t distribution and Monte Carlo simulation method

## TL;DR

This study improves the accuracy of determining closure and crack initiation stress in fractured rocks using statistical methods and simulations.

## Contribution

A novel method combining Student t distribution and Monte Carlo simulation to reduce subjectivity and errors in stress determination.

## Key findings

- Traditional methods for determining closure and initiation stress show significant differences.
- The proposed method provides stable and accurate results without extreme deviations.
- Monte Carlo simulation enhances the convergence and reliability of stress estimates.

## Abstract

Traditional method of determining closure and initiation stress of fractured rocks by analyzing the stress-strain curve has problems such as strong subjectivity and large errors. This study utilized the rock closure stress values and onset stress values determined by three traditional methods, namely, axial strain method, fracture volume method and empirical value taking method, as the base database. The Student t distribution theory was used to obtain a confidence interval based on its overall distribution of values and to achieve a combination of the advantages of multiple methods. Within confidence interval, the Monte Carlo stochastic simulation was used to determine the convergence interval of the second stage to further improve the accuracy. Finally, mean value of the randomly sampled values after reaching the convergence stage was taken as the probability value of rock closure and crack initiation stress. The results showed that the 3 traditional methods for calculating rock closure and initiation stresses are significantly different. In contrast, the proposed method biases more towards multi-numerical distribution intervals and also considers the preference effects of different calculation methods. In addition, this method does not show any extreme values that deviate from the confidence intervals, and it has strong accuracy and stability compared to other methods.