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Kirsch Elastic Circular Tunnel Stress Calculator

Easily calculate and compute kirsch elastic circular tunnel stress calculator with accurate equations, live formulas, and expert guidance.

Virgin overburden vertical stress.

Ratio of horizontal to vertical tectonic stress.

Radius of circular bored tunnel.

Distance from tunnel centerline (r = a on the boundary wall).

0° = sidewall, 90° = crown/roof.

Calculated Result
55 MPa

Hoop Stress (σ_θ)

Hoop Stress (σ_θ)

55 MPa

Tangential Hoop Stress Sigma Theta M Pa

55

Radial Stress Sigma R M Pa

0

Crown Roof Hoop Stress At Wall M Pa

35

Sidewall Hoop Stress At Wall M Pa

55

55 — MPa

Calculation Breakdown

  1. Applied FormulaCalculates elastic stress concentrations, tangential hoop stresses, and radial confinement around circular underground mine drifts using Kirsch equations.\sigma_\theta = \frac{p}{2}\left( (1+K)(1+\frac{a^2}{r^2}) - (1-K)(1+3\frac{a^4}{r^4})\cos 2\theta \right)

Kirsch Tunnel Stresses Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.014284155Hoop Stress (σ_θ)

What Is the Kirsch Elastic Circular Tunnel Stress Calculator?

This tool computes kirsch elastic circular tunnel stress calculator with high precision arithmetic.

How Does the Kirsch Elastic Circular Tunnel Stress Calculator Work?

Calculates elastic stress concentrations, tangential hoop stresses, and radial confinement around circular underground mine drifts using Kirsch equations.

Kirsch Elastic Circular Tunnel Stress Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

σθ=p2((1+K)(1+a2r2)−(1−K)(1+3a4r4)cos⁡2θ)\sigma_\theta = \frac{p}{2}\left( (1+K)(1+\frac{a^2}{r^2}) - (1-K)(1+3\frac{a^4}{r^4})\cos 2\theta \right)

Calculates elastic stress concentrations, tangential hoop stresses, and radial confinement around circular underground mine drifts using Kirsch equations.

How to Use the Kirsch Elastic Circular Tunnel Stress Calculator

  1. Enter your parameters into the designated input fields to calculate the result immediately.

Step-by-Step Example Calculation

Kirsch Elastic Circular Tunnel Stress Calculator Example

Input Values:

verticalInSituStressSigmaVMPa:25.0
lateralStressRatioK:0.8
tunnelRadiusAM:2.5
evaluationDistanceRM:2.5
polarAngleThetaDeg:90.0
Worked Steps: Sample evaluation based on standard reference conditions.

Understanding Your Result

The calculated primary figure indicates the optimal or required MPa.

Factors That Affect the Result

  • Measurement tolerances, operational variance, and real-world conditions.

When Should You Use This Calculator?

  • Everyday budgeting, technical homework, professional estimation, and household projects.

Assumptions & Limitations

  • Assumes standard atmospheric or environmental parameters unless specified.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Double-precision IEEE 754 arithmetic with validated empirical constants.

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