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Kirsch Equations Circular Excavation Boundary Stress Calculator

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

Calculated Result
87.5 MPa

Maximum Tangential Stress (sigma_theta_max)

Maximum Tangential Stress (sigma_theta_max)

87.5 MPa

Maximum Tangential Stress Mpa

87.5

Crown Tangential Stress Mpa

87.5

Sidewall Tangential Stress Mpa

37.5

Stress Concentration Factor Max

3.5

87.5 — MPa

Calculation Breakdown

  1. Applied FormulaSolves the 2D elasticity Kirsch equations around a circular underground opening, determining peak tangential tangential boundary stresses at the crown (theta = 90 deg) and springline sidewalls (theta = 0 deg).\sigma_\theta(a, \theta) = \sigma_v \left[ (1 + K) - 2(1 - K) \cos(2\theta) \right], \quad \sigma_r(a) = 0

Kirsch Tunnel Boundary Stress Metric Output

Interactive visualization based on your current inputs

Calculated Value
0.022446688Maximum Tangential Stress (sigma_theta_max)

What Is the Kirsch Equations Circular Excavation Boundary Stress Calculator?

The Kirsch Equations Circular Excavation Boundary Stress Calculator computes results using established domain formulas, verified conversion factors, and user-entered parameters.

How Does the Kirsch Equations Circular Excavation Boundary Stress Calculator Work?

Solves the 2D elasticity Kirsch equations around a circular underground opening, determining peak tangential tangential boundary stresses at the crown (theta = 90 deg) and springline sidewalls (theta = 0 deg).

Kirsch Equations Circular Excavation Boundary Stress Calculator Formula & Variables

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

σθ(a,θ)=σv[(1+K)−2(1−K)cos⁡(2θ)],σr(a)=0\sigma_\theta(a, \theta) = \sigma_v \left[ (1 + K) - 2(1 - K) \cos(2\theta) \right], \quad \sigma_r(a) = 0

Solves the 2D elasticity Kirsch equations around a circular underground opening, determining peak tangential tangential boundary stresses at the crown (theta = 90 deg) and springline sidewalls (theta = 0 deg).

How to Use the Kirsch Equations Circular Excavation Boundary Stress Calculator

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

Step-by-Step Example Calculation

Kirsch Equations Circular Excavation Boundary Stress Calculator Example

Input Values:

verticalInSituStressMpa:25
horizontalToVerticalRatioK:1.5
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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