Bearing Capacity Calculations User Guide

Bearing Capacity Calculations User Guide

Introduction

In underground coal mines, weak floor material beneath coal seams can significantly limit the load-carrying capacity of pillars. The Bearing Capacity Calculator provides a method to evaluate the ultimate bearing capacity of weak foundations using limiting equilibrium analysis, with slip surface extents constrained by the roadway or bord width. The analysis takes into account both homogeneous and multilayer dry or saturated floors. For detailed information about the calculator, please refer to our publication: Watson, J., Canbulat, I., Wei, C., and Gao, M. (2024). Ultimate Bearing Capacity of Weak Foundations under Coal Pillars. Rock Mechanics and Rock Engineering. doi: 10.1007/s00603-024-03999-z

Input Fields

1. Basic Parameters

Analysis with Pore Water

Purpose: Specifies whether pore water pressure should be considered in the analysis.

Options:

  • Yes: Includes pore pressure effects.
  • No: Ignores pore pressure effects.

Slip Extends to Far Ribsides or to Centreline

Purpose: Determines the slip failure location relative to the pillar.

Options:

  • Far Ribsides: Assumes bearing capacity failure occurs on one side only, with the slip surface extending to the opposite ribside.
  • Centreline: Assumes failure occurs on both sides, with the slip surface extending symmetrically to the pillar's centreline.
    • Illustration of slip extending to centreline

Tributary Area Factor for Square Pillar or Chain Pillar

Purpose: Sets the tributary area factor based on the pillar shape.

Options:

  • Square Pillar: For square pillars (w1 = w2).
  • Chain Pillar: For chain pillars (w1 < w2).

Roadway Width lroad (unit: m)

Purpose: Specifies the roadway width in the analysis.

Input: Numeric value in metres with maximum 2 decimals (e.g., 6.0 m).

Illustration of analysis area

Pillar Width (unit: m)

Purpose: Specifies the pillar width in the analysis.

Input: Numeric value with maximum 2 decimals (e.g., 15.0 m).

Yield Length ly (unit: m)

Purpose: Defines the yield length occurs at the ribsides.

Input: Numeric value with maximum 2 decimals (e.g., 1.0 m).

Initial Bearing Pressure q0 (unit: MPa)

Purpose: Specifies the initial bearing pressure.

Input: Numeric value in megapascals with maximum 2 decimals (e.g., 2.5 MPa).

2. Layer Properties

Number of Floor Layers for Analysis (Maximum 5)

Purpose: Specifies the number of floor layers included in the analysis.

Input: Integer value between 1 and 5.

Illustration of floor layers

Geomechanical Properties for Each Layer

For each layer, provide the following properties:

  1. Cohesion (unit: MPa):
    • Purpose: Indicates the cohesion of the floor material.
    • Input: Numeric value in megapascals up to 2 decimals (e.g., 0.5 MPa).
  2. Friction Angle (unit: °):
    • Purpose: Defines the friction angle of the floor layer.
    • Input: Numeric value in degrees up to 1 decimals (e.g., 30°).
  3. Unit Weight (unit: MPa/m):
    • Purpose: Specifies the unit weight of the floor layer.
    • Input: Numeric value in MPa/m up to 3 decimals (e.g., 0.025 MPa/m).
  4. Biot Coefficient (from 0 to 1):
    • Notes: Requires to fill when you select Yes in Analysis with Pore Water.
    • Purpose: Represents the Biot coefficient of the floor layer.
    • Input: Numeric value between 0 and 1 up to 2 decimals (e.g., 0.7).
  5. Pore Pressure (unit: MPa):
    • Notes: Requires to fill when you select Yes in Analysis with Pore Water.
    • Purpose: Specifies the pore water pressure within the layer.
    • Input: Numeric value in megapascals up to 3 decimals (e.g., 0.981 MPa).
  6. Layer Thickness (unit: metre):
    • Notes: Requires to fill when you include more than 1 layer in the analysis.
    • Purpose: Specifies the layer thickness abover the current layer.
    • Input: Numeric value in metre up to 3 decimals (e.g., 0.2 m).

How to Use the Bearing Capacity Calculator

  1. Enter Basic Parameters: Fill in all fields in the Basic Parameters section based on your specific analysis scenario.
  2. Define Layer Properties:
    • Specify the number of layers for analysis.
    • Input the geomechanical properties for each layer in the provided table.
  3. Run the Analysis: After completing all inputs, click the Calculate button to run the analysis.
  4. Interpret the Results: The calculator will display results for Average pillar stress at failure, Length of slip, Depth of slip surface, and Factor of safety.

Troubleshooting

  • Ensure all required fields are filled before running the analysis.
  • Double-check units for all input values to ensure they match the expected format.
  • If errors occur, consult us for support.