How to do Tunel Excavation Calculations - Tunel Design

Excavation Calculations for Tunnel Design

In tunnel design, excavation calculations are essential for determining the volume of material to be removed, planning construction logistics, and ensuring that the tunnel’s structural integrity is maintained during excavation. These calculations help engineers assess the excavation work, choose the appropriate support system, and optimize the tunneling process.

In this article, we will focus on the key calculations involved in determining tunnel excavation volumes and the related support requirements.

Key Parameters for Tunnel Excavation Calculations

Before diving into the calculations, let's define the primary parameters used for tunnel design:

• Tunnel Shape: Circular, rectangular, or horseshoe-shaped.
• Dimensions: Tunnel radius (r), diameter (d), width (w), height (h), and length (L).
• Excavation Method: The method used (Tunnel Boring Machine (TBM), cut-and-cover, New Austrian Tunneling Method (NATM)) influences excavation rates.

1. Circular Tunnel Excavation Calculation

For a circular tunnel, the excavation volume can be calculated by first determining the cross-sectional area and then multiplying by the tunnel’s length.

Step 1: Calculate Cross-Sectional Area (A)

The formula for the area of a circle is:

A=π×r²

Where:

• A = Cross-sectional area (m²)
• r = Radius of the tunnel (m)
• π = 3.1416

Step 2: Calculate Excavation Volume (V)

Once the cross-sectional area is determined, multiply it by the tunnel length to find the excavation volume:

V=A×L

Where:

• V = Excavation volume (m³)
• A = Cross-sectional area (m²)
• L = Length of the tunnel (m)

Example for Circular Tunnel:

• Radius (r) = 5 meters
• Tunnel Length (L) = 100 meters

Step 1: Calculate the cross-sectional area:

A = 3.1416 × 5² = 3.1416 × 25 = 78.54 m²

Step 2: Calculate the excavation volume:

V = A×L = 78.54 m² × 100 m = 7,854 m³

So, the excavation volume is 7,854 cubic meters.

---

2. Rectangular Tunnel Excavation Calculation

For a rectangular tunnel, the calculation is simpler. The area is simply the product of the tunnel's width and height.

Step 1: Calculate Cross-Sectional Area (A)

A = Width × height

Where:

• A = Cross-sectional area (m²)
• Width = Width of the tunnel (m)
• Height = Height of the tunnel (m)

Step 2: Calculate Excavation Volume (V)

V=A×L

Where:

• V = Excavation volume (m³)
• A = Cross-sectional area (m²)
• L = Length of the tunnel (m)

Example for Rectangular Tunnel:

• Width = 6 meters
• Height = 4 meters
• Tunnel Length (L) = 100 meters

Step 1: Calculate the cross-sectional area:

A = 6×4=24 m²

Step 2: Calculate the excavation volume:

V = 24 m²×100 m = 2,400 m³

So, the excavation volume is 2,400 cubic meters.

---

3. Horseshoe Tunnel Excavation Calculation

A horseshoe-shaped tunnel is more complex to calculate, but it can be approximated by dividing the shape into simpler geometric parts, such as a combination of a circle and a rectangle.

Step 1: Approximate Cross-Sectional Area (A)

For a horseshoe shape, you can use an approximation based on the formula for the area of a circle plus the area of a rectangle. The detailed calculation involves integrating the geometry, but for simplicity, assume the following:

A = rectangle area + semi-circle area

Where:

• Rectangle area = width × height
• Semi-circle area = 1/2π × r²

Step 2: Calculate Excavation Volume (V)

Once the area is determined, use the standard formula for volume:

V = A×L

---

4. General Excavation Volume Formula for Any Tunnel Shape

For any tunnel shape, you can generalize the formula:

V = A×L

Where:

• V = Excavation volume (m³)
• A = Cross-sectional area (m²)
• L = Length of the tunnel (m)

The only variation is in how you calculate the cross-sectional area based on the tunnel's shape.

---

5. Factors Affecting Excavation Calculations

• Ground Conditions: Hard rock vs. soft soil requires different methods and equipment, which affect excavation rates.
• Water Table: Excavation below the water table will need additional calculations for dewatering systems.
• Tunnel Depth: Deeper tunnels may face higher ground pressures and require stronger support systems.
• Excavation Rate: This depends on the method used, such as Tunnel Boring Machine (TBM), manual excavation, or mechanical excavation.

---

Summary of Key Formulas

• Circular Tunnel Area:

A=π×r²

• Rectangular Tunnel Area:

A = width × height

• Excavation Volume:

V=A×LV

By using these formulas, you can calculate the excavation volume for different tunnel shapes and plan your construction accordingly.