The Lugeon Test: Methodology, Interpretation, and Applications in Geotechnical Engineering

Structural Design: Concrete Thrust Block for 90° Pipe Bend

1. Design Parameters & Initial Conversions

• Pipe Diameter (D): 315 mm = 0.315 m
• Water Pressure (P): 3.7 kg/cm² = 37,000 kg/m²
• Deviation Angle (θ): 90°
• Concrete Density (γ_c): 2500 kg/m³
• Soil Density (γ_s): 1800 kg/m³
• Angle of Internal Friction (φ): 30°
• Cohesion (c): 0
• Soil Cover: 1.2 m above the pipe face

2. Thrust Force Calculation

First, we determine the cross-sectional area of the pipe and the total outward thrust force generated by the water pressure at the 90° bend.

Pipe Area (A):

A = (π / 4) × D² A = (π / 4) × (0.315)² = 0.0779 m²

Thrust Force (T):

T = 2 × P × A × sin(θ / 2) T = 2 × 37000 × 0.0779 × sin(45°) T = 5764.6 × 0.7071 = 4076.6 kg

3. Soil Passive Resistance & Bearing Capacity

Passive Earth Pressure Coefficient (K_p):

K_p = (1 + sin(φ)) / (1 - sin(φ)) K_p = (1 + sin(30°)) / (1 - sin(30°)) = (1 + 0.5) / (1 - 0.5) = 3.0

Depth to Pipe Centerline (h_c):

h_c = Soil Cover + (D / 2) h_c = 1.2 + (0.315 / 2) = 1.3575 m

Passive Earth Pressure at Centerline (P_p):

P_p = K_p × γ_s × h_c P_p = 3.0 × 1800 × 1.3575 = 7330.5 kg/m²

Safe Bearing Pressure (q_a):

Applying a Factor of Safety (F.S.) of 1.5:

q_a = P_p / 1.5 q_a = 7330.5 / 1.5 = 4887 kg/m²

4. Required Thrust Block Dimensions

Required Contact Area (A_req):

A_req = T / q_a A_req = 4076.6 / 4887 = 0.834 m²

Proposed Block Dimensions:

• Height (H_b): The block must encapsulate the 315 mm pipe. Let's provide a height of 0.8 m.
• Width (B_b): B_req = 0.834 / 0.8 = 1.04 m. Let's round this up to 1.1 m.
• Length (L_b): Let's assume a length of 1.0 m along the pipe axis.

5. Check for Sliding Stability

• Block Volume (V): 1.1 m × 0.8 m × 1.0 m = 0.88 m³
• Weight of Block (W): V × γ_c = 0.88 × 2500 = 2200 kg
• Coefficient of Base Friction (μ): tan(30°) = 0.577
• Frictional Resistance (F_f): μ × W = 0.577 × 2200 = 1269 kg

Total Safe Resisting Force:

Total Resistance = (B_b × H_b × q_a) + F_f Total Resistance = (1.1 × 0.8 × 4887) + 1269 Total Resistance = 4300.5 + 1269 = 5569.5 kg

Conclusion: Since the Total Safe Resistance (5569.5 kg) is greater than the Thrust Force (4076.6 kg), the proposed dimensions are safe.

Final Recommended Design

Component	Dimension
Block Width (transverse to thrust)	1.1 m
Block Height	0.8 m
Block Length (parallel to thrust)	1.0 m
Concrete Volume Required	~0.88 m3

Note: The block should be cast directly against undisturbed trench soil on the outside of the bend to ensure the passive earth pressure is fully mobilized.