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

1. Initial Parameters

Project Timeline: 50 years Discount Rate: 5% per annum Initial Investment: $70 million

2. Annual Cash Flows

Annual Costs

• Maintenance: $500,000
• Inspection: $100,000
• Staff: $200,000 Total Annual Costs: $800,000

Annual Benefits

1. Direct Benefits:
   • Toll revenue: $2,000,000
   • Reduced congestion value: $1,500,000
   • Vehicle operating savings: $1,000,000 Subtotal: $4,500,000
2. Indirect Benefits:
   • Economic development: $2,000,000
   • Property value increase: $1,000,000
   • Environmental benefits: $500,000 Subtotal: $3,500,000

Total Annual Benefits: $8,000,000

3. Present Value Calculations

Formula Used

PV = FV / (1 + r)^t where:

• PV = Present Value
• FV = Future Value
• r = Discount rate (5% = 0.05)
• t = Time period (years)

A. Present Value of Costs

1. Initial Investment (Year 0): $70,000,000
2. Annual Costs Present Value:

PV of Annual Costs = Annual Cost × Present Value Annuity Factor
PVAF = [1 - (1 + r)^-n] / r
where:
r = 0.05
n = 50 years

PVAF = [1 - (1 + 0.05)^-50] / 0.05
PVAF = 18.256

PV of Annual Costs = $800,000 × 18.256 = $14,604,800

Total Present Value of Costs:

• Initial Investment + PV of Annual Costs
• $70,000,000 + $14,604,800 = $84,604,800
• Rounded to $85 million

B. Present Value of Benefits

Annual Benefits Present Value:

PV of Annual Benefits = Annual Benefits × PVAF
= $8,000,000 × 18.256
= $97,881,600

Rounded to $98 million

4. Cost-Benefit Ratio Calculation

CBR = Present Value of Benefits / Present Value of Costs
CBR = $98,000,000 / $85,000,000
CBR = 1.15

5. Interpretation

• The CBR of 1.15 means that for every $1 of cost (in present value terms), the project generates $1.15 in benefits
• This represents a 15% return over costs
• Since CBR > 1, the project is economically viable

6. Sensitivity Analysis

To test the robustness of our conclusion, let's analyze how CBR changes with different discount rates:

Discount Rate
PV Benefits (M)
PV Costs (M)
CBR
3%
$120.4
$96.2
1.25
5%
$98.0
$85.0
1.15
7%
$82.6
$76.8
1.08
10%
$65.8
$67.2
0.98

This sensitivity analysis shows that:

1. The project remains viable (CBR > 1) up to a discount rate of approximately 9%
2. Lower discount rates improve project viability
3. The break-even discount rate is approximately 9.5%

7. Risk Factors to Consider

1. Construction cost overruns
2. Lower than projected traffic volume
3. Maintenance cost escalation
4. Economic growth variation
5. Environmental compliance cost changes

For conservative estimation, it's recommended to:

• Add 10-15% contingency to cost estimates
• Reduce benefit estimates by 10%
• Consider multiple discount rate scenarios