PROJECT CONTEXT

The project involved pile foundation design in soil conditions characterized by significant spatial variability:

• Location: Europe (confidential project).
• A bored reinforced concrete pile was analyzed.

→ Cone Penetration Testing (CPT) data was used as the primary source for evaluating soil parameters. Design was initially performed in accordance with Eurocode 7 (EN 1997-1), using deterministic characteristic values. Verification was against Static Load Test (SLT) results.

ENGINEERING CHALLENGE

In standard design:

• variability is simplified into characteristic values,
• uncertainty is absorbed through safety factors.

However, this approach often leads to:

• overdesign (higher costs),
• or hidden risks (if variability is not well represented).

→ The key issue was: How to account for variability in soil parameters without excessive conservatism.

LIMITATIONS OF THE STANDARD APPROACH

The deterministic design framework:

• reduces complex soil behavior to single representative values,
• does not explicitly model variability,
• cannot quantify probability of failure.

→ As a result, design decisions are not directly linked to risk levels. This is a critical limitation for high-value or sensitive projects.

ADVANCED METHODOLOGY – PROBABILISTIC ANALYSIS

The methodology included:

• statistical characterization of soil parameters from CPT data,
• modeling of parameter variability,
• probabilistic evaluation of pile bearing capacity.

Instead of using a single CPT profile, the analysis incorporated variability:

• 20 simulated CPT tests generated from the real CPT data
• coefficient of variation considered: 5%, 10%, 20%, 30%.

This allowed:

• simulation of a range of possible outcomes,
• estimation of reliability levels,
• direct assessment of uncertainty.

→ To overcome deterministic limitations, a probabilistic approach was introduced based on CPT-derived parameters.

Charts of the original CPT test and generated CPT tests: a) Cv = 5%, b) Cv = 10%, c) Cv = 20%, d) Cv = 30%

KEY ENGINEERING INSIGHT

The analysis showed that:

• variability in CPT parameters significantly affects predicted capacity,
• deterministic values may not represent actual behavior,
• reliability can be quantified rather than assumed.

→ Pile capacity is not a single value — it is a distribution.

RESULTS AND PRACTICAL IMPACT

The probabilistic approach enabled:

• more realistic assessment of pile performance,
• explicit understanding of risk levels,
• improved alignment between design and actual ground conditions.

Practical outcomes:

• potential optimization of design (reduced conservatism),
• better-informed engineering decisions,
• increased confidence in foundation reliability,
• optimization of design approach – DA2 identified as most realistic.

→ Design moved from assumption-based to risk-informed.

Cumulative distribution function of the normal distribution F[Rc,d/Pu|(Rc,d/Pu)mean,σR] and discrete values of normalized pile capacity
F[Rc,d,sim/Pu|(Rc,d/Pu)mean,σR]: a) Cv = 5%, b) Cv = 10%, c) Cv = 20%, d) Cv = 30%

STRATEGIC CONCLUSION

This case demonstrates that:

• integrating CPT data with probabilistic analysis,
• provides a more accurate and transparent basis for decision-making.

→ Modern pile design requires understanding variability, not ignoring it.

Cosic M., Susic N., Folic R., Bancila R.: Probabilistic Analysis of Bearing Capacity of Piles with Variable Parameters in CPT Test and Calculation According to the Requirements of Eurocode 7 (EN 1997-1: 2004) Regulations, Structural Integrity and Life, Vol. 16, No. 1, 2016. pp. 25-34.