La progettazione di grandi strutture geotecniche è significativamente influenzata dalla variabilità intrinseca delle proprietà del terreno e dall’incertezza associata ai modelli geotecnici. Gli approcci deterministici tradizionali, comunemente adottati nella pratica ingegneristica e implementati in normative di progettazione come l’Eurocodice 7, affrontano le incertezze attraverso fattori di sicurezza parziali. Tuttavia, questo approccio non quantifica esplicitamente né la probabilità di cedimento né il livello di affidabilità della struttura. Questo articolo analizza l’applicazione dei principi di progettazione basata sull’affidabilità (RBD) a grandi strutture geotecniche, concentrandosi sui rivestimenti di gallerie e sui sistemi di sostegno profondi. Infatti, la progettazione geotecnica si distingue da quella strutturale “classica” per la forte dipendenza da materiali naturali, intrinsecamente eterogenei e difficilmente caratterizzabili in modo esaustivo. Le proprietà del terreno (resistenza al taglio, deformabilità, permeabilità) presentano variabilità spaziale e incertezza epistemica legata a:

• limitata investigazione in sito;
• errori di misura e interpretazione;
• schematizzazioni modellistiche (leggi costitutive semplificate).

Questa combinazione di variabilità intrinseca (aleatoria) e incertezza modellistica (epistemica) rende il problema geotecnico tipicamente dominato dall’incertezza.

Uncertainty and Reliability-Based Design in Geotechnical Engineering

Geotechnical engineering is inherently affected by a high level of uncertainty due to the natural variability of soil properties, limited site investigation data, and simplifications in analytical and numerical models. Unlike structural materials such as steel or concrete, soil exhibits significant spatial variability and complex stress–strain behaviour, which introduces substantial uncertainty into the design process.

Current design practice in Europe is largely governed by Eurocode 7 (EN 1997), which adopts a semi-probabilistic limit state design format based on partial safety factors. While this framework provides a practical methodology for design verification, it does not explicitly quantify the reliability level associated with the adopted safety factors.
In recent decades, reliability-based design (RBD) methods have gained increasing attention in geotechnical engineering. These approaches allow engineers to explicitly evaluate the probability of failure and the reliability index of a structure by incorporating statistical descriptions of soil properties and model uncertainties.

Large geotechnical structures, such as tunnel linings and deep retaining systems, represent particularly suitable applications for reliability-based approaches. These structures are characterized by complex soil–structure interaction, high construction costs, and significant consequences in case of failure. Therefore, improving the understanding and quantification of uncertainty can lead to more rational and optimized design solutions.

 The objective of this paper is to explore the integration of reliability-based design concepts with the Eurocode 7 framework, with specific applications to tunnel linings and retaining structures.

Sources of Uncertainty in Geotechnical Design

Uncertainty in geotechnical engineering arises from several sources that can significantly influence the performance of underground structures.

Soil variability

Natural soils are highly heterogeneous materials whose properties vary both spatially and with depth. Parameters such as:

• shear strength;
• stiffness;
• permeability;
• compressibility

may show considerable variability even within relatively small areas.

This variability is commonly represented through statistical parameters such as:

• mean value;
• standard deviation;
• coefficient of variation (COV);
• probability distribution functions.

Typical coefficients of variation reported in literature are:

• friction angle: 5÷15%;
• undrained shear strength: 20÷40%;
• stiffness modulus: 30÷60%.

Such variability can significantly affect the stability and serviceability performance of geotechnical structures.

Model uncertainty

In addition to soil variability, uncertainties arise from the analytical or numerical models used in design. Simplified analytical formulations often rely on assumptions that may not fully represent the real soil–structure interaction mechanisms.

Model uncertainty can arise from:

• simplifications in constitutive soil models;
• boundary condition assumptions;
• construction sequence simplifications;
• limitations of empirical correlations.

These uncertainties can significantly influence calculated structural responses such as ground settlements, lining forces, and wall bending moments.

Measurement and investigation uncertainty

Site investigations provide limited information about subsurface conditions. Borehole spacing, sampling quality, and laboratory testing procedures all contribute to uncertainty in the estimated soil parameters.
Consequently, the parameters used in design represent only an approximation of the true ground conditions.

Eurocode 7 and the Partial Factor Approach

Eurocode 7 adopts a limit state design framework based on the use of partial safety factors applied to actions, material properties, and resistances.

The fundamental verification condition can be expressed as:

where:

• E_d= design value of the effect of actions
  R_d= design resistance.

Design values are obtained by applying partial factors to characteristic values:

where:

• X_k= characteristic value of a soil parameter;
• γ_M= partial factor for the material property.

The characteristic value is typically defined as a cautious estimate of the parameter, often related to a lower fractile of the statistical distribution.

While the Eurocode framework incorporates uncertainty through partial factors, it does not explicitly quantify the reliability level associated with a design. Reliability-based approaches can therefore provide a useful complement to the existing design format.

Reliability-Based Design Framework

Reliability-based design aims to quantify the probability that a structure will perform satisfactorily over its intended life.

The structural performance can be described using a limit state function:

where:

• 𝑅𝑋= resistance;
• 𝑆𝑋= load effect;
• 𝑋= vector of random variables.

Failure occurs when:

The probability of failure P_f is defined as:

A commonly used measure of reliability is the reliability index β, defined as:

where Φ is the standard normal cumulative distribution function.

Typical target reliability indices for geotechnical structures range between:

• β ≈ 3.0 ÷ 3.8 depending on consequence class.

Reliability analysis can be performed using several methods, including:

• First Order Reliability Method (FORM);
• Monte Carlo simulation;
• Response Surface Methods.

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