INGENIO del 19 Marzo 2026, Imready Srl – RSM –

M.Chiarelli – Reliability – Based Design in Large Geotechnical Structures: Applications to Tunnel Linings and Retaining Systems

Abstract

The design of large geotechnical structures is significantly affected by the inherent variability of soil properties and the uncertainty associated with geotechnical models. Traditional deterministic approaches, commonly adopted in practical engineering and implemented in design standards such as Eurocode 7, address uncertainties through partial safety factors. However, this framework does not explicitly quantify the probability of failure nor the reliability level of the structure.

This paper investigates the application of reliability-based design (RBD) principles to large geotechnical structures, focusing on tunnel linings and deep retaining systems. The study explores the relationship between the partial factor format of Eurocode 7 and probabilistic design approaches, highlighting how soil variability and model uncertainty influence structural reliability. A probabilistic framework is presented in which geotechnical parameters are treated as random variables and structural performance is evaluated through reliability indices and failure probabilities.

Applications to tunnel linings and retaining structures are discussed to demonstrate the potential benefits of reliability-based approaches in improving design transparency, optimizing safety margins, and enhancing risk management in large underground and geotechnical infrastructure.

1. Introduction

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.

2. Sources of Uncertainty in Geotechnical Design

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

2.1 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.

2.2 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.

2.3 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.

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