Scipedia: Alessandro Calvi's personal collection

Dynamic Energy Balance and Size Effect in Tunnel Linings under Sudden Support Loss: A Load-Sharing Formulation of Robustness for Hierarchical Support Systems

Alessandro Calvi — Sun, 18 Oct 2026 08:52:14 +0200

Previous work by the author showed that progressive collapse of hierarchical reinforced concrete frames can be read as a ductile-to-brittle transition with a geometric and an energetic threshold, and proposed to carry the same reading over to tunnel linings. That framework is quasi-static and does not explain why robustness depends on the number of structural elements. This paper replaces it with a mechanical model of sudden support loss in a tunnel lining. Three ingredients are combined: (i) a dynamic energy balance for the elements adjacent to the lost ones, which gives a closed-form capacity for a suddenly applied load increment as a function of utilisation and ductility; (ii) a load-sharing length of the ring on elastic ground, derived from the beam-on-elastic-foundation solution, which separates a local-sharing regime (segmental or weakly jointed linings) from a distributed-sharing regime (continuous rings); and (iii) a Bažant-type size effect that links the ductility and the strength of the lining to its thickness through the characteristic length E·Gf/ft². The model gives a critical damaged arc fraction ψcrit that decreases as 1/n for n below a transition value n* = πD/ℓs and becomes independent of n above it. For an illustrative hydropower tunnel (D = 6 m, tl = 0.30 m) the lining tolerates the loss of about 1.8 elements for n ≤ 9 and a damaged arc of about 0.64 diameters in the distributed regime, consistent in order of magnitude with the geometric threshold a/D ≈ 0.5 found for frames. The formulation is analytical and hypothesis-level; a calibration programme with discrete-element simulations is outlined.

From Frames to Tunnels: A Multi-scale Fracture-Mechanics Framework for Progressive Collapse and Robustness of Underground Support Systems

Alessandro Calvi — Sun, 18 Oct 2026 08:49:27 +0200

Progressive collapse is usually discussed for buildings, whereas tunnel failures are discussed through case histories, ground-reaction curves and support-design charts. This paper brings the two literatures together. Starting from three previous studies by the author (on tunnel collapse mechanisms, on the robustness of intact and damaged framed structures, and on the multi-scale ductile-to-brittle transition in hierarchical reinforced concrete frames), it proposes a framework in which a tunnel lining and its surrounding ground are treated as a hierarchical load-bearing system subjected to sudden local damage. The framework combines (i) a second-order robustness ratio R = λd/λi between the damaged and intact critical load multipliers, (ii) a geometric criterion based on the ratio between the width of the damaged zone and the tunnel diameter, and (iii) an energetic criterion based on a Griffith-type critical flaw length and on the material characteristic length E·Gf/ft². The transfer of the two thresholds identified for frames (a/H ≈ 0.5 and an energetic ratio of ≈ 0.75) to tunnels is formulated as a working hypothesis. A parametric illustration for a hydropower tunnel crossing a fault-damaged zone shows how mineralogical degradation shrinks the critical flaw length (by more than an order of magnitude for severe degradation), bringing the energetic threshold within the thickness of the lining and shifting the sequence of failure from a purely geometric to a combined energetic–geometric path. Limits of the analogy, in particular ground confinement and three-dimensional arching, and a programme for calibration with discrete-element simulations are discussed.

Predictive Modeling of Ductile-to-Brittle Transition in Hierarchical RC Frames: A Comparative Study of Deep Learning and Machine Learning Surrogate Models

Alessandro Calvi — Sun, 13 Sep 2026 08:39:04 +0200

This research addresses the critical challenge of progressive collapse in Reinforced Concrete (RC) frames by establishing a rigorous multi-scale link between material fracture mechanics and macroscale structural hierarchy. The study investigates the highly non-linear 'Ductile-to-Brittle' transition, identifying two dimensionless ratios as the fundamental governing parameters: the Geometric Ratio (a/H), which marks the onset of brittle behavior at a threshold of approximately 0.5, and the Energetic Ratio (L

In-Situ Stress State in Rock Masses and Its Application to Road and Railway Tunnel Excavation: Integrating Reservoir Geomechanics with a New Analytical Framework (ISAF-RT)

Alessandro Calvi — Sun, 13 Sep 2026 08:21:03 +0200

The accurate characterization of in-situ stress states within rock masses is a critical prerequisite for the safe design and construction of road and railway tunnels. This paper synthesizes and extends the reservoir geomechanics framework developed by Zoback (2010, Stanford University) — originally conceived for petroleum wellbore applications — and rigorously adapts it to the problem of underground rock excavation in civil engineering contexts. The paper presents a new analytical methodology, the Integrated Stress Analysis Framework for Rock Tunnels (ISAF-RT), which combines in-situ stress characterization techniques (extended leak-off tests, hydraulic fracturing in pilot boreholes, wellbore breakout analysis) with classical rock mechanics tools (Kirsch analytical solution, Mohr-Coulomb and Hoek-Brown failure criteria, ConvergenceConfinement Method) within a unified probabilistic design workflow. The ISAF-RT framework introduces a novel six-phase sequential procedure that explicitly accounts for tectonic stress regime (normal, strike-slip, thrust faulting), anisotropic stress ratios (K₀), rock mass quality (GSI index), and time-dependent deformation, enabling the engineer to select appropriate support systems with quantified reliability. Application of the framework is demonstrated through numerical examples representative of Alpine railway tunnels and highway tunnels in folded mountain belts, where thrust-faulting regimes impose horizontal stresses up to 1.8 times the vertical overburden. The results highlight the importance of pre-excavation stress measurement campaigns and show that neglecting stress anisotropy can lead to underdesign of support by factors of 2-3. The ISAF-RT framework provides a rigorous, systematic, and practically applicable tool for geotechnical engineers engaged in subsurface infrastructure in challenging rock conditions.

Geomechanical Analysis of Inclined Fractured Zones in Road and Railway Tunnel Excavation: Stress Field Assessment, Failure Mechanics, and the ISAF-FZ Framework

Alessandro Calvi — Sun, 13 Sep 2026 08:20:02 +0200

The excavation of road and railway tunnels through inclined fractured zones represents one of the most challenging scenarios in underground engineering. The stress state within the rock mass undergoes complex perturbations when the tunnel axis intersects fault zones, shear bands, or preexisting fracture sets at non-perpendicular angles. Drawing on the theoretical framework developed by Zoback (2010) for failure analysis of deviated wells — specifically the generalised borehole wall stress equations, drilling-induced tensile fracture (DITF) diagnostics, and shear velocity anisotropy measurements — this article extends these principles to the three-dimensional geomechanical problem of inclined tunnel excavation. A critical review of stress transformation theory, breakout analysis for inclined openings, and the role of fracture dip in governing tunnel stability is presented. On this basis, the article proposes a new geomechanical methodology: the Integrated Stress Analysis Framework for Fractured Zones (ISAF-FZ). The ISAF-FZ is a sixphase, adaptive workflow that integrates in-situ stress characterisation, fracture network analysis, inclined opening stability assessment, support design, and real-time monitoring. Application to two case studies — the Gotthard Base Tunnel and the A1 Apennine Motorway Tunnel — demonstrates the framework's predictive capacity for support pressure requirements and excavation sequencing in crossed fractured zones. The results show that fracture dip angle is a primary control on required support pressure, and that the ISAF-FZ framework reduces prediction uncertainty by up to 35% compared to conventional isotropic approaches.

Geomechanical Behaviour of Fault Zones During Tunnel Excavation: Critically-Stressed Fault Analysis, In-Situ Stress Assessment, and the FZSEI Framework

Alessandro Calvi — Sun, 13 Sep 2026 08:16:03 +0200

Fault zones represent the most challenging geological discontinuities encountered during road and railway tunnel construction. When tunnel excavation intersects active or reactivated faults, the in-situ stress state within the rock mass undergoes profound perturbations: the fault core and damage zone display sharply contrasting mechanical and hydraulic properties compared with intact host rock, preferential slip planes exist at critically stressed orientations, and elevated pore pressures may transiently destabilise the excavation face. Conventional tunnel design methods, which treat the rock mass as a homogeneous elastic medium, systematically underestimate the support requirements and the risk of sudden failure events — including face collapse, large-displacement squeezing, and rockburst — in these settings. This article presents a rigorous geomechanical analysis of fault zone behaviour during tunnel excavation, grounded in the critically-stressed fault theory of Zoback (2010) and in the extensive body of evidence from deep borehole studies, seismic reflection surveys, and fault zone hydraulics. The Mohr-circle framework for evaluating fault criticality, the Stress Criticality Index (SCI) quantifying the proximity of a fault to frictional reactivation, the fracture density powerlaw model governing damage zone architecture, and the permeability-stress coupling equations are all translated into tools applicable to the tunnel design workflow. On this basis, the article proposes a new predictive framework — the Fault Zone Stress-Excavation Interaction (FZSEI) framework — that integrates SCI computation, damage zone geometry characterisation, pore-pressure transient modelling, and adaptive support classification into a unified design methodology

Application of the ISAF-RT Integrated Stress Analysis Framework to the Gorges du Verdon (Southwestern French Alps): In-Situ Stress State, Tunnel Geomechanics, and Comparative Evaluation with Barton's Q- System

Alessandro Calvi — Sun, 13 Sep 2026 08:08:23 +0200

The Gorges du Verdon (Haute-Provence, SW French Alps) constitute a spectacular deep fluvial canyon incised into Upper Jurassic to Lower Cretaceous Tithonian limestones of the Castellane fold-and-thrust belt, a region characterised by active thin-skinned compression (~0.1 mm/yr uplift), a complex network of N–S and E–W fault systems, and topographic relief of 300–700 m. Recent cosmogenic ³⁶Cl exposure dating by Cardinal et al. (2024) has quantified river incision rates of 0.06–0.20 mm/yr for the Late Pleistocene (60–15 ka), with a marked acceleration to 0.90

Technical Due Diligence Report – Anderson Dam & Hydropower Plant (California, USA)

Alessandro Calvi — Sat, 22 Nov 2025 19:50:23 +0100

This study represents the technical due diligence of the hydroelectric plant consisting of the
Anderson Dam (Leroy Anderson) and its power station, located in California, USA.
This technical contribution is structured analyzing the hydrogeological aspects of the dam site's
geographical context, including its structural behavior in the event of significant seismic events, and
then going more in detail on the energy assessments that take into account the temporal distribution
of rainfall and flow rates, as well as the efficiency of the hydraulic machinery installed.

Advanced Equilibrium Analysis of Spherical Masonry Domes: An Integral Formulation

Alessandro Calvi — Sat, 29 Mar 2025 21:36:14 +0100

The equilibrium of spherical domes is a fundamental topic in structural engineering, particularly for masonry structures, where the material’s inability to resist tension influences the force distribution. This study proposes an integral formulation for the equilibrium of a spherical dome, incorporating normal stresses and shear stresses, explicitly considering their spatial variations. The formulation extends classical membrane and bending theories by integrating the effects of stress gradients and torsional moments, providing a more detailed understanding of force equilibrium. The proposed approach aligns with and extends the concept of thrust surfaces, as discussed by Sajtos et al. (2020), introducing a framework that accommodates general force distributions and possible cracking patterns. The results suggest that the inclusion of moment equilibrium considerations leads to a more precise determination of the structural safety of cracked domes. This study contributes to the ongoing research on the stability and failure mechanisms of domes by offering a more comprehensive analytical framework.

Statistical and Probabilistic Parameters Used as Reference for Hydrological-Energy Studies

Alessandro Calvi — Sat, 22 Feb 2025 00:11:04 +0100

Hydropower plant future production estimation is based on hydrological-hydraulic data. The present metholodogy validates the median as the reference parameter to be used for a better interpretation of statistical series, because it is a centered value where duration curves and their complementary curves intersect. Then, it is not affected by extreme events, providing a well representation of the whole dataset.

Geomechanical Challenges and Engineering Solutions for Tunnel Stability in the Himalayas: A Case Study Approach

Alessandro Calvi — Sun, 09 Feb 2025 22:30:03 +0100

The Himalayan region, characterized by complex geological formations and high tectonic activity, presents significant challenges for tunnel construction. This paper examines geomechanical issues such as tunnel squeezing, stress-induced instability, and rock bursting, with a focus on hydropower and railway tunnel projects in Nepal and India. Case studies, including the Chameliya Hydroelectric Project, Parbati II Hydroelectric Project, Nilgirikhola Hydroelectric Project, and railway tunnels in the Garhwal Himalaya, highlight the impact of weak, schistose rock masses and extreme overburden pressures. Various engineering methodologies, including empirical, semianalytical, analytical, and numerical modeling approaches, are discussed to assess stress states and deformation behavior. The study underscores the need for adaptive excavation techniques, such as the New Austrian Tunneling Method (NATM) and rock mass classification systems, to ensure tunnel stability. By integrating probabilistic analysis and advanced support systems, this research contributes to optimizing underground construction strategies in geologically challenging terrains.

The Twin Towers Collapse, Event Analyses and Structural Lessons, Master's Degree Thesis

Alessandro Calvi — Tue, 16 Apr 2024 09:51:04 +0200

This thesis is divided into two parts: in the first part the collapse of the WTC1, WTC 2 (Twin Towers) and WTC 7 buildings following the terrorist attacks of 11 September 2001 is analysed. In the second part, the collapse type and strength of frame buildings with different topological characteristics. What links the two parts is structural robustness.
Below is an overview of the work with a description of the topic covered in each Chapter.
Chapter 1: description of the structural and fire protection characteristics of the WTC 1, WTC 2 and WTC 7 buildings.
Chapter 2: timeline of the terrorist events of September 11, 2001.
Chapter 3: description of the types of fire, the performance of structures and the behavior of the main building materials (steel, concrete) to fire.
Chapter 4: analysis of the main hypotheses of the collapse of the Twin Towers present in the literature.
Chapter 5: definition of structural robustness, structural toughness, vulnerability. Description of project strategies to prevent progressive collapses.
Chapter 6: measurement of the structural strength of buildings with a reinforced concrete frame structure. through Discrete Element simulations (DEM).
Chapter 7: discussion of progressive collapse due to impacts from an analytical and bibliographical point of view.

Tunnel Collapse: Case Studies and Key Failure Mechanisms

Alessandro Calvi — Sat, 08 Feb 2025 12:22:03 +0100

Tunnel collapse is a critical issue in geotechnical engineering, affecting the safety, functionality, and economic viability of underground structures. This study examines the primary failure mechanisms of tunnels, including roof instability, shear failure of sidewalls, base heave, wedge failure, and progressive collapse, with a particular focus on hydropower tunnels. The role of principal stress directions and stress redistribution in failure processes is analyzed, highlighting the effects of excavation-induced unloading, in situ stress concentration, and external influences such as groundwater infiltration and seismic activity. Special attention is given to hydropower tunnels, where transient hydrostatic pressure variations, mineralogical degradation, and high in situ stresses increase the likelihood of collapse. The study integrates limit analysis and fracture mechanics to model tunnel failure mechanisms, emphasizing how plastic deformation and crack propagation contribute to instability. Numerical simulations and real-world case studies illustrate the interaction between stress conditions and structural response. The findings suggest that tunnel stability is rarely governed by a single factor but rather by a combination of geological, structural, and environmental influences that evolve over time. Future research should focus on the development of real-time monitoring systems using artificial

Professional Presentation - Alessandro Calvi

Alessandro Calvi — Mon, 03 Feb 2025 19:11:03 +0100

Unlocking the Full Potential of Hydropower

Alessandro Calvi — Wed, 15 May 2024 21:42:03 +0200

In this paper, a number of innovative technologies are presented that have the potential to improve the efficiency and utilization of hydropower. These technologies include new turbine designs, improved efficiency, small hydro.

Italian Dams Bibliography

Alessandro Calvi — Sun, 21 Apr 2024 19:03:12 +0200

RASSEGNA BIBLIOGRAFICA DELLA LETTERATURA ITALIANA SULLE DIGHE DI RITENUTA

EURCOLD - Dam Legislation

Alessandro Calvi — Sat, 20 Apr 2024 20:26:10 +0200

Hydro Forecasting Model

Alessandro Calvi — Sat, 20 Apr 2024 21:00:03 +0200

DRENAGGI NELLE DIGHE MURARIE

Alessandro Calvi — Sat, 20 Apr 2024 20:52:02 +0200

CORSO AGGIORNAMENTO INGEGNERI ENEL 2021

Alessandro Calvi — Sat, 20 Apr 2024 20:46:03 +0200