Phd in STRUCTURAL AND GEOTECHNICAL ENGINEERING

Lecturer: Alba Bisante

Dates:
5, 12, 19, 26 May – 15:00–17:00
7, 14, 21, 28 May – 16:00–18:00
4, 16 June – 15:00–17:00

Venue: Aula Riunioni Architettura

Lecturers: Claudio Durastanti – Anna Vidotto

Dates: 13, 20, 27 May 09:00–13:00; 7, 14, 21 October 09:00–13:00

Venue: Sala riunioni 329 SPV

Description: Structural and geotechnical systems are characterised by multiple sources of uncertainty, including variability in material and soil properties, uncertainty in loads and mathematical models. The course introduces the main tools of probability and applied statistics to:
• model the variability of engineering parameters
• analyse experimental data from laboratory and in-situ tests
• quantify uncertainty in model predictions
• introduce fundamental concepts of structural and geotechnical reliability
Particular attention is devoted to applications in civil engineering.

Programme: 
1. Probabilistic modelling of uncertainty in engineering systems (4 hours)
Sources of uncertainty in civil engineering problems:
• variability of material properties
• variability of geotechnical parameters
• uncertainty in environmental loads
• model uncertainty

Review of probability:
• random variables
• probability distributions
• statistical moments
Distributions commonly used in civil engineering:
• normal distribution
• lognormal distribution
• Weibull distribution
• distributions for extreme phenomena
Applications to the modelling of material resistance, mechanical properties of soils and environmental loads.

2. Statistical dependence and uncertainty propagation (4 hours)
• random vectors and dependence between variables
• covariance and correlation
• covariance matrices
• multivariate normal distribution
Uncertainty propagation in engineering models:
• linear combinations of random variables
• first-order approximations
• error propagation
Applications to the combination of structural loads and correlation between geotechnical parameters.

3. Elements of structural and geotechnical reliability (4 hours)
• limit state function
• failure probability
• reliability index
Basic methods for reliability assessment:
• FOSM method (First Order Second Moment)
• introduction to FORM methods
Applications to structural safety and slope stability.

4. Statistical analysis of experimental data (4 hours)
• samples and sample statistics
• estimation of distribution parameters
• method of moments
• maximum likelihood method
• confidence intervals
Applications to statistical analysis of material tests and estimation of soil property variability.

5. Statistical tests and empirical models (4 hours)
• hypothesis testing
• t-test
• chi-square test
• goodness-of-fit tests
Regression models:
• simple linear regression
• interpretation of parameters
• residual analysis
Applications to empirical correlations in geotechnics and models based on experimental data.

The course includes applied examples relating to:
• statistical analysis of geotechnical data
• probabilistic modelling of structural loads
• probabilistic assessment of the safety of structural and geotechnical systems

Lecturer: Jacopo Ciambella

Dates: 7, 9, 10, 14, 15, 16 July, 10:00–13:00

Venue: Sala riunioni 329 SPV

Programme: 
Lecture 1 — Structural Dynamics and the Time-Domain Foundations (3 h)

- The structure as an input–output dynamical system; excitation sources and response quantities
- Sensor technologies for SHM: accelerometers, strain gauges, FBG, LVDTs; the measurement chain
- Linearity, superposition, time invariance; the LTI framework
- SDOF equation of motion, free vibration, logarithmic decrement
- Impulse response and Duhamel's integral for arbitrary loading
- MDOF eigenvalue problem, mode-shape orthogonality, modal superposition
- Participation factors, effective modal mass, Rayleigh damping
- Stationarity, ergodicity, environmental variability
- Observability, optimal sensor placement, damage types, the SHM data pipeline

Lecture 2 — Fourier Analysis, Laplace Transform, and Frequency Response (3 h)

- Fourier series, Fourier transform, key properties and Parseval's theorem
- DFT, FFT, frequency resolution, spectral leakage, windowing functions
- STFT, wavelet transform, spectral features for SHM
- Laplace transform: definition, properties, key pairs
- Transfer function $H(s)$, poles and zeros, $s$-plane interpretation
- Frequency response function $H(j\omega)$: Bode diagram, Nyquist plot, real/imaginary decomposition
- Resonance, half-power bandwidth, energy balance
- MDOF modal transfer matrix, dynamic amplification factor, transmissibility, FRF types
- Input–output PSD relationship and connection to output-only identification

Lecture 3 — Sampling, Discrete-Time Systems, and the $z$-Transform (3 h)

- Shannon–Nyquist sampling theorem, aliasing, anti-aliasing filters
- ADC resolution, quantisation noise, sigma-delta oversampling
- Multi-sensor synchronisation; sampling-rate selection for SHM
- Discrete-time convolution, resampling, decimation
- $z$-transform: definition, ROC, inverse via partial fractions
- Difference equations, discrete transfer function $H(z)$
- Poles, zeros, and the unit circle; stability criterion
- Bilinear transform, frequency warping, frequency response from $H(z)$
- AR and ARMA models for structural identification; model-order selection

Lecture 4 — Digital Filtering, Feature Engineering, and Output-Only Identification (3 h)

- FIR filter design: window method, linear phase, Parks–McClellan
- IIR filter design: Butterworth, Chebyshev, elliptic prototypes; zero-phase filtering
- Notch filtering, envelope detection via the Hilbert transform, cepstral analysis
- Numerical differentiation and integration of vibration signals
- Hand-crafted SHM features: time-domain, spectral, modal, cepstral
- Wiener–Khinchin theorem, PSD, cross-spectral density, coherence
- Spectral estimation: periodogram, Welch's method, bias–variance trade-off
- Operational modal analysis: FDD and EFDD damping estimation, SSI and stabilisation diagrams
- Uncertainty quantification of spectral and modal estimates

Lecture 5 — Machine Learning for Structural Health Monitoring (3 h)

- The ML pipeline: feature matrix, labels, temporal and grouped splitting strategies
- Feature scaling, PCA for dimensionality reduction and environmental normalisation
- Hyperparameter tuning: grid search, random search, Bayesian optimisation
- Supervised methods: logistic regression, SVMs, random forests, gradient boosting
- Unsupervised and novelty detection: one-class SVM, isolation forest, Mahalanobis distance
- Evaluation metrics, cost-sensitive interpretation, bias–variance trade-off
- MLPs, batch normalisation, loss functions for imbalanced data
- 1-D and 2-D CNNs for vibration signals; architecture design and training
- RNNs, LSTMs, GRUs; transformer-based sequence models

Lecture 6 — Deep Generative Models, Physics-Informed AI, and the Digital Twin (3 h)

- Autoencoders for anomaly detection; variational, denoising, and contractive variants
- Residual networks and skip connections; contrastive and self-supervised learning
- Transfer learning from simulation to field; data augmentation strategies
- Residual learning and physics-informed neural networks (PINNs)
- Surrogate modelling with Gaussian processes; FE model updating via ML
- Uncertainty quantification: Bayesian neural networks, deep ensembles, conformal prediction
- Interpretability: SHAP, saliency maps, domain-consistency checks
- The digital twin paradigm: architecture, challenges, scalability

Lecturer: Stefano Vidoli

Dates: 21 April (11:00-13:00), 22 (10:00-13:30), 23 April (10:00-13:30); 5, 6, 7 May (10:00-13:00)

Venue: Aula Caveau SPV

Description: The course aims to provide doctoral students with the advanced mathematical tools necessary for the formulation and solution of complex problems in solid and structural mechanics. Starting from the foundations of functional analysis, the programme will explore how variational methods allow the search for solutions to be extended to problems that do not admit a classical treatment, with particular attention to nonlinear phenomena such as damage and plasticity.

Programme: 
1. Introduction to Variational Methods
• Limitations of the classical formulation of partial differential equations (PDEs).
• Why variational methods? Extension of the concept of solution and weak formulations.

2. Formulation of the Classical Elasticity Problem
• Review of continuum mechanics.
• Total potential energy and the principle of virtual work.
• Variational formulation of the linear elastic problem.

3. Functional Spaces and Distribution Theory
• Normed vector spaces and completeness: Banach and Hilbert spaces.
• Sobolev spaces; embedding and trace theorems.

4. Variational Inequalities: Damage and Plasticity
• Constrained minimisation problems and convexity.
• Introduction to variational inequalities.
• Applications to nonlinear mechanics: damage and plasticity models for materials.

5. Numerical Methods and Well-Posedness Analysis
• Existence and uniqueness of the solution.
• The concept of coercivity and continuity in the engineering context.
• Galerkin approximation and mathematical foundations of the Finite Element Method.

6. Locking Phenomena and Mixed Methods 
• Analysis of the numerical locking problem.
• Introduction to mixed variational methods. Stability conditions (Inf-Sup).

Lecturer: Andrea Arena

Dates: 22, 24, 26 June; 1, 3, 6, 8 July 10:00–13:00

Venue: Aula Riunioni 329 SPV

Description: The course aims to provide the basic knowledge for understanding the linear and nonlinear dynamic behaviour of structures. The introduction will be devoted to the modelling of dynamical systems, including the identification of kinematic descriptors of motion, the characterisation of the constitutive behaviour of a structure and of the actions acting on it. Paradigmatic structural models will be introduced to discuss the main dynamic phenomena that emerge in both the linear and nonlinear regimes. Applications will also be presented with reference to case studies implemented in software capable of performing symbolic analysis.

Programme:

Introduction
The dynamic model of a structure: kinematic parameters describing motion; rheological models representative of the constitutive behaviour of structures; actions acting on structures. Linear and nonlinear structural models; equations of motion.

Linear dynamics
Harmonic motion. Free dynamics of the "simple harmonic oscillator". Effect of damping on the free dynamic response of the "simple oscillator". State-space representation of the equations of motion. Dynamic stability of a mechanical system.
Forced dynamics: direct resonance in harmonically excited systems. Resonance in parametrically excited systems.
Multi-degree-of-freedom systems (MDoF). Modal analysis and its applications in linear dynamic systems via the modal expansion theorem.
Harmonic excitation in multi-degree-of-freedom systems and the concept of passive vibration control.
Indirect actions: the case of earthquakes; analysis via response spectrum.

Nonlinear dynamics
The Duffing oscillator. Methods for solving nonlinear equations of motion (with particular attention to the method of multiple scales). Nonlinear normal modes. Effect of damping in nonlinear systems. Direct resonance in harmonically excited systems. Resonance in parametrically excited systems. The Van der Pol oscillator and the case of nonlinear damping.
Multi-degree-of-freedom systems: effect of nonlinearities in the case of internal resonances.

Lecturer: Stefano Pampanin

Dates: 23, 24, 25, 28, 29 September, 10:00–14:00

Venue: Aula Riunioni 329 SPV

Programme: 
-    Overview of the Canterbury earthquakes sequence: lessons learnt, impact on performance-based design philosophy and opportunity for a wide implementation of the next generation of damage-resisting structures
-    Alternative design philosophies and solutions for the seismic design of precast concrete structures. Emulation of cast-in situ concrete. Introduction to jointed ductile connections,  
-    Research and Development of PRESSS-concrete Technology and the hybrid system concept. Research & Development of these systems.  
-    Extension to Timber: development of multi-storey long-span prestressed timber (Pres-Lam) buildings using engineered wood materials (Glulam, LVL, Cross-Lam)
-    Examples of on-site applications worldwide of PRESSS and PRES-LAM technology in low-, medium- or high-seismic areas. Constructability aspects, sequence and detailing.
-    Cost/Performance evaluation of low-damage technologies. Resilience and Sustainability considerations

Lecturer: Angelo Amorosi

Dates: 6, 8, 13, 15, 20, 22 October 2026, 10:00–13:00

Venue: Sala riunioni 329 SPV

Description: This 6 days course is aimed at introducing, at the post-graduate level, the basic principles of the mechanics of soils by discussing some of their experimental features and constitutive modelling strategies, with particular emphasis to clayey materials. The fundamental field equations for a two-phase medium are first derived, followed by an overview of typical experimental results and their interpretation in the frame of Critical State Soil Mechanics.
The key ingredients of plasticity theory are then introduced, first under 1D conditions and then generalised to 3D ones, aiming at providing the general theoretical setting then adopted to illustrate a wide class of plasticity-based models for soils, ranging from standard perfectly plastic ones to more advanced mixed-hardening multi-surface formulations.
An alternative constitutive approach based on thermodynamics with internal variables is introduced and its merits are illustrated with reference to different forms of elasto-plastic coupling of soils. 
Finally, the above approach is generalised and applied to the development of a micro-informed thermodynamics-based constitutive framework. This is then adopted for the formulation of an innovative model accounting of double porosity and fabric of fine-grained soils.           

Programme: 

The soil as a two-phase continuum medium
Principle of effective stress. Solid-fluid compatibility. Elements of soil hydraulics. Field equations for a deformable porous medium under static conditions; special cases: dry soil, saturated soil with water flow under stationary or transient conditions, undrained conditions, consolidation. Field equations under dynamic conditions.

Experimental observations
Laboratory equipment. Typical experimental observations on reconstituted clays: radial paths, deviatoric paths. Dependence on the current stress state and stress history: contracting or dilating response. Critical state. Normalisation, state boundary surface and their mechanical interpretation. Effects of anisotropic radial compression: experimental observations and their mechanical interpretation; relationship between macro and micro scales via scanning electron microscope observations. Effects of bonding between grain aggregates on the mechanical behaviour of natural clays: experimental observations and their mechanical interpretation.
The behaviour of clays for states far from failure: initial shear stiffness and non-linear dependence of stiffness on the amplitude of the stress/strain perturbation. Experimental observations of the initial shear stiffness: dependence on the effective stress state, dependence on previous stress history, anisotropy.

Elements of plasticity theory
Elements of phenomenological one-dimensional elasto-plasticity: experimental evidence, reversibility, yielding, loading-unloading conditions, perfect plasticity, hardening.
Elements of phenomenological multidimensional elasto-plasticity: experimental evidence, elastic domain, yielding, plastic flow, loading-unloading conditions. Direct and inverse formulation of perfect plasticity. Isotropic hardening, kinematic hardening, anisotropic hardening. Direct and inverse formulation of hardening plasticity.

Plasticity-based constitutive modelling of soils
Hypo-elasticity and hyper-elasticity. The soil as an elastic-perfectly plastic medium. Simple elastoplastic models with isotropic hardening: Modified Cam-Clay (MCC) and its evolutions. Cementation and mechanical debonding processes: ad hoc isotropic hardening laws. Anisotropic strain history described by tensorial variables: kinematic and anisotropic hardening, mixed hardening. Multi-surface hardening plasticity models.

Constitutive modelling based on thermodynamics with internal variables
Motivations. Energy and its rate under isothermal conditions. 1st Law. Legendre transform. 2nd Law. Rate of dissipation. Yield functions in the generalised and Cauchy stress spaces. MCC with linear and non-linear elasticity. Isotropic coupling: MCC reformulation and consequences. Anisotropic hardening: Saniclay-T. Beyond Saniclay-T: anisotropic coupling.

Micro-informed constitutive modelling of clays based on thermodynamics
Motivations. Micro-macro experimental evidences: the role of clusters of particles and related porosities and fabrics. Relevant observable internal variables for clays. A double porosity and fabric framework for fine-grained soils: thermodynamics framework; energy and rate of dissipation functions; equivalent single-surface hardening plasticity model; calibration of model parameters and initialisation of internal variables; validation against multiscale experimental results. Final remarks. 

Lecturer: Daniela Boldini

Dates: 19, 21, 23, 27, 29 October, 15:00–19:00

Venue: Sala riunioni 329 SPV

Description: This 20-hour course is designed to provide a comprehensive understanding, at the post-graduate level, of the key aspects of saturated soil modelling using the Finite Element method. It begins by introducing the field equations that govern the interaction between soil skeleton and pore fluid under static conditions, followed by their finite element discretization and solution. The course also delves into the implementation of soil constitutive laws at the level of Gauss integration points, encompassing both common explicit and implicit numerical algorithms. The scope of the governing equations is then expanded to cover dynamic conditions, offering insights into addressing earthquake geomechanical problems. In the final session, the course explores relevant challenges in practical applications, including considerations such as 2D versus 3D schematization, initial and boundary conditions, staged construction, and soil-structure problems, illustrated with practical examples.

Programme: 
A review of finite element theory for linear and non-linear materials

Pore pressure calculation, seepage and consolidation

Numerical implementation of soil constitutive laws 

Seismic geotechnical problems

Relevant issues in practical applications