# Numerical modelling of geomaterials at failure

Alex Spetz

Research output: ThesisDoctoral Thesis (compilation)

## Abstract

Geotechnical engineering is the science dealing with mechanics of soils and rocks and its engineering applications. Geotechnical engineering projects vary in a wide range, from evaluation of the stability of natural slopes and man-made soil deposits, to the design of earthworks and foundations. Traditional methods, using manual calculations or simplified computational methods, do not, as a rule, take into account the effects of soil-structure interaction, which can have a significant impact on the behaviour of the structure. The aim of the research presented in this dissertation is focussed on developing methods to analyse soil and rock behaviour. The research is in one part concerned with how soil-structure interaction can affect the design of foundations and geotechnical structures. The second part of the work is focussed on developing new methods to model geotechnical applications.

When designing foundations it is a common practice that separate numerical models are used in the analysis of soil behaviour and of structural behaviour. A common procedure is that the geotechnical engineer establishes a model of the site conditions and performs a simulation of the behaviour of the ground using pre calculated load values received from the structural engineer. The resulting settlements can then in turn be used in the dimensioning of the structure. Using separate models can lead to unrealistic prediction of the behaviour of both structure and load, as the soil-structure interactions are disregarded. As the use of computational methods is increasing, both to simulate the response in soil and during the structural design. Paper A enlightens some of the risk that misuse of simplifications can lead to. The paper includes an evaluation of how using the modulus of subgrade reaction during the design of foundations can affect the dimensioning of the reinforcements in shallow foundations.

Isogeometric analysis, is a numerical method that uses non-uniform rational B-splines (NURBS) as basis functions instead of the Lagrangian polynomials often used in the finite element method. These functions have a higher-order of continuity, making it possible to represent complex geometries exactly. The Higher-order continuity of the basis functions is also beneficial for problems that include frictional sliding and large displacements, overcoming the numerical instability caused by the C0-continuous basis functions often used in finite element formulations. A common problem in many geotechnical simulations. Paper B presents numerical simulations of soil plasticity using isogeometric analysis comparing the results to the solutions from conventional finite element method.

The ability to predict rock behaviour using numerical models is pivotal to solve many rock-engineering problems. Numerical modelling can also be used to improve our understanding of the complicated failure process in rock. With models that better capture the fundamental failure mechanisms observed in laboratory, our ability to generate reliable large-scale models improves. Prediction of brittle fractures in rock and soil is a complex problem with a number of active research areas, ranging from landslides and fault mechanics to hydraulic fracturing.

In this work a modified phase-field fracture model that can predict crack nucleation in porous rock and rock-like material is presented. In porous rock, the critical release rate for tensile cracks can be orders of magnitude smaller than the critical energy release rate for shear cracks and compressive stresses can lead to the formation of compaction driven cracks. Paper C and Paper D demonstrates the capability of the proposed phase-field model for simulating the evolution of mixed mode fractures and compressive driven fractures in porous artificial rocks and Neapolitan Fine Grained Tuff.
Original language English Dahlblom, Ola, SupervisorTudisco, Erika, Assistant supervisorDenzer, Ralf, Assistant supervisor Lund Department of Construction Sciences, Lund University 978-91-7895-288-5 978-91-7895-289-2 Published - 2019 Sept 19

### Bibliographical note

Defence details
Date: 2019-10-16
Time: 10:15
Place: Lecture Hall MA:5, Matteannexet, Sölvegatan 20, Lund University, Faculty of Engineering LTH
External reviewer(s)
Name: Sciarra, Giulio
Title: Professor
Affiliation: Research Institute in Civil and Mechanical Engineering (GeM), Nantes, France
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## Subject classification (UKÄ)

• Geotechnical Engineering

## Free keywords

• soil-structure interaction
• soil plasticity
• phase-field fracture model
• compression driven fractures
• artificial rock
• porous rock
• finite element analysis
• isogeometric analysis
• NURBS
• numerical methods

## Fingerprint

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• ### Isogeometric Analysis of Soil Plasticity

Spetz, A., Tudisco, E., Denzer, R. & Dahlblom, O., 2017 Jul 28, 7, 3, p. 96-116 21 p.

Research output: Contribution to journalArticlepeer-review

Open Access