Periodic Reporting for period 1 - LEMMA (Landslide and avalanchE Mechanics with Multiphysical datA)
Reporting period: 2022-09-01 to 2024-08-31
The context of project LEMMA is the increase in large mass movements (rockfalls, landslides and avalanches) in alpine regions that is predicted to occur due to climate change. Predicting these phenomena is difficult, because it requires models with resolution at very fine scales (millimetric) that must also operate at very large scales (kilometric). Further, the mechanical, thermal and hydrological aspects of these models must all be taken into account in order to accurately model the melting of permafrost, the underlying process that triggers these large movements.
In order to address these challenges, project LEMMA proposes developments in the modelling of fractures and granular flows, as well as the numerical implementation of these models, in order to obtain a better understanding of the underlying processes. By obtaining these more refined models, large scale implementations can be envisioned using advanced numerical techniques, that will enable a comparison of the model predictions with reality at certain well-instrumented sites located in the Alps. These predictions are very challenging, not only due to the previously mentioned changes of scale, but also the large displacements and distortions of the material involved, that may travel kilometres down and alpine valley. Further, using these advanced numerical techniques, predictions can be made that describe the increased risk of large mass movements in certain localities as the climate changes, and enable governments and communities to make better-informed decisions about where, what and whether to build to protect themselves from these risks.
The project has three objectives:
1. The development of thermo-hydro-mechanical models for cracks and granular flows that are specialised to the task of predicting melting and phase changes in permafrost,
2. The development of an advanced "data-driven mechanics" numerical solver that takes the output of the models and renders predictions in a numerically efficient manner, and
3. Implement the data-driven mechanics solver in the material point method, allowing predictions of large mass movements that can experience kilometres of displacement from their point of origin to their stopping point.
The expected impact of these objectives is that the geomechanics community, the intersection between geologists and engineers, will have the necessary tools available to make concrete predictions about alpine gravitational risks linked to climate change. Armed with these tools, scientists will be able to provide accurate and timely advice to local, regional and national governments, as well as the affected citizenry, about these risks, as well as the necessary precautions to mitigate them and ensure continued safe habitation of the Alps.
In order to address these challenges, project LEMMA proposes developments in the modelling of fractures and granular flows, as well as the numerical implementation of these models, in order to obtain a better understanding of the underlying processes. By obtaining these more refined models, large scale implementations can be envisioned using advanced numerical techniques, that will enable a comparison of the model predictions with reality at certain well-instrumented sites located in the Alps. These predictions are very challenging, not only due to the previously mentioned changes of scale, but also the large displacements and distortions of the material involved, that may travel kilometres down and alpine valley. Further, using these advanced numerical techniques, predictions can be made that describe the increased risk of large mass movements in certain localities as the climate changes, and enable governments and communities to make better-informed decisions about where, what and whether to build to protect themselves from these risks.
The project has three objectives:
1. The development of thermo-hydro-mechanical models for cracks and granular flows that are specialised to the task of predicting melting and phase changes in permafrost,
2. The development of an advanced "data-driven mechanics" numerical solver that takes the output of the models and renders predictions in a numerically efficient manner, and
3. Implement the data-driven mechanics solver in the material point method, allowing predictions of large mass movements that can experience kilometres of displacement from their point of origin to their stopping point.
The expected impact of these objectives is that the geomechanics community, the intersection between geologists and engineers, will have the necessary tools available to make concrete predictions about alpine gravitational risks linked to climate change. Armed with these tools, scientists will be able to provide accurate and timely advice to local, regional and national governments, as well as the affected citizenry, about these risks, as well as the necessary precautions to mitigate them and ensure continued safe habitation of the Alps.
The work performed in this project ultimately focused on the development of models of fracture, friction and impact, namely the mechanical part of the intended thermo-hydro-mechanical models for cracks. The main achievements of this work are two preprints and associated code bases.
The first preprint focuses on impact and friction problems in the "nonsmooth dynamics" context. WIthin this field, there has been an open problem of 40 years standing that causes seemingly dissipative models to create energy, and thus violate the laws of thermodynamics. This preprint shows how to resolve this problem, and comes with a comprehensive code base that allows other scientists to quickly implement and modify the results. This can also be used by technically advanced engineers to make predictions about the impact of rockfalls on solid objects, an example that is treated within the preprint.
The second preprint focuses on the prediction of "mixed mode I-II" fracture (when a crack is created by the two faces being both pulled apart and slid along each other), including the effects of impact and friction on the newly created crack faces. This is a technically challenging problem, and this preprint builds on previously published work by the grant awardees that resolved several technical defects in what is known as "extrinsic cohesive zone modelling". The contributions of the preprint are to extend the model to including the sliding effects, which substantially increases the degree of theoretical and numerical difficulty. In addition, this preprint is accompanied by a very substantial code base that allows the prediction of arbitrary crack paths, using the "finite element method". Engineers are able to use this code base to make predictions about fracture propagation in any brittle material, not only rocks. Thus, this model can be adapted to model both the detachment of a rock, the fragmentation as it falls and bounces, and the damage that it will cause as it impacts on a protection structure.
There was also work performed on the problem of models for granular flows. These flows slide on "shear bands", regions of intense deformation that cannot be correctly predicted with standard tools. A previously existing software suite developed by the awardees was adapted and expanded to enable the prediction of these band structures, and this method is adaptable to a wide variety of models, including future models that can be developed to address the problem of more granular large mass movements (such as avalanches and landslides).
The outcomes of this work (one preprint and code base for impact and friction, one preprint and code base for fracture, impact and friction, and one software suite for model integration and prediction of shear band structures) were not exactly as foreseen in the description of the action, but nevertheless constitute a substantial contribution to the scientific literature, and form the necessary base from which to launch future developments including thermal and hydrological effects.
The first preprint focuses on impact and friction problems in the "nonsmooth dynamics" context. WIthin this field, there has been an open problem of 40 years standing that causes seemingly dissipative models to create energy, and thus violate the laws of thermodynamics. This preprint shows how to resolve this problem, and comes with a comprehensive code base that allows other scientists to quickly implement and modify the results. This can also be used by technically advanced engineers to make predictions about the impact of rockfalls on solid objects, an example that is treated within the preprint.
The second preprint focuses on the prediction of "mixed mode I-II" fracture (when a crack is created by the two faces being both pulled apart and slid along each other), including the effects of impact and friction on the newly created crack faces. This is a technically challenging problem, and this preprint builds on previously published work by the grant awardees that resolved several technical defects in what is known as "extrinsic cohesive zone modelling". The contributions of the preprint are to extend the model to including the sliding effects, which substantially increases the degree of theoretical and numerical difficulty. In addition, this preprint is accompanied by a very substantial code base that allows the prediction of arbitrary crack paths, using the "finite element method". Engineers are able to use this code base to make predictions about fracture propagation in any brittle material, not only rocks. Thus, this model can be adapted to model both the detachment of a rock, the fragmentation as it falls and bounces, and the damage that it will cause as it impacts on a protection structure.
There was also work performed on the problem of models for granular flows. These flows slide on "shear bands", regions of intense deformation that cannot be correctly predicted with standard tools. A previously existing software suite developed by the awardees was adapted and expanded to enable the prediction of these band structures, and this method is adaptable to a wide variety of models, including future models that can be developed to address the problem of more granular large mass movements (such as avalanches and landslides).
The outcomes of this work (one preprint and code base for impact and friction, one preprint and code base for fracture, impact and friction, and one software suite for model integration and prediction of shear band structures) were not exactly as foreseen in the description of the action, but nevertheless constitute a substantial contribution to the scientific literature, and form the necessary base from which to launch future developments including thermal and hydrological effects.
The results of the impact and friction work go substantively beyond the state of the art. The problem of energy creation of frictional models during sliding reversal has been open for 40 years in the contact mechanics community. In this project, we proved that an already existing model, the Frémond model of impact and friction, always avoided energy creation in continuous time (when treated analytically), while the existing and widely used model, the Moreau model, could only avoid energy creation in continuous time in certain special cases. We then demonstrated how to treat the Frémond model numerically to guarantee that the energy creation was avoided in discrete time (as occurs when models are integrated numerically on computers), and provided an example of where the special case of the Moreau model that avoids energy creation in continuous time, still creates energy in discrete time. An example of practical application (a rockfall impacting a protection wall made of concrete blocks) was treated, showing how even in the least favourable case beyond where our mathematical proofs are valid, the new numerical treatment of the Frémond model performed much better than the old Moreau model. The paper was accompanied by a collection of codes and data allowing other researchers to immediately reproduce our results, and extend them if they so choose. The potential impacts of this work are that scientists can now have greater confidence in the quality of the model used when studying rapid impacts combined with friction, and engineers who study practical problems such as rockfall impacts have access to a model that is more accurate. Wider uptake can occur with further research, particularly in the large rotations case, and development of faster software implementations of the numerical solution technique.
The results of the fracture, impact and friction work also go substantively beyond the state of the art. Previous work by the awardees considered a purely mode I fracture problem (the crack is created by the surfaces being pulled apart) with impact. This work manged to avoid certain pathologies that previously existed in the broader model family (extrinsic cohesive zone models), prove that the numerical method always has a solution (and that solution is unique), so the computer will always return a sensible answer when we give it sensible information, and never creates energy. However, it is very rare that a crack occurs in pure mode I (in fact, this essentially only ever occurs in experiments designed to force this to occur). As such, a model that had the benefits of the previous work in pure mode I, but that could also handle mode II (cracking due to the surfaces being slid alongside each other) was required. Mode II fracture also implies the presence of friction along the crack surfaces, so this aspect also needed to be included in the model. Once again, the model that was developed avoided the pathologies that previously existed in the extrinsic cohesive zone model family, the numerical method always has a solution, and it is dissipative. In addition, this work comes with a very substantial code base that allows the crack to be inserted "on-the-fly", meaning that arbitrary crack paths can be treated. This means that essentially any geometry can be treated and any crack path can be followed, with the model implementation in code always able to handle the solution accurately while maintaining the appropriate guarantees. Further uptake and success can be assured by further research to include the desired thermal and hydrological effects in the model, and by fully integrating the model in the Akantu software suite that it currently relies on to follow the arbitrary crack paths. These are both the subject of ongoing work.
The results of the fracture, impact and friction work also go substantively beyond the state of the art. Previous work by the awardees considered a purely mode I fracture problem (the crack is created by the surfaces being pulled apart) with impact. This work manged to avoid certain pathologies that previously existed in the broader model family (extrinsic cohesive zone models), prove that the numerical method always has a solution (and that solution is unique), so the computer will always return a sensible answer when we give it sensible information, and never creates energy. However, it is very rare that a crack occurs in pure mode I (in fact, this essentially only ever occurs in experiments designed to force this to occur). As such, a model that had the benefits of the previous work in pure mode I, but that could also handle mode II (cracking due to the surfaces being slid alongside each other) was required. Mode II fracture also implies the presence of friction along the crack surfaces, so this aspect also needed to be included in the model. Once again, the model that was developed avoided the pathologies that previously existed in the extrinsic cohesive zone model family, the numerical method always has a solution, and it is dissipative. In addition, this work comes with a very substantial code base that allows the crack to be inserted "on-the-fly", meaning that arbitrary crack paths can be treated. This means that essentially any geometry can be treated and any crack path can be followed, with the model implementation in code always able to handle the solution accurately while maintaining the appropriate guarantees. Further uptake and success can be assured by further research to include the desired thermal and hydrological effects in the model, and by fully integrating the model in the Akantu software suite that it currently relies on to follow the arbitrary crack paths. These are both the subject of ongoing work.