Evaluating the temporal stability and risk of unsaturated soil slopes during rainfall is essential for early warning and emergency response to landslides. However, limited research has been conducted on the transition timing of sliding mechanisms, instability/failure time and the integration of sliding consequences into quantitative risk assessment. In order to extend the research in this field, the Random Finite Element Method (RFEM) is used in this paper to investigate the influence of spatial variability of hydraulic properties (related to the fundamental parameter porosity) on the temporal stability and risk of soil slopes subject to rainfall. The findings indicate that the advancing speed of the wetting front is more rapidly in zones with low porosity than that in zones with high porosity. As rainfall progresses, the sliding mechanism of the slope shifts from deep sliding to shallow sliding. The homogeneous case tends to underestimate the rise in groundwater levels, leading to an overestimation of slope stability. Hydraulic boundary conditions significantly affect slope stability, making it crucial to consider horizontal (or near the toe of the slope) drainage conditions in practical applications. Additionally, the time of instability/failure predicted in the homogeneous case may be delayed compared to the actual conditions. Both probability of instability/failure and risk increase with continued rainfall. Compared to scenarios where the spatial variability of internal friction angle is not considered, the probability of instability/failure and risk will be higher when the spatial variability of internal friction angle is additionally considered. Risk-based assessment can define the risk levels, reflecting the severity of sliding consequences. Furthermore, the Malin slope failure record from the Chibo region of India is used to validate the effectiveness of the proposed approach. The probabilities of slope failure align well with actual observations, and the risk-based assessment provides additional information into the Malin landslide. This paper proposes a general model for studying the performance of heterogeneous slopes subject to rainfall, providing valuable guidance for landslide early warning systems and the scope and timing of emergency measures taken.

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This study presents a thermo-hydro-mechanical framework to model hydrothermal systems within a simplified faulted synthetic reservoir, replicating current production scenarios in The Netherlands and Germany. The reservoir, composed of porous and permeable sandstone, and the confining layer, made of porous but less permeable shale, undergoes a process where cold water is injected and hot water is extracted. A fault, situated 750 meters from the injection well, is investigated to examine the conditions when fault slip could occur. Various fault and formation stiffnesses are modeled to assess their impact on fault stability. Our analysis reveals that stress changes induced by hydrothermal operations can lead to fault reactivation, with the stiffness contrast between the reservoir and confining layers playing a significant role in when and where fault reactivation can occur. Stiffer confining layers lead to reactivation occurring more closely associated with the passage of the cooling front. In contrast, a stiffer reservoir results in greater and more gradual stress changes, making reactivation more closely related to the total volume of cooled rock.

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Ground source heat pumps (GSHP) coupled to shallow borehole heat exchangers (BHE) represent a low emission technology to provide space heating and cooling. However, ongoing long-term heating or cooling of the ground caused by unbalanced loads leads to a performance decline and in the worst case to a system shutdown. Enhanced regeneration can increase the system efficiency, reduce the necessary borehole length or compensate unbalanced loads. In this study, a literature review about the regeneration of shallow BHE fields to counteract ground thermal imbalance is conducted to give an overview about the state-of-the-art and identify research gaps. The most common heat sources for artificial regeneration in heating-dominated applications are space cooling and solar thermal flat-plate collectors, while the most common heat sinks in cooling-dominated applications are space heating and cooling towers. In heating-dominated applications, mostly single buildings are studied. There is a lack of studies on district heating and cooling applications, which are especially needed as the benefit of regeneration increases with system size. There is also a lack of long-term, large system size experimental work to validate theoretical studies.

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Nearly half of the Netherlands’ natural gas consump tion is allocated to heating, with direct -use geothermal heating being one of the available low-carbon energy solutions. A geothermal well doublet, designed with the two primary aims of research and commercial heat supply, is currently being installed on the campus of Delft University of Technology. The project is a key national research infrastructure and is being incorporated into the European sustainable and distributed infrastructure (EPOS: European Plate Observing System, https://www.epos-eu.org/), such that accessibility and data availability will be as wide as possible. All observations will be included in a digital-twin framework, which will allow us to make better decisions in future geothermal projects. The project includes a comprehens ive research program, involving the installation of a wide range of instruments alongside an extensive logging and coring program and monitoring network. The doublet has been cored, with substantial continuous samples from the heterogeneous reservoir, alongside a large suite of well logs in both the reservoir and overlying geological units. Such investigation is rarely undertaken in geothermal projects. A fiber-optic cable will monitor the producer well all the way down to the reservoir section, at approximately 2300m depth, in the Lower Cretaceous Delft Sandstone that is used as a geothermal reservoir in a series of existing and planned doublets in the West Netherlands Basin. A local seismic monitoring network has been installed in the surrounding area with the aim of monitoring very low-magnitude natural or induced seismicity. A vertical observation well with electromagnetic sensors will be drilled in the near future between the injector and producer to monitor cold-front propagation. This paper presents the initial modeling for the project and steps towards the production of a digital twin. Two modeling examples in the paper will emp hasize current operational challenges relevant to the project.@en

A geothermal well doublet, designed with two primary aims; one of research and the second of commercial thermal energy supply, is currently being installed on the campus of Delft University of Technology, with the wells being drilled in the second half of 2023. The project includes a comprehensive research program, involving the installation of a wide range of instruments alongside an extensive logging and coring program and monitoring network. The doublet has been cored, with continuous samples from the heterogenous reservoir being complimented with more distributed side-wall cores, alongside a large suite of open-hole well logs in the reservoir section of both wells. Such investigation is rarely undertaken in geothermal projects. A fiber optic cable will monitor the production well, and will be installed all-the-way down to the reservoir section when the well completion is installed, at approximately 2300m depth. The reservoir is the fluvial Lower Cretaceous Delft Sandstone that is used as a geothermal reservoir in a series of existing and planned doublets in the West Netherlands Basin. A local seismic monitoring network has been installed in the surrounding area with the aim of monitoring very low-magnitude natural or induced seismicity. A vertical observation well with electromagnetic sensors will be drilled in a few y ears’ time between the injector and producer to monitor cold-front propagation. The total project is targeted to supply around 25 MW of thermal energy at peak conditions, next to this project a thermal energy storage system is planned to provide a seasonal buffer. The project is a key national research infrastructure and is being incorporated into the European infrastructure EPOS (European Plate Observing System, https://www.epos-eu.org/), such that accessibility and data availability will be as wide as possible. All observations will be included in a digital-twin framework that will allow better decisions to be made in future geothermal projects. This paper presents the implementation and initial data collection from the project, including an initial evaluation of the logging and coring campaigns.@en

At present, over half of all primary energy used in Europe is used for heating and cooling. Therefore, decarbonizing the heating supply is essential to achieve climate targets. Underground thermal energy storage is a key enabling technology for the energy transition to buffer the large seasonal mismatch between thermal energy demand and sustainable thermal energy production capabilities. In Delft, a High-Temperature Aquifer Thermal Energy Storage (HT-ATES) system will be installed at the campus of Delft University of Technology (TU Delft). It will be integrated in the wider heating system on and around the TU Delft campus, which itself is undergoing a transformation to optimally supply sustainable thermal energy. The district heating network will be extended and utilize the thermal energy from a geothermal doublet producing heat at around 75-80°C with a flow rate of ~350m3/hr. Excess energy produced by the geothermal well in summer will be stored in the HT-ATES system, and will be utilised when demand exceeds production throughout the winter. The HT-ATES system will comprise of 7 wells (3 hot wells of 80°C and 4 warm wells of 50°C) to a depth of approximately 200m, with storage in an unconsolidated sedimentary aquifer between 160-200m depth. It is designed so that the instantaneous excess power from the geothermal project can be stored and demand from the district heating network be extracted from the system. The HT-ATES system at TU Delft is partially funded by local stakeholders and the European commission within the PUSH-IT project and has two primary goals: (i) to reduce carbon emissions on TU Delft campus , and (ii) to create a unique demonstration, education and research infrastructure. The complexity of a HT-ATES requires innovative solutions during the entire system life cycle. The scientific programme that is initially planned within the project is therefore focusing on various research fields and includes: - Characterisation of the subsurface formations including mechanical, hydraulic, thermal, and chemical properties. - Evaluation and monitoring of the biological conditions and microbial diversity, and potential impact on water quality. - Innovations in drilling and completion, monitoring and performance. - Quantification of the system performance and system impact during multiple storage cycles and the full lifecycle of the HT-ATES. This will include extensively monitoring temperature distribution and water quality in the subsurface to characterise behaviour and improve models. - Demonstrate and develop the implementation of HT-ATES in an urban setting, including control of the system in the built-environment and transforming the conventional heat network to a future-proof heat network. - To allow access to other universities or institutions with active programmes in the field of Geothermal Science and Engineering to jointly carry out research and perform experiments. -Societal engagement and legal evaluation for improving the just energy transition.@en

A geothermal doublet has been installed in a sedimentary reservoir for direct-use heating on the TU Delft campus, targeted to supply around 25 MW of thermal energy at peak conditions. This contribution presents the implementation and initial data collection from the doublet, including an initial evaluation of the logging and coring campaign. Nearly half of Netherlands natural gas consumption is allocated to heating, and the on-campus CO2 emissions from heating exceed 50%. The doublet has been designed with two primary aims of research and commercial heat supply, with the wells being completed in December 2023. The project will be operated by a commercial entity, and built into a larger thermal energy system including a high temperature underground storage system, with the first energy production planned in 2025. The research questions relate to field-scale geothermal operations, e.g. how reliable is the long-term energy production?, how do materials perform in the long-term? and how can geothermal projects be best monitored? The research programme involves the installation of a wide range of instruments alongside an extensive logging and coring program and monitoring network. The doublet has been cored, with substantial continuous samples from the heterogenous reservoir, alongside a large suite of open hole well logs in the reservoir and through casing logs in overlying geological units. A fiber-optic cable will monitor distributed pressure throughout the producer reservoir section, at approximately 2300m depth, which will be installed during commissioning. A local seismic monitoring network has been installed in the surrounding area with the aim of monitoring very low-magnitude natural or induced seismicity. The project is a key national research infrastructure and is being incorporated into the European EPOS (European Plate Observing System, https://www.epos-eu.org/), such that accessibility and data availability will be as wide as possible. All observations will be included in a digital-twin framework that will allow to make better decisions in future geothermal projects.@en

Drilling wells in unconsolidated formations is commonly undertaken to extract drinking water and other applications, such as aquifer thermal energy storage (ATES). To increase the efficiency of an ATES system, the drilling campaigns are targeting greater depths and enlarging the wellbore diameter in the production section to enhance the flow rates. In these cases, wells are more susceptible to collapse. Drilling fluids for shallow formations often have little strengthening properties and, due to single-string well design, come into contact with both the aquifer and the overburden. Drilling fluids and additives are experimentally investigated to be used to improve wellbore stability in conditions simulating field conditions in unconsolidated aquifers with a hydraulic conductivity of around 10 m/d. The impact on wellbore stability is evaluated using a new experimental setup in which the filtration rate is measured, followed by the use of a fall cone penetrometer augmented with an accelerometer to directly test the wellbore strengthening, and imaging with a scanning electron microscope (SEM) to investigate the (micro)structure of the filter cakes produced. Twelve drilling fluids are investigated with different concentrations of bentonite, polyanionic cellulose (PAC), Xanthan Gum, calcium carbonate (CaCO₃), and aluminum chloride hexahydrate ([Al(H₂O)₆]Cl₃). The filtration results indicate that calcium carbonate, average d_p <20 μm, provides pore throat bridging and filter cake formation after approximately 2 min, compared to almost instantaneous discharge when using conventional drilling fluids. The drilling fluid containing 2% [Al(H₂O)₆]Cl₃ forms a thick (4 mm) yet permeable filter cake, resulting in high filtration losses. The fall cone results show a decrease of cone penetration depth up to 20.78%, and a 40.27% increase in deceleration time while penetrating the sample with CaCO₃ compared with conventional drilling fluid containing bentonite and PAC, indicating a significant strengthening effect. The drilling fluids that contain CaCO₃, therefore, show high promise for field implementation.

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This paper presents a combined laboratory and numerical investigation on the injection-induced permeability changes in pre-existing fractures. The analyses conducted were primarily based on the results of an innovative laboratory experiment designed to replicate the key mechanisms that occur during hydraulic stimulation of naturally fractured rocks and/or faulted zones. The experiment involved pressure-controlled fluid injection into a laboratory-scale pre-existing fracture within a granite block, which was subjected to true triaxial stress conditions. Rough and smooth fractures are investigated, and the results are discussed. Based on the experimental results, two contributing mechanisms were considered to describe the pressure-driven permeability changes in pre-existing fractures: (1) elastic opening/closure leading to a reversible permeability change, and (2) fracture sliding in shear mode, causing dilation and hence an irreversible permeability increase. With these assumptions, an aperture-dependent permeability function was adopted to couple the hydraulic flow with the mechanical deformations along the fracture. Subsequently, a 3D coupled hydro-mechanical model was developed to replicate fluid-injection tests conducted at various conditions, including different stress conditions and fracture surface roughness. The employed modeling framework effectively captured the experimental observations. Our results indicate that the maximum permeability increases twofold.@en

The TU Delft campus geothermal project has joint objectives of research and commercial thermal energy production. It has been developed and will be operated by the Geothermie Delft (GTD) consortium, a commercial cooperation between TU Delft, Aardyn, EBN and Shell Geothermal. This report gives an overview of the research activities that have been carried out during the implementation of the doublet drilling the wells DEL-GT-01 and DEL-GT-02, and the sidetracks DEL-GT-02-S1 and DEL-GT-02-S2 in the period June - December 2023. The research programme and related operations during the installation of the campus geothermal wells have been led by the scientific team of TU Delft department of Geoscience and Engineering. The project is part of the national research infrastructure for solid Earth science (https://epos-nl.nl/), and offers the possibility to do state of the art research on an operating geothermal system.
The main research activities that were carried out during the implementation of the geothermal wells included rock sampling in the form of a detailed drill cutting sampling set, full cores and sidewall cores of the caprock and the geothermal reservoir, open-hole logging of the reservoir formations and the installation of a fibre optic cable in the producer (still to be carried out).
Overall, the following samples and data were collected as part of the scientific programme:
- 15m of 4”core from the direct caprock of the producer reservoir section
- 71m of 4”core from the reservoir section of the producer
- 78 sidewall cores from the injector reservoir section
- 2400 cutting samples
- 3000m of open-hole and closed-hole logging data
Details of these activities can be found in the report and the related appendices. All data presented in this report have been published via TU Delft institutional data repository and can be found online as part of the data collection associated with the research programme of the project: Geothermal Project on TU Delft Campus Collection at https://doi.org/10.4121/85b3725b-80fa-4b0b-9db2-475bfd8f0265.@en

This study presents a fully coupled hydro-mechanical framework for modeling hydraulic shearing in a mesoscale reservoir located at the Grimsel Test Site, Switzerland. The experiment was conducted on a ductile–brittle fault embedded in low-permeable granite. We observe that normal fracture opening increases flow channel recoverably, while fracture sliding locks asperities leading to a non-recoverable increase in flow. To couple these processes, we use a poro-elasto-plastic constitutive framework and employ a permeability function that depends on several parameters, such as dilation angle, in-situ stresses, residual aperture and maximum aperture. Our results capture the recorded pressure responses well, and indicate that the permeability changes by one order of magnitude during the experiment.

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In recent decades, there has been a notable rise in the utilization of the subsurface as a source for heating and cooling through shallow geothermal installations. This trend is exemplified by the emergence of Energy Geostructures (EGs), an innovative technology that not only provides structural support to the ground or buildings but also facilitates the exchange of heat with the subsurface. EGs offer versatile applications for various energy needs, including their integration with ground source heat pumps for space heating, cooling, and domestic hot water provision. Energy Quay Walls (EQWs) represent a promising type of energy Geostructures that demonstrate a unique ability to exchange heat with both the surrounding soil and open water. Despite the considerable potential for energy efficiency that EQWs hold, their limited implementation underscores the need for extensive research to comprehend their thermal behavior. This study conducts an in-depth examination of EQWs, employing two Finite Element numerical models to reconstruct the undisturbed temperature profile within the soil and conduct a detailed 3D analysis of heat exchange processes in an EQW application. These models are validated using real data obtained from a full-scale test in Delft, The Netherlands. The results emphasize the significance of transitioning from laminar to turbulent flow regimes within the heat exchanger pipes, showcasing improved energy extraction efficiency, particularly from the open water layer. Moreover, the study underscores the critical role of open water movement in the energy extraction process. This finding emphasizes the dynamic nature of open water in contributing to the overall effectiveness of EQWs as an EG. The study's outcomes provide important considerations for optimizing the design and implementation of EQWs, pointing towards the benefits of promoting turbulent flow regimes within the heat exchanger pipes and emphasizing the advantages of harnessing energy from actively moving open water layers. As the implementation of EQWs continues to expand, these insights contribute to advancing our understanding and enhancing the energy efficiency of this innovative technology.@en

This paper investigates the implementation of a nonlocal regularisation of the material point method to mitigate mesh-dependency issues for the simulation of large deformation problems in brittle soils. The adopted constitutive description corresponds to a simple elastoplastic model with nonlinear strain softening. A number of benchmark simulations, assuming static and dynamic conditions, were performed to show the importance of regularisation, as well as to assess the performance and robustness of the implemented nonlocal approach. The relevance of addressing stress oscillation issues, due to material points crossing element boundaries, is also demonstrated. The obtained results provide relevant insights into brittle materials undergoing large deformations within the MPM framework.

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Numerous full-scale in situ tests have been conducted to assess the effect of thermal cycles on the pile response. However, those studies investigated the response of only precast and cast in-situ energy piles, with limited focus on the impact of the applied mechanical load on the pile response. This study presents the results of a field test conducted on a new type of energy pile, i.e. a displacement cast in-situ energy pile in multilayered soft soils, subjected to different fixed mechanical loads while undergoing simultaneous thermal cycles. Four tests were carried out, each corresponding to various axial loads ranging from 0 % to 60 % of the pile's estimated bearing capacity. After applying the axial load on the pile head (0 %, 30 %, 40 %, or 60 % of the bearing capacity), the pile was subjected to up to ten thermal cycles. The highest magnitudes of thermal axial strains were observed near the pile top due to the lowest restraint provided by the made ground layer in all tests. Under zero (0 %) mechanical load, the thermal axial strains near the pile head were elastic and recoverable, while residual strain was observed near the toe. Under reasonable working mechanical loads (30 %, 40 %, or 60 %) residual strains were observed near both the pile head and the toe, with higher residual strains observed under higher mechanical loads. The results indicate that the cyclic thermal loadings could induce an increase in the compressive stress in the energy pile, attributed to the drag-down effects of the surrounding soil. The compressive stress induced by drag-down effects counteracts thermally induced tensile stress and thus leads to an insignificant effect on the energy pile during cooling. A limited impact of the shaft capacity was observed and was mainly attributed to the drag-down of the surrounding soil and thermal creep along the pile-soil interface.

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As the Material Point Method (MPM) uses both a mesh and a point discretisation scheme, the application of boundary conditions is difficult, currently limiting the flexibility of the method. While many boundary condition options have been used in the literature, the accuracy of Neumann boundary condition options has not yet been studied. Four options have here been evaluated for 1D and 2D benchmarks, although none of the options were found to be both accurate and generally applicable in MPM. However, for the generalised interpolation material point method (GIMP), the application of surface tractions on support domain boundaries or on a detected surface are valid options. Large differences between these two accurate options and the application of tractions at surface material points, a method regularly used in the literature, have been observed.

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Heating and Cooling constitute a major part of society's final energy use and a significant contributor to greenhouse gas emissions. The world society ought to mitigate climate change through decarbonisation, which must include the transition to low-temperature, sustainable and renewable heating and cooling technologies. Shallow Geothermal Energy is one of the most energy efficient and least greenhouse gas emitting available alternatives to provide space heating and cooling. The decarbonisation of the heating and cooling sector may have to comprise both individual systems and shared electrified heating and cooling systems from renewable sources of energy, where economies of scale and synergies between different types of consumers can be exploited. To this end, the focus of this paper is on the integration of shallow geothermal energy technologies into district heating and cooling systems. A key contribution of this work is the illustration of a number of practical case studies, highlighting the potential of existing shallow geothermal systems for DHC networks, which, as front runners in adopting such technologies, serve as paradigms for future development. Follows a discussion providing an outlook over the next 25 years. All in all, the future of utilizing shallow geothermal energy for district heating and cooling seems to be promising to play a pivotal role in sustainable urban development and decarbonizing the heating and cooling sector.@en

The technical and economic success of an Aquifer Thermal Energy Storage (ATES) system depends strongly on its thermal recovery efficiency, i.e. the ratio of the amount of energy that is recovered to the energy that was injected. Typically, conduction most strongly determines the thermal recovery efficiency of ATES systems at low storage temperatures (<25 °C), while the impact of buoyancy-driven flow can lead to high additional heat losses at high storage temperatures (>50 °C). To date, however, it is unclear how the relative contribution of these processes and mechanical dispersion to heat losses across a broad temperature range is affected by their interaction for the wide range of storage conditions that can be encountered in practice. Since such process-based insights are important to predict ATES performance and support the design phase, numerical thermo-hydraulic ATES simulations were conducted for a wide range of realistic operational storage conditions ([15–90 °C], [50,000–1,000,000 m³/year]) and hydrogeological conditions (aquifer thickness, horizontal hydraulic conductivity, anisotropy). The simulated heat loss fractions of all scenarios were evaluated with respect to analytical solutions to assess the contribution of the individual heat loss processes. Results show that the wide range of heat losses (10–80 % in the 5th year) is the result of varying contributions of conduction, dispersion and buoyancy-driven flow, which are largely determined by the geometry of the storage volume (ratio of screen length / thermal radius, L/R_th) and the potential for buoyancy-driven flow (q₀) as affected by the storage temperature and hydraulic conductivity of the aquifer. For ATES systems where conduction dominates the heat losses, a L/R_th ratio of 2 minimizes the thermal area over volume ratio (A/V) and resulting heat losses for a given storage volume. In contrast however, the impact of dispersion decreases with L/R_th and particularly for ATES systems with a high potential for buoyancy-driven flow (q₀ > 0.05 m/d), increasingly smaller L/R_th ratios (<1) strongly reduce the heat losses due to tilting. Overall, the results of this study support the assessment of thermal recovery efficiencies for particular aquifer and storage conditions, thereby aiding the optimization of initial ATES designs.

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Geological Disposal Facilities (GDF) for radioactive waste will generally rely on clay-rich materials as a host geological formation and/or engineered barrier. Gas will be produced within the GDF, which can build up significant gas pressure and will activate the migration of gas through the clay materials via different transport mechanisms. These transport mechanisms are usually investigated in laboratory tests on small clay samples of a few centimetres. In this paper, a new Pneumo-Hydro-Mechanical (PHM) Finite Element model to simulate gas migration in saturated clay samples of this scale is presented. In the proposed modelling approach, continuum elements are used to represent the mechanical and flow processes in the bulk clay material, while zero-thickness interface elements are used to represent existing or induced discontinuities (cracks). A new triple-node PHM interface element is presented to achieve this. The performance of model is illustrated with synthetic benchmark examples which show the ability of the model to reproduce observed PHM mechanisms leading to propagation of cracks due to the gas pressure (gas fracturing).

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Data assimilation methods have been implemented on a slope stability problem, and the performance of different constitutive models and data assimilation schemes has been investigated. In the first part, a data assimilation scheme called the ensemble Kalman filter (EnKF) is implemented using a finite element model (FEM) and its performance with different constitutive models (the Mohr-Coulomb (MC) and Hardening Soil (HS) material models) is investigated to study their effect on the parameter and the factor of safety (FoS) estimation. Measurements of horizontal displacement are assimilated. The results from a synthetic example show that the HS model can generally be used to get reliable results for parameter and FoS estimation. However, using the MC model does not always output reliable parameter and FoS estimation. In the second part, the performance of different data assimilation schemes, i.e., the EnKF and ensemble smoother with multiple data assimilation (ESMDA), is studied with the preferred constitutive material model (the HS model). The results of a synthetic case show that the EnKF results in a narrower distribution for the FoS than the ESMDA method, while the latter results in FoS estimation which is closer to the ‘truth’.@en

Different data assimilation schemes such as the ensemble Kalman filter (EnKF), ensemble smoother (ES) and ensemble smoother with multiple data assimilation (ESMDA) are implemented in a hydro-mechanical slope stability analysis. For a synthetic case, these schemes assimilate displacements at the crest and the slope to estimate strength and stiffness parameters. These estimated parameters are then used to estimate the system's state and factor of safety (FoS). The results show that EnKF provides an FoS estimation with a mean close to the truth and with the smallest standard deviation, with ESMDA using the largest amount of assimilation steps also providing a mean close to the truth but with less confidence. The ES and ESMDA with fewer assimilation steps underestimate the FoS approximation and have low confidence. Assimilating measurements over a longer period provides a more accurate parameter, state and FoS estimation. ES has the best computational performance, with ESMDA performing worse, with its performance dependent on the number of assimilation steps. The computational performance of the EnKF is better than ESMDA but around 50% worse than the ES. Non-linearity of the underlying problem is a key cause of the multi-step assimilation processes having a better performance.

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