M. Mohsan
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Slope stability applications are vital assets for a country. These slope stability systems include dikes, dams, levees, embankments and enable applications such as open-pit mining. The failure of these systems pose huge impacts on society and the economy and hence the accurate stability assessment of these systems are of primary concern. Existing methods such as limit equilibrium methods, numerical methods (e.g. the finite element method, FEM), empirical methods and probabilistic methods all provide an approximate estimate of the factor of safety (FoS), and are often observed to have inaccuracies when failures occur. This lack of ability to make accurate predictions is due to many reasons, such as missing physical processes incorporated into the methods, inaccurate boundary and initial conditions, constitutive model selection, uncertainty in model parameters and limited mechanism understanding. This thesis suggests using data assimilation to combine monitoring data with a finite element model to improve the predictive capabilities of the FEM model. These days, geotechnical systems are equipped with measurement devices to monitor their response to external changes. These measurements can be in the formof surface displacements, porewater pressures, strains, etc. These measurements can be obtained from in-situ devices (such as inclinometers, strain gauges, etc.) or can be measured remotely (with Light Detection and Ranging (LIDAR), Interferometric Synthetic Aperture Radar (InSAR), etc.). These measurements can be assimilated into the popular ensemble-based well-established data assimilation methods, e.g., the ensemble Kalman filter (EnKF), ensemble smoother (ES) and ensemble smoother with multiple data assimilation (ESMDA) to improve the predictability of FEM models.
In the first stage, an FEM model of slope stability has been integrated with EnKF. Based upon the slope deformation measurements, this approach estimates the key material parameters (strength and stiffness parameters), the state (displacement), and the FoS of a slope. The effect of two different constitutive models (Mohr-Coulomb (MC) and Hardening Soil (HS) model) on the FoS was studied via a synthetic twin experiment. The HS model was able to estimate the FoS with a narrow posterior distribution, starting from a wide prior distribution of material parameters, including those not encompassing the actual parameters, demonstrating the advantage of using advanced constitutive models when combining with data assimilation.
In the second stage, the constitutive model which produced relatively more accurate results (the HS model) was selected from the first stage has been tested with three data assimilation schemes, i.e., EnKF, ES and ESMDA. Each of these schemes was integrated with the FEM to assimilate measurements of deformation of the slope and the crest of the slope stability system. The accuracy of these schemes was evaluated by comparing their FoS to the synthetic true FoS and evaluating their computation time in a synthetic twin experiment. The results of the synthetic twin experiment show that EnKF estimated an FoS that was close to the true FoS with a small standard deviation. ESMDA, when using four iterative assimilation steps, was also able to estimate an FoS close to the truth, yet had a higher standard deviation compared to EnKF. The ES and ESMDA (with two iterative assimilation steps) were not able to reconstruct the true FoS as well as the other schemes, most likely due to the mostly linear updates of these schemes. The theoretical computation time required by the ES was the smallest, followed by ESMDA with two iterative assimilation steps, ESMDA with four assimilation steps, and finally the EnKF.
In the third stage, a data assimilation scheme was implemented on a case study of an open pit mine in Cottbus, Germany. The LIDAR measurements of the vertical displacements were assimilated into a FEM model of slope stability. Model parameters, displacement ensemble and FoS are estimated from this analysis. The posterior estimation of FoS is compared with slope failure observed in the field. The data assimilation results provide better results than only using FEM models when comparing the ground truth of slope failure. However, it was clear that not all physical processes were included in the model, resulting in a considerable mismatch of the modeled and observed deformations, although a considerable improvement was observed. This initial observation led to the choice of a data assimilation method, which is able to update the parameters to generally improve the results, as opposed to those which incrementally improved parameters.
Furthermore, as the data assimilation approach developed involved multiple FEM analyses, it is computationally expensive and therefore developing a real-time assessment system is likely to be impractical. Therefore, an effort was made to reduce the required computational resources by developing a surrogate model. The surrogate model was trained and tested based on the output of the FEM model ensemble. Specifically, it used the displacements at different locations as input and the FoS as output. The output of the surrogate model in the validation stage was compared with the observed FoS from the case study. It was found that the prediction made by the surrogate model was not reliable. This is probably due to the mismatch between the training/testing dataset (from FEM) and the validation dataset (i.e., the measurements from LIDAR). This mismatch was identified to be due to the identified missing physical processes in the model, and the fact that the on-ground measurements had a different nature than training and testing data. It is further suggested that a surrogate model can only be used provided the training testing and validation datasets are compatible - and as the FoS is rarely identifiable in reality leads to challenges using surrogate models to predict slope failure.
...
In the first stage, an FEM model of slope stability has been integrated with EnKF. Based upon the slope deformation measurements, this approach estimates the key material parameters (strength and stiffness parameters), the state (displacement), and the FoS of a slope. The effect of two different constitutive models (Mohr-Coulomb (MC) and Hardening Soil (HS) model) on the FoS was studied via a synthetic twin experiment. The HS model was able to estimate the FoS with a narrow posterior distribution, starting from a wide prior distribution of material parameters, including those not encompassing the actual parameters, demonstrating the advantage of using advanced constitutive models when combining with data assimilation.
In the second stage, the constitutive model which produced relatively more accurate results (the HS model) was selected from the first stage has been tested with three data assimilation schemes, i.e., EnKF, ES and ESMDA. Each of these schemes was integrated with the FEM to assimilate measurements of deformation of the slope and the crest of the slope stability system. The accuracy of these schemes was evaluated by comparing their FoS to the synthetic true FoS and evaluating their computation time in a synthetic twin experiment. The results of the synthetic twin experiment show that EnKF estimated an FoS that was close to the true FoS with a small standard deviation. ESMDA, when using four iterative assimilation steps, was also able to estimate an FoS close to the truth, yet had a higher standard deviation compared to EnKF. The ES and ESMDA (with two iterative assimilation steps) were not able to reconstruct the true FoS as well as the other schemes, most likely due to the mostly linear updates of these schemes. The theoretical computation time required by the ES was the smallest, followed by ESMDA with two iterative assimilation steps, ESMDA with four assimilation steps, and finally the EnKF.
In the third stage, a data assimilation scheme was implemented on a case study of an open pit mine in Cottbus, Germany. The LIDAR measurements of the vertical displacements were assimilated into a FEM model of slope stability. Model parameters, displacement ensemble and FoS are estimated from this analysis. The posterior estimation of FoS is compared with slope failure observed in the field. The data assimilation results provide better results than only using FEM models when comparing the ground truth of slope failure. However, it was clear that not all physical processes were included in the model, resulting in a considerable mismatch of the modeled and observed deformations, although a considerable improvement was observed. This initial observation led to the choice of a data assimilation method, which is able to update the parameters to generally improve the results, as opposed to those which incrementally improved parameters.
Furthermore, as the data assimilation approach developed involved multiple FEM analyses, it is computationally expensive and therefore developing a real-time assessment system is likely to be impractical. Therefore, an effort was made to reduce the required computational resources by developing a surrogate model. The surrogate model was trained and tested based on the output of the FEM model ensemble. Specifically, it used the displacements at different locations as input and the FoS as output. The output of the surrogate model in the validation stage was compared with the observed FoS from the case study. It was found that the prediction made by the surrogate model was not reliable. This is probably due to the mismatch between the training/testing dataset (from FEM) and the validation dataset (i.e., the measurements from LIDAR). This mismatch was identified to be due to the identified missing physical processes in the model, and the fact that the on-ground measurements had a different nature than training and testing data. It is further suggested that a surrogate model can only be used provided the training testing and validation datasets are compatible - and as the FoS is rarely identifiable in reality leads to challenges using surrogate models to predict slope failure.
...
Slope stability applications are vital assets for a country. These slope stability systems include dikes, dams, levees, embankments and enable applications such as open-pit mining. The failure of these systems pose huge impacts on society and the economy and hence the accurate stability assessment of these systems are of primary concern. Existing methods such as limit equilibrium methods, numerical methods (e.g. the finite element method, FEM), empirical methods and probabilistic methods all provide an approximate estimate of the factor of safety (FoS), and are often observed to have inaccuracies when failures occur. This lack of ability to make accurate predictions is due to many reasons, such as missing physical processes incorporated into the methods, inaccurate boundary and initial conditions, constitutive model selection, uncertainty in model parameters and limited mechanism understanding. This thesis suggests using data assimilation to combine monitoring data with a finite element model to improve the predictive capabilities of the FEM model. These days, geotechnical systems are equipped with measurement devices to monitor their response to external changes. These measurements can be in the formof surface displacements, porewater pressures, strains, etc. These measurements can be obtained from in-situ devices (such as inclinometers, strain gauges, etc.) or can be measured remotely (with Light Detection and Ranging (LIDAR), Interferometric Synthetic Aperture Radar (InSAR), etc.). These measurements can be assimilated into the popular ensemble-based well-established data assimilation methods, e.g., the ensemble Kalman filter (EnKF), ensemble smoother (ES) and ensemble smoother with multiple data assimilation (ESMDA) to improve the predictability of FEM models.
In the first stage, an FEM model of slope stability has been integrated with EnKF. Based upon the slope deformation measurements, this approach estimates the key material parameters (strength and stiffness parameters), the state (displacement), and the FoS of a slope. The effect of two different constitutive models (Mohr-Coulomb (MC) and Hardening Soil (HS) model) on the FoS was studied via a synthetic twin experiment. The HS model was able to estimate the FoS with a narrow posterior distribution, starting from a wide prior distribution of material parameters, including those not encompassing the actual parameters, demonstrating the advantage of using advanced constitutive models when combining with data assimilation.
In the second stage, the constitutive model which produced relatively more accurate results (the HS model) was selected from the first stage has been tested with three data assimilation schemes, i.e., EnKF, ES and ESMDA. Each of these schemes was integrated with the FEM to assimilate measurements of deformation of the slope and the crest of the slope stability system. The accuracy of these schemes was evaluated by comparing their FoS to the synthetic true FoS and evaluating their computation time in a synthetic twin experiment. The results of the synthetic twin experiment show that EnKF estimated an FoS that was close to the true FoS with a small standard deviation. ESMDA, when using four iterative assimilation steps, was also able to estimate an FoS close to the truth, yet had a higher standard deviation compared to EnKF. The ES and ESMDA (with two iterative assimilation steps) were not able to reconstruct the true FoS as well as the other schemes, most likely due to the mostly linear updates of these schemes. The theoretical computation time required by the ES was the smallest, followed by ESMDA with two iterative assimilation steps, ESMDA with four assimilation steps, and finally the EnKF.
In the third stage, a data assimilation scheme was implemented on a case study of an open pit mine in Cottbus, Germany. The LIDAR measurements of the vertical displacements were assimilated into a FEM model of slope stability. Model parameters, displacement ensemble and FoS are estimated from this analysis. The posterior estimation of FoS is compared with slope failure observed in the field. The data assimilation results provide better results than only using FEM models when comparing the ground truth of slope failure. However, it was clear that not all physical processes were included in the model, resulting in a considerable mismatch of the modeled and observed deformations, although a considerable improvement was observed. This initial observation led to the choice of a data assimilation method, which is able to update the parameters to generally improve the results, as opposed to those which incrementally improved parameters.
Furthermore, as the data assimilation approach developed involved multiple FEM analyses, it is computationally expensive and therefore developing a real-time assessment system is likely to be impractical. Therefore, an effort was made to reduce the required computational resources by developing a surrogate model. The surrogate model was trained and tested based on the output of the FEM model ensemble. Specifically, it used the displacements at different locations as input and the FoS as output. The output of the surrogate model in the validation stage was compared with the observed FoS from the case study. It was found that the prediction made by the surrogate model was not reliable. This is probably due to the mismatch between the training/testing dataset (from FEM) and the validation dataset (i.e., the measurements from LIDAR). This mismatch was identified to be due to the identified missing physical processes in the model, and the fact that the on-ground measurements had a different nature than training and testing data. It is further suggested that a surrogate model can only be used provided the training testing and validation datasets are compatible - and as the FoS is rarely identifiable in reality leads to challenges using surrogate models to predict slope failure.
In the first stage, an FEM model of slope stability has been integrated with EnKF. Based upon the slope deformation measurements, this approach estimates the key material parameters (strength and stiffness parameters), the state (displacement), and the FoS of a slope. The effect of two different constitutive models (Mohr-Coulomb (MC) and Hardening Soil (HS) model) on the FoS was studied via a synthetic twin experiment. The HS model was able to estimate the FoS with a narrow posterior distribution, starting from a wide prior distribution of material parameters, including those not encompassing the actual parameters, demonstrating the advantage of using advanced constitutive models when combining with data assimilation.
In the second stage, the constitutive model which produced relatively more accurate results (the HS model) was selected from the first stage has been tested with three data assimilation schemes, i.e., EnKF, ES and ESMDA. Each of these schemes was integrated with the FEM to assimilate measurements of deformation of the slope and the crest of the slope stability system. The accuracy of these schemes was evaluated by comparing their FoS to the synthetic true FoS and evaluating their computation time in a synthetic twin experiment. The results of the synthetic twin experiment show that EnKF estimated an FoS that was close to the true FoS with a small standard deviation. ESMDA, when using four iterative assimilation steps, was also able to estimate an FoS close to the truth, yet had a higher standard deviation compared to EnKF. The ES and ESMDA (with two iterative assimilation steps) were not able to reconstruct the true FoS as well as the other schemes, most likely due to the mostly linear updates of these schemes. The theoretical computation time required by the ES was the smallest, followed by ESMDA with two iterative assimilation steps, ESMDA with four assimilation steps, and finally the EnKF.
In the third stage, a data assimilation scheme was implemented on a case study of an open pit mine in Cottbus, Germany. The LIDAR measurements of the vertical displacements were assimilated into a FEM model of slope stability. Model parameters, displacement ensemble and FoS are estimated from this analysis. The posterior estimation of FoS is compared with slope failure observed in the field. The data assimilation results provide better results than only using FEM models when comparing the ground truth of slope failure. However, it was clear that not all physical processes were included in the model, resulting in a considerable mismatch of the modeled and observed deformations, although a considerable improvement was observed. This initial observation led to the choice of a data assimilation method, which is able to update the parameters to generally improve the results, as opposed to those which incrementally improved parameters.
Furthermore, as the data assimilation approach developed involved multiple FEM analyses, it is computationally expensive and therefore developing a real-time assessment system is likely to be impractical. Therefore, an effort was made to reduce the required computational resources by developing a surrogate model. The surrogate model was trained and tested based on the output of the FEM model ensemble. Specifically, it used the displacements at different locations as input and the FoS as output. The output of the surrogate model in the validation stage was compared with the observed FoS from the case study. It was found that the prediction made by the surrogate model was not reliable. This is probably due to the mismatch between the training/testing dataset (from FEM) and the validation dataset (i.e., the measurements from LIDAR). This mismatch was identified to be due to the identified missing physical processes in the model, and the fact that the on-ground measurements had a different nature than training and testing data. It is further suggested that a surrogate model can only be used provided the training testing and validation datasets are compatible - and as the FoS is rarely identifiable in reality leads to challenges using surrogate models to predict slope failure.
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.
...
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.
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’.
...
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’.
This paper investigates the settlement in a pavement due to soil liquefaction. Four 1-g shaking table tests were performed on saturated sand bed-pavement model to understand the factors affecting the liquefaction-induced settlements and their relation to the pavement thickness and width. All the tests were performed with a base acceleration of 320 gal in a laminar box. The shaking table tests revealed that the total settlement reduced with the increase in the pavement thickness. The pavement with the same thickness but different width showed that the total settlement reduced with the increase in the pavement width. The co-seismic settlement and post-seismic settlement depend upon the thickness and width of the pavement, and the maximum contribution of the sand ejecta is around 7.7% in the total settlement.
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This paper investigates the settlement in a pavement due to soil liquefaction. Four 1-g shaking table tests were performed on saturated sand bed-pavement model to understand the factors affecting the liquefaction-induced settlements and their relation to the pavement thickness and width. All the tests were performed with a base acceleration of 320 gal in a laminar box. The shaking table tests revealed that the total settlement reduced with the increase in the pavement thickness. The pavement with the same thickness but different width showed that the total settlement reduced with the increase in the pavement width. The co-seismic settlement and post-seismic settlement depend upon the thickness and width of the pavement, and the maximum contribution of the sand ejecta is around 7.7% in the total settlement.
A recursive ensemble Kalman filter (EnKF) is used as the data assimilation scheme to estimate strength and stiffness parameters simultaneously for a fully coupled hydro-mechanical slope stability analysis. Two different constitutive models are used in the hydro-mechanical model: the Mohr-Coulomb (MC) model and the Hardening Soil (HS) model. The data assimilation framework allows the investigation of the effect of constitutive behaviour on its ability to estimate the factor of safety using measurements of horizontal nodal displacement at the sloping face. In a synthetic study, close-to-failure and far-from-failure cases of prior property estimations illustrate the effect of initial material property distribution with different material models. The results show that both models provide a reliable factor of safety when the distribution of prior parameters is selected close-to-failure. However, the HS model results in the improved estimation of factor of safety for the far-from-failure case while this is not the case for the MC model. In addition, for the same level of accuracy the computational effort required for the HS model is comparatively less than for the MC model.
...
A recursive ensemble Kalman filter (EnKF) is used as the data assimilation scheme to estimate strength and stiffness parameters simultaneously for a fully coupled hydro-mechanical slope stability analysis. Two different constitutive models are used in the hydro-mechanical model: the Mohr-Coulomb (MC) model and the Hardening Soil (HS) model. The data assimilation framework allows the investigation of the effect of constitutive behaviour on its ability to estimate the factor of safety using measurements of horizontal nodal displacement at the sloping face. In a synthetic study, close-to-failure and far-from-failure cases of prior property estimations illustrate the effect of initial material property distribution with different material models. The results show that both models provide a reliable factor of safety when the distribution of prior parameters is selected close-to-failure. However, the HS model results in the improved estimation of factor of safety for the far-from-failure case while this is not the case for the MC model. In addition, for the same level of accuracy the computational effort required for the HS model is comparatively less than for the MC model.